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

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

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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

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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 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

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

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

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11 Random pipe Re

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12 Boundary layer

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

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

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

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16 Continuity equation or

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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

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18 Forces 1.Gravity force Pressure force

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19 Convection transition

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20 Molecular transition Shear stress

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21 Molecular transition

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22 For x direction

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23 Navier-stokes equation

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24 Newtonian equation

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25 stocks equation

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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.

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

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28 Primary instability of free shear flow

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29 Primary instability of free shear flow

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

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31 Problems

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32 The end Thank you

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