2. Development of Thermodynamic Models for Engine Design P M V Subbarao Professor Mechanical Engineering Department Methods to Design for Performance….

3. First Law Analysis: Transient Compression of gaseous Control Mass Compression Process Fuel+Air+residual gas Air+residual gas SI EngineCI Engine

4. Expressing the gradient of the specific heat as: Transient Thermodynamic Model for Compression Process

5. Variable Property Model

6. Properties of Gases GasC p0 C1C1 C2C2 C3C3 Air1.05-0.3650.85-0.39 Methane1.23.250.75-0.71 CO 2 0.451.67-1.270.39 Steam1.790.1070.586-0.20 O2O2 0.88-0.00010.54-0.33 N2N2 1.11-0.480.96-0.42

7. Specific Heat of flue gas:

8. Properties of Fuels Fuel C0C0 C1C1 C2C2 C3C3 C4C4 Methane-0.2914926.327-10.6101.56560.16573 Propane-1.486774.339-39.0658.05430.01219 Isooctane-0.55313181.62-97.78720.402-0.03095 Gasoline-24.078256.63-201.6864.7500.5808 Diesel-9.1063246.97-143.7432.3290.0518

9.  cpcp cvcv

10. Frictionless Compression Equation

11. In above Eq., the rate of the heat loss  Q loss /dθ is expressed as: The convective heat transfer coefficient is given by the Woschni model as

12. The velocity of the mixture is given as: The value of C 1 is given as: for compression process: C 1 =0 and for combustion and expansion processes: C 1 =0.00324. Instantaneous Mean Velocity of Cylinder Gas Mixture

13. Pressure Profile During Compression

14. Surface Area for heat loss/gain

15. Measurement of Engine Wall Temperature Crank Angle, 

16. Explicit Numerical Integration For a crank rotation of 

17. The Onset of Compression Process

18. Inlet Valve : Operation Schedule p cyl P atm

19. Work Consumed by compression Process

20. In above Eq., the rate of the heat loss  Q loss /dθ is expressed as: The convective heat transfer coefficient is given by the Woschni model as Modeling of Combustion Process For combustion and expansion processes: C 1 =0.00324.

21. Finite Rate of Heat Release : Single Phase Combustion A typical heat release curve consists of an initial spark ignition phase, followed by a rapid burning phase and ends with burning completion phase The curve asymptotically approaches 1 so the end of combustion is defined by an arbitrary limit, such as 90% or 99% complete combustion where x b = 0.90 or 0.99 corresponding values for efficiency factor a are 2.3 and 4.6 The rate of heat release as a function of crank angle is:.99

22. Real MFB Curve in an Engine

25. Dual Phase Combustion Where p and d refer to premixed and diffusion phases of combustion. The parameters θ p and θ d represent the duration of the premixed and diffusion combustion phases. Q p and Q d represent the integrated energy release for premixed and diffusion phases respectively. The constants a, m p and m d are selected to match experimental data. It is assumed that the total heat input to the cylinder by combustion for one cycle is: The rate of the heat input  Q gen /dθ (heat release)can be modeled using a dual Weibe function