Particle-wall impact

Fig. 3. Visualization of particle wall impact locations for 2000 particles of PP 1040N with a diameter xp = 4mm and initial gas and particle velocities i>x,i 41 m/s.

Similar to the normal impact experiments, the attrition rates were determined after three, six and nine impacts. Here it is assumed that only the first particle wall impact in the pipe bend contributes significantly to attrition formation and that further impacts are of minor importance. Again 25 g of the granular polymers were used. In order to maintain conditions close to those in conveying processes the particle velocity was set to be approximately equal to the gas velocity of 41 m/s. 

For dilute phase conveying numerical simulations with a commercial computational fluid dynamics code were carried out. The analysis of particle wall impact conditions in a pipe bend showed that they take place under low wall impact angles of 5-35° which results in low normal (5-25 m/s) and high tangential (33-44 m/s) impact velocity components. These findings lead to the conclusion that not only normal stresses caused by the impacts are important in dilute phase conveying but that sliding friction stresses play an important role as well. 

A simplified schematic of a particle in a centrifuge is illustrated in Fig. 12-3. It is assumed that any particle that impacts on the wall of the centrifuge (at r2) before reaching the outlet will be trapped, and all others won t. (It might seem that any particle that impacts the outlet weir barrier would be trapped. However, the fluid circulates around this outlet corner, setting up eddies that could sweep these particles out of the centrifuge.) It is thus necessary to determine how far the particle will travel in the radial direction while in the centrifuge. To do this, we start with a radial force (momentum) balance on the particle ... 

The mechanisms of a single particle-wall collision are given in Chapter 2. A particle-wall collision in pneumatic transport systems is a complex process. The bouncing characteristics depend on many parameters, including impact angle, translational and rotational velocities of the particle before collision, physical properties of the wall and particles, and wall roughness and particle shape. 

Now let s consider how an individual gas particle moves. For example, how often does this particle strike the two walls of the box that are perpendicular to the x axis Note that only the x component of the velocity affects the particle s impacts on these two walls, as shown in Fig. 5.13. The larger the x component of the velocity, the faster the particle travels between these two walls, thus producing more impacts per unit of time on these walls. Remember that the pressure of the gas is caused by these collisions with the walls. 

How is ZA expected to depend on the average velocity of the gas particles For example, if we double the average velocity, we double the number of wall impacts, so ZA should double. Thus ZA depends directly on wavg ... 

One important parameter contributing to different breakage mechanisms is solids concentration or density in the mill. This directly influences the number of particle-particle or particle-wall collisions and the force of those collisions. Particle density in the mill is controlled not only by feed rate to the mill, but also by mill residence time. Depending on the type of equipment and how it is operated, solids density in the mill can impact both the milling rate and its efficiency so understanding and control of this parameter are important for scale-up. 

Because of the particle-wall and particle-classifier impacts, one drawback of this type of mill is the potential for buildup of compressed product in the mill or on the classifier. This can affect milled particle size by changing the open volume in the mill or open area in the classifier, especially if classifier vanes or gas nozzles become plugged or blocked. Buildup at the exit of the mill or in the classifier typically results in a gradual increase in the average-milled particle size over time owing to reduced classification efficiency. Specifically,... 

Cyclone inlet velocity not only affects efficiency of separation but also reflects in pressure loss and possible erosion. Gas viscosity has an important effect on particle efficiency, and so it is advisable to check its dependency with temperature and consider those cases in which a gas different from air is involved in the process. Smaller cyclone diameters increase overall efficiency, but also promote erosion. In addition to this, it is sometimes necessary to consider possible attrition of solids in the cyclone, which will result in pr< uction of fines and considerable losses. Erosion occurs primarily where the particles first impact the cyclone wall, but also occur at the bottom of cyclones too short to accommodate the length of the naturally occurring vortex. 

The greater the value of this ratio is above unity, the greater will be the tendency for particles to impact with the airway walls and so deposit. The further the value is below unity, the greater will be the tendency for the particles to follow the gas. This dimensionless ratio is known as the Stokes number ... 

In any fluidized bed process—be it a combustor, a dryer, or a chemical reactor— the bed material is in vigorous motion and thus inevitably subjeeted to mechanical stress due to interparticle collisions and bed-to-wall impacts. This mechanical stress leads to a gradual degradation of the individual bed particles, which is quite often an unwanted phenomenon that is therefore termed attrition. ... 

After identiflcation of the thresholds, Reppenhagen and Werther (1999a) derived the value of the exponent n in Eq. (19) from all measurements taken under conditions of pure abrasion (straight lines drawn in Fig. 19) to n = —0.5. They explained the negative value of n by some kind of cushioning effect, i.e., the chance for a given particle to impact on the wall decreases with increasing solids concentration in the flow. With n = —0.5, the model equation can now finally be written as... 

If, for the cone section of a given cyclone we assume that the rate of erosive wear (wall material removed per unit time per unit area) is proportional to the total kinetic energy of the particles that impact the wall per unit time and area, then,... 

The coefficients of normal restitution of the sugar pellets was obtained at an impact velocity of 1.28 0.03m/s for particle-steel apparatus wall impact with Cp w = 0.54 0.08 and for particle- lass wall impact with... 

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