Velocity slip ratio

Babinsky and Sojka [23] used DPF to study non-Newtonian liquid drop size distributions. For a single fluctuation, their results showed that fluctuations in ALR and interphase velocity slip ratio have the largest effect on effervescent atomizer/q. For two simultaneously fluctuating quantities, the influence on/o is found by adding... 

An annular flow is assumed in the nozzle exit orifice (see Fig. 21.17). Calculation of the liquid sheath thickness fp is based on the nozzle outlet diameter do, ALR, fluid and air densities, as well as liquid velocity slip ratio, sr. 

In the following sections, the flow patterns, void fraction and slip ratio, and local phase, velocity, and shear distributions in various flow patterns, along with measuring instruments and available flow models, will be discussed. They will be followed by the pressure drop of two-phase flow in tubes, in rod bundles, and in flow restrictions. The final section deals with the critical flow and unsteady two-phase flow that are essential in reactor loss-of-coolant accident analyses. 

Their results for the non-slip flow ease agreed with [26], who also used the integral transform teehnique to solve for the Nusselt number for flow through a maerosized reetangular ehannel. They did not inelude viscous dissipation in the work, but they did inelude variable thermal aeeommodation eoefficients. Similar to [15], they concluded that the Knudsen number, Prandlt number, aspeet ratio, velocity slip and temperature jump can all cause the Nusselt number to deviate from the eonventional value. 

From the observed broadening of the cluster intensity profiles in the velocity slip experiments one cannot determine how many isomers each of the assumed two isomer classes contains. However, it is possible to extract from the broadening of the cluster intensity profiles the ratio of all isomers having a more compact, spherical shape to all of the isomers having a less compact, elongated shape. From the areas of the two gaussians in Figure 21.2 (b) one obtains the temperature-dependent intensity ratio of the two silicon cluster isomers, which is the intensity of the spherical isomers divided by the intensity of the non-spherical isomers. 

The large surface-to-volume ratio in microchannels tends to enhance several factors that were neglected in macroscale flow and heat transfer, such as surface frictiOTi, compressibility, surface roughness, viscous, channel surface geometry, surface electrostatic charges, axial wall heat conduction, and measurement errors. Velocity slip flow has been widely studied accurately to model the characteristics of gas flow in the Knudsen layer for aU flow regimes. A review of the slip velocity can be fotmd in Zhang et al. [4]. 

In Type I fully dispersed waves, the gradients of the flow properties are comparatively mild and an excellent approximation is to assume that the droplet temperatures and velocity slip instantaneously relax to their equilibrium values. Thus, in equations (9) and (10) we let 0 and Xd - 0, the ratios Au/x and ATf/Xp remaining finite such that (in steady flow) riua ATf ciTg ... 

Slip ratio in a riser reactor versus the superficial gas velocity. From Whittington [1972]. 

In a horizontal pipeline the velocity of the particles will typically be about 80% of that of the air. This is usually expressed in terms of a slip ratio, defined in terms of the velocity of the particles divided by the velocity of the air transporting the particles, and in this case it would be 0.8. The value depends upon the particle size, shape and density, and so the value can vary over an extremely wide range. In vertically upward flow in a pipeline a typical value of the slip ratio will be about 0.7 in comparison. 

Since the velocities of air and liquid could not be measured, an iterative calculation method of Ishii [35] for the slip ratio sr and the void fraction a was used. 

The above results indicate that with an increase in temperature jump, Nu(cx>) decreases. It may be remembered that Kn x controls the velocity slip and y controls the temperature jump. The limiting Nusselt number (Nu(oo)) results as a function of Kn X at different values of Pt/Pv ratio has been shown in Figure 9.7. The heat transfer, that is, the Nusselt number, reduces with an increase in P /Pv that is, the temperature jump. The heat transfer also increases with an increase in velocity slip. Hence, the velocity slip and temperature jump have opposite influences on the heat transfer of a microchannel flow. 

The force balance model equation that we shall derive below must be solved in an iterative manner for the vapor void fraction. Knowing this void fraction and the cyclone diameter, the wall film thickness can be computed. It is then possible to compute the average gas and wall film velocity, as well as the slip velocity , the ratio of the average gas velocity to the average liquid film velocity. 

For design, the slip velocity is derated to 70-80 percent of the calculated value to give some margin of safety this sets the design value of the continuous phase velocity (V ). The column cross sectional area (and therefore diameter) is set by QJVc- With the diameter set, the other dimensions can be set using the ratios given above. 

Find the equilibrium, homogeneous specific volume v given by Eq, (26-85) and estimate the slip velocity ratio using the following correlation ... 

Slip factor is defined as the ratio of catalyst residence time in the riser to the hydrocarbon vapor residence time. Some of the factors affecting the slip factor are circulation rate, riser diameter/geometry, and riser velocity. 

Slip Factor. The ratio of vapor velocity to catalyst velocity. 

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