PART 2 POWER AND PROPULSION CYCLES
PART 2 POWER AND PROPULSION CYCLES
PART 2- POWER AND PROPULSION CYCLE 2A -Gas Power and propulsion cycles SB&vW-118,119,11.10,11.11,11.12,1113,11.14] In this section we analyze several gas cycles used in practical applications for propulsion and power generation, using the air standard cycle. The air standard cycle is an the actual cycle behavior, and the term specifically refers to analysis using the folpproximation to assumptions Air is the working fluid(the presence of combustion products is neglected) Combustion is represented by heat transfer from an external heat source The cycle is 'completed' by heat transfer to the surroundings All processes are internally reversible Air is a perfect gas with constant specific heats 2.A. I The Internal combustion engine(Otto Cycle The different processes of an idealized otto cycle (internal combustion engine) are shown in Figure 2A-1 P Adiabatic reversible Q Po V,=V Figure 2A-1: Ideal Otto cycle Intake stroke, gasoline vapor and air drawn into engine (5->1) i1. Compression stroke, P, Tincrease(1->2) ii1. Combustion( spark), short time, essentially constant volume (2->3) Model: heat absorbed from a series of reservoir at temperatures T2 to T3 Power stroke: expansion (3->4) Valve exhaust: valve opens, gas escapes vi.(4->1)Model: rejection of heat to series of reservoirs at temperatures T4 to TI vil. Exhaust stroke, piston pushes remaining combustion products out of chamber 1->5 2A-1
2A-1 PART 2 – POWER AND PROPULSION CYCLES 2A – Gas Power and Propulsion Cycles [SB&VW - 11.8, 11.9, 11.10, 11.11, 11.12, 11.13, 11.14] In this section we analyze several gas cycles used in practical applications for propulsion and power generation, using the air standard cycle. The air standard cycle is an approximation to the actual cycle behavior, and the term specifically refers to analysis using the following assumptions: • Air is the working fluid (the presence of combustion products is neglected) • Combustion is represented by heat transfer from an external heat source • The cycle is ‘completed’ by heat transfer to the surroundings • All processes are internally reversible • Air is a perfect gas with constant specific heats 2.A.1 The Internal combustion engine (Otto Cycle) The different processes of an idealized Otto cycle (internal combustion engine) are shown in Figure 2A-1: P V P0 V2 = V3 V1 = V4 5 2 3 4 1 QH QL Adiabatic reversible Figure 2A-1: Ideal Otto cycle i. Intake stroke, gasoline vapor and air drawn into engine (5 -> 1) ii. Compression stroke, P, T increase (1->2) iii. Combustion (spark), short time, essentially constant volume (2->3) Model: heat absorbed from a series of reservoir at temperatures T2 to T3 iv. Power stroke: expansion (3 ->4) v. Valve exhaust: valve opens, gas escapes vi. (4->1) Model: rejection of heat to series of reservoirs at temperatures T4 to T1 vii. Exhaust stroke, piston pushes remaining combustion products out of chamber 1->5
The actual cycle does not have these sharp transitions between the different processes and might be as sketched in figure 2A-2 ISentropic Spark Exhaust Exhaust valve closes Figure 2A-2: Sketch of actual Otto cycle Efficiency of an ideal otto cycle The starting point is the general expression for the thermal efficiency of a cycle york L=1+L heat input engine, so QL Is negative. The heat absorbed occurs during combustion when the spark occp or The convention, as previously, is that heat exchange is positive if heat is flowing into the system or roughly at constant volume. The heat absorbed can be related to the temperature change from state 2 to state 3 as Qn=Q23=AU23(W23=0 C=C(T3-T2) The heat rejected is given by(for a perfect gas with constant specific heats) (T1-T4) Substituting the expressions for the heat absorbed and rejected in the expression for thermal efficiency yields T 2A-2
2A-2 The actual cycle does not have these sharp transitions between the different processes and might be as sketched in Figure 2A-2 Spark Exhaust valve opens Not isentropic Exhaust valve closes P P0 V Figure 2A-2: Sketch of actual Otto cycle Efficiency of an ideal Otto cycle The starting point is the general expression for the thermal efficiency of a cycle: η = = + = + work heat input Q Q Q Q Q H L H L H 1 . The convention, as previously, is that heat exchange is positive if heat is flowing into the system or engine, so QL is negative. The heat absorbed occurs during combustion when the spark occurs, roughly at constant volume. The heat absorbed can be related to the temperature change from state 2 to state 3 as: QQ U W C dT C T T H T v T v == = ( ) = ∫ = − ( ) 23 23 23 2 3 3 2 ∆ 0 The heat rejected is given by (for a perfect gas with constant specific heats) Q Q U CT T L v == = − 41 41 1 4 ∆ ( ) Substituting the expressions for the heat absorbed and rejected in the expression for thermal efficiency yields η = − − − 1 4 1 3 2 T T T T
We can simplify the above expression using the fact that the processes from l to 2 and from 3 to 4 are isentropic Tw-=T3w-,T;w-=T2V2-1 (T4-7)W-1=(T3-72) 74-7_(V T-72(V The quantity ==r is called the compression ratio. In terms of compression ratio, the efficiency of an ideal Otto cycle is ne The ideal otto cycle efficiency is shown at the right, as a function of the compression ratio As the compression ratio, r, increases .E月 noo increases, but so does T. If T is too high, the mixture will ignite without a park(at the wrong location in the cycle) Ideal Otto cycle thermal efficiency Engine work, rate of work per unit enthalpy flu he non-dimensional ratio of work done(the power )to the enthalpy flux through the engine is given by Powe 22 Enthalpy flux mcpl cpTl There is often a desire to increase this quantity, because it means a smaller engine for the same power. The heat input is given by fuel(an fu Ah fuel is the heat of reaction, ie the chemical energy liberated per unit mass of fuel I fuel is the fuel mass flow rate The non-dimensional power is 2A-3
2A-3 We can simplify the above expression using the fact that the processes from 1 to 2 and from 3 to 4 are isentropic: TV TV TV TV T TV T TV T T T T V V 4 1 1 3 2 1 1 1 1 2 2 1 4 11 1 3 22 1 4 1 3 2 2 1 1 γγ γγ γ γ γ −− −− − − − = = ( ) − = − ( ) − − = , The quantity V V r 1 2 = is called the compression ratio. In terms of compression ratio, the efficiency of an ideal Otto cycle is: ηOtto γ γ V V r =− =− − − 1 1 1 1 1 2 1 1 . The ideal Otto cycle efficiency is shown at the right, as a function of the compression ratio. As the compression ratio, r, increases, ηOtto increases, but so doesT2 . If T2 is too high, the mixture will ignite without a spark (at the wrong location in the cycle). Ideal Otto cycle thermal efficiency Engine work, rate of work per unit enthalpy flux: The non-dimensional ratio of work done (the power) to the enthalpy flux through the engine is given by Power Enthalpy flux = = ˙ ˙ ˙ ˙ W mc T Q p mc T Otto 1 p 23 1 η There is often a desire to increase this quantity, because it means a smaller engine for the same power. The heat input is given by ˙ Qm h ˙ 23 = fuel fuel ( ) ∆ , where • ∆hfuel is the heat of reaction, ie the chemical energy liberated per unit mass of fuel • m˙ fuel is the fuel mass flow rate. The non-dimensional power is ˙ ˙ ˙ ˙ W mc T m m h p c T r fuel fuel 1 1 p 1 1 1 = − − ∆ γ . 0 0 10 20 30 40 50 60 70 2468 Compression ratio, rv Thermal efficiency, ηth 10 12 14 16
The quantities in this equation, evaluated at stoichiometric conditions are fuel 0. pTT Muddy points Ho △ h., calculated?(MP2A1) What are"stoichiometric conditions"?(MP 2A.2 2. 4.2. Diesel cycle The Diesel cycle is a compression ignition(rather than spark ignition)engine. Fuel is sprayed into the cylinder at P,(high pressure)when the compression is complete, and there is ignition without a spark. An idealized Diesel engine cycle is shown in Figure 2A-3 Adiabatic Figure 2A-3 Ideal Diesel cycle The thermal efficiency is given by eL C,(T-T) (T This cycle can operate with a higher compression ratio than otto cycle because only air is compressed and there is no risk of auto-ignition of the fuel. Although for a given compression ratio the Otto cycle has higher efficiency, because the Diesel engine can be operated to higher compression ratio, the engine can actually have higher efficiency than an Otto cycle when both are operated at compression ratios that might be achieved in practice 2A-4
2A-4 The quantities in this equation, evaluated at stoichiometric conditions are: ˙ ˙ , m m 1 15 h c T 4 10 10 288 fuel fuel p 1 7 3 ≈ ≈ × × ∆ so, ˙ ˙ W mc Tp 1 r 1 9 1 1 ≈ − γ − . Muddy points How is ∆ h fuel calculated? (MP 2A.1) What are "stoichiometric conditions"? (MP 2A.2) 2.A.2. Diesel Cycle The Diesel cycle is a compression ignition (rather than spark ignition) engine. Fuel is sprayed into the cylinder at P2 (high pressure) when the compression is complete, and there is ignition without a spark. An idealized Diesel engine cycle is shown in Figure 2A-3. QH P V2 V V3 V4 = V1 QL Adiabatic reversible 2 3 4 1 Figure 2A-3 Ideal Diesel cycle The thermal efficiency is given by: η η γ Diesel L H v p Diesel T T T T Q Q CT T CT T T T =+ =+ ( ) − ( ) − = − ( ) − ( ) − 1 1 1 1 1 1 4 3 2 1 4 1 2 3 2 This cycle can operate with a higher compression ratio than Otto cycle because only air is compressed and there is no risk of auto-ignition of the fuel. Although for a given compression ratio the Otto cycle has higher efficiency, because the Diesel engine can be operated to higher compression ratio, the engine can actually have higher efficiency than an Otto cycle when both are operated at compression ratios that might be achieved in practice