Lecture n2 Turbulent flow Modelling （讲座n2湍流模型）.pdf

Turbulent flow Henryk Kudela Contents 1 Turbulence modeling 1 2 Velocity profiles: the inner, outer, and overlap layers 4 2.1 Turbulent-Flow Solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.2 Power-law velocity profile . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 3 Turbulence: some important thoughts 12 4 Problems 14 1 Turbulence modeling We will be assume constant density and viscosity of fluid. We also assume that no thermal inter- action of the fluid with the solid boundary. In this way only continuity and momentum equations describe fluid velocity (u,v,w) and pressure p distribution (Navier -Stokes equation): ∂ v 1 +v ∇v = − ∇p +ν ∆v momentum equation (1) ∂ t ρ ∂ u ∂ v ∂ w ∇ v = + + = 0 continuity equation–conservation of mass (2) ∂x ∂y ∂z Equations (1),(2) are subjected to no–slip boundary condition at the walls and knows inlet and exit conditions. Both laminar and turbulent flows satisfy (1),(2). For laminar flow, where there are no random fluctuations, we can sometimes solve them for a variety of geometries, like flow in pipe (see lec- ture n5–viscous–flow). Most flows encountered in engineering practice are turbulent. This is particularly true for pipe flows, so it is essential at this time t