Shock/boundary-layer interaction (on airplanes)

Underlying Flow Regime 3-05 © copyright ERCOFTAC 2004

Best Practice Advice

Best Practice Advice for the UFR

Key Physics

For an aircraft wing operating at transonic cruise conditions, the interaction of a shock wave with a turbulent boundary layer can have a significant effect on key aerodynamic parameters such as lift and drag. Therefore, it is essential that the key physical processes of this interaction be captured with sufficient accuracy by a numerical method.

The rapid change in the mean flow through a shock can cause rapid normal straining of the boundary layer. This results in thickening of the boundary layer and possible flow separation. This may be followed by flow re-attachment of the separated shear layer and flow recovery.

There will generally be a time lag in the response of the turbulence structure to the rapid changes in the mean flow through the shock. That is, the flow is far from equilibrium. It is essential that the turbulence model used is able to model the effect of this non-equilibrium flow. In addition, during the flow recovery following re-attachment, the turbulence model must be able to model the interaction between the growth of the new boundary layer and the attaching shear layer.

Numerical modelling issues

Discretisation Method

USE a high order accurate scheme, at least second order accurate in space, with as little numerical dissipation as possible

Grids and grid resolution

For low Reynolds number turbulence models, USE a mesh that has wall adjacent cell heights of y⁺ < 1.

For a wall function approach, USE a mesh with wall adjacent cell heights in the range 50<y⁺<100

USE a mesh that has at least 10 grid points in the streamwise direction across the shock.

USE a mesh that has between 5-10 grid points within a distance of y⁺=20 from the wall.

USE a mesh that has between 30-60 grid points across the boundary layer

Boundary conditions and computational domain

USE constant velocity and temperature profiles (i.e. plug flow) at an inlet plane 4-chord lengths upstream of the bump to give the experimental velocity profile by 0.25 chords upstream.

USE extrapolation of variables at outflow.

USE an inflow turbulent kinetic energy in the range 0.01%<k<0.2%

Physical modelling

Turbulence modelling

Do NOT USE standard linear models such as k-ε or k-ω. These typically result in a delayed shock position with weak or non-existent flow separation.

If a linear model is to be used, USE the MENTER SST (Shear Stress Transport) model. However, note that this model tends to predict a slightly earlier separation.

If a better prediction of shock location, pressure plateau and separation location is required, USE a cubic non-linear model such as the cubic k-ε model of Suga[13] or that of Apsley and Leschziner[14]. The Speziale variant [12] performs least well in capturing the separation location and pressure plateau and should not be used.

Transition modelling

No transition modelling has been applied as part of this UFR.

Other modelling

None

Application Uncertainties

The advice given here is not applicable to laminar boundary layers undergoing transition due to shock wave interaction.

The advice is limited to transonic flows.

None of the models considered perform particularly well in predicting velocity profiles in the flow recovery region.

Recommendations for future work

Calculations should be submitted which evaluate the performance of other, very promising modern turbulence models such as Spalart and Allmaras [18] and Durbins v2f [19].