Acceleration of solid particles

In ejectors and tube bends the most important part of the pressure loss comes from the acceleration of solid particles. In a bend the velocity of the particles is reduced due to the friction and the pressure loss is cairsed by the reacceleration of the particles after the bend. 

Equation (14.128) can be used for calculating the pressure drop due to the acceleration of. solid particles provided that the velocity change C2 - C can be estimated. In addition to the acceleration pressure loss we have the normal" pre.ssure drop... 

Borkent BM, Arora M, Ohl CD, Jong ND, Versluis M, Lohse D, Morch KA, Klaseboer E, Khoo BC (2008) The acceleration of solid particles subjected to cavitation nucleation. J Fluid Mech 610 157-182... 

The pressure drop inside the draft tube is more complicated because it involves acceleration of solid particles from essentially zero vertical velocity. However, the model for calculating the pressure drop in vertical pneumatic conveying lines suggested by Yang (1977) can be applied. The acceleration length can be calculated from numerical integration of the following equation. 

Draft Tube Pressure Drop The pressure drop across the draft tube, AP2-3, is usually similar to that across the downcomer, AP1-4, in magnitude. Thus for a practical design basis, the total pressure drop across the draft tube and across the downcomer can be assumed to be equal. In most operating conditions, the pressure drop at the bottom section of the draft tube has a steep pressure gradient due primarily to the acceleration of solid particles from essentially zero vertical velocity. The acceleration term is especially significant when the solid circulation rate is high or when the draft tube is short. 

Many engineering operations involve the separation of solid particles from fluids, in which the motion of the particles is a result of a gravitational (or other potential) force. To illustrate this, consider a spherical solid particle with diameter d and density ps, surrounded by a fluid of density p and viscosity /z, which is released and begins to fall (in the x = — z direction) under the influence of gravity. A momentum balance on the particle is simply T,FX = max, where the forces include gravity acting on the solid (T g), the buoyant force due to the fluid (Fb), and the drag exerted by the fluid (FD). The inertial term involves the product of the acceleration (ax = dVx/dt) and the mass (m). The mass that is accelerated includes that of the solid (ms) as well as the virtual mass (m() of the fluid that is displaced by the body as it accelerates. It can be shown that the latter is equal to one-half of the total mass of the displaced fluid, i.e., mf = jms(p/ps). Thus the momentum balance becomes... 

Batch centrifuges with imperforate bowls are used either for producing an accelerated separation of solid particles in a liquid, or for separating mixtures of two liquids. In the former case, the solids are deposited on the wall of the bowl and the liquid is removed through an overflow or skimming tube. The suspension is continuously fed in until a suitable depth of solids has been built up on the wall this deposit is then removed either by hand or by a mechanical scraper. With the bowl mounted about a horizontal axis, solids are more readily discharged because they can be allowed to fall directly into a chute. 

On the resistance constitution of the equipment system, the major conclusions that can be drawn from the investigation are (1) Where millets or rapeseeds are the material to be processed, the power for the operation of the impinging stream contactor is mainly (>80%) consumed in the acceleration of particles (2) The pressure loss due to the impingement between the opposing streams is independent of the presence of solid particles. 

In these studies, however, it remained unclear whether the accelerated breakdown of a foam in contact with a hydrocarbon was due to the formation of unstable asymmetric aqueous films (including inside the Plateau borders) or because of the worsened conditions of wetting of foam borders contacting the hydrocarbon are worsen compared to that on glass walls. The latter mechanism of foam breakdown is realised when hydrophobic bridges of solid particles or oils were formed in the foam film [19,20,57]. This mechanism will be considered in Section 9.4. 

For stable moving-bed uptransport of particles in a tapered spout, the drag force of the flowing gas on the particles is used to overcome gravity, acceleration, and wall friction. Vertical force balance on a horizontal element of solid particles in a trapezoidal pneumatic moving bed, shown in Fig. 7, gives... 

In equation 41, it was assumed that the flow profile in the vessel is parabolic. Obviously, elutriation is only suitable for large particle suspensions. With small particles, sedimentation may be accelerated by using a centrifuge. This technique is used when classifying aerosols of solid particles using a stream of air that flows in the direction opposite to the centrifugal force. 

Stream, and the amount of solids in the reactor can only be maintained by recycling the entrained solids (circulating fluidized bed [Contractor 1999], e = 0.9-0.98). Beyond a certain fluid velocity, the system enters the realm of pneumatic conveying, in which the solid particles are carried out of the reactor without residence time, and the pressure drop increases noticeably due to acceleration of the particles. 

FIGURE 26.30 Snapshots from simulations of dispersion of coUoidal slab made of solid particles in DPD and FPM fluids in 2-D (a,b) and 3-D (c). The gravitational acceleration is directed downward. We can observe crystallization process along the mixing front (a) for a properly defined interparticle force. 

The above analysis does not consider the possible acceleration of solid dissolution due to the chemical reaction.This happens when the interfacial concentration of the dissolved gas is comparable or even higher than the saturation concentration of the solid particles.This case has been considered by Uchida et.al.(7). then Equation 6 becomes ... 

The solutions according to Ramachandran and Sharma(4) and Uchida et.al.(7) are both shown in Figure 6 schematically.lt is seen that simultaneous acceleration in the specific rate of solid particles(that is,Uchida et.al. s modification) results even more enhancement of gas absorption rate. 

The cyclone separator (Figure 14-18) is a device that uses centrifugal forces to accelerate the settling of solid particles. Basically, a particulate-laden gas stream is introduced tangentially in the unit. Particles move to the cyclone separator walls and then to the bottom of the device. The gas first moves downward, then up to the top,... 

Here Ps and p, are the densities of solid particles and liquid respectively, g is the acceleration due to gravity, R is the particle radius (in this context called the Stokes settling radius) and r] is the viscosity of the medium. Thus... 

Destruction of metals by the abrasive action of moving fluids accelerated by the presence of solid particles in suspension. When corrosion occurs simultaneously, the term erosion-corrosion is often used. 

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