1. 1 Physics of turbulence muna Al_khaswneh Dr.Ahmad Al-salaymeh

2. 2 Introduction Turbulence cannot exist by itself, however; it requires a continuous supply of energy& changes in velocity& direction.

3. 3 Objective The Definition of turbulence Examples of turbulence Boundary layer Study Reynolds numbers Study the differential continuity equation Study Navier-Stocks equation Kolmogorov theory Laminar-turbulent transition Problems of turbulence

4. 4 Definition & properties It is a flow with disordered in time & space. 1-three-dimensionality. 2-Unsteadiness. 3-strong vorticity. 4-Unpredictability. 5-Broad spectrum.

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8. 8 Reynolds number 1. inertia forces 2. viscous forces 1. ρ u 2, ρ: fluid density,u : fluid speed 2. μ u, μ: viscous fluid, d : diameter fluid d

9. 9 Re = inertia forces viscous forces = ρ d u μ

10. 10 So that Reynolds number depend on fluid properties as ; speed, pipe diameter,viscosity & density.

11. 11 Random pipe Re

12. 12 Boundary layer

13. 13 Laminar-turbulent transition. 1.Linear stability theory. 2.Primary instability of free shear flow. 3.Later stage of transition in free shear flows.

14. 14 Continuity equation The conservation of mass principle is applied to the control volume

15. 15 Continuity equation For three dimension (our interest ) x z y ΔyΔy ΔxΔx ΔzΔz = u x î + u y ў +u z ќ

16. 16 Continuity equation or

17. 17 Navier-stokes equation the momentum translate with tow ways & tow forces ways 1.Convection transition 2.Molecular transition forces 1.Gravity force 2.Pressure force

18. 18 Forces 1.Gravity force Pressure force

19. 19 Convection transition

20. 20 Molecular transition Shear stress

21. 21 Molecular transition

22. 22 For x direction

23. 23 Navier-stokes equation

24. 24 Newtonian equation

25. 25 stocks equation

26. 26 Kolmogorov theory 1.The physics of turbulence is the same in all turbulent system. 2.It is independent of large scale forcing & small scale dissipative 3.Fluctuation occur in an incompressible medium-density 4.Energy flows from large scales to small scales.

27. 27 pressure (drop) flow (average speed) laminar turbulent

28. 28 Primary instability of free shear flow

29. 29 Primary instability of free shear flow

30. 30 Later stage of transition in free shear flows. Some vorticity remains between the vortices, we will call it {secondary instability}.

31. 31 Problems

32. 32 The end Thank you