# Flow around oscillating airfoil

## Best Practice Advice and Conclusions

Best practice advice (based on the presented evidence)

• Use any turbulence model or even an invicid solver to obtain satisfactory Cp and CL
• Ensure that the transition is fixed for calculation of Cm
• At present no advice on turbulence modelling can be given for accurate computation of Cm.

Best practice advice (Unsuported by the presented evidence)

Grid

• Ensure that good quality grid is maintained in the wake region, check for estimated extreme wake position.
• Take care that good quality grid extend at least to 1/3 distance behind the aerofoil since accurate near-wake resolution can influence the shock position.
• For deforming meshes fulfill geometry conservation laws. Dynamic mesh movement produces errors. In order to ensure that the mesh changes do not affect flow field the geometric conservation equations should be additionally solved during time integration. There is (I) volume conservation law obtained by applying the continuity equation with zero velocity and constant density (II) surface conservation law, obtained by applying the continuity equation to a constant density flow in arbitrary direction on a fixed grid use the same integration scheme as for the flow solver. See ref [21] for more details.
• Include mesh velocity in the equation.
• Use sufficiently low aspect ratio to ensure good shock capturing during the shock movement. (A study is recommended).

Discretisation Method

• Use a higher order scheme (second or above) with as little numerical dissipation as possible.
• Perform time step sensitivity study.
• Ensure that sufficient number of cycles has been computed to achieve a converged periodical flow.

Boundary conditions

• Use non-slip boundary conditions on the wall and Rieman characteristic based conditions for inlet and outlet.
• Perform sensitivity study of the position of the outer boundaries, 25 x chord behind the aerofoil should be safe.

Conclusions and recommendation for further work.

It is evident that the state of the art in prediction methods for unsteady flows on oscillating aerofoils is still behind that achieved by CFD for steady state calculations. While, even inviscid calulations can provide satisfactory results for pressure coefficients as well as lift coefficient history, the accuracy of modelling viscous effects still needs improvement. In particular, this can be observed by examining histories of the locus of shock movement and by comparisons of moment coefficients histories, as both depend on the shock-boundary-layer interaction. It has been observed by a study of a range of test cases and turbulence models (ref [8]), that for transient, turbulent problems of oscillating aerofoils, the numerical predictions depend strongly on the turbulent closure employed. More studies are required before recommendations on turbulence models can be made. This needs to be complemented by rigorous treatment of transition. For this test case the transition was fixed in the experiment but there is no information if it was fixed in any of the computations. If not it could substantially alter the results. Also more mesh and time sensitivity studies are required to investigate if the Cm results, could not be improved by better discretisation. In particular to investigate the relation between an aspect ratio of computational cells on the moving shock and wake. It is known from studies of steady-state problems that shock position is very sensitive to the mesh quality of the wake in the distance up to the 1/3 of the chord from the aerofoil. Therefore such quality should be maintained also for oscillating aerofoils when the position of the wake changes in an oscillatory manner. Initial studies of oscillating aerofoils problems [18] and [19] conclude at present that some approximations can be achieved by one-equation models, but these seem to be inaccurate for dip-stall, Cm and buffet. In general, algebraic models and k-ε give poor results. There is no significant improvement over SA with k-ω and non-linear models reported. Reynolds-stress models have not been investigated.