ch946 - Chapter 9 Compressible Flow 9.1 9.2 9.3 9.4 9.5 9.6...

Info iconThis preview shows pages 1–20. Sign up to view the full content.

View Full Document Right Arrow Icon
Chapter 9: Compressible Flow 9.1 Introduction: Review of Thermodynamics 9.2 The Speed of Sound 9.3 Adiabatic and Isentropic Steady Flow 9.4 Isentropic Flow with Area Changes 9.5 The Normal Shock Wave 9.6 Operation of a Converging and Diverging Nozzles
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Calculating Area start
Background image of page 2
Ch.9 - COMPRESSIBLE FLOW Flow can be affected by: Q Q friction shock shock area change, shock, friction, heat transfer for adiabatic, steady flow T o , h o , a o are constant along flow for isentropic flow ρ o and p o are also constant along flow
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Missing relation for Area since stagnation state does not provide area information*. So to get area information use critical conditions as reference. *mathematically the stagnation area is infinity
Background image of page 4
If M = 1 the critical state; p * , T * , ρ *…. c = [kRT] 1/2 ; c * = [kRT * ] 1/2 isentropic Local conditions related to stagnation Critical conditions related to stagnation isentropic adiabatic
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
p*/p o = { p b /p o = p e /p o (choked) } = 0.528
Background image of page 6
Want to Relate Area to Mach Number and Critical Area
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
c*= a = [kRT*] 1/2 ; c = [kRT] 1/2
Background image of page 8
EQ. 9.26 EQ. 9.32 EQ. 9.28b EQ. 9.32
Background image of page 9

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
A x A y = A x+y A = [1 + (k-1)M 2 ]/[(k + 1)/2] x + y = 1/(k-1) + ½ = 2/2(k-1) +(k-1)/2(k-1) = (k+1)/(2(k-1))
Background image of page 10
isentropic, ideal gas, constant specific heats EQs. 9.34, 9.44 Provide property relations in terms of local Mach numbers, critical conditions, and stagnation conditions. NOT COUPLED LIKE ORIGINAL EQUATIONS
Background image of page 11

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Isentropic Flow of Ideal Gas 0 1 2 3 4 5 0 0.5 1 1.5 2 2.5 3 3.5 Mach Number (M) A r e a R a t i o A / A * * Note two different M #’s for same A/A * SUPERSONIC TUNNELS Not built this way because of separation A*
Background image of page 12
Isentropic Flow of Ideal Gas 0 1 2 3 4 5 0 0.5 1 1.5 2 2.5 3 3.5 Mach Number (M) Area Ratio A/A* accelerating • For accelerating flows, favorable pressure gradient, the idealization of isentropic flow is generally a realistic model of the actual flow behavior. • For decelerating flows (unfavorable pressure gradient) real fluid tend to exhibit nonisentropic behavior such as boundary layer separation, and formation of shock waves.
Background image of page 13

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Isentropic Flow In A Converging Nozzle What happens to p(x) as lower p b ?
Background image of page 14
As lower p b by vacuum pump, how does p(x)/p o change? IDEAL GAS, ISENTROPIC, QUASI-1-D, STEADY, only PRESSURE WORK, Ignore gravity effects, c p v are constant x
Background image of page 15

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon