Generation of Entropy in Spark Ignition Engines

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

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

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.

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) 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