3D flow around blades

Underlying Flow Regime 2-07 © copyright ERCOFTAC 2004

Best Practice Advice

Best Practice Advice for the UFR

This study highlights the importance of the back pressure in numerically modeling an experimentally-tested turbomachinery configuration. If there is doubt in the back pressures measured in the experiment or in those of the computation, the comparability of the experiment and computation is, at best, questionable.

Use a radial equilibrium equation rather than direct specification of the back pressure. The distribution of this radial equilibrium should be based on the static pressure on the hub rather than on the casing. This is because the hub static pressure has much less uncertainty, because there exists no tip-leakage jet in the vicinity of the hub.

The contours of experimental data in the near wall regions in Figures 13 through 15 do not compare well with the computed data, in which the boundary layer is modeled. Experimenters working with LV often extrapolate freestream data to the wall inside a certain region in which the apparatus no longer functions.

When comparing field data from experimental results derived from Laser Velocimetry with those from computations, note that LV cannot resolve boundary layers, due to reflective interference close to the wall.

With regard to grid dimensioning, observe the following:

To obtain a solution in a reasonable amount of time (1 day), size the grid to about 200,000 cells, whose maximum stretching factor does not exceed 1.2.

The resulting y+ (100) requires a wall function, because the turbulence model does not usefully predict wall shear. Use of a Spalding wall-function, for instance, yields accurate wall-shear for a modicum of computational expense.

The differencing scheme seems to play a less crucial role, although the following advice may be stated:

If shock resolution is a goal, use a downwind differencing scheme. However, because the relative inlet Mach number reaches a maximum of only 1.38, it is assumed that the difference between central and downwind schemes for such a case are overshadowed by the effect of the grid. Were the inlet Mach number higher, the differencing scheme would play a more crucial role.

The selection of Spalart-Allmaras for a turbulence model seems to be sufficient for such cases, as it presents a decent compromise between sophistication and computational cost. Because the grid sizing and stretching constrains the wall y+ values to 100 or more, the above-mentioned wall function was required.

Artificial viscosity was used in this study to counter instabilities resulting from the central differencing scheme. The artificial viscosity scheme used in this study was the Symmetric Limited Positive scheme, also known as SLIP. A test for sensitivity to the parameters for this artificial viscosity scheme was conducted; it was shown that the case is very mildly sensitive to changes in the input parameters for the SLIP viscosity. Grid effects and differencing scheme effects are much more important to running such a case.

Recommendations for Future Work

With regard to studies of this nature (slightly transonic, low aspect-ratio), grid effects seem to predominate solution success. This is followed in terms of importance by differencing-scheme selection. Finally, artificial viscosity and turbulence-model selection play minor roles for these cases. In terms of future work this can be quantified by the following measures:

The grid featured in this study is highly skewed near the tip, as shown in Figure 6. The tip region is the transonic region of the domain as well. This skewed-ness is a result of using a straight-edged mesh. A higher lever of sophistication (multiple blocks, innovative tip gap solutions) in the design of a mesh for such case could yield some returns for shock resolution, for example. Due to time-constraints the effects of a more sophisticated grid could not be fully investigated.

It is also recommended that the tip-gap size be reduced by around 40% to improve convergence behavior. In later iterations the tip gap may be enlarged to more accurately simulate the flow field. As always, the CFD engineer must balance physical accuracy with convergence capability.

Contributors: William Anderson - ALSTOM Power (Switzerland) Ltd