Explain the advantages disadvantages and derication differen

Explain the advantages, disadvantages and derication differenecs between the differential control volume (dx,dy) formulation and the Von Karman formulation of the governing equations

Solution

One advantage of the k- model is that it requires no modification and can be directly integrated to the wall with acceptable results. Some areas of concern when resolving the viscous sublayer include computational demands and possible convergence difficulties. Resolution of the viscous sublayer requires a major increase in the number of computational cells near the wall to accurately predict the velocity profile.

The primary advantage of using such a non-linear constitutive equation is the ability to predict anisotropy in the normal Reynolds stresses. This is very useful for cases where secondary flows occur, such as when a pipe or channel is curved. The primary disadvantage of using a formulation is that the local equilibrium assumption is still present, leaving flow history effects unaccounted for.

Inherent in such a model are the effects of flow history, as the Reynolds stress equation does include convection and diffusion terms for the stresses. Also, the Reynolds stress equations include production and body force terms that can respond to effects given by streamline curvature, rotation, and buoyancy. Another advantage is that there is no reason why the normal Reynolds stresses as predicted from the modeled equation should be equal. The major computational requirement for these models is that for a three-dimensional flow, six additional transport equations for the Reynolds stresses must be solved in addition to the typical NavierStokes and continuity equations. In most cases, the k and equations must also be solved. A major difficulty in working with such models is that the user must be skilled in tensor calculus to understand different models.