Transition in Turbine Flows

We have further developed our capabilities to analyze transition in turbine boundary layers from first principles by integrating the nonlinear parabolized stability equations (PSE) with improved initial and boundary conditions. With modified iteration schemes, we are able to proceed deeper into the transition region where skin friction coefficient and heat transfer coefficient significantly increase. Initial and boundary conditions at elevated turbulence levels can be derived by receptivity analysis. Test runs for ERCOFTAC test case T3A at 2.4\% turbulence level provide results in good agreement with the experimental data. The sharper minimum of the skin coefficient also shown by DNS results is likely due to the missing intermittency. The method has been applied to various experimentally studied turbine blades (UTRC, VKI, Zierke, Langston, Hippensteele, and others). The PSE results, though physically reasonable, do not agree as well as expected with the experimental findings. We have, therefore, performed an extensive search for the reasons of the seemingly systematic deviations. A first source of uncertainty has been found in the often insufficient documentation of the experiments (e.g. on blockage by end-wall boundary layers). However, variation of the relevant parameters does not lead to more satisfactory agreement. A second reason has been found in the "standard procedure" which considers a 2D flow at midspan and uses a panel code and subsequent boundary-layer code to obtain the laminar basic flow for the transition analysis. Comparison with the pressure distribution obtained with a 3D design code (RVC3D) shows significant three-dimensionality of the flow (e.g. in the UTRC experiments). The spanwise variation has been neglected in our original PSE code. To overcome this problem, we have developed the PSE/3D for fully 3D boundary layers to account for streamwise and spanwise variations. Since the design code does not provide the boundary-layer flow with sufficient resolution, we have generated the Euler solution and employed a 3D boundary-layer code to obtain the viscous basic flow. Although only the linear stability level of PSE/3D has been implemented so far, the discrepancies with the experiments change but do not disappear. We still find deviations between the computed and experimental variations of C(sub f), and St along the blade for laminar flow. The main reason can be seen by comparing the solution of the boundary-layer code with the viscous results of the design code. The conventional boundary-layer solution exhibits an asymptotic behavior appropriate in external aerodynamics but does not match the steep gradients of the inviscid flow through the passage and consequently provides biased results for C(sub f), and St. An attempt is currently being made to correct this deficiency. Before attempting to perform the transition analysis for the viscous flow provided by the design code, we have analyzed the implementation and "best possible" results. Code and results exhibit flaws that may negatively affect the design and are intolerable for transition analysis. Therefore, we have decided to develop a new code to obtain a reliable basis for stability and transition studies. We expect to report improved results by the time of the meeting.