Development of Thermodynamic Models for Engine Design P M V Subbarao Professor Mechanical Engineering Department Methods to Design for Performance….
First Law Analysis: Transient Compression of gaseous Control Mass Compression Process Fuel+Air+residual gas Air+residual gas SI EngineCI Engine
Expressing the gradient of the specific heat as: Transient Thermodynamic Model for Compression Process
Variable Property Model
Properties of Gases GasC p0 C1C1 C2C2 C3C3 Air Methane CO Steam O2O N2N
Specific Heat of flue gas:
Properties of Fuels Fuel C0C0 C1C1 C2C2 C3C3 C4C4 Methane Propane Isooctane Gasoline Diesel
cpcp cvcv
Frictionless Compression Equation
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
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 = Instantaneous Mean Velocity of Cylinder Gas Mixture
Pressure Profile During Compression
Surface Area for heat loss/gain
Measurement of Engine Wall Temperature Crank Angle,
Explicit Numerical Integration For a crank rotation of
The Onset of Compression Process
Inlet Valve : Operation Schedule p cyl P atm
Work Consumed by compression Process
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 =
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
Real MFB Curve in an Engine
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