流体力学与传热课件Heterogeneous-Flow-and-Separation.ppt
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- 流体力学 传热 课件 Heterogeneous Flow and Separation
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1、3.Heterogeneous Flow and Separation 3.1 Flow Past Immersed ObjectsDefinition of Drag Coefficient for Flow Past Immersed Objects 1.Introduction and types of drag The flow of fluids outside immersed bodies appears in many chemical engineering applications and other processing applications.For example
2、settling,drying and filtration,and so on.2.Drag coefficient Correlations of the geometry and flow characteristics for solid objects suspended in fluid are similar in concept and form to the friction factor-Reynolds number correlation given for flow inside conduits.In flow through pipes,the friction
3、factor was defined as the ratio of the drag force per unit area to the product of fluid density and velocity head.220 220 For flow past immersed objects the drag coefficient is obtained by substituting CD for the friction factor Kf in equation(1.4-32)2222uCuKpDff3.1-1 therefore2/2uCAFpDDfThe Reynold
4、s number for a particle in a fluid is defined as0ReuDpFrom dimensional analysis,the drag coefficient of a smooth solid in an incompressible fluid depends upon a Reynolds number and the necessary shape ratios.For a given shape(Re)DC3.1-2 Drag coefficients of typical shapes For each particular shape o
5、f object and orientation of the object with respect to the direction of flow,a different relation of CD versus Re exists.Correlations of drag coefficient versus Reynolds number are shown in figure.These curves have been determined experimentally.However,in the laminar region for low Reynolds numbers
6、,less than about 1.0,the experimental drag force for a sphere is the same as the theoretical Stokes law equation as follows:03uDFpD03uDFpDpDDuF033.1-3 Combining Eqs.(3.1-1)and(3.1-3)and solving for CD,the drag coefficient predicted by Stokes law isRe24242/020uDuAFCpD3.1-4 The variation of CD with Re
7、 is quite complicated because of the interaction of the factors that control skin drag and form drag.For a sphere,as the Reynolds number is increased beyond the Stokes law range,separation occurs and a wake is formed.Further increases in Re cause shifts in the separation point.At about Re=3105 the s
8、udden 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 1103 to 2105,the drag coefficient is approximately constant for each shape and CD=0.44 for a sphere.3.1.2 Flow through Beds of Solids 1.Introduct
9、ion A system of considerable importance in chemical and other process engineering fields is the packed bed,which is used for a fixed-bed catalytic reactor,adsorption of a solute,absorption,filter bed,and so on In the theoretical approach used,the packed column is regarded as a bundle of crooked tube
10、s of varying cross-sectional area.The theory developed in Chapter 1 for single straight tubes is used to develop the results for the bundle of crooked tubes.2.Laminar flow in packed beds Certain geometric relations for particles in packed beds are used in the derivations for flow.The void fraction i
11、n a packed bed is defined as The specific surface of a particle av is defined asppvSaFor a spherical particle,pvDa62ppDS36ppDv)1(6)1(pvDaawhere a is the ratio of total surface area in the bed to total volume of bed(void volume plus particle volume)Since(1-)is the volume fraction of particles in the
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