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Int. J. of ISSN 1301-9724 Vol. 10 (No. 2), pp. 53-60, June 2007

Generation of in Spark Ignition

Bernardo Ribeiro, Jorge Martins*, António Nunes Universidade do Minho Departamento de Engenharia Mecânica 4800-058 – Guimarães – PORTUGAL [email protected]

Abstract Recent development has focused mainly on the improvement of and output emissions. The improvements in efficiency are being made by friction reduction, combustion improvement and modification. New technologies such as Variable Valve Timing (VVT) or Variable (VCR) are important for the latter. To assess the improvement capability of engine modifications, thermodynamic analysis of indicated cycles of the engines is made using the first and second . The Entropy Generation Minimization (EGM) method proposes the identification of entropy generation sources and the reduction of the entropy generated by those sources as a method to improve the thermodynamic performance of engines and other devices. A computer model created and implemented in MATLAB Simulink was used to simulate the conventional and the various processes (combustion, free expansion during exhaust, heat transfer and fluid flow through valves and throttle) were evaluated in terms of the amount of the entropy generated. An Otto cycle, a Miller cycle (over-expanded cycle) and a Miller cycle with compression ratio adjustment are studied using the referred model in order to evaluate the amount of entropy generated in each cycle. All cycles are compared in terms of produced per cycle.

Keywords: IC engines, Miller cycle, entropy generation, over-expanded cycle

1. Introduction work to pump air across the partially closed throttle valve. In the Miller cycle engine the load Several technologies are used for the is controlled by inlet valve timing, eliminating the thermodynamic improvement of internal throttle valve and the subsequent pumping losses combustion engines, such as VVT (Flierl and (Flierl and Kluting, 2000). A comparison between Kluting, 2000) or VCR (Drangel et al. (2002). To the Otto and Miller cycles was already presented evaluate the potential for thermodynamic in a theoretical study (Martins, 2004). In the same improvement of these and other technologies, study the Miller cycle was presented as an numerical studies must be performed using alternative to the conventional Otto cycle engine different tools. EGM (Drangel et al., 2002 and when used under part load conditions. A Bejan, 1996) is proposed as a tool for internal significant improvement to the Miller cycle may combustion engine improvement based on the be achieved if compression ratio adjustment is measurement of the entropy generated at several used in addition to valve timing variation. processes taking place with the engine operation. With these results it is possible to define The Miller cycle is different from the strategies for engine improvement, reducing the conventional Otto cycle engine for it has a longer amount of entropy generated.* expansion. This longer expansion is achieved using an effective shorter intake stroke. The Spark ignition internal combustion engines, intake valve, which in the Otto cycle closes running at low loads, have their thermal shortly after BDC, in the Miller cycle closes a efficiency reduced due to the effect of the throttle significant time before BDC (early intake valve valve that controls the engine load and by the fact closure - EIVC), creating a depression inside the that the compression starts at low . Under cylinder (1-8 of Figure 1), or closes significantly part load conditions, engines use some of the after BDC (late intake valve closure - LIVC), expelling the air and fuel mixture back to the intake manifold (5-1 of Figure 2). The effect is to * Author to whom correspondence should be sent Int. J. of Thermodynamics, Vol. 10 (No.2) 53 start the compression (point 1 of Figure 1 and 2. Thermodynamic Engine Model Figure 2) after the compression starting point of An entropy generation analysis was applied the Otto cycle, which is near BDC. In fact, in the to internal combustion engines and an entropy Miller cycle the intake is always at atmospheric generation calculation model was developed. A pressure, and work is not used to pump the charge computer model capable of calculating the into the cylinder as in the Otto cycle. At the same entropy generation due to several processes time, pressure and temperature at the exhaust within the engine shows that the main entropy valve opening are lower, which means that a generators in an internal combustion engine are smaller amount of of the exhaust gases is the combustion, free expansion of gas during lost during the exhaust process. exhaust and intake, heat transfer and fluid flow It was shown in a previous work (Martins, through valves (including the throttle valve). A 2004) that the Miller cycle only with intake valve scheme of this calculation model is presented in closure time variation brings some improvement Figure 3. This model is divided in a first law of to engine cycle efficiency. However the same thermodynamic model and a entropy generation cycle with a compression ratio adjustment brings model. a significant improvement to the thermal 1st law model efficiency of the theoretical cycle. The Wall Temperature dS gen due to compression ratio adjustment is made in order to Heat transfer ratio heat transfer maintain the same effective compression ratio, Engine geometry Intake /Exhaust dSgen due to free just to avoid knock onset. As the intake valve conditions (p, T, r, ...) expansion Cylinder conditions closure is delayed, the effective compression ratio (p, T, ...) of the engine decreases and the maximum Mass transfer ratio Cylinder mass dS due to temperature and pressure inside the cylinder caracteristics gen S combustion S òdSgen gen decrease, leading to less efficient cycles. This (cp, cv, r, R) Flow mass effect should be inverted by increasing the caracteristics dSgen due to flow through valves effective compression ratio. (cp , cv, r, R)

dSgen due to Throttle valve

3 Figure 3. Computer model structure for entropy generation calculation.

A single zone model is based on the first law of thermodynamics expressed as: Pressure dU = dQ - dW + hindmin - houtdmout (1) From (1) temperature can be calculated by 2 dT the integration of : dt 4 6 1 dm patm 5 dT cyl 7 8 mcylcv (T) + Tcv,m (T) = dt dt dQ dV dm = - p + T c (T) i Figure 1. Miller cycle with EIVC. dt dt å i p i dt (2)

3 And pressure is calculated from the integration of:

dp dV dm i dT V + p = T R i + R imi Û Pressure å å dt dt i dt i dt (3) dm i dT dV Tå Ri + åR imi - p 2 dp dt dt dt Û = i i dt V 4 6 where mcyl is the mass of working fluid p atm 5 1 dmi Volume trapped in the cylinder and is the flow rate dt of each species i through the valves. Figure 2. Miller cycle with LIVC.

54 Int. J. of Thermodynamics, Vol. 10 (No.2) In the model, heat from combustion is In the case of the free expansion process, the supplied using a Wiebe function (Heywood, lost work is calculated by the enthalpy of the 1988): engine gases:

é m+1ù & m& m& æ q- q0 ö Sgen,enthalpy= å (h - h0 )- å (h - h0 ) xb = 1- exp ê- aç ÷ ú (4) T T ê è Dq ø ú in 0 out 0 ë û (12) With a = 5 and m = 2, q0 is the spark time where h is the enthalpy of each chemical species at the beginning of combustion in crank angle and inducted or exhausted from the cylinder and h0 is Dq is the burning interval in crank angle. The the enthalpy of the same chemical species at heat release rate is given by: environment conditions, considering normal atmospheric conditions of pressure and dQ dx = Q b (5) temperature. dq r dq Entropy generated in a combustion process where: may be calculated using the adiabatic combustion Q = h m Q (6) chamber model. As there is no mass, heat or work R c f LHV transferred, any change in the system entropy and (Abd Alla, 2002) during the combustion process is directly caused by the process itself. Entropy generation due to h = h -1.6082 + 4.6509l - 2.0764l2 c c max( ) combustion can be calculated by the difference in (7) entropy of the combustion products and reactants: where, Blair (1999) hc max = 0.9 n n S& = m& s - m& s (13) To calculate the mass flow through the valve gen,comb å pi pi å ri ri two situations are considered depending on the i=1 i=1 flow regime (i.e. relation between the where subscripts pi and ri are products and up and downstream). The flow rate through the reactants respectively, s is the entropy and m& is valve is given by (Heywood, 1988): the mass burning rate. 1/ 2 1 ì é g-1 ùü During the operation of the engine, heat is C A p æ p ö g ï 2g ê æ p ö g úï exchanged between the cylinder charge and the m& = D r u ç d ÷ í 1 - ç d ÷ ý 1/ 2 ç p ÷ g -1 ê ç p ÷ ú cylinder walls and then between the engine and (RTu ) è u ø ï ê è u ø úï îï ë ûþï the surrounding environment. Applying the second law of thermodynamics to the cylinder (8) results in: When the flow is choked, i.e. the flow speed & & equals the speed of sound: & Qw Qcyl Sgen,heat = - (14) g Tw Tcyl p æ 2 ö g-1 d £ ç ÷ (9) & & ç ÷ where Qw and Qcyl is the heat transferred from pu è g + 1ø the cylinder content to the cylinder walls. Q& Then the flow rate is given by: w & (g+1)/ 2(g -1) and Qcyl have the same value but different signs CDARpu 1/2 æ 2 ö m& = g ç ÷ (10) and Tw and Tcyl are respectively the wall 1/2 ç g +1÷ (RTu ) è ø temperature and the cylinder gas temperature. As Where C is the discharge coefficient, p and the heat is not stored at the engine walls but is D u transferred to the surroundings, equation (14) may T are the upstream pressure and temperature u be written as (Ribeiro, 2006): respectively, pd is the downstream pressure and R is the gas constant. & & Q(Tcyl- T0 ) Sgen,heat = (15) 3. Entropy Generation T0Tcyl

At exhaust valve opening, cylinder gases are where T0 is the environment temperature, still at high pressure and temperature. That considered as 25ºC. The value of the heat transfer enthalpy could be recovered if expanded until the rate (Q& ) is calculated using the Annand heat environment pressure and temperature conditions. transfer coefficient (Blair,1999): As these gases are freely released to the dQ surroundings, that potential work is lost. Entropy Q& = = (C + C )(T - T )m A (16) generated in this process is calculated using the dt h r cyl w cyl tr Gouy-Stodola theorem: Wlost = T0 × Sgen (11)

Int. J. of Thermodynamics, Vol. 10 (No.2) 55 where Atr is the heat transfer area that is fixed for M – Mach number of gases at valve inlet: the engine head and piston and variable for the u M = cylinder walls, Tcyl is the inside cylinder gas c temperature and Tw is the wall (cylinder, piston or engine head) temperature, assumed as constant u –velocity of gases in pipe during the overall engine cycle. The radiation heat c – sound velocity in gases: c = g RT transfer coefficient (Cr) is given by: 4 4 Entropy is generated at the throttle valve in -9 Tcyl- Tw Cr = 4.25 ´10 (17) the case of the Otto cycle engine, and at the intake Tcyl- Tw and exhaust valves for all the engines.

The convection heat transfer coefficient (Ch) 4. Results is related to the Nusselt number 0.7 The model is used hereafter to calculate the ( Nu = 0.49 Re ) as: entropy generated in an internal combustion kcylNu engine working under the Otto cycle and the C = (18) Miller cycle. The load of the Otto cycle is h B controlled by the intake pressure (throttle valve), where B is the cylinder bore, kcyl the the thermal while the load of the Miller cycle is controlled by conductivity of the gases inside the cylinder and the extent of the effective intake stroke (opening Re is the Reynolds number period of the intake valve). This obviously results in different effective compression ratios when the æ rcylup B ö ç Re = ÷ . engine is running at part load (the Otto and the ç ÷ è mcyl ø Miller engines at full load have the same CR as the Miller VCR engine at part load). Another source of energy loss during the engine working is internal friction. Friction is The following sections analyze each entropy calculated using a proposed method (Sandoval, generation mechanism and how it reacts to cycle changes. The simulations were performed in a 2003). Entropy generation is calculated using 3 again the Gouy-Stodola theorem (11): single cylinder engine (211 cm ) running at 36% of load (3 bar bmep) and 2500 rpm. TABLE I & & Wlost,friction describes various engine characteristics and Sgen,friction= (19) working conditions. T0 Analyzing the importance of each of the when passing through a valve the gas flow suffers entropy generating processes referred to above, a pressure drop due to the valve and duct one can see that the free expansion process is the geometry. The engine spends work on most important (Figure 4). This is mainly caused overcoming this resistance to fluid flow. by the blow-down effect after exhaust valve Considering a quasi-steady gas flow through the opening. valve, the entropy generation rate can be calculated from the state properties: Combustion is the second entropy generating process, followed by heat transfer. These three d é ù & æ Tu ö æ pu ö processes are responsible for more than 80% of S = m& ds = m& êc lnç ÷ - R lnç ÷ú = gen,valve ò p ç T ÷ ç p ÷ u ëê è d ø è d øûú the total amount of entropy generated in the engine. é æ g -1 ö g -1 æ p öù (20) & 2 ç u ÷ = mêcp lnç1 - M ÷ + cp lnç ÷ú = TABLE I. ENGINE CHARACTERISTICS AND ëê è 2 ø g è pd øûú WORKING CONDITIONS. é g-1ù ê g -1 æ p ö g ú & æ 2 öç u ÷ Miller = mcp lnêç1- M ÷ç ÷ ú Otto Miller êè 2 øè pd ø ú VCR ë û Bore x stroke [mm] 70 x 55 where: Spark time [CA] 15 º BTDC Burn duration [CA] 40 p ; p – gases pressure upstream and u d IVC [º ABDC] 32 137 135 downstream of valve respectively; Geometric CR 11.5:1 11.5:1 19:1 Tu; Td – gases temperature upstream and Effective CR 3.1:1 2.4:1 4.2:1 downstream of valve respectively; Mean eff. pres. [bar] 3 c Fuel injected [mg] 6.72 5.56 4.76 g – ratio: g = p Tmax [K] 1979 1958 1870 cv Pmax [bar] 25.9 21.8 29.5 Texhaust [K] 974 953 830 Pexhaust [bar] 1.6 1.3 1.0

56 Int. J. of Thermodynamics, Vol. 10 (No.2) 0.80 at the intake stroke. The elimination of blow-back

0.70 on the Miller cycle when EIVC is used makes the

0.60 entropy generated at the intake be reduced by

0.50 Flow through valves 39%. However at higher loads, when the blow- Friction 0.40 Heat transfer back is not so significant, the LIVC method may Combustion have less entropy generated at the intake than the 0.30 Free expansion EIVC method because with LIVC the intake valve 0.20 Entropy generated [J/K] has wider opening area. 0.10

0.00 Otto Miller Miller VCR Engine configuration TABLE II. ENTROPY GENERATED PER

CYCLE (J/K). Figure 4. Entropy generated in each cycle. Miller Otto Miller VCR 4.1. Free Expansion Free expansion 0.294 0.271 0.208 Combustion 0.220 0.190 0.162 During the mass exchange processes, intake Heat transfer 0.162 0.148 0.127 and exhaust, the flow is achieved by the pressure Friction 0.050 0.063 0.076 differences across each valve. This difference of pressures leads to an expansion resulting in the Flow through valves 0.036 0.018 0.020 exergy lost of the gases, or in other words, TOTAL 0.762 0.691 0.593 entropy generation. This phenomenon is more severe during the blow-down phase just after the 4.2. Combustion exhaust valve opening. During this period the The entropy generated during combustion pressure inside the cylinder reduces suddenly and corresponds to the entropy increase due to the a great amount of mass flows out of the cylinder. chemical reaction taking place inside the engine In conventional spark ignition (Otto) engine, this cylinder and heat transferred within that mass of mass of burned gases is at a significant high gas. It depends mainly on three variables: the temperature (usually higher than 900K) and amount of fuel burned, the temperature and the pressure (~1.5 bar) (TABLE ) and is completely pressure of the gases inside the engine. As can be released into the environment (considered at seen from Table II, the entropy generated by this atmospheric conditions). As the over-expansion is process decreases (by 14%) when the Miller cycle increased, the pressure and temperature inside the is used and decreases even more (by 26%) if VCR engine at the exhaust valve opening are lower, is used. In fact, with the Miller VCR cycle the leading to a reduced amount of entropy generated maximum pressure in the cycle is higher but the in this process (reduction by 29% when temperature is slightly lower. With this increase comparing the Otto and the Miller VCR engine of the pressure, the specific entropy of the burned cycles). gases decreases. However, the quantity of fuel As it can be seen from Figure 4 (Table II) needed to produce the same load reduces (by the difference between the Otto cycle and the 29%), decreasing the amount of generated Miller cycle is small because in both cycles, the entropy. load decreases with a decrease of the maximum temperature and pressure of the cycle, resulting in 4.3. Heat Transfer an approximately equal temperature and pressure In internal combustion engines, the heat at the exhaust valve opening. In the case of the transfer is a significant process during the Miller cycle, the benefits achieved by the over- combustion and expansion stroke. In the rest of expansion are almost the same as the losses due to the cycle the value for heat transfer is small (due the blow-back at the end of intake. to the small difference between the in-cylinder The Miller VCR cycle engine has a gas temperature and the wall temperature) and the significantly lower amount of entropy generated amount of heat that flows in and out of the engine (Table II) because the temperature and pressure at is small. During combustion (when the maximum the exh aust valve opening are lower, despite the temperature is reached), the heat transfer from the higher cycle peak pressure. In fact, in this cycle engine gases to the cylinder walls is high. the rate of temperature and pressure decrease Comparing the Miller cycle with the Otto during expansion is higher due to the lower cycle (Figure 4, Table II), there is a reduction of combustion volume (much smaller combustion the amount of heat transferred and of the entropy chamber) and less mass (better efficiency). generated due to this process, because the The two methods to implement the Miller maximum cycle temperature in the Miller cycle is cycle (LIVC and EIVC) have different results in lower than in the Otto cycle. In the Miller VCR terms of entropy generated due to free expansion cycle engine, the entropy generated due to the

Int. J. of Thermodynamics, Vol. 10 (No.2) 57 heat transfer is less (Table II). The combustion generation. In fact, the absolute reduction of the chamber in the case of the Miller VCR cycle is entropy generated in the combustion process is more compact, with less heat transfer area and the 0.058 J/K, while the absolute reduction of the mean gas cycle temperature is also lower, leading entropy generated in the free expansion process is to an overall reduction of the entropy generated 0.086 J/K. due to heat transfer. From the above it can be seen that the Miller 4.4. Friction cycle with compression ratio adjustment can play a very important role in this achievement. The friction component of the entropy In terms of specific entropy generated generated is the only one that increases when the (amount of entropy generated divided by the work engine is modified from Otto to Miller and even produced by the engine - Figure 5). In both more when VCR is used (Table II). For the same Figures 4 and 5 it is possible to see that the Miller load level and from the Otto to the Miller cycle, cycle engine with compression ratio adjustment is there is an increase of the intake pressure the most efficient engine. This means an (considered as atmospheric on the Miller cycle), improvement of 20.4% in the absolute entropy raising the pressure level of the cycle. When the generated and 19.8% on the specific entropy cycle is changed to the Miller VCR, the intake generated in relation to the Otto cycle at similar pressure is higher than in the Otto cycle and the load (3 bar bmep). compression ratio increases, increasing even more 0.009 engine friction. In terms of entropy generated, 0.0084 0.008 0.0078 which is directly proportional to the work loss in -1 friction, the increase is 52% from the Otto cycle 0.007 0.0067 to the Miller VCR cycle. Since the weight of the 0.006 friction component of the entropy generated is 0.005 low, there is no significant effect on the overall 0.004 entropy generated in the cycle. 0.003 0.002

4.5. Flow Through Valves Specific entropy generated [K ] 0.001 0 Otto Miller Miller VCR The mass flow through valves takes place Engine configuration during the intake and exhaust stroke in all the engines. The entropy generated by this process is Figure 5. Specific entropy generated per cycle. a result of the friction of the gases on the surface 5. Conclusions of the elements of the valve and seat and in the throttle valve of the Otto cycle engine. In this article the Otto cycle, the Miller cycle As can be seen from Figure 4 (Table II), in and the Miller cycle with compression ratio the Otto cycle the entropy generated is adjustment (Miller VCR) are compared under part significantly higher than in the Miller cycle, load conditions. The EGM method was used to mainly because of the passage through the throttle study the improvement of the use of the Miller valve. If this was not considered, the entropy cycle engines for automotive applications. generated in the cylinder valves would be lower In a computer model implemented in Matlab than in any of the Miller cycles, because in the Simulink it is possible to calculate and compare Otto cycle there is no back-flow to the intake the several comp onents of the entropy generation manifold and the intake pressure is low. In the in an internal combustion engine. From these five case of the Miller VCR, the amount of entropy main sources of entropy (combustion, free generated is significantly higher when LIVC is expansion, heat transfer, friction and flow through used instead of the EIVC strategy. This is caused valves), the free expansion and combustion are by the back-flow from the cylinder to the intake the most important, always being responsible for manifold during the upward movement of the more than 60% of the entropy generated for all piston. the engine cycles studied. 4.6. Overall Entropy Generation If the Miller cycle is used, the amount of gases expanding at the exhaust blow-down is From the analysis of the several entropy reduced and the entropy generated drops, generating processes it is possible to determine obtaining more efficient engines. the best strategy for improvement of internal combustion engines. It is possible therefore to Using the work and the entropy generated to establish that the recovering of the exergy determine the most efficient engine, it can be seen destroyed during the free expansion, especially that the Miller cycle (with load controlled by the during the exhaust stroke, should be the main duration of the inlet valve opening) and objective of engine development, because any compression ratio adjustment produces less improvement on that process may lead to a entropy than the Otto cycle with the load significant improvement in the overall entropy controlled by a throttle valve. 58 Int. J. of Thermodynamics, Vol. 10 (No.2) The results obtained from the EGM model r - reactants allow the establishment of an improvement u – upstream direction for SI internal combustion engines when w - wall working under part load conditions. The improvement is obtained through the reduction of Abbreviations the entropy generated during the engine work, ABDC – After Bottom Dead Center specially reducing the entropy generated due to BDC – Bottom Dead Center free expansion at the exhaust process. BTDC – Before Top Dead Center CA – Crank Angle CR – Compression Ratio List of Symbols EGM – Entropy Generation Minimization EIVC – Early Intake Valve Closure Ar – cross flow area IVC – Intake Valve Closure Atr – heat transfer area B – cylinder bore LIVC – Late Intake Valve Closure c – sound velocity VCR – Variable Compression Ratio VVT – Variable Valve Timing CD – discharge coefficient Ch – convection heat transfer coef. Acknowledgments cv – specific heat capacity cp – specific heat capacity Bernardo Ribeiro thanks the FCT and FSE (in the Cr – radiation heat transfer coef. scope of QCA III) for the financial support given h – specific enthalpy for his research activities. This work was funded k - thermal conductivity by FCT/FEDER POCI/ENR/59168/2004. m – mass M – Mach number m& – mass rate References Nu – Nusselt number Abd Alla, G. H., 2002, “Computer simulation of a p – pressure Q – heat four stroke spark ignition engine”, En. Convers. Mng. Nº 43, pp. 1043-1061. QLHV – lower heating value QR – heat released Bejan, A., 1994, Entropy generation through heat Q& - heat rate and fluid flow, John Wiley & Sons, New York. R – gas constant Bejan, A., 1996, Entropy Generation Re – Reynolds number Minimization, CRC Press, Boca Raton. s – specific entropy Bejan, A., 1997, Advanced Thermo- & dynamics, Second Edition, John Wiley & Sons, Sgen - rate of entropy generation New York. t – time T – temperature Bejan, A., 2002, “Fundamentals of exergy u – velocity analysis, entropy generation minimization, and U – the generation of flow architecture”, Int. J. Energy Res., Nº 26, pp.545-565. up – mean piston velocity V – volume Blair, G. P., 1999 “Design and Simulation of W – work Four-Stroke Engines”, SAE. x – fraction of burned gases b Drangel, H., Reinmann, R., Olofsson, E., 2002, g – heat capacity ratio “The Variable Compression (Svc) and the h – efficiency Combustion Control (Scc) – Two Ways to l – excess air Improve Fuel Economy and Still Comply With m - viscosity World-Wide Emission Requirements”, SAE 2002- q – crank angle 01-0996. r - density Flierl, R., Kluting, M., 2000, “The Third subscripts Generation of Valvetrains-New Fully Va riable 0 – environmental Valvetrains for Throttle-Free Load Control”, SAE c – combustion 2000-01-1227. cyl – of the gas inside the cylinder Heywood, J. B., 1988, Internal Combustion d – downstream Engines Fundamentals, McGraw-Hill. f – fuel Martins, J., et al., 2004, « Thermodynamic in – entering analysis of an Over-Expanded Engine”, SAE m – mean value 2004-01-0617. out – exiting p – products of combustion Int. J. of Thermodynamics, Vol. 10 (No.2) 59 Ribeiro, B., 2006, “Thermodynamic Optimisation Sandoval, D., Heywood, J., 2003, “An Improved of Spark Ignition Engines at Part-Load Friction Model for Spark-Ignition Engines”, SAE Conditions”, Ph.D Thesis, Universidade do 2003-01-0725. Minho, Portugal.

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