In the continuity equation the new equation is identical

In
all turbulent flows velocity fields fluctuate rapidly both in space and time. Computationally
it is very expensive to directly simulate both the small scale and high
frequency fluctuations for any useful engineering problem. There are two
methods to eliminate the need to resolve these small scales and high
frequencies namely, Reynolds Averaging and Filtering. For this paper, we are
only concerned with the Reynolds Averaging. In this method all flow variables
are divided into a mean component and a rapidly fluctuating component and then
all equations are time averaged to remove the rapidly fluctuating components.
For the continuity equation the new equation is identical to the original
equation, except that the transported variables now represent the mean flow
quantities. In the Navier-Stokes equation however new terms appear which
involve mean values of products of rapidly varying quantities. These new terms
are known as the Reynolds Stresses, and solution of the Reynolds Averaged
Navier-Stokes (RANS) equation initially involves the construction of suitable models
to represent these Reynolds Stresses. These models include various one equation
and two equation models, like Spalart Allmaras,
K-omega, K-epsilon etc.

A
low Reynolds number one equation Spalart-Allmaras turbulence model has been
selected for numerically simulating the junction flow with localized suction in
order to study the RANS capability for prediction of such flows. This has been
selected due to its known ability of the turbulence model to predict the flow
within the boundary layer right down into the laminar sub-layer. This
turbulence model is widely used for predictions of wall-bounded flows and it is
believed to perform well for boundary layers subjected to adverse pressure
gradients 9. This aspect of the turbulence model should be important in the
planned three dimensional half wing application, since this involves junction
flow separation which originates due to the adverse pressure gradient effects
upstream of the wing leading edge.

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