For turbine flow phenomena which are dominated by viscous effects, many valuable insights into the flow physics can be gained through low-speed cascade measurements. For example, for low-pressure turbines unsteady wake-blade interactions can be investigated in cascade provided that the Reynolds number, freestream turbulence conditions and the pressure coefficient distributions are the same in the cascade as in the high-speed counterpart.
This paper describes an iterative procedure for inversely designing low-speed linear cascades with prescribed blade pressure-coefficient distributions. The inverse-design problem is treated as an optimization problem. The optimization strategy features the use of a genetic algorithm and a gradient-type algorithm. At the end of each global iteration of the design procedure a Navier-Stokes analysis is used to see if the final cascade geometry gives the specified pressure-coefficient distribution to the desired degree of accuracy.
Although the resulting cascade may be designed to the level of accuracy afforded by the Navier-Stokes analysis, the method takes advantage of the fact that the pressure distribution in the low-speed cascade can be predicted with good accuracy and very rapidly using a panel method solution for the potential flow through the cascade. A panel method flow solver is used to minimize the number of Navier-Stokes evaluations to three or four for a given inverse-design problem. As a result, the present procedure is very efficient.