Int. J. of Thermodynamics ISSN 1301-9724 Vol. 10 (No. 2), pp. 53-60, June 2007
Generation of Entropy in Spark Ignition Engines
Bernardo Ribeiro, Jorge Martins*, António Nunes Universidade do Minho, Departamento de Engenharia Mecânica 4800-058 Guimarães PORTUGAL [email protected]
Abstract Recent engine development has focused mainly on the improvement of engine efficiency and output emissions. The improvements in efficiency are being made by friction reduction, combustion improvement and thermodynamic cycle modification. New technologies such as Variable Valve Timing (VVT) or Variable Compression Ratio (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 laws of thermodynamics. 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 heat engines and other devices. A computer model created and implemented in MATLAB Simulink was used to simulate the conventional Otto cycle 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 work produced per cycle.
Keywords: IC engines, Miller cycle, entropy generation, over-expanded cycle
1. Introduction Under part load conditions, engines use some of the work to pump air across the partially closed Several technologies are used for the throttle valve. In the Miller cycle engine the load thermodynamic improvement of internal is controlled by inlet valve timing, eliminating combustion engines, such as VVT (Flierl and the throttle valve and the subsequent pumping Kluting, 2000) or VCR (Drangel et al. 2002). To losses (Flierl and Kluting, 2000). A comparison evaluate the potential for thermodynamic between the Otto and Miller cycles was already improvement of these and other technologies, presented in a theoretical study (Martins, 2004). numerical studies must be performed using In the same study the Miller cycle was presented different tools. EGM (Drangel et al., 2002 and as an alternative to the conventional Otto cycle Bejan, 1996) is proposed as a tool for internal engine when used under part load conditions. A combustion engine improvement based on the significant improvement to the Miller cycle may measurement of the entropy generated at several be achieved if compression ratio adjustment is processes taking place with the engine operation. used in addition to valve timing variation. With these results it is possible to define strategies for engine improvement, reducing the The Miller cycle is different from the amount of entropy generated. i conventional Otto cycle engine for it has a longer expansion. This longer expansion is achieved Spark ignition internal combustion engines, using an effective shorter intake stroke. The running at low loads, have their thermal intake valve, which in the Otto cycle closes efficiency reduced due to the effect of the throttle shortly after BDC, in the Miller cycle closes a valve that controls the engine load and by the significant time before BDC (early intake valve fact that the compression starts at low pressure. closure - EIVC), creating a depression inside the *Author to whom correspondence should be addressed Int. J. of Thermodynamics, Vol. 10 (No. 2) 53 cylinder (1-8 of Figure 1 ), or closes significantly 2. Thermodynamic Engine Model after BDC (late intake valve closure - LIVC), expelling the air and fuel mixture back to the An entropy generation analysis was applied intake manifold (5-1 of Figure 2 ). The effect is to internal combustion engines and an entropy to start the compression (point 1 of Figure 1 and generation calculation model was developed. A Figure 2 ) after the compression starting point of computer model capable of calculating the the Otto cycle, which is near BDC. In fact, in the entropy generation due to several processes Miller cycle the intake is always at atmospheric within the engine shows that the main entropy pressure, and work is not used to pump the generators in an internal combustion engine are charge into the cylinder as in the Otto cycle. At the combustion, free expansion of gas during the same time, pressure and temperature at the exhaust and intake, heat transfer and fluid flow exhaust valve opening are lower, which means through valves (including the throttle valve). A that a smaller amount of enthalpy of the exhaust scheme of this calculation model is presented in gases is lost during the exhaust process. Figure 1. This model is divided in a first law of thermodynamics model and a entropy generation It was shown in a previous work (Martins, model. 2004) that the Miller cycle only with intake valve 1st law model closure time variation brings some improvement Wall Temperature dS gen due to to engine cycle efficiency. However the same Heat transfer ratio heat transfer cycle with a compression ratio adjustment brings Engine geometry Intake/Exhaust dS gen due to free a significant improvement to the thermal conditions (p, T, ρ, ...) expansion Cylinder conditions efficiency of the theoretical cycle. The (p, T, ...) compression ratio adjustment is made in order to Mass transfer ratio Cylinder mass dS due to maintain the same effective compression ratio, caracteristics gen S combustion Σ ∫dS gen gen just to avoid knock onset. As the intake valve (cp, cv, ρ, R) closure is delayed, the effective compression Flow mass caracteristics dS gen due to flow through valves ratio of the engine decreases and the maximum (cp, cv, ρ, R) temperature and pressure inside the cylinder decrease, leading to less efficient cycles. This dS gen due to Throttle valve effect should be inverted by increasing the effective compression ratio. Figure 1. Computer model structure for entropy generation calculation.
3 A single zone model is based on the first
law of thermodynamics expressed as:
dU = dQ − dW + hindmin − houtdmout (1) Pressure From (1) temperature can be calculated by dT 2 the integration of : dt 4 6 1 dT dmcyl patm 5 m c ()T + Tc ()T = 7 8 cyl v dt ,v m dt Volume (2) dQ dV dmi Figure 1. Miller cycle with EIVC . = p + ‡”Ti cp()T dt dt i dt 3
And pressure is calculated from the integration of:
Pressure dp dV dmi dT V + p = T∑ Ri + ∑ Rimi ⇔ dt dt i dt i dt (3) dmi dT dV 2 T∑ Ri + ∑ Rimi − p dp dt dt dt ⇔ = i i 4 dt V 6 p atm 5 1 where mcyl is the mass of working fluid Volume dmi Figure 2. Miller cycle with LIVC . trapped in the cylinder and is the flow rate dt of each species i through the valves.
54 Int. J. of Thermodynamics, Vol. 10 (No. 2) In the model, heat from combustion is In the case of the free expansion process, supplied using a Wiebe function (Heywood, the lost work is calculated by the enthalpy of the 1988): engine gases: m+1 m& m& θ − θ0 S& gen,enthalpy = ∑ ()h − h0 − ∑ ()h − h0 xb = 1− exp− a (4) T T θ in 0 out 0 (12) With a = 5 and m = 2, θ0 is the spark time where h is the enthalpy of each chemical species at the beginning of combustion in crank angle inducted or exhausted from the cylinder and h0 is and θ is the burning interval in crank angle. the enthalpy of the same chemical species at The heat release rate is given by: environment conditions, considering normal atmospheric conditions of pressure and dQ dx = Q b (5) temperature. dθ R dθ Entropy generated in a combustion process where: may be calculated using the adiabatic Q = η m Q (6) combustion chamber model. As there is no mass, R c f LHV heat or work transferred, any change in the and (Abd Alla, 2002) system entropy during the combustion process is directly caused by the process itself. Entropy η = η − .1 6082 + .4 6509λ − .2 0764λ2 c c max ( ) generation due to combustion can be calculated (7) by the difference in entropy of the combustion where, Blair (1999) ηc max = 9.0 products and reactants: To calculate the mass flow through the n n S& = m s − m s valve two situations are considered depending on gen,comb ∑ & pi pi ∑ & ri ri (13) the flow regime (i.e. relation between the i=1 i=1 pressures up and downstream). The flow rate where subscripts pi and ri are products and through the valve is given by (Heywood, 1988): reactants respectively, s is the entropy and m& is 2/1 the mass burning rate. 1 γ−1 C A p p γ 2γ p γ During the operation of the engine, heat is m = D r u d 1 − d & 2/1 exchanged between the cylinder charge and the ()RT pu γ −1 pu u cylinder walls and then between the engine and the surrounding environment. Applying the (8) second law of thermodynamics to the cylinder When the flow is choked, i.e. the flow results in: speed equals the speed of sound: Q& Q& cyl γ S& = w − (14) gen,heat T T pd 2 γ−1 w cyl ≤ (9) pu γ +1 where Q& w and Q& cyl is the heat transferred from Then the flow rate is given by: the cylinder content to the cylinder walls. Q& w (γ+1) 2/ (γ−1) CDAR pu 2/1 2 and Q& have the same value but different signs m& = γ (10) cyl 2/1 γ +1 ()RTu and Tw and Tcyl are respectively the wall temperature and the cylinder gas temperature. As Where CD is the discharge coefficient, pu and T are the upstream pressure and temperature the heat is not stored at the engine walls but is u transferred to the surroundings, equation (14) respectively, pd is the downstream pressure and R is the gas constant. may be written as (Ribeiro, 2006): Q& (Tcyl − T0 ) 3. Entropy Generation S& = (15) gen,heat T T At exhaust valve opening, cylinder gases 0 cyl are still at high pressure and temperature. That where T 0 is the environment temperature, enthalpy could be recovered if expanded until the considered as 25ºC. The value of the heat environment pressure and temperature transfer rate ( Q& ) is calculated using the Annand conditions. As these gases are freely released to heat transfer coefficient (Blair,1999): the surroundings, that potential work is lost. dQ Entropy generated in this process is calculated Q& = = ()C + C (T − T )m A (16) using the Gouy-Stodola theorem: dt h r cyl w cyl tr
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 T w is the wall (cylinder, piston or engine head) temperature, assumed as u –velocity of gases in pipe constant during the overall engine cycle. The c – sound velocity in gases: c = γ RT radiation heat transfer coefficient (Cr) is given by: Entropy is generated at the throttle valve in 4 4 the case of the Otto cycle engine, and at the −9 Tcyl − Tw Cr = .4 25×10 (17) intake and exhaust valves for all the engines. Tcyl − Tw 4. Results The convection heat transfer coefficient The model is used hereafter to calculate the (Ch) is related to the Nusselt number 7.0 entropy generated in an internal combustion ( Nu = .0 49Re ) as: engine working under the Otto cycle and the kcyl Nu Miller cycle. The load of the Otto cycle is C = (18) controlled by the intake pressure (throttle valve), h B while the load of the Miller cycle is controlled by where B is the cylinder bore, k cyl the the thermal the extent of the effective intake stroke (opening conductivity of the gases inside the cylinder and period of the intake valve). This obviously Re is the Reynolds number results in different effective compression ratios when the engine is running at part load (the Otto ρcyl up B Re= . and the Miller engines at full load have the same cyl CR as the Miller VCR engine at part load). Another source of energy loss during the The following sections analyze each engine working is internal friction. Friction is entropy generation mechanism and how it reacts to cycle changes. The simulations were calculated using a proposed method (Sandoval, 3 2003). Entropy generation is calculated using performed in a single cylinder engine (211 cm ) again the Gouy-Stodola theorem (11): running at 36% of load (3 bar bmep) and 2500 rpm. TABLE I describes various engine W& lost,friction characteristics and working conditions. S& gen,friction = (19) T0 Analyzing the importance of each of the entropy generating processes referred to above, when passing through a valve the gas flow one can see that the free expansion process is the suffers a pressure drop due to the valve and duct most important ( Figure ). This is mainly caused geometry. The engine spends work on by the blow-down effect after exhaust valve overcoming this resistance to fluid flow. opening. Considering a quasi-steady gas flow through the valve, the entropy generation rate can be Combustion is the second entropy calculated from the state properties: generating process, followed by heat transfer. These three processes are responsible for more d Tu pu than 80% of the total amount of entropy S& = m& ds = m& c ln − R ln = gen,valve ∫ p T p u d d generated in the engine. γ −1 γ −1 p (20) TABLE I. ENGINE CHARACTERISTICS AND = m c ln 1− M2 + c ln u = & p p WORKING CONDITIONS. 2 γ pd γ−1 Miller Otto Miller γ −1 2 pu γ VCR = m& cp ln1− M 2 pd Bore x stroke [mm] 70 x 55 Spark time [CA] 15 º BTDC where: Burn duration [CA] 40 IVC [º ABDC] 32 137 135 pu; p d – gases pressure upstream and downstream of valve respectively; Geometric CR 11.5:1 11.5:1 19:1 Effective CR 3.1:1 2.4:1 4.2:1 Tu; Td – gases temperature upstream and Mean eff. pres. [bar] 3 downstream of valve respectively; Fuel injected [mg] 6.72 5.56 4.76 c Tmax [K] 1979 1958 1870 γ – heat capacity ratio: γ = p Pmax [bar] 25.9 21.8 29.5 cv Texhaust [K] 974 953 830 Pexhaust [bar] 1.6 1.3 1.0 56 Int. J. of Thermodynamics, Vol. 10 (No. 2) 0.80 back on the Miller cycle when EIVC is used
0.70 makes the entropy generated at the intake be
0.60 reduced by 39%. However at higher loads, when
0.50 Flow through valves the blow-back is not so significant, the LIVC Friction 0.40 Heat transfer method may have less entropy generated at the Combustion intake than the EIVC method because with LIVC 0.30 Free expansion the intake valve has wider opening area. 0.20 Entropy generated [J/K] generated Entropy
0.10 TABLE II. ENTROPY GENERATED PER
0.00 CYCLE (J/K). Otto Miller Miller VCR Engine configuration Miller Otto Miller VCR Figure 4. Entropy generated in each cycle. Free expansion 0.294 0.271 0.208 4.1. Free expansion 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 Flow through valves 0.036 0.018 0.020 pressures leads to an expansion resulting in the TOTAL 0.762 0.691 0.593 exergy lost of the gases, or in other words, entropy generation. This phenomenon is more 4.2. Combustion severe during the blow-down phase just after the 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 I) 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 process decreases (by 14%) when the Miller is increased, the pressure and temperature inside cycle is used and decreases even more (by 26%) the engine at the exhaust valve opening are if VCR is used. In fact, with the Miller VCR lower, leading to a reduced amount of entropy cycle the maximum pressure in the cycle is generated in this process (reduction by 29% higher but the temperature is slightly lower. With when comparing the Otto and the Miller VCR this increase of the pressure, the specific entropy engine cycles). of the burned gases decreases. However, the quantity of fuel needed to produce the same load As it can be seen from Figure 4 (Table II) reduces (by 29%), decreasing the amount of the difference between the Otto cycle and the generated entropy. Miller cycle is small because in both cycles, the load decreases with a decrease of the maximum 4.3. Heat transfer temperature and pressure of the cycle, resulting in an approximately equal temperature and In internal combustion engines, the heat pressure at the exhaust valve opening. In the case transfer is a significant process during the of the Miller cycle, the benefits achieved by the combustion and expansion stroke. In the rest of over-expansion are almost the same as the losses the cycle the value for heat transfer is small (due due to the blow-back at the end of intake. to the small difference between the in-cylinder gas temperature and the wall temperature) and The Miller VCR cycle engine has a the amount of heat that flows in and out of the significantly lower amount of entropy generated engine is small. During combustion (when the (Table II) because the temperature and pressure maximum temperature is reached), the heat at the exhaust valve opening are lower, despite transfer from the engine gases to the cylinder the higher cycle peak pressure. In fact, in this walls is high. cycle the rate of temperature and pressure decrease during expansion is higher due to the Comparing the Miller cycle with the Otto lower combustion volume (much smaller cycle ( Figure , Table II), there is a reduction of combustion chamber) and less mass (better the amount of heat transferred and of the entropy efficiency). generated due to this process, because the maximum cycle temperature in the Miller cycle The two methods to implement the Miller is lower than in the Otto cycle. In the Miller cycle (LIVC and EIVC) have different results in VCR cycle engine, the entropy generated due to terms of entropy generated due to free expansion the heat transfer is less (Table II). The at the intake stroke. The elimination of blow- Int. J. of Thermodynamics, Vol. 10 (No. 2) 57 combustion chamber in the case of the Miller generation. In fact, the absolute reduction of the VCR cycle is more compact, with less heat entropy generated in the combustion process is transfer area and the mean gas cycle temperature 0.058 J/K, while the absolute reduction of the is also lower, leading to an overall reduction of entropy generated in the free expansion process the entropy generated due to heat transfer. is 0.086 J/K. 4.4. Friction From the above it can be seen that the Miller cycle with compression ratio adjustment The friction component of the entropy can play a very important role in this generated is the only one that increases when the achievement. engine is modified from Otto to Miller and even In terms of specific entropy generated more when VCR is used (Table II). For the same (amount of entropy generated divided by the load level and from the Otto to the Miller cycle, work produced by the engine - Figure 2). In both there is an increase of the intake pressure Figures 4 and 5 it is possible to see that the (considered as atmospheric on the Miller cycle), Miller cycle engine with compression ratio raising the pressure level of the cycle. When the adjustment is the most efficient engine. This cycle is changed to the Miller VCR, the intake means an improvement of 20.4% in the absolute pressure is higher than in the Otto cycle and the entropy generated and 19.8% on the specific compression ratio increases, increasing even entropy generated in relation to the Otto cycle at more engine friction. In terms of entropy similar load (3 bar bmep). generated, which is directly proportional to the 0.009 work loss in friction, the increase is 52% from 0.0084 0.008 0.0078 the Otto cycle to the Miller VCR cycle. Since the -1 weight of the friction component of the entropy 0.007 0.0067 generated is low, there is no significant effect on 0.006 the overall entropy generated in the cycle. 0.005 0.004 4.5. Flow through valves 0.003 0.002
The mass flow through valves takes place Specific entropy generated [K ] 0.001 during the intake and exhaust stroke in all the 0 Otto Miller Miller VCR engines. The entropy generated by this process is Engine configuration a result of the friction of the gases on the surface of the elements of the valve and seat and in the Figure 2. Specific entropy generated per cycle. throttle valve of the Otto cycle engine. 5. Conclusions As can be seen from Figure (Table II), in the Otto cycle the entropy generated is In this article the Otto cycle, the Miller significantly higher than in the Miller cycle, cycle and the Miller cycle with compression ratio mainly because of the passage through the adjustment (Miller VCR) are compared under throttle valve. If this was not considered, the part load conditions. The EGM method was used entropy generated in the cylinder valves would to study the improvement of the use of the Miller be lower than in any of the Miller cycles, cycle engines for automotive applications. because in the Otto cycle there is no back-flow to In a computer model implemented in the intake manifold and the intake pressure is Matlab Simulink it is possible to calculate and low. In the case of the Miller VCR, the amount compare the several components of the entropy of entropy generated is significantly higher when generation in an internal combustion engine. LIVC is used instead of the EIVC strategy. This From these five main sources of entropy is caused by the back-flow from the cylinder to (combustion, free expansion, heat transfer, the intake manifold during the upward movement friction and flow through valves), the free of the piston. expansion and combustion are the most important, always being responsible for more 4.6. Overall entropy generation than 60% of the entropy generated for all the From the analysis of the several entropy engine cycles studied. generating processes it is possible to determine If the Miller cycle is used, the amount of the best strategy for improvement of internal gases expanding at the exhaust blow-down is combustion engines. It is possible therefore to reduced and the entropy generated drops, establish that the recovering of the exergy obtaining more efficient engines. destroyed during the free expansion, especially during the exhaust stroke, should be the main Using the work and the entropy generated objective of engine development, because any to determine the most efficient engine, it can be improvement on that process may lead to a seen that the Miller cycle (with load controlled significant improvement in the overall entropy by the duration of the inlet valve opening) and compression ratio adjustment produces less 58 Int. J. of Thermodynamics, Vol. 10 (No. 2) entropy than the Otto cycle with the load p products of combustion controlled by a throttle valve. r reactants The results obtained from the EGM model u upstream allow the establishment of an improvement w wall direction for SI internal combustion engines Abbreviations when working under part load conditions. The improvement is obtained through the reduction ABDC After Bottom Dead Center of the entropy generated during the engine work, BDC Bottom Dead Center specially reducing the entropy generated due to BTDC Before Top Dead Center free expansion at the exhaust process. 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 Cr radiation heat transfer coef. the scope of QCA III) for the financial support h specific enthalpy given for his research activities. This work was k thermal conductivity funded by FCT/FEDER POCI/ENR/59168/2004. m mass M Mach number References m& mass rate Abd Alla, G. H., 2002, “Computer simulation of Nu Nusselt number a four stroke spark ignition engine”, En. p pressure Convers. Mng. Nº 43, pp. 1043-1061. Q heat Bejan, A., 1994, Entropy generation through QLHV lower heating value heat and fluid flow , John Wiley & Sons, New QR heat released York. Q& heat rate Bejan, A., 1996, Entropy Generation R gas constant Minimization , CRC Press, Boca Raton. Re Reynolds number Bejan, A., 1997, Advanced Engineering Thermo- s specific entropy dynamics , Second Edition, John Wiley & Sons, S& gen rate of entropy generation New York. t time Bejan, A., 2002, “Fundamentals of exergy T temperature analysis, entropy generation minimization, and u velocity the generation of flow architecture”, Int. J. U internal energy Energy Res. , Nº 26, pp.545-565. u mean piston velocity p Blair, G. P., 1999 “Design and Simulation of V volume W work Four-Stroke Engines”, SAE . xb fraction of burned gases Drangel, H., Reinmann, R., Olofsson, E., 2002, γ heat capacity ratio “The Variable Compression (Svc) and the η efficiency Combustion Control (Scc) – Two Ways to Improve Fuel Economy and Still Comply With λ excess air World-Wide Emission Requirements”, SAE viscosity 2002-01-0996. θ crank angle Flierl, R., Kluting, M., 2000, “The Third ρ density Generation of Valvetrains-New Fully Variable subscripts Valvetrains for Throttle-Free Load Control”, SAE 2000-01-1227 . 0 environmental c combustion Heywood, J. B., 1988, Internal Combustion cyl of the gas inside the cylinder Engines Fundamentals , McGraw-Hill. d downstream Martins, J., et al., 2004, « Thermodynamic f fuel analysis of an Over-Expanded Engine”, SAE in entering 2004-01-0617 . out exiting Int. J. of Thermodynamics, Vol. 10 (No. 2) 59 Ribeiro, B., 2006, “Thermodynamic Sandoval, D., Heywood, J., 2003, “An Improved Optimisation of Spark Ignition Engines at Part- Friction Model for Spark-Ignition Engines”, SAE Load Conditions”, Ph.D Thesis, Universidade do 2003-01-0725. Minho, Portugal.
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