Abstract
An axial turbine rotor cascade‐shape optimization with unsteady passing wakes was performed to obtain an improved aerodynamic performance using an unsteady flow, Reynolds‐averaged Navier‐Stokes equations solver that was based on explicit, finite difference; Runge‐Kutta multistage time marching; and the diagonalized alternating direction implicit scheme. The code utilized Baldwin‐Lomax algebraic and k‐ε turbulence modeling. The full approximation storage multigrid method and preconditioning were implemented as iterative convergence‐acceleration techniques. An implicit dual‐time stepping method was incorporated in order to simulate the unsteady flow fields. The objective function was defined as minimization of total pressure loss and maximization of lift, while the mass flow rate was fixed during the optimization. The design variables were several geometric parameters characterizing airfoil leading edge, camber, stagger angle, and inter‐row spacing. The genetic algorithm was used as an optimizer, and the penalty method was introduced for combining the constraints with the objective function. Each individual′s objective function was computed simultaneously by using a 32‐processor distributedmemory computer. The optimization results indicated that only minor improvements are possible in unsteady rotor/stator aerodynamics by varying these geometric parameters.
Highlights
The major cause of flow unsteadiness in stator and rotor interaction is the combination of circumferential direction nonuniform flow due to the wake of the stator and the relative motion of the rotor
This paper focuses on the possibilities for improvement of the aerodynamic performance of a rotor cascade subjected to unsteady flow due to the wakes of the stator cascade located upstream
The Navier-Stokes solver was based upon the Runge-Kutta (RK) explicit time marching [2] and Diagonalized Alternating Direction Implicit (DADI) schemes [3]
Summary
The major cause of flow unsteadiness in stator and rotor interaction is the combination of circumferential direction nonuniform flow due to the wake of the stator and the relative motion of the rotor. Pritchard’s [9] formulation for geometric shape parameterization was selected due to its simplicity and robustness It allows for the variation of leading edge radius, leading wedge angle, blade inlet angle, and tangential chord length (Figure 2). Only four geometric design variables were used to represent the airfoil cascade geometry (Figure 2): airfoil inlet angle (the higher lift coefficient can be obtained by controlling this angle), inlet wedge angle (the airfoil thickness and slope of the leading edge region can be controlled by this parameter), leading edge radius (location of the stagnation point and the pressure peak at the leading edge can be controlled), and tangential chord length ( controlling the pitch length and the stagger angle). Case and Case maximize the lift while the total pressure loss cannot be greater than a specified value and mass flow rate is fixed (Table 5). The specified values of lift, total pressure loss, and mass flow rate were obtained from the calculation results of the original DFVLR single stage turbine
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