07_part2a

07_part2a - PART 2 POWER AND PROPULSION CYCLES PART 2 POWER...

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PART 2 POWER AND PROPULSION CYCLES
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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 P 0 V 2 = V 3 V 1 = V 4 5 2 3 4 1 Q H Q L 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 T 2 to T 3 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 T 4 to T 1 vii. Exhaust stroke, piston pushes remaining combustion products out of chamber 1->5
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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 P 0 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 QQ Q Q Q HL H L H 1. The convention, as previously, is that heat exchange is positive if heat is flowing into the system or engine, so Q L 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: U W CdT C T T H v T T v = () = =− 23 23 23 2 3 32 0 The heat rejected is given by (for a perfect gas with constant specific heats) U C T T Lv = 41 41 1 4 Substituting the expressions for the heat absorbed and rejected in the expression for thermal efficiency yields 1 41 TT
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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 TT V V V V 41 1 32 1 11 1 22 1 1 1 2 1 2 1 1 γγ γγ γγ 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: η Otto V V r =− 1 1 1 1 1 2 .
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This note was uploaded on 01/28/2012 for the course AERO 16.050 taught by Professor Zoltanspakovszky during the Fall '02 term at MIT.

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07_part2a - PART 2 POWER AND PROPULSION CYCLES PART 2 POWER...

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