Solids particle velocity

Two major effects contribute to the pressure drop in horizontal flow acceleration and friction loss. Initially the inertia of the particles must be overcome as they are accelerated up to speed, and then the friction loss in the mixture must be overcome. If Vs is the solid particle velocity and ms = ps I7s( l — ) is the solids mass flow rate, the acceleration component of the pressure drop is... 

The effect of downcomer aeration, of distance between the distributor plate and the draft tube inlet, and of the distributor plate design configuration on solid circulation rate is discussed below. For ease of presentation for materials of different densities, the solid particle velocity in the downcomer rather than the solid circulation rate is used. 

Two different series of experiments were carried out. In one series, the three draft tube velocities were maintained essentially constant while the aeration to downcomers was varied. One of the three draft tube velocities was purposely increased to simulate possible unbalanced operation conditions in an actual industrial plant in the second series of experiments. Each experiment was characterized by solid particle velocity in each downcomer, the pressure drop across each draft tube, and the pressure drop across each downcomer. 

When all three draft tubes were operated at similar velocities, the pressure drops across all draft tubes and downcomers were comparable. However, solid particle velocities in outside downcomers close to the walls were substantially less due to wall effect and redistribution of downcomer aeration flow. Smooth operations under these conditions were possible. The solid particle velocities in outside downcomers can be increased by enlarging the downcomer cross-section or by increasing downcomer aeration through separate plenums to minimize wall effects. 

The solids particle velocity in the gas-solid two-phase jet can be calculated as shown in Eq. (27), assuming that the slip velocity between the gas and the solid particles equals the terminal velocity of a single particle. It should be noted that calculation of jet momentum flux by Eq. (26) for concentric jets and for gas-solid two-phase jets is only an approximation. It involves an implicit assumption that the momentum transfer between the concentric jets is very fast, essentially complete at the jet nozzle. This assumption seems to work out fine. No further refinement is necessary at this time. For a high velocity ratio between the concentric jets, some modification may be necessary. 

V = solid particle velocity, cm/s Z = distance from jet nozzle, cm... 

V-z = horizontal component of the solid particle velocity into the jet at z... 

FIGURE 4-32 Histogram of solid particle velocity (Militzer et ah, 1992). 

A constant proportional to the frequency spectrum Solid particle velocity... 

The average flowing solids particle velocity can be defined as ... 

Interesting pattern formations also occur in surfactants spreading on water due to a hydrodynamic instability [52]. The spreading velocity from a crystal may vary with direction, depending on the contour and crystal facet. There may be sufficient imbalance to cause the solid particle to move around rapidly, as does camphor when placed on a clean water surface. The many such effects have been reviewed by Stemling and Scriven [53]. 

Erosion is the deterioration of a surface by the abrasive action of solid particles in a liquid or gas, gas bubbles in a liquid, liquid droplets in a gas or due to (local) high-flow velocities. This type of attack is often accompanied by corrosion (erosion-corrosion). The most significant effect of a joint action of erosion and corrosion is the constant removal of protective films from a metal s surface. This can also be caused by liquid movement at high velocities, and will be particularly prone to occur if the solution contains solid particles that have an abrasive action. 

A. Solid particles suspended in agitated vessel containing vertical baffles, continuous phase coefficient -2 + 0.6Wi f,.Wi D Replace Osi p with Vj = terminal velocity. Calculate Stokes law terminal velocity [S] Use log mean concentration difference. Modified Frossling equation K, -< T.d,P. [97] [146] p.220... 

Fluidized This is an expanded condition in which the sohds particles are supported by drag forces caused by the gas phase passing through the interstices among the particles at some critical velocity. It is an unstable condition in that the superficial gas velocity upward is less than the terminal setting velocity of the solids particles the gas... 

Dilute This is a fully expanded condition in which the solids particles are so widely separated that they exert essentially no influence upon each other. Specifically, the solids phase is so fuUy dispersed in the gas that the den sity of the suspension is essentially that of the gas phase alone (Fig. 12-29). Commonly, this situation exists when the gas velocity at all points in the system exceeds the terminal setthng velocity of the solids and the particles can be lifted and continuously conveyed by the gas however, this is not always true. Gravity settling chambers such as prilling towers and countercurrent-flow spray diy-ers are two exceptions in which gas velocity is insufficient to entrain the sohds completely. 

For a shock wave in a solid, the analogous picture is shown schematically in Fig. 2.6(a). Consider a compression wave on which there are two small compressional disturbances, one ahead of the other. The first wavelet moves with respect to its surroundings at the local sound speed of Aj, which depends on the pressure at that point. Since the medium through which it is propagating is moving with respect to stationary coordinates at a particle velocity Uj, the actual speed of the disturbance in the laboratory reference frame is Aj - -Ui- Similarly, the second disturbance advances at fl2 + 2- Thus the second wavelet overtakes the first, since both sound speed and particle velocity increase with pressure. Just as a shallow water wave steepens, so does the shock. Unlike the surf, a shock wave is not subject to gravitational instabilities, so there is no way for it to overturn. 

In the case of most nonporous minerals at sufficiently low-shock stresses, two shock fronts form. The first wave is the elastic shock, a finite-amplitude essentially elastic wave as indicated in Fig. 4.11. The amplitude of this shock is often called the Hugoniot elastic limit Phel- This would correspond to state 1 of Fig. 4.10(a). The Hugoniot elastic limit is defined as the maximum stress sustainable by a solid in one-dimensional shock compression without irreversible deformation taking place at the shock front. The particle velocity associated with a Hugoniot elastic limit shock is often measured by observing the free-surface velocity profile as, for example, in Fig. 4.16. In the case of a polycrystalline and/or isotropic material at shock stresses at or below HEL> the lateral compressive stress in a plane perpendicular to the shock front... 

Figure 7.2. Response of elastic-plastic solid to planar impact at X = 0 u = longitudinal particle velocity. Measurements are made as a function of time at fixed Lagrangian position X.

Cyclone mist eliminators and collectors have virtually the same efficiency for both liquid aerosols and solid particles. To avoid reentrainment of the collected liquid from the walls of the cyclone, an upper limit is set to the tangential velocity that can be used. The maximum tangential velocity should be limited to the inlet velocity. Even at this speed, the liquid film may creep to the edge of the exit pipe, from which the liquid is then reentrained. 

Small solid particles, present in dust and grit emissions, have very low settling velocities (Table 4.4) The collection efficiencies of simple cyclones are tlierefore, as shown in Figure 17.3, relatively low. Fabric filters, electrostatic precipitators or wet scrubbers may be required to remove particles <5 pm in size with an acceptable efficiency. Therefore the cost of pollution control inevitably increases when dealing with particle size distributions skewed towards the lower end. 

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