Introduction and Basic Concepts

Transcription

1 Topic 1 Introduction and Basic Concepts 1

2 Flow Past a Circular Cylinder Re = 10,000 and Mach approximately zero Mach = 0.45 Mach = 0.64 Pictures are from An Album of Fluid Motion by Van Dyke

3 Flow Past a Circular Cylinder Mach = 0.80 Mach = 0.90 Mach = 0.95 Mach = 0.98 Pictures are from An Album of Fluid Motion by Van Dyke

4 Flow Past a Sphere Mach = 1.53 Mach = 4.01 Pictures are from An Album of Fluid Motion by Van Dyke

5 Shock wave: Very strong, thin wave, propagating supersonically, producing almost instantaneous compression of the flow, and increase in pressure and temperature. Expansion or isentropic compression wave: Finite wave moving at the sound speed, producing gradual compression or expansion of a flow (and raising or lowering of the temperature and pressure). Hypersonic vehicle re entry NASA Image Library Cone cylinder in supersonic free flight, Mach = Picture from An Album of Fluid Motion by Van Dyke.

6 Compressible Aerodynamics What is meant by compressibility? When is compressibility important in fluid flows? What are the effects of compressibility in fluid flows? How can we analyze compressible flows? 2

7 What is compressibility? Consider a volume of pressurized air V p V+ dv p+dp Compressibility (Proportionate change in volume)/(change in pressure) Will this definition give a single answer? 3

8 To be precise we can define the Isothermal compressibility Isothermal? Isentropic compressibility Isentropic? Compressibility (Proportionate change in volume)/(change in pressure), so Pressure change that resists a given proportionate change in volume ~ 1/ 4

9 When is Compressibility Important in Fluid When Flow? Pressure changes occur primarily in response to 5

10 The degree to which hcompressibility bl is important in a flow is characterized by Scale of Scale of Forces Inertial Forces Resisting Compression Scale of the inertial forces ~ Force resisting a given compression of the fluid ~ So 6

11 Compressibility and speed of sound are related a 1 Air: a=340 STP s Water: a=1400 STP So M V 2 s In Summary: the magnitude of compressibility effects depends on the velocity of the flow relative e to the speed of sound 7

12 What Are the Effects of Compressibility on a Flow? E.g. Uniform flow past an airfoil vs Mach no. Entirely subsonic flow V, a M =V /a <<1 Smooth streamlines. Even far upstream of the airfoil the streamlines have begun to move under its influence How does the airfoil exert this upstream influence? 8

13 Mixed subsonic/supersonic flow Subsonic V, a M =V /a <1 Shock wave: Very strong, thin wave, propagating supersonically, producing almost instantaneous compression of the flow, and increase in pressure and temperature. 9

14 RAE 2822 Transonic Airfoil 2.3 degrees angle of attack Pressure contours M =

15 Transonic flow over an airfoil M very close to 1 Schlieren photograph history.nasa.gov/sp-440/ch7-2.htm 11

16 Supersonic free stream flow V, a M =V /a >1 Bad design for supersonic flow (lots of drag), better to have sharp leading edge: 12

17 Supersonic Flow Past an Airfoil Visualization of constant density lines by Laser Holography. Image produced by Laboratoire de Thermique Appliquee et de Turbomachines, EPF - Lausanne 13

18 Flow Regimes Incompressible Cessna 150 Subsonic P51 Mustang Transonic Global Express Supersonic SR 71 Hypersonic X 43 14

19 4. How Can We Analyze Compressible Flows? Like for incompressible flows we use Conservation of Mass Conservation of Momentum However for compressible flows we must consider Thermodynamics (since the fluid properties are variables) Conservation of energy ( 1 st law of thermodynamics) Heat, Work, internal energy 2 nd law of thermodynamics Entropy Equation of state (to relate variables) We will neglect viscosity Can be ignored in many situations (just like for incompressible flows) Viscous effects are generally localized in a thin region close to the wall (Boundary Layer AOE 3044) 15