Mixing length model

Zero equation model—mixing length model. 

A proper representation of the effective viscosity is often problematic. Based on the Prandtl mixing length model for turbulence, Bloor and Ingham-suggest that the variation in p, should be of the form... 

Prausnitz (PIO) has devised an approximate mixing length model for estimating the axial dispersion coefficient that allows for the interaction of the velocity profile. He used... 

Reynolds stresses generated by time averaging. Thus, additional equations are needed to correlate these terms with time-averaged quantities. These additional equations may come from turbulence models. The two most commonly used turbulence models, the mixing length model and the k-e model, are introduced. 

In efforts to increase the range of applicability of the mixing length model, numerous others have modified it. 

One of the better versions of the modified mixing length model is... 

In the mixing length model it is next assumed that the magnitude of the velocity fluctuation at 0 is proportional to the average of A i and Au2, i.e. ... 

The last term in the momentum equation, i.e., Eq. (9.78). represents the affect of the buoyancy forces on the mean momentum balance. However, these buoyancy forces also affect the variation of e and e in the flow. To illustrate how the buoyancy forces can effect e and e, consider again the simple mixing length model discussed in Chapter 5. Lumps or eddies of fluid are assumed to move across the flow through a transverse distance, lm, while retaining their initial velocity and temperature. They then interact with the local fluid layer giving rise to the fluctuations in velocity and temperature that occur in turbulent flow. 

The equation set (5-73) is called the universal velocity profile and matches very well with experimental data however, we should note once again that the constants in the equations must be determined from experimental velocity measurements. The satisfying point is that the simple Prandtl mixing-length model yields an equation form which fits the data so well. 

The solutions of equations (5.9) and (5.11) for the shear stress layer and the upper canopy layer are more complicated as we now have to account for shear stress divergence but we can note the following points. Because the shear stress layer is a region of local equilibrium (turbulence production dissipation) it is feasible to model the shear stress with a mixing length model,... 

We parameterize the background scalar flux FB(z) using the same mixing length model that we used for momentum,... 

For another class of models, the mixing length models, a different approach is used. Here, the turbulent eddy viscosity is assumed to be of the form... 

Damping constant in van Driest mixing length model [ — ]... 

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