where P is the 'pee function' given by (Launder and Spalding, 1974)

where Pr is the Prandtl number, A is van Driest's constant (= 26) and E is a wall function constant (~ 9 for smooth walls). yT is dimensionless thermal sublayer thickness (the point of intersection of the linear law and the logarithmic law).

The modeled form of scalar transport equations can be used to simulate mixing and concentration fields within the reactor. Such computational models can, therefore, be used to link the reactor hardware and operating parameters with the mixing and residence time distribution, which will ultimately lead to estimation of reactor performance. A reactor engineer has to make appropriate selection of the turbulence model depending on the objectives under consideration. For example, for a heat transfer limited reactor, reactor hardware may be modified to install turbulence promoters. Unsteady vortices around these turbulence promoters may enhance the heat transfer rates and overcome heat transfer limitation. For such applications, capturing these vortices and simulating their influence on heat transfer rates is of primary importance. It is then necessary to select a turbulence model as well as its numerical implementation in such a way that it does not smear local structures such as vortices. If the interest is in estimating wall heat or mass transfer rates, it may be worthwhile to use more rigorous, non-equilibrium wall functions, which are sensitized to pressure gradient

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