Gas Power Cycles Thermodynamics Professor Lee Carkner Lecture 17

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 = (200 kJ/h) / (3600 s/hr) =  Absorbing heat raises water temp by 2 C  m’ w = Q’ w /c p  T = / (4.18)(2) =

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) – /298 =  X’ destroyed = T 0 S’ gen = (298)( ) =

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

Diagrams  Pv diagram   Ts diagram   But, net heat = net work 

Ideal Diagrams

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 

Carnot Diagrams

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 

Reciprocating Engine  Top dead center   Bottom dead center   Stroke   Bore   Intake Valve   Exhaust value  Allows combustion products to leave

Volumes of a Cylinder

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 )

MEP Illustrated

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

Ideal Otto Cycle  We can approximate the cycle with   An isochoric (no  V ) heat addition   An isochoric heat rejection 

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 =

Otto Compression Ratios

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 ~

Otto Engine Exercise

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

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

Diesel Compression Ratios

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 

Next Time  Read:  Homework: Ch 9, P: 22, 37, 47, 75