1. 20th Century Thermodynamic Modeling of Automotive Prime Mover Cycles
P M V Subbarao
Professor
Mechanical Engineering Department
Respect True Nature of Substance…..

2. Theoretical Learnings from Carnot’s Analysis
Any model developed for a prime mover be a cyclic model.
The most important part of the model is the process that generates the highest temperature.
Very important to develop a model, which predicts the temperatures more accurately.
Higher the accuracy of temperature predictions, higher will be the reliability of the predictions…
Enhances the closeness between theory & Practice.

3. Important Feature of An Artificial Horse
Predictions by Air-standard Cycle
Actual Prime Mover
Stoichiometric Mixture
th, %
Lean
Rich
Air/fuel Ratio

4. The Thermodynamics Importance of Temperature
From the Gibbsian equations, the change of specific entropy of any substance during any reversible process.
Consider a control mass executing a Isothermal heat addition process as suggested by Carnot:
For an Ideal gas executing above process:
Heat addition at a highest absolute temperature leads a lowest increase in entropy for a given increase in specific volume of a control mass.
Temperature is created by mere Compression ??!!!!???

5. The Thermodynamics of Temperature Creation : Otto’s Model
From the Gibbsian equations, the change of specific entropy of any substance during any reversible process.
Consider a control mass executing a constant volume heat addition process:
The relative change in internal energy of a control mass w.r.t. change in entropy at constant volume is called as absolute temperature.

6. The Thermodynamics of Temperature Creation : Diesel’s Model
Consider a control mass executing a reversible constant pressure heat addition process:
The relative change in enthalpy of a control volume w.r.t. change in entropy at constant pressure is called as absolute temperature.

7. 20th Century Models for Engine Cycles
Fuel-air analysis is more accurate analysis when compared to Air-standard cycle analysis.
An accurate representation of constituents of working fluid is considered.
More accurate models are used for properties of each constituents.
Process
Otto’s Model
Diesel’s Model
Intake
Air+Fuel +Residual gas
Air+ Residual gas
Compression
Air+Fuel vapour +Residual gas
Air + Residual gas
Expansion
Combustion products
Combustion Products
Exhaust

8. Fuel-Air Model for Otto Cycle
Air+Fuel vapour +Residual gas TC BC
Compression
Process
Const volume
combustion
Expansion
Blow down
Products of Combustin
Otto
Cycle

9. 20th Century Analysis of Ideal Otto Cycle
This is known as Fuel-air Cycle.
1—2 Isentropic compression of a mixture of air, fuel vapour and residual gas without change in chemical composition.
2—3 Complete combustion at constant volume, without heat loss, with burned gases in chemical equilibrium.
3—4 Isentropic expansion of the burned gases which remain in chemical equilibrium.
4—5 Ideal adiabatic blow down.

10. Isentropic Compression Process: 1 - 2
For a infinitesimal compression process:
Assume ideal gas nature with variable properties:
Mass averaged properties for an ideal gas mixture:

11. Variation of Specific Heat of Ideal Gases
Air
1.05
-0.365
0.85
-0.39
Methane
1.2
3.25
0.75
-0.71
CO2
0.45
1.67
-1.27
0.39
Steam
1.79
0.107
0.586
-0.20 O2
0.88
0.54
-0.33 N2
1.11
-0.48
0.96
-0.42

12. g cp cv

13. Properties of Fuels C0 C1 C2 C3 C4 Fuel Methane -0.29149 26.327
1.5656
Propane
74.339
8.0543
Isooctane
181.62
20.402
Gasoline
256.63
64.750
0.5808
Diesel
246.97
32.329
0.0518

14. Isentropic Compression model with variable properties : 1 - 2

15. True Phenomenological Model for Isentropic Compression
Let the mixture is modeled as:

16. Generalized First Order Models for Variable Specific Heats
For design analysis of Engine Models:
ap = – kJ/kmol.K
bv = – kJ/kmol.K
k1 = – kJ/kmol.K2

17. Isentropic Compression model with variable properties
For compression from 1 to 2:

18. Engineering Strategy to Utilize A Resource
Engineering constraint: Both combustion and expansion have to be finished in a single stroke.
Rapid combustion : Constant Volume combustion
Less time to combustion process.
More time to adiabatic expansion
Slow combustion : Constant pressure combustion
More time to combustion process.
Less time to adiabatic expansion