Drag parameterization

However, Drew [54] also discusses this approach and argues that this formulation is questionable, as it may not be consistent with the interfacial drag parameterizations used. 

It was shown that this approach gives real characteristics only if (p/>A/ is lower than pi)vi-A value of is used by several researchers [145, 173]. However, Drew [58] also discusses this approach and argues that this formulation is questionable, as it may not be consistent with the interfacial drag parameterizations used. 

The drag force /, = fu,fv on the right-hand side of equations (1.4) or (1.5) parameterizes the influence of the canopy it equals zero outside it but depends on the local velocity and on the density within the canopy. All the individual obstructions that produce drag forces onto the flow in a unit volume Q, smeared into an average... 

Drag Coefficients for Wind Stress and for the Sensible and Latent Heat Flux For the numerical simulations of the Baltic Sea circulation discussed here, the parameterization of Smith and Banke (1975)... 

Anyhow, (1.255) is not properly closed yet as the pressure drop variable is still undetermined. Therefore, before we can apply (1.255) we need to parameterize the losses in terms of known flow parameters in pipes, valves, fittings, and other internal flow devices. Assuming that the viscous stress tensor reduces to a single shear stress component per unit wall surface (e.g., [102] ]185]), Apf per unit cross sectional area can be related directly to the friction drag force on the tube wall surface —Cwt DL. That is, since the friction drag force in a horizontal tube with a constant rate of flow is given by Z p/(- )D, the wall shear stress 3uelds ... 

In practice, however, it is difficult to parameterize the interfacial area averaged velocity so in the momentum equation it s often set equal to the bulk velocity and in the momentum jump condition the mass transfer terms are simply neglected enabling a closure relation for the interfacial drag terms which are in agreement with Newton s 3. law. Hence,... 

By the principles of material indifference Slattery [196] (pp 228-230) elucidated the functional relationship between the variables in the empirical friction or drag force parameterizations . It is noted that the dimensionless wall drag or friction factors of Darcy (fo) and Fanning (fp) are related in the following manner (e.g., [124, 240]) ... 

The standard drag curve refers to a plot ot Cp as a function of Re for a smooth rigid sphere in a steady uniform flow field. The best fit of the cumulative data that have been obtained for this drag coefficient is shown in Fig 5.2. Numerous parameterizations have been proposed to approximate this curve (e.g., many of them are listed by [22]). 

However, there is generally considerable discrepancy in the data for the drag coefficient dependence on turbulence. The spread in the data obtained for the drag coefficient of a sphere in turbulent flows is indicated in Fig 5.6. For this reason the standard drag curve parameterizations are normally used and the effects of turbulence is disregarded. 

The drag coefEcient parameterizations proposed by Ishii and co-workers [62, 63, 64] for bubbles in liquid at different flow regimes are often used in reactor simulations. In the churn-turbulent regime they obtained ... 

More recently, Tomiyama and co-workers [154, 155, 156, 157] performed detailed experiments investigating the drag coefficient of a single bubble in a stagnant liquid. They proposed a drag coefficient parameterization which is split in three categories. These are pure, gently-contaminated, and contaminated systems, respectively. 

This parameterization of the drag coefficient for bubbles in stagnant liquids is very often used in the latest reports on bubbly flow simulations. 

The Lagrangian steady drag force on a single particle is commonly expressed by (5.48). For Eulerian model formulations one normally employs (5.34), hence for the multifluid models the standard steady drag force parameterization 3delds ... 

An alternative parameterization for the drag coefficient is given by [34, 50]. The particle Reynolds number is given by ... 

An accurate representation of wave drag is essential for chemical modeling because chemical species are advected by the mean meridional circulation and are also transported by the irreversible mixing which accompanies wave drag. Modeling studies (e.g., Schoeberl and Strobel, 1978 Holton and Wehrbein, 1980) sometimes use a Rayleigh coefficient to crudely parameterize the effects of wave dissipation. In this case, a deceleration is assumed to act linearly on u, and is substituted for the wave drag term Gu as follows ... 

Medvedev, A.S., and G.P. Klaassen, Vertical evolution of gravity wave spectra and the parameterization of associated wave drag. J Geophys Res 100, 25,841, 1995. 

Particle turbulent (or kinetic) diflusion coeflScient (m /s) Wave number for the integral scale of turbulence (m ) Empirical parameter in drag coeflhcient parameterization ( ) Reaction rate constant (1/s)... 

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