Separation Modeling

When air flows over a surface, it forms a boundary layer where the air’s velocity changes from zero at the surface to the free stream velocity away from the surface. If the pressure in the direction of the flow increases (adverse pressure gradient), it can slow down the air in the boundary layer. If this adverse pressure is too severe, the boundary layer separates from the surface, leading to increased drag and possibly stall in the case of aircraft wings.

After the inviscid solution is calculated, FlightStream uses analytical models to estimate where the flow becomes separated.

Separation Criterion

FlightStream implements a modified Stratfod separation criterion to estimate boundary layer separation location. The Stratford criterion predicts a condition where this separation can be delayed or prevented, even under strong adverse pressure gradients. Stratfod derived an expression for predicting laminar boundary layer separation.

$\bar{C_{p}} = 1.0 - \left(\frac{u}{U_{max}}\right)^{2.0}$ Eq. (1)

$\bar{X}^{2}\bar{C_{p}}\frac{dC_{p}}{dx}^{2}=0.0104$ Eq. (2)

$\bar{X}=x-x^\prime$ Eq. (2)

Here $(x-x^\prime)$ is the effective length of the boundary layer and $x^\prime$ is the origin of the layer. Typically the point of maximum velocity.

For turbulent boundary layers, Cebeci-Smith modified Stratford’s original formulation to say that the boundary layer is separated where:

$0.4 (10^{-6}Re)^{0.1} = \bar{C_{p}} (\bar{X} \frac{d\bar{C_{p}}}{dx})^{\frac{1}{2}}$

Surface Pressure on Separated Regions

Swafford velocity profile is used to estimate the pressures in the separated flow field.

Further Reading

1. The Prediction of Separation of the Turbulent Boundary Layer
2. Calculation of Separation Points in Incompressible Turbulent Flows