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Mechanical separations:,separate heterogeneous mixtures,sedimentation, filtration,Separations are divided into two classes.,Mechanical methods are based on the physical difference between particles, such as size, shape or density, is the subject of this chapter.,2,Application examples of mechanical separations,Heterogeneous mixtures,Solids from gases,Liquid drops from gases,Solids from solids,Solids from liquids,3,Content,Chapter 29,Screening(p986-991),29.6. Filtration(p991-1017),29.3. Gravity sedimentation process (p1035-8),29.4 Centrifugal sedimentation process (p1045-8),Chapter 7,29.1. Drag and drag coefficient(p150-p157),29.5. Flow through beds of solids(p157-161),29.2. Motion of particles through fluid(p162-171),29.7. Fluidization(p171-182),4,Topics in this chapter,1. Gravity(centrifugal) sedimentation process.,重力（离心）沉降过程,2. Filtration,过滤,3. Fluidization,流态化,5,29.1. Drag and drag coefficient (p150-p157),1. Drag coefficients,2. Drag coefficients of typical shapes,3. Form drag and streamlining,4. Stagnation pressure,6,1. Drag coefficients,FIGURE 7.2 Flow past immersed sphere.,7,1. Drag coefficients,p,cos,a,dA,Figure 7.1 Wall drag and form drag on immersed body,pressure,shear forces,wall drag,form drag,8,Total drag = wall drag + form drag,F,D,=,w,sin,a dA +,p,cos,a,dA.,(1). Drag F,D,The force in the direction of flow exerted by the fluid on the solid .,9,(2) drag coefficients,Just as friction factor, drag coefficient is defined:,Where,F,D:,is the total drag, N.,A,p,projected area, m,2,.,u,0,is the velocity of the approaching stream (by assumption u,0,is constant over the projected area), m/s.,(7.1),10,From dimensional analysis, the drag coefficient of a smooth solid in an incompressible fluid depends upon a Reynolds number and the necessary shape factor.,C,D,= (Re,p, shape factor),The Reynolds number for a particle in a fluid,where,D,p,= characteristic length of the particle,11,sphericity,s,球形度,The surface-volume ratio for a sphere of diameter D,p,divided by the surface-volume ratio for the particle whose nominal size is D,p,.,This surface-volume ratio is 6/D,p,for a sphere, since S,p,=,D,p,2,and v,p,=(1/6),D,p,3, Thus,(7.10),(P158) Table 7.1 Sphericity of several materials,12,2. Drag coefficients of typical shapes,13,For a sphere,When Re particle will go down,p,= particle will float,p, particle will go up,17,Three forces act on a particle moving through a fluid:,Only one-dimensional motion is consider here,.,F,e,F,b,F,D,(3) the drag force,F,D,.,(1) the external force, gravitational or centrifugal,F,e,;,(2) the buoyant force,F,b,;,18,2. Equations for one-dimensional motion of particle through fluid,Newtons 2nd law of motion,(7.25),u,is the velocity of particle relative to the fluid.,19,Therefore,The external force,The buoyant force,The drag force,(7.26),(7.27),(7.28)(7.1),(7.29),20,Motion from gravitational force,a,e,=,g,(7.30),Motion in a centrifugal field,.,(7.32),where r = radius of path of particle, m;, = angular velocity, rad/s;,u = the velocity of the particle relative to the fluid and is directed outwardly along a radius, m.,21,3. Terminal velocity,terminal velocity,u,t,(7.29),the time for acceleration to the terminal velocity is still quite small and is often ignored in analysis of the process.,22,For centrifugal sedimentation,For gravitational sedimentation,(7.33),(7.34),23,4. Drag coefficient,Figure 7.6 Drag coefficients for spheres and irregular particles.,24,25,free settling,(,自由沉降）,: the particles fall is not affected by the boundaries of the container and other particles.,hindered settling,（干扰沉降）,: the motion of the particle is impeded by other particles.,26,5. Motion of spherical particles,If the particles are spheres of diameter,D,p,Substituting,(7.33),(7.37),27,For Re,p,1,-Stokes law,For 1,000 Re,p, 200,000,-Newtons law,(7.40),(7.43),28,For 1 Re,p, 1000 , intermediate range,or,29,Calculation the terminal velocity of spheres,1. the terminal velocity,（,or diameter of particle,）,can be found by trial and error.,Choose equation to calculate,u,t,Check flow regime,Assume flow regime,Calculate,Re,t,NO,YES,u,t,30,2. Find a criterion,which does not contain ut.,31,6. Criterion for settling regime,Let,Stokes law regime,Therefore,When Re,p,1,32,Therefore, for 1,000 Re,p, 200,000,Same for Newtons law regime,Use,33,If K less than 2.6, Stokes law applies.,If K greater than 2.6 but less than 68.9, intermediate range applies.,If K is greater than 68.9 but less than 2,360, Newtons law applies.,EXAMPLE 7.1 p167,Criterion,34,中文教材,is used as criterion of settling regime when calculating D,p,.,is used as criterion of settling regime when calculating u,t,.,35,36,7. Hindered settling干扰沉降,1. each particle are affected by the presence of nearby particles,2. the particles in settling displace liquid, which flows upward and makes the particle velocity relative to the fluid greater than the absolute settling velocity,3. Comparing with free settling, the drag force is much greater, and terminal velocity is much small for hindered settling.,37,29.3. Gravity sedimentation process (p1035-1038),1. Removal of solids from gases,2. Sorting classifiers,38,Clarifier,(,澄清器,): A settler that removes virtually all the particles from a liquid.,Classifier,(,分级器,):,a device that separates the solids into two fractions.,The same principles of sedimentation apply to both kinds of equipment.,39,1. Removal of solids from gases,Gravity settling chamber is shown in the following figure.,Settling box or settling tank,40,Chamber: length-,l,width-,b,height-,H,u,-velocity of the gas,u,t,-velocity of the particle settling towards floor, terminal velocity.,-the time of residence for the gas in the chamber,=,l,/,u,.,t,-the time of particle settling from top to bottom of the chamber,t,=,H,/,u,t,.,41,Where,V,s,is the volumetric flow rate of gas.,Therefore,It should be satisfactory,Therefore,V,s is independent of the height of the chamber, and,t can be reduced by decrease,H,.,42,Multilayer chamber,多层降尘室,V,s,=(n+1)(,bl,),u,t,But on the other hand, u=Vs/bH must smaller than a certain value to prevent from particle being blowing away again.,43,Figure for the multilayer settling box,44,2. Sorting classifiers,Devices that separate particles of differing densities are known as sorting classifiers.,There are two method:,(1). sink-and-float,(2). differential settling,45,(1). Sink-and-float method(heavy-fluid separation),A particle + B particle + a liquid sorting medium,A,B,m,A,(or ,B,),m,B,(or ,A,),Separation depends only on the difference in the densities of the two substance and is independent of the particle size.,46,(2). Differential-settling method,A particle + B particle + a liquid sorting medium,A,B,m,A,(or ,B,) ,B,(or ,A,) ,m,Separation of the particles into several size fractions based upon the difference in terminal velocity.,The density of the medium is less than that of either substance.,47,Classifier,水力分级器,Water velocity can be adjusted by the position of M.,48,Consider particles of two materials A and,B,settling through a medium with density and viscosity ,.,(29.66),(29.67),A is galena,方铅矿,(diameter D,pA, density ,pA,),B,is quartz,石英,(diameter D,pB, density ,pB,).,For settling in the Stokes law regime.,49,The relationship of,D,pA,and,D,pB,for equal-settling particles is,equal-settling particles: particles which have equal settling velocity,From:,(29.68),50,For settling in the intermediate range, the relation of diameters of equal-settling particles is,For settling in the Newtons law regime, the relation of diameters of equal-settling particles is,(29.69),51,Figure 29.27 equal-settling particles,52,EXERCISE A mixture of galena(A) and silica(B) sphere particles has a size range of 0.14mm to 1.0mm in diameter and is to be separated by rising stream of water at 293.2K. The density of A is 7500kg/m,3,and that of B is 2650kg/m,3,. What is the size range of pure product? And what velocity of water flow is needed to get pure product?,53,classifier,54,29.4 CENTRIFUGAL SEDIMENTATION PROCESSES (p1045-1048),Principles of centrifugal sedimentation,Separation of solids from gases; cyclones,Liquid-solid separations; hydroclones,Centrifuges,55,Settling velocity,For a sphere particle,For the settling in stokes law regime,(7.34),1. Principles of centrifugal sedimentation,56,Separation Factor :,分离因数,The ratio of the centrifugal force to the gravity force.,(29.72),For a cyclone 1 ft (0.3 m) in diameter with a tangential velocity of 50 ft/s (15 m/s) near the wall, the,separation factor, is,2,500/(0.5 x 32.2) = 55.,Separation efficiency is much greater in centrifugal separator.,57,2. Separation of solids from gases; cyclones,旋风分离器,an outlet for dust,Figure 29.33 cyclone,a vertical cylinder,a conical bottom,STRUCTURE:,a rectangular inlet,Outlet for gas,58,Operation Process,Cyclone 3-03,59,60,Performance of a cyclone,(1). Capacity,(2). Collection Efficiency,critical diameter and efficiency,(3). Pressure Drop,61,Critical Diameter,临界粒径,D,pc,The minimum particle diameter that can be completely separated by the cyclone.,Assume the settling velocity(terminal velocity) is,62,When,=,t,D,p,=,D,pc,63,(1). Total collection efficiency,总效率：,mass fraction of particles that are collected by cyclone.,(2). Fractional collection efficiency,粒级效率,：,the efficiency of separation for a given particle diameter. The mass fraction of the sized particles that are collected.,Collection efficiency,64,FIGURE 29.34 Collection efficiency of typical cyclones.,65,Pressure drop in a cyclone,The pressure drop in a cyclone is proportional to the gas density and the square of the inlet velocity.,66,Cut diameter 分割粒径,Where,D,is cyclone diameter, m.,Diameter for which collection efficiency is 50%.,67,68,
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