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

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

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

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

View Full Document
Calculating Area start
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

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

View Full Document
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
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

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

View Full Document
p*/p o = { p b /p o = p e /p o (choked) } = 0.528
Want to Relate Area to Mach Number and Critical Area

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

View Full Document
c*= a = [kRT*] 1/2 ; c = [kRT] 1/2
EQ. 9.26 EQ. 9.32 EQ. 9.28b EQ. 9.32

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

View Full Document
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))
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

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

View Full Document
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*
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.

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

View Full Document
Isentropic Flow In A Converging Nozzle What happens to p(x) as lower p b ?
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

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

View Full Document