水利旋流器英文PPT

3. The Equilibrium Orbit Hypothesis
Drag force = Fd = 0.5C D ( v r − u r ) 2 ρ f Ac
(1)
CD= drag coefficient（阻力系数） v r = radial velocity of the fluid ur = radial velocity of the particle ρf = fluid density A C =cross-sectional area（横截面积） of the particle
The Hydrocyclone
1. Introduction 2. General Principles of the Operation of the Hydrocyclone 3. The Equilibrium(平衡) Orbit Hypothesis（假设） Equilibrium(平衡) Hypothesis（假设） 平衡 4. Capacity Limitations of the Hydrocyclone
Figure 5
Forces acting on an orbiting particle.
The centrifugal force developed accelerates the settling rate of the particles, thereby separating particles according to the size and specific gravity.
3), Fc = Fd
3. The Equilibrium Orbit Hypothesis
Balancing these forces
vθ2 0.5CD (vr − ur ) 2 ρ f Ac = v p ( ρ s − ρ f ) r On an equilibrium orbit , ur = 0
2. General Principles of the Operation of the Hydrocyclone
Particles that experience this centrifugal field will tend to move outwards relative to the carrier fluid because of their relatively greater density. The larger, heavier particles will migrate rapidly to the outside walls of the cylindrical section and will then be forced to move downward on the inside of the conical wall. Small, light particles, on the other hand will be dragged inwards by the fluid as it moves toward the vortex finder. The drag force experienced by any particle will be a complex function of the hydrodynamic （流体力学）conditions inside the hydrocyclone and the shape and size of the particle.
1. Introduction
A typical hydrocclone consists of a conically shaped vessel, open at its apex, or underflow, joined to a cylindrical section, which has a tangential feed inlet. The top of the cylindrical section is closed with a plate through which passes an axially mounted overflow pipe. The pipe is extended into the body of the cyclone by a short, removable section known as the vortex finder（涡流探 测器）, which prevents short-circuiting（短 路） of feed directly into the overflow.
(2)
3. The Equilibrium Orbit Hypothesis
1), Fc > Fd 2), Fc < Fd particle moves toward the wall, passes the locus at vv = 0 and will eventually exit the cyclone via underflow. particle moves toward the center of the cyclone, passes the locus at vv = 0 and will eventually exit the cyclone via overflow. particle is in equilibrium. Any particle that experiences an equilibrium between these two forces inside the hydrocyclone will have an equal chance to exit through either the underflow or the overflow.
vp 0.5CD ρ f rvr2 = . 2 Ac ( ρ S − ρ f ) vθ
vp Ac = 2 dp 3(源自)(5)so that
ρ f CD rvr2 d50 = 0.75 . 2 ρ s − ρ f vθ
(6)
3. The Equilibrium Orbit Hypothesis
The key to the equilibrium orbit theory is the drag force experienced by a particle due to the relative motion between it and the fluid. It is known that these relative velocities are small and the particle Reynolds number（雷诺数） is usually so low that it is commonly assumed that the drag force can be calculated from the formula for the slow relative motion between a sphere and a Newtonian fluid. This is the well-known Stokes formula. This approach neglects two important phenomena: the highly turbulent nature of the fluid inside the hydrocyclone and the relatively high concentration of particles. Thus the use of Stokes flow theories which assumes that only a single isolated particle is present is not very realistic.
vθ2 Centrifugal force = Fc = v p ( ρ s − ρ f ) r
vθ=tangential component of the particle velocity vector r =radius of the tangential motion vp=volume of the particle ρs=density of the solid
3. The Equilibrium Orbit Hypothesis
The classical theory of hydrocyclone is that particles within the flow pattern are subjected to two opposing forces- an outward centrifugal force and an inwardly drag force.
vp 0.5CD ρ f rvr2 = . 2 Ac ( ρ S − ρ f ) vθ
(3)
So that
(4)
The size of this particle is designated as d50, which is the cut size of the cyclone.
3. The Equilibrium Orbit Hypothesis
Figure 2 Typical partical trajectories in hydroclone .
Figure3 Schematic representation of the net flow of water and the counter flow of larger particles in the hydrocyclone.
Figurer 1 Hydrocyclone.
2. General Principles of the Operation of the Hydrocyclone
The principle of operation of the hydrocyclone is based on the concept of the terminal settling velocity（沉降末速） of a solid particle in a centrifugal field. The conditions in an operating hydrocyclone can be described by reference to Figures 2 and 3.
2. General Principles of the Operation of the Hydrocyclone
The feed enters tangentially into the cylindrical section of the hydrocyclone and follows a circulating path with a net inward flow of fluid from the outside to the vortex finder on the axis. The circulating velocities are very high and these generate large centrifugal fields inside the hydrocyclone. The centrifugal field is usually high enough to create an air core（空心气柱） on the axis that often extends from the spigot opening at the bottom of the conical section through the vortex finder to the overflow at the top. In order for this to occur the centrifugal force field must be many times larger than the gravitational field.
1. Introduction
It is a continuously operating classifying device that utilises centrifugal force （离心力） to accelerate the settling rate of particles. It main use in mineral processing is as a classifier, which has proved extremely efficient at fine separation sizes. It is used increasingly in closed circuit grinding operations but has found many other uses, such as desliming （脱泥）, degritting（除沙）, and thickening（浓缩）. It has also found wide acceptance for the washing of fine coal.