This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: FLOW IN A CONSTANTAREA DUCT WITH HEAT EXCHANGE (Combustion Chambers, Heat Exchangers) Frictionless Flow in a Constant Area Duct with Heat Exchange Quasionedimensional flow affected by: area change, friction, heat transfer , shock R x = 0 δ Q/dm h 1 , s 1 , h 2 , s 2 , C O N S T A N T A R E A N O F R I C T I O CH 124 Governing Equations • Cons. of mass • Cons. of mom. • Cons. of energy • 2 nd Law of Thermo. Ideal Gas/Const. c p ,c v • p = ρ RT • h 2h 1 = cp(T 2 – T 1 ) • Δ s = c p ln(T 2 /T 1 ) Rln(p 2 /p 1 ) {1D, Steady, F Bx =0 only pressure work} H E A T E X C H A N G E QuasiOneDimensional, Steady, F Bx = 0, dW s /dt = 0, dW shear /dt = 0, dW/dt other = 0, effects of gravity = 0, ideal gas*, c v , c p is constant Property relations for ideal gas with c v and c p constant Cons. of Momentum Cons. of Energy 2 nd Law of Thermodynamics Cons. Of Mass Constant area , frictionless, heat exchange = Rayleigh Flow No R x Can find: p 2 , ρ 2 , T 2 , s 2 , h 2 , V 2 δ Q/dm If know: p 1 , ρ 1 , T 1 , s 1 , h 1 , V 1 and Constant area , frictionless, heat exchange = Rayleigh Flow breath C O N S T A N T N O F R I C T I O N TS curve H E A T E X C H A N G E A R E A Frictional, Constant Area, Adiabatic Flow Fanno Line Isentropic Flow T s ? Frictionless, Constant Area with Heat Transfer Isentropic Flow Rayleigh Line dA ≠ No Frictional, Changing Area, Adiabatic Flow s 2s 1 = c p ln(T 1 /T 2 )Rln(p 2 /p 1 ) Need p 2 /p 1 in terms of T 2 and T 1 After manipulation eqs 12.30a – 12.30g T s Rayleigh Line s T x For the same mass flow, each point on the curve corresponds to a different value of q added or taken away. T 1 , s 1 x T o ss 1 = c v ln(T/T 1 ) + ½Rln [(T oT 2 )/(T oT 1 )] FLASHBACK FANNO LINE, ADIABATIC & CONSTANT AREA BUT FRICTION h 1 + V 1 2 /2 = h 2 + V 2 2 /2 h O1 = h O2 c p T O1 = c p T O2 T O1 = T O2 RALEIGH LINE, NOT ADIABATIC & CONSTANT AREA BUT NO FRICTION q +h 1 +V 1 2 /2 = h 2 +V 2 2 /2 q = h O2 – h O1 q = c p (T O2T O1 ) The effect of heat addition is to directly change the stagnation ( total ) temperature of the flow C O N S T A N T N O F R I C T I O N TS curve properties H E A T E X C H A N G E A R E A where is sonic ? Rayleigh Line s T A ds/dT = 0 B dT/ds = 0 Properties: at A – highest s at B – highest T pA – (p+ Δ p)A = ( ρ + Δ ρ ) A (V + Δ V) 2 ρ AV 2 Δ p A= ρ V A(V + Δ V)  ρ AV 2 Δ p A= ρ V A Δ V dp/ ρ = VdV ρ V = ( Δρ + Δ ρ )(V + Δ V) Want differential form of governing equations. Momentum : dp/ ρ = VdV Ideal gas : p = ρ RT dp = ρ Rd(T) + RTd( ρ ) dp/p = dT/T+ d ρ / ρ Continuity : ρ V = constant d ρ / ρ + dV/V = 0 ds/dT = 0 dp/ ρ = VdV Tds = du + pd v (1.10a) du = d(hpv) = dh – pd v – v dp Tds = dh – v dp = dh – dp/ ρ Ideal gas: dh = c p dT Tds = c p dT – dp/ ρ Tds = c p dT + VdV ds/dT = c p /T + (V/T)(dV/dT) ds/dT = c p /T + (V/T)( dV/dT ) Momentum : dp/ ρ = VdV Ideal gas : dp/p =d ρ / ρ + dT/T Continuity : d ρ / ρ + dV/V = 0 ρ VdV /p = d...
View
Full
Document
This note was uploaded on 04/26/2010 for the course MAE 101B 101B taught by Professor Rohr during the Summer '09 term at UCSD.
 Summer '09
 Rohr

Click to edit the document details