GAS DYNAM ICS IN EXHAUST SYSTEM S OF
TURBOCHARGED
MEDIUM -SPEED DIESEL ENGINES
by
Clare Margaret Carden
Thesis submitted for the degree of Doctor of Philosophy of the University of London and for the Diploma of Membership of Imperial College
February 1989
Mechanical Engineering Department Imperial College of Science and Technology
1 ABSTRACT
There axe several different engine simulation programs existing in academic insti tutions and the diesel engine and related industries world-wide. Most are based on either the filling-and-emptying technique or the method of characteristics. The former method is simple but can not simulate the effects of momentum. The latter accommodates the simulation of gas dynamics but is complex.
Turbocharged medium-speed engines axe commonly fitted with exhaust manifolds which are designed to improve engine performance by utilising the gas-dynamic effects. In order to facilitate modelling such engine systems whilst retaining a high level of simplicity and generality the homentropic method of characteristics was integrated into the Imperial College filling-and-emptying program, TRANSENG.
To test the theoretical model the predicted results were compared with results of full-scale engine tests conducted on a Paxman 16RP200 medium-speed engine. Instantaneous measurements of static pressure at several locations in the pulse exhaust manifold confirmed that pressure waves could be predicted accurately using the author’s model. The overall engine performance, however, was shown to be predicted equally well by the filling-and-emptying method alone and by the combined method of characteristics and filling-and-emptying method.
The sensitivity of the program to various input data was tested. The program was found to be sensitive to changes in effective valve flow area and it was demon strated that the elasticity of the exhaust valve should be accounted for. Differences in exhaust manifold heat transfer data and pressure recovery factors also had a noticeable effect on the exhaust pressure traces.
2 CONTENTS
A b s t r a c t ...... 2 A cknow ledgem ents...... 8 N o t a t io n ...... 9 Variable Names in T R A N S E N G ...... 12
CHAPTER 1 INTRODUCTION ...... 19 1.0 In tr o d u ctio n ...... 19
1.1 Turbocharging S y s t e m s ...... 20 1.2 Engine Performance Simulation Programs ...... 23
CHAPTER 2 EXPERIMENTAL WORK ...... 26 2.0 In tro d u ctio n ...... 26 2.1 The Paxman Valenta 16RP200 Engine ...... 27 2.2 Measurements Taken ...... 28 2.3 Instrumentation ...... 29 2.3.1 Crank-Angle Position ...... 29 2.3.2 Exhaust Manifold Static Pressures ...... 30 2.3.3 Cylinder Pressure ...... 32 2.3.4 Inlet Manifold Pressure ...... 33 2.3.5 Needle L i f t ...... 33 2.3.6 Engine Speed and Load ...... 33 2.3.7 Fuel and Air Consumption ...... 33 2.3.8 Turbocharger S p e e d ...... 34 2.3.9 Atmospheric Pressure ...... 34 2.3.10 Gas Temperature ...... 34 2.3.11 Exhaust Back Pressure ...... 34 2.3.12 Coolant Temperatures and Pressures ...... 34 2.4 Data A cq u isition ...... 35 2.5 Data Transfer ...... 36
3 2.6 Engine Test Conditions ...... 36 2.7 Arrangement of Instrumentation ...... 37 2.8 Test P roced u re...... 39 2.9 Raw R e s u l t s ...... 40 2.10 Data Reduction ...... 41 2.11 Final R e s u lts ...... 42
CHAPTER 3 THEORY ...... 45 3.0 In tro d u ctio n ...... 45 3.1 Mathematical Models to Simulate Gas-Dynamic Effects ...... 46 3.1.1 Finite Difference M e t h o d s ...... 46 3.1.2 Method of C haracteristics...... 47 3.2 Choice of Mathematical Model ...... 48 3.2.1 The Filling-and-Emptying Method ...... 49 3.2.2 The Method of Characteristics ...... 51 3.3 Pipe Junction Models ...... 55 3.3.1 Equal-Pressure Junction M o d e l ...... 55 3.3.2 Pressure Loss M o d e l...... 55 3.3.3 Two- and Three-Dimensional M odels ...... 56 3.3.4 Deckker and Male’s Empirical Method ...... 56 3.3.5 Review of Junction Models for use in a Filling- and-Emptying Program ...... 57 3.3.6 Volume Junction M od el ...... 58 3.3.6.1 Flow from a Pipe into a Junction Volume ...... 59 3.3.6.2 Flow out of the Junction Volume into a Pipe ...... 61
CHAPTER 4 DEVELOPMENT OF THE PROGRAM ...... 62 4.0 In tr o d u ctio n ...... 62 4.1 The TRANSENG Program ...... 63 4.1.1 Combustion ...... 64
4 4.1.2 Heat Transfer 65 4.1.3 Gas P ro p erties...... 65 4.1.4 Friction ...... 65 4.1.5 Mass-Flow R a t e s ...... 66 4.1.6 Turbocharger ...... 67 4.2 Preliminary Program Development ...... 68 4.2.1 Provision for Burning Fuels of Different Calorific Values ...... 68 4.2.2 Unequal Phase Angle ...... 68 4.2.3 Increasing the Maximum Allowable Number of C ylin d ers ...... 69 4.2.4 Increasing the Number of Permissible Turbine Entries. . . 69 4.3 Simulation of Exhaust Manifold S ystem s ...... 70 4.4 Numerical Instability ...... 74 4.4.1 Solutions to the Filling-and-Emptying Instability Problem ...... 76 4.4.2 Control Volume Size in the Gas-Dynamic Exhaust Manifold Model ...... 77 4.4.3 Mesh Size for Gas-Dynamic Simulation of Ex haust Manifolds ...... 78
CHAPTER 5 BASE-LINE PERFORMANCE PREDICTION AND SENSITIVITY OF PROGRAM TO INPUT DATA...... 79 5.0 In tr o d u ctio n ...... 79 5.1 Combustion Coefficients and Combustion Correlation ...... 80 5.2 Initial Prediction using Gas-Dynamic Model at Test Point 6 ...... 83
5 5.2.1 Input Data for the Base-Line Prediction at Test Point 6 ...... 84 5.2.2 Results of Base-Line Simulation for Test Point 6 ...... 86 5.2.3 Sensitivity of Program to Heat Transfer in Ex haust V o lu m e s ...... 91 5.2.4 Pressure Recovery F a c to r s ...... 92 5.2.5 Nozzle Boundary C o n d itio n ...... 94 5.2.6 Turbine M a p ...... 95 5.2.6.1 Reducing the Swallowing Capacity ...... 95 5.2.6.2 Limiting the Minimum Turbine Efficiency ...... 96 5.2.6.3 Turbine Back-Pressure ...... 96 5.2.6.4 Partial Admission and Unsteady-Flow Effects. . . 97 5.2.6.5 Revised Turbine Characteristics ...... 99 5.2.7 Valve Effective-Flow Areas ...... 101 5.2.8 Correct Inlet Manifold Volume and Rotor Inertia ...... 102 5.2.9 Summary of Tests on Sensitivity to Input D a t a ...... 102
CHAPTER 6 ASSESSMENT OF EXHAUST-MANIFOLD MODEL. . . . 104 6.0 In tro d u ctio n ...... 104 6.1 Pulse System: Predictions using Gas-Dynamic Model ...... 105 6.2 Pulse System: Gas-Dynamics and Filling-and-Emptying Compared ...... 108 6.3 Modular-Pulse Converter Exhaust System ...... 110 6.4 Constant Pressure Exhaust S y s t e m ...... 113 6.5 Comparison of Predicted Performance for Three Engine Systems ...... 114
CHAPTER 7 CONCLUSIONS AND RECOMMENDATIONS ...... 116 7.0 Conclusions ...... 116 7.1 Recommendations for Future W o r k ...... 118
R E F E R E N C E S ...... 119
6 Plates Tables Figures
Appendix A: The Equal-Pressure Junction Boundary Condition Appendix B: The Interdependence of Lower Calorific Value and Absolute Enthalpy Appendix C: The Numerical Instability Problem Appendix D: The Dominant Pipe Hypothesis ACKNOWLEDGEMENTS
This project was conceived by Dr W A Connor of Napier Turbochargers Ltd, and it was his suggestion that I should conduct the research. I wish to express my deepest gratitude to him for giving me the opportunity to undertake this research and for his unflagging enthusiasm, guidance and support. I also wish to thank the late Prof N Watson who supervised the project until his sad and untimely death in June 1988. Dr N C Baines kindly supervised the last stages of the project and his advice on the preparation of this thesis is deeply appreciated.
I gratefully acknowledge Napier Turbochargers Ltd for their financial support which gave me the pleasure of being a professional student. I am also indebted to many colleagues at Napier for their technical and moral support, and in particular, Mr P M Came, Mr P Hirst, Mr I H Stevenson, Dr R Backhouse, Mr A Fyles and Mr R Jillings.
I wish to thank the Royal Aircraft Establishment (Naval Division), and Com mander J R C Furse and Mr G Ridgway, who generously made available to me a complete engine test bed, instrumentation, a data acquisition system, and sup porting facilities.
I am also grateful to the engineers at Paxman Diesels Ltd who supplied data, and to Mr B Whitfield in particular.
Finally I would like to thank all those who have extended their friendship to me during the course of my studies.
8 NOTATION
Variable Name Description
a Sonic velocity (m /s) A Non-dimensional sonic velocity (/)
A eq Turbine equivalent area (m2) Aex Exit area (m2)
A-in Inlet area (m2) A n oz Turbine nozzle area (m2)
A r o t Turbine rotor area (m2)
CP Specific heat at constant pressure (kJ/(kg.K)) CD1 Coefficient in diffusion burning formula (/) CD2 Coefficient in diffusion burning formula (/) CPI Coefficient in premixed burning formula (/) CP2 Coefficient in premixed burning formula (/) F Equivalence ratio (/)
F s to Stoichiometric equivalence ratio (/)
F± recov Pressure recovery factor (/) h Specific enthalpy (k J /k g )
or Specific enthalpy of formation of fuel [kJ/kg)
H Enthalpy (k J ) m Mass (kg) rh Mass flow rate (k g /s ) rrif Mass of fuel (kg) mfb Mass of fuel burned (kg) N Turbocharger speed (rpm) n /V t Turbocharger speed parameter (rpm/y/K)
Q Heat (kJ)
Q s f Heat transfer across the surface (kJ)
R Gas constant (k J / (kg.K))
9 Variable Name Description
t Time (s)
T Absolute temperature (K) u Particle velocity ( m / s ) u Specific internal energy ( k J /k g )
U Non-dimensional particle velocity (/)
U Internal energy (kJ) u/c Turbine blade speed ratio (/)
V Volume (m3) w Work ( k J )
X Distance (m)
X Non-dimensional grid size (/) z Non-dimensional time (/)
Greek Letters p Left-bound Riemann variable (/) p Proportion of total fuel burned in premixed mode (/) 7 Ratio of specific heat capacities (/)
Sign Ignition delay ( degC A )
S in j Injection delay (degCA)
6 Crank angle (degCA) n v d y n .in j Crank angle of dynamic injection (degCA)
@eob Crank angle at end of burning (degCA)
Sign Crank angle of ignition (degCA)
Ss t .in j Crank angle of static injection (degCA) A Right-bound Riemann variable (/)
P Density (k g /m 3)
T Non-dimensional time in heat release calculation (/) Variable Name Description
Subscripts in In-flowing out Out-flowing r e f Reference condition s At constant entropy tr Trapped condition vol Control volume 0 Stagnation condition
Abbreviations ADC Analogue-to-digital converter BDC Bottom dead centre bmep Brake mean effective pressure bsac Brake specific air consumption bsfc Brake specific fuel consumption BTDC Before top dead centre Cd Coefficient of discharge CPU Central processing unit EVC Exhaust valve closure EVO Exhaust valve opening imep Indicated mean effective pressure IVC Inlet valve closure IVO Inlet valve opening LCV Lower calorific value MPC Modular pulse converter RAE(ND) Royal Aircraft Establishment (Naval Division) TDC Top dead centre
11 VARIABLE NAMES IN TRANSENG
Variable Units Description
A (I) degC A Firing phase angle of cylinder I ACH m 2 Cylinder head area
ALCON m 2 Cylinder liner area at TDC
APNOZ6 / Ratio of pipe area to turbine effective area for boundary condition 6
APNOZ7 l Ratio of area of main-pipe to nozzle in MPC exhaust system for boundary condition 7
AP(I) m 2 Cross-sectional area of gas-dynamic pipe I
APIS m 2 Cross-sectional area of piston
AREAEM(I) m 2 Surface area of exhaust manifold volume I
AREAIM(I) m 2 Surface area of inlet manifold volume I
BDUR degC A Nominal duration of combustion in cylinders
BETA / Fraction of burning in premixed mode BETAEX deg Seat angle of exhaust valve
BETAIN deg Seat angle of inlet valve
BORE m Cylinder bore
BYPS logical Bypass valve
CAC(I) logical Charge-air cooler 1=1: high pressure (HP) 1=2: low pressure (LP)
CACEF1 to 3 % Coefficients in charge-cooler effectiveness formula
CACK(I) / Charge-cooler pressure loss coefficient 1=1: HP 1=2: LP
CACTC(I) s Charge-cooler time constant 1=1: HP 1=2: LP
CACV(I) m 3 Volume of charge-coolers 1=1: HP 1=2: LP
CASINJ degC A Crank angle of static injection referred to BDC=0 degCA
CCC(I) / Coefficients of injection delay formula, 1=1,3
12 Variable Units Description
CDEFEX / Constant coefficient of discharge assumed by effective exhaust-valve area data
CDEFIN / Constant coefficient of discharge assumed by effective inlet-valve area data
CD1 / Coefficient for diffusion-burning combustion curve CD2 / Coefficient for diffusion-burning combustion curve CHP logical High pressure compressor
CLP logical Low pressure compressor
CPI / Shape parameter for premixed-burning curve
CP2 / Shape parameter for premixed-burning curve
CRATIO i Geometric compression ratio
CSFE / Scaling factor for compressor efficiency
CSFM / Scaling factor for compressor mass-flow rate DCOMP(I) m Compressor blade-tip diameter 1=1: HP 1=2: LP
DELTA degC A Crank-angle interval for valve area data
DEX m Diameter of exhaust valve
DIN m Diameter of inlet valve
DTURB(I) m Turbine blade-tip diameter 1=1: HP 1=2: LP
EFMEC(I) / Turbine mechanical efficiency 1=1: HP 1=2: LP
ENGI kg.m 2 Engine inertia
ESPD rpm Engine speed
EVC degC A Crank angle of exhaust valve closure
EVO degC A Crank angle of exhaust valve opening
FP(I) 1 Initial estimate of equivalence ratio in control volume I
FREF(I) / Reference equivalence ratio in gas-dynamic pipe I HYP logical Hyperbar fuelling
IB 1(1) l Boundary number at upstream end of pipe I
IB2(I) / Boundary number at downstream end of pipe I
ICYL / Cylinder number for which output data are recorded
13 Variable Units Description
IDEX l to 4 / Exhaust volume numbers for which output data are recorded
ID P l to 4 / Exhaust system gas-dynamic pipe numbers for which output data are recorded
INJDEL 5 Injection delay
ITURB(I) kg.rri 2 Turbocharger rotor inertia 1=1: HP 1=2: LP
IVC d eg C A Crank angle of inlet valve closure
IVO d eg C A Crank angle of inlet valve opening
LCV k J /k g Fuel lower calorific value
LENGTH m Connecting-rod length
MESH(I) / Number of mesh points for gas-dynamic pipe I
NATASP logical Naturally aspirated
NCACY / Number of crank-angle steps per cycle
NCAFAC / Scale factor for number of steps per cycle for last cycle
NCSS / Number of steady-state cycles
NCTR1 / Number of pseudo-transient cycles
NCTR2 / Number of transient cycles
NCVMAX / Total number of filling-and-emptying control volumes
NCYCOP / Skip cycle - printed output given every ‘NCYCOP’ cycle in transient mode
NCYL l Number of cylinders
NEM / Number of control volumes in exhaust system
NEP l Number of gas-dynamic pipes in exhaust system
NEXCV(I) / Control volume number downstream of cylinder I
NFEDN(I) / Control volume number downstream of pipe I
NFEUP(I) / Control volume number upstream of pipe I
NIM / Number of inlet manifold control volumes
NINL(I) / Control volume number upstream of cylinder I
14 Variable Units Description
NPRETUR(I) / Number of control volume immediately preceding turbine 1=1: HP 1=2: LP NSPLC(I) / Number of constant speed parameter lines on compressor map 1=1: HP 1=2: LP NSPLE(I) / Number of constant speed parameter lines on turbine efficiency characteristic 1=1: HP 1=2: LP NSPLM(I) / Number of constant speed parameter lines on turbine mass-flow rate map 1=1: HP 1=2: LP NTEM(I) / Number of turbine sectors 1=1: HP 1=2: LP N V Bl(I) / Control volume number at inlet of pipe I NVB2(I) / Control volume number at exit of pipe I NVDATE / Number of exhaust valve area data NVDATI / Number of inlet valve area data PAMB k N /m 2 Ambient pressure PBACK k N /m 2 Turbine back-pressure PBOOST k N /m 2 Estimated boost pressure
PEI to PE5 / Polynomial coefficients for exhaust-valve coefficient of discharge vs lift at pressure ratio PR1
P F l / Pressure recovery factor at upstream pipe-end
PF2 / Pressure recovery factor at downstream pipe-end PIPCY logical Gas-dynamic calculations in inlet ports
PIPCYL logical Losses associated with gas dynamics in inlet ports
PIPJC logical Gas-dynamic model in CSER resonant intake system
PIPJCL logical Losses associated with gas dynamics in CSER system
PIPL(I) m Length of pipe I PI1 to PI5 / Polynomial coefficients for inlet-valve coefficient of discharge vs lift at pressure ratio PR1 pp(i) k N /m 2 Initial estimate of pressure in control volume I PPIPE(I) k N /m 2 Initial estimate of average pressure in pipe I
15 Variable Units Description
PR1 / Lower pressure ratio at which valve coefficient of discharge is known
PR2 / Upper limit to pressure ratio at which valve coefficient of discharge may be calculated
PREF(I) k N / m 2 Reference pressure in gas-dynamic pipe I
PREFEX / Pressure ratio at which exhaust-valve coefficient of discharge was experimentally determined
PREFIN / Pressure ratio at which inlet-valve coefficient of discharge was experimentally determined
RF1 / Corrector relaxation factor for rates of change at end of step
R2 K .m ? / k W Thermal resistance of cylinder liner multiplied by liner area
R4 K / k W Thermal resistance between node at piston centre and liner
R5 K / k W Thermal resistance between piston crown and node in piston body
R7 K / k W Thermal resistance between piston under-side and node in piston body
R8 K / k W Thermal resistance of piston to oil interface at piston under-side
RIO K / k W Thermal resistance of cylinder head between gas face and coolant
SIMTC logical Simulate turbocharger using orifice-nozzle model
STROKE m Stroke
TAMB K Ambient temperature
TBOOST K Initial estimate of boost temperature
TCLPCD logical Turbocompound low-pressure system
TCO K Engine oil temperature under the piston
16 Variable Units Description
TCOOL(I) K Charge-cooler coolant inlet temperature 1=1: HP 1=2: LP
TCOOLEX(I) K Temperature of coolant for exhaust system control volume I
TCSP(I) r p m Initial estimate of turbocharger speed 1=1: HP 1=2: LP
TCW K Engine cooling water temperature
THG K Cylinder-head surface temperature: gas side
THP logical High-pressure turbine
THPVG logical Variable-geometry high-pressure turbine
THP2I logical Interaction between gas flows in twin-entry radial-inflow turbine
TLG K Temperature of liner surface: gas side
TLP logical Low-pressure turbine
TLPCD logical Turbocompound low-pressure turbine
TLPVG logical Variable-geometry low-pressure turbine
TP (I) K Estimated temperature in control volume I
TPG K Estimated piston temperature: gas side
TRANS logical Transient test simulation
TREF(I) K Estimated reference temperature of pipe I
TSFE(I) / Turbine efficiency scale factor 1=1: HP 1=2: LP TSFM(I) / Turbine mass-flow scale factor 1=1: HP 1=2: LP TTTS(I) logical Compressor map total-to-total to total-to-static transformation 1=1: HP 1=2: LP
VAREA(I) m 2 Valve area at data point I
VECDMAX / Valve lift-to-diameter ratio for maximum exhaust valve coefficient of discharge
VEM(I) m 3 Volume of exhaust manifold control volume I
VIM (I) m 3 Volume of inlet manifold control volume I
17 Variable Units Description
VLMAX m Maximum valve lift
WFCY kg Mass of fuel supplied to each cylinder each cycle
WG(I) logical Waste gate 1=1: HP 1=2: LP
18 C H A P T E R 1
INTRODUCTION
1.0 Introduction
By turbocharging an engine its specific power may be increased by a factor of two, and primarily for this reason diesel engines for rail traction, industrial and marine applications are almost exclusively turbocharged today. Engine manufacturers are under pressure both to reduce capital and running costs, and to improve engine performance. One of the most versatile tools available to the engine industry is an engine performance simulation program which can be used, for example, to optimise valve timing, to check the predicted maximum cylinder pressures, or to optimise the turbocharging system. The performance of an engine fitted with different exhaust manifold and turbocharger arrangements can be simulated at any engine operating point, and for any load conditions, on a computer for a small fraction of the cost of producing and testing the hardware. In this way more decisions can be made at the design stage, and the number of development tests can be reduced.
The objective of the research undertaken by the author was to improve predictive techniques to design and optimise turbocharging systems for medium-speed four- stroke industrial and marine diesel engines.
19 1.1 Turbocharging Systems
The aim of turbocharging is to increase the specific power output of an engine. This is achieved by introducing compressed air into the cylinders, energy for the air-compression process being supplied by a turbine driven by the exhaust gas of the engine. The compressor and turbine are connected by a common shaft, the arrangement comprising a turbocharger. Up to 40% of the energy released by combustion is rejected in the exhaust gas, and to utilise this energy, the exhaust manifold and turbocharger (or turbocharging system) must be optimised for a particular engine or engine application. The turbocharging systems of, for ex ample, rail-traction engines must contribute to good transient response and must withstand the hostile operating conditions. Additionally the number of cylinders supplying one exhaust manifold and the space limitations influence the choice of turbocharging system.
There are four types of exhaust manifold which are commonly fitted to medium- speed diesel engines, namely constant-pressure, pulse, simple pulse-converter, and modular pulse-converter (MPC) systems, each of which offers different advantages. The constant-pressure exhaust manifold, depicted diagrammatically in figure 1.1, constitutes a large manifold in which no attempt is made to harness the energy contained in the pressure pulsations from the cylinders which are damped out. All cylinders exhaust to one manifold and the resulting constant turbine-admission pressure and steady flow yield high turbine efficiencies. At the cylinder end of the manifold, however, the constant pressure is a disadvantage: significant throttling losses are incurred across the exhaust valves since the pressure just downstream of the exhaust valve can not rise rapidly upon exhaust valve opening. A further con sequence of the large volume of gas contained in this system is that its inertia can prevent an adequate transient response from being achieved. The simple construc tion of the manifold and its applicability to engines with any number of cylinders can be sufficient to out-weigh these disadvantages for certain applications.
The pulse system, in contrast to the constant-pressure system, comprises narrow bore pipes, as shown in figure 1.1, which preserve the pressure pulses from the
20 cylinders. The relatively small capacity of the manifold enables the pressure just downstream of the exhaust valve to rise rapidly when the exhaust valve opens and the throttling losses are much reduced. Additionally the reduced inertia of the gas in this system facilitates a rapid response to changes in the demanded engine operating point. The turbine operates at an off-design condition for most of the engine cycle due to large fluctuations in turbine-admission conditions in herent in the pulse system. This problem can be made less severe by grouping cylinders together to achieve as nearly steady-flow turbine conditions as possible. The optimum number of cylinders to be grouped together is three, provided that
their phase angle relative to one another is 240 d eg C A . In this case the turbine receives three pulses of approximately equal shape. If more than three cylinders exhaust to one pulse manifold the exhaust-valve-open periods overlap and interfer ence between pulses may result in impaired scavenging efficiency of the cylinders concerned. If fewer than three cylinders are connected the mean pressure level in the manifold is lower and the turbine admission conditions depart further from steady flow: they may vary from the choked condition to the no-flow condition within an engine cycle. Engines with a multiple of three cylinders are best suited to the pulse system, each group of three supplying a different turbine-entry sec tor. Where the number of cylinders can not be grouped into three, an alternative exhaust system may be chosen in preference to connecting only pairs of cylinders to a turbine entry, but the latter is not uncommon.
Another factor which must be considered in the design of a pulse system is the effect of interference of the source pressure wave with pressure waves reflected from the turbine and from pipe junctions. Depending on when, during the exhaust- valve-open period, a reflected wave arrives at the open valve, it can improve or impair performance, or it can have no effect. Jenny [l] * gives a comprehensive discussion of how these differences in performance are brought about. In brief the wave reflection time is a function of pipe length, engine speed, and the reciprocal of the sonic velocity. Engine speed and sonic velocity are usually specified before the
* figures in square brackets denote references
21 exhaust manifold is designed. Pipe length is not: its influence on pressure-wave reflection is profound and is best summarised in figure 1.2.
To combine the advantages of the constant-pressure and pulse systems, Birmann proposed the pulse-converter junction [2]. The principle of operation of the pulse- converter junction is that the exhaust gas expands initially into a short length of converging narrow pipe keeping the throttling losses low and then accelerates into a pipe which is common to the other cylinders connected to the manifold. In this way the pressure pulsations are preserved upstream of the pulse converter, by the exhaust valves, but are smoothed out downstream, before the turbine. There axe two main types of pulse-converter manifold: the modular pulse-converter (MPC) system developed by Curtil and Magnet [3], and the simple pulse-converter sys tem. The former, as the name implies is of modular construction: identical pulse- converter junctions are situated close to each cylinder as shown in figure 1.3. The system is compact and lends itself to any cylinder arrangement. In simple pulse- converter manifolds the pulse-converter junction is situated close to the turbine as illustrated in figure 1.3. Simple pulse converters are usually considered for four-, eight-, fourteen- and sixteen-cylinder engines. Their construction is more complex and less rugged than that of the MPC system and the latter is more frequently used today.
22 1.2 Engine Performance Simulation Programs
There are several different engine performance simulation programs existing in academic institutions and the diesel engine and related industries world-wide. In the majority of these programs the mathematical analysis is based on solving the conservation equations for mass and energy transfer across conceptual boundaries which divide the engine into a series of control volumes which are successively filled and emptied, at discrete time intervals during the engine cycle. This method of analysis is termed the “filling-and-emp tying” method, and notable pioneers of the method are Borman [4], Janota [5] and Wallace [6]. During the last twenty years filling-and-emptying programs have been refined but there is still much work to be undertaken in terms of, for example, being able to model the combustion and heat transfer processes accurately.
The second largest group of engine simulation programs is based on the one dimensional method of characteristics in which the conservation of momentum is considered in addition to the conservation of mass and energy. Within this category, the method may be further divided into programs which employ the non- homentropic method of characteristics, which solves for the effects of pipe friction, heat transfer, pressure losses, and in some programs the spatial variation of gas composition; and the less sophisticated homentropic method in which it is assumed that the entropy level is equal at all locations within a pipe. Both homentropic and non-homentropic methods were initially solved by graphical procedures and it was not until the early 1960s, when the method of characteristics was configured for solution on computers by Benson [7], that it became a useful tool for engine development. The non-homentropic method requires more detailed input data and longer computer execution times than the homentropic method.
The method of characteristics requires a solution for all boundaries encountered in an engine system: open and closed valve boundaries across which the pressure gradient may be either positive or negative, compressor and turbine boundaries, and boundaries describing the flow at simple pipe junctions and pulse-converter
23 junctions. For all but the simplest boundary, the closed valve, the problem is sim plified by assuming that over a very small time interval the flow is steady, ie. the quasi-steady assumption is applied. Some of the more complex boundaries, such as the pipe and pulse-converter junction boundaries require further simplifying assumptions to be made before they can be solved. The flow at a pipe junction is three-dimensional, turbulent flow and pressure losses are incurred which are a function of the geometry of the junction and the flow rates in each branch. Ex perimental investigations by Deckker and Male [8] revealed the complex nature of the flow at a T-junction. They concluded that a quasi-steady analysis was insufficient and they supplied graphical information for the calculation of the re flected pressure wave from a T-junction [9]. Experimental data are not available for the majority of pipe junctions, however, and several researchers have devel oped semi-empirical and theoretical solutions. Benson’s constant-pressure model [10] is purely theoretical and is rendered very simple by the assumption that the pressures at the boundaries of all pipes with the junction are equal. More so phisticated models allow for some pressure loss at the junction and several semi- empirical models were put forward [11, 12, 13]. Zhender [14] and Watson and Janota [15] conducted experimental investigations into flow behaviour at pulse- converter junctions, and semi-empirical models for these junctions were proposed by Watson and Janota [15], Benson and Toms [16], and Benson and Alexander[17]. To avoid the need for empirically derived pressure-loss coefficients required by all the semi-empirical methods, a purely theoretical three-dimensional model is being developed by Leschziner [18]: it is necessarily complex and involves high computer execution costs. The accuracy and general applicability of this model are yet to be proved.
The method of characteristics is more complex, costs significantly more to run, and requires more detailed input data than the filling-and-emptying method, but it enables momentum effects such as pressure waves in the exhaust manifolds to be modelled and this can not be achieved using the filling-and-emptying technique alone. For many applications the filling-and-emptying method suffices and there is little or no advantage in using the more complex method of characteristics. When
24 evaluating the performance of an engine fitted with different exhaust manifold types, however, the method of characteristics makes a significant contribution: the filling-and-emptying method alone can not predict any momentum-related phenomena such as pressure-wave interference.
The accuracy of both types of engine simulation program is dependent upon the quality of the input data. Geometric data such as the bore and stroke can be accurately determined but much of the data can not, particularly if an engine still under design is to be modelled. Combustion data for a particular operating point can be derived from experimental cylinder-pressure diagrams but data from several operating points must be analysed before the combustion data can be extrapolated to simulate engine performance at conditions for which no experimental data are available. Similarly cylinder and manifold heat transfer data and their variation with engine operating point are not easily derived but representative values are necessary if the energy balance is to be well predicted. Flow coefficients for the valves and flow characteristics for the turbocharger are also required. They are almost exclusively evaluated on steady-flow test rigs and it is debatable whether such data are truly representative when applied to the transient flows of an engine. The cost of evaluating the data described above to a high degree of accuracy for each engine simulation is prohibitively high. Fortunately, however, overall engine performance, together with some detailed performance data can be accurately predicted using input data that are readily available.
The research described in the following chapters illustrates how the method of characteristics was integrated into a filling-and-emptying program to facilitate prediction of pressure waves in gas-dynamic exhaust manifolds, whilst retaining a level of generality that is not commonly found in programs based on the method of characteristics. It also shows that the program accurately predicted the per formance of a medium-speed pulse-turbocharged four-stroke engine despite the compromise that had to be accepted in terms of the input data.
25 C H A P T E R 2
EXPERIMENTAL WORK
2.0 Introduction
Experimental data were sought in order to assess the author’s work on developing the engine simulation program, TRANSENG, for application to medium-speed diesel engines, and in particular the theoretical models relating to momentum ef fects in exhaust manifolds of such engines. The four types of exhaust-manifold sys tem considered in the project were constant-pressure, pulse, simple pulse-converter and modular pulse-converter systems. Filling-and-emptying programs such as TRANSENG are known to model engines fitted with constant-pressure exhaust systems better than those fitted with the other exhaust systems mentioned above since these programs can not predict pressure waves which are present in pulse and pulse-converter systems. Much of the author’s research was concerned with developing models compatible with TRANSENG to model accurately the simplest manifold in which pressure waves are significant, ie. the pulse manifold. Ex perimental data were therefore sought to validate the pulse model. Measurements were taken of time-varying static pressure at several locations in the pulse-exhaust manifolds together with cylinder and inlet-manifold pressure diagrams, and mea surements indicating the overall engine performance.
The test facilities at Imperial College are limited to small high-speed engines. The experimental work for this project was therefore carried out at the Royal Aircraft Establishment’s Naval Division (RAE(ND)) situated at Pyestock where a Paxman Valenta 16RP200 engine, instrumentation and a data-acquisition system were made available. The author specified the instrumentation and test schedule required, calibrated the transducers and logged the data. RAE fitters fitted the instrumentation and operated the engine. The engine, the measurements taken, instrumentation, data-acquisition system and test procedure are described below
26 together with brief discussions of the data reduction process and the quality of the results obtained.
2.1 The Paxman Valenta 16RP200 Engine
The Paxman Valenta 16RP200 engine is a turbocharged V16 direct-injection four- stroke diesel engine used by the Royal Navy for marine propulsion and electricity generation. Figure 2.1 shows a cross-sectional general arrangement drawing of the engine, and a photograph of the engine installation is given in plate 2.1. Some of the salient parameters of the test engine are: Bore 0.1969 m Stroke 0.2159 m Compression Ratio 12.13 Speed Range 700 - 1500 rp m Rated Power at 1500 r p m 2.2 MW BMEP at 1500 rp m 17.4 bar Valve Timing EVO 96 d e g C A EVC 430 d e g C A IVO 288 d e g C A IVC 585 d e g C A
\ 60 30 / d e g C A
Firing Order A bank 1 3 7 5 8 6 2 4 \ /\/\/\/\ ' \ / \ / \ B bank 8 6 2 4 1 3 7 5
The engine is fitted with two inlet manifolds, one serving each bank; and two ex haust manifolds, one supplied with gases from the eight cylinders nearest the drive end, the other supplied by the eight cylinders nearest the free end of the engine. The exhaust manifolds are of cast aluminium: they are water-cooled and are sub divided internally into four, such that each branch of the manifold receives gas from two cross-connected cylinders as shown in figure 2.2. Two Napier SA084DPMkII turbochargers are fitted: the compressor-inlet casings are bifurcated and four-entry turbine-inlet casings accommodate the exhaust manifold arrangement.
27 The most notable differences between this engine and the smaller high-speed en gines tested at Imperial College, in addition to the large size and low speed, are the large valve open periods, (in particular the large valve-overlap period of 142 d e g C A), the exhaust manifold arrangement and the four-entry turbine casing. Ad ditionally, since the tests were conducted by the RAE(ND) as part of a routine programme the tests were subject to some constraints which might not have been imposed had it been possible to test such an engine at Imperial College. The main constraints were:
(a) no physical alterations to the installation such as drilling and tapping holes in which to fit pressure transducers could be effected,
(b) the time available for testing was fixed and was limited to three consecutive days.
2.2 Measurements Taken
The following parameters were measured:
(1) crank position
(2) instantaneous exhaust manifold static pressures
(3) instantaneous cylinder pressure
(4) instantaneous inlet manifold static pressures
(5) instantaneous needle lift
(6) engine speed and load
(7) fuel and air consumption
(8) turbocharger speed
(9) atmospheric pressure
(10) gas temperatures in the inlet and exhaust systems
(11) turbine back pressure
28 (12) coolant temperatures and pressures
The instrumentation used for each measurement is described in the following sec tion.
2.3 Instrumentation
2.3.1 Crank-Angle Position
The crank-angle position was determined by using two magnetic-inductive Orbit probes and a Cussons Microsync P4450. One magnetic-inductive pick-up was set to detect a 10 m m diameter hole in the flywheel positioned 70 d e g C A BTDC on cylinder A6 giving a pulse once per revolution. The second Orbit probe gave a signal each time one of the 228 teeth of the starter gear passed it. The Microsync, which is based on a phase-locked loop, operates on the signals received from the
Orbit probes yielding a square-wave output of 1/2 d e g C A period synchronised with
TDC. The 1/2 d e g C A period square wave was then passed through a divide-by-two device to give the desired wave form for the AVL Indiskop 647 data-acquisition system used (see section 2.4). This sequence is illustrated in figure 2.3, and figure 2.4 shows the operation of the Microsync.
29 2.3.2 Exhaust Manifold Static Pressures
The accurate instantaneous measurement of oscillating static pressure is not a simple task. Armentrout and Kicks [19] and Weyer and Schodl [20] reviewed methods for measuring instantaneous static pressures. They discuss the problem of gas-dynamic resonance and suggest how best to mount transducers. The Paxman 16RP200 engine is fitted with thermocouple wells close to each exhaust port in the exhaust manifold. These locations only were available for measurement of instantaneous static pressure and no modification, except the withdrawal of the thermocouple well could be made. Transducers suitable for measurement of time- varying exhaust-manifold pressure were not held by the RAE(ND) at the outset of the project and their specification was based on the recommendations of the above-mentioned research [19, 20], the severe space restrictions, and the cost of the transducers and amplifiers.
Strain-gauge transducers are most commonly used for manifold pressure measure ments but their natural frequency is typically 20 k H z , which is less than half that of the alternative transducers considered. The highest frequency excited by the engine in one of the sub-manifolds was estimated to be 500 H z from a knowledge of the maximum engine speed of 1500 r p m and the knowledge that two exhaust pulses each of approximately 70 d e g C A duration occur each cycle. Due to the relatively large size of strain-gauge transducers and their cooling requirements the transducers would need to be mounted at the end of a passage up to 150 m m long which might have introduced some damping and phase-shifting of the ‘true’ signal, and the superposition of a high-frequency signal upon it. Additionally strain-gauge transducers might not have withstood the high temperatures of the exhaust gases despite water-cooling.
Piezo-electric transducers are rarely used for measuring manifold pressures because of their high cost and the need for a reference pressure. They also suffer problems of charge leakage and drift.
Piezo-resistive transducers offer advantages of a natural frequency in excess of
45 k H z , a linear output, excellent repeatability, and a lower cost than that of
30 a piezo-electric transducer. The principle of operation of a piezo-resistive trans ducer is that the resistivity of some semi-conductor materials changes when the material is mechanically loaded. The Kistler piezo-resistive transducers comprise four miniature piezo-resistors diffused into a sensing element and connected to a Wheats tone-bridge circuit. The transducers have integral thermal compensation and the thermal sensitivity and zero shift are quoted to be less than -1% and - 0.5% of the full-scale output respectively in the operating temperature range 20 to
120 d eg C . A comprehensive discussion of the design, construction and thermal compensation of these transducers is given by Winteler and Gautschi [21].
Six Kistler piezo-resistive transducers type 4075A10 which have a range 0 to 10 bar absolute were purchased together with their associated amplifiers, type 4611, and water-cooling jackets, type 7505. Adapters were made to fit the water-cooling jackets to the thermocouple wells of the exhaust manifold such that the passage length was kept to a minimum. The longest passage length was 76 ram.
The transducers and amplifiers were calibrated before and after the tests using a Druck DPI600 pneumatic constant-pressure device and the analogue-to-digital converter (ADC) of the AVL Indiskop 647 data-acquisition system. There was no detectable difference in the calibrations before and after the tests and all showed good linearity.
31 2.3.3 Cylinder Pressure
Piezo-electric transducers are commonly used for instantaneous cylinder pressure measurements. Strain-gauge transducers are not able to measure such high pres sures, and although there are high-pressure piezo-resistive transducers, the au thor was unable to find literature supporting the use of the latter, except that of the manufacturer. Piezo-electric transducers have been used extensively by the RAE(ND) for cylinder-pressure measurement and the three Kistler piezo-electric transducers type 6121 together with AVL HICF3059 charge amplifiers which had been used before were used in this project.
The principle of operation of piezo-electric transducers is that when the quartz crystal situated directly behind the steel diaphragm is mechanically loaded the crystal yields an electric charge voltage proportional to the applied pressure.
In the absence of thermal shock effects it is desirable to mount the transducer flush with the cylinder-head face in order to avoid the superposition of high-frequency signals caused by gas-dynamic resonances in the passage on the ‘true’ cylinder trace. Often, however, the transducer is recessed slightly to protect it from the flame front. In these tests there was no choice of passage length: the transducer was flush-mounted, and though it was fitted with a protective heat shield thermal- shock effects were evident. They are discussed more fully in section 2.10.
Each piezo-electric transducer was calibrated together with the charge amplifier and high impedance connecting cable using a Budenberg dead-weight tester and the ADC of the AVL Indiskop 647 data-acquisition system before and after the tests. There was no detectable change in the calibrations which were linear over the range of interest ( 0 to 150 bar ) and which deviated only marginally from this linearity at pressures up to 250 bar.
32 2.3.4 Inlet Manifold Pressure
Two Bell and Howell strain-gauge transducers, type BHL4100, with integral bridge amplifiers were used to measure the pressure in the inlet manifolds. The transduc ers were calibrated before and after the tests against a Druck DPI600 pneumatic constant-pressure device, the output voltage being measured on the Solartron Orion data logger.
2.3.5 Needle Lift
A Wolff Controls Corp Hall-effect transducer with an integral amplifier was used to measure needle lift.
2.3.6 Engine Speed and Load
The engine speed was measured with Orbit magnetic-inductive pick-ups, type 70D1303, and the load was measured using a Heenan Froude DP78 water brake.
2.3.7 Fuel and Air Consumption
Fuel consumption was measured using a Cussons Compuflo 10 kg gravimetric device.
To measure air mass-flow rate two pairs of non-standard orifice plates were fitted, one between each air-filter and compressor-inlet-casing flange. They were spe cially designed and made by Napier Turbochargers Ltd and were of rectangular cross-section to fit the bifurcated compressor-inlet casing, as illustrated in plate 2.2. The downstream edge of the orifice plates fitted to the drive end of the engine was bevelled: that of the pair of plates fitted to the free end was not. The pres sure differential across each orifice plate was measured with a water-manometer inclined at approximately 12 deg. The angles of inclination were measured using a clinometer. Napier have been unable to calibrate the orifice plates, thus the differential pressures could not be accurately translated into mass-flow rates.
33 2.3.8 Turbocharger Speed
A magnetic-inductive tachometer was used to measure turbocharger speed. Only one probe was functioning correctly: it was moved from one turbocharger to the other on different test days to facilitate the speed measurement of both turbocharg ers.
2.3.9 Atmospheric Pressure
Atmospheric pressure was read on the site barometer.
2.3.10 Gas Temperature
K-type thermocouples were employed to measure all air and exhaust-gas temper atures. In the exhaust manifold the thermocouples were fitted in protective wells.
2.3.11 Exhaust Back Pressure
The exhaust back pressure was measured by a Bell and Howell BHL4100 strain- gauge transducer which incorporates a bridge amplifier. The transducer was lo cated in the exhaust ducting close to the turbine exit.
2.3.12 Coolant Temperatures and Pressures
Temperatures of the coolants, including the raw water for the inter-cooler and the exhaust-manifold water coolant were measured using K-type thermocouples and strain-gauge transducers were used to measure the pressures.
34 2.4 Data Acquisition
An AVL Indiskop 647 data-acquisition system was used to record eight signals simultaneously at every degree of crank angle throughout the cycle; to perform the conversion of ADC steps to mechanical units; to calculate at each crank-angle position the average of 64 consecutive cycles; and to store the average values on floppy discs. The Indiskop incorporates a 12-bit ADC but only 11-bit resolution was available since the signals input to the Indiskop were positive and the 12-bit resolution is utilised only when the signals fill the ±10 V window (or ± 1 V window if selected, as in the case of inlet-manifold pressure measurement).
To record measurements every 1 d e g C A the Indiskop requires two signals: a once per revolution signal and a once per 1/2 d eg C A signal. The latter signal must be a square wave of 5 V amplitude and 1/2 d e g C A period. These signals are supplied by passing the square wave with a 1 d e g C A period which is output from the Microsync through a divide-by-two switch. The arrangement of magnetic pick ups, the Microsync, divide-by-two switch and Indiskop is shown in figure 2.3.
In addition to the Indiskop which was used to record instantaneous static pressures in the inlet and exhaust manifolds, cylinder pressure and needle lift, a Solartron Orion data logger was used to record measurements 6 to 12 listed in section 2.2 which were logged twice during a test and not each crank angle. The dependence of these measurements on crank-angle is either not of importance in this project, or could not be accurately measured at high frequencies. The Orion, which was already installed at the RAE(ND), takes a snapshot view at any point in the cycle.
The measurements of atmospheric pressure and pressure drop across the orifice plates fitted to the compressor-inlet casings were logged manually.
35 2.5 Data Transfer
To facilitate processing the data on the Imperial College Cyber 180/855 mainframe computer a method for transferring the data from the Indiskop at the RAE(ND) establishment at Pyestock to the mainframe at Imperial College was devised. The idea of using a modem link between the two sites was rejected in favour of using an intermediate portable micro-computer because of the lower risk of data cor ruption using the latter method. An Apricot PC micro-computer was therefore used at Pyestock to receive data from the Indiskop and to send data to the Cy ber mainframe computer at Imperial College. The data were processed by the Indiskop to convert them to mechanical units and were transferred to the Apricot PC in a hexadecimal format via an RS232 connection using the Polycom commu nications package. They were then transferred to the Cyber mainframe without further processing via an RS232 link using a version of the KERMIT communica tions package specially configured for use with the Apricot PC. The data transfer process is summarised in figure 2.5.
2.6 Engine Test Conditions
The engine is used for marine propulsion and for electricity generation and there fore a set of test points covering a range of operating conditions for the engine in both these applications was selected. The test points coincided with those of the RAE(ND)’s standard Type-test procedure enabling the tests to contribute to the Type-test for this engine and to provide the project with data that could be cross-checked if necessary. Results were recorded at the six test conditions shown in figure 2.6: four points lie on the propeller-law curve (points 1, 2, 4 and 6), and three on the curve demanded by electricity generation (points 3, 4, and 5), one point being common to both applications.
36 2.7 Arrangement of Instrumentation
It was not practicable to record simultaneously all the time-varying pressures of interest in a sixteen-cylinder engine with two turbochargers, two inlet manifolds, and two exhaust manifolds, each of which is sub-divided into four. The engine was therefore split conceptually into two V8 engines as shown diagrammatically in figure 2.7. One V8 comprises cylinders 1 to 4 of A and B banks, and the other comprises cylinders 5 to 8 of A and B banks. The latter ‘engine’ was chosen for the experimental validation work since accessibility for transducers was marginally improved at this, the drive end, of the engine and the error in measurement of the crank angle due to crank-shaft wind-up was reduced since this measurement was taken at the drive end of the engine. Note that by splitting the engine in this way one exhaust manifold serves one V8 but air is supplied by both A and B bank inlet manifolds so the gas-flow paths through the V8 engines are not entirely independent.
In each exhaust manifold there are twelve locations at which time-varying static- pressure could be measured: one at each entry to the manifold connected to each of the eight cylinders, and one at each sector of the four-entry turbine-inlet casing. In addition the time-varying measurements of the two inlet-manifold pressures, cylinder pressures and needle lifts were required. A few limitations imposed by the RAE(ND) helped to simplify the problem of logging these signals ( a total of thirty ) simultaneously using an eight-channel data logger.
Firstly, only one cylinder head could be fitted with a pressure transducer, and only one needle-lift transducer was available: cylinder B8 was selected for both pressure and needle-lift measurements as this cylinder is connected to the turbine by the longest exhaust manifold, and therefore gas-dynamic effects were most likely to be observed in this manifold.
Secondly, six, and not twelve, piezo-resistive transducers for exhaust-manifold pressure measurements had been purchased. To measure pressures at all twelve locations, therefore, the transducers were moved from one test day to the next. The locations are shown diagrammatically in figure 2.8.
37 The measurements taken each day are summarised in table 2.1, from which it can be seen that cross-referencing of most signals was facilitated. With seven channels of the Indiskop dedicated to cylinder and exhaust-manifold pressure measurements, the last channel was used such that the pressure in the B-bank inlet manifold was logged on test day 1, and A-bank inlet-manifold pressure on test days 2 and 3. On the latter two test days two sets of results were recorded for each operating point, one set logging inlet-manifold pressure on the eighth channel, and one logging needle lift on the eighth channel.
On each test day, therefore, the cylinder pressure, exhaust-manifold pressures at six locations and an inlet-manifold pressure were recorded, and on the latter two days needle lift was also logged. To provide a set of reference values from one test day to the next the three exhaust pressure transducers fitted to the three locations in the sub-manifold serving cylinders 8 were kept in the same locations, while the remaining three were moved each day to different sub-manifolds. A transducer could not be fitted to the exhaust manifold at the location closest to cylinder B5 due to a lack of space. Since this pressure could not be recorded a second set of pressures for the location by cylinder B7 was obtained. A further change in measurements between the first and the latter two test days was that on the first the speed of the turbocharger fitted to the free end was measured, and on the latter days that of the turbocharger fitted to the drive end was measured. This was necessary because only one speed probe was functioning correctly .
38 2.8 Test Procedure
To protect the piezo-electric transducers from the effects of a cold start, the engine was run for thirty minutes prior to fitting the transducer in the cylinder head and a different transducer was fitted each day. During the thirty-minute warm-up period the atmospheric pressure was recorded and the data set for the Indiskop was modified to account for the different calibration constants of the cylinder and inlet-manifold transducers used on different days and the changes in location of the transducers in the exhaust manifold.
Once the cylinder-pressure transducer was fitted the engine was run up to the first
operating point of 700 rpm, 5.6 bar bmep, and was held at this point for approx imately half an hour or until the engine operator considered that it had reached equilibrium. To test whether the engine had reached an equilibrium condition the results output by the Orion indicating the scatter between temperature mea surements in the exhaust manifold were inspected. The charge amplifier, located in the test cell, was then manually grounded. High-frequency data logging was initiated on the Indiskop (situated in the control room above the test cell) as soon afterwards as was physically possible. Following visual inspections on the Indiskop screen of the pressure traces being logged, and of the output from the Orion, the pressure differentials across the orifice plates fitted to the compressor-inlet casings were measured on the inclined water manometers using a ruler. On test days 2 and 3 the inlet-manifold pressure lead was then disconnected from channel 8 of the Indiskop, the needle-lift lead was substituted, and the high-frequency data- acquisition procedure was repeated.
The engine speed and load were then adjusted for the next operating condition and the procedure was repeated until data for the six test points had been acquired.
39 2.9 Raw Results
The raw results logged onto the Indiskop were translated from their hexadecimal format to a decimal format on the main-frame computer, and were inspected to see whether shifts in the pressures, needle lift or crank angle were necessary.
Several cylinder pressure signals were negative at BDC before compression. This was due to the fact that when the charge amplifier was manually grounded it was not known where in the engine cycle the grounding occurred, and if it was not at a position of minimum pressure an artificially low cylinder pressure was recorded. The cylinder pressures were all shifted, therefore, such that at BDC before compression the cylinder pressure and inlet-manifold pressure were equal. This is common practice in engine research at Imperial College, and is supported by results of filling-and-emptying analyses.
The information sought from measurement of needle lift during the cycle was the dynamic injection timing and not the amount by which the needle lifted. These traces were therefore shifted vertically simply to look at a positive signal, this having no effect on the timing. The shifted data were plotted as a function of crank-angle.
There was no need to post-process the results recorded on the Orion.
The average of the pressure differentials across the orifice plates fitted to the compressor-inlet casings taken each day are listed in table 2.2. It was not possible for the orifice plates to be calibrated during the time-scale of this project, thus the air mass-flow rate through the engine could not be measured. The air mass-flow rates listed in table 2.2 were calculated from the pressure differentials across the bevelled-edge orifice plates using a discharge coefficient of 0.73 which was estimated from British Standard 1042.
The average of the temperatures measured each day just downstream of the cylin ders are listed in table 2.3. The agreement between test days was excellent. No
40 measurement was available at exhaust manifold transducer locations near cylin ders A8 and B8 as instantaneous pressure measurements were recorded each day at these positions.
The scatter of the turbine back-pressure measurements and the values themselves suggested that the readings were erroneous.
2.10 Data Reduction
It can be seen from table 2.1 that a large amount of data was duplicated. While this was a useful indication of repeatability it also called for a method of reducing the data to a single set for each test point. Consider the data recorded for any test point: there are
- 5 sets of cylinder pressure traces
- 5 sets of pressure traces for the exhaust manifold of cylinders 8
- 2 sets of traces for exhaust manifolds of cylinders 5 and 7
- 2 sets of A-bank inlet-manifold pressure traces
- 2 sets of needle-lift data
- 1 set of pressure data for the exhaust manifold of cylinders A6 and B6
- 1 set of B-bank inlet-manifold pressure traces.
There was good agreement between all traces at each test condition, though some traces were slightly more spiky than others. The data were reduced to a single set for each test point by selecting the least spiky diagram for each measurement yielding a total of fifteen diagrams. Note that exhaust traces for a set of three transducers fitted in a sub-manifold were either chosen or rejected: diagrams re ferring to a sub-manifold were not split up. A sample set of diagrams is given in figures 2.9 to 2.15.
41 2.11 Final Results
An example of a final set of time-varying results is given in figures 2.9 to 2.15.
These results are for test point 4 for which the engine speed was 1200 r p m and the bmep was 12.8 bar.
The repeatability of all traces was excellent between test days. The inlet mani fold pressure remained approximately constant throughout the cycle as would be expected for a manifold of this size supplying eight cylinders. The exhaust pres sure traces have some high-frequency oscillations superimposed on the main trace * due to resonance in the passage connecting the transducer to the manifold. They also exhibit a step-like initial pressure rise which is characteristic of gas-dynamic pressure waves. The exhaust pulse from one cylinder was sensed by the trans ducer near the exhaust port of the second cylinder common to the sub-manifold, and by the time the pulse reached the turbine-entry casing the wave fronts were steeper and less influenced by the gas-dynamic ‘steps’ observed in the traces near the cylinder.
Figure 2.15 shows that for much of the exhaust stroke the exhaust manifold pres sure exceeded the cylinder pressure which suggests that one of these two pressure traces is erroneous in this region. The piezo-electric transducer could have suffered the effects of thermal shock. Benson and Pick [22] observed this phenomenon when they measured cylinder pressure using piezo-electric transducers. They suggested that the cause was the uneven expansion of the diaphragm, the effect being that the recorded cylinder pressure is artificially depressed during the exhaust stroke but recovers before compression. They found several solutions to the problem: the simplest was to recess the transducer by one passage diameter from the face of the cylinder head, and a second solution was to fit a heat shield to the transducer. They also put forward two methods for determining the extent of the effect: one is to introduce a second transducer such as a strain-gauge transducer to measure cylinder pressure during the low-pressure part of the cycle and to compare the two traces; and the other is to see how far the measured imep is below the bmep, the latter method being more comprehensively discussed by Brown [23]. Regarding
42 * A simple organ-pipe calculation gave an approximate wave period of 7 d eg C A at test point 4. the first method, Chan [24] measured cylinder pressure using a low-pressure strain- gauge transducer and a high-pressure piezo-electric transducer. The low-pressure transducer was assigned an offset such that at bottom-dead-centre (BDC) before compression the low-pressure and high-pressure measurements were equal. At EVO Chan observed that the low-pressure transducer always recorded a slightly higher pressure than the high-pressure transducer. The error was assigned to ‘the effect of higher pressure gas trapped in between the piston rings sweeping past this transducer’, and is not quantitatively discussed. The author’s interpretation of this result is that thermal shock affecting the high-pressure piezo-electric trans ducer may have caused the mis-match between the low-pressure and high-pressure transducer readings.
In the full-scale engine tests performed in this project a low-pressure transducer could not be fitted but the second of Benson’s suggestions for assessing the thermal shock problem was considered. For test point 4, for which a set of results is given in figures 2.9 to 2.15, the imep calculated from the measured cylinder pressure diagram was 8.6 bar while the measured bmep was 12.8 bar. This difference is, however, too great for the cause to be thermal shock alone.
The apparent thermal shock problem was not identified until after the tests had been concluded and no alteration to the mounting of the transducer, or the trans ducer type could have been effected during the time allocated to these tests. The transducers used were Kistler type 6121, two of which were new. In accordance with Kistler’s installation instructions these transducers were not water cooled. The data sheet for the instrument says that the transducer “works reliably in ambient temperatures of up to 350 d eg C” and the diaphragm has a ceramic front- plate which “keeps pressure measurements unaffected by high intermittent flash temperatures” of up to 2500 deg C. It is thought unlikely that these temperatures have been exceeded.
An alternative reason for poor cylinder pressure traces was sought and it was found that by advancing the experimental trace for each test condition by approximately
43 8 d e g C A the imep calculated from the experimental data was in good agreement with the bmep measured on the engine at the same test condition.
An error of 8 d e g C A is too large to be accounted for by, for example, crankshaft wind-up, or the accumulation of tolerances on the Orbit correctly identifying the centre of the hole in the flywheel. It is thought that the error was a result of an incorrect crank-angle offset being input on the Microsync, in which case all data logged including the inlet- and exhaust-manifold static pressures need to be advanced. This means that although the measured bmep and calculated imep now correlate well, the cylinder pressure still falls below the exhaust-manifold pressure towards the end of the exhaust stroke, as in figure 2.15, signifying that some thermal shock does occur.
The 8 d e g C A data advancement was further justified when the shifted cylinder pressure diagrams were analysed using the Apparent Heat Release Rate computer program, as discussed in section 5.1 of chapter 5.
44 C H A P T E R 3
THEORY
3.0 Introduction
The most widely used numerical method for predicting engine performance is the filling-and-emptying method which solves the conservation equations for mass and energy in inter-connected thermodynamic control volumes representing the chambers of an engine system. In each control volume it is assumed that the gas properties are constant with respect to space. Consider the implication of this assumption when modelling exhaust manifolds. For a constant-pressure manifold the assumption is fair; for a gas-dynamic exhaust system it is not. Gas-dynamic exhaust systems are designed to preserve the kinetic energy of the exhaust gas, and in so doing pressure waves are set up in the manifold. To minimise pressure-wave interaction within a gas-dynamic manifold pulse-converter systems were designed.
If the overall engine performance is of interest, and not, for example, the effect of pipe length on volumetric efficiency, the filling-and-emptying method is a use ful tool. Where the lengths of pipes comprising a pulse system are short, as in automotive pulse-exhaust manifolds, there may be no advantage in using a more complex method that would model the effects of momentum. Where pipes axe long and pressure-wave effects are of interest the assumption of spatially-constant gas properties must be relaxed, and a method which solves the momentum equa tion in addition to the continuity and energy equations must be used. There are two principal methods for solving these equations, namely finite-difference tech niques and the method of characteristics. Each is discussed briefly below, followed by a section on the choice of mathematical model employed in the development of the Imperial College engine simulation program TRANSENG. The mathemat ics describing the filling-and-emptying method and the model chosen to simulate gas-dynamic effects are then presented.
45 3.1 Mathematical Models to Simulate Gas-Dynamic Effects
3.1.1 Finite-Difference Methods
Several one-dimensional finite-difference methods have been developed, notably those of Yano and Harp [25], Meisner and Sorenson [26], and Ledger [27]. The first of these uses an explicit time-marching scheme: each mesh of the finite-difference grid has a thermodynamic and a momentum zone superimposed upon it. The momentum zone divides the thermodynamic zone in half as shown in figure 3.1. Throughout the thermodynamic zone thermodynamic variables are assumed to have a constant value equal to their values at the mid-point of the zone. Similarly in the momentum zone the velocity is assumed to be that at the mid-point of the momentum zone, and constant throughout the zone. Total pressures predicted by this method were shown to agree well with experimental results but the details of the experimental work were not given. There was also no information on numerical stability, on boundary treatments (in particular at junctions), or on computer run times.
Meisner and Sorenson [26] simulated the performance of a small single-cylinder spark-ignition engine by integrating the continuity, energy, and momentum equa tions directly using the MacCormack method [28]: a centred-difference predictor- corrector technique which allows prediction of wave propagation in both directions. It is an explicit, conditionally stable method. The predicted results compared rea sonably well with experimental data and discrepancies were well explained. As in Yano and Harp’s paper [25], however, there was no mention of computer run times or of how a branched pipe would be modelled.
Ledger [27] also developed a centred-difference prediction technique to simulate exhaust-manifold flow. The results of his prediction, based on a Ruston single- cylinder AW engine, showed good agreement with those obtained by the method of characteristics but neither set of results was compared with experimental data.
46 The finite-difference program took more than six times longer to run than the method of characteristics program.
3.1.2 M ethod of Characteristics
The method of characteristics is an alternative technique for solving the govern ing equations of one-dimensional unsteady compressible flow. These equations are non-linear, hyperbolic partial-differential equations, and by the method of characteristics they are converted to ordinary differential equations along the char acteristic lines in the x —t plane. The solution of the ordinary differential equations with the relevant boundary conditions yields the spatial and temporal variation of pressure and temperature through the exhaust manifold.
The method was initially set up for solution by graphical procedures and it was not until the late 1950s that it was configured for solution on computers. Various numerical solutions were then developed, one of the most well-known being that of Benson and co-workers which has been documented over the thirty years of its development. Reference 29 describes some of the early work, and reference 30 is a comprehensive text on the subject, giving details of the homentropic and the more complex non-homentropic methods. The non-homentropic method allows for pipe friction, changes in cross-sectional area, and temporal and spatial changes in entropy in the pipe, all of which are assumed to be negligible in the homentropic method.
The form of the solution most widely used superimposes a rectangular mesh on a non-dimensional distance-time field such that the points along the distance axis are fixed and are equally-spaced along the pipe. The time-step size varies from one time step to the next as discussed in section 3.2.
The method of characteristics has been used extensively to model pressure-wave propagation in engine manifolds. Curiously, however, most researchers appear not to have compared their predictions with experimental data. In Benson’s text [30] many comparisons are drawn between homentropic and non-homentropic predic tions, and between results from using different initial conditions or numbers of
47 spatial grid points, but very few are drawn between predicted and experimental results. In figure 3.2 one of the few comparisons of predicted and experimental data is given. It shows that the two sets of results are in good agreement, but the information on the experimental procedure is scant and the gas conditions at exhaust-valve opening do not seem representative of engines in service: the engine speed is quoted as 394 rpm, the release pressure as 35 p s ig , and release temperature 130 degF .
3.2 Choice of Mathematical Model
The finite-difference methods reviewed were all lacking information in one or more of the following areas: experimental verification, boundary, and in particular, junc tion treatments, numerical stability considerations, and computer execution times. Where a computer execution time was given [27], it was over six times greater than that for a method of characteristics simulation of the same engine. Further, all the finite-difference methods reviewed are different and little supporting information was found.
The method of characteristics has been used over a longer period of time and is better documented yet it too seems to lack rigorous experimental verification.
In the light of the above, it was decided that the method of characteristics would be integrated into the Imperial College filling-and-emptying program, TRANSENG, provide to^the option for predicting gas-dynamic effects in exhaust manifolds fitted to medium-speed diesel engines. The homentropic method of characteristics was employed in preference to the non-homentropic method since the former offers greater simplicity, shorter computer execution times and fewer detailed input data to describe the exhaust system. By incorporating the homentropic method of characteristics into a filling-and-emptying program the advantages of simplicity, versatility, and low computer execution costs of the filling-and-emptying method have been maintained whilst removing the restriction that only temporal, and not spatial, variations of gas properties in exhaust manifolds can be modelled. The
48 theory on which the filling-and-emptying method and the method of characteristics is based is given in the following sections.
3.2.1 The Filling-amd-Emptying M ethod
The filling-and-emptying method describes an engine system as a series of thermo dynamic control volumes which are successively filled and emptied by mass flowing through the valves, nozzles and orifices which connect the control volumes. Gas conditions within each control volume are assumed to be homogeneous stagnation conditions and are governed by the principles of conservation of mass and energy. By expressing these principles as the unsteady continuity and energy equations it can be shown that a set of first order, non-linear, ordinary differential equa tions describes the flow. Knowing the initial conditions in each volume this set of equations is solved at a series of discrete crank-angle intervals in the engine cycle yielding the rates of change of mass, temperature and equivalence ratio in each volume. Using a numerical integration technique and the equation of state the gas conditions in the volume at the next crank-angle step are evaluated. This method is described in detail by Watson and Janota [31]. Briefly, however, consider a general control volume which could represent an inlet manifold, a cylinder, or an exhaust manifold.
The continuity equation for the volume , considering both fuel and air is:
and conservation of energy demands that:
dU_ dQ _ d u'rr W y - d H c d H 0 (3.2) ~d0 dQ dQ d() + 2 ^ dQ -E dQ out
The rate of change of temperature may be determined by rearranging equation 3.2 as follows.
49 The internal energy of a gas, t/, is given by
U = m u (3.2 a)
and therefore, its rate of change is: dU du d m — = m ----- \- u ---- (3.26) dd dd dO
Assuming that the gas is a perfect gas, the specific internal energy, u, is a function of temperature and equivalence ratio and the left-hand side of equation 3.2 can be written: d U fdudT ! dudF\i d m —— = m (3.2c) dd 'vdT dO + d F d9 ) Using the equation of state, the rate of change of work done by the gas is d W m R T dV (3.2 d) d9 ~ V dO
Substitution of equations 3.2c and 3.2 d into equation 3.2 and rearranging it yields the expression below for the rate of change of temperature.
dT 1 d Q 8f / dH p \ ( d H o \ d m d9 ~ [~d$~ + L , \~de~) in ~ ^ \~ d f ) out ~ u~dd_ RT dV du dF d u (3.3) ~ V d9 ~ dF dO d T
where Q sf is the heat transferred across the surface of the volume. Heat released by combustion is inherent in equation 3.3 by virtue of representing the energy of the working fluid as an absolute value.
By considering the relation between the fuel-air ratio for stoichiometric combus
tion, f sto, the equivalence ratio, F , the mass of fuel burned, m/&, the mass of air, ma, and the mass of working fluid, m, an expression for the rate of change of equivalence ratio can be determined. The fuel-air ratio is:
/ = mfb (3.3 a) ma
and the mass of the working fluid is:
m = ma - f rn/b (3.36)
50 The equivalence ratio is: f mf b F = (3.3c) fsto mafsto or mfb F = (3.3d) (m — m fb ) fsto For convenience the mass of air can be expressed: m m a (3.3e) 171(1 (m a + m Jh)
Dividing both numerator and denominator by m a: m m n = (3.3/) (1 + ”L£6) ' ma • m m n = (3.3 g) (1 + Fftto) Similarly the mass of fuel burned can be expressed: m F f8to 771/6 (3.3 h) (1 + F fsto) Differentiating equation 3.3d: dF_ _ 1 t \ drrijb d m d m jb (m - m fb) — mfb (3.3i) dO { m - m Sb)2 fsto . ~d0 ~ dO Rearranging the above equation: d F drnjb m fb m j h d m 1 + (3-3 j) d$ (m — m f b ) f ato L dO (m — m/b) J (m — m/b) dO From equation 3.3d, d m d F _ 1 fb (3.3k) dO (m - mJb)fsto do + F f ‘ to do And, finally, using equation 3.3<7,
d F (1 + F f , to) (l “h F fs to ) d m jb j^ d m (3.4) dO m fsto do dO
Thus knowing the mass, temperature and equivalence ratio, and solving equations 3.1, 3.3, and 3.4 for the rates of change of these parameters at the beginning of crank-angle step ti, a numerical integration can be performed to evaluate the properties in the volume at the beginning of crank-angle step n -\-1. Employing the equation of state the pressure in the volume at this time is also established and the calculation procedure is repeated for each successive step until a sufficient number of engine cycles have been completed to achieve satisfactory cyclic convergence.
50 a 3.2.2 The Method of Characteristics
The method of characteristics is a mathematical technique used to solve the non linear hyperbolic partial-differential equations governing one dimensional com pressible flow by reducing them to ordinary differential equations which are valid along characteristic lines in the distance-time ( 2 — t) plane. Comprehensive pre sentations of the analytical method and its arrangement for numerical solution on computers are given by Benson [30], Shapiro [32], and Oswatitsch et al [33], to name but a few. A summary of the equations is given below.
Consider unsteady one-dimensional homentropic flow in a frictionless pipe of con stant cross-sectional area. The continuity equation is: d p d p d u . . i + u a i + ^ = ° (3‘5>
The momentum equation is: d u d u 1 d P ------f- u ------1------= 0 (3.6) d t d x p d x
The sonic velocity is defined by
(3.7) and, assuming a perfect gas,
P = p R T (3.8)
Using the latter two equations the partial-differential equations, 3.5 and 3.6 can be re-stated: da \ du (3.9) dt ) dt = ° along the characteristic dx — = u 4- a (3.10) dt and, ^
da 0 II 1^3 (3.11) dt (V along the characteristic HI** 3 II |^ — a (3.12)
51 Equations 3.10 and 3.12 are termed the direction equations and they define the
slope of the characteristics in the x — t plane, while the compatibility equations, 3.9 and 3.11 relate the sonic velocity and the particle velocity along the characteristic.
For convenience a reference sonic velocity, are/, is introduced: it is the sonic velocity of the gas at a reference pressure, P ref, to which the gas is isentropically expanded or compressed from the local conditions. A reference length is also
introduced, x rej . These reference parameters are used to non-dimensionalise the salient parameters:
A=— , U=— , X=— , Z = ^ (3.13) O'ref ^ref %ref %ref
and introducing the Riemann variables which are the constants obtained from integrating the compatibility equations:
A = A + ^ —U (3.14)
7 — 1 13 = A - -— — U (3.15)
The direction conditions, 3.10 and 3.12, can be re-stated:
d X = ( 7 + 1 3 - 7 A- (3 along {U + A ) (3.16) d Z ~ \ 2 ( 7 — 1) 2(7-1) v and d X _ / 7 + 1 3 - 7 P- X along (U — A ) (3.17) d Z ~ \ 2 ( 7 — 1 ) 2(7-1)
To solve the ordinary differential equations 3.16 and 3.17 a mesh is created in the
x — t plane. The mesh points are equally spaced along the distance axis but not along the time axis: each time interval is determined by the Courant, Friedericks, Lewy stability criterion [34]. This stability criterion demands that:
d Z < (3.18) dX ~ A + \U\
52
'\ where dZ is the non-dimensional time step and dX is the non-dimensional interval between successive points on the x-axis. The maximum allowable time step is calculated for each point along the x-axis at time t and the smallest value of dZ is selected to advance the solution in the time domain. This is illustrated in figure 3.3.
Within the pipe the Riemann variables are calculated from a knowledge of their values at the previous time step, but at the pipe boundaries only one Riemann variable is known, ie the incident characteristic (see figure 3.3). The reflected characteristic is calculated as a function of the boundary condition imposed. In an exhaust manifold typical boundaries include valves, junctions, and turbine nozzles.
The simplest pipe boundary condition is a closed valve. A pressure wave incident upon a closed end is reflected without a phase change; the gas velocity is zero, and from equations 3.14 and 3.15 it can be seen that the reflected and incident characteristics are equal. At other boundaries it is usually assumed that the temporal variation in gas properties is insignificant compared with the spatial variation at a boundary and steady-flow conditions are applied at the boundary. This assumption leads to the straight-forward determination of reflected characteristics at open ends, valves and nozzles as described fully by Smith [35], and briefly below.
Different solutions are required for inflow through a valve to a cylinder and outflow from a cylinder. For inflow to a cylinder a poppet valve is modelled as a partially open end, as depicted in figure 3.4. It is assumed that the fluid accelerates isen- tropically from the upstream to the throat conditions, and that the flow is steady for the duration of the crank-angle step, ie. quasi-steady, between planes 1 and
2 of figure 3.4. By using the quasi-steady assumption the fluid flow is completely described by the continuity and energy equations. For outflow from a cylinder the “constant pressure” model is employed. This model assumes an initial isentropic acceleration from the stagnation cylinder conditions to the valve throat, followed by an adiabatic expansion at constant static pressure from the throat to a plane a short distance downstream of the throat. The process is shown in figure 3.5.
53 As with inflow to a cylinder, the quasi-steady assumption enables the steady-flow continuity and energy equations to be used.
If the pressure ratio across a valve exceeds the critical pressure ratio, the reflected characteristic is calculated such that the local gas velocity equals the sonic velocity. For the case of reverse flow through an inlet valve the boundary equations for forward flow through an exhaust valve are solved and vice versa.
The analysis for the nozzle boundary condition is identical with the inlet-valve boundary condition, except that for the valve the flow area is a function of crank angle, and for the nozzle it is constant. It too is derived by Smith [35].
The most common boundary in exhaust manifolds is the junction and it is the least simple to describe mathematically. Deckker and Male [9] used Schlieren pho tography and a hydraulic analogy, supported by stagnation and static pressure measurements, to show the complex nature of flow at a three-way junction: it is three-dimensional and pressure losses across even a simple T-junction are signifi cant and are a function of the geometry, the velocities and the mass-flow rates in the different branches. To describe the flow simplifying assumptions are made.
There are several available junction models ranging from purely empirical to purely theoretical ones, and simple to complex ones. These will be discussed below, greater detail being given to the models which are most nearly appropriate to the research undertaken by the author. The model employed by the author will then be described.
54 3.3 Pipe Junction Models
3.3.1 Equal-Pressure Junction Model
The equal-pressure junction model, sometimes misleadingly referred to as the constant-pressure junction model was developed by Benson [10]. It assumes: i) the static pressures at all pipe ends bounding the junction are equal ii) the entropies at all pipe ends bounding the junction, and therefore throughout all pipes connected together, are equal iii) flow in the junction is steady and one-dimensional
The analysis is purely theoretical and is widely used in programs structured for the method of characteristics due to its simplicity and computational efficiency.
3.3.2 Pressure Loss Model
Benson, Woollatt, and Woods [ll] recognised that the equal-pressure assump tion is in many cases an over-simplification, and they developed a semi-empirical model from their examination of flow in an equal-area T-junction. The pressure loss across the junction is accounted for by assuming a quasi-steady momentum equation which incorporates a loss coefficient determined from steady-flow tests. This method gives improved accuracy compared with the equal-pressure model but has three disadvantages: - empirical loss coefficients for all permutations of flow direction are required
- the solution is not generalised: in its original form a full solution could not be found for a junction of more than three pipes, but Daneshyar and Pearson [12] did extend the method for a four-pipe junction, - it is costly to run.
It was not until 1985 that Bingham and Blair [13] proposed a simplified generalised pressure-loss model but their model still suffers from requiring all pipes to operate on the same entropy level and time step, and although they claim their model is as accurate as conventional pressure-loss models, their comparison of predicted
55 and experimental pressure traces in an exhaust manifold do not lead the author to have great confidence in either model.
3.3.3 Two- and Three-Dimensional Models
Two-dimensional models have been developed by the motor industry in Japan for use in engine simulation programs based on the Lax-Wendroff finite-difference scheme [36, 37]. These models divide the junction into triangular elements which facilitates the simulation of flows through complex junction geometries. The ve locity, density, and pressure at the centre of each element is calculated using the modified fluid-in-cell method [38]: a two-step finite difference method. Tosa et al [36] report that their program incorporating the two-dimensional junction model takes twice as long to run as the one-dimensional method of characteristics pro gram but they do not specify the junction model used in the latter.
A wholly theoretical three-dimensional junction model has been developed by Leschziner and Dimitriadis [18]. Their objective was to provide a facility to com pute the pressure-loss coefficients required by the quasi-steady pressure-loss mod els. In this way the need for empirical data is removed. A complex finite-volume technique is used to solve the transport equations in the junction. Computer execution times vary greatly depending on whether the flow is joining or separat
ing and for the latter are of the order of 90 C P U m in u te s on a Cyber CDC7600 mainframe computer.
3.3.4 Deckker and M ale’s Empirical M ethod
In contrast to the theoretical models Deckker and Male [9] provided purely exper imental results relating the flow in each branch of a three-way junction to that in another of the branches. They presented their results in graphical format suitable for use with the method of characteristics. The author has been unable to find documented results of the application of this method.
56 3.3.5 Review of Junction Models for use in a Filling-and-Emptying Program
By choosing to develop a filling-and-emptying program to include gas-dynamic calculations rather than choosing to develop an existing method of characteristics program the junction model chosen had to be computationally inexpensive, give good predictions of pressure in the exhaust manifold and fit into the existing program structure. None of the models described in sections 3.3.1 to 3.3.4 is entirely suitable. The two- and three-dimensional models are too complex and too expensive to run. The purely empirical model concerns only three-way T-junctions and, in the absence of reports on its application would have to be extensively tested. The equal-pressure junction can not predict pressure differences across the limbs of a junction and has been shown by the author in Appendix A to contravene the conservation of energy unless the gas velocity at at least one of the pipe ends is zero. The pressure-loss model requires a complete set of eighteen empirically determined loss coefficients for each of angular arrangement of a three- way junction. Bingham and Blair’s generalised model [13] is a simplified version of the pressure-loss model. It takes a shorter time to run and the loss coefficients are calculated using simple equations relating the loss coefficient to the branch angle. The last model is the most suitable of the above methods but the author’s proposed volume junction model described below is considered superior in terms of generality, versatility and low computer execution time.
57 3.3.6 Volume Junction Model
The proposed volume junction model was developed to operate within the context of a filling-and-emptying program. It considers the junction of any number of pipes to be a small filling-and-emptying thermodynamic control volume in which the unsteady-flow continuity and energy equations are solved.
At each pipe end bounding the junction volume, and each method of characteristics time step, the method of characteristics solution yields values for density and velocity of the gas. In figure 3.6, therefore, the gas velocity and density are known at each of planes Al, A 2 , and A3. These values are time-averaged over the period of the crank-angle step, and at each crank-angle step the averaged values are used to calculate the mass-flow rates into and out of the junction volume, and hence to solve the unsteady continuity equation for the junction volume.
The use of the homentropic method of characteristics means that the entropy level within a pipe is constant along its length at any time step. The entropy level is related to the reference temperature which is taken to be the time-averaged temperature over the previous engine cycle in the upstream volume. In exhaust manifolds where there is significant heat transfer or stagnation pressure loss, the junction volume provides the opportunity to allow for an entropy increase. In figure 3.6, for example, the amount of heat transferred from the junction volume represents that transferred to the cooling water of the upstream pipes ie. pipes 1 and 2 of figure 3.6, and there is an entropy increase between pipes 1 and 3, and pipes 2 and 3.
Referring to figure 3.6, therefore, the enthalpy transferred to the junction volume across plane A l is
^ 0 A l = ^ 0 c y l l ^ A l
58 Across plane 2 , if flow is towards the junction, it is:
H 0a7 = h 0cyl7rhA2 and across plane A3 it is:
H oa> = h0volmA3
Then, knowing also the heat transferred from the volume, the energy equation for the junction volume can be solved according to equation 3.3. The volume thus presents a common boundary condition to each of the connecting pipes.
Consider the T-junction of figure 3.6. The volume is finite, unlike those met in conventional method of characteristics programs where the volume is either infinite, as in the atmosphere, or zero, as at a junction. This complicates the choice of a suitable assumption. The assumptions made and the calculations for the reflected characteristics are discussed in the following sections.
3.3.6.1 Flow from a P ip e into a Ju nction Volume
There will be a step change in stagnation enthalpy at planes A 1 and A 2 of figure 3.6, since flows of different enthalpies are assumed to be instantaneously mixed in the junction volume from which heat is also transferred. If the non-homentropic method of characteristics was used the assumption of an instantaneous change in stagnation enthalpy would not be necessary, but at the cost of substantially increased complexity and computer execution time.*
See recommendations, section 7.1 In order to calculate the reflected characteristic at the boundary between pipe 1 and the volume, however, it is assumed that at the plane of the boundary, the stagnation enthalpy, hoi, is that of the volume, thus
/ioi — h voi (3.19)
From the definition of stagnation enthalpy, U\2 hovoi — h i ^ (3.20) where h i is the specific enthalpy at the end of pipe 1 : II c*
£3 (3.21) •o and, since stagnation temperature is defined by: u2 (3.22) To = T + ^ and therefore
hovol '^OvolC’p (3.23) the velocity can be written:
u 2 — 2 cp (Toi — 2 \) (3.24)
Non-dimensionalising the parameters as in equation 3.13, and introducing the isentropic relation:
2 2 U 1 (3.25) 7 - 1 where Pi is the static pressure at the boundary and U i is the non-dimensional gas velocity at the boundary. The U i2 term represents the kinetic energy of the gas and if the gas were brought to rest isentropically, 1 0 0 % pressure recovery would be achieved and the static pressure at the end of the pipe would equal the stagnation pressure in the volume. It is not known how much pressure is recovered at a junction in an exhaust manifold, but it is clearly between 0 % and
59 100%. This boundary condition is therefore arranged so that the program user can specify what fraction of the dynamic head is to be recovered (see section 5.2.4). A pressure-recovery factor, Frecov, is introduced, where Frecov is between zero and unity: 2 ,U i (3.26) 7 - 1
Where P i is not equal to Pi of equation 3.25 unless Frecov is unity. Now non-dimensional stagnation sonic velocity, Aoi is given by: „ [ToT fPovol^ (3.27) = 7 ) and the non-dimensional sonic velocity, is given by: i-i I'i T t / ____ P i A t = (3.28) T ref V Pref
So, turning to the calculation of the reflected characteristic, equation 3.26 can be re-stated:
F recovV\2 = — j- (^-Ol2 “ (3.29)
This equation implies that an amount of energy corresponding to (l — Frecov)U 2 is lost at the boundary. Poi and Aoi are fixed by the conditions in the junction volume and Pi, and thus A\ are then raised relative to the values they would have if there was no loss of available energy, in which case equation 3.25 would apply.
Using equations 3.14 and 3.15 the above equation can be expressed as a quadratic in terms of the Riemann variables, A, and /?, one of which is known; the non- dimensional stagnation sonic velocity, Aoi; and the pressure-recovery factor,
Frec0v • Taking the positive root, for a given /?, A is given by
7 ~ 1 2F r A = 1 + ) Aoi2 + 7 - 1 + 2 Pr 7 - 1 7 - 1
2 F recot (3.30) 7 - 1 1)0 Note that the solution can be found only when the sum of the contents of the square root is positive. This condition demands that
2 Frecov____02 A o i2 > (3.31) 7 - 1 + 2 Fr
60 This can be violated when the pressure-recovery factor approaches unity. The problem may be overcome by limiting the pressure-recovery factor to the maximum allowable value at any time step where the factor selected by the user is in excess of that permitted for numerical stability. The physical significance of imposing
this limitation has not been identified but the demanded change in F recov is small.
In the event of the velocity at the end of the pipe exceeding the sonic velocity, it is limited to the sonic velocity.
If there is reverse flow a different boundary condition is applied, namely that for flow out of the junction volume into a pipe is used, as described in the next section.
3.3.6.2 Flow out of a Junction Volume into a P ip e
For in-flow to a pipe it is assumed that the process between the stagnation condi tions in the volume and the static conditions at the boundary is isentropic. Then applying the assumption that the specific stagnation enthalpy at each pipe end is equal to that of the volume, the following equation may be written:
Ao^2 = A z2 + ^ U3 2 (3.32) which is the same as for outflow from a pipe into a volume with 1 0 0 % pressure recovery, see equation 3.29. The calculation of the reflected characteristic is:
7 ~ 1 7 + 1 2 A = 2 Ao$2 — (3.33) 7 + 1 A 7 - 1 7 - 1
61 C H A P T E R 4
DEVELOPMENT OF THE PROGRAM
4.0 Introduction
The Imperial College filling-and-emp tying program, TRANSENG, was originally designed to predict the performance of high-speed, turbocharged four-stroke diesel engines typically used to power passenger cars and trucks. For these applications it provides a versatile, accurate performance-prediction facility capable of mod elling both steady-state and transient response. It is also capable of simulating the performance of medium-speed four-stroke engines, but these engine configurations require even greater flexibility: for example they may be fitted with one of four different types of exhaust manifold, each of which has different modelling require ments; the firing interval between cylinders may not be equal; and the turbine may be fitted with a multi-entry inlet casing.
This chapter commences with a brief description of the TRANSENG program, followed by details of preliminary modifications such as the allowance for un-equal firing intervals between cylinders. The single major development is then described, namely the inclusion of a facility to model any of the four common exhaust mani fold systems fitted to medium-speed engines, using the method of characteristics. Preliminary simulations showed that numerical instability occurred when mod elling an engine running at low speed. A summary of the subsequent investigation and program development is then given.
62 4.1 The TRANSENG Program
The TRANSENG program is written in Fortran 77. It is based on the filling- and-emptying philosophy but incorporates subroutines which solve the equations describing compressible flow in pipes using the method of characteristics. The engine system is defined by filling-and-emptying thermodynamic control volumes and, if selected, gas-dynamic pipes in which the flow is described by the method of characteristics. In this project the program was developed to allow gas-dynamic simulation of exhaust manifolds. Gas conditions in filling-and-emptying thermo dynamic control volumes are assumed to be constant with respect to space, and quasi-steady flow is assumed over each time step. In gas-dynamic pipes the gas properties, with the exception of composition, are variable with respect to space. Using the differential forms of the equations of conservation of mass and energy the derivatives of the gas properties are calculated and a predictor-corrector inte gration method is used to calculate the gas conditions in the control volumes for the next step.
The component terms of the conservation equations such as the energy released by combustion, the work lost to friction, and mass-flow rates through the inlet and exhaust valves, are calculated in sub-models. These models axe described below and their interaction within the program is illustrated by the flow chart of figure 4.1.
63 4.1.1 Combustion
The process of combustion itself is not modelled. Instead the energy released by combustion is modelled by an apparent fuel-burning rate whose variation with time is mathematically defined by analysing experimental cylinder-pressure dia grams. The model assumes that two modes of combustion, namely premixed and diffusion burning, co-exist in varying proportions throughout the burning dura tion as illustrated in figure 4.2. Clearly the point at which burning starts ie. the ignition point must be accurately predicted. In TRANSENG the Woschni and Anisits expression for ignition delay is used [39]:
S = aexpp(c6/r ) (4.1)
T and P are the mean temperature and pressure in the cylinder during ignition delay and a, b, and c are empirically determined coefficients. The mathematical expression for the premixed burning rate, mp, is:
rhp(r) = CPl.CP2.r(c,pi_1*(l - TCP1)(CP2- 1) (4.2) where r is the non-dimensional time: crank angle — crank angle at ignition t = ------;------;------total burning duration and CP 1 and C P 2 are shape factors.
The diffusion burning rate, m^, is described by a Wiebe function:
md(r) = C D l.C D 2.rl-aD2- 1) exp ( - C D 1 . t c d 2 ) (4.3)
The overall rate of fuel burning is then given by:
m(T-) = /?mp(r) + (1 - /?)md(r) (4.4) where /? is the ratio of the cumulative fuel burnt by premixed burning to the total amount of fuel injected.
At a given crank angle, therefore, four shape factors and /3 have to be known. These vary as a function of numerous parameters but may be determined at any test point for which a good quality cylinder-pressure trace is available as described
64 in section 5.1. The program includes the combustion correlation developed by Watson, Pilley and Marzouk [40] which enables combustion coefficients at one operating point to be related to those at another.
4.1.2 Heat Transfer
Heat transfer to the cylinder walls is calculated using the Woschni convective heat transfer correlation which considers both convection due to piston motion and that due to combustion [41]. Heat transfer from the manifolds is evaluated assuming convective pipe flow.
4.1.3 Gas Properties
The internal energy, the gas constant, and the ratio of specific heats for the fuel-air mixture in a control volume are determined from curve fits of these parameters with temperature, fuel-air equivalence ratio and pressure. For mixtures which are weaker than the stoichiometric mixture Krieger and Borman’s curve fits are used [42]. They are based on the Newall and Starkman data for equilibrium combustion products of a C n H 2n fuel [43]. For mixtures richer than the stoichiometric mixture Marzouk’s curve fits are used [44].
4.1.4 Friction
Frictional losses in the engine system are calculated using a simple relation devel oped by Chen and Flynn for turbocharged engines [45]. The loss is a function of the maximum cylinder pressure and the mean piston speed. The coefficients of these variables used in TRANSENG are identical with those given by Chen and Flynn for their ERl engine design.
65 4.1.5 Mass-Flow Rates
Flow direction is determined by the sign of the pressure gradient across the plane separating adjacent control volumes, or pipes and control volumes. When engine manifolds are modelled simply as thermodynamic control volumes and not gas- dynamic pipes, the mass-flow rate through a valve is computed using the equation describing one-dimensional compressible flow through an orifice. It is assumed that the static pressure at the throat is equal to the downstream stagnation pressure, and that the flow upstream of the valve throat is isentropic.
The calculation requires a value of instantaneous effective-flow area. Dynamic effective-flow area measurements are rarely made, and the accuracy of such mea surements is debatable. Static effective-flow areas for the valves can be determined by flow-testing the cylinder head. In the absence of experimental data effective areas can be calculated from valve and cam geometries, and an estimated coeffi cient of discharge, which is defined as the ratio of the effective-flow area to the geometric area normal to the flow. It is commonly assumed that the coefficient of discharge is constant with respect to valve lift and flow conditions, including flow direction, although it has been shown that it is not [46, 47, 48, 49]. The coefficient of discharge is discussed further in section 4.4.1.
When gas-dynamic pipes are selected to model the exhaust manifolds the gas ve locity and density at the pipe ends are calculated using the method of character istics, and the mass-flow rates are computed as a function of these variables and the effective area as described above.
66 4.1.6 Turbocharger
The program offers two options by which to model the turbocharger. The first is to simulate the compressor by an orifice, and the turbine by a nozzle with an area equal to the turbine equivalent area. This model calculates the mass and energy flow rates through the turbocharger as for flow through the valves. It is a simple model requiring a minimum amount of data and it poses no problem when used to simulate axial-flow turbines. For radial-inflow turbines, however, the flow characteristic is quite strongly speed dependent. Additionally, the pressure ratio at which choking occurs in a radial-inflow turbine is higher than for a simple nozzle, and at high turbocharger speeds a significant expansion ratio may yield considerably less flow than a nozzle, as illustrated in figure 4.3.
The second option is to store families of swallowing-capacity and efficiency curves for a range of turbocharger speeds for both the turbine and the compressor in large arrays. The instantaneous mass and energy transfer through each component are determined assuming quasi-steady flow. At each crank-angle step the required data are read from the steady-flow turbine and compressor maps knowing the pressure ratio, non-dimensional turbocharger speed and non-dimensional blade speed at that crank-angle position.
The latter approach is more comprehensive but relies on the quantity and quality of data provided. Manufacturers do not usually plot performance at pressure ratios below approximately 1.2. The predicted instantaneous pressure ratios may fall below this figure and the maps have to be extrapolated to cater for the lowest predicted pressure ratio. If the turbocharger manufacturer is unable to provide any turbine data at all, they may be predicted for axial-flow turbines using the Ainley-Mathieson technique [50]
There is insufficient information to quantify the error incurred by using steady- flow characteristics for a highly pulsating flow, and from using full-admission data to model multi-entry turbines, though some research has been conducted in these fields [51, 52, 53].
67 Twin-entry turbines axe modelled as two turbines in parallel, each of proportion ately lower flow capacity, operating at a common rotational speed. The efficiency of each turbine sector may be different from the other at any time, and is as for the single-entry turbine. The instantaneous torques developed by the compressor and turbine are calculated at each crank-angle step and the turbocharger speed is adjusted according to the difference between them.
4.2 Preliminary Program Development
4.2.1 Provision for Burning Fuels of Different Calorific Values
The original program was most frequently used to simulate the combustion of road-vehicle diesel fuel only which typically has a lower calorific value (LCV) of
43690 kJ/kg. Medium-speed engines sometimes burn road-vehicle fuel but they may also burn heavier fuels with calorific values as low as 39800 kJ/kg. The lower calorific value of the fuel was therefore made a data-input requirement of the program.
The LCV is used to calculate the absolute enthalpy of formation of the fuel entering the cylinder, this being one of the terms in the energy equation, see section 3.2. The interdependence of absolute enthalpy and LCV is examined in appendix B.
4.2.2 Un-Equal Phase Angle
The firing interval between successive cylinders of medium-speed engines is not necessarily equal, and it is therefore not sufficient to define the phase angle by firing order alone. The data-input requirement was changed accordingly from firing order to phase angle.
68 I
4.2.3 Increasing the Maximum Allowable Number of Cylinders
The largest number of cylinders known to be connected to a single turbocharger is ten. To facilitate the simulation of such an engine the maximum number of cylinders that can be modelled was increased from eight to ten.
4.2.4 Increasing the Number of Permissible Turbine Entries
Four-entry turbine-inlet casings are commonly fitted to turbochargers of medium- speed engines, and there may be as many as eight entries. The program was modified to allow for a maximum of ten entries ie. one per cylinder although it is understood that the need for modelling such a system is minimal.
The program initially catered for either a single-entry or a twin-entry turbine. The logical data-input statement used to identify the number of entries was replaced by a request for the number of turbine entries to be modelled.
Multiple-entry turbine sectors are modelled as a series of turbines in parallel run ning at a common speed. For a casing with n entries the mass-flow rate through "tit each sector for a given expansion ratio is (^) of that which would flow if there were a single entry instead. The program assumes that the efficiency of each sector is unaffected by the number of entries.
The structure of the program subroutines, and the statements in the main program by which these subroutines are called, were modified to accommodate the variable number of turbine entries. In essence, the Fortran IF-THEN-ELSE structure was replaced by the D O-loop structure whereby the instructions contained in the loop are executed for each turbine entry in turn until all turbine entries have been operated on.
69 4.3 Simulation of Exhaust Manifold Systems
The four types of exhaust manifold commonly fitted to medium-speed diesel en gines were discussed in section 1 .1 of the Introduction. It was explained that the large capacity of constant-pressure exhaust manifolds smoothes out pressure pul sations whereas pulse manifolds preserve the exhaust gas kinetic energy in long, narrow-bore pipes connecting the cylinders to the turbocharger turbine, and there fore give rise to pressure pulsations. It was also said that the simple pulse-converter and modular pulse-converter (MPC) systems are designed to combine the benefits of the pulse and constant-pressure systems.
The filling-and-emptying method which assumes that gas properties are constant throughout a manifold, or cylinder, has been used successfully for many years to predict the performance of engines fitted with constant-pressure exhaust manifolds, and other manifold types if the component pipes have small length-to-diameter ra tios. To assess optimum pipe lengths for a pulse manifold to ensure that reflected waves do not impair performance, a filling-and-emptying program is of little assis tance: but if a comparison is to be made between the overall performance of an engine fitted first with one manifold type, and then with another, the filling-and- emptying program may suffice.
To provide a facility to model gas-dynamic effects in exhaust systems and to assess the filling-and-emptying method when used to evaluate the overall performance of engines fitted with gas-dynamic exhaust systems a flexible exhaust model was developed. In this model any exhaust manifold that can be represented by gas- dynamic pipes and filling-and-emptying control volumes can be simulated subject to the conditions that
( 1 ) pipes may not be joined directly together but must be joined by small filling-and-emptying control volumes,
(2 ) all turbine nozzle sectors are immediately preceded by a control volume, and
70 (3) the total numbers of pipes and volumes used to simulate the engine system do not exceed 32 and 35 respectively.
The first two conditions effectively state that all pipes in an exhaust manifold axe bounded by filling-and-emptying control volumes, and this in itself lends consid erable advantage to the model. The ga s flow in the pipes is calculated using the homentropic method of characteristics for pipes of constant cross-sectional area. The entropy is thus everywhere the same within a pipe: no heat may be trans ferred from a pipe, and there may be no stagnation pressure loss in a pipe. The inclusion of a filling-and-emptying control volume between pipes partially redeems these restrictions. The surface area of the pipes across which heat is transferred and thus the heat transfer can be associated with the control volume, as can losses in stagnation pressure due to friction or the junction geometry. The entropy levels of different pipes connected by volumes need not be the same, and there is no difficulty in modelling pipes of different cross-sectional area joined by a control volume. A further advantage of the separation of pipes by control volumes is that, unlike conventional method of characteristics programs, one pipe may operate on a different time step to that of an adjoining pipe thus saving unnecessary computer execution time.
The filling-and-emptying program marches through the engine cycle in equal inter vals of crank angle (usually one-degree intervals). The method of characteristics subroutines were arranged for pipes with equally spaced mesh points but unequal time intervals. For most engine conditions and a crank-angle step of one degree the method of characteristics time steps are much smaller than the real-time equiva lent of one degree. The flows into and out of pipes must be known at the precise intervals defined by the crank-angle step and so the method of characteristics time step which takes the cumulative real-time to a value exceeding the crank-angle step is shortened to exactly fit the filling-and-emptying crank-angle step.
The values of gas velocity and density at the pipe ends are calculated at each method of characteristics time step and are time-averaged over the crank-angle
71 step such that the flow rates are representative of those occurring during the whole crank-angle step.
The flow charts of figures 4.4 and 4.5 illustrate the organisation of the program before and after the inclusion of the flexible exhaust manifold model. Clearly the exhaust manifold must be defined for the model: it is defined by
(1) the total number of gas-dynamic pipes in the exhaust system, (< 2 2 )
(2 ) the identification numbers for the upstream and downstream boundaries,
(3) the number of turbine entries,
(4) the identification numbers of the control volumes upstream and down stream of each pipe, respectively
(5) the identification numbers of the volumes directly preceding the turbine nozzles.
Figure 4.6 shows the exhaust system for a pulse-turbocharged three-cylinder engine and its definition for the exhaust-manifold model. There are two facets of the definition which need further explanation. Firstly, within the exhaust system the order in which the control volumes are numbered is arbitrary, subject to the conditions that the highest control volume number is assigned to one of the turbine- entry volumes, and the lowest number is one greater than the sum of the number of inlet manifolds and cylinders. For an n-cyUnder engine fitted with m inlet manifolds the control volumes representing the cylinders must be numbered 1 to n, and the inlet manifolds must be assigned numbers n + 1 to n + m.
Secondly, there are seven possible pipe boundary conditions:
(1) Pipe is open to atmosphere.
(2 ) Pipe is bounded by a volume: no pressure recovery at pipe end.
(3) Pipe end is closed.
72 (4) Pipe is bounded by a volume: variable pressure recovery at pipe end (used at pipe junctions and for pipes upstream of turbines).
(5) Valve boundary.
(6 ) Pipe bounded by a nozzle, downstream of which pressure is turbine back pressure (to simulate reflection from turbine nozzle).
(7) Pipe bounded by a nozzle, downstream of which pressure is variable, equal to that of downstream control volume (to simulate reflection from pulse- converter nozzle).
Boundary 1 is encountered on naturally-aspirated engines only. Boundary 2 is a special case of boundary 4 and boundary 3 is rare except as a subset of boundary 5 when the valve is shut. Boundary conditions 4 to 7 are most commonly required in exhaust manifolds of medium-speed engines, and are discussed in section 3.3. The application of boundary conditions 4 and 5 are illustrated in figure 4.6. The pressure-recovery factors at the upstream and downstream pipe ends, PF 1 and PF 2 respectively, are zero unless the boundary is 4 in which case a pressure-recovery factor between zero and unity is assigned. See section 5.2.4.
To simulate a reflection from the nozzle of a turbine, boundary 6 solves for flow through a partially open end for which the area ratio is that of the effective area of the turbine sector to the area of the pipe, variable name APNOZ 6 . Note that a volume is required between the pipe and the turbine to supply the turbine with the upstream gas conditions as illustrated in figure 4.7, which shows the definition of a MPC exhaust system for a four-cylinder engine. For the calculation of the reflected characteristic, the pressure downstream of the pipe-end nozzle is always the turbine back-pressure, and not the pressure in the volume. This rather cumbersome arrangement was used in the development of the program to see whether the simpler boundary, boundary 4, caused significant errors in the prediction of static pressure at the turbine. The nozzle boundary was not found to yield better predictions (see section 5.2.5) and the author does not recommend the use of boundary 6 .
73 Boundary 7 is as for boundary 6 except that the pressure in the junction volume downstream of the nozzle is variable and is equal to that of this junction volume,
V and the nozzle area ratio APNOZ7 is the ratio of the exit to inlet nozzle areas.
It has now been shown that any of the gas-dynamic exhaust manifold types can be modelled if they are first defined as a system of inter-connected pipes and small control volumes. The control volumes must be small so as not to damp out the pressure waves, but must not be too small or numerical instability may result.
4.4 Numerical Instability
The two main differences between medium-speed and high-speed engines which may cause numerical instability are (a) the large valve overlap periods, and (b) the low engine speeds. Engine performance predictions for a Paxman Valenta engine using a simple filling-and-emptying model of the exhaust manifold showed that as the time step was increased by maintaining a one degree crank-angle step and reducing the engine speed, keeping all other data the same, instability in mass-flow rates through the valves became more pronounced. This is shown in figure 4.8. The instability did not cause the program to crash and did not have a significant effect on the overall predicted performance but it was decided that a method of achieving a solution involving little additional computer cost should be sought. Several methods were tested including reducing the crank-angle step size, applying numerical flow-relaxation factors, reducing the convergence toler ance, and applying a variable coefficient of discharge. A detailed report on this investigation may be found in appendix C: it is summarised below.
The predictor-corrector numerical scheme employed in TRANSENG proceeds in three steps:
step 1 : the predictor formula is a coarse method of extrapolation and is
used to obtain a predicted value at the new time step, y pn + 1
step 2 : the predicted value is substituted into a differential equation to
calculate the derivative, f n+ i
74 step 3: the derivative is inserted into the corrector formula to yield a
corrected value, y c n + 1
If the difference between the predicted and corrected values exceeds a given tol erance, which is a percentage of the predicted value, steps 2 and 3 are repeated, using the corrected value computed in step 3 to evaluate the derivative in step 2, until either the convergence criterion is satisfied or the maximum number of three iterations have been performed.
The predictor formula used in TRANSENG is a first order Euler:
yPn+ 1 = y°n + h fn (4-5) where h is the step size. The corrector is known as the modified Euler. It uses first-order derivatives but is of second-order accuracy since the derivative at the previous step is also used:
y Cn+1 = y°n + °*5 X Hfn + fn+1) (4-6)
The predictor-corrector is applied to calculate the mass, temperature, and equiv alence ratio in each control volume. The method assumes that the derivative is constant over the step. If the ratio of the rate of change of a parameter to the pa rameter itself is large, this assumption can cause errors which manifest themselves as instabilities. This is most likely to occur if the volume is small or the real-time step is large, or both. For a simulation using filling-and-emptying control volumes only, the volume size is fixed by the geometry of the manifold, and the real-time step size can not be reduced for a particular engine speed without increasing the computational costs. Following an initial study of the effect of real-time step size alternative solutions were investigated, and the program was modified accordingly. Using the modified program the effects of mesh and volume size on numerical sta bility and on the accuracy of a method of characteristics simulation were studied.
75 4.4.1 Solutions to the Filling-and-Emptying Instability Problem
The instability illustrated in the lowest graph of figure 4.8 was eliminated by reducing the crank-angle step from 1 degree to -^ th of a degree but the computer execution time was increased by a factor of nine. The increase in cost prevented this solution from being adopted. The introduction of a variable crank-angle step proved to be complex and unsuccessful. The application of four tuned flow- relaxation factors to the valve flow rendered the instability negligible without distorting the mass-flow rate diagram and without increasing the computational cost. This solution was rejected, however, because there is no physical justification for applying relaxation factors and the four factors would need to be tuned for each engine and each operating condition simulated. Reducing the convergence tolerance from 1% to 0 .0 1 % greatly improved the stability outside the valve-overlap period: during valve-overlap the instability was reduced but was still unacceptably high. Combining the latter solution with the introduction of an instantaneous coefficient of discharge for the valves which varies with valve lift and pressure ratio and considers the effect of transient flow reduced the instability to an acceptable level. The program was modified to incorporate this combined solution. Figure 4.9 shows graphs of mass-flow rate through the valves of a single-cylinder Paxman
RP 2 0 0 engine running at 700 rp m before and after program development. Note that the results were generated using a boost pressure of 1.9 bar in the top graph and 1 .1 bar in the lower graph.
The size of the turbine nozzle used in the simulations conducted in the investigation was subsequently found to be only half of what it should have been: on correction of the data no instability was observed. Despite this, the investigation into numerical stability was considered to be a valuable piece of work and the incorrect data set was considered the worst case that might be simulated.
The modified version of the program was then used to model the exhaust manifold by a single pipe and a small controlvolume preceding the turbine nozzle, as shown in figure 4.10. The effects of volume and mesh size on stability and accuracy were
76 studied as detailed below. The volume and mesh size were non-dimensionalised in order to maintain a fully generalised solution.
4.4.2 Control Volume Size in the Gas-Dynamic Exhaust Manifold Model
The control volumes at junctions and preceding turbine entries need to be large enough to maintain a stable solution but small enough to transmit the wave form. In order to recommend a volume size for any engine system simulated the volume is described as a cylinder of diameter equal to that of the upstream pipe, and of length equal to a number of pipe diameters. In this way the volume size is defined simply by a number of pipe-diameters’ length, ie the length-to-diameter ratio. The system of figure 4.10 was simulated with volumes of 2, 1 and ^ a pipe- diameter’s length. Some numerical instability occurred when the volume was only ^ a pipe-diameter’s length. The traces for static pressure at the ends of the pipe are given in figure 4.11. Static pressure is less sensitive to numerical instability than mass-flow rate but it can be seen that the trace for the case of the volume of one pipe diameter’s length is stable and that there is no advantage in using a larger volume. Similar results were observed when the same tests were carried out for a junction volume. It is therefore recommended that a volume size of one pipe-diameter’s length is used.
Tests were also conducted to determine whether the sum of the volumes associ ated with the pipes and the volumes should equal the volume of the manifold, or whether, since gas-dynamic effects can only be modelled in the pipes, and the volume is there for convenience, the control volume should be considered to be a non-contributory volume, and the sum of the pipes alone should equal that of the manifold. Additionally, the question of whether the upstream or downstream pipe should be shortened to accommodate the small control volume was addressed. The differences between results of both sets of tests were too small to conclude that one set of data gave a more accurate prediction. For consistency, however the author recommends that the pipe length associated with the volume is subtracted from the upstream pipe or pipes. At a junction of three pipes, two of which are
77 nominally upstream of the junction volume, these two pipe lengths should be re duced by half a pipe diameter. It is recommended that the sum of the volumes of the control volumes and pipes in a gas-dynamic simulation is equal to that for a filling-and-emptying simulation of the same manifold.
4.4.3 Mesh Size for Gas-Dynamic Simulation of Exhaust Manifolds
Although many gas-dynamic simulations have been conducted for widely differ ing engine sizes and systems, the author was unable to find any documentation recommending a mesh size that could be applied to a gas-dynamic simulation in dependently of the engine or operating conditions. Wright [54] reports that ten meshes per pipe section gave an accurate solution but he does not give the di mensions of the pipe or a comparison of the predicted and experimental results. Benson [30, figure 6.18] indicates that pressures predicted with four and sixteen meshes are very similar but that one single mesh smoothes the diagram: again no pipe dimensions are given. In order to recommend a mesh size for use with the program developed in this project a series of simulations were performed for the engine of figure 4.10 keeping all data except the mesh size constant. The pipe diameter in this investigation was 0.0762 m and the length was 18 diameters ie 1.37 m. The mesh sizes tested were multiples of the pipe diameter so that the result could be applied to any engine simulated. Mesh sizes of one and two pipe diameters both gave rise to slight numerical instability at the turbine end of the pipe: mesh sizes of half a diameter and less gave stable solutions. There was no change in the predicted trace as the mesh size was reduced from half a pipe diameter to one third of a pipe diameter. This is illustrated in figure 4.12 which shows graphs of static pressure at the pipe ends calculated using different mesh sizes. It is recommended that a mesh size of half a diameter is used.
78 C H A P T E R 5
BASE-LINE PERFORM ANCE PREDICTION AND
SENSITIVITY OF PROGRAM TO INPUT DATA
5.0 Introduction
The accuracy of engine performance programs is heavily dependent on the quality of input data. A good prediction of maximum cylinder pressure requires both that accurate turbocharger data and valve flow coefficients yield the correct cylinder conditions when the inlet valve closes, and that the combustion model and as sociated data accurately represent the apparent heat release. Assessing various individual models within the TRANSENG program is therefore complicated by the sensitivity of the models to the input data, and by the interaction between models. In this project the gas-dynamic exhaust-manifold model developed by the author was assessed. To ensure that the cylinder release conditions were accurately predicted:
( 1) all predictions were conducted for eight cylinders of the Paxman 16RP200 medium-speed engine running at the six operating points for which experi mental data were taken, figure 2.6.
( 2) the compressor operating point was fixed for each test condition by setting the boost conditions equal to the experimental values which were constant throughout the engine cycle, and by holding them constant by entering val ues of inlet manifold volume and turbine inertia four orders of magnitude greater than their actual values. This contrivance did not otherwise affect the simulations.
( 3) the combustion coefficients were determined for each test point such that brake mean effective pressure and maximum cylinder pressure were accu rately predicted.
79 The work involved in (3) is described in detail in section 5.1. The performance of eight cylinders of the Paxman 16RP200 engine fitted with the pulse exhaust manifold of figure 2.2 was then simulated at the full-speed, full-load condition for which experimental data were recorded using the gas-dynamic exhaust model. The results were compared with experimental data, and in an effort to explain the discrepancies, the sensitivity of the program to various input data was tested, as discussed in section 5.2.
Employing the conclusions of this study, the engine performance was simulated at the other five test conditions for which experimental data were available, us ing both the gas-dynamic and the simple filling-and-emptying exhaust-manifold models, as described in chapter 6.
5.1 Combustion Coefficients and Combustion Correlation
Five combustion coefficients are required to describe the apparent heat release rate by a combination of premixed and diffusion burning as described in section 4.1.1. Four of these coefficients are shape parameters, CPI, CP2, CD1, and CD2, the former pair for premixed burning, and the latter pair for diffusion burning. The fifth parameter is /? , the proportion of fuel burned in the premixed mode. Coefficients for a particular operating point can be evaluated by performing the iterative process of running the TRANSENG program with an estimated set of coefficients, comparing the predicted and experimental cylinder-pressure diagrams and other combustion-related data, and re-estimating the coefficients. If cylinder pressure diagrams for a sufficiently large number of operating points are analysed it may be possible to compute a second set of coefficients for a combustion correlation which relates the combustion coefficients at one operating point to those at another for which experimental data are not available.
In chapter 2 it was observed that, contrary to expectation, the cylinder pressure fell below the exhaust manifold pressure, and initially thermal shock effects were thought to be responsible. Before performing the iterative process of calculating
80 the combustion coefficients the experimental cylinder-pressure traces were studied more closely.
The experimental cylinder-pressure diagrams, each of which is the average of 64 cycles, were processed by an Apparent Heat Release Rate (AHRR) program which gives the maximum cylinder pressure, its position with respect to TDC, the indicated-mean-effective pressure, the mechanical efficiency, the percentage of total fuel burned, and the instantaneous apparent fuel-burning rate. Each of these output data give information on the quality of the data. Consider the re sults for the raw data of test point 1. The maximum pressure was 62 b a r , which was within the range expected by the engine operators: it occurred one degree after TDC which was thought to be too early. By the second law of thermody namics the indicated-mean-effective pressure, imep, must exceed the brake-mean- effective pressure, bmep, yet in these results the imep was approximately half the experimentally-determined bmep. Additionally, the cumulative fuel burned was only 55% of the total fuel injected: for an engine of this type, where there is Significant scavenge flow, only a very small amount of fuel will pass into the ex haust unburned and this figure is expected to be close to 100%. A further point of interest was that the experimental cylinder-pressure trace lagged the predicted trace.
For all six test points similar observations were made which led to a study in which the experimental pressure traces were advanced by an amount sufficient that all fuel was burned and a sensible imep and hence mechanical efficiency were achieved. It was concluded that the cylinder pressure data could be salvaged if they were advanced by 8 d e g C A. The resulting imeps, mechanical efficiencies, and percentages of fuel burned are listed in table 5.1. The 8 d e g C A lag was thought to have been erroneously entered into the microsynch, one of the pieces of equipment in the data-acquisition system (see sections 2.4 and 2.11).
The crank-angle of static injection, 09t,in3- was also derived from the shifted data:
) (5-l)
81 The ignition point, 6ign, was determined by finding the point at which the experi mental curves for cylinder pressure departed from the predicted pressure diagrams for a motored engine during the compression stroke. The ignition delay, 8ign, was determined using equation 4.1 and coefficients determined experimentally by
Wolfer [55]. The crank-angle of dynamic injection, 9dyn.in j? was evaluated from the needle-lift diagrams, and the injection delay, Knowing the static injection timing, the computation of the combustion coeffi cients could proceed. The fuel-burning rate curves derived from the experimental cylinder pressure traces were used to obtain a first estimate of (3 at each test point. The curves for test points 1, 4 and 6 shown in figure 5.1 illustrate that at high load and speed, test point 6, a very small proportion of the burning is premixed burning, but that at low speed and load , test point 1, this proportion is high. Watson et al [40] showed that the value of the shape factor CP2 could be fixed at 5000 without impairing the representation of the first peak of the fuel-burning rate curve (refer to figure 4.2). The timing of the first peak in the apparent heat release profile is sensitive to the value of CPI, while the timing and magnitude of the second is dependent on both CDl and CD2. Values of CPI, CD1, and CD2 were estimated, TRANSENG was executed and the predicted cylinder pressure was compared with the experimental trace. Using the results of the parametric study of Watson et al [40], the values of the coefficients were modified and the process was repeated until the maximum pressure, its position, and the bmep were within ± 2% of the experimental values. The final combustion coefficients are given in table 5.2 together with the relevant experimental results. The predicted and experimental cylinder pressure traces for test points 1, 4, and 6 are given in figure 5.2. To see whether the combustion coefficients could be correlated by the Watson et al correlation [40], each coefficient was plotted against the relevant correlation parameter for all test points as shown in figures 5.3 and 5.4: the Watson et al correlation curves are superimposed. There is a correlation for /? as a function 82 of the trapped equivalence ratio, Ftr, and the ignition delay, 6ign. The curve is steeper than for the case of the higher speed engines tested by Watson et al. For the other combustion coefficients, CPI, CD1, and CD2, the scatter of points is too great to draw a conclusive correlation but nevertheless it can be seen that the points are clustered over a small range around the Watson et al correlation. It was decided to input the values of the combustion coefficients at each test point, by-passing the combustion correlation model in TRANSENG. Equipped with combustion data, and keeping the inlet manifold conditions con stant, and equal to the values measured at each test point, the performance of the exhaust manifold model was investigated. 5.2 Initial Prediction using Gas-Dynamic Model at Test Point 6 The eight cylinders at the drive end of the Paxman 16RP200 engine were simulated using the combination of gas-dynamic pipes and thermodynamic control volumes of figure 5.5. Figure 2.2 shows the actual geometry of the pulse exhaust manifold fitted to the engine. Initially the program was executed to simulate the engine running at full speed and full load, ie. test point 6. The results for this operating point were compared with experimental data and discrepancies were investigated before the engine per formance at the other five test points was simulated. The data input for the initial prediction, hereinafter referred to as the base-line data, are discussed in the section below prior to the presentation of the results. 83 5.2.1 Input Data, for the Base-Line Prediction at Test Point 6 The complete base-line data for test point 6 are given in figure 5.6. A list of program variable names is given on pages 12 to 18. Most of the data are self- explanatory. However those of most relevance to this project will be discussed below in the order in which they occur in figure 5.6. (1) Inlet manifold volume, VIM, was set to 100 m 3 to ensure constant inlet manifold conditions equal to those set in the section on operating conditions. (2) The volume of all exhaust control volumes, VEM, were equivalent to one pipe diameter’s length. (3) Data for calculation of instantaneous coefficients of discharge are described in appendix C. (4) The surface area of each exhaust control volume, AREAEM, includes the area of the upstream pipes bounding the volume. (5) Combustion coefficients are as described in section 5.1 (6) Ignition delay coefficients are those of Wolfer [55] (7) Compressor map data were supplied by Napier Turbochargers Ltd and were extrapolated for low pressure ratios and speed parameters, N / y / T (8) Charge cooler pressure loss coefficients and effectiveness constants were de rived for each test point from the experimental data. (9) The number of mesh points for a pipe, MESH, was such that the mesh size was as close to half a pipe diameter as possible. (10) Pipe reference pressure, PREF, and temperature, TREF, were set approxi mately equal to the time-averaged values in the exhaust control volumes. In all but the first cycle TREF is reset equal to the time-averaged temperature in the control volume upstream of the pipe for the previous cycle. The refer ence equivalence ratio, FREF, should reflect the average equivalence ratio in the pipe. The value of 0.206 was erroneous. A back-to-back run with FREF 84 corrected to 0.5 showed, however, that it had a negligible effect. The variable PPIPE is used only once to calculate the initial values of characteristics in the pipes at the first crank-angle step of the simulation. PPIPE is assigned any value within the range of pressures occurring in the exhaust manifolds. (11) The four-entry turbine-inlet casing was modelled as four parallel-sided pipes of diameter equal to that at each entry and length equal to the centre-line length from the casing entry flange to the exit flange less one pipe diameter for the control volume preceding the turbine. (12) For cylinders whose exhaust valves form the boundary between a control volume and pipe, the identification number of the volume downstream of the cylinder, NEXCV, is zero. (13) For pipes whose upstream volume is a cylinder, the upstream boundary identification number, IBl, is 5, and there is no pressure recovery at this boundary ie. P F l= 0.0. For all boundaries with small control volumes and volumes preceding turbines the boundary identification number was 4, and the pressure-recovery factors were initially set to 0.5 and 0.0 respectively. (14) the turbine characteristics are shown in figure 5.7 and 5.8. They were gen erated in the following way: (i) for pressure ratios greater than 1.2, and turbocharger speed pa rameter, N / y / T , between 280 and 840 r p m / y / K data generated by the Ainley-Mathieson technique [50] were supplied by Napier Tur bochargers Ltd. (ii) at a pressure ratio of 1.2 the mass-flow characteristics for different N / y / T tend to converge, and below this the curve was extrapolated assuming compressible flow through a nozzle whose area is the equiv alent area of the turbine nozzle and rotor: x A r o t A e q — (5.2) s/A2 i A2 n o z ' r o t 85 (iii) turbine efficiency data were linearly extrapolated at high and low non-dimensional blade speed, TJ/C, such that for values of Z7/C of 0.0 and approximately 1.3 the turbine efficiency was zero. The peak turbine efficiency predicted using the Ainley-Mathieson program was 78%. Napier engineers advised that when fitted to an engine the maximum efficiency was more likely to be 74% and the data were scaled accordingly using the scale factor, TSFE. (iv) A swallowing capacity curve for N / y / T of 980 r p m / y / K was extrap olated. The variation of efficiency with N / y / T could not be clearly defined in the regions of highest efficiency and the curve for N / y/T of 840 r p m / y / K was taken to be the limiting curve. 5.2.2 Results of Base-Line Simulation for Test Point 6 The overall predicted performance parameters are given in figure 5.9. Several observations may be made regarding these data: (1) The volumetric efficiency of one cylinder in each pair connected to a common manifold is significantly higher than that of the other, the lower efficiency being associated with the cylinder that fires 300 d e g C A later relative to the other cylinder of the pair. The volumetric efficiency is defined by the ratio of the total mass of air passing into a cylinder in one cycle to the mass of air at inlet manifold conditions which would fill the swept volume of the cylinder. Peak volumetric efficiencies in excess of 100% are due to the large amount of scavenge flow. (2) The scavenge efficiency is defined as the ratio of the total mass of air induced into the cylinder to the trapped mass in compression. The scavenge efficiency in each cylinder is greater than the volumetric efficiency: the trapped mass in compression is therefore less than the mass of air at inlet manifold conditions that would fill the cylinder, indicating that some reverse flow occurs. This is supported by diagrams of mass-flow rate through the valves, as shown in 86 figure 5.10. The variation in scavenge efficiency between cylinders is domi nated by the different amounts of air induced into each cylinder: the trapped mass in compression varies little between cylinders. (3) There is little cylinder-to-cylinder variation in ignition data, maximum cylin der pressure and temperature, or their locations within the cycle. (4) The time-averaged turbine expansion ratios are different across each sector. The minimum, that across turbine-entry 1, which is fed by cylinders 1 and 2 (A8 and B8), is 2.402 which is 1.5% lower than the maximum which occurs across turbine-entry 2, fed by cylinders 3 and 4 (A7 and B7). The variation in mass-flow rates, efficiencies and powers of the different sectors is as for that of the expansion ratio. (5) The sum of the turbine mass-flow rates is 2.017 k g / s which is 9% less than the compressor mass-flow rate, and the total mass-averaged turbine power generated is 13% less than the power absorbed by the compressor. These dis crepancies arise from the use of a huge inlet manifold volume which effectively prevents feedback from the turbine altering the inlet manifold conditions. Air mass-flow rate could not be accurately measured since the orifice plates could not be calibrated. Assuming a coefficient of discharge of 0.73, however, (see section 2.9), the experimental air mass-flow rate for eight cylinders at test point 6 was 1.97 k g /s , which is 10% less than the predicted compressor air mass-flow rate. (6) The compressor operating point lies within the compressor map boundaries throughout the cycle but the turbine sector operating points lie within the map boundaries for less than 8% of the cycle. The latter result is due largely to the fact that the highest N / y / T for the efficiency map was 840 r p m / y / K and this value of N / y / T was exceeded for more than 85% of the cycle. If the assumption that at higher values of N / y / T the efficiency is little different to that at 840 r p m / y / K is valid, this result is of little importance. The N / y / T exceeds 980 r p m / y / K for 33% of the cycle: conceivably both efficiency and the mass-flow characteristics should have been extrapolated for even higher 87 speed parameters but the author has no evidence to suggest that this would be more accurate. (7) The charge-cooler data compare well with the experimental values as would be expected since the relevant input data were derived from the experimental data for each test point. (8) Looking at the cycle-averaged integration parameters, the differences be tween cylinders for values of in-flow and out-flow, cylinder work, and imep are supported by the differences in volumetric efficiency (see (1) above). The difference between time-averaged and mass-averaged pressures and temper atures, (P.TA and P.MA, and T.TA and T.MA), in the exhaust volumes are indicative of a highly pulsating flow. The total heat transfer from the exhaust volumes is comparable with that from the cylinders. (9) The bmep of 17.43 bar and brake power of 1.146 MW compare well with the experimental values of 17.44 bar and 1.146 MW respectively. Predicted air-flow measurements can not strictly be compared with the experimental values of table 2.2 since the latter were calculated assuming a coefficient of discharge since the orifice plates were not calibrated. (10) The number of iterations, 1064, shows that for more than half the crank- angle steps only one iteration was required to achieve convergence. The program took 185 C P U s e c o n d s on the Cyber 855 mainframe to execute five steady-state cycles for eight cylinders of the Paxman 16RP200 engine using the method of characteristics to model the exhaust manifold. The predicted instantaneous static pressures at mesh points most nearly coincident with the transducer locations near cylinders A8 and B8 and the corresponding turbine entry are shown in figure 5.11 together with experimental values. The predicted traces at the three locations within a manifold (see figure 2.8) were almost identical to the corresponding traces of the other manifolds taking into account the relative cylinder phase angles as illustrated by the comparison of figures 2.11, 2.12, and 2.13 with figure 2.10. For this reason only the traces for 88 the manifold serving cylinders A8 and B8 are presented unless otherwise specified. On inspection of figure 5.11 the following points may be observed: (11) The pressure profiles near cylinders A8 and B8 are similar but not identical: the secondary pulse, ie. the pulse from cylinder B8 arriving at the transducer near A8 or vice versa, is steeper than the primary in each case since the wave has travelled further from its source cylinder. The trace just upstream of the turbine is steeper still and is more strongly pulsating. (12) The overall shape of the predicted trace compares favourably with the ex perimental trace. (13) The predicted pressure rises after EVO approximately 30 d e g C A earlier than the experimentally measured pressure. (14) The three “steps” occurring in the experimental trace after EVO for cylinder B8, which indicate gas-dynamic reflections, are not predicted. (15) The peak pressures are under-predicted. (16) When the pressure falls after each pulse, at crank angles of approximately 300 and -130 d e g C A, the predicted pressure does so too rapidly and it falls too far. (17) At the turbine end, the peak pressures are not well predicted. In connection with observation (13) above, Bulaty and Neissner [56] produced a similar result although they did not quantify the lag between predicted and ex perimental results. To obtain a more accurate prediction they allowed for the elasticity of the exhaust-valve control system by delaying and steepening the ini tial rate of opening of the exhaust valve. Following their example the author modified the exhaust-valve lift profile as indicated in figure 5.12 for test points 6, 5, and 4: at the remaining test points the valve opened 6 d e g C A earlier. The resulting predicted pressure for locations B8 and T8 given in figure 5.13 show a marked improvement: the gas-dynamic reflections immediately following EVO are 89 evident and the positions of reflections during the remainder of the cycle are bet ter predicted. Despite this improvement points (15), (16), and (17) noted above still apply: at the turbine end where there is a peak in the experimental data at 190 d e g C A, there is a trough in the predicted data. There were no significant changes in overall predicted performance parameters. The exhaust-valve elasticity was accommodated as described above in all further tests. Before further investigating the discrepancies between the predicted and experi mental exhaust-manifold pressure traces questions were asked concerning the qual ity of the latter. There may have been a transducer offset, or an offset may have been erroneously entered into the AVL data-acquisition system. Conceivably the answer to these questions is affirmative but: (i) the calibration curves of all piezo-resistive transducers before and after the three-day test period were identical, and showed good linearity. (ii) the pressure traces measured in the manifold serving cylinders A8 and B8 were recorded on each of the three test days and all displayed the same phenomena. (iii) at test point 6 the experimental pressure in the region 0 to 130 d e g C A is still falling: at low speed and load conditions it levels out to a value marginally above atmospheric pressure. This indicates that at test point 6 the pressure does not fall to the turbine back-pressure, but that at low load and speed it does. In the light of the above it was thought that the error lies in the predicted re sults, the quality of which are heavily dependent on the input data. Much of the input data can be easily accessed through the engine manufacturer, but some are not, and are not easy to determine accurately, such as the heat transfer data for the cylinders and manifolds, instantaneous flow coefficients for the valves, tur bocharger characteristics over the entire operating range, and combustion data. There is an element of uncertainty associated with all these data but, as will be seen, the overall performance parameters axe not very sensitive to them, with the 90 exception of combustion data. The pressure traces, however were found to be sensitive to changes in some of the data. 5.2.3 Sensitivity of Program to Heat Transfer in Exhaust Volumes To see how sensitive the predicted results are to heat transfer in the exhaust control volumes the program was executed to simulate engine performance at test point 6 firstly with heat transfer in the exhaust manifolds and secondly without. In the first case a heat transfer coefficient of 0.363 k W / m 2K and cooling-water temper ature of 355 K supplied by Paxman Diesels Ltd were input, and in the second the heat-transfer coefficient was set to zero. The heat transfer related output are given in the top portion of table 5.3: the lower part gives some of the predicted overall performance parameters. The most noticeable difference is in the time-averaged temperatures in the exhaust volumes. This result is supported by the differences in the predicted pressure traces. Figure 5.14 shows the exhaust pressure traces predicted with and without heat transfer together with the experimental data: the pressure traces for the case of no heat transfer are higher than for the case of some heat transfer throughout the cycle at all locations at which measurements were taken in the manifold. The higher pressure supports the greater isentropic enthalpy available at the turbine for the case of no heat transfer. The compar ison of both sets of predicted pressure traces with experimental data yielded no conclusion as to which prediction data-set was more accurate. At the onset of the scavenge period the higher exhaust pressure near the valves predicted by the simulation with no heat transfer would cause less scavenge flow as indicated by the 3% lower volumetric efficiency. The time-averaged predicted temperatures in the exhaust manifold junction volume closest to cylinders A7 and B7 were 727 and864 K for the cases of heat transfer and no heat transfer respectively. Since turbine bladelife is reduced by temperatures in excess of 853 FT, it was expected h dexperimentally • i determined exhaust-valve temperature would support tht x-.oriiionwith heat transfer. Contrary to this expectation the experimentalv ■ ensuredapproximately 290 m m downstream of exhaust 91 valves A 7 and B7 were 806 and 816 K respectively (see table 2.3). Temperatures were not measured in the manifold serving cylinders A8 and B8. There is no doubt that there is heat transfer in the exhaust manifolds, the question of how much remains unanswered, and in view of the above, subsequent predictions were performed with the heat transfer data quoted by the engine manufacturer, as used in the simulation described here with heat transfer. 5.2.4 Pressure Recovery Factors Two methods for evaluating the pressure recovery factors at junctions and in the volumes preceding the turbine were considered. The simplest is to assume in compressible flow through a sudden expansion in which case the pressure recovery factor is: F ree „ = ^ (5.3) ■A-ex The second method is to assume compressible flow and isentropic diffusion through a cone-like duct. By repeated iteration the static pressure at the upstream bound ary can be evaluated, and the pressure recovery factor can then be calculated according to: Frecov = p ^ p - M ) At a junction the change in area is more nearly a sudden expansion. For the exhaust manifold modelled where all pipes within the exhaust system had the same cross-sectional area, the area ratio is 2:1 and the pressure recovery factor, according to equation 5.3, is 0.5. The turbine-entry casing bears greater resemblance to a diffuser than a sudden expansion, and its recovery factor was evaluated using the second method, to be 0.83. This is summarised in figure 5.15. To test the program sensitivity to pressure recovery factor it was executed for the following cases: 92 Case Pressure Recovery Factor Junction Volume Preceding Turbine 1 0.0 0.0 2 0.5 0.83 3 1.0 1.0 The pressure traces nearest the cylinders were more sensitive to the changes in pressure recovery than those at the turbine end of the manifold. The pressure traces nearest cylinder B8 are presented in figure 5.16 for each case together with the experimental traces. The amount of pressure recovered does influence the pressure traces and, as might be expected, the influence is greatest during the rapid pressure rises shortly after EVO, where the “step” profiles are different in each case. Note that with 100% recovery the third step in pressure following EVO of cylinder B8 is absent. There is little difference between cases 1 and 2 when their results are compared with the experimental trace. The factors of case 2 were used in the final predictions for all test conditions since pressure recoveries of zero could not be justified. 93 5.2.5 Nozzle Boundary Condition In section 5.2.2 it was noted (observation 17) that at the turbine end of the exhaust manifold, at the point where the peak pressure is achieved in the experimental data there is a trough in the predicted data (see figure 5.11). For this prediction the boundary condition at the turbine-end of the pipe was for a pipe to a volume (IB2=4) and there was zero pressure recovery. It was thought that if this bound ary was simulated instead by a nozzle, (IB2=6), with an area ratio equal to the pipe area to the turbine equivalent area, the correct pressure-wave reflection could be predicted. The result is shown in figure 5.17 with the base-line and experi mental pressure traces for comparison. The nozzle boundary did not translate the predicted trough occurring at the location of peak experimental pressure into a peak but it did increase the amplitude of the peaks either side of the trough which, to some extent, gives a better prediction of the pressure pulse. The nozzle boundary affects the whole pressure trace but not conclusively for the better: its use was not adopted. It is thought that the correct calculation of the reflection at the turbine end would invert the above-mentioned trough in the predicted pressure. The author expressed doubts concerning the limitations of this boundary condition in section 4.3 and recommends that the effects of a full turbine boundary analysis should be investigated in future research. 5.2.6 Turbine M ap The sensitivity of engine performance prediction programs to turbine data has been recognised by several researchers. To improve predictions Chan [24] and Nichols [57] “tuned” the turbine data. Unfortunately they do not discuss the na ture of their modifications and do not illustrate the improvement achieved. Their final predictions do, however, illustrate an under-prediction of the minimum ex haust pressure. In this section the author discusses the effects of modifications to turbine data that could be responsible for the under-prediction of peak and min imum pressures in the exhaust manifold, observations 15 and 16 of section 5.2.2. The turbine data were generated assuming steady flow through a single-entry tur bine for pressure ratios in excess of 1.2, and for speed parameter, N / y / T between 280 and 840 r p m / y / K . The mass-flow curves were extrapolated for pressure ra tios as low as unity and for a maximum N / y / T of 980 r p m / y / K . The turbine modelled has four entries and the exhaust pressure traces indicate that the flow in each sector is highly pulsating. The question of how turbine characteristics are affected by partial admission and pulsating flow was addressed after some simpler investigations were undertaken. 5.2.6.1 Reducing the Swallowing Capacity If the turbine presented a greater restriction to flow it would be expected that the peak pressure in the exhaust manifold would be higher, the mass-flow rate would be lower, and the expansion ratio would fall less rapidly after the dominant pulse had passed. For 30% of the cycle the predicted speed parameter was in excess of the maximum of 980 r p m / y / K . If the trend that the swallowing capacity falls with increasing N / y / T continues at higher N / y / T the swallowing capacity would indeed be less but only over the 30% of the cycle in which the N / y / T of 980 r p m / y / K is exceeded. This would be expected to raise the peak pressure but would not solve the problem of the predicted pressure being too low when the exhaust valve opens. Alternatively it is possible that an accumulation of combustion products on the turbine blades has actually reduced the flow area. To model the latter case the total 95 total flow area was reduced to 90% and then 80% of its base-line value using the turbine mass-flow scaling factor, TSFM. The maximum and minimum pressures predicted at the turbine end of the manifold serving cylinders A8 and B8 did marginally improve as flow capacity was reduced from 100% to 80% but the entire trace was modified as shown in figure 5.18. It is debatable whether the results predicted using the modified map compare more favourably with the experimental ones. Such large reductions in swallowing capacity could not be justified and this solution was not pursued. 5.2.6.2 Limiting the Minimum Turbine Efficiency The extrapolation of turbine efficiency to zero at high and low non-dimensional blade speeds was also considered to be a possible source of error. Napier advised that the turbine efficiency was unlikely to fall below 50%, and the turbine efficiency curves were modified such that where the base-line curves fell below 50% the efficiency was maintained at a constant 50%. This modification made a negligible difference to the predicted traces which is perhaps not surprising since the turbine operating point is in these regions for a small proportion of the cycle. 5.2.6.3 Turbine Back-Pressure The turbine back-pressure measurements were erroneous and were therefore not used (see section 2.9). The minimum pressure measured in the exhaust manifold was approximately 1.2 bar at test point 6. The program was executed with the back-pressure raised from ambient pressure to 1.2 bar. The result was that over the lowest pressure region the trace was slightly improved but the peak pressure was still far short of the experimental value. The exhaust ducting downstream of the turbine was thought not to contain a restriction sufficient to cause a pressure drop of 0.2 bar. In the absence of experimental justification for raising the back-pressure it was returned to ambient pressure. 96 5.2.6A Partial-Admission and Unsteady-Flow Effects Several researchers have observed that if one sector of a twin-entry turbine is blanked off the mass-flow rate through the turbine exceeds half the full-admission value for the same expansion ratio, and that the peak turbine efficiency is reduced [51, 52, 53]. The former observation is due to the increase in the ratio of rotor flow area available to stator flow area available. The drop in efficiency is due to the combination of windage losses and end-of-sector losses in addition to secondary losses. The windage loss is the energy required to drive the turbine wheel past a sector through which there is zero mass flow. As the name implies the end-of- sector loss occurs at the junction of adjacent sectors where the flows join creating a disordered flow field. The windage loss usually dominates the end-of-sector loss, but since the latter increases with the number of turbine entries and the former decreases as full admission is approached, they may be of equal importance in certain applications. Craig et al performed experimental tests on a Napier twin-entry, axial-flow tur bocharger turbine [52]. They found that when one entry was blanked off the loss in peak efficiency was 11% at an expansion ratio of 1.25:1,decreasing to 6% at an expansion ratio of 3.5:1, and that the peak occurred at a lower U/C. They also observed that the mass flow per sector increased by 10% over the range of pressure ratios 1.25:1 to 2.25:1 for 50% admission. Dibelius [51] described the effects of partial admission on efficiency and flow rate mathematically and supported this work with experimental tests. His work was conducted on a Brown Boveri VTR500 axial-flow turbocharger turbine fitted with single-entry, twin-entry and four-entry casings and partial admission was simulated by blanking off one or more sectors. His results are reproduced in figure 5.19. While they are in agreement with those of Craig et al [52], Dibelius does not specify the pressure ratio for which the results are given. Note that when two sectors of the four-entry turbine are blanked off, ie 2/4 admission, the results are not equal to those for the case of 50% admission through a twin-entry turbine: they lie between the results for 1/2 and 1/4 admission. The reasons for the lower 97 efficiency and increased mass-flow rate in the case of 2/4 admission compared with 1/2 admission lie in the greater end-of-sector losses and the fact that the flow is more evenly distributed respectively. The results described above are for steady flow. Craig et al [52] extended their investigation to unsteady flow. They concluded that mass-flow rates and turbine efficiencies were over-estimated for both full and partial admission when quasi steady flow data were applied to pulsating flows: the extent of the error being a function of (1) pulse frequency (2) pulse pressure ratio (3) pulse shape and rate of change of pressure (4) turbine speed Daneshyar et al [58] compared full-admission axial-flow turbine characteristics under steady and pulsating flow. They found that the error incurred by applying the quasi-steady assumption to mass-flow rate and turbine efficiency was greater than that evaluated by Craig et al [52]. Dale and Watson also investigated turbine performance under unsteady-flow conditions, but for a radial-flow turbine [53]. They concluded that for the particular turbine they tested the maximum flow and efficiency were greater than their corresponding steady-state values but that when integrated over the cycle the use of steady-state data would cause only slight errors. From the above it can be seen that the evaluation of the instantaneous operat ing point for a multi-entry turbine fitted to a pulse exhaust system is complex and that there is still much research to be undertaken before a steady-flow, full- admission turbine map can be translated into an unsteady-flow partial-admission map applicable over the entire range. The predicted instantaneous turbine-sector mass-flow rates and expansion ratios for the four-entry turbine fitted to the Paxmanl6RP200 engine running at the 98 full-load, full-speed condition, test point 6, are shown in figures 5.20 and 5.21 re spectively. The extent of partial admission momentarily approaches 3/4 as flow through each sector in turn falls close to zero in the first part of the cycle. In the latter part the flow pattern is more nearly that of full admission. Arguably a combination of a full admission and a 3/4 admission unsteady-flow turbine char acteristic would yield a more accurate prediction of the turbine flow. The 3/4 admission data could, in the first instance, be assumed to lie between Dibelius’ 2/4 and 1/1 admission data (see figure 5.19). The expected result is that the turbine mass-flow would increase by a small amount, and the exhaust pressure trace would be slightly lower in the region where it is under-predicted using full- admission data causing further departure from the experimental results (see figure 5.11). In the absence of suitable data and justification for doing so none of the partial- admission or unsteady-flow results described above were applied. It was concluded, however, that the steady-flow, full-admission turbine data used in the base-line prediction are likely to be , in part, responsible for the under-predicted extremes of pressure in the exhaust manifold. 5.2.6.5 Revised Turbine Characteristics None of the investigations above improved the base-line predictions of the instanta neous exhaust static pressure. The quality of the base-line turbine characteristics was questioned. The limiting N / y / T of 840 r p m / y / K of the efficiency map, figure 5.8, was exceeded for 86% of the cycle. The turbine power generated was 11% less than that absorbed by the compressor: the huge inlet manifold volume and turbine inertia fixed the compressor operating point to give the experimental in let manifold conditions and prevented turbine and compressor interaction. The mass-flow rate through the turbine did not equal that through the compressor. The size of the inlet manifold was such that it accumulated mass without causing a noticeable change in gas properties. A possible source of error was that the turbine was presenting the system with too great a restriction to flow. 99 On discussion of these points with Napier Turbochargers Ltd., they revised the turbine characteristics, basing the new data on results of recent experimental tests. The new data are shown in figures 5.22 and 5.23, and comparable base line characteristics in figures 5.7 and 5.8. The revised swallowing-capacity data are little different to the base-line data but there is a marked difference between the revised and base-line efficiency curves. The revised efficiencies are lower, the peaks occur at lower blade-speed ratios, U/C, and the curves span a smaller range of U/C. The lower efficiencies are due to a combination of assuming a lower aerodynamic efficiency which was based on ex perimental tests and allowing for the increase in mechanical losses as turbocharger speed is reduced. The new turbine data caused a negligible change in predicted overall engine perfor mance and instantaneous exhaust pressures. The lower turbine efficiencies caused a 5% deterioration in the turbine-compressor power mis-match, but there was lit tle change in the corresponding mass-flow imbalance due to the similarity of the flow characteristics. Note that if the turbine inertia and inlet manifold volume were assigned their actual values, the lower turbine power generated using the new data would result in a lower boost pressure and inferior engine performance. The revised data were not adopted. 100 5.2.7 Valve Effective-Flow Areas In figure 5.13 the predicted pressure for the case where exhaust-valve system elas ticity was accounted for is compared with the experimental data. If more mass were allowed to flow through the system one might expect the predicted pressure trace to shift upwards. Conceivably the valves offer too great a restriction to flow. Indeed, on inspection of the instantaneous coefficient of discharge, the time- averaged values for the inlet and exhaust valves were approximately 0.48 and 0.88 respectively. The validity of the variable coefficient of discharge model developed by the author (see section 4.5 of appendix C), and the associated programming were questioned, and it is recommended that the model is investigated in the future. A constant coefficient of discharge of 0.8 was employed for both valves during forward and reverse flow. The result was to raise the mass-flow rate through the system by 5% . This in turn raised the bmep and the mass-averaged pressures in the volumes preceding the turbine nozzle all by 2% . The pressure traces predicted with variable and constant coefficients of discharge at locations near cylinders A8 and B8, and turbine entry T8 are compared with experimental data in figure 5.24. The differences between the sets of predicted pressures are greatest at the turbine-end of the manifold: where the experimental peak pressure is achieved after cylinder B8 exhausts, the pressure trace predicted using a constant coefficient of discharge also peaks, and the peak is of the same shape as the experimental peak, unlike the trace predicted using a variable coefficient of discharge where there is a trough at this point. The predicted pressure traces and the turbine and compressor mass-flow match are predicted more accurately using the constant coefficient of discharge and it was employed in all tests discussed hereafter. 101 5.2.8 Corrected Inlet Manifold Volume and Rotor Inertia In the results discussed hitherto the inlet manifold volume and the rotor inertia were set to 100 m 3 and 100 k g .m 2 respectively to ensure that the boost conditions and turbocharger speed remained constant at the experimentally determined val ues. With pressure recovery factors of 0.5 and 0.83 in the junction volumes and turbine-entry volumes respectively, the program was executed using the actual volume for the inlet manifold, 0.0525 m3, and the correct rotor inertia, 0.086 k g .m 2 . The results were poor: the boost pressure and turbocharger speed were both under-predicted by 11%, and the knock-on effects caused reduced mass-flow rates, and lower bmep, in addition to lower pressures in the exhaust. 5.2.9 Summary of Tests on Sensitivity to Input Data With the exception of the changes in inlet manifold volume and rotor inertia, none of the changes in input data discussed above significantly affected the overall pre dicted engine performance. The single modification which most altered the exhaust pressure trace was the allowance for the exhaust valve elasticity. The amount of heat transferred from the manifolds and the extent of pressure recovery also made noticeable differences to the pressure traces. The turbine map modifications tested made little difference. An unsteady-flow turbine map for 3/4 admission was not available: the effects could therefore not be quantitatively assessed. The variable Cd model was found to be erroneous and the substitution of a constant Cd of 0.8 for inlet and exhaust valves for both forward and reverse flow markedly improved the predictions. The final predicted pressure traces in the exhaust manifold for cylinders A8 and B8 are shown in figure 5.25. In figure 5.26 the experimental traces have been shifted vertically such that the predicted and experimental mini mum pressures are equal. There is now a good comparison between predicted and experimental results. The n nic:- :as been unable to justify the shift, and hypothesises that the depar ture 7/ ' - h edicted instantaneous exhaust static pressures from the experimental ones :•••; rily due to: 102 (1) the uncertainty associated with both turbine and compressor maps at low pressure ratios, (2) the use of steady-flow full-admission turbine data for a four-entry turbine fitted to a pulse exhaust, (3) the use of an open-end boundary to a small volume preceding the turbine instead of a full turbine boundary condition, (4) the homentropic assumption, ie that the entropy everywhere within a pipe throughout an engine cycle is equal. 103 C H A P T E R 6 ASSESSM ENT OF EXHAUST-MANIFOLD MODEL 6.0 Introduction The predicted performance of the Paxman 16RP200 engine fitted with a pulse exhaust manifold, running at the full-speed, full-load condition was examined in detail in the previous chapter. The overall performance and pressure traces were well predicted and the differences between the latter and the experimental traces were concluded to be functions of simplifications of the gas-dynamic model and the data set. To assess how well the program incorporating the author’s gas-dynamic model predicts engine performance in general, the performance of the pulse-turbocharged Paxman 16RP200 engine was simulated at the six operating points for which experimental data were recorded (see figure 2.6) using both the gas-dynamic model of the pulse manifold and the filling-and-emptying model for the same manifold. To test the flexibility of the program it was executed for the case of the same engine fitted with first a modular-pulse-converter (MPC) exhaust system and then a constant pressure system. No experimental data were available for verification of the model when used to simulate engines fitted with the MPC or constant pressure exhaust systems. Indeed these two exhaust systems are not available options for the Paxman 16RP200 engine: the manifolds described here were designed by the author. In the simulations described in this chapter the base-line data set of figure 5.6 was modified for elasticity in the exhaust-valve system, pressure-recovery factors of 0.5 and 0.83 in the junction volumes and turbine-entry volume respectively, and a constant coefficient of discharge of 0.8 was applied to inlet and exhaust valves for both forward and reverse flow. The artificially high inlet manifold volume and 104 turbine inertia were retained so that the exhaust manifold model could be fairly assessed. Additionally, the following data were corrected for each test condition: engine speed and fuelling, combustion coefficients, crank-angle of static injection, charge-cooler effectiveness, boost pressure and temperature, turbocharger speed, and the initial estimates of pressure and temperature in the control volumes. The results of the predictions using the gas-dynamic model to simulate the pulse system fitted to the Paxman 16RP200 are discussed first. They are then compared with those of predictions for which the filling-and-emptying method alone was used to simulate the pulse system. The flexibility of the exhaust model is then illustrated by the results of simulating the same engine fitted with the MPC and constant-pressure systems. The final section discusses differences in performance predicted for the engine fitted with each of the three exhaust systems. 6.1 Pulse System: Predictions using Gas-Dynamic Model The definition of the engine system using the gas-dynamic model is given in figure 5.5. The overall performance parameters, such as the brake-mean-effective pressure (bmep) and maximum cylinder pressure, were well predicted at all test points since the combustion coefficients for each operating point were derived such that the bmep and maximum cylinder pressure were within 2% of the experimental values, as described in section 5.1. The instantaneous predicted pressure traces at the transducer locations A8, B8,and T8 (see figure 2.8) at each test condition are compared with the experimental data in figures 6.1 to 6.6; those for the other manifolds being very similar. The overall forms of the pressure pulses were well predicted at all three locations and all operating points but the gas-dynamic pressure steps following EVO were not so well defined by the predictions. At the lowest load conditions, test points 1 and 3, the peak and minimum predicted pressures correlated well with the experimental values. At the remaining test points the departure of the predicted peak and minimum pressures from the experimental values increased as speed and load were 105 increased, ie from test point 2 to test point 6, the poorest prediction of pressure occurring at the turbine-end of the the manifold at each test point. The pulse from B8 was predicted more accurately when it arrived at the location A8 than at the nearer B8 location. The same may be said for the pulse from A8. A satisfactory explanation for this observation has not been found. The turbocharger operating point was not accurately predicted at any operating condition. The compressor operating point was fixed by the boost and speed which were held constant and equal to the experimental values at each test point by the large inlet manifold volume and turbine inertia. The compressor power and mass- flow rate were therefore fixed. At no test point did the turbine power or mass-flow rate match that of the compressor, as shown in figure 6.7, though at test point 4 the power mis-match was small. The mass-flow rate imbalance is attributed to the combination of errors associated with the extrapolation of turbine and compressor flow characteristics at pressure ratios below 1.2; the use of steady-flow characteristics for a highly pulsating flow; and the flow coefficients of the valves. The power imbalance is thought to be due to errors in the turbocharger and compressor efficiencies and in the prediction of instantaneous expansion ratio, evident from figures 6.1 to 6.6. At test point 1 the turbine power was 86% greater than the compressor power, but it is worth noting that both turbine and compressor powers were very small. The two exhaust pulses shown in figure 6.1 are of small amplitude and duration: the peak pressure is 1.42 bar and the pressure rises above 1.05 bar for only 20% of the cycle. The turbine efficiency at this operating point can be expected to be severely affected by windage losses, mechanical losses, and partial-admission effects. The turbine efficiency data used assume that the mechanical losses at the minimum N / y / T are equal to those at the maximum N / y / T . The turbine efficiency at N / y / T of 280 r p m / y / K is likely to be significantly over-optimistic. To test the hypothesis that the turbine data were inaccurate the efficiencies were shifted downwards by 12%. The result was that the mismatch in turbine and compressor power at test point 106 1 was reduced from 86% over-prediction of turbine power to 41%. It was therefore concluded that the turbine efficiencies do have a significant effect on turbine power. At the other end of the operating range, at test point 6, the percentage imbalances were smaller but still significant. The power imbalance here suggests that the turbine efficiency was higher than that assumed in the data input. It may be concluded that overall engine performance and the instantaneous static pressures in the exhaust may be well predicted by the program using the gas- dynamic exhaust model over the entire engine operating range. The turbocharger operating point was not so well predicted, however, the percentage error being greatest at test point 1. Engine manufacturers and operators are less concerned with how well near-idle conditions may be modelled, and more concerned with higher speed and load conditions. The poorer prediction of turbocharger operating point at test point 1, which may be due to the inaccuracy of the turbocharger data or the measured compressor operating point or a combination of both at this condition, is therefore not of great practical significance. 107 6.2 Pulse System: Gas-Dynamics and Filling-and-Emptying Compared To compare the gas-dynamic and filling-and-emptying exhaust-manifold models the Paxman 16RP200 engine was simulated at the same six operating conditions using filling-and-emptying volumes to model the exhaust manifold. The engine definition for this case is given in figure 6.8. The brake-mean-effective pressure (bmep), brake-specific-fuel consumption (bsfc), and brake-specific-air consumption (bsac), predicted by the two models are given in figure 6.9. The experimentally derived bmep is plotted for comparison, but the experimental bsfc and bsac are not: the latter was not measured, and since the experimental fuel consumption was entered into the program, a comparison of experimental and predicted bsfc would be meaningless. Inspection of figure 6.9 shows that the performance predicted using the gas- dynamic model is marginally more optimistic for test points 3 to 6. At test points 1 and 2 the filling-and-emptying model predicts higher bmep and lower bsfc than the gas-dynamic model. The predicted bmeps do not all lie within 2% of the ex perimental values, which might have been expected following the way in which the combustion coefficients were derived: see section 5.1. The greatest departure of the predicted bmep from the experimental is at test point 5 using the gas-dynamic model: the bmep is over-predicted by 5%. The differences are attributed to the fact that the combustion coefficients were derived using the base-line data set which did not allow for the exhaust-valve system elasticity or pressure recovery. The instantaneous pressure in the exhaust manifold of cylinders A8 and B8 pre dicted using only filling-and-emptying volumes to simulate the pulse manifold is compared with the pressures predicted by the gas-dynamic model and the exper imental data at transducer locations A8, B8, and T8 at all test points in figures 6.10 to 6.15. The filling-and-emptying model yields smooth pressure profiles of the same overall shape as the experimental profiles, but they do not capture the minor pressure variations. The relatively large size of the exhaust volumes pre vents the pressure in a volume from rising as rapidly as the experimental pressure following EVO. This difference is most clearly exhibited at the turbine-end of the 108 manifold: the initial wave-front steepens as it passes from the cylinder to the turbine. In this respect the filling-and-emptying exhaust model is inferior to the gas-dynamic model. It is superior, however, in the prediction of peak pressure in the exhaust manifold, but following the peak the pressure is over-predicted by the filling-and-emptying model. Both exhaust manifold models predict overall engine performance and the general shape of the exhaust pressure pulses well. While neither model accurately predicts the low pressures preceding EVO, the method of characteristics model does predict some of the finer details and is potentially the better model. The times taken to execute five steady-state cycles at test point 6 using the gas- dynamic and filling-and-emptying models on the Imperial College Cyber 855 main frame computer were 195.8 and 43.4 C PU seconds respectively: it is four-and-a- half times more expensive to simulate the pulse-turbocharged Paxman 16RP200 engine using the gas-dynamic exhaust model than the filling-and-emptying model. For this particular engine system where the pipe lengths are relatively short and gas-dynamic interference has a negligible effect on performance the higher addi tional cost of the gas-dynamic model can not be justified by the improved re sults. Considering how seriously pressure-wave interference can affect engine per formance, however, the increased cost of the gas-dynamic model may be viewed as a small price to pay. In an effort to reduce the computer execution time the author proposed a dominant pipe model in which the characteristics calculations are performed in only one of the pipes defining a system supplying one turbine entry, the dominant pipe at any time being the pipe carrying the dominant flow. The dominant pipe hypothesis is described in outline in appendix D. The complexity of the logic involved in selecting the dominant pipe at any point in the cycle prevented the successful implementation of the model. If the problems associated with this hypothesis could be overcome great savings in computer storage and execution time could be achieved. 109 6.3 Modular-Pulse-Converter Exhaust System To illustrate the flexibility of the model the performance of eight cylinders of the Paxman 16RP200 engine fitted with a hypothetical MPC system was simulated at the same six operating points as before. The differences to the input data described for the case of the pulse-turbocharged engine were the exhaust-system definition and the single-entry turbine-inlet casing. The diagrammatic definition of the MPC exhaust system is shown in figure 6.16: it comprises gas-dynamic pipes, in which the flow is solved by the method of characteristics, bounded by filling-and-emptying control volumes. The arrangement of the pipes and their boundary conditions differentiate between the pulse and MPC systems. Pressure losses at the MPC junctions were not simulated but they could be associated with the junction volumes. All volumes within the exhaust system are equivalent to a cylinder of diameter equal to the main-pipe diameter, and length equal to one main-pipe diameter. The nozzle area ratio and pipe dimensions are given in figure 6.17 and were based on information supplied in a private correspondence with Ruston Diesels Ltd. The overall predicted performance of the engine fitted with the MPC system was comparable with that of the engine fitted with the pulse system. The notable differences at all test points were the greater variation of volumetric efficiency between cylinders, the predicted exhaust manifold pressure traces, and the turbine operating conditions, all of which are inter-related. The minimum and maximum volumetric efficiencies predicted by the gas-dynamic model for the pulse system were 105.3% and 108.6% at test point 6 respectively. For the MPC system, the minimum was 80.9%, occurring in cylinder B6 , and the maximum was 112%, occurring in cylinder A8 at test point 6. The inlet-manifold conditions were the same for both the MPC and pulse systems: the exhaust- manifold conditions were quite different. The instantaneous static pressure in the pulse exhaust manifold, at transducer locations A8, B8 and T8 are given in figure 6.6. The shape of the pressure traces at the corresponding locations in the other sub-manifolds differed little from those of figure 6.6, and are therefore not 110 presented. The comparable traces for the MPC system are given in figure 6.18, and pressure traces at the remaining cylinder-end transducer locations are given in figures 6.19, and 6.20. For the pulse system, the pressure in the exhaust manifold at the points when the exhaust valve and inlet valve open were approximately equal for all cylinders. For the MPC system the exhaust pressures at EVO and IVO differ significantly between cylinders. A comparison of the exhaust pressure traces during valve overlap for cylinders A8, for which the volumetric efficiency was a maximum at test point 6 (figure 6.18), and B6, for which it was a minimum (figure 6.19), explains the 31% difference in volumetric efficiency. The inlet manifold pressure throughout the cycle is 2.76 bar: the exhaust pressure falls below the inlet-manifold pressure for a large proportion of the scavenge period at transducer location A8, and for a smaller fraction of the scavenge period at location B6. The location within the valve-overlap period during which the pressure gradient is positive from the inlet manifold to the exhaust manifold also influences the volumetric efficiency. At transducer location A8, the pressure gradient is adverse at the beginning of the overlap period but the inlet valve flow area is very small and only a small amount of reverse flow occurs. Towards the end of the overlap period, the exhaust valve flow area is small and although the gradient becomes less conducive to good scavenging the effect is small. At location B6, however, the pressure gradient is positive only during the final stages of exhaust-valve closure, thus preventing a high volumetric efficiency from being achieved. For test points 1 to 5 the overall shape of the pressure trace at each location was similar to the comparable trace at test point 6, and these pressure traces are therefore not shown. Figure 6.18 illustrates that at transducer locations A8 and B8 there are five distinct pulses, and not eight, due to the superposition of pressure pulses emanating from cylinders whose exhaust periods overlap. The distinction of the five pulses becomes less clear at locations A7, B6 and A6, but strengthens again at B5 and A5 which are closest to the turbine: see figures 6.19 and 6.20. I l l The turbine and compressor characteristics used were the same for the MPC sys tem as for the pulse system. The large amplitude pressure fluctuations observed near the cylinders are much reduced at the turbine end of the MPC manifold, providing more favourable turbine flow conditions than the pulse manifold did, as illustrated by a comparison of figures 6.18 and 6.6. The energy-averaged turbine isentropic efficiency of the MPC system was greater than that for the pulse system. The improvement may be attributed to the reduced pressure fluctuations at turbine entry. The difference at test point 6 was 2.8%. At test point 1 the difference was greatest. The long periods of no flow in the pulse system caused the energy-averaged isentropic efficiency to fall to 57% but the continuous flow of the MPC system yielded a turbine efficiency of 68%. It has been proved above that the author’s exhaust manifold model can be used to model a MPC exhaust system by simply changing the data input to the program, the MPC system being defined in terms of pipes bounded by small control volumes. In the absence of experimental data for verification of the predicted results their accuracy can not be assessed but it may be said that the overall performance at each test condition was predicted to be comparable with that of the pulse- turbocharged engine. The additional pipes and volumes, and the nozzle boundary conditions increased the computer execution time by 37% relative to the gas- dynamic simulation of the pulse system. 112 6.4 Constant Pressure Exhaust System The third type of exhaust manifold to be modelled was the constant pressure system which is the only one that could be modelled accurately by TRANSENG before the author’s gas-dynamic model was included in the program since the program previously allowed only a filling-and-emptying simulation of the exhaust manifold. Constant pressure systems are not fitted to Paxman 16RP200 engines, and the author designed a hypothetical manifold based on the physical limitations of fitting the manifold into the vee of the engine. As for the predictions for the engine fitted with the MPC system no experimental data were available for verification of the results. The definition of this system for the program is shown in figure 6.21. The volumes of the manifold, the ports in the cylinder head and the turbine inlet casing, which are represented by a single control volume, control volume 10 of figure 6.21, was 0.105 m 3. The overall predicted performance at all test points was comparable with that for the other exhaust types. The pressure trace for the exhaust manifold at test point 6 is given in figure 6.22. There are seven small-amplitude excursions from the mean pressure level, the ‘pulses’ from cylinders A7 and B6 combining imperceptibly due to the short interval between the points at which their exhaust valves open. The computer execution time for the performance of the engine fitted with the constant pressure exhaust system at test point 6 was 31.7 C PU seconds on the Cyber 855 main-frame computer. 113 6.5 Comparison of Predicted Performance for Three Engine Systems The author’s versatile exhaust manifold model has been used to predict the per formance of the Paxman 16RP200 engine fitted with pulse, MPC, and constant- pressure exhaust systems. It has been demonstrated that different systems can be modelled simply by changing the input data describing the exhaust manifold, and that the program can be used to assess how different exhaust systems can affect performance. Figure 6.23 shows the predicted bmep, bsfc, and bsac at each test point for the engine fitted with each of the three exhaust systems. There is little difference between the bmeps predicted for the different systems. The bsfc is most optimistically predicted for the case of the constant pressure system throughout the operating range, and the MPC system performs marginally better than the pulse system at low speeds and loads and vice versa at high speeds and loads. The bsac is consistently predicted to be lower for the MPC system. The predicted average volumetric efficiency and energy-averaged isentropic turbine efficiency are plotted against test point in figure 6.24. The latter is noticeably lower for the pulse system and the average volumetric efficiency for the MPC system is consistently lower relative to that of the other systems. For these simulations the compressor operating point was fixed throughout the cycle and the inlet manifold was suffi ciently large to supply the engine with air at constant conditions. The differences in these performance parameters therefore reflect the differences in the predicted pressure pulsations in the three exhaust systems. The differences are illustrated in figures 6.25 and 6.26 where the instantaneous pressures predicted in each exhaust manifold at transducer locations B8 and T8 for test point 6 are given. The above demonstrates that the program incorporating the author’s exhaust manifold model can be used to compare engine performance at all operating points within the range for engines fitted with different exhaust systems. If experimental data were to confirm the accuracy of the MPC and constant pressure system pre dictions the program could also be used to optimise the choice of exhaust system. Investigations into the optimum MPC nozzle area ratio could be conducted, the 114 effect of regrouping the cylinders of the pulse system could be studied, and the effect of changing pipe lengths and diameter could be investigated. The penalty paid for the facility to design and optimise exhaust systems is an in crease in computing cost. The computer execution time increases with the number of pipes and volumes modelled as can be seen in figure 6.27 which compares the execution times for each exhaust system modelled. While it is thought that many program users would accept the higher cost, work is currently being undertaken at Imperial College to reduce the computer execution time of the program as a whole, and the author has suggested a method for reducing the cost of simulat ing a gas-dynamic exhaust manifold in appendix D. It is anticipated that a more computationally efficient program will be developed in the near future. 115 C H A P T E R 7 CONCLUSIONS AND RECOMMENDATIONS 7.0 Conclusions The Imperial College filling-and-emptying program, TRANSENG, has been devel oped by the author to enable more accurate predictions of medium-speed engine performance to be made. Minor but significant modifications to the program include the allowance for un-equal firing intervals, burning fuels with different calorific values, and turbocharger turbines with more than two entries. The single major development was the inclusion of a flexible model of the exhaust mani fold which facilitates simulation of any exhaust manifold that may be fitted to a medium-speed engine. Gas-dynamic exhaust manifolds may be modelled by defin ing the exhaust system as a series of interconnected pipes and volumes, flow in the former being solved by the method of characteristics, and in the latter by the filling-and-emptying method. Full scale experimental tests confirmed that the in stantaneous static pressures in a pulse exhaust manifold could be well predicted by simulating the exhaust system with pipes and volumes using the author’s exhaust manifold model. Differences between the predicted and experimental results were thought to be due to inaccuracies in the turbine data and simplifications inherent in the gas-dynamic model. A comparison of results obtained from two simulations of the pulse-turbocharged Paxman 16RP200 engine first using the filling-and-emptying method alone, and then using the gas-dynamic exhaust manifold model revealed that both methods predict overall performance parameters well, but that the latter method enables details of the instantaneous exhaust pressure to be predicted more accurately. The sensitivity of the program to various input data was tested. The program was found to be sensitive to changes in effective valve flow area and it was demonstrated 116 that the elasticity of the exhaust valve system should be accounted for, and that changes in coefficient of discharge of the valves significantly affect predicted perfor mance. Differences in exhaust manifold heat transfer data and pressure recovery factors also had a noticeable effect on the exhaust pressure traces. The modifi cations to the turbine map tested made little difference to the exhaust pressure traces but the author believes that alternative data allowing for partial-admission and unsteady-flow effects could yield a closer match between predicted and exper imental pressures in the exhaust. The turbine and compressor power balance was very sensitive to changes in turbine efficiency. At test point 1 a 12% decrease in turbine efficiency yielded a 45% reduction in predicted turbine power. The cost of simulating five steady-state cycles of the pulse-turbocharged Paxman 16RP200 engine using the gas-dynamic exhaust manifold was 195.8 C PU seconds on a Cyber 855 main-frame computer. A simulation of the same engine system using the filling-and-emptying method to model the exhaust manifold took four- and-a-half times less computer execution time. 117 7.1 Recommendations for Future Research (1) Perform a more comprehensive assessment of the author’s exhaust manifold model by comparing predicted and experimental results of several different medium-speed diesel engines fitted with different types of exhaust manifold. (2) Conduct experimental research to: (a) determine combustion correlations for medium-speed engines, (b) study the effects of partial-admission and unsteady-flow conditions on axial-flow turbine performance, and (c) evaluate a correlation for translating steady-flow coefficients of dis charge for the valves evaluated at low pressure ratios to instantaneous coefficients of discharge at engine operating conditions. (3) Develop the engine simulation program to: (a) include the full turbine boundary condition for the method of character istics, and then assess the error incurred in the author’s exhaust man ifold model where the boundary at the pipe end nearest the turbine is an open-end boundary to a small volume which directly precedes the turbine entry, and (b) solve the flow in the pipes by the non-homentropic method of character istics to assess the error incurred in the author’s exhaust manifold model which assumes homentropic flow within a pipe. (4) Investigate the author’s proposed dominant pipe model to reduce computer execution time and study other methods of making the program more com putationally efficient. 118 REFERENCES 1 Jenny, E. The Utilisation of Exhaust Gas Energy in the Supercharging of the Four- stroke Diesel Engine Brown Boveri Review, Vol 37, No 11 (1950) 2 Birmann, R. 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A Comparison of the Performance of Three Model Axial Flow Turbines Tested under both Steady and Pulse Flow Conditions ProcIMechE Vol 184 Pt 1 No 61 (1969-70) 128 Plate 2.1 Engine Test Bed P la te 2.2 Non-standard Orifice Plate for Measurement of Air-mass flow Rate TEST DAY 1 2 3 LOCATION DATA SET 'NAME t PAX1B1D PAX2A1D PAX2A1N PAX3A1D PAX3A1N Cylinder B8 * ** * ♦ Exhaust A8 * * * * 4c B8 * * * * 4c T8 ** * 4c 4c Exhaust A7 ** B7 * * 4c 4c T7 * * Exhaust A6 * B6 * T6 * Exhaust A5 * 4c B5 T5 * 4c Inlet Man. A * * Inlet Man. B * Needle Lift B8 * * Table 2.1 Experimental Data Logged Each Test Day T est Point Manometer Average Pressure Averaged Mass-flow Rate (mbar) (k g /s) 1 1 0.10 2 0.13 3 0.27 4 0.27 0.75 2 1 0.39 2 0.45 3 0.60 4 0.62 1.12 3 1 0.49 2 0.68 3 0.90 4 0.89 1.37 4 1 2.02 2 2.14 3 2.54 4 2.82 2.36 5 1 2.95 2 3.23 3 3.62 4 4.44 2.89 6 1 5.33 2 5.90 3 7.09 4 7.84 3 .9 4 Averaged air mass-flow rate is for all sixteen cylinders and was calculated assuming compressible flow through an orifice with a Cd of 0.73. Manometers 3 and 4 had a bevelled edge and were situated at the drive end of the engine. Table 2.2 Pressure Differentials across the Orifice Plates Fitted to Compressor Inlet-casing Flanges Transducer Test Point Location 1 2 3 4 5 6 A5 587 645 638 707 750 856 B5 595 659 653 731 767 851 A6 576 655 653 729 768 861 B6 576 637 649 712 748 866 A7 579 630 636 690 737 806 B7 564 628 639 696 736 816 Table 2.3 Exhaust Manifold Temperatures Expressed in Kelvin Test Point Engine Speed 0 ( P m a x ) bmep imep 'Hm ech % fuel burned (/) (rpm) (degCA) (bar) (bar) (/) (/} 1 700 9 5.6 6.9 0.81 100 2 950 10 8.9 10.9 0.81 100 3 1200 9 6.9 8.2 0.84 100 4 1200 13 12.8 15.2 0.84 100 5 1200 12 16.4 19.4 0.85 100 6 1500 14 17.4 19.8 0.88 95 Table 5.1 Performance Data Derived from Cylinder-pressure Diagrams Advanced by 8 degCA Test Point 1 2 3 4 5 6 CPI 2.5 1.8 2.8 3.9 4.5 2.2 CP2 5000 5000 5000 5000 5000 5000 CD1 19.0 25.0 8.0 21.0 19.3 17.6 CD2 1.75 1.44 1.30 1.50 1.50 1.80 P 0.60 0.33 0.38 0.18 0.19 0.027 P m a x (bar) exp. 62 77 69 100 122 127 P m a x (bar) pred. 60 78 66 102 126 128 0 { P m a x) (degCA) exp. 189 190 189 193 192 194 0 { P m a x) (degCA) pred. 188 190 189 193 193 192 bmep (bar) exp. 5.6 8.9 6.9 12.8 16.4 17.4 bmep (bar) pred. 5.7 9.0 6.5 12.8 16.6 17.2 CAIGN (degCA) exp. 180.8 179.7 180.0 176.8 174.0 174.0 CAIGN (degCA) pred. 180.8 179.9 179.8 176.7 174.0 172.8 Table 5.2 Combustion Coefficients and Salient Performance Parameters at 6 Operating Conditions Parameter Predicted Value With Heat Transfer With No Heat Transfer Energy available from fuel (kJ) 105.23 103.46 Heat transfer from cylinders (kJ) 26.93 72.26 Heat transfer from exhaust (kJ) 24.27 0.00 Isentropic work available at turbine (kJ) 27.16 32.38 Thermal efficiency of engine (%) 44.1 43.3 Total thermal efficiency of 55.5 56.9 engine system (%) Time-averaged temperature in 650 858 volume preceding turbine (K) bmep (bar) 17.48 17.30 bsfc (kg/kW h) 0.2198 0.2217 Average scavenge efficiency (%) 101.8 98.6 Table 5.3 Comparison of Performance Predicted With and Without Heat Transfer from the Exhaust Manifolds Constant pressure manifold exhaust manifold ---- turbine cylinder Pulse manifold exhaust manifold Figure 1.1 Constant Pressure and Pulse Exhaust Systems L p Reflected tvave arrives after EUC: no effect Inlet valve open Reflected ivave arrives during scavenge: impaired performance Reflected ivave arrives during enpulsion stroke: no effect Reflected ivave arrives during bloiv-doivn: improved performance Figure 1.2 Influence of Pipe Length on Pressure-wave Reflection Simple-pulse-conuerter manifold Modular-pulse-conuerter manifold Figure 1.3 Simple and Modular Pulse-converter Exhaust Systems Figure 2.1 Cross-sectional General Arrangement of Paxman 16RP200 Engine (courtesy of Paxman Diesels Ltd) SECTION R-R. SECTION W-W. Figure 2.2 Water-cooled Exhaust Manifold of Paxman 16RP200 Engine Figure 2.3 Arrangement of Data-acquisition Equipment Block Diagram ofCussons Microsync P4450 Block Diagram of Phase-Locked Loop (PLL) Fvco is R * N * 720 (Hz) Figure 2.4 Operation of Cussons Microsync P4450 AVL Indiskop 647 Apricot PC High-speed Data-Acquisition System Micro-computer Apricot PC Imperial College Mainframe Micro-computer Cyber CDC 180/855 Run on Apricot PC Figure 2.5 Data Transfer from Indiskop to Cyber Mainframe Computer gure 2. nie et Conditions Test Engine .6 2 e r u ig F BMEP (bar) l 0 2 nieSed (rpm) Speed Engine V8 at Drive End supplied by a single exhaust manifold but two inlet manifolds Figure 2.7 Conceptual Split of Engine into Two V8 engines Distance from cylinder-head flange to cylinder-end transducer is 60 mm. Distance from turbine-end transducer to turbine nozzle is 80 mm. Figure 2.8 Locations of Transducers in Exhaust Manifold Figure 2.9 Cylinder Pressure and Needle Lift for Cylinder B8 at Test Point 4 CRANK ANGLE (OEG.) Figure 2.10 Static Pressures in Exhaust at Locations A8, B8, and T8 at Test Point 4 gure 2. ttc rsue i Ehut t oain A, 7 ad 7 t Test at T7 and B7, A7, Locations at Exhaust in Pressures Static 1 .1 2 e r u ig F EXHAUST PRESSURE T7 (BAR) .EXHAUST PRESSURE B7 (BAR) .EXHAUST PRESSURE A7 (BAR) on 4 Point C R A NAN K G( L E O E G ) C R A NAN K C(D L E E C . ) Figure 2.12 Static Pressures in Exhaust at Locations A6, B6, and T6 at Test Point 4 gure 2. ttc rsue i Ehut t oain A, n T a Ts Point Test at T5 and A5, Locations at Exhaust in Pressures Static 3 .1 2 e r u ig F EXHAUST PRESSURE T5 (BAR) EXHAUST PRESSURE A5 (BAR) 4 C R A NAN K G(O L E E G ) gure 2. - n Bbn Ilt aiod rsue a Ts Pit 4 Point Test at Pressures Manifold Inlet B-bank and A- 4 .1 2 e r u ig F -BANK INL• MAN. PRESSURE (BAR) INLET MANIFOLD A BANK PRESSURE (BAR) C R A NAN K G(O L E E G ) C R A NAN K G(D L E E G ) cn cl CD CO UJ OC ZD CO CO UJ QC Q_ UJ O 2 d X <_) X UJ CO cr O CRANK ANGLE (DEG) Figure 2.15 Gas-exchange Pressures for Cylinder B8 at Test Point 4 Exhaust manifold arrangement showing thermodynamic zones Thermodynamic zone Momentum Zone Figure 3.1 Thermodynamic and Momentum Zones of the Yano and Harp Model [25] 0 40 80 120 160 200 240 Crank angle (degrees) ------Measured pa = 4.68 (lbf/in2) gauge N = 394 rev/min ------Calculated P rele,*. = 35.0 (lbf/in2) gauge TreICas, = 130°F Comparison of non-homentropic inlet and exhaust pressure predic- tions with experimental results (a) Exhaust nozzle. (1) (b) Cylinder. (2 ) (c) Inlet pipe. (3 ) (d) Inlet pipe. (4 ) Taken from Benson [ 30 ] Figure 3.2 Comparison of Method of Characteristics Predictions with Experi mental Results ------Incident characteristic ------Reflected characteristic nominal flow direction ! i n ...... i Figure 3.3 Diagram Showing A and /? Characteristics and Time-step Size for Pipe Figure 3.4 In-flow to a Cylinder through a Poppet Valve pipe, p Figure 3.5 Outflow from a Cylinder through a Poppet Valve filling-and-emptying control volume ttiai is the mass-flow rate at plane A l calculated as a function of the gas velocity and density at the pipe end at plane Al h0cy[1 is the specific stagnation enthalpy of the fluid in the volume upstream of plane A l 2ToAi is stagnation enthalpy transferred across plane Al calculated as a func tion of the mass-flow rate across plane A l and hocyll since this is also the stagnation enthalpy in the pipe due to the homentropic assumption. Figure 3.6 Junction Volume Model Figure 4.1 Flow Chart of TRANSENG Figure 4.2 Diagram Illustrating Co-existence of Premixed and Diffusion Burning for Combustion Model gure 4. asfo Caatrsis o a ailfo Trie n a Nozzle a and Turbine Radial-flow a for Characteristics Mass-flow .3 4 e r u ig F Turbine expansion ratio Non-dimensional mass-flow rate mass-flow Non-dimensional Figure 4.4 Detail of Pre-development Flow Chart Figure 4.5 Detail of Post-development Flow Chart Number of pipes, NEP 5 Number of turbine entries, N TEM 1 Identification number of control volume preceding turbine, NPRETUR 7 Parameter Pipe Number 1 2 3 4 5 Control volume number 1 2 3 5 6 thermodynamic control volume turbine upstream of pipe, NFEUP(I) Control volume number 5 5 6 6 7 downstream of pipe, NFEDN(I) Boundary number at upstream 5 5 5 4 4 pipe end IB 1 (I) Boundary number at downstream 4 4 4 4 4 pipe end IB2(I) Pressure recovery factor at 0.0 0.0 0.0 0.0 0.0 upstream pipe end P Fl(I) Pressure recovery factor at 0.5 0.5 0.5 0.5 0.8 downstream pipe end PF2(I) control volume numbers in plain text pipe numbers in italics Figure 4.6 Definition of Pulse Exhaust System for Gas-dynamic Model Number of pipes, NEP 8 Number of turbine entries, N TEM 1 Identification number of control volume preceding turbine, N PR ETUR 10 Parameter Pipe Number 1 2 3 4 5 6 7 8 Control volume number 1 2 3 4 6 7 8 9 upstream of pipe, NFEUP(I) thermodynamic control volume turbine Control volume number 6 7 8 9 7 8 9 10 downstream of pipe, NFEDN(I) Boundary number at upstream 5 5 5 5 4 4 4 4 pipe end IB 1(1) Boundary number at downstream 7 7 7 7 4 4 4 7 pipe end IB2(I) Pressure recovery factor at 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 upstream pipe end PF1(I) Pressure recovery factor at 0.0 0.0 0.0 0.0 0.5 0.5 0.5 0.0 downstream pipe end PF2(I) control volume numbers in plain text pipe numbers in italics Figure 4.7 Definition of Modular Pulse-converter Exhaust System for Gas-dynamic Model Figure Figure Mass Flow Rates Through Inlet and Enhaust Ualues (kg/s) 0.5 -0 -0.5 0.0 . - 0.5 -0.5 0.0 . - 0.5 . - 0.5 0.0 4 .8 Numerical Instability in Mass-flow Rates as Engine Speed is Reduced is Speed Engine as Rates Mass-flow in Instability Numerical .8 4 1.0 1.0 1.0 - -180 - oi ln: ne vle rkn ie ehut valve exhaust line: broken valve inlet line: solid N=1200rpm N=950rpm N=700rpm rn Age (degrees) Angle Crank ltll 1* lll* lllt i l i 8 360 180 m i i i s l i l i ...... W w 540 Figure Figure Mass FIolu Rates Through Inlet and Enhaust Ualues (kg/s) 0.0 0.5 1.0 9 Peitd asfo Rts eoe n Atr rga Development Program After and Before Rates Mass-flow Predicted .9 4 oi ln: ne vle rkn ie ehut valve exhaust line: broken valve inlet line: solid Before Crank Angle (degrees) Angle Crank V — turbine Figure 4.10 Single-cylinder Method of Characteristics System gure 4. ttc rsue a Pp Ed fr ifrn Cnrl oue Sizes Volume Control different for Ends Pipe at Pressures Static 1 .1 4 e r u ig F Static Pressures in Enhaust Manifold (bar) 4 oi ln: yidr n boe ln: ubn end turbine line: broken end cylinder line: solid Ms sz o 1/ ie diameter) pipe /2 1 of size (Mesh rn Age (degrees) Angle Crank g e 12 Sai Pesrs t ie ns o ifrn Ms Sizes Mesh Different for Ends Pipe at Pressures Static 2 .1 4 re igu F Static Pressures in Enhaust Manifold (bar) 4 oi ln: yidr n boe ln: ubn end turbine line: broken end cylinder line: solid Vlm sz 1 ie imtrs length) diameter’s pipe 1 size (Volume rn Age (degrees) Angle Crank F ig u re 5.1 Non-dimensional Fuel-burning Rates Derived from Cylinder-pressure from Derived Rates Fuel-burning Non-dimensional 5.1 re u ig F Non-dimensional Fuel Burning Rate (/) 25 10 igas o Clne B8 Cylinder for Diagrams Crank Angle (degrees) Test Point 1 Test Point 6 g e . Peitd n Eprmna Clne Pressures Cylinder Experimental and Predicted 5.2 re igu F Pressure in Cylinder B8 (bar) oi ln: rdce dte ln: experimental line: dotted predicted line: solid 10 l CM - 10° 1 Cl. <_) M 10-1 10' 1 0 Ignition Delay, <$ign(deg Cfl) Figure 5.3 Combustion Coefficients as a Function of Correlation Parameters of Watson et al [ 40 ] solid line: correlation for Paxman engine broken line: Watson et al correlation 10 □ "J V a i o 101 10' "> — i -1 10 1 o' Trapped Equiualence Ratio,F tr (/) rvj a o CD 1 Figure 5.4 Combustion Coefficients as a Function of Correlation Parameters of Watson et al [40'] broken line: Watson et al correlation Figure 5.5 Definition of Paxman 16RP200 Pulse Exhaust Manifold for Gas-dynamic Manifold Model ** 1- BASIC ENGINE SYSTEMS:- * 1- NATURALLY SIMULATED TURBOCHARGING * ASPIRATED: V IA E X H A U ST NOZZLE: * N A T A S P ? SIM T C ? F F *2- SINGLE STAGE TW O STAGE * TURBOCHARGING: TURBOCHARGING: * C H P ? TH P ? CLP ? TLP ? T T F F ** 2- ENGINE SYSTEM OPTIONS: * 1- PIPES INLET MAN. PIPE LOSSES: * T O CYLINDERS: * P IP C Y ? PIPC Y L ? F F * 2- CSER RESONANT INTAKE PIPE LOSSES * SYSTEM OR JUNCTIONS: * PIPJC ? PIPJCL ? F F * 3- AIR BYPASS: HYPERBAR FUELING: * B Y P S ? HYP? F F * 4 - A F T E R COOLER: V/G HP TURBINE: * C A C (l) ? THPVG? T F * 5- TURBOCOMPOUND W /G HP T U R B IN E INTERACTION * LP TURBINE: SINLE EXH ONLY: TWIN EXH ONLY: * T L P C D ? W G (1) ? T H P 2I ? F F F * 6- IN T E R C O O LER : V/G LP TURBINE: * C A C (2 ) ? TLPVG ? F F * 7- COMPOUND LP T/C: W/G LP TURBINE: * T C L P C D ? W G (2) ? F F ** 3- CYLINDERS AND CONTROL VOLUMES:- * 1- NUMBER OF CONTROL VOLUMES: * N C Y L ? N IM ? N E M ? N C V M A X ? * (/) 00 * 2- CYLINDER GEOMETRY: * CRATIO ? LENGTH ? STROKE ? BORE? ENGI ? * 00 (M) (M) (M) (K G .M 2) 1.213E + 01 4.064E-01 2.159E-01 1.969E -01 O.OOOE+OO * 3- INLET MANIFOLD VOLUMES: * V IM (I) ? ,1=1,N IM * (M 3) 1.0 0 0 E + 0 2 Figure 5.6 Data Input for TRANSENG, Tape 5 (1 of 13) * 4- EXHAUST FILLING AND EMPTYING VOLUMES: * VEM(I) ? J=1,NEM (HP FIRST THEN LP) © * (M 3) 3.475E-04 3.475E-04 3.475E-04 3.475E-04 3 .4 7 5 E -0 4 3 .4 7 5 E -0 4 3 .4 7 5 E -0 4 3 .475E -04 * 5- NUMBER OF HP AND LP TURBINE ENTRIES: * NTEM(l) ? NTEM(2) ? * (/) ,(/) 4 0 ** 4- EVENT TIMING DATA:- * 1- PHASE ANGLE WRT 0 DEG.CA TDC CYLINDER 1 * A (I) ? ,I= 1,N C Y L * (D E G .C A ) 0 0 0 .0 42 0 .0 180.0 6 0 0 .0 6 3 0 .0 3 3 0 .0 9 0 .0 510.0 * 2 - V A L V E T IM IN G DA TA : * EVO ? EVC ? TVO? IVC? * (D E G .C A ) (DEG.CA)(DEG.CA)(DEG.CA) (0= T D C ) 9 6 .0 430 .0 2 8 8 .0 5 8 5 .0 * 3- EFFECTIVE AREA DATA: (DIGITISATION) * N V D A T I ? NVDATE?DELTA? * (/) 00 (DEG.CA) 51 57 6 .000E + 00 * 4- INLET VALVE AREA * VAREA(I) ? 1=1 , NVDATI * (M 2) O.OOOE+OO 2.500E -05 5.515E -05 1.130E -04 2.060E-04 3.600E-04 5.660E-04 8 .0 0 0 E -0 4 1.110E -03 1.400E-03 1.805E-03 2.220E-03 2.630E-03 3.040E-03 3.425E-03 3.760E-03 4.020E-03 4.250E-03 4 .4 8 0 E -0 3 4 .7 2 0 E -0 3 4 .8 8 0 E -0 3 4 .9 8 0 E -0 3 5.050E-03 5.100E-03 5.100E-03 5 .100E -03 5.100E -03 5 .100E -03 5.050E-03 4.980E-O3 4.88 0 E -0 3 4 .7 5 0 E -0 3 4.550E-03 4.330E-03 4.080E-03 3.820E-03 3.510E-03 3.070E-03 2.740E-03 2 .2 7 0 E -0 3 1.880E -03 1.450E -03 1.080E -03 8.250E-04 5.700E-04 3 .6 0 0 E -0 4 2 .3 0 0 E -0 4 1.300E-04 5.000E-05 1.000E -05 0 .000E + 00 * 5- EXHAUST VALVE AREA: * VAREA(I) ? 1=1 .NVDATE * (M 2) 0 .0 0 0 E + 0 0 2.500E -05 6.000E-05 1.300E-04 2 .3 0 0 E -0 4 3.60 0 E -0 4 5 .700E -04 8 .0 0 0 E-04 1.080E -03 1.380E-03 1.700E-03 2.000E-03 2.320E-03 2.630E-03 2 .9 2 0 E -0 3 3.170E -03 3.430E -03 3 .680E -03 3.850E-03 3.970E-03 4.080E-03 4.180E-03 4.250E-03 4.250E-03 4.250E-03 4.250E-03 4.250E-03 4 .2 5 0 E -0 3 4 .2 5 0 E -0 3 4.250E -03 4.25 0 E -0 3 4 .2 5 0 E -0 3 4.250E-03 4.250E-03 4.200E-03 4.120E-03 4.020E-03 3.900E-03 3.710E-03 3.530E-03 3.250E-03 2.980E-03 2.740E-03 2.420E-03 2.060E-03 1.750E-03 1.470E-03 1.190E -03 8 .8 0 0 E -0 4 6.200E-04 4.400E-04 2 .8 0 0 E -0 4 1.500E-04 6.000E-05 2.000E-05 5 .0 0 0 E -0 6 O.OOOE+OO * 6- CALIBRATED STEADY COEFFICIENT OF DISCHARGE AT GIVEN PRESSURE RATIO: * CDEFIN ? PREFIN? CDEFEX ? PREFEX? * (/) ( f ) ( 1 ) ( f ) 8 .000E -01 1.014E+00 8.000E-01 1.014E+00 * 10- POLYNOMIAL COEFFS FOR INLET VALVE STEADY CD VS. 1VD PI1 ? PI2 ? PI3 ? PI4 ? PI5 ? (/) 00 00 (!) (f) 1 .000E + 00 -1.830E + 00 O.OOOE+OO O.OOOE+OO O.OOOE+OO Figure 5.6 Data Input for TRANSENG, Tape 5 (2 of 13) * 11- POLYNOMIAL COEFFS FOR EXHAUST VALVE STEADY CD VS. L/D P E I ? PE 2 ? PE3 ? P E 4 ? PE5 ? (/) (D (/) (/) (!) 1.123E+00 -1.673E+00 0.0 0 0 E + 0 0 0 .0 0 0 E + 0 0 O.OOOE+OO 12- L/D AT MAX EV CD AND MIN AND MAX PRESSURE RATIOS VECDMAX ? PR1 ? P R 2 ? (/) (/) (/) 1.000E -01 1.014E + 00 2 .0 0 0 E + 0 0 13- VALVE DIAMETERS, ANGLES AND MAXIMUM LIFT DIN?DEX? BET AIN? BETAEX? VLMAX? (M) (M) (DEG) (DEG) (/) 6 .1 9 1 E -0 2 5.790E-02 3.000E+01 4.500E+01 1.740E-02 14- INJECTION TIMING: C A S IN J ? INJDEL? (DEG.CA) (S) (T D C = 180) 1.6 0 5 E + 0 2 8.333E -04 5- HEAT TRANSFER AND COMBUSTION:- * 1- COMBUSTION CHAMBER SURFACE AREAS: * ACH ? APIS ? ALCON? * (M2) (M2) (M 2) 3.04515E-02 3.46450E-02 1.02580E-02 * 2- CYLINDER THERMAL RESISTANCE COEFFICIENTS: * R 2 ? R 4 ? R5 ? R 7 ? R 8 ? R IO ? * (K.M2/KW) (K/KW) (K/KW) (K/KW) (K/KW) (K/KW) 1.750E-01 1.950E+00 9.750E-01 9.750E-01 1.265E+01 5.400E+00 * 3- INLET MANIFOLD SURFACE AREAS: * AREAIM(I) ? ,I=1,NIM * (M 2) 0 .0 0 0 E + 0 0 * 4- INLET MANIFOLD HEAT TRANSFER COEFFICIENTS: * HTCOIM(I) ? ,1=1,NIM * (KW/(M2.K)) 0 .0 0 0 E + 0 0 * 5- EXHAUST MANIFOLD SURFACE AREAS: * A R E A E M (I) ? .1=1,N EM * (M 2) 3.590E-01 3.020E-01 3.590E-01 2.000E-01 3.590E-01 2.750E-01 3.340E-01 2.450E -01 * 6- EXHAUST MANIFOLD HEAT TRANSFER COEFFICIENTS: * HTCOEM(I) ? 1=1,NEM * (K W /(M 2.K )) 3.628E-01 3.628E-01 3.628E-01 3.628E-01 3.628E-01 3.628E-01 3.628E-01 3.628E -01 * 7- COOLING MEDIUM TEMP FOR EXHAUST CVS: * TCOOLEX(I) ? 1=1,NEM * (K ) 3.550E+02 3.550E+02 3.550E+02 3.550E+02 3.550E+02 3.550E+02 3.550E+O2 3.550E + 02 * 8- ENGINE BLOCK RUNNING TEMPERATURES: * T C W ? TC O ? TLG ? TPG ? TH G ? * (K) (K) (K) (K) (K) 3.560E+02 3.480E+02 4.930E+02 4.840E+O2 4.310E-HJ2 Figure 5.6 Data Input for TRANSENG, Tape 5 (3 of 13) * 9- FUEL DATA: * LCV? * (K J/K G ) 4.25000E+04 *11- DATA IF CAIGN IS INPUT BDUR? CPI? CP2? C D 1? C D 2? BETA? (DEG) if) , if) if) if) if) 1.2 5 0 E + 0 2 2 .2 0 0 E + 0 0 5.000E + 03 1.760E+01 1.800E+00 2.700E-02 * 12- IGNITION DELAY CORRELATION COEFFICIENTS * CCC (I) ? ,1=1,3 * if) 4.40000E-04 4.65000E+03 1.19000E+00 ** 6- INLET FLOW SYSTEM * 1- HP COMPRESSOR WHEEL TIP DIAMETER AND SCALE FACTORS: * DCOMP ? CSFM ? CSFE ? * (M ) if) if) 3.124E -01 1.000E + 00 1.000E + 00 * 2- HP COMPRESSOR NUMBER OF CONSTANT SPEED AND GRID LINES * NSPLC ? NGRID ? TT -> TS ? * if) if) if) 8 9 F * 3- HP COMPRESSOR PERFORMANCE MAP: GRID LINE = 1 OFF 9 * SP E E D ? P.R.? M.F.P.? EFFC ? * (R P M /S Q R T (K )) if) (KG/S )S QRT(K)/(KN/M2) if) 3.000E+02 1.040E+00 1.283E-01 6.500E -01 7 .0 0 0 E + 0 2 1.270E+00 1.744E-01 6.500E -01 9.000E+02 1.500E+B0 2.105E -01 6.500E -01 1.100E+03 1.825E+00 2.664E -01 6.500E -01 1.300E+03 2.250E+00 3.322E-01 6.500E -01 1.400E + 03 2 .5 3 5 E + 0 0 3.684E -01 6.500E -01 1.500E + 03 2 .8 5 0 E + 0 0 4.079E -01 6.500E -01 1.600E + 03 3 .4 0 0 E + 0 0 4.605E -01 6.500E -01 * 3- HP COMPRESSOR PERFORMANCE MAP: GRID LINE = 2 OFF 9 * SPEED ? P.R.? M.F.P.? EFFC? ♦ (RPM/SQRT(K)) if) (KG/S )S QRT (K)/(KN/M 2) if) 3 .0 0 0 E + 0 2 1.044E + 00 1.119E -01 7.200E -01 7 .0 0 0 E + 0 2 1.320E + 00 1.612E -01 7.100E -01 9 .0 0 0 E + 0 2 1.550E + 00 2.039E -01 7.100E -01 1.100E + 03 1.880E+00 2.632E -01 6.800E-01 1.300E + 03 2 .3 2 0 E + 0 0 3.323E -01 6.750E -01 1.400E + 03 2 .6 2 5 E + 0 0 3.684E -01 6.750E -01 1.500E + 03 2 .9 4 0 E + 0 0 4.079E -01 6.700E -01 1.600E + 03 3.465E+00 4.572E-01 6.700E -01 * 3-HP COMPRESSOR PERFORMANCE MAP: GRID LINE = 3 O FF 9 * SP E E D ? P.R.? M.F.P.? EFFC? * (RPM/SQRT(K)) if) (KG/S)SQRT(K)/(KN/M2) if) 3 .0 0 0 E + 0 2 1.048E+00 9.870E-02 7.500E -01 7 .0 0 0 E + 0 2 1.320E + 00 1.513E -01 7.500E -01 9 .0 0 0 E + 0 2 1.600E+00 1.974E-01 7 .4 0 0 E -0 I 1.100E + 03 1.940E+00 2.566E-01 7.200E -01 1.300E + 03 2 .3 9 0 E + 0 0 3.322E -01 7.000E -01 1.400E + 03 2 .7 0 0 E + 0 0 3.664E -01 7.000E -01 1.500E + 03 3.030E+00 4.072E-01 6.900E -01 1.600E + 03 3.530E+00 4.553E 01 6.850E -01 Figure 5.6 Data Input for TRANSENG, Tape 5 (4 of 13) 3-HP COMPRESSOR PERFORMANCE MAP: GRID LINE = 4 OFF 9 SPEED ? P.R.? M.F.P.? EFFC ? (RPM/SQRT(K)) if ) (KG/S )SQRT(K)/(KN/M2) (/) 3.000E+02 1.052E+00 7 .7 3 0 E -0 2 7.800E -01 7.000E+02 1.360E+00 1.316E -01 7.750E -01 9 .0 0 0 E + 0 2 1.630E + 00 1.809E -01 7.700E -01 1.100E + 03 1.980E + 00 2 .5 0 0 E-01 7.500E -01 1.300E+03 2.450E+00 3.289E -01 7.250E -01 1 .400E + 03 2 .7 7 0 E + 0 0 3.651E -01 7.200E -01 1.500E+03 3.120E+00 4.059E-01 7.150E-01 1.600E + 03 3 .6 0 0 E + 0 0 4.520E-01 7.000E-01 HP COMPRESSOR PERFORMANCE MAP: GRID LINE = 5 O FF 9 SP E E D ? P.R.? M.F.P.? EFFC? (RPM/SQRT(K)) HP COMPRESSOR PERFORMANCE MAP: GRID LINE = 6 OFF 9 SPEED ? P.R.? M.F.P.? EFFC? (RPM/SQRT(K)) 00 (KG/S )S QRT(K)/(KN/M2) if) 3 .0 0 0 E + 0 2 1.060E-KK) 3.620E-02 8.000E -01 7 .0 0 0 E + 0 2 1.375E+00 0.987E-01 7.950E -01 9.000E+02 1.665E+00 1.513E-01 7.900E -01 1.100E+03 2.060E+00 2.204E-01 7.850E -01 1.300E + 03 2.5 8 5 E + 0 0 3.059E -01 7.720E -01 1.400E+03 2.925E+00 3.519E -01 7.650E -01 1.500E + 03 3.2 9 0 E + 0 0 3.914E -01 7.500E -01 1.600E+03 3.750E+00 4.355E-01 7.200E -01 HP COMPRESSOR PERFORMANCE MAP: GRID LINE = 7 OFF 9 SP E E D ? P.R.?M.F.P.? EFFC? (RPM/SQRT(K)) 00 (KG/S)SQRT(K)/(KN/M2) if) 3 .0 0 0 E + 0 2 1.064E + 00 1.150E -02 8.000E -01 7 .0 0 0 E + 0 2 1.380E+00 0.757E-01 8.000E -01 9 .0 0 0 E + 0 2 1.675E + 00 1.283E -01 8.000E -01 1.100E + 03 2.070E+00 1.974E-01 8.000E -01 1.300E + 03 2 .6 2 0 E + 0 0 2.829E -01 7.850E -01 1.400E + 03 2.975E+00 3.289E-01 7.800E -01 1.500E + 03 3.380E+00 3.783E-01 7.700E -01 1.600E + 03 3 .8 2 0 E + 0 0 4.276E -01 7.300E -01 HP COMPRESSOR PERFORMANCE MAP: GRID LINE = 8 O FF 9 SP E E D ? P.R.? M.F.P.? EFFC? (RPM/SQRT(K)) 00 (KG/S)SQRT(K)/(KN/M2) if) 3 .0 0 0 E + 0 2 1.065E + 00 1.150E -02 8.000E -01 7 .0 0 0 E + 0 2 1.380E + 00 0.757E -01 8.000E -01 9 .0 0 0 E + 0 2 1.690E+00 1.086E-01 8.000E -01 1.100E + 03 2 .0 8 0 E + 0 0 1.776E -01 8.000E -01 1.300E + 03 2.650E+00 2.632E-01 7.900E -01 1.400E + 03 3 .0 1 0 E + 0 0 3.125E -01 7.850E -01 1.500E + 03 3 .4 6 0 E + 0 0 3.618E -01 7.800E -01 1.600E + 03 3 .9 0 0 E + 0 0 4.112E -01 7.500E -01 Figure 5.6 Data Input for TRANSENG, Tape 5 (5 of 13) * 3- HP COMPRESSOR PERFORMANCE MAP: GRID LINE = 9 O FF 9 * SP E E D ? P.R.?M.F.P.? E FFC ? * (RPM/SQRT(K)) if) (KG/S )S QRT(K)/(KN/M2) if) 3 .0 0 0 E + 0 2 1.065E + 00 0.001E+00 8.000E-01 7 .0 0 0 E + 0 2 1.385E + 00 0.559E -01 8.000E -01 9 .0 0 0 E + 0 2 1.715E + 00 0.888E-01 8.000E-01 1.100E + 03 2.1 0 0 E + 0 0 1.546E-01 8.000E-01 1.300E + 03 2.6 7 0 E + 0 0 2.401E -01 7.950E -01 1.400E + 03 3.0 3 0 E + 0 0 2.895E -01 7.900E -01 1.500E + 03 3.5 2 0 E + 0 0 3.454E-01 7.880E-01 1.600E+03 3.970E+00 3.947E-01 7.700E-01 * 4- HP CHARGE AIR COOLER DIMENSIONS: * CACA ? CACV ? * (M2) (M3) 1.824E-02 1.770E-02 * 5- HP CHARGE AIR COOLER PRESS. LOSS COEFF. AND EFFECTIVENESS CONSTANTS: % CACK? CACEF1 ? C A C E F 2 ? CACEF3 ? TCOOL ? c a c t c ? % if) if) (S/KG) (S 2/K G 2) (K) (S) 5.000E+00 7.500E-01 O.OOOE+OO O.OOOE+OO 3 .0 0 6 E + 0 2 O.OOOE+OO ** 7 A - GAS DYNAMICS IN EXHAUST FLOW SYSTEM:- * 1-NUMBER OF PIPES: * NEP? 0 < N E P < 20 * if) 12 * 2- PIPE DATA,EXHAUST: (PIPE U 1) * PIPL?AP?MESH? PREF?TREF? FREF? PPIPE ? * (M ) (M 2) if) (K N /M 2) (K) if) (K N /M 2 ) 5.072E-01 4.560E-03 14 2 .6 6 0 E + 0 2 7 .5 0 0 E + 0 2 2.060E-01 3.300E+02 * 3- PIPE DAT A, EXHAUST: (PIPE # 2) * PIPL?AP?MESH? PREF?TREF? FREF? PPIPE ? * (M ) (M 2) if) (K N /M 2) (K) if) (K N /M 2 ) 3.929E -01 4 .5 6 0 E -0 3 11 2 .6 6 0 E + 0 2 7 .5 0 0 E + 0 2 2.060E -01 3 .3 0 0 E + 0 2 * 4- PIPE DATA,EXHAUST: (PIPE # 3) * PIPL?AP?MESH?PREF? TREF? FREF? P PIPE ? * (M ) (M 2) if) (K N /M 2) (K) if) (K N /M 2 ) 7.562E -01 4.560E-03 21 2.660E+02 7 .5 0 0 E + 0 2 2.060E-01 3.300E+02 * 5- PIPE DAT A,EXHAUST: (PIPE # 4) * PIPL?AP?MESH? PREF?TREF? FREF? PPIPE ? * (M) (M 2) if) (K N /M 2) (K) if) (K N /M 2 ) 4.310E -01 4 .560E -03 12 2.660E+02 7.500E+02 2.060E-01 3 .3 0 0 E + 0 2 * 6- PIPE DAT A,EXHAUST: (PIPE #5) * PIPL?AP? MESH?PREF? TREF? FREF? PPIPE ? * (M) (M 2) if) (K N /M 2) (K) if) (K N /M 2 ) 4.691E -01 4 .5 6 0 E -0 3 13 2 .6 6 0 E + 0 2 7 .5 0 0 E + 0 2 2.060E -01 3 .3 0 0 E + 0 2 * 7- PIPE DAT A, EXHAUST: (PIPE # 6) * PIPL?AP? MESH?PREF? TREF?FREF? PPIPE ? 4c (M) (M 2) if) (K N /M 2) (K) if) (K N /M 2 ) 5.022E -01 4.56 0 E -0 3 14 2.660E+02 7.500E+02 2.060E-01 3.300E+02 4c 8- PIPE DATA,EXHAUST: (PIPE # 7 ) * PIPL? AP? MESH? PREF ? TREF? FREF? PPIPE ? 4 (M) (M 2) if) (K N /M 2) (K) if) (K N /M 2 ) 5.072E-01 4.560E-03 14 2 .6 6 0 E + 0 2 7 .5 0 0 E + 0 2 2.060E -01 3 .3 0 0 E + 0 2 Figure 5.6 Data Input for TRANSENG, Tape 5 (6 of 13) * 9 -PIPE DATA,EXHAUST: (PIPE # 8) * PIPL ? AP?MESH? PREF? TREF? FREF? PPIPE ? * (M ) (M 2) (/) (K N /M 2) (K) (/) (K N /M 2 ) 3 .9 2 9 E -0 1 4.560E-03 11 2 .6 6 0 E + 0 2 7 .5 0 0 E + 0 2 2.060E -01 3 .3 0 0 E + 0 2 * 10- PIPE DATA.EXHAUST: (PIPE # 9 ) * P IP L ? AP?MESH? PREF? TREF? FREF? PPIPE ? * (M ) (M 2} in (K N /M 2) (K) in (K N /M 2 ) 6.895E-01 4.560E-03 19 2 .6 6 0 E + 0 2 7.500E+02 2.060E-01 3 .3 0 0 E + 0 2 * 11- PIPE DATA,EXHAUST: (PIPE # 1 0 ) * PIPL ? AP? MESH? PREF? TREF?FREF? PPIPE ? * (M ) (M 2) U) (K N /M 2) (K) in (K N /M 2) 3.548E-01 4.560E-03 10 2 .6 6 0 E + 0 2 3.300E+02 2.060E-01 3 .3 0 0 E + 0 2 * 12- PIPE DATA,EXHAUST: (PIPE # 1 1 ) * PIPL ? A P ? M E S H ? PREF?TREF?FREF? PPIPE ? * (M ) (M 2) in (K N /M 2) (K) in (K N /M 2) 4 .8 1 8 E -0 1 4.56 0 E -0 3 13 2.660E+02 7.500E+02 2.060E-01 3 .3 0 0 E + 0 2 * 13- PIPE DATA,EXHAUST: (PIPE # 1 2 ) * PIPL ? AP? MESH? PREF? TREF?FREF? PPIPE ? * (M ) (M 2) in (K N /M 2) (K) in (K N /M 2) 6.133E-01 4.560E-03 17 2 .6 6 0 E + 0 2 7.500E+02 2.060E-01 3 .3 0 0 E + 0 2 :- CONNECTION OF CYLINDERS TO MANIFOLDS/PIPES:- * 14- CONTROL VOL. NO. AT INLET OF CYLINDER I: * N IN L (I) ? 1==1,NCYL * (/) 9 9 9 9 9 9 9 * 14- CONTROL VOL NO AT OUTLET OF CYLINDER I: * N E X C V (I) ? I= 1,N C Y L * (/) 0 0 0 0 0 0 0 * 14- CONTROL VOL NO AT HP TURBINE ENTRY I : * NPRETUR(I) ? I=1,NTEM(1) * (/) 11 13 15 17 * 15- CONTROL VOL NO UPSTREAM OF PIPE I : * N F E U P (I) ? I= 1,N E P * (/) 1 2 10 3 4 12 5 14 7 8 16 * 15- C O N T R O L VOL NO DOWNSTREAM OF PIPE I : * N F E D N (I) ? 1=1, NE P * (/) 10 10 11 12 12 13 14 15 16 16 17 * 16- E X H A U S T PIPE BOUNDARY DATA: (PIPE # 1) * N V B 1 ? IB1 ? PF1 ? N V B 2 ? EB2 ? PF2 ? * (/) (/) in (/) in in 0 5 Q.000E+-00 0 4 5.000E -01 * 17- E X H A U S T PIPE BOUNDARY DATA: (PIPE # 2) * N V B 1 ? EB1 ? PF1 ? N V B 2 ? IB 2 ? PF2 ? * (/) 09 in in in in 0 5 O.OOOE+OO 0 4 5.000E -01 Figure 5.6 Data Input for TRANSENG, Tape 5 (7 of 13) * 18- EXHAUST PIPE BOUNDARY DATA: (PIPE #3 ) * NVB1 ? EB1 ? PF1 ? NVB2 ? m 2 ? PF2 ? 4c if) if) if) if) if) if) 0 4 O.OOOE+OO 0 4 O.OOOE+OO ★ 19- EXHAUST PIPE BOUNDARY DATA: (PIPE #4 ) 4c NVBl ? IB1? PF1 ? NVB2 ? m 2 ? PF2 ? * if) (/) , (/) (/) (/) if) 0 5 O.OOOE+OO 0 4 5.000E-01 4c 20- EXHAUST PIPE BOUNDARY DATA: (PIPE # 5) 4c NVBl ? IB1? PF1 ? NVB2 ? ffi2? PF2 ? * if) (/) V) (/) if) if) 0 5 O.OOOE+OO 0 4 5.000E-01 4< 21- EXHAUST PIPE BOUNDARY DATA: (PIPE # 6) * NVBl ? IB1 ? PF1 ? NVB2 ? m2 ? PF2 ? * if) (/) (I) (/) (/) if) 0 4 O.OOOE+OO 0 4 O.OOOE+OO 4c 22- EXHAUST PIPE BOUNDARY DATA: (PIPE # 7) 4c NVBl ? m i ? PFl ? NVB2 ? m 2 ? PF2 ? * (/) if) (/) (/) (/) if) 0 5 O.OOOE+OO 0 4 5.000E-01 * 23- EXHAUST PIPE BOUNDARY DATA: (PIPE # 8) * NVBl ? m i ? PFl ? NVB2 ? m 2 ? PF2 ? * if) 00 00 if) if) if) 0 5 O.OOOE+OO 0 4 5.000E-01 * 24- EXHAUST PIPE BOUNDARY DATA: (PIPE # 9) * NVBl ? m i ? PFl ? NVB2 ? m2 ? PF2 ? * if) 00 if) (/) if) if) 0 4 O.OOOE+OO 0 4 O.OOOE+OO * 25- EXHAUST PIPE BOUNDARY DATA: (PIPE #10) * NVBl ? m i ? PFl ? NVB2 ? m 2 ? PF2 ? 4c if) (0 if) (/) (/) if) 0 5 O.OOOE+OO 0 4 5.000E-01 4" 26- EXHAUST PIPE BOUNDARY DATA: (PIPE #11) * NVBl ? m i ? PFl ? NVB2 ? m 2 ? PF2 ? 4c if) 00 if) if) if) (/) 0 5 O.OOOE+OO 0 4 5.000E-01 * 27- EXHAUST PIPE BOUNDARY DATA: (PIPE #12) 4c NVBl ? m i ? PFl ? NVB2 ? m 2 ? PF2 ? 4c if) (/) if) if) (/) if) 0 4 O.OOOE+OO 0 4 O.OOOE+OO 9- EXHAUST FLOW SYSTEM:- 4c 1 - HP TURBINE IDENTIFICATION AND SIZE: ★ DTURB ? it u r b ? EFMEC ? * (M) (KG.M2) if) 2.460E-01 1.000E+02 1.000E+00 * O UP IDDIWC ______-MAP# 1 * SCALE FACTORS NUMBER OF SPEED LINES TURNDOWN * TSFM ? TSFE ? NSPLM ? NSPLE? S V G M A P ? * if) (/) if) if) if) 1.000E->-00 9.500E-01 6 5 1.000E+00 Figure 5.6 Data Input for TRANSENG, Tape 5 (8 of 13) 3-HP TURBINE DIGITISATION OF P.R. -VS- M.F.P. SPEED PARAMETER DATA POINTS ------SPP(I)? NDATA(I) ? 1=1,6 SPEED LINES (RPM/SQRT(K)) if) 2 .8 0 0 E + 0 2 13 4 .2 0 0 E + 0 2 13 5 .6 0 0 E + 0 2 13 7 .0 0 0 E + 0 2 13 8 .4 0 0 E + 0 2 13 9 .8 0 0 E + 0 2 11 4- HP TURBINE, P.R. -VS- M.F.P. DATA @ 2.800E+02 (RPM/SQRT(K)) P R (I) ? M.F.P(I) ? 1=1,13 POINTS if) ((KG/S)S QRT (K)/(KN/M2)) 1 .000E + 00 O.OOOE+OO 1.020E + 00 6.140E -02 1.0 5 0 E + 0 0 9.420E -02 1.100E + 00 1.267E -01 1 .206E + 00 1.643E -01 1 .287E + 00 1.850E -01 1.376E + 00 2.016E -01 1.469E + 00 2.145E -01 1.563E + 00 2.241E -01 1.659E + 00 2.310E -01 1.758E + 00 2.354E -01 1.862E + 00 2.379E -01 1 .983E + 00 2.389E -01 5- HP TURBINE, P.R. -VS- M.F.P. DATA @ 4.200E+02 (RPM/SQRT(K)) PR (I) ? M.F.P(I) ? 1=1,13 POINTS if) ((KG/S)SQRT(K)/(KN/M2)) 1.000E + 00 O.OOOE+OO 1.020E + 00 6.140E -02 1.050E + 00 9 .420E -02 1 .100E + 00 1.267E -01 1.232E + 00 1.643E -01 1.327E + 00 1.848E -01 1.432E + 00 2.013E -01 1.547E + 00 2.141E -01 1.671E + 00 2.237E -01 1.810E + 00 2 .3 0 4 E-01 2 .1 8 8 E + 0 0 2.374E -01 2 .6 9 5 E + 0 0 2.384E -01 6- HP TURBINE, P.R. -VS- M.F.P. DATA @ 5.600E+02 (RPM/SQRT(K)) PR(I) ? M.F.Pa)? 1=1,13 POINTS if) ((KG/S)SQRT(K)/(KN/M2)) 1.000E + 00 O.OOOE+OO 1.020E + 00 6.140E -02 1.050E + 00 9 .4 2 0 E -0 2 1.100E + 00 1.267E -01 1.262E + 00 1.642E -01 1.359E + 00 1.844E -01 1.475E + 00 2.006E -01 1 .603E + 00 2.131E -01 1.745E + 00 2.225E -01 1.908E + 00 2.292E -01 2 .1 0 0 E + 0 0 2.335E -01 2 .3 4 9 E + 0 0 2.360E -01 2 .8 2 0 E + 0 0 2.369E -01 Figure 5.6 Data Input for TRANSENG, Tape 5 (9 of 13) 7- HP TURBINE, P.R. -VS- M.F.P. DATA @ 7.000E+02 (RPM/SQRT(K)) PR(I)? M.F.P(I) ? 1=1,13 POINTS (/) ((KG/S)SQRT(K)/(KN/M2)) 1 .0 0 0 E + 0 0 0 .0 0 0 E + 0 0 1 .020E + 00 6.140E -02 1 .050E + 00 9 .4 2 0 E -0 2 1.1 0 0 E + 0 0 1.267E -01 1.2 7 8 E + 0 0 1.642E -01 1 .404E + 00 * 1.839E-01 1.525E+00 1.996E-01 1.655E + 00 2.118E -01 1 .805E + 00 2.210E -01 1.979E+00 2.274E-01 2.186E+00 2.317E-01 2.442E+00 2.352E-01 2.889E+00 2.350E-01 8- HP TURBINE. P.R.-VS-M.F.P. DATA @ 8.400E+02 (RPM/SQRT(K)) PR(I)? M.F.P(I) ? 1=1,13 POINTS (/) ((KG/S )S QRT(K)/(KN/M2)) 1.0 0 0 E + 0 0 O.OOOE+OO 1.020E+00 6.140E-02 1.050E+00 9.420E-02 1 .100E + 00 1.267E -01 1.200E+00 1.633E-01 1 .405E + 00 1.826E -01 1.567E+00 1.974E-01 1 .725E + 00 2.089E -01 1.885E + 00 2.175E -01 2.060E+00 2.236E-01 2 .2 5 8 E + 0 0 2.276E -01 2 .4 9 2 E + 0 0 2.298E -01 2 .8 5 4 E + 0 0 2.307E -01 9- HP TURBINE, P.R. -VS- M.F.P. DATA @ 9.800E+02 (RPM/SQRT(K)) PR(I) ? M.F.Pa)? 1=1,11 POINTS (/) ((KG/S)SQRT(K)/(KN/M2» 1 .000E + 00 O.OOOE+OO 1.020E+00 6.140E-02 1.050E+00 9.420E-02 1.100E + 00 1.267E -01 1.200E+00 1.633E-01 1.425E+00 1.830E-01 1.580E-KX) 1.960E-01 1.750E+00 2.020E-01 1.9 0 0 E + 0 0 2.120E -01 2.250E+00 2.200E-01 2.850E+00 2.250E-01 10-HP TURBINE DIGITISATION OF U/C-VS-EFnCIENCY SPEED PARAMETER DATA POINTS ------SPP(I) ? NDATA(I) ? 1=1,5 SPEED LINES (RPM/SQRT(K)) (/) 2.800E+02 12 4.200E+02 11 5 .6 0 0 E + 0 2 11 7.000E+02 12 8 .4 0 0 E + 0 2 10 Figure 5.6 Data Input for TRANSENG, Tape 5 (10 of 13) * 1 1 - H P T U R B IN E , U /C -VS- EFFCY DATA DA @ 2.800E+02 (RPM/SQRT(K)) * U /C (I) ? EFFC Y (I) ? 1=1,12 POINTS * (/) (D O.OOOE+OO 0.0 0 0 E + 0 0 2.160E-01 5.380E-01 2 .610E -01 6.040E -01 2.970E-01 6.460E-01 3.640E-01 7.090E-01 4 .2 1 0 E -0 1 7.450E -01 4.500E-01 7.550E-01 5.000E-01 7.670E-01 5.500E-01 7.670E-01 6.000E -01 7.600E -01 7.560E-01 6.400E-01 1.3 0 0 E + 0 0 O.OOOE+OO *12-HP TURBINE, U/C -VS- EFFCY DA' * U /C (I) ? EFFC Y (I) ? 1=1,11 POINTS * (/) (!) O.OOOE+OO O.OOOE+OO 3.20 0 E -0 1 6.630E -01 3 .630E -01 7.110E -01 4.20 0 E -0 1 7.500E -01 4.60 0 E -0 1 7.680E -01 5.160E-01 7.780E-01 5.600E-01 7.780E-01 5.980E -01 7.660E -01 6.960E -01 7.000E -01 7.560E -01 6.400E -01 1 .250E + 00 O.OOOE+OO *13-HP TURBINE, U/C -VS-EFFCY DArDATA @ 5.600E+02 (RPM/SQRT(K)) * u/ca> ? E F FC Y (I) ? 1=1,11 POINTS * (/) ( f) O.OOOE+OO O.OOOE+OO 3.600E-01 6.750E-01 4.100E -01 7.370E -01 4.370E-01 7.570E-01 4.660E-01 7.720E-01 4 .9 9 0 E -0 1 7.810E -01 5.390E -01 7.840E -01 5.910E-01 7.750E-01 6.620E-01 7.400E-01 7.560E -01 6.390E -01 1 .300E + 00 O.OOOE+OO *14-HP TURBINE, U/C -VS-EFFCY DA"DATA @ 7.000E+02 (RPM/SQRT(K)) * U /C (I) ? E F FC Y (I) ? 1=1,12 POINTS * (/) (/) O.OOOE+OO O.OOOE+OO 4.19 0 E -0 1 6.990E -01 4 .4 8 0 E -0 1 7.360E -01 4.66 0 E -0 1 7.520E -01 5.030E -01 7.750E -01 5.330E -01 7.830E -01 5.670E -01 7.830E -01 6.070E -01 7.730E -01 6.540E -01 7.480E -01 7.880E -01 6.000E -01 9.210E -01 4.210E -01 1 .300E + 00 O.OOOE+OO Figure 5.6 Data Input for TRANSENG, Tape 5 (11 of 13) *15- HP TURBINE, U/C -VS-EFFCY DADATA @ 8.400E+02 (RPM/SQRT(K)) * U /C (I) ? E FFC Y (I) ? 1=1,10 POINTS * if) if) 0 .0 0 0 E + 0 0 O.OOOE+OO 4 .990E -01 7.100E -01 5.34 0 E -0 1 7.390E -01 5.62 0 E -0 1 7.520E -01 6.700E -01 7.560E -01 6.280E -01 ' 7.480E-01 7.050E -01 6.910E -01 8.280E -01 5.480E -01 9 .440E -01 3.970E -01 1.2 1 0 E + 0 0 O.OOOE+OO 10- SIMULATION PARAMETERS:- * 1- NO. STEPS PER CYCLE FACTOR FOR LAST CYCLE * N C A C Y NCAFAC * if) if) 7 2 0 1 * 2- RELAXATION FACTORS: * RF1 ? * if) 5 .0 0 0 E -0 1 * 3- NUMBER OF CYCLES REQUESTED FOR SIMULATION: * N C S S ? NCTR1? NCTR2 ? NCYCOP? TRANS ? * if) if) if) if) if) 5 0 0 0 F * 4- VOLUME NUMBERS FOR OUTPUT TAPES * ID C Y L ? ID IN ? IDEX1 ? IDEX2 ? IDEX3 ? IDEX4 * if) if) if) if) if) (/) 1 9 10 11 12 13 * 5- PIPE NUMBERS FOR OUTPUT TAPES : * I D P 1 ? IDP2 ? IDP3 ? IDP4 ? * if) if) if) (/) 1 3 3 1 Figure 5.6 Data Input for TRANSENG, Tape 5 (12 of 13) 11- ENGINE OPERATING CONDITIONS:- * 1- AMBIENT CONDITIONS AND EXHAUST BACK PRESSURE: * PAMB? TAMB? PBACK ? PBOOST? TBOOST? * (KN/M2) (K) (KN/M2) (KN/M2) (K) 1.014E+02 2.930E+02 1.014E+O2 2.763E+02 3.340E+02 * 2- ENGINE SPEED AND FUELLING: * E S P D ? W F C Y ? * (RPM) (KG) 1.500E+03 7.018E-04 * 3- TURBOCHARGER SPEED: * TCSP(I) ? I=l,NCOMP * (R PM ) 2.4 3 5 E + 0 4 * 4- PRESSURE IN CONTROL VOLUMES: * PP(I) ? I= 1,N C V M A X * (K N /M 2) 2.680E+02 3.600E+02 1.000E + 04 2 .6 0 0 E + 0 2 2 .7 0 0 E + 0 2 7 .0 0 0 E + 0 2 6.0 0 0 E + 0 2 3 .0 0 0 E + 0 2 2 .7 6 0 E + 0 2 3 .4 7 0 E + 0 2 3 .0 0 0 E + 0 2 1.800E + 02 1.600E + 02 2 .8 7 0 E + 0 2 2.670E+02 3.160E+02 3.100E+02 * 5- TEMPERATURES IN CONTROL VOLUMES: * T P (I) ? I= 1,N C V M A X * (K ) 3.590E+02 8.500E+02 1.100E+03 3.590E+02 3.590E+02 9.900E+02 4.500E+02 8.000E+02 3.340E+02 9.000E+02 9.000E+02 6.400E+02 6.400E+02 9.000E+02 9.000E+02 8.300E+02 8.300E+02 * 7- EQUIVALENCE RATIO IN CONTROL VOLUMES: * FP(I) ? I=1,NCVMAX * 00 8.000E-04 5.000E-01 5.000E-01 8.000E-04 8.000E-04 5.000E-01 5.000E-01 8.000E-04 1.000E-06 5.000E-01 5.000E-01 5.000E-01 5.000E-01 5.000E-01 5.000E-01 5.000E-01 5.000E-01 Figure 5.6 Data Input for TRANSENG, Tape 4 (13 of 13) gure 5. air A8 Trohre Trie wloig Capacity Swallowing Turbine Turbocharger SA084 Napier .7 5 e r u ig F Turbine Total-to-Static Enpansion Ratio (/) .0 3 Mass-floiu Parameter (kg/s sqrt (K)/kPa) sqrt (kg/s Parameter Mass-floiu 420 o 560 • 280 - 840 * ' 980 ' * 700 ♦ ( K [ \ j m p r n /V t ) g e . Npe S04 ubcagr ubn Efficiency Turbine Turbocharger SA084 Napier 5.8 re igu F Turbine Total-to-static Efficiency (/) ld SedRto UC (/) U/C Ratio, Speed Blade 700 — 560 — 420 — —-" 840 —'— ( 280 rpm/y/K) N/y/f STEADY STATE CYCLE # 5 IN CYCLE CYLINDER DATA: (CRANK ANGLES W.R.T.,BDC=0 INCLUDE CYL.PHASE ANGLE) C Y L . 1 C Y L . 2 C Y L . 3 C Y L . 4 C Y L . 5 C Y L . 6 C Y L . 7 C Y L . 8 VOLJEFF. 102.855 99 .9 0 2 101.030 99.978 102.375 9 9 .9 4 4 101.207 99.841 (INLET MAN.COND (/) SCAVENGE EFF.(/) 104.404 101.575 102.647 101.619 103.968 101.5 9 5 102.816 101.502 MASS OF AIR .1947E -01 .1891E -01 .1913E -01 .1893E-01 .1938E-01 .1892E -01 .1916E -01 .1890E -01 INDUCED (KG) DYN.INJ.PT 168.00 168.00 168.00 168.00 168.00 168.00 168.00 168.00 (DEG.CA, BDC=0) IG N . P O IN T 172.96 172.93 172.94 172.93 172.95 172.93 172.94 172.93 (DEG.CA, BDC=0) END OF BURNING 297.96 297.93 297.94 2 97.93 297.95 297.93 2 9 7 .9 4 2 97.93 (DEG.CA, BDC=0) INJECTION DELAY (S) .8333E-03 .8333E-03 .8333E-03 .8333E-03 .8 333E -03 .8333E-03 .8333E-03 .8333E -03 IGNITION DELAY (S) .5507E-03 .5474E-03 .5485E-03 .5481E-03 .5498E-03 .5477E-03 .5491E-03 .5476E-03 MEAN PRESS. IN 7 2 .0 7 5 72.021 72.049 72.031 72.058 72.030 72.048 72.025 IGNITION DELAY (BAR) M E A N TEM P. 874.7 0 9 875.7 2 0 875.348 875.509 8 7 4 .9 9 4 875.620 875.208 875.648 IN IGNITION DELAY (K) TRAPPED MASS IN .1865E-01 .1862E-01 .1863E-01 .1863E-01 .1864E-01 .1862E-01 .1863E -01 .1862E -01 COMPRESS.(KG) TOTAL FUEL BURNT .7013E-03 .7014E-03 .7014E-03 .7014E-03 .7013E-03 .7014E-03 .7014E-03 .7014E -03 (KG/CYC/CYL) TRAPPED EQUIVALENCE .5635 .5653 .5 6 4 6 .5648 .5 6 4 0 .5 6 5 0 .5644 .5651 RATIO E.O.B (/) MAX. CYLINDER PRESS 12634.55 12640.78 12638.00 12639.45 126 3 6 .0 6 126 4 0 .7 8 12637.64 12640.41 (K N /M 2) POS. OF PMAX. 192.00 192.00 192.00 192.00 1 92.00 192.00 192.00 192.00 (DEG.CA,TDC=0) MAX. CYLINDER TEMP. 1844.74 1847.26 1846.27 1846.76 1845.46 1846.97 1845.99 1847.10 (K) POS. OF TMAX. 2 1 0 .0 0 210.00 210.00 210.00 2 1 0 .0 0 2 1 0 .0 0 2 1 0 .0 0 2 1 0 .0 0 (DEG.CA,TDC=0) MAX. DP/DT IN CYL. 4.18E+02 4.19E+02 4.19E+02 4.19E+02 4 .1 8 E + 0 2 4 .1 9 E + 0 2 4.19E+02 4.19E+02 ((KN/M2)/S) POS MAX DP/DT 175.00 175.00 175.00 175.00 175.00 175.00 175.00 175.00 (DEG.CA,TDC=0) PRESSURE CHARGING SYSTEM: TURBOCHARGER PERFORMANCE (TIME AVERAGED OVER THE CYCLE) HP.TURB HP.TURBHP.TURB HP.TURB HP.COMP ENTRY 1 ENTRY 2 E N T R Y 3 E N T R Y 4 PRESSURE RATIO (TOTAL TO STATIC) 2.402E+00 2.439E+00 2.411E+00 2 .4 3 1 E + 0 0 2 .8 7 8 E + 0 0 MASS FLOW PARAMETER 5.213E-02 5.132E-02 5 .1 9 2 E -0 2 5 .128E -02 3.734E -01 ((KG/S).SQRT(K)/(KN/M2)) MASS FLOW RATE (KG/S) 5.067E -01 5.024E -01 5.055E -01 5.025E -01 2.2 1 2 E + 0 0 ISENTROPIC EFFICIENCY 6.598E -01 6.517E -01 6.580E-01 6.525E-01 7.279E -01 (TOTAL TO STATIC, ENERGY AVG) TURBOCHARGER ISEN. EFFICIENCY 4.77 1 E -0 1 (TOTAL TO STATIC) MASS-AVERAGED POWER (KW) 6.657E + 01 7.121E+01 6.773E+01 7.059E + 01 3 .183E + 02 SPEED (REV/MIN) O.OOOE+OO 0.0 0 0 E + 0 0 O.OOOE+OO 0 .0 0 0 E + 0 0 2.435E + 04 TORQUE (NM) 2.180E + 01 2.291E+01 2.209E+01 2.272E + 01 1.249E +02 ISENTROPIC WORK AVAILABILITY 8.426E+01 8.964E+01 8.559E+01 8.878E + 01 FROM EXHAUST GAS ENERGY (KJ) Figure 5.9 Predicted Overall Performance at Test Point 6 (1 of 2) DIAGNOSTICS FOR TURBINE AND COMPRESSOR MAPS: OPERATION WITHIN MAP BOUNDARIES 6.9 7.4 6 .8 7 .4 100.0 (% OF CYCLE) COMPESSOR SURGE (% OF CYCLE) .0 .0 .0 .0 .0 CHOKE (% OF CYCLE) 31.7 38.1 3 1 .8 3 6 .9 .0 OVERSPEED 33.6/85.8 31.1/81.3 31.0/85.0 32.9/81.5 .0 / .0 (M.F.P MAP / TURB. EFFCY. MAP) (% OF CYCLE) UNDERSPEED .0/ .0 .0/ .0 .0/ .0 .0 / .0 .0 / .0 (M.F.P MAP / TURB. EFFCY. MAP) (% OF CYCLE) TURB. U/C RATIO ABOVE , 10.1 9.3 10.4 9.7 SPECIFIED MAX. (% OF CYCLE) TURB. U/C RATIO BELOW .0 .0 .0 .0 SPECIFIED MIN. (% OF CYCLE) TURB. P.R BELOW SPECIFIED MIN. .0 2.1 .0 2.1 (% OF CYCLE) CHARGE AIR COOLER PERFORMANCE (TIME AVERAGED OVER THE CYCLE) HP.CAC INLET TEMPERATURE (K) 4 .3 3 5 E + 0 2 OUTLET TEMPERATURE (K) 3 .3 3 8 E + 0 2 EFFECTIVENESS (/) 7.500E -01 PRESSURE LOSS (KN/M2) 1.569E + 01 CYCLE AVERAGED INTEGRATION PARAMETERS: VOL. FLOW IN FLOW H.T. CYL.WK. IMEPP.TA T .T A P .M A T.MA NO.(KG)OUT(KG)(KJ) (KJ) (KN/M2) (K N /M 2) (K) (KN/M2) (K) 1 1.947E-02 2.055E-02 3.276E+00 1.323E +01 2 .0 1 2 E + 0 3 2 1.890E-02 1.995E-02 3.338E+00 1.307E +01 1.988E + 03 3 1.912E-02 2.020E-02 3.304E+00 1.316E +01 2.0 0 2 E + 0 3 4 1.891E-02 1.996E-02 3.347E+00 1.303E+01 1.982E + 03 5 1.938E-02 2.046E-02 3.285E+00 1.321E+01 2 .0 1 0 E + 0 3 6 1.890E-02 1.996E-02 3.339E+00 1.306E +01 1.987E + 03 7 1.915E-02 2.023E-02 3.300E+00 1.317E +01 2 .0 0 4 E +03 8 1.888E-02 1.994E-02 3.347E+00 1.303E+01 1.983E+03 9 1.770E-01 1.527E-01 0 .0 0 0 E + 0 0 2.761E+02 3.341E+02 10 4 .0 5 1 E -0 2 4.051E-02 4.096E+00 2 .485E + 02 7.481E+02 2.751E+02 8.033E +O 2 11 4.054E-02 4.054E-02 2.779E+00 2.435 E+02 6.720E+02 2.681E+02 6.9 8 2 E + 0 2 12 4.018E-02 4.018E-02 4.107E+00 2 .526E + 02 7.492E+02 2.836E+02 8.0 3 1 E + 0 2 13 4.019E-02 4.019E-02 1.966E + 00 2.473E+02 6.936E+02 2.760E+02 7 .2 8 7 E + 0 2 14 4.042E-02 4.042E-02 4 .1 1 7 E + 0 0 2.496E+02 7.501E+02 2.773E+02 8.0 3 0 E + 0 2 15 4.044E-02 4.044E-02 2.580E+00 2.445E + 02 6.782E+02 2.700E+02 7 .0 6 0 E + 0 2 16 4.018E-02 4.018E-02 3 .8 2 7 E + 0 0 2 .517E + 02 7.498E+02 2.823E+02 8 .129E + 02 17 4.020E-02 4 .0 2 0 E -0 2 2.3 4 5 E + 0 0 2.465E + 02 6.848E+02 2.749E+02 7 .2 3 0 E + 0 2 OVERALL ENGINE PERFORMANCE PARAMETERS: IMEP BMEP FMEP INDICATED POWER BRAKE POWER MECH. EFFICIENCY (K N /M 2) (K N /M 2) (K N /M 2) (KW) (KW) (/) 1.996E + 03 1.743E + 03 2.5 2 8 E + 0 2 1.312E + 03 1.146E +03 8.733E -01 ISFC ISAC BSFC BSAC AIR/FUEL RATIO (KG/KW-HR) (KG/KW-HR) (KG/KW-HR) (KG/KW-HR) (OVERALL) 1.926E -01 5 .2 3 7 E + 0 0 2.205E -01 5 .9 9 7 E + 0 0 2.720E + 01 NO. ITERATIONS CYBER 180-855 CPS (/) (S) 1064 185 Figure 5.9 Predicted Overall Performance at Test Point 6 (2 of 2) g e .0 rdce Ms-lw ae truh ne ad xas Valves Exhaust and Inlet through Rates Mass-flow Predicted 5.10 re igu F Mass Flow Rates Through Inlet and Enhaust Uali/es (kg/s) et on 6 Point Test Crank Angle (degrees) g e .1 ntnaeu Sai Pesrs n xas Mnfl at Manifold Exhaust in Pressures Static Instantaneous 5.11 re igu F Static Pressures in Euhaust Manifold (bar) oi ln: xeietl rkn ie predicted line: broken experimental line: solid et on 6 Point Test rn Age (degrees) Angle Crank gure 5. dfcto t Ehut av Ae Poie o lo fr Elasticity for Allow to Profile Area Valve Exhaust to odification M 2 .1 5 e r u ig F EHhaust-ualue Floiu Area (mA2 ) n xas Vle System Valve Exhaust in Crank Angle (degrees) CrankAngle gure 51 Cmaio o Sai Pesrs rdce Wt ad ihu Ex Without and With Predicted Pressures Static of Comparison 5.13 e r u ig f Static Pressures in Enhaust Manifold (bar) oi ln: xeietl og ah wt elasticity with dash: long elasticity no dash: short experimental line: solid Elasticity Valve haust Crank Angle (degrees) Angle Crank Enhaust Static Pressure By Cylinder B8 (bar) gure 5. oprsn fSai Pesrs rdce Wih n Wihu Ha Transfer Heat ithout W and ith W Predicted Pressures Static of Comparison 4 .1 5 e r u ig F oi ln: xeietl og ah wt ha tase sot ah n ha transfer heat no dash: short transfer heat with dash: long experimental line: solid 0 4 5 Actual Geometry Approximate Model Pressure Recovery Geometry Factor (/) I Sudden 0.5 Junction -** Expansion Turbine Diffuser 0.83 Entry ( r Figure 5.15 Summary of Pressure Recovery Models Applied gure 5. oprsn f ttc rsue Peitd ih ifrn Pesr-eoey Factors Pressure-recovery Different with Predicted Pressures Static of Comparison 6 .1 5 e r u ig F Exhaust Static Pressure By Cylinder B8 (bar) oi ln: xeietl og ah cs 1 eim ah cs 3 hr ds: ae 2 case dash: short 3 case dash: medium 1 case dash: long experimental line: solid CrankAngle(degrees) gure 5. oprsn f ttc rsue Peitd ih oze onay n Oe-n Budr Peeig Turbine Preceding Boundary Open-end and Boundary Nozzle with Predicted Pressures Static of Comparison 7 .1 5 e r u ig F Exhaust Static Pressure fit Turbine End (bar) oi ln: xeietl eim ah oe ed hr ds: nozzle dash: short end open dash: medium experimental line: solid CrankAngle(degrees) g e 5.18 re igu F Euhaust Static Pressure By Cylinder B8 (bar) oprsn f ttc rsue Peitd sn Dfeet ubn Salwn Capacities Swallowing Turbine Different Using Predicted Pressures Static of Comparison oi ln: xeietl og ah 10 cpct mdu ds: 0 cpct sot ah 8% capacity 80% dash: short capacity 90% dash: medium capacity 100% dash: long experimental line: solid Crank flngleCrank (degrees) .80 Figure 5.19 Dibelius’ Variation of Turbine Efficiency and Coefficient of Dis charge for Partial Admission [ 51 ] g e .0 rdce asfo ae hog h orTrieEtisa et on 6 Point Test at Entries Turbine Four the through Rates Mass-flow Predicted 5.20 re igu F Turbine Mass-flow Parameter (kg/s sqrt(K)/kPa) Crank Angle (degrees) Turbine Pressure Ratio (/) g e .1 rdce ubn xaso aisars h orTrieScos t et on 6 Point Test at Sectors Turbine Four the across Ratios Expansion Turbine Predicted 5.21 re igu F -180 0 Crank Angle (degrees) 180 360 540 gur 52 Rvsd ubn Salwn Cpct Data Capacity Swallowing Turbine Revised 5.22 re u ig F Turbine Total-to-static Enpansion Ratio (/) 4 Mass-flow Parameter (kg/s Parameter sqrt(K)/kPa) Mass-flow □ 196 « 392 □ a o m 784 ♦ K [ \ / m p ( r 588 1176 n 980 V / t ) g e .3 eie Trie fiiny Data Efficiency Turbine Revised 5.23 re igu F Turbine Total-to-static Efficiency (/) 0.6 0.4 0.0 0.2 0.8 . 05 1.0 0.5 0.0 Blade Speed Ratio, U/C (/) T 392 □ 196 ♦ a 980 o 1176 ■ 784 ♦ 588 ( p /y/K rpm /y/T N ) gur 52 Cmaio o Sai Pesrs rdce wt Vral ad Con and Variable with Predicted Pressures Static of Comparison 5.24 re u ig F Static Pressures in Enhaust Manifold (bar) oi ln: xeietl eim ah cntn Cd constant dash: medium Cd variable dash: short experimental line: solid Cd Valve stant Crank Angle (degrees) gure 5. ia Peitd xas Sai Pesrs t et on 6 Point Test at Pressures Static Exhaust Predicted Final 5 .2 5 e r u ig F Static Pressures in Enhaust Manifold (bar) oi ln: xeietl ah predicted dash: experimental line: solid Crank Angle (degrees) g e 26 Cmaio o ia Peitd ttc rsue ih Shifted with Pressures Static Predicted Final of Comparison 6 .2 5 re igu F Static Pressures in Enhaust Manifold (bar) 5 oi ln: experimental line: solid xeietl Data Experimental Location fl8 Location Crank Angle (degrees) ahd ie predicted line: dashed gure 6. et on 1 Peitd n Eprmna Ehut Pressures Exhaust Experimental and Predicted 1. Point Test .1 6 e r u ig F Static Pressures in Enhaust Manifold (bar) oi ln: xeietl ah gsdnmc oe prediction model gas-dynamic dash: experimental line: solid gure 6. et on 2 Peitd n Eprmna Ehut Pressures Exhaust Experimental and Predicted 2. Point Test .2 6 e r u ig F Static Pressures in Enhaust Manifold (bar) oi ln: xeietl ah gsdnmc oe prediction model gas-dynamic dash: experimental line: solid Crank Angle (degrees) gure 6. et on 3 Peitd n Eprmna Ehut Pressures Exhaust Experimental and Predicted 3. Point Test .3 6 e r u ig F Static Pressures in EHhaust Manifold (bar) oi ln: xeietl ah gsdnmc oe prediction model gas-dynamic dash: experimental line: solid Crank Angle (degrees) gure 6. et on 4 Peitd n Eprmna Ehut Pressures Exhaust Experimental and Predicted 4. Point Test .4 6 e r u ig F Static Pressures in Enhaust Manifold (bar) oi ln: xeietl ah gsdnmc dl prediction odel m gas-dynamic dash: experimental line: solid Crank Angle (degrees) gure 6. et on 5 Peitd n Eprmna Ehut Pressures Exhaust Experimental and Predicted 5. Point Test .5 6 e r u ig F Static Pressures in Enhaust Manifold (bar) oi ln: xeietl ah gsdnmc oe prediction model gas-dynamic dash: experimental line: solid Crank Angle (degrees) gure 6. et on 6 Peitd n Eprmna Ehut Pressures Exhaust Experimental and Predicted 6. Point Test .6 6 e r u ig F Static Pressures in Enhaust Manifold (bar) oi ln: xeietl ah gsdnmc dl prediction odel m gas-dynamic dash: experimental line: solid Crank Angle (degrees) gure 6. rdce Trie n Cmrso Ms-lw ae n Power and Rate Mass-flow Compressor and Turbine Predicted .7 6 e r u ig F Imbalances Power (kLIJ) Mass-flow rates (kg/s) 200 300 300 400 1 00 0 H 0 ------# Turbine Compressor □ Compressor □ Turbine ♦ jp 2 4 6 5 4 3 2 1 ♦ * □ 2 4 6 5 4 3 2 1 1 ------Test Point Number Test Point Number ° a 6 o . 1 ------, 1 ------ ♦ □ . 1 ------□ ♦ ♦ □ , 1 ------□ ♦ r r Figure 6.8 Definition of Paxman 16RP200 Pulse Exhaust Manifold for Filling-and-emptying Exhaust Model Test Point Number Figure 6.9 Comparison of Overall Engine Performance Parameters Predicted Using Different Models g e 10 Ts Pit . oprsno xas aiodPesrs Predicted Pressures Manifold Exhaust of Comparison 1. Point Test 0 .1 6 re igu F Static Pressures in Enhaust Manifold (bar) oi ln: xeietl eim ah gsdnmc prediction gas-dynamic dash: medium prediction filling-ajid-emptying dash: short experimental line: solid sn Dfeet Models Different using Crank Angle (degrees) g e 11 Ts Pit2 Cmaio fEhutMnfl Pesrs Predicted Pressures Manifold Exhaust of Comparison 2. Point Test 1 .1 6 re igu F Static Pressures in Enhaust Manifold (bar) oi ln: xeietl eimds: a-yai prediction gas-dynamic dash: medium prediction filling-and-emptying dash: short experimental line: solid sn Dfeet Models Different using Crank Rngle (degrees) gur 61 Ts Pit . oprsno xas aiod rsue Predicted Pressures Manifold Exhaust of Comparison 3. Point Test 6.12 re u ig F Static Pressures in Enhaust Manifold (bar) oi ln: xeietl eimds: a-yai prediction gas-dynamic dash: medium prediction filling-and-emptying dash: short experimental line: solid sn Dfeet Models Different using Crank Angle (degrees) F igu re 6 .1 3 Test Point Point Test 3 .1 6 re igu F Static Pressures in Euhaust Manifold (bar) oi ln: xeietl eim ah gsdnmc prediction gas-dynamic dash: medium prediction filling-and-emptying dash: short experimental line: solid sn Dfeet Models Different using 4. oprsno xas Mnfl Pesrs Predicted Pressures Manifold Exhaust of Comparison Crank Angle (degrees) g e 14 Ts Pit . oprsno xas aiod rsue Predicted Pressures Manifold Exhaust of Comparison 5. Point Test 4 .1 6 re igu F Static Pressures in Enhaust Manifold (bar) short dash: filling-and-emptying prediction filling-and-emptying dash: short oi ln: xeietl eim ah gsdnmc prediction gas-dynamic dash: medium experimental line: solid Models Different using Crank Angle (degrees) g e .5 et on . oprsno xas aiod rsue Predicted Pressures Manifold Exhaust of Comparison 6. Point Test 6.15 re igu F Static Pressures in Enhaust Manifold (bar) oi ln: xeietl eimds: a-yai prediction gas-dynamic dash: medium prediction filling-and-emptying dash: short experimental line: solid Models Different using Crank Angle (degrees) control volume numbers in plain text pipe numbers in italics junction volume turbine Figure 6.16 Definition of Modular Pulse-converter System for Gas-dynamic Model Main Pipe / Dp 0.0847 D 0.0825 m n 2 D Nozzle Rrea Ratio = 0.53 Centre-line length of nozzle section = 0.0910 m Centre-line length of main-pipe section = 0.3695 m Figure 6.17 Modular Pulse Converter Geometry gure 6. ttc rsue rcs n C xas Sse a Ts Pit 6 Point Test at System Exhaust PC M in Traces Pressure Static 8 .1 6 e r u ig F Static Pressures in Enhaust Manifold (bar) 1 0 10 6 540 360 180 0 -180 2- 3- 4- L> 4- 1- 4- 3- 2- rr _ 0 2- 3- 5“ 1 - 1- oi ln: ne mnfl ds: xas manifold exhaust dash: manifold inlet line: solid Location B8 Location H8 LocationT8 EUO,R8 IU0,R8 i i i i Crank Angle (degrees) EUO,B8 \ \ J \ l IU0,B8 gure 6. ttc rsue rcs n C xas Sse t et on 6 Point Test at System Exhaust PC M in Traces Pressure Static 9 .1 6 e r u ig F Static Pressures in Enhaust Manifold (bar) -180 - 3 - 4 2 - 3 5 - 1 2 4- 2 - 1 1 - - - - oi ln: ne mnfl ds: xas manifold exhaust dash: manifold inlet line: solid Location fl7 Location B6 Location B7 IU0,fl7 IU0,B6 Crank Angle (degrees) EUO,B7 180 IUO,B7 360 EUO,B6 EUO,A7 540 gure 6. ttc rsue rcs n C xas Sse t et on 6 Point Test at System Exhaust PC M in Traces Pressure Static 0 .2 6 e r u ig F Static Pressures in Euhaust Manifold (bar) -180 4- 1 4- - 1 5 2 4- 2 3- - 1 - - oi ln: ne mnfl ds: xas manifold exhaust dash: manifold inlet line: solid Location R6 Location B5 Location R5 IU0,R5 EUO,fi6 Crank Angle (degrees) 1UO,R6 EUO,B5 180 IU0,B5 360 EUO,R5 540 turbine exhaust manifold 10 J ----- X------A 8 V"- cylinder inlet manifold Figure 6.21 Definition of Constant Pressure System for TRANSENG g e 22 Pesr i Cntn Pesr Ehut aiod t et on 6 Point Test at Manifold Exhaust Pressure Constant in Pressure 2 .2 6 re igu F Pressure in Enhaust Manifold (bar) 20 □ pulse • ♦ MPC B “ B const, press. 15 CD £3 B CL a> E 10 - a H □ a ------1------1------1------|------1------1 2 3 4 5 6 Test Point Number 0.25 □ pulse • B 0.24 * MPC “ const, press. 9 0.23 a 0.22 9 ♦ ■ a □ 0.21 8 a - D 0.20 i i i 1 1 i 1 2 3 4 5 6 Test Point Number □ □ pulse Q a ♦ MPC ♦ “ const, press. B □ D u B CD B ♦ a JD ♦ ♦ ------1------1------1----—i------1------1------1 2 3 4 5 6 Test Point Number Figure 6.23 Predicted Performance for Different Exhaust Systems 75 n £ D ♦ S 3 ) 4 a o 70 c □ ♦ 0) ♦ a D □ 65 □ □ □ 0) C 60 □ pulse S ♦ MPC 3 o n const, press. 55 ------1------1------1—----1------1------r------2 3 4 5 Test Point Number Si y 130 c 0) □ U 120 - a B B w V- □ UJ O 110- ♦ □ ♦ • ‘Z a 0 4 D £ 100- ♦ 4 3 □ pulse ° 90- ♦ MPC a> n const, press. ©05 80on 1- ” 1 i i i i i k. a> 1 2 3 4 5 6 3 a: Test Point Number Figure 6.24 Predicted Volumetric Efficiency and Turbine Efficiency for Different Exhaust Systems gure 6. yidred rsue rcsfrDfeet xas Sse t Test at s System Exhaust Different for Traces Pressure Cylinder-end 5 .2 6 e r u ig F Enhaust Static Pressure By Cylinder B8 (bar) on 6 Point Crank Angle (degrees) gure 6. ubn-n Pesr Tae fr ifrn Ehut ytms t Test at s System Exhaust Different for Traces Pressure Turbine-end 6 .2 6 e r u ig F Euhaust Static Pressure at Turbine End (bar) 10 10 6 540 360 180 0 -180 2- 3- 4- 4- 5 3- 2- 1- J CT _ 4- 2- 3- 5 l - 1- ------on 6 Point Constant pressure MPC Pulse 1 ------Crank Angle (degrees) 1 ------1 gure 6. optr xcto Ti s o Smltn 5 taysae Cycles Steady-state 5 Simulating for es im T Execution Computer 7 .2 6 e r u ig F Computer Enecution Time (CPS) o te ifrn Ehut ytms System Exhaust Different the for osat Pressure Constant Pulse, gas.dyn. Pulse, us, & 13 F&E Pulse, System P 816 18 MPC Exhaust Manifold System Manifold Exhaust o Volumes No. 0 0 1 17 o Pipes No. 2 1 0 APPENDIX A EQUAL-PRESSURE JUNCTION BOUNDARY CONDITION Consider the junction depicted diagrammatically below. The sign convention em ployed is that flow towards the junction is positive. In Benson’s analysis [Al], it is assumed that the static pressure, p, at all pipe ends is equal ie. P i = P2 = P3 = P ( A l) It is further assumed that the entropy, s, in each pipe connected at the junction is equal throughout the pipe and is equal to that in any other connected pipe ie. si = s2 = s3 = s (A 2 ) Equations Al and A2 demand that the static density of the gas, p, at the end of each pipe is also equal, thus: Pi = P2 = P3 = P (A3) Continuity requires that for pipes of cross-sectional area F , in which the fluid velocity is u: p \U iF i + P2u 2 ^ 2 + P3 W3 E3 = 0 (A4) A l and using equation A3, this reduces to: U\F\ 4~ U2F2 4" uqFq — 0 (A5) Introducing the reference sonic velocity, are/, and reference static pressure, pre/, the particle velocity, u, and sonic velocity, a, may be non-dimensionalised: .3—* u . . a ( p 3Tf U = and A (A 6) Q>ref G r e f P r e f where 7 is the ratio of the specific heats. From equation A l, therefore, the non-dimensional sonic velocities are equal: A i = A 2 = A 3 = A (A 7) A and £7 may also be defined in terms of the Riemann variables, A»n, and A^*: ^ _ ^ m i 4* A ou ti TT _ \ ‘n i ^ o u tl 1 2 7 - 1 A At-na 4” A ou ti j-t A m 3 A out? U2 — , (AS) 2 ~~ 2 7 - 1 i Ajn.3 4” A outs TT ^ in s ~ ^out$ A 3 = n U3 — - 2 7 - 1 Substituting for Ai, and A 2 from A 8 into A7: Am i d" A outi Atrij 4“ A outi (A9) By using a similar substitution for the characteristics at boundary 3 equation A5 can be re-arranged to yield relations for the reflected characteristics as functions of the area ratio and incident characteristics only, eg. Aouti — K i^ in x 4~ 4” K 3^inj ^»ni ( A io ) where 2 Fi K i F i 4- F2 4- F3 2 F2 k 2 = ( ^ n ) F 1 4~ F2 4" F3 2 F3 k 3 = F± 4- F2 4- F3 Now consider the conservation of energy: m ihoi 4" na 2 ^Q2 4" fn3h33 — 0 (An) where m is the mass-flow rate and ho is the stagnation enthalpy of the fluid. Taking the simplest case where the cross-sectional areas of the pipes are equal, and recalling that the static densities are also equal (equation A3), equation A12 can be expanded to: Uihoi + u 2ho2 + U3/103 = 0 (A13) The stagnation enthalpy, hoi is a function of the stagnation sonic velocity, A 01 which is defined: < = A l + U 2 ( A li) Substituting from A14 into A13: + U 3 { a 2 + ( l y i ) U 2 } 3 = 0 (A15) Now, for pipes of equal area, the continuity equation demands that Ut = - U 2 - Uz (A16) Recalling that the static sonic velocities are equal (equation A7), and substituting for Ui into the equation for the conservation of energy, A15: (-Ui - ua){ a 2 + ( 1^ i ) (tfa + ^3)2} ’ + U2{ a 2 + (3 ^ 1 ) I72J 3 + u 3{a 2 + ( l ^ l ) u 2} 3 = 0 (All) Thus for a given sonic velocity, A, and velocity at pipe end 1, Ui there are two unknowns in the equation namely U2, and Uq. By setting the right-hand side of the equation to a variable name, Z , such that the equation can be represented by W + X + Y = Z (A18) a family of curves of Z as a function of U2. (or U3) for different values of sonic velocity and/or Ui can be generated. Figure A1 shows values of Z as a function of U2 for a constant sonic velocity, a, of 500 m/s, and for gas velocities at pipe-end 1 varying between -100 m/s and 500 m/s. The reference sonic velocity is 500 m/s. The curves show clearly that Z is only zero when the velocity at at least one pipe end is zero. A3 The equal-pressure junction model therefore contravenes the conservation of en ergy if there is flow at each of the pipe ends connected at a three-way junction. References A 1 Benson, R.S. Instantionare Stromung in Verzweigten Systemen (Unsteady Flow in Branched Systems) MTZ, Vol 23, No 1 0 (1962) A4 gur A re u ig F Variable Z in equation A18 1 aito o wt U frVros l. U Various for U2 with Z of Variation Non-dimensional Velocity U2 Velocity Non-dimensional APPENDIX B THE INTERDEPENDENCE OF LOWER CALORIFIC VALUE AND ABSOLUTE ENTHALPY To provide for fuels other than vehicle-type diesel fuel to be burnt, a relationship between the lower calorific value (LCV) of the fuel and its absolute enthalpy must be established. This appendix examines the interdependence of absolute enthalpy and LCV for C nH<2n fuels. Consider the stoichiometric combustion of a hydrocarbon whose general formula is (C H x)y . The chemical equation for the reaction is: ( C B m)y + [ y + ( f ) ) 0 2 ------> yC 0 2 + (f) H20 (Bl) On completion of this reaction an amount of heat, Q, at the temperature, T, will have been liberated. The energy balance for the above chemical reaction is therefore: HT(CHs)y + (y + (-“ )) HT02 — yHTco2 + Hth>o ~ QT (£2) where HT is the absolute enthalpy of constituent i at the reference temperature T, in kJ/kg-mol, and is defined by Powell [Bl] as: / sensible heat / heat of formation at \ at temperature OK from the elements \ Absolute enthalpy = + T above that in their standard I V at OK V reference states at OK ) or H Toi = ( H Toi - H °0i) + H°oi (B 3) B l where the superscript refers to temperature, subscript i to the species, and sub script 0 to the reference state of one atmosphere and the temperature under con sideration. Rearranging equation B 2 , and dividing by the mass of one mole of fuel, in kg, and using the following substitution for the LCV: LCV = — (heat of reaction for all elements in their standard state) we get: g y * . ) , y (HTco, + f H t „, q - (1 + f ) HT0l) + L C V t AT(CH.), ym(CHI)y y (0.012010 + x X 0.001008) (B4) The property data in TRANSENG are based on a C nH 2n fuel, and this is the same form as ( CHx)y for x=2. The term in the square brackets of equation B4 is thus a function of temperature only, and at any temperature, h[CH2)y = CONSTANT + L C V (B 5) TRANSENG requires the absolute enthalpy of the fuel at 298.15K, and to calculate this value the absolute enthalpies of the products of combustion, C 0 2i H 20 > and C>2 must be known at 298.15K and 1 atmosphere. These data are given in the JANAF tables [B2] and are reproduced below. Species T H t o - JJ298 15o H T 0J (K) (kcal/mol) (kcal/mol) c o 2 0 -2.238 -93.965 h 2o 0 -2.367 -57.103 o 2 0 -2.075 0 .0 0 0 where (H t o — if298-150) indicates the enthalpy in the standard state at tem perature T less the enthalpy in the standard state at 298.15K. B2 H T af represents the standard heat of formation which is the increment in enthalpy associated with the reaction of forming the given compound from its elements, with each substance in its thermodynamic standard state at the given temperature. The standard state, referred to variables by subscript 0 , is taken as the state at one atmosphere pressure, at the temperature under consideration, and one mole is that amount of substance containing as many elementary entities as there are atoms of C 12 in 0 .0 1 2 kg of C i 2. So, from equation B3, for C 02, omitting the subscript 0 for clarity: o298.15 _ ( o 0 o-298.15\ ■ ttO ■“ CO = —91.727 kcal/m ol Similarly, H 298'15 h 2o = —54.736 kcal/m ol H 2g8 15 o 2 = 2.075 kcal/m ol Thus for a C nH 2n fuel, the constant in equation B5 is: -91.727 + | (-54.736) - (l + f ) (-2.075) CONSTANT = (0 .0 1 2 0 1 0 + 2 x 0.001008) C O N S T A N T = -10664.16 kcal/m ol CONSTANT = -44618.80 kcal/kg The absolute enthalpy of a C nH 2n fuel at 298.15K, and 1 atmosphere , HF, may be expressed: H F = -44618.8 + LCV m References B l Powell, H.N. Applications of an Enthalpy-Fuel/Air Ratio Diagram to First Law Com bustion Problems ASME 56-SA-68 (1956) B 2 JANAF Thermochemical Data Tables Compiled by Dow Chemical Corporation, Midland, Mich. (1960) B4 APPENDIX C THE NUMERICAL INSTABILITY PROBLEM 1.0 Introduction The equations describing fluid flow through an engine system are not amenable to an analytical solution and have to be solved numerically. The numerical method employed in the Imperial College filling- and-emptying program, TRANS ENG, is the predictor-corrector method which uses a pair of formulae and proceeds in three steps: step 1 : the predictor formula is a coarse method of extrapolation and is used to obtain a predicted value at the new time step, y £ + 1 step 2 : the predicted value is substituted into a differential equation to calculate the derivative, f n+i step 3: the derivative is inserted into the corrector formula to yield a corrected value, 2/°+ 1 If the difference between the predicted and corrected values exceeds a given tol erance steps 2 and 3 may be repeated (using the corrected value found in step 3 to find the derivative in step 2) until either the difference between the latter two corrected values lies within the specified tolerance or the maximum allowable number of iterations is reached. The predictor formula used in TRANSENG is a first order Euler: s£+l = !& + ' (C1) where h is the step size. The corrector is known as the modified Euler. It uses first- order derivatives but is of second order accuracy as the derivative at the previous step is also used: l£ + i= l£ + 0.5xM/» + /«+i) (C2) C l The predictor-corrector is applied to calculate the mass, temperature and equiv alence ratio in each control volume. This method assumes that the derivative is constant over the step. If the ratio of the rate of change of a parameter to the parameter itself is large then this assumption can cause errors which manifest themselves as instabilities. Instabilities are most likely to occur when the volume size is small and/or the real-time step is large. For a simulation using filling- and-emptying control volumes only, the size of the volume simulating an exhaust manifold is fixed by the geometry of the manifold, and the real-time step cannot be reduced without regard to the increased computational costs. Following an initial study of the effect of real-time-step size, alternative solutions were investigated. Engine performance predictions for a single cylinder of a Paxman Valenta engine, using a filling-and-emptying exhaust manifold model showed that as the real time step was increased, by maintaining a 1 deg crank-angle step and reducing the engine speed, keeping all other data the same, instability in mass-flow rates through the valves occurred. This is shown in figure Cl. The instability did not cause the program to fail and did not have a significant effect on the overall predicted engine performance but it was decided that if a method of achieving a solution involving little or no additional computing cost could be found it should be implemented. Several methods were therefore tested including reducing the crank-angle-step size, applying numerical relaxation factors, varying the crank- angle-step size during the cycle, increasing the number of corrector iterations by reducing the convergence tolerance, and applying a variable coefficient of discharge to the valve flow. Of these methods only the last has any physical significance. By implementing this method together with that of reducing the convergence tol erance a more stable solution was achieved. A general description of the engine modelled will be followed by a discussion of the original instability and each of the listed methods of solution. C2 2.0 The Engine and Operating Conditions Since the overall objective of the project was to develop predictive techniques to design and optimise turbocharging systems for medium-speed four-stroke indus trial and marine diesel engines, all developments made to TRANSENG by the author have been based on the demands of such an engine. Experimental data for a Paxman Valenta 16RP200 engine are available, thus the instability was inves tigated using data for this engine. The two main differences between this engine and the smaller engines usually modelled by TRANSENG are (a) the large valve open and overlap periods, and (b) the lower engine speeds. The engine speed at the idling condition is 700 rpm and it is at this speed that the methods of solving the instability have been investigated. To simplify the analysis only one cylinder was modelled and the turbocharger compressor and turbine were simulated by an orifice and a nozzle respectively. Data for the engine geometry and operating conditions are given in figure C 2 . Note that two sets of data are given: the first was used before the more accurate data of the second set were available. The value of the turbine nozzle area for both sets of data was found to be in error after the completion of the instability study: it was only half of what it should have been. Insertion of the correct value reduced the instability considerably. Conceivably there could be a demand to model an engine system containing such a high flow restriction; and in any case this investigation is a useful reference for researchers whose combination of data and program trigger ‘the instability problem’. C3 3.0 The Original Instability The lowest graph of figure Cl shows the variation of mass-flow rate through the inlet and exhaust valves for a single-cylinder engine based on the Paxman Valenta running at 700 rpm. It is reproduced in figure C3 with the gas-exchange diagram which shows that mass-flow rate is more sensitive to numerical instability than pressure, and the former parameter was therefore chosen as a measure of instability in this investigation. In the initial simulation the crank-angle step was 1 degCA, no flow relaxation was applied, the convergence tolerance for determining whether corrector iterations should be applied was 1 %, and the coefficient of discharge was a constant 0 .8 for inlet and exhaust valves. Looking more closely at the instability, it first starts near bottom dead centre (BDC) on the exhaust stroke when the pressure ratio across the valve is close to unity, it then recovers, and becomes pronounced again at 160 degCA. When the inlet valve opens both inlet- and exhaust-mass-flow rates are unstable. Following the peak during scavenge flow the exhaust-mass-flow rate stabilises but the inlet- valve mass-flow rate remains unstable until after the exhaust valve has closed. C4 4.0 Methods for Solving the Instability Problem 4.1 Reducing Crank-Angle Step Leaving all parameters as for the original version of the program except for crank- angle-step size, the effect of reducing the step size was investigated. Figure C4 shows the improvement in stability as the step size was reduced from 1 degCA to I degCA to ■— degCA. Complete stability was achieved when the step was jQih degCA but the increase in execution time compared with the one-degree run was nine-fold so that solution is not acceptable. The program was modified such that the crank-angle step in the last engine cycle could be a fraction of that in the preceding cycles, and the latter value which is usually one degree could be greater or less than one degree. 4.2 Use of Numerical Relaxation Factors Numerical relaxation of the form below was applied to the mass-flow rates entering and leaving the cylinder. .dm. „,dm. . „wrfm. (~ j 7" ) = (C 3) at n + l F(~ir)at n +(1- F)(-7r) at n + l where F is the relaxation factor which may have a value between 0 and 1 . In this way the mass flow-rate is quite arbitrarily restricted regardless of the temperatures and pressures which were used to calculate the first estimate of the mass-flow rate. Various tests were conducted: at first a single flow relaxation factor was applied only to exhaust flow, then an additional factor was used to relax the inlet flow also. Finally four different relaxation factors were applied: a different one for flow through each valve during overlap and one for each valve outside the overlap period. Figure C5 shows the use of the four factors and a graph of stable flow achieved at no extra computing cost by finely tuning the four factors. Note that the data set used in this investigation was for a two-cylinder engine thus the results can not be directly compared with those of figure C4. Comparison with the relevant results showed, however, that negligible distortion was introduced. C5 Despite the induced stability the method was considered unsatisfactory in that (a) the solution is not general: for different operating conditions and different engine geometries a new set of relaxation factors would have to be derived, and (b) there is no physical justification for relaxing the flow. 4.3 Variable Crank-Angle Step The program was modified such that when the slope of the curve for mass-flow rate through the valves changed sign the 1 degCA step was repeated with five steps of degCA. At each jrth degCA step the cylinder conditions were predicted and corrected but to economise on computer run time the conditions in the manifolds were linearly interpolated for the degCA intervals over a 1 degCA step as shown in the flow chart of figure C 6 . The instability in mass-flow rate through the exhaust valve was seen to persist despite the reduction in crank-angle step, and was found to be due to the assump tion that the conditions in the exhaust manifold varied linearly over a 1 degCA interval while those in the cylinder did not. The conclusion was that both volumes either side of the boundary across which mass is being transferred must operate on the same crank-angle step. The only way to program this without incurring great complexity is to allow the whole engine system to operate on the smaller step whenever it is demanded by one or more boundaries between volumes. When simulating an engine with a large number of cylinders it is conceivable that one cylinder will always be demanding a smaller crank-angle step and that the whole program may as well run with the smaller step. This method of solving the prob lem was therefore put to one side while the effects of reducing the convergence tolerance were investigated. C6 4.4 Reducing the Convergence Tolerance The convergence tolerance is expressed as a percentage of the predicted value of the variable concerned. The three variables considered each iteration are the in tensive properties of pressure, temperature, and equivalence ratio. If the difference between predicted and corrected values of pressure and/or temperature and/or equivalence ratio exceed a specified percentage of the predicted value in any con trol volume, a further corrector iteration is performed up to a maximum of three iterations. Initially a tolerance of 1 % was set. When it was reduced to 0 .1 % a significant change in instability was observed. On further reduction of the toler ance from 0 .1 % to 0 .0 1 % the instability in both inlet and exhaust valve mass-flow rates was rendered negligible outside the valve-overlap period. No change in the instability occurring during valve overlap was effected by this method. Figure C7 gives the graphs of mass-flow rates through the valves for the three convergence tolerances. There was no increase in execution time between simulations with convergence tolerances of 1 % and 0 .1 % but there was a slight increase between these and the simulation where the tolerance was 0 .0 1 %. To minimise the cost the program was modified such that in all but the last cycle the convergence tolerance was 0 .1 %, and in the last cycle it was 0 .0 1 %. In this way the increased number of iterations in the last cycle caused stable flow outside the valve-overlap period while incurring a negligible increase in computer execution time. C7 4.5 Variable Coefficient of Discharge In order to predict flow through an engine the coefficient of discharge for each boundary across which mass flows must be known. Commonly engine manufac turers quote an effective valve area in which a coefficient of discharge is implicit, the effective area being the product of the geometric area and the coefficient of discharge. Such effective areas are usually evaluated under conditions of steady flow, and a constant, low pressure ratio across the valve (typically 1 .0 1 ). In an engine, the flow is not steady, the pressure ratio across the valve is not constant, and in the case of an exhaust valve the pressure ratio is low only for a very short period. Much research has been conducted to establish relationships between the coeffi cient of discharge and both valve lift and pressure ratio under steady-flow condi tions . In addition some researchers have investigated the effects of unsteady flow, flow direction, valve-seat angle, and gas temperature. This research will be briefly discussed below. Its application to TRANSENG and the results thereof will then be described. 4.5.1 Literature Review The literature survey covered investigations into the variation of coefficient of discharge with various parameters for three types of orifice: standard orifice plates [05], two-stroke-engine ports [Cl, 02], and poppet valves [C2, C3, C4, C 6 , C7, C8 ], and revealed that the coefficient of discharge is a function of: - pressure ratio across the valve , - valve lift, - valve-seat angle, - whether flow is steady or unsteady,. - flow direction, and C8 - gas temperature. Several of the above variables are interdependent. Adding to the complexity are the facts that not all the researchers investigated all the effects; and where similar trends were given by more than one researcher, there was usually a discrepancy in their findings at the extremes of the conditions investigated. The investigations are summarised in table Cl. It was not within the scope of the project to investigate all the effects listed above, each is mentioned below with greater attention being paid to those variables which most influence the coefficient of discharge ( hereinafter referred to as Cd ). Pressure ratio and valve lift are the two variables which most affect Cd. The results of research on poppet valves documented in references C2, C3, C4, C 6 , and C 8 , showed that in general the steady-flow Cd increases with pressure ratio for a single value of valve lift above a minimum valve lift, and Deckker and Chang [C5] showed that for standard orifice plates the steady-flow Cd is a strong function of pressure ratio. It was also shown that for a given pressure ratio and very low valve lifts the Cd increases with valve lift, while at higher lifts the Cd falls. These phenomena are illustrated in figure C 8 (compiled from references C 2 , C3, C4, C6 and C 8 ) and may be explained in terms of a trade-off between the effects of viscosity and compressibility: at very low lifts, region 1 , the conical seating surfaces provide a long narrow passage through which flow passes in a well ordered manner. In this region the effects of viscosity dominate those of compressibility, and as the flow area increases so the Cd increases until the higher valve lifts of region 2 axe reached. In this region the flow passage ceases to resemble a convergent nozzle and the curve flattens. In region 3 compressibility dominates, and Cd falls with increasing lift. Looking at some details of the curve of steady-flow Cd against non-dimensional valve lift (figure C 8 ), note firstly that with the exception of Fukutani et al. [C 6 ] no data were available below an 1/d of 0.05 due to difficulties in obtaining accurate measurements at such low 1/d. Secondly there is some discrepancy in the literature over the value of 1/d at which the peak Cd occurs, as-Jie^/n in Table Cl: the range C9 of 1/d for maximum Cd for poppet valves is 0.05 to 0.07 for inlet valves, and 0 .1 0 to 0.13 for exhaust valves with a 45 deg seat angle. Thirdly, there is some discrepancy as to whether the Cd falls at low lifts as lift is further reduced. Blair and Blair [C4], and Wallace and Mitchell [C 2 ] did not show the trend of region 1 , figure C 8 , the former showed a slight increase in Cd ( see figure C9 ), while the latter gave a constant peak value. Differences may also be found where Cds were evaluated at pressure ratios in excess of the sonic pressure ratio at low lifts: Blair and Blair [04] reported that Cd falls as pressure ratio increases beyond the critical pressure ratio (see figure C9 ); Wallace and Mitchell [C 2 ] reported that Cd increases with pressure ratio tending to a constant value when the pressure ratio exceeded 5; and Woods and Khan [C3] and Deckker and Chang [C5] also found that Cd does not fall for a given valve lift at pressure ratios in excess of the critical ratio. Finally, note that Wallace [Cl] found Cd vs. 1/d profiles for valves with seat angles of 30 and 60 deg are quite different. Now consider the effects of pressure ratio and unsteady flow at other than very low valve lift. Several researchers have shown that the coefficient of discharge under unsteady-flow conditions is less than for steady flow [C4, C5, C 6 , CIO]. Fukutani and Watanabe [C 6 ] conducted experiments on inlet valves of a small high-speed engine. They found that the ratio of mean dynamic Cd to the mean steady-flow Cd, termed the ‘dynamic factor’, decreased with increasing engine speed above 2 0 0 0 rpm. Below 2 0 0 0 rpm the dynamic factor varied between 0.90 and 0.98 depending on the pressure ratio which varied in these tests from 1 .0 1 to 1.03. They showed that the unsteady-flow Cd is consistently less than the steady-flow Cd and that the difference between them grows as the pressure ratio tends to unity. The latter point is contradicted by Deckker and Chang [C5]. In their work on slow transient flow through a standard orifice plate they showed that as the pressure ratio tends to unity the unsteady- and steady-flow Cds tend to the same value as illustrated in figure CIO. Their work covers a much wider range of pressure ratios and they found that the ratio of unsteady- to steady-flow Cd decreased from unity at a pressure ratio of unity to 0.92 at a pressure ratio of 1.33 after which it remained approximately constant. CIO Blair and Blair [C4] measured unsteady flow on a test rig and compared the values with flow rates predicted for the rig using experimentally obtained steady-flow Cds. They found that for the inlet valve the flow calculated using steady-flow Cd was under-predicted by 2.7% at 1500 rpm: for the exhaust valve flow was over-predicted by 9.8% at 1 0 0 0 rpm and 9.5% at 1500 rpm. The pressure ratio across the inlet valve is much lower than that across the exhaust valve, and recalling Deckker and Chang’s results above, this may account for the great error in exhaust valve mass- flow rate. The over-estimation of exhaust-valve flow by 9.8% compares well with Deckker and Chang’s figures. Flow direction also influenced the coefficient of discharge. Blair and Blair’s graphs for steady-flow Cd as a function of valve lift for inlet valves show the normal- and reverse-flow diagrams to be quite different. See figure C9. The exhaust valve normal-flow profiles show the same trends as the inlet valve reverse-flow profiles which may be expected. Woods and Khan [03] report that hardly any difference may be observed between Cd measured for normal and reverse flow on inlet and exhaust valves, but flow in the ports of the cylinder head they were testing had to pass round severe bends which may have significantly affected the flow. The effect of gas temperature was investigated too: Wallace and Mitchell [C 2 ] considered the dependence of the steady-flow Cd for an exhaust port on gas tem perature, and Deckker and Chang [C5] looked at the effect of heat transfer during discharge on the unsteady-flow Cd. The former found that steady-flow Cd in creases with gas temperature: for conditions of port height of 0.25in, pressure ratio of 1.5 and gas temperature of 6 8 degF ( 293 K ), the steady-flow Cd was 0.74 whereas at 125 degF ( 325 K ) they give a steady-flow Cd of 0.98. Deckker and Chang found that heat transfer during expansion through an ori fice resulted in a higher mass-flow rate than during isentropic expansion, and attributed this to the lower density in the cylinder. C l l 4.5.2 Application of Variable Cd to TRANSENG Clearly a large quantity of experimental data would be required for each engine modelled if the coefficient of discharge was to be a function of all the variables dis cussed above. The original version of TRANSENG takes account of the variation of Cd with seat angle, and depending on how the effective areas were determined, with lift at one pressure ratio only. This information is provided by the manufac turers in the form of a single graph for each of the inlet and exhaust valves giving the effective valve area against crank angle. Sometimes the graphs have not been experimentally determined at all: the ‘effective areas’ can simply be the geometric areas multiplied by a typical Cd. If effective areas have been experimentally deter mined the pressure ratio at which they were evaluated is often not quoted but it is commonly around 1 .0 2 [C9]. Looking at figure C 8 it can be seen that a significant error will occur if the valve is at high lift and the pressure ratio is approaching the sonic value. This error is usually made larger still by the assumption that the Cd will be the same under steady or unsteady flow conditions. Further errors are introduced by neglecting the variation in Cd with flow direction, engine speed and gas temperature. These are considered to be secondary effects but the first may be easily applied to TRANSENG if a simplifying assumption is made, namely that the exhaust valve reverse flow Cd vs. lift profile is as for the inlet valve for ward steady-flow Cd, and vice-versa. The effects of temperature and engine speed were outside the scope of this project: the speed range of engines considered in this project was lower than that at which Cd was shown to vary significantly with engine speed; and there was insufficient information available to justify making Cd a function of gas temperature. The changes effected in TRANSENG were thus: (1) The provision for a graph of steady-flow Cd vs. non-dimensional valve lift as for figure C 8 enabling steady-flow Cd to be calculated as a function of 1/d and pressure ratio. A fifth-order polynomial is used to describe the curve at the pressure ratio for which steady-flow data are given. The maximum Cd is restricted to unity. For 1/d greater than that at which the peak Cd occurs, the variation of Cd with pressure ratio, up to a pressure C12 ratio of 2.0, is such that at the maximum valve excursion, the Cd is 12% greater than at a pressure ratio of 2 .0 than at the lower pressure ratio. This linear variation with pressure was roughly estimated from references C2 , C4, and C5, and this model assumes that the pressure ratio at which steady-flow data are given is close to unity. (2 ) The calculation of reverse flow Cd by assuming that the exhaust-valve reverse-flow steady Cd is equal to the forward-flow steady Cd for the inlet valve and vice-versa unless reverse-flow data are available. (3) The calculation of unsteady-flow Cd simply by assuming a constant dy namic factor of 0.94. In the literature the range of dynamic factors found was 0.90 to 0.98 The medium-speed engine on which the instability investigation was based was a Paxman 16RP200. The data available for calculation of instantaneous Cd are the ‘effective areas’ and a curve of steady-flow Cd as a function of 1/d for a pressure ratio of 1.014. The effective areas were provided by Paxman and are calculated as the product of the geometric area and a constant Cd of 0 .8 . The Cd vs. 1/d data were derived by the author from information supplied by Paxman in a private communication. These are shown in figure C ll. They were simplified such that the variation of Cd with valve lift was linear. Figure C 1 2 shows the simplified curves which have been extrapolated at low 1/d to give a constant Cd of unity, and the assumption of a 1 2 % increase in Cd at maximum valve lift and a pressure ratio of 2 .0 . The data input for this part of the program were therefore - CDEFIN (CDEFEX) Steady flow Cd assumed in valve effective area data supplied by manufacturer for inlet (exhaust) valve 0.8 (0.8 ) - PREFIN (PREFEX) pressure ratio at which CDEFIN (CDEFEX) assumed 1.014 (1.014) C13 - P I1 to PI5 (PEI to PE5) coefficients of fourth order-polynomial describing vari ation of steady-flow Cd as a function of inlet-valve (exhaust-valve) lift 1.000 -1.830 0.000 0.000 0.000 (1.123 -1.673 0.000 0.000 0.000) - VECDMAX valve lift-to-diameter ratio at maximum exhaust valve Cd 0.10 - PR 1 (PR 2 ) lower (upper) pressure ratios at which Cd vs. valve lift profile are available 1.014 (2.000) - DIN (DEX) Inlet (exhaust) valve diameter 0.0619 m (0.0579 m) - BETAIN (BETAEX) Inlet (exhaust) valve seat angle 30 deg (45 deg) - VLMAX Maximum valve lift 0.0174 m The subroutine which calculates the instantaneous Cd is listed in figure C13. The modified program was executed for a hypothetical single-cylinder Paxman RP 2 0 0 engine running at a speed of 700 rpm and 5.6 bar bmep. In previous simu lations using a constant Cd and a convergence tolerance of 0 .0 1 %, an unacceptable level of instability in inlet- and exhaust-valve mass-flow rates during the scavenge period had been observed as shown in the top graph of figure C14. Using the variable Cd model of figure C 1 2 and a dynamic factor of 0.94 the amplitude and duration of the instability was significantly reduced as shown in the lower graphs of figure C14. Note that the Cd in this case was the same for forward and reverse flow. C14 In the cases of reverse flow, where the inlet valve forward flow Cd was applied to the reverse flow through the exhaust valve and vice-versa, the instability was not improved as the Cd also oscillated between the forward and reverse values which differed by up to 0 .2 . The predicted mass flow through the engine was 1 % lower than in the previous simulation where Cd was constant, but it can not be realistically compared with Blair and Blair’s result of a 10 % reduction either due to the very different operating conditions. 5.0 Conclusions The conclusions drawn from the above investigation are firstly that a convergence tolerance of 0 .0 1 % reduces the instability outside the valve-overlap period to a negligible amount, and secondly that there is much evidence to support the hy pothesis that the instantaneous Cd is not constant. A much simplified form of the dependence of steady- and unsteady-flow Cd on pressure ratio and valve lift was implemented with the result that stability of predicted mass-flow rates was greatly improved for a marginal increase in program-execution cost. A further development was the facility to reduce the crank-angle step in the last cycle to a fraction of its value in the preceding cycles. C15 References Cl. Wallace, W.B. High-output Medium Speed Diesel Engine Air and Exhaust Flow Losses Proc Instn Mech Engrs 1967-68 Vol 182 Pt 3D C2 . Wallace, F. J., Mitchell, R.W.S. Wave Action Following the Sudden Release of Air Through an Engine Port System Proc Instn Mech Engrs 1952-53 Vol IB (No 8 ) C3. Woods, W.A., Khan, S.R. An Experimental Study of Flow Through Poppet Valves Proc Instn Mech Engrs 1965-66 Vol 180 Pt 3N C.4 Blair, A.J., Blair, G.P. Gas Flow Modelling of Valves and Manifolds in Car Engines Proc Instn Mech Engrs Computers in Engine Technology 1987 Paper No C ll/8 7 C5. Deckker, B.E.L., Chang, Y.F. Slow transient Compressible Flow Through Orifices Proc Instn Mech Engrs 1967-68 Vol 182 Pt 3H C6 . Fukutani, I., Watanabe, E. Air Flow Through Poppet Inlet Valves - Analysis of Static and Dynamic Flow Coefficients SAE 820154 C16 C7. Rabbitt, R.D. Fundamentals of Reciprocating Airflow Part 1 : Valve Discharge and Com bustion Chamber Effects SAE 840337 C8 . Woods, W.A. Steady Flow Tests on Twin Poppet Valves Proc Instn Mech Engrs 1967-68 Vol 182 Pt 3D C9. Lilly, L.R.C Diesel Engine Reference Book Chapter 6 , Butterworths, 1st ed., 1984 CIO. Benson, R.S. Experiments on Two-Stroke Engine Exhaust Ports Under Steady and Un steady Flow Conditions Proc Instn Mech Engrs 1959 Vol 173 No 19 C17 F ig u r e C l Numerical Instability in Mass-flow Rates as Engine Speed is Reduced is Speed Engine as Rates Mass-flow in Instability Numerical l C e r u ig F Mass FIouj Rates Through Inlet and Enhaust Ualues (kg/s) ,0 1 N=1200rpm - oi ln: ne vle rkn ie ehut valve exhaust line: broken valve inlet line: solid rn Age (degrees) Angle Crank Parameter Data Set 1 Data Set 2 Compression ratio (/) 13.0 12.13 Con-rod length (mm) 431.8 406.4 Fuel consumption (kg/cycle) 6.970E-04 2.398E-04 Boost pressure (bar) 1.9 1 .1 Injection delay(s) 4.167E-04 1.786E-04 Data Common to Both Sets Engine speed (rpm) 700 Turbine Bore (mm) 196.9 Stroke (mm) 215.9 IVO (degCA) 198 IVC (degCA) 495 EVO (degCA) 6 EVC (degCA) 340 Figure C2 Engine Data and Diagram of Filling-and-emptying Arrangement of Engine F ig u r e C 3 Gas-exchange and and Gas-exchange 3 C e r u ig F Gas-eHchange Diagram (bar) Mass-floiu Rates (kg/s) Sensitivity of of Sensitivity sfow ;o w ss-flo a M Mass-do\^ Mass-do\^ it Darm Soig Greater Showing Diagrams riate Instability gure C4 lmnto o ntblt b Rdcn Cakage Step Crank-angle Reducing by Instability of Elimination 4 C e r u ig F Mass FIolu Rates Through Inlet and Enhaust Ualues (kg/s) 0.5 -0 0.5 -0 -0.5 0.5 . - 0.0 1.0 1.0 0.5 . - 0.0 1.0 -180 oi ln: ne vle rkn ie ehut valve exhaust line: broken valve inlet line: solid Crank-angle step of of step Crank-angle rn-nl se o /0 deg 1/10 of step Crank-angle rn-nl tp f15 deg 1/5 of step Crank-angle 1 deg rn fnl (degrees) fingle Crank 180 360 540 g e C re igu F Mass-flow Rates (kg/s) Flow-relaHation Factor (/) -0.5 0.0 0.5 1.0 0.4 0.2 0.6 0.8 0.0 1.0 5 180 lmnto o ntblt uig or lwrlxto Factors Flow-relaxation Four using Instability of Elimination solid line: inlet valve broken line: exhaust valve exhaust line: broken valve inlet line: solid (Data set set (Data 1 ) ~i 10 6 540 360 180 0 ------Crank Angle (degrees) 1------1 i i r EX2 N ! INI ------ CA is the current crank-angle position CAST is crank-angle step Figure C6 Flow Chart Detailing Variable Crank-angle Step Scheme gure C7 Ipoeet n ntblt a Cnegne oeac i Reduced is Tolerance Convergence as Instability in Improvement 7 C e r u ig F Mass FIolu Rates Through Inlet and Euhaust Ualues (kg/s) oi ln: ne vle rkn ie ehut valve exhaust line: broken valve inlet line: solid rn Age (degrees) Angle Crank 1 2 3 [■* ----- ► f* *1 Figure C8 Typical Variation of Cd with Non-dimensional Valve Lift and Pressure Ratio 10 J - rang* o» Co *otu*s for opplitd pressure ratios inlet value diam. » SO » tt\ 0-3 0 2 01 0 0 5 01 015 0 2 0-25 INLET VALVE NOttMAL FLOW V0 l v , *diwri* ,# l,# 0-05 01 015 02 0 25 0 3 EXHAt/ST VALVE NORMAL ELQW V o t v .l^ jra t .o 10 I 0 9 0« 0 7 0-6 0 5 press Re. no. rotio f on9* os 12 S 6 -5-3.101 1 5 71-73 - 0 3 20 • 9 -10 0 - 0 2 evtiowst valve d*0ffii34inm 0 1 0 0 5 0-1 0 15 0 25 0 3 e x h a u s t v a l v e n q o m a l e l P* 1*5* at>« Figure C9 Variation of Steady-flow Cd with Valve Lift Taken from Blair and Blair [C4] F ig u r e CIO Variation of Steady-flow and Unsteady-flow Cd with Pressure Ratio Pressure with Cd Unsteady-flow and Steady-flow of Variation CIO e r u ig F Coefficient of Discharge (/) ae fo Dckr n Cag [C5] Chang and Deckker from Taken g e da aFnto fNndmninlVle it t rsue Ratio Pressure a at Lift Valve Non-dimensional of Function a as Cd l l C re igu F Steady-flow Cd Steady-flow Cd f .1 o aR20 yidr Head Cylinder RP200 a for 1.01 of Drvd rmDt Sple b Pxa Dees Ltd) Diesels Paxman by Supplied Data from (Derived nas Ule owr Flow Forward Ualue Enhaust o-iesoa Ule it l/d Lift Ualue Non-dimensional ne Ule owr Flow Forward Ualue Inlet F igu re C 12 Simplified Variation of Cd with Valve Lift for Simulation of Paxman of Simulation for Lift Valve with Cd of Variation Simplified 12 C re igu F Steady-floiD Cd Steady-floiu Cd 6P0 Engine 16RP200 xas Ule omr Floui Formard Ualue Exhaust ne Ule owr Flom Forward Ualue Inlet SUBROUTINE CDCAlC(CA»IDV#PR»VL#CD#VLMAX) COMMON /MODE /TRANS#NCYC#NCYC1#NCYC 2#NCSS#NCTR1#NCTR 2#NCYCOP . COMMON /QUADTC/AllN# B1IN#C1IN#A1EX#B1EX#C1EX#DIN#DEX,BETAIN» 1 BET AE X COMMON /VARCO /P11#PI2#P13#PIA/PI 5#P16#PEI»PE2#PE 3# PEA#PF5#PE6# 1 VECDMAX#PR1#PR2 C* * SUBROUTINE TO CALCULATE EV FORWARD FLOW AS FUNCTION OF L/D t* * AND PRESSURE RATIO* IV FORWARD FLOW CD AS F'JNTION Oc L/D C* * ONLY. FOR REVERSE FLOW EV CD- NORMAL FLOW IV CD AND VICE C + * VERSA C C* * INITIALISE CDSTDY AND TRK C CDSTDY-0.0 TRK.0,0 VLM-VLMAX c c* * IF ■1 IV FORWARD FLOW IS CONSIDERED c* * IF ■2 IV REVERSE FLOW IS CONSIDERED c* ♦ IF >3 EV FORWARD FLOW IS CONSIDERED c* * IF ><* EV REVERSE FLOW IS CONSIDERED c* * OEP c c* * FIR c c* * CALi c IF { IOV VLDMAX-VLM/DIN ELSE VLDMAX-VLM/DEX ENDIF c IF(VL.i VI-VL V2-V1* V3-V2*' VA-V3* V5-V4* c IF (IDV CDST0Y«PI1+PI2*V1+PI3*V2+PI4*V3+PI5*V4+PI6*V5 ELS El F(IDV.EQ.2.0R.IDV.EQ.3) THEN C0$TDY-PE1+PE2*V1+PE3*V2+PE4*V3+PE5*V4+PE6*V5 ENDIF c c* * EV 1 c+ * NOW AT PR-2.0# CD AT MAX LIFT IS c* ♦ 12T FOR L/D WHERE CD .Figure C13 Subroutine to Calculate Instantaneous Cd F ig u r e C 14 Instability Instability 14 C e r u ig F Mass Flow Rates Through Inlet and Enhaust Ualues (kg/s) -0.5 1.0 oi ln: n t v boe ln: xas valve exhaust line: broken dve t ini line: solid rr- sfo Rts eue b Uig aibe Cd Variable Using by Reduced Rates ss-flow rn Rge (degrees) Rngle Crank R e se a r c h e r Test Conditions S te a d y or Orifice Type Engine Type Pressure IV/EV Forward or 1 /d fo r V a lv e -S e a t Temperature D y n a m ic C d R a tio Reverse Flow M a x im u m C d A n g le E ffe c ts Wallace (l) Steady 4 8c 2-stroke Large medium speed. 1.12 EV Forward 0.10 EV 45 deg No exhaust ports EV dia 100mm W a lla c e 8c Steady 2-stroke Sm all bore 1.0 - 8.0 EV Forward 0.02in port - Yes M itchell (2) exhaust ports opening, not 1/d W o o d s 8c Steady Poppet valves Small. EV dia l.lin 1.0 - 5.0 IV, EV Forward 8c 0.13 EV 45 deg No K a h n (3 ) IV dia 40mm reverse 0.07 IV B la ir 8c Steady 8c Poppet valves Small. EV dia 34mm 1.2 - 3.0 IV, EV Forward 8c 0.07 EV - No B la ir (4 ) dynam ic IV dia 40mm reverse none, IV D e c k k e r 8c Steady 8c Standard N/A 1.0 - 10.0 N/A Forward N/A N/A Yes C h a n g (5) dynam ic orifice plate F u k u ta n i 8c Steady 8c Poppet valves Small. IV dia 40mm 1.0 - 1.6 IV Forward 0.05 IV - No W atanabe (6) dynam ic Rabbitt (7) Steady 8c Poppet valves theoretical, generalised investigation only dynam ic Woods (8) Steady Poppet valves Small EV dia 1.37in 1.0 - 2.0 EV Forward 0.10 EV 45 deg No Table C l Summary of Previous Research on Variable Coefficients of Discharge APPENDIX D DOMINANT PIPE HYPOTHESIS On inspection of the experimental pressure traces measured in the exhaust mani fold of the Paxman 16RP200 engine close to the exhaust ports of cylinders A8 and B8, shown in figure D l, the following points were observed: (1) the B8 pulse arrives at the A8 location shortly after it has passed the B8 transducer with a slightly higher maximum pressure but with the same shape, (2) the A8 pulse arrives at the B8 location shortly after it has passed the A8 transducer also with a slightly higher maximum pressure and increased slope but following the initial rise there is little phase change, (3) when the B8 pulse arrives at cylinder A8 it has no effect on the perfor mance of A8 since the exhaust valve of A8 is shut except at the tail end of the B8 pulse. Similarly for the effect of the A8 pulse on performance of B8. Computer simulation of a single-cylinder engine and a single exhaust pipe of length equal to that from the valve of cylinder B8 to the turbine nozzle yielded a good comparison of the predicted pulse from cylinder B8 with the experimental B8 pulse. Computer simulation of a pulse system for two cylinders exhausting to a common manifold using the author’s gas-dynamic exhaust manifold model requires flow in three pipes and two volumes to be solved, and the characteristic values at all mesh points within the pipe have to be stored at each time step. For a system where three cylinders exhaust to one pulse manifold five pipes and three control volumes are required to define the system. From the above observations the following hypothesis was proposed: D l (1) Assume that the pulse arriving at A8 generated by the primary pulse from B8 is identical with the primary pulse from B8. (2) Assume that at all times flow through one pipe dominates, and that the pressure traces in all other pipes connected to the same turbine entry as the dominant pipe are represented by that of the dominant pipe. (3) For all pipes connected to one turbine entry compute the pressures in only one pipe, the length of each pipe being the distance between the exhaust valve and the turbine nozzle. This is illustrated in figure D2 which also shows that for a system where two cylinders exhaust to one manifold flow in only one pipe and one volume would need to be solved as opposed to three pipes and two volumes of the current system. (4) The determination of which pipe dominates is decided by which open exhaust valve has the highest pressure ratio across it at any instant, the pipe downstream of the valve with the highest pressure ratio being the dominant pipe. Some implications of the proposed model are: (1) all pipes in one manifold must operate on the reference temperature, pres sure and equivalence ratio, ie. the same entropy level, (2) junction reflections are assumed to be of no significance, (3) the Riemann variables, A and /? are the same in all pipes at a given instant, (4) significant savings in computer storage and execution time. Some foreseeable problems which would have to be overcome are: (1) assignation of meshes such that sections of the pipes are interchangeable, (2) determination of dominant pipe under conditions of reverse flow, (3) step changes in turbine flow caused by switching of pipes may give rise to numerical instability, D2 (4) during period when more than one exhaust valve is open flow from more than one cylinder must be allowed to flow through the turbine. D3 gure Dl Eprmnal Maue Sai Pesrs n h Ehut Manifold Exhaust the in Pressures Static Measured Experimentally l D e r u ig F EXHAUST PRESSURE 88 (8AR) EXHAUST PRESSURE A8 (BAR) of the Paxm an 16RP200 Engine Running at 1500 rpm, 17.5 bar bmep bar 17.5 rpm, 1500 at Running Engine 16RP200 an Paxm the of CRANK ANGLE DEG- ( ) CRANK DEG. ANGLE ( ) Original Gas-Dunamic Model 14 = ii + 13 + d 15 = 12 + 13 + d 14 Dominant Pipe Model Arrangement Figure D 2 Comparison of Original and Dominant Pipe Arrangements