北京航空航天大学：《工程流体力学》课程PPT教学课件（双语版）Chapter 6 Compressible flow Introduction

Chapter 6 Compressible flow Introduction

1 Chapter 6 Compressible flow Introduction

When is a flow compressible? A compressible flow differs from an incompressible one in that significant change happens in the density dp Pathline dt xo Fluid element Pressure

2 When is a flow compressible? Pressure Fluid element Pathline A compressible flow differs from an incompressible one in that significant change happens in the density.  0 dt d

Density of a fluid element increases or decreases as the pressure does in compressible flow P= pRT =50m/s =100m/s I=300m/s 4=P-p=p12 =1.54% =6.17% =55.5 100 Pa/00 k

3 Density of a fluid element increases or decreases as the pressure does in compressible flow V = 50m/s V =100m/s V = 300m/s 2 2 1 p = pa − p = V 1.54% 50 =          pa p 6.17% 100 =          pa p 55.5% 300 =          pa p p = RT C p k = 

When is compressibility important? When a fluid moves at high speed, density changes become significant Change in density only about 5% 0.8 flow speed c-sound speed 0.6 0,4 Ma0.3 compressible Mach Number

4 When is compressibility important? When a fluid moves at high speed, density changes become significant c V Ma = - flow speed - sound speed Ma0.3 compressible

Examples of high speed flow Ma=085 Ma=2.35 Ma4 Ma=25

5 Examples of high speed flow Ma=0.85 Ma=2.35 Ma=4 Ma=25

Flow speed in a typical aeroengine cfm CFMS6-7 DAC MODULAR DESIGN

6 Flow speed in a typical aeroengine

History a Untill the late 1930s, engineers could ignore the compressibility of air a Aerodynamics, a subject to compressible gas and air flow, makes possible the remarkable progress in modern aeronautics and astronautics Ernst mach Prandtl von karman

7 History ❑ Untill the late 1930s, engineers could ignore the compressibility of air ❑ Aerodynamics, a subject to compressible gas and air flow,makes possible the remarkable progress in modern aeronautics and astronautics Ernst Mach Prandtl von Karman

Distinctive features of compressible flow Shock wave Supersonic nozzle Mas1 M as Laval nozzle

8 Distinctive features of compressible flow Shock wave Supersonic nozzle Laval Nozzle Ma1

Assumptions for compressible flow Adiabatic flow with negligible heat transfer Reversible process with fluid isentropic flow friction being neglected Perfect gas P=pRT Internal energy u and enthalpy h: u=C,th=cpt Specific heat ration: k=C/C C,EREX kR R k-1 k-1

9 Assumptions for compressible flow Internal energy u and enthalpy h: u = Cv T h = Cp T •Adiabatic flow with negligible heat transfer •Reversible process with fluid friction being neglected isentropic flow •Perfect gas p = RTCp Cv Specific heat ration: k = / Cp −Cv = R −1 = k kR Cp −1 = k R Cv

Tds= dh For isentropic flow k/(k-1) p2 p2_P2 k

10  dp Tds = dh − For isentropic flow: / ( 1) 1 2 1 2 −         = k k T T p p const p k =  k p p         = 1 2 1 2  