The UMIST-N Near-Wall Treatment Applied to Periodic Channel Flow

CHAPTER 1. INTRODUCTION & LITERATURE SURVEY 7
work of Kolmogorov [31] and Saffman [65], Wilcox [89] proposed the most
well-known k-ω model. The model does not require the same damping terms
employed by the standard k-ε model in order to be effective in the near-wall
region, but boundary conditions are more difficult to apply. The principal
difficulty associated with the k-ω model is in specifying a value for ω in free-
stream turbulence [40]. Speziale et al. [76], Menter [41], Peng et al. [52],
and Wilcox [90] have proposed modifications to the k-ω that further improve
its performance at the cost of adding much the same degree of complexity
found in the standard k-ε model.
The SST 2 model of Menter [42] may be thought of as a hybrid k-ε / k-ω
approach. It employes a k-ω model near solid boundaries and a k-ε model
elsewhere. The SST model is appealing because the principal strength of
the k-ω model is its simplicity and relative accuracy in the near-wall region,
while the k-ε model is generally more effective in free-stream flow. The SST is
implemented by the use of a blending function to provide a smooth transition
between the two models.
1.3 Wall Functions & the Subgrid Approach
Near solid boundaries, the gradients of turbulence quantities become large.
Numerically, this means that greater storage and computational demands are
placed on a CFD code that performs calculations in the near-wall region. To
avoid this, wall functions are often employed. A wall function is a solution
method that provides a means of characterising turbulence at some point,
2 Shear Stress Transport