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Gas Power Cycles Thermodynamics Professor Lee Carkner Lecture 17
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PAL # 16 Exergy Balance Cooling chickens with a water stream Mass flow of chickens m’ c = (500 c/hr)(2.2 kg/c) / (3600 s/hr) = Heat removed from chickens can be found from specific heat Q’ c = m’ c c p T = (0.3056)(3.54)(15-3) = Heat gained by water is Q’ w = Q’ c + Q’ environ = 13.0 + (200 kJ/h) / (3600 s/hr) = Absorbing heat raises water temp by 2 C m’ w = Q’ w /c p T = 13.056 / (4.18)(2) =
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PAL # 16 Exergy Balance Find S gen from equation of flow systems S’ gen = But s = c ln (T 2 /T 1 ) for an incompressible substance S’ gen = (0.3056)(3.54) ln(276/288) + (1.56)(4.18) ln(275.5/273.5) – 0.0556/298 = X’ destroyed = T 0 S’ gen = (298)(0.00128) =
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Modeling Power Cycles We often generate power by performing a series of processes in a cycle We use instead an ideal cycle We will often be looking for the thermal efficiency th = W net /Q in = w net /q in
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Diagrams Pv diagram Ts diagram But, net heat = net work
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Ideal Diagrams
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Carnot The Carnot cycle is the most efficient It is very hard to build even an approximation th,Carnot = 1 – (T L /T H ) In general want high input and low output temperatures
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Carnot Diagrams
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Air Standard For most internal combustion engines the working substance is a gas and is a mixture of air and fuel Can assume: All processes are internally reversible Can think of exhaust as heat rejection to an external sink Cold-air standard
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Reciprocating Engine Top dead center Bottom dead center Stroke Bore Intake Valve Exhaust value Allows combustion products to leave
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Volumes of a Cylinder
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Compression Clearance volume Displacement volume Compression ratio r = V max / V min = V BDC / V TDC Mean Effective Pressure (MEP) is the equivalent pressure that would produce the same amount of work as the actual cycle MEP = W net / ( V max – V min )
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MEP Illustrated
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Otto Cycle The ideal cycle for reciprocating engines ignited by a spark was developed in 1876 by Nikolaus Otto Basic cycle: Can also combine the exhaust and intake into the power stroke to make a two-stroke engine
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Ideal Otto Cycle We can approximate the cycle with An isochoric (no V ) heat addition An isochoric heat rejection
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Otto Analysis We can write the heats as c v T q in = q out = th = 1 – q out /q in = But we also know that for the isentropic process (T 1 /T 2 ) = ( v 2 / v 1 ) k-1 and r = v 1 / v 2 th,Otto =
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Otto Compression Ratios
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Efficient Otto Engines As we increase r the efficiency gain levels off at about 8 Also, high r can mean the fuel is compressed so much it ignites without the spark Can’t really increase k since we are using air Typical values for th,Otto ~
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Otto Engine Exercise
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Diesel Cycle We can approximate the cycle with An isobaric heat addition An isochoric heat rejection Only the second process is different from the Otto
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Diesel Efficiency The heat in is the change of internal energy plus the isobaric work q in = u + P v = h 3 -h 2 = The heat out is just the change in internal energy q out = u 4 -u 1 = So then the efficiency is th,diesel = 1 – q out /q in = 1 – (T 4 -T 1 ) / k(T 3 -T 2 ) We can rewrite as: th,diesel = 1 – (1/r k-1 )[(r k c -1)/k(r c -1)] r c = v 3 / v 2
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Diesel Compression Ratios
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Making Diesels Efficient Want large r and small r c Diesels can operate at higher compression ratios and are usually more efficient th,diesel ~ Diesels also have lower fuel costs because they don’t have to worry about autoignition and engine knock
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Next Time Read: 9.8-9.12 Homework: Ch 9, P: 22, 37, 47, 75
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