# η th W = Q Gas Power Cycles: Working fluid remains in the gaseous state through the cycle.

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1 Gas Power Cycles:

2

3 Gas Power Cycles: Working fluid remains in the gaseous state through the cycle. Sometimes useful to study an idealised cycle in which internal irreversibilities and complexities are removed. Such cycles are called: Air Standard Cycles he performance is often measured in terms of the cycle efficiency. η th W = net in

4 Sadi Carnot (796-83) French engineer who provided the basis of the future Second Law of hermodynamics in his paper: "Considerations on the motive power of fire and on engines able to develop that power" 84.

5 Carnot Cycle Four processes. - Isothermal Heat Addition -3 Isentropic Expansion 3-4 Isothermal Heat Rejection 4- Isentropic Compression he net cycle work done is the area enclosed by the cycle on the P-v diagram. he net heat added is the area enclosed by the cycle on the -s diagram. For a cycle W net = net ; the areas on the P-v and -s diagrams are equal., = η th Carnot L H

6 Air-Standard Assumptions Assume the working fluid is air which undergoes a thermodynamic cycle even when the actual power system does not undergo a cycle. he following assumptions are made: he air continuously circulates in a closed loop and behaves as an ideal gas. All the processes that make up the cycle are internally reversible. he combustion process is replaced by heat-addition from an external source. A heat rejection process replaces the exhaust and induction processes. he cold-air-standard assumptions apply when the working fluid is air and has a constant specific heat evaluated at 5 o C.

7 erminology for Reciprocating Engines he compression ratio r V max r = = V min V V BDC DC

8 he mean effective pressure (MEP) A fictitious pressure that, if it were applied to the piston during the power stroke, would produce the same amount of net work as that produced during the actual cycle. Wnet wnet MEP = = V V v v max min max min Can also be viewed as the normalised work ie Work per cycle, per unit swept volume. Useful to compare engines of different sizes and speeds. IMEP or BMEP depending on whether cylinder or shaft work used.

9 INERNAL COMBUSION ENGINE PERFORMANCE INDICAORS: Specific Fuel Consumption (SFC) kg/kw hr: he fuel consumption per unit power output and has been found useful in comparing engines of different outputs. SFC = Fuel flow rate/ Brake power. Brake hermal Efficiency: BE = Brake power/energy input rate (energy input rate = fuel flow rate X fuel energy content) Mechanical Efficiency: his indicates the effectivness with which the engine is transmitting power from the face of the piston to the output shaft. ME = Brake power /Indicated power Volumetric Efficiency: his compares the actual airflow into the engine with the theoretical airflow if the cylinders were completely filled with atmospheric air every cycle. VE = actual air volume flowrate/swept volume flowrate.

10 he Four Stroke Spark-Ignition Engines and Ideal Otto Cycle.

11 he four-stroke spark-ignition cycle: Piston strokes: Intake Compression Power (expansion) Exhaust One complete cycle requires two revolutions of the crankshaft. Often the ignition and combustion process begin before the end of the compression stroke. he number of crank angle degrees before the piston reaches DC at which the spark occurs is called the spark or ignition timing.

12 Nikolaus August Otto (83-89) German engineer. First to build the four stroke indirect ignition internal combustion engine even though it was first patented in 86 by Alphonse Beau de Rochas.

13 876: 3 HP, 80 rpm

14 he Air-Standard Otto Cycle approximates the spark-ignition combustion engine - Isentropic Compression -3 Constant Volume Heat Addition 3-4 Isentropic Expansion 4- Constant Volume Heat Rejection P 3 s = const P P 4 4 V = const v S

15 hermal Efficiency of the Otto Cycle: o find in and out. η th W net net = = = in in in in out = out in Apply First Law Closed System to Process -3, constant volume heating. hus for constant specific heats W net, = pdv 3 = 0 3 net, 3 Wnet, 3 = U 3 P in 3 S = const = U net, 3 3 net, 3 = in = mcv ( 3 ) 4 3 v

16 Apply First Law Closed System to Process 4-, constant volume cooling net 4 W,4 = U 4 P W, 4 = pdv net = hus for constant specific heats: S = const = U net, 4 4 net, 4 = out = mcv ( 4 ) = mc ( ) = mc ( ) out v 4 v he thermal efficiency becomes: out η th, Otto = out in mcv ( 4 ) = mc ( ) v 3 v

17 or ( 4 ) η th, Otto = ( ) 3 ( 4 / = ( / 3 ) ) Recall processes - and 3-4 are isentropic (reversible adiabatic), so P 3 S = const 3 k F V 3 V4 = H G I and V K J F = H G I V K J 4 3 k 4 out Since V 3 = V and V 4 = V 3 or = 4 4 = 3 v

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