Laskowski, G., Medic, G., Durbin, P., Stanford University, USA

A new method for experimentally investigating the turbulent flowfield in transonic turbines has been developed using STAR-CD. Typically, linear cascades consisting of 5-11 blades are used to ensure periodic flow about the central blade. However, such experimental models require large and expensive compressor facilities and do not lend themselves to optical experimental techniques such as PIV (Particle Image Velocimetry) and LDA (Laser Dopler Anemometry).

Using STAR-CD, we have designed a new rig by an inverse design procedure. In order to achieve the correct periodic behavior, a blade is placed in a passage consisting of two solid walls shaped to give the same flow features that the blade would experience in an infinite cascade. Using the method of steepest descent with a line search, the walls are shaped such that the blade surface isentropic Mach number (SIMN) distribution along the blade surface matched the SIMN of the blade in an infinite cascade (the objective function), while maintaining attached flow along both passage walls (a penalty function). A secondary objective was to match the wall shear stress of the blade in the double passage with the wall shear stress of the blade in an infinite cascade. The cost function is thus a composite function of a viscous and inviscid flow property.

The double passage has an advantage over other cascade models in that it provides realistic flow conditions with minimal compressor requirements without the need for bleeds or tailboards, which tend to be difficult to design and calibrate. The walls are machined of Plexiglas to allow the transmission of laser light necessary for PIV and LDA measurements of the turbulent flowfield.

The infinite cascade (IC) was first simulated to provide the SIMN to be used as the target in the inverse design. The pressure side and suction side stagnation streamlines were extracted and offset by +/- the pitch, to be used as an initial guess for the wall shapes.

The double passage (DP) optimization procedure was controlled by a script, which linked together the STAR-CD executables, various STAR files
and macros, as well as the support routines for the inverse design. Fig. 1 depicts the starting geometry and resulting wall shape from the optimization procedure. Fig. 2 presents the resulting SIMN distribution for the geometries shown in Fig. 1. It is evident that excellent agreement has been achieved between the CFD-IC and the CFD-DP while maintaining attached flow
along both passage walls. Not only is the SIMN in good agreement, but the Mach number flowfield as well as shown in Fig. 3. The rig has been constructed and preliminary experimental measurements are in excellent agreement with the CFD results [1].