Inverse design of a turbine cascade passage and DNS of a stationary and rotating serpentine passage

Experimental investigations of the flow physics past a single stationary transonic turbine blade in a cascade are complicated by the periodic nature of the problem. Typically up to seven blades in a cascade are required to guarantee periodicity about the center blade that, in turn, requires large compressors at transonic speeds. One possibility to circumvent the constraint of so many blades, and allow the necessary optical access, is to place a single blade in a passage consisting of two plexiglass walls that are designed to obtain certain representative periodic flowfield characteristics. Using an optimization procedure based on the method of steepest descent and the RANS equations, the walls were designed to ensure that the Surface Isentropic Mach Number (SIMN) distribution on the blade matched the SIMN of the same blade in an infinite cascade. The experimental setup imposed an additional constraint requiring the flow remained attached along both passage walls. A robust and autonomous design method using a weighted composite cost function was developed and successfully applied. Excellent agreement was achieved between CFD of the infinite cascade SIMN, CFD of the designed double passage SIMN, and the experimentally measured SIMN.; Serpentine passages are found in a number of engineering applications including turbine blade cooling passages. The serpentine passage is an ideal candidate for conducting a thorough DNS study due to its geometric simplicity but complex flow physics. The serpentine passage geometry investigated has dimensions 12pidelta x 2delta x 3pidelta and radius of curvature delta/r c = 0.5 in the curved section. Simulations of a test matrix consisting of two different Reynolds numbers, Retau = 180 and Retau = 250, subjected to two different orthogonal rotation numbers, Ro tau = 0 and Rotau = 5 was conducted. Whereas the stationary case results in a symmetric flowfield for the two U-bends constituting the passage, the effect of rotation coupled with convex and concave curvature, and its' effect on separation, is striking and is easily identifiable. Numerous interesting features have been identified, and an outstanding unique database for RANS validation of flows with strong streamline curvature and rotation has been developed.