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Lect-7 Gas power cycles In this lecture... he Carnot cycle and its significance Air-standard assumptions An oeriew of reciprocating engines Otto cycle: the ideal cycle for sparkignition engines Diesel cycle: the ideal cycle for compression-ignition engines Dual cycles
Lect-7 Gas power cycles Study of power cycles of immense importance in engineering. Actual cycles: irreersibilities (like friction etc.),not in thermodynamic equilibrium, non-quasi static processes etc. For thermodynamic analysis we assume none of the aboe effects present: ideal cycles Ideal cycle analysis starting point of indepth analysis.
Lect-7 Gas power cycles he ideal cycles are internally reersible, but, unlike the Carnot cycle, they are not necessarily externally reersible. Hence, the thermal efficiency of an ideal cycle, in general, is less than that of a totally reersible cycle operating between the same temperature limits. But, the thermal efficiency is ideal cycles is higher than that of actual cycles. 4
Lect-7 Gas power cycles Gas power cycles are usually represented on P- and -s diagrams. On these diagrams the area enclosed by the process cures represent the net work done by the cycle. For a cyclic process this is also equal to the net heat transferred during the cycle. In an ideal power cycle, the only effect that can change the entropy of the working fluid during a process is heat transfer. 5
Lect-7 Gas power cycles On a -s diagram, Q in proceeds in the direction of increasing entropy and Q out proceeds in the direction of decreasing entropy. he difference between areas under Q in and Q out is the net heat transfer, and hence the net work of the cycle. he ratio of the area enclosed by the cyclic cure to the area under the heataddition process cure represents the thermal efficiency of the cycle. 6
Lect-7 Gas power cycles Q H Net heat input, Q H area under cure - W net,out Q L 4 S Net work output, W net (area under cure - ) (area under cure -4) Hence, thermal efficiency, η th W net /Q H 7
he Carnot cycle and its significance he Carnot cycle consists of four reersible processes: two reersible adiabatics and two reersible isotherms. Carnot efficiency is a function of the source and sink temperatures. L ηth he efficiency of a Carnot heat engine increases as H is increased, or as L is decreased. H Lect-7 8
he Carnot cycle and its significance Lect-7 he Carnot cycle seres as a standard against which actual cycle performance can be compared. In practice the source and sink temperatures are also limited. Source temperature limited by the materials that are used in these deices. Sink temperature limited by the temperature of the medium to which heat is rejected like atmosphere, lake, oceans etc. 9
Lect-7 Air standard assumptions o simplify analysis, the following assumptions are made:. he working fluid is air, which continuously circulates in a closed loop and always behaes as an ideal gas.. All the processes that make up the cycle are internally reersible.. he combustion process is replaced by a heataddition process from an external source. 4. he exhaust process is replaced by a heatrejection process that restores the working fluid to its initial state. 0
Lect-7 Air standard assumptions Air Fuel Combustion chamber Actual process Combustion products Heat addition Air Heating section Air Ideal process
Lect-7 Oeriew of reciprocating engines Reciprocating engines are one of the most commonly used power generating deices. hese engines can operate on a ariety of thermodynamic cycles. Piston and cylinder form the basic components of reciprocating engines, besides ales, connecting rods, flywheels and seeral other components.
Lect-7 Oeriew of reciprocating engines Intake ale Exhaust ale Bore DC DC BDC BDC DC: op Dead Centre BDC: Bottom Dead Centre Displacement olume Nomenclature for reciprocating engines Clearance olume
Oeriew of reciprocating engines he minimum olume formed in the cylinder when the piston is at DC is called the clearance olume. he olume displaced by the piston as it moes between DC and BDC is called the displacement olume. he ratio of the maximum olume formed in the cylinder to the minimum (clearance) olume is called the compression ratio, r of the engine: Vmax VBDC r V V min DC Lect-7 4
Oeriew of reciprocating engines Mean Effectie Pressure (MEP): is a fictitious pressure that, if it acted on the piston during the entire power stroke, would produce the same amount of net work as that produced during the actual cycle. W net MEP x Piston area x Stroke MEP x Displacement olume Wnet wnet MEP V V max min max min Lect-7 5
Lect-7 Oeriew of reciprocating engines P W net W net MEP x (V max -V min ) MEP V min DC V max BDC V he net work output of a cycle is equialent to the product of the mean effectie pressure and the displacement olume. 6
Lect-7 Oeriew of reciprocating engines wo types of reciprocating engines: Spark Ignition (SI) engines and Compression Ignition (CI) engines SI engines: the combustion of the air fuel mixture is initiated by a spark plug. CI engines, the air fuel mixture is selfignited as a result of compressing the mixture aboe its self-ignition temperature. 7
Lect-7 Otto cycle Otto cycle is the ideal cycle for sparkignition reciprocating engines. Named after Nikolaus A. Otto, who built a successful four-stroke engine in 876 in Germany. Can be executed in two or four strokes. Four stroke: Intake, compression, power and exhaust stroke wo stroke: Compression and power strokes. 8
Lect-7 Otto cycle Otto cycle consists of four processes: Isentropic compression (-) Isochoric (constant olume) heat addition (-) Isentropic expansion (-4) Isochoric (constant olume) heat rejection (4-) All the processes are internally reersible. Currently we shall analyse the ideal Otto cycle. Practical implementation and the actual cycle will be discussed in later chapters. 9
Otto cycle Lect-7 P q in Isentropic Isochoric q in 4 4 q out q out DC BDC s Ideal Otto cycle on P- and -s diagrams 0
Otto cycle Lect-7 Applying energy balance and assuming KE and PE to be zero: ( q he heat transfer to and from the working fluid can be written as : q q in in out q u u out 4 ) u + ( w u in c c ( ( w 4 out ) u ) )
Otto cycle he thermal efficiency of the ideal Otto cycle under the cold air standard assumptions becomes: Lect-7 4 4 4 4 4, herefore,. and Processes- and - 4 are isentropic and ) / ( ) / ( q q q w in out in net Otto th γ γ η
Otto cycle Lect-7 Substituting these equations into the thermal efficiency relation and simplifying: ηth, Otto γ r V where, r V And γ is max min V V the ratio of is the compression ratio. specific heats c p / c.
Lect-7 Diesel cycle he Diesel cycle is the ideal cycle for CI reciprocating engines proposed by Rudolph Diesel in the 890s. In SI, the air fuel mixture is compressed to a temperature that is below the autoignition temperature of the fuel, and the combustion process is initiated by firing a spark plug. In CI engines, the air is compressed to a temperature that is aboe the autoignition temperature of the fuel, and combustion starts on contact as the fuel is injected into this hot air. 4
Diesel cycle Lect-7 P q in Isentropic Pconstant q in 4 4 q out q out constant s Ideal Diesel cycle on P- and -s diagrams 5
Lect-7 Diesel cycle Diesel cycle consists of four processes: Isentropic compression (-) Isobaric (constant pressure) heat addition (-) Isentropic expansion (-4) Isochoric (constant olume) heat rejection (4-) All the processes are internally reersible. hermodynamically the Otto and Diesel cycles differ only in the second process (- ). For Otto cycle, -: constant olume and for Diesel cycle, -: constant pressure. 6
Diesel cycle Applying energy balance and assuming KE and PE to be zero: 7 Lect-7 ) ( ) ( ) ( ) ( can be written as : he heat transfer to and from the working fluid ) ( ) ( 4 4 c u u q c h h u u P q u w w q q out p in out in out in + +
Diesel cycle he thermal efficiency of the ideal Diesel cycle under the cold air standard assumptions becomes: wnet qout 4 ηth, Otto q q γ ( ) in ( 4 / ) γ ( / ) he cutoff ratio r c, as the ratio of the cylinder olumes after and before the combustion process: r c / in Lect-7 8
Diesel cycle Lect-7 Substituting these equations into the thermal efficiency relation and simplifying: η th, Diesel Where, r, is r γ rc γ ( r the compression ratio he quantity in the brackets is always >0 and therefore η th,diesel > η th,otto for the same compression ratios. γ c ) V V max min 9
Lect-7 Dual cycle Approximating heat addition by a constant pressure or constant olume process is too simplistic. Modelling the heat addition process by a combination of constant pressure and constant olume processes: dual cycle. he relatie amounts of heat added during the two processes can be appropriately adjusted. Both Otto and Diesel cycle can be obtained as a special case of the dual cycle. 0
Lect-7 Dual cycle P q in Isentropic 4 q out Ideal dual cycle on P- diagram What will this cycle look like on -s diagram? What is the thermal efficiency of such a cycle?
Lect-7 Gas power cycles In this lecture... he Carnot cycle and its significance Air-standard assumptions An oeriew of reciprocating engines Otto cycle: the ideal cycle for sparkignition engines Diesel cycle: the ideal cycle for compression-ignition engines Dual cycles
Lect-7 In the next lecture... Stirling and Ericsson Cycles Brayton Cycle: he Ideal Cycle for Gas- urbine Engines he Brayton Cycle with Regeneration he Brayton Cycle with Intercooling, Reheating, and Regeneration Rankine Cycle: he Ideal Cycle for Vapor Power Cycles