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mcl721-8.pptx

  1. 1. 20th Century Thermodynamic Modeling of Automotive Prime Mover Cycles P M V Subbarao Professor Mechanical Engineering Department Respect True Nature of Substance…..
  2. 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.               1 ) 1 ( 1 1 1 1 c k c k c const Dual r k r r v    
  3. 3. Important Feature of An Artificial Horse Air/fuel Ratio Stoichiometric Mixture  th , % Lean Rich Predictions by Air-standard Cycle Actual Prime Mover
  4. 4. The Thermodynamics Importance of Temperature • From the Gibbsian equations, the change of specific entropy of any substance during any reversible process. vdp dh pdv du Tds     • Consider a control mass executing a Isothermal heat addition process as suggested by Carnot: pdv du Tds   Heat addition at a highest absolute temperature leads a lowest increase in entropy for a given increase in specific volume of a control mass. ds dv p ds du T   • For an Ideal gas executing above process: ds dv p ds dT c T v   ds dp R or ds dv R T   Temperature is created by mere Compression ??!!!!???
  5. 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. vdp dh pdv du Tds     • Consider a control mass executing a constant volume heat addition process: pdv du Tds   constant     v s u T 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. 6. The Thermodynamics of Temperature Creation : Diesel’s Model vdp dh Tds   • Consider a control mass executing a reversible constant pressure heat addition process: constant     p s h T The relative change in enthalpy of a control volume w.r.t. change in entropy at constant pressure is called as absolute temperature.
  7. 7. Phenomenological 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 Combustion products Combustion Products
  8. 8. Fuel-Air Model for Otto Cycle Otto Cycle Air+Fuel vapour +Residual gas TC BC Compression Process Const volume combustion Process Expansion Process Const volume Blow down Process Products of Combustin Products of Combustin
  9. 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. 10. Isentropic Compression Process: 1 - 2 For a infinitesimal compression process: pdv du Tds   pdv du   0 dv v T dT R cv   Mass averaged properties for an ideal gas mixture:          n i i i n i i v i v n i i p i p R x R c x c c x c 1 1 , 1 , & & 0   pdv dT cv 0   dv v RT dT cv v dv T dT R cv                0   dv v RT dT cv Assume ideal gas nature with variable properties:
  11. 11. Variation of Specific Heat of Ideal Gases kgK kJ T C T C T C C cp / 1000 1000 1000 3 3 2 2 1 0                 Gas C0 C1 C2 C3 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 -0.0001 0.54 -0.33 N2 1.11 -0.48 0.96 -0.42
  12. 12. Variable Properties of Air 0.5 0.7 0.9 1.1 1.3 1.5 0 200 400 600 800 1000 1200 1400 Temperature,K g cp cv
  13. 13. Properties of Fuels kgK kJ T C T C T C T C C C f p / 1000 1000 1000 2 4 3 3 2 2 1 0 ,                        Fuel C0 C1 C2 C3 C4 Methane -0.29149 26.327 -10.610 1.5656 0.16573 Propane -1.4867 74.339 -39.065 8.0543 0.01219 Isooctane -0.55313 181.62 -97.787 20.402 -0.03095 Gasoline -24.078 256.63 -201.68 64.750 0.5808 Diesel -9.1063 246.97 -143.74 32.329 0.0518
  14. 14. Isentropic Compression model with variable properties : 1 - 2 v dv T dT R cv                        2 2 sin cos 1 2 1 1        R R r V V c                      2 2 sin cos 1 2 1 1 R R r m V v c          v T R p 
  15. 15. True Phenomenological Model for Isentropic Compression dv v RT dT cv   v dv R T dT cv   kgK kJ T c T c T c c c v v v v v / 3 3 , 2 2 , 1 , 0 ,     Let the mixture is modeled as:                                     1 2 3 1 3 2 3 , 2 1 2 2 2 , 1 2 1 , 1 2 0 , ln 3 2 ln v v R T T c T T c T T c T T c v v v v          2 1 2 1 3 3 , 2 2 , 1 , 0 , v dv R T dT T c T c T c c v v v v                                   r R T T c T T c T T c T T c v v v v 1 ln 3 2 ln 3 1 3 2 3 , 2 1 2 2 2 , 1 2 1 , 1 2 0 ,
  16. 16. Generalized First Order Models for Variable Specific Heats T k a c p p    1 T k b c v v    1 ap = 28.182 – 32.182 kJ/kmol.K bv = 19.868 – 23.868 kJ/kmol.K k1 = 0.003844–0.009844 kJ/kmol.K2 For design analysis of Engine Models:
  17. 17. Isentropic Compression model with variable properties • For compression from 1 to 2:                    1 2 1 2 1 2 1 ln ln v v R T T b T T k v        2 1 2 1 1 v dv R T dT T k bv                    r R T T b T T k v 1 ln ln 1 2 1 2 1
  18. 18. The Role of Isentropic Compression         r R T T c T T c T T c T T c v v v v ln 3 2 ln 3 1 3 2 3 , 2 1 2 2 2 , 1 2 1 , 1 2 0 ,                          r R T T b T T k v ln ln 1 2 1 2 1           Second order Property Model: First order Property Model: • Ready for combustion: • In a combustion reaction, bonds are being broken and formed between different atoms in molecules. • The parts of the molecules that undergo bond breakage and formation need to line up with each other. • There needs to be the appropriate overlap in the orbitals that are "donating" and "accepting" electrons. • The probability of occurrence of appropriate overlap is proportional to temperature of reacting molecules.
  19. 19. Collision Theory • Collision theory says that ”in order for a chemical reaction to happen, three separate things need to happen” : • 1. The molecules have to hit each other • 2. The molecules have to hit each other in the right way (both have to be facing the right way) • 3. The molecules have to hit each other with enough speed (energy of motion, or "kinetic energy") to activate the reaction. Number of successful collisions  Frequency of collisions  Time available for collision.
  20. 20. Phenomenological Modeling of Combustion • Engineering Objective of Combustion: • To Create Maximum Possible Temperature through conversion of free energy into microscopic kinetic energy. Thermodynamic Strategy for conversion: Constant temperature combustion Constant volume combustion Constant pressure combustion
  21. 21. 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

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