Drag coefficient empirical

Above a Reynolds number of around 2, Equation 8.5 will underestimate the drag coefficient and hence overestimate the settling velocity. Also, for Re > 2, an empirical expression must be used7 ... 

Due to computer storage and run time limitations, it is not yet possible to accurately model the details of flows around each individual droplet in a spray. Thus, empirical or semi-empirical correlations are typically used to model the exchange processes between droplets and gas. Correlations for drag coefficients have been suggested by many researchers.[45l[559h568Fl571l For thin sprays, the drag... 

Apr = the area of the particle projected on a plane normal to the direction of flow (projected area perpendicular to flow) ula. = the terminal velocity CD = an empirical drag coefficient. 

When applied to fluidization, the empirical correlation between the drag coefficient CD and the Reynolds number Re needs to be extended to account for the automatic adjustment in particle array that results in a regular increase in the fraction void e in the interstitial spaces with increased fluid flow— that is,... 

In case 3 the relative size of the particles (with respect to the computational cells) is large enough that they contain many hundreds or even thousands of computational cells. It should be noted that the geometry of the particles is not exactly represented by the computational mesh and special, approximate techniques (i.e., body force methods) have to be used to satisfy the appropriate boundary conditions for the continuous phase at the particle surface (see Pan and Banerjee, 1996b). Despite this approximate method, the empirically known dependence of the drag coefficient versus Reynolds number for an isolated sphere could be correctly reproduced using the body force method. Although these computations are at present limited to a relatively low number of particles they clearly have their utility because they can provide detailed information on fluid-particle interaction phenomena (i.e., wake interactions) in turbulent flows. 

The following relationship is an empirical fit to experimental data for spherical particles, between drag coefficient and Reynolds number for Reynolds number between 0.01 and 1.0 ... 

Haider and Levenspeil [26] presented the following empirical equation relating drag coefficient and Reynolds number for spherical and non-spherical particles, where Reynolds number is based on volume diameter ... 

Although both expressions are commonly used, they fail to predict some important macroscopic properties of solid-fluid suspensions, such as the expansion and sedimentation profiles. To overcome this limitation Mazzei Lettieri (2007) developed a relationship for the drag coefficient that is based on the empirical correlation by Richardson Zaki (1954) describing the expansion profiles of homogeneous fluid-solid suspensions. Its main feature resides in the fact that the expression is consistent with the Richardson and Zaki correlation over the whole range of fluid-dynamic regimes and for any value of the suspension void fraction. It has the following formulation ... 

Formulas (1.6.1) and (1.6.2) have formed the basis of most theoretical investigations on the determination of the average fluid velocity and the drag coefficient in the stabilized region of turbulent flow in a circular tube (and a plane channel of width 2a). The corresponding results obtained on the basis of Prandtl s relation (1.1.21) and von Karman s relation (1.1.22) for the turbulent viscosity can be found in [276,427]. In what follows, major attention will be paid to empirical and semiempirical formulas that approximate numerous experimental data quite well. 

These equations have formed the basis of most theoretical investigations on the determination of the average fluid velocity and the drag coefficient in the stabilized region of turbulent flow on a flat plate. In what follows, major attention will be paid to empirical and semiempirical formulas that approximate numerous experimental data quite well. 

A jet model of flow around balls in a porous layer was proposed in [153]. Such flow is characterized by a decrease of the drag due to the suppression of wakes. For a sufficiently close packing ( > 0.35), the layer becomes steady-state. For the drag coefficient of a ball in such a system, the following empirical formula was proposed ... 

Our analysis so far is applicable to Re < 0.1 or particles smaller than about 20 pm (Table 9.2). For larger particles, one needs to use the drag coefficient as an empirical means of representing the drag force for higher Reynolds numbers. The equation along the direction of motion of the particle in scalar form, assuming no gas velocity, is then... 

Stokes law has been derived for Re 1, neglecting the inertial terms in the equation of motion. If Re = I, the drag predicted by Stokes law is 13% low, due to the errors introduced by the assumption that inertial terms are negligible. To account for these terms, the drag force is usually expressed in terms of an empirical drag coefficient Co as... 

Constant in the formula for D below, value 2.1 x 10 m /s. Diffusivity of water in membrane m /s. An empirical function of membrane temperature T and water content c [10]. Electro-osmotic drag coefficient, taken to be 1. 

The following empirical equation for drag coefficient proposed by Crowe et al. [17] and simplified by Hermsen [18] has been used extensively in the numerical analysis of the flow in solid propellant rocket nozzles. 

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