Flow around (airfoils and) blades (transonic)

Underlying Flow Regime 2-06 © copyright ERCOFTAC 2004

Best Practice Advice

Best Practice Advice for the UFR

Numerical Issues

Grid and Grid Resolution

Such a grid topology should be chosen that allows the high gradients at the leading edge and in the shocks to be adequately captured (approx. 20 to 30 points around the leading edge radius). The O-H grid seems to be appropriate in this case. Generally, using of adaptive grid is to be preferred.

Further, the grid structure should allows the sharp gradients in the shocks to be captured, preferably an adaptive grid, but otherwise with an appropriate grid distribution that allows 1-3 grid points across the shock. A lower grid density can be used outside of the regions with shocks.

Be aware that the inclusion of more grid points close to the blunt trailing edge will cause the unsteady vortex shedding from the trailing edge to be captured and cause convergence difficulties with a steady simulation.

Grid resolution close to the solid surfaces needs to be consistent with the modelling of the thin boundary layers on the blade.

Discretisation Scheme

Use a higher order scheme (second or higher) with as little numerical dissipation as possible.

Use appropriate damping in the regions of high gradients in the shocks and near the leading and trailing edge.

Explicit schemes (TVD Mac Cormack, multistage Runge-Kutta, Roe, Ni) as well as some implicit schemes (especially upwind) give relatively good results for 2D viscous turbulent flows.

Computational Domain and Boundary Conditions

Computational domain is given by one and/or two blade pitch with profile located inside of the domain. Periodic boundary conditions on the upper-lower boundary have to be prescribed.

Inlet boundary conditions are given by total values of flow parameters. Mean flow rate cannot be given as inlet boundary condition. Static pressure in the integral form is given at the outlet boundary in the distance 1.5-2 chords behind the cascade.

Ensure that the code includes appropriate non-reflecting discretisation of the boundary conditions for the supersonic waves on the downstream boundary.

End-wall influence of the cascade needs to be taken into account.

Physical Modelling

Turbulence and Transition Modeling

Due to the strong flow acceleration in the blade cascade and thin shear layers, the capturing of the flow field and the prediction of pressure distribution with viscous codes is not sensitive to the turbulence model used. The effect of the laminar/turbulent transition is important rather in the subsonic case.

Flow structure in the boundary layers and in the wake is sensitive to the turbulence model and the position of transition, although in the highly accelerated flow the overall sensitivity of the flow-field to the turbulence model is low.

But for appropriate capturing of important phenomena of the transonic flow through the blade cascade, the prediction of the shock wave pattern and their interaction with boundary layers is crucial. The application of the numerical scheme of the higher order, adaptive grid near the shock region, and appropriate boundary conditions is necessary to capture the shock/boundary layer interaction adequately.

The appropriate prediction of the energy losses requires a high-order numerical scheme with low numerical viscosity and adapted grid in the shock-wave region and near the leading edge and the trailing edge. The main source of energy losses in the transonic regime is the existence of shock waves. The turbulence models used in the in-house codes give the loss coefficient approximately 20% lower than experimental data for both flow regimes.