Superficial velocity dimensionless

In vertical downward flow as well as in upward and downward inclined flows, the flow patterns that can be observed are essentially similar to those described above, and the definitions used can be applied. Experimental data on flow patterns and the transition boundaries are usually mapped on a two dimensional plot. Two basic types of coordinates are generally used for this mapping - one that uses dimensional coordinates such as superficial velocities, mass superficial velocities, or momentum flux and another that uses dimensionless coordinates in which some kind of dimensionless groups are used as coordinates. The dimensional coordinates maps are inherently limited to the range of data and flow conditions under which the experiments were conducted. In spite of this limitation, it is widely used because of its simplicity and ease of use. Figure 24 provides an example of such a map. 

G = superficial mass vapor velocity based on the cross-sectional area of the column, Ib/hr-sq ft M = molecular weight, Ib/lb mole N = dimensionless number P = pressure, consistent units [P] = Sugden parachor sg = specific gravity T = temperature, °F U = superficial velocity, ft/hr... 

For adiabatic, steady-state, and developed gas-liquid two-phase flow in a smooth pipe, assuming immiscible and incompressible phases, the essential variables are pu, pG, Pl, Pg, cr, dh, g, 9, Uls, and Uas, where subscripts L and G represent liquid and gas (or vapor), respectively, p is the density, p is the viscosity, cr is the surface tension, dh is the channel hydraulic diameter, 9 is the channel angle of inclination with respect to the gravity force, or the contact angle, g is the acceleration due to gravity, and Uls and Ugs are the liquid and gas superficial velocities, respectively. The independent dimensionless parameters can be chosen as Ap/pu (where Ap = Pl-Pg), and... 

Experimental data on flow patterns and the transition boundaries are usually mapped on a two-dimensional plot. Two basic types of coordinates may be used for the flow regime maps - one that uses dimensional coordinates such as superficial velocities, and another that uses some kind of dimensionless group. Di-... 

Bar above symbol refers to dimensionless variable Refers to perturbation variable, superficial velocity or stripping section... 

Equation (14-8) gives the (dimensionless) superficial velocity (Fmf) for incipient fluidization. 

Ishii and Murakami (1991) evaluated the CFB scaling relationships of Horio et al. (1989) using two cold CFB models. Solids flux, pressure drop, and optical probe measurements were used to measure a large number of hydrodynamic parameters to serve as the basis for the comparison. Fair to good similarity was obtained between the beds. Dependent hydrodynamic parameters such as the pressure drop and pressure fluctuation characteristics, cluster length and voidage, and the core diameter were compared between the two beds. The gas-to-solid density ratio was not varied between the beds. As seen in Table 7, the dimensionless solids flux decreased as the superficial velocity was increased because the solids flux was held constant. 

This method can be easily used to show the logic behind the scale-up from original R D batches to production-scale batches. Although scale-of agitation analysis has its limitations, especially in mixing of suspension, non-Newtonian fluids, and gas dispersions, similar analysis could be applied to these systems, provided that pertinent system variables were used. These variables may include superficial gas velocity, dimensionless aeration numbers for gas systems, and terminal settling velocity for suspensions. 

Figure A3.3 is a plot of average void fraction, a, versus the dimensionless superficial velocity, for the different flow regimes and values of C0. The correlations presented here may overestimate level swell for pure vapour pressure systems if there is a non-boiling region (in which static head suppresses boiling) at the bottom of the reactor. This is conservative for relief system sizing and is discussed further by DIERS151.

XA = conversion Z = axial position in reactor, z/L (dimensionless) superficial velocity, Q/A reactor length... 

Sorption characteristics for hollow stirrers are not different from those for turbine stirrers. In non-manipulated gas feed in the hollow shaft (no constriction or no feed of externally compressed gases into the hollow shaft) the gas throughput and the stirrer power are coupled with one another via the stirrer speed, so that the pi-number v (dimensionless superficial velocity) does not apply in the sorption characteristic. 

The specific liquid holdup (i.e., volume of liquid holdup/volume of packed bed) in the preloading region has been found from extensive experiments by Billet and Schultes (1995) for a wide variety of random and structured packings and for a number of gas-liquid systems to depend on packing characteristics, and the viscosity, density, and superficial velocity of the liquid according to the dimensionless expression... 

When spheres or other particles are in a packed bed, the mass and heat transfer coefficients are higher than for isolated particles exposed to the same superficial velocity. There is also more uncertainty in the coefficients, because published data show considerable scatter and significant differences in the Reynolds number exponents. Most of the published data are reported as /-factors, which are dimensionless groups that are functions of the Reynolds number ... 

The two dimensionless groups are based on the empty pipe diameter (D,), including the value of u, which is a superficial velocity. In principle it only requires one value of AP to be measured at one value of v, to define the product Re for any static mixer but a range of measurements can give useful information regarding the slight variability of tf> Re and also the upper limit of the laminar flow regime in terms of Re ... 

In the case of fixed beds a piston or plug flow of the flow is desirable however, this flow can only be achieved at very high superficial velocities v. Deviations from the piston flow can be characterized by the dimensionless nmnber D according to... 

To define the different parameters responsible for the flow formation, flow pattern maps are used, where the axes represent the superficial velocities or the volumetric flow rates of phases, mixture velocity or total volumetric flow rate against the fraction of one of the phases while dimensionless numbers have also been used (Table 2.1). Depending on the dimensionless numbers, different zones where the specific forces are dominant can be defined. 

Dimensionless numbers are scale independent and contain a characteristic length term (L) that adjusts their magnitude to match the scale of the model. The velocity, v (m/sec), in these definitions is the superficial velocity of the fiuid. 

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