Thermodynamic Analysis of Internal Combustion Engines P M V SUBBARAO

Thermodynamic Analysis of Internal Combustion Engines P M V SUBBARAO Professor Mechanical Engineering Department IIT Delhi Work on A Blue Print Before You Ride on an Actual Engine . It is a Sign of Civilized Engineering .

SI Engine Cycle FUEL A I Ignition R Fuel/Air Mixture Combustion Products Actual Cycle Intake Stroke Compression Stroke Power Stroke Exhaust Stroke

Actual SI Engine cycle Total Time Available: 10 msec Ignition

Early CI Engine Cycle Fuel injected at TC A I R Combustion Products Air Actual Cycle Intake Stroke Compression Stroke Power Stroke Exhaust Stroke

Modern CI Engine Cycle Fuel injected at 15o bTC A I R Air Combustion Products Actual Cycle Intake Stroke Compression Stroke Power Stroke Exhaust Stroke

Thermodynamic Cycles for CI engines In early CI engines the fuel was injected when the piston reached TC and thus combustion lasted well into the expansion stroke. In modern engines the fuel is injected before TC (about 15o) Fuel injection starts Early CI engine Fuel injection starts Modern CI engine The combustion process in the early CI engines is best approximated by a constant pressure heat addition process Diesel Cycle The combustion process in the modern CI engines is best approximated by a combination of constant volume and constant pressure Dual Cycle

Thermodynamic Modeling The thermal operation of an IC engine is a transient cyclic process. Even at constant load and speed, the value of thermodynamic parameters at any location vary with time. Each event may get repeated again and again. So, an IC engine operation is a transient process which gets completed in a known or required Cycle time. Higher the speed of the engine, lower will be the Cycle time. Modeling of IC engine process can be carried out in many ways. Multidimensional, Transient Flow and heat transfer Model. Thermodynamic Transient Model USUF. Fuel-air Thermodynamic Mode. Air standard Thermodynamic Model.

Ideal Thermodynamic Cycles Air-standard analysis is used to perform elementary analyses of IC engine cycles. Simplifications to the real cycle include: 1) Fixed amount of air (ideal gas) for working fluid 2) Combustion process not considered 3) Intake and exhaust processes not considered 4) Engine friction and heat losses not considered 5) Specific heats independent of temperature The two types of reciprocating engine cycles analyzed are: 1) Spark ignition – Otto cycle 2) Compression ignition – Diesel cycle

FUEL A I Otto Cycle R Ignition Fuel/Air Mixture Combustion Products Actual Cycle Intake Stroke Otto Cycle Compression Stroke Qin Air Power Stroke Exhaust Stroke Qout TC BC Compression Process Const volume heat addition Process Expansion Process Const volume heat rejection Process

Air-Standard Otto cycle Process 1 2 Process 2 3 Process 3 4 Process 4 1 Isentropic compression Constant volume heat addition Isentropic expansion Constant volume heat rejection Compression ratio: r Qin Qout v2 v1 TC BC TC BC v1 v4 v 2 v3

First Law Analysis of Otto Cycle 1 2 Isentropic Compression (u 2 u1 ) AIR W Q ( in ) m m Win (u2 u1 ) cv (T2 T1 ) m T2 v1 T1 v2 k 1 r k 1 P2 T2 v1 P1 T1 v2 2 3 Constant Volume Heat Addition (u3 u 2 ) ( Qin W ) m m Qin (u3 u2 ) cv (T3 T2 ) m P3 T3 P2 T2 AIR Qin TC

3 4 Isentropic Expansion (u 4 u3 ) W Q ( out ) m m AIR Wout (u3 u4 ) cv (T3 T4 ) m T4 v3 T3 v4 k 1 1 r k 1 P4 T4 v3 P3 T3 v4 4 1 Constant Volume Heat Removal (u1 u 4 ) ( Qout W ) m m AIR Qout (u4 u1 ) cv (T4 T1 ) m Qout BC P4 P1 T4 T1

First Law Analysis Parameters Net cycle work: Wcycle Wout Win m u3 u4 m u2 u1 Cycle thermal efficiency: Wcycle u3 u4 u2 u1 u u u4 u1 u u 3 2 1 4 1 th u3 u 2 u3 u 2 u3 u 2 Qin 1 cv (T4 T1 ) T 1 1 1 1 k 1 cv (T3 T2 ) T2 r Indicated mean effective pressure is: W imep Qin r 1 Qin / m r imep cycle th th V1 V2 P1 P1V1 r 1 k 1 u1 r 1

Effect of Compression Ratio on Thermal Efficiency th const cV 1 1 r k 1 Typical SI engines 9 r 11 k 1.4 Spark ignition engine compression ratio limited by T3 (autoignition) and P3 (material strength), both rk For r 8 the efficiency is 56% which is twice the actual indicated value

Effect of Specific Heat Ratio on Thermal Efficiency th const cV 1 1 r k 1 Specific heat ratio (k) Cylinder temperatures vary between 20K and 2000K so 1.2 k 1.4 k 1.3 most representative

Factors Affecting Work per Cycle The net cycle work of an engine can be increased by either: i) Increasing the r (1’ 2) ii) Increase Qin (2 3”) Wcycle Q r imep in th V1 V2 V1 r 1 3’’ P (ii) 3 4’’ Qin Wcycle 4 4’ 2 (i) 1 V2 V1 1’

Effect of Compression Ratio on Thermal Efficiency and MEP imep Qin r 1 1 k P1 P1V1 r 1 r k 1.3

Ideal Diesel Cycle Qin Qout Air BC Compression Process Const pressure heat addition Process Expansion Process Const volume heat rejection Process

Air-Standard Diesel cycle Process 1 2 Process 2 3 Process 3 4 Process 4 1 Isentropic compression Constant pressure heat addition Isentropic expansion Constant volume heat rejection Cut-off ratio: Qin rc Qout v2 v1 TC BC TC BC v3 v2

Thermal Efficiency Diesel cycle Qout m u4 u1 1 1 Qin m h3 h2 For cold air-standard the above reduces to: Diesel const cV 1 1 rck 1 1 k 1 r k rc 1 recall, Otto 1 1 rk 1 Note the term in the square bracket is always larger than one so for the same compression ratio, r, the Diesel cycle has a lower thermal efficiency than the Otto cycle Note: CI needs higher r compared to SI to ignite fuel

Thermal Efficiency Typical CI Engines 15 r 20 When rc ( v3/v2) 1 the Diesel cycle efficiency approaches the efficiency of the Otto cycle Higher efficiency is obtained by adding less heat per cycle, Qin, run engine at higher speed to get the same power.

Thermodynamic Dual Cycle Qin Dual Cycle Qin Qout Air TC BC Compression Process Const volume heat addition Process Const pressure heat addition Process Expansion Process Const volume heat rejection Process

Dual Cycle Process 1 2 Isentropic compression Process 2 2.5 Constant volume heat addition Process 2.5 3 Constant pressure heat addition Process 3 4 Isentropic expansion Process 4 1 Constant volume heat rejection 2.5 Qin 3 Qin 2 4 1 2.5 4 2 1 3 Qout Qin (u2.5 u2 ) (h3 h2.5 ) cv (T2.5 T2 ) c p (T3 T2.5 ) m

Thermal Efficiency Dual 1 cycle Dual Qout m u4 u1 1 Qin m (u2.5 u2 ) (h3 h2.5 ) const cv rck 1 1 1 k 1 r ( 1) k rc 1 v where rc 3 v 2 .5 and P3 P2 Note, the Otto cycle (rc 1) and the Diesel cycle ( 1) are special cases: Otto 1 1 rk 1 Diesel const cV 1 1 rck 1 1 k 1 r k rc 1

The use of the Dual cycle requires information about either: i) the fractions of constant volume and constant pressure heat addition (common assumption is to equally split the heat addition), or ii) maximum pressure P3. Transformation of rc and into more natural variables yields rc 1 k 1 Qin 1 1 k P1V1 r k 1 k 1 1 P3 r k P1 For the same inlet conditions P1, V1 and the same compression ratio: Otto Dual Diesel For the same inlet conditions P1, V1 and the same peak pressure P3 (actual design limitation in engines): Diesel Dual otto

For the same inlet conditions P1, V1 and the same compression ratio P2/P1: For the same inlet conditions P1, V1 and the same peak pressure P3: Pressure, P Pmax th 1 Po Specific Volume Temperature, T tto O al Du sel Die Entropy 1 Qout Qin Po Specific Volume 1 4 Tds 3 2 Tds Tmax Temperature, T Pressure, P “x” “2.5” el Dies al Du to Ot Entropy