1. Introduction Some Basic Concepts

Transcription

1 1. Introduction Some Basic Concepts

2 1.What is a fluid? A substance that will go on deforming in the presence of a deforming force, however small

3 2. What Properties Do Fluids Have? Density ( ) Pressure ( ) Temperature ( ) Viscosity Kinematic ( ), Dynamic ( ) Velocity ( ) Compressibility Inertia Continuum

4 Fourier s Law of Heat Conduction q& = k T n q n Newton s Law of Viscosity U τ = μ y y U

5 3. What Constrains a Fluid? How these constraints work depends upon how important viscosity and compressibility are.

6 Two Important Parameters Rate of change of = momentum (inertial force) Scale of the Inertial Forces Scale of the Viscous Forces NACA 0012 Airfoil, Re = , M ~ 0 Large Eddy Simulation Institute of Computational Fluid Dynamics Japan Scale of the Inertial Forces Scale of Forces Resisting Compression

7 3a. Ideal Flow Viscous and compressible effects small (large Re, low M). Flow is a balance between inertia and pressure forces, i.e. acceleration vector balances the pressure gradient vector

8 3a. Viscous Flow Importance of viscous effects governed by Re = VL ν Re= Boundary layer: No-slip condition:

9 3b Viscous Flow Viscous region not always confined to a thin layer Separation:

10 3b. Viscous Flow Separation and Wake Formation Circular cylinder, Re = , M ~ 0 Large Eddy Simulation Institute of Computational Fluid Dynamics Japan

11 3b Viscous Flow Turbulence: Laminar Flow:

12 Turbulence Re θ =3500, Turbulent boundary layer Guezenec and Nagib Illinois Institute of Technology

13 3c. Compressibility V Importance of viscous effects governed by M = c Incompressible Regime M< Negligible compressibility effects Subsonic Regime <M< Quantitative effects, no qualitative effects Transonic Regime <M< Large regions of subsonic and supersonic flow. Large qualitative effects. Supersonic Regime M> Almost entirely supersonic flow. Large qualitative effects

14 Flow Past a Circular Cylinder Re = 10,000 and Mach approximately zero Re = 110,000 and Mach = 0.45 Re = 1.35 M and Mach = 0.64 Pictures are from An Album of Fluid Motion by Van Dyke

15 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

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

17 3c. Compressibility Some Qualitative Effects Shock wave: Very strong, thin wave, propagating supersonically, producing almost instantaneous compression of the flow, and increase in pressure and temperature. Hypersonic vehicle re-entry NASA Image Library

18 3c. Compressibility Some Qualitative Effects Expansion or isentropic compression wave Finite wave (often focused on a corner), moving at the sound speed, producing gradual compression or expansion of a flow (and raising or lowering of the temperature and pressure). Cone-cylinder in supersonic free flight, Mach = Picture from An Album of Fluid Motion by Van Dyke.

19 Summary What a fluid is. Its properties. The governing laws Reynolds number. Mach number How Newton s 2 nd Law works as a vector equation Viscous effects: no-slip condition, boundary layer, separation, wake, turbulence, laminar Compressibility effects: Regimes, shock waves, isentropic waves. Initial ideas of concepts such as streamlines/eddies Qualitative understanding