流体力学与 及传热课件Heterogeneous Flow and Separation.pptVIP

3. Heterogeneous Flow and Separation ;1. Introduction and types of drag ;2. Drag coefficient ; In flow through pipes, the friction factor was defined as the ratio of the drag force per unit area to the product of fluid density and velocity head. ; ; These curves have been determined experimentally. However, in the laminar region for low Reynolds numbers, less than about 1.0, the experimental drag force for a sphere is the same as the theoretical Stokes law equation as follows: ;;The variation of CD with Re is quite complicated because of the interaction of the factors that control skin drag and form drag. ;Further increases in Re cause shifts in the separation point. At about Re = 3×105 the sudden drop in CD is the result of the boundary layer becoming completely turbulent and the point of separation moving downstream. ;In the region of Re about 1×103 to 2×105, the drag coefficient is approximately constant for each shape and CD = 0.44 for a sphere. ;3.1.2 Flow through Beds of Solids ;In the theoretical approach used, the packed column is regarded as a bundle of crooked tubes of varying cross-sectional area. ;2. Laminar flow in packed beds ;The specific surface of a particle av is defined as;where a is the ratio of total surface area in the bed to total volume of bed (void volume plus particle volume) ;The average interstitial velocity in the bed is u and is related to the superficial velocity u based on the cross section of the empty container by ;To determine the equivalent channel diameter De, the surface area for n parallel channels of length L is set equal to the surface-volume ratio times the particle volume S0L (1 - ε) . ;The void volume in the bed is the same as the total volume of the n channels;For flow at very low Reynolds numbers, the pressure drop should vary with the first power of the velocity and inversely with the square of the channel size, in accordance with the Hagen-Poiseulli equation for laminar flow in straight tubes.;The equatio