| With this work, a new Lagrangian based inverse technique for constructing turbomachinery blade geometries is presented. This method, which consists of a 2-D flow field integrator, a camber line generator and a passage averaged momentum/pressure boundary condition, generates a blade geometry in response to a prescribed flow turning distribution.By describing a blade geometry as a mean camber line with a specified thickness distribution, it is shown how this camber line can be obtained from a Lagrangian analysis that overlays the blade onto a material line that convects from inflow to outflow. This treatment enhances both the global convergence of the calculation and the flow resolution near the leading and trailing edges of the blade. Also, the unsteady form of the pressure boundary condition is derived and is shown to produce convergence acceleration.Finally, a new unsteady pressure boundary condition is derived from a complex-lamellar decomposition of the flow field, and its passage average flow turning. With this new shock-fitting approach, transonic blades, with strong passage shocks, can be designed that are both geometrically continuous and faithful to the prescribed flow turning distribution. |
