A short introduction to Fluid Dynamics , Heat Transfer and CFD

1. A short introduction to Fluid Dynamics, Heat Transfer and CFD

2. Outline • Fluid Dynamics • Heat Transfer • CFD

3. Outline • Fluid Dynamics • Heat Transfer • CFD

4. Fluid Dynamics • Study of fluids in motion, including aerodynamics, i.e. the study of gases (internal and external), and hydrodynamics, i.e. the study of liquids. • A fluid dynamical problem involves calculation of fluid properties, such as velocity, pressure, density and temperature • A set of governing equations (conservation laws) are solved using a numerical method (CFD) External link 

5. Fluid Dynamics -governing equations- • Based on conservation laws of mass, momentum and energy • Applied on a small fluid element; control volume (CV) • Conservation of mass (continuity eqn): CV the rate of change of mass = net flow through the boundaries of the volume (the control volume is fixed in space) External link 

6. Fluid Dynamics -governing equations- • Conservation of momentum (Navier-Stokes): • Substantial derivative: the rate of change of a property (F) for a CV moving with the fluid CV the rate of change of momentum = net force exerted on the volume (the control volume moves with the fluid) substantial or material derivative local or Eulerian derivative advection External link 

7. Fluid Dynamics -governing equations- • Differential form (valid for arbitrary control volume) continuity equation momentum equations External link 

8. Fluid Dynamics -Reynolds number- • Most important dimensionless number in Fluid dynamics • For low Re-flows stabilizing viscous forces are dominant  laminar flow • For high Re-flows inertia forces are dominant  flow is unstable / turbulent • Re is used to determine scale similarity in experiments and simulations U: velocity scale L: length scale External link 

9. U=2m/s U=10m/s Fluid Dynamics -boundary layer- • A thin layer of fluid, adjacent to the bounding surface, where viscosity is dominant • The treatment of the boundary layer is, due to the present physical processes, crucial • Strong shear (wall friction)  growth of instabilities, production of turbulence • Separation • Heat/mass transfer • Dissipation External link 

10. Fluid Dynamics -laminar flow- • Characterizes a flow in parallel layers • In laminar flows • High momentum diffusion • Low momentum convection • U and P independent of time • The boundary layer in laminar flows is smooth • Smooth (weak) boundary layer  low wall friction • Low energy level  susceptible for adverse pressure gradients  easy separation External link 

11. transition phase stable flow unstable flow turbulent flow Fluid Dynamics -transitional flow- • Transition from the laminar to the turbulent state External link 

12. Fluid Dynamics -turbulent flow- • Consists of a large number of vortices, i.e. eddies, of various size (scales) in space and time • Turbulent flows are of a random character • Extremely efficient in mixing processes • Nearly all practical flows are of a turbulent character • Turbulence is three-dimensional External link 

13. Fluid Dynamics -scales of motion- • Turbulent flows are non-linear, i.e. there is transformation of information (energy) between different scales • Energy is supplied at the large scales, by the mean flow (production) • By, so-called, vortex stretching energy is transformed into smaller and smaller scales • Finally, at the viscous scales, energy is transformed into heat (dissipation) • Without production the turbulence decays External link 

14. Fluid Dynamics -vortex dynamics- • … External link 

15. Fluid Dynamics -statistical description- • As turbulence is a non-repeatable random like process, statistical methods are needed to describe the flow • The flow is described by different statistical moments • 1st-moment: mean ( ) • 2nd-moment (about the mean): variance ( ) • 3rd-moment (about the mean): skewness ( ) • 4th-moment (about the mean): kurtosis ( ) External link  std. deviation

16. Fluid Dynamics -statistical description- Turbulent signal Sinus wave value sample sample • Probe measurements would identify two identical flows w.r.t. mean and variance (and std. deviation) • Higher order statistics are needed External link 

17. 4 10 2 10 0 10 -2 10 -4 10 -6 10 0 1 2 3 10 10 10 10 Fluid Dynamics -statistical description- power spectral density Histograms Turbulent signal Sinus wave turbulent “high peakedness” samples psd / energy “heavy tails” symmetric sinus value value • Turbulent: distribution close to Gaussian • Sinus: distribution heavy in the tails due to the intermittent “flow character” frequency / wavenumber • Turbulent: energy concentrated to large scales • Sinus: energy “solely” in the dominant frequency External link 

18. Fluid Dynamics -terminology- • Vorticity • Potential flow • Irrotational flow • Stokes flow • Wake flow • Separation External link 

19. Fluid Dynamics-from a practical view- External link 

20. Outline • Fluid Dynamics • Heat Transfer • CFD

21. Heat Transfer • … External link 

22. Heat Transfer -Prandtl number- External link 

23. Heat Transfer -convection heat transfer- External link 

24. Heat Transfer -diffusion heat transfer- External link 

25. Heat Transfer -radiation heat transfer- External link 

26. Heat Transfer -terminology- External link 

27. Heat Transfer -from a practical view-

28. Outline • Fluid Dynamics • Heat Transfer • CFD

29. CFD • … External link 

30. CFD -solution strategies- External link 

31. CFD -basic criteria- External link 

32. CFD -finite difference approach- External link 

33. CFD-modeling techniques- External link 

34. CFD-terminology- External link 

35. CFD -from a practical view- External link 