S2 Stream Surface Approximation Approach for Quasi Three-Dimensional Turbine Time-Marching Design Method

A fast and reliable turbine design method is necessary in aeroengine development practice. As Q3D time-marching method iteration process can be time consuming and unstable, a novel S2 stream surface approximation approach coupled with flow tangential condition is proposed to reduce the computation requirement. The surface approximation uses a quadratic function of axial coordinate x to formulate distribution of circumferential coordinate theta. The flow tangential condition inherently represents inviscid blade force effect, and the formulation of inviscid blade force is not needed. A corresponding personal Q3D turbine computer code was developed, which was suitable for both design and analysis applications. The Q3D design method solves Euler's equation through third-order Godunov's scheme with TVD property in finite volume method. Semi-implicit Crank-Nicolson's temporal scheme is implemented. Profile, secondary, and tip clearance energy loss models are added to predict viscous losses. Blade row exit swirl is required as the convergence target for Q3D design. A two-stage turbine and a single-stage high-pressure turbine were designed and analyzed by the Q3D method. Viscous 3D CFD was utilized to check design performances. The results showed that the Q3D method could finish a design case within 1 min. At design point, Q3D mass flow rate error was no more than 1.25%, expansion ratio error was no less than -0.022, and isentropic efficiency error was no more than 0.37 percentage points. The Q3D design method is fast and accurate. The stream surface approximation approach is suitable for Q3D design and analysis.