Unsteady Phenomena due to Shock Wave / Boundary Layer Interaction in Three Dimensional Transonic Flow

实验研究了5种不同叶型和展弦比的线性跨音速涡轮叶栅在激波/边界层相互作用下的激波振荡。利用纹影光学装置和线性图像传感器测量了尾流激波的位移。在所测试的叶栅中，在压力比略低于设计条件的一定范围内，均检测到固有频率的尾流激波振荡。固有频率取决于叶型和出口马赫数，五个叶栅的固有频率范围为300Hz至1100Hz。位移幅值小于弦长1%。宽高比对固有频率的影响可以忽略不计。从这一事实可以推断，振荡的原因可以用二维的考虑来解释，而不能用三维的考虑来解释。为了验证这一推断，采用了一种新发展的Navier-Stokes非定常流场方程的隐式迎风松弛格式进行了数值模拟。二维，reynolds -average Navier-Stokes方程在空间上使用以细胞为中心的有限体积公式离散，在时间上使用欧拉隐式方法离散。无粘通量采用基于TVD公式和Roe近似黎曼解算器的高精度逆风格式进行评估，粘性通量以中心差分方式确定。采用Baldwin和Lomax的代数湍流模型。为了简化网格的生成，采用复合分区网格系统的分区方法，将周期边界作为分区边界。详细介绍了用罗伊近似黎曼解算器计算的一种新的无粘通量时间线性化方法。不引入近似分解，用点松弛法求解未分解方程。为了获得时间精确的解，在每个时间步执行30次内部迭代。数值计算结果表明，周期非定常具有高、低频重叠。较高的信号来自叶片尾缘的卡门涡脱落，较低的信号对应于实验检测到的固有频率振荡。少

The shock wave oscillation due to shock-wave / boundary-layer interaction has been investigated experimentally for five linear transonic turbine cascades with different blade profile and / or aspect ratio. Displacement of the wake shock was measured by means of a schlieren optical equipment and a linear image sensor. The wake shock oscillation with inherent frequency was detected in a certain range of pressure ratio somewhat lower than the design condition in all the cascades tested. The inherent frequency, which ranges from 300Hz to 1100Hz for the five cascades, depends on the blade profile and the outlet Mach number. The displacement amplitude is less than 1 % of chord length. The aspect ratio has negligible effect on the inherent frequency. It is inferred from this fact that the cause of the oscillation can be explained by the two-dimensional consideration, but not by the three-dimensional one.In order to verify the inference, the numerical simulation was carried out by means of a n … More ewly developed implicit upwind relaxation scheme for the Navier-Stokes equations of unsteady flow. The two-dimensional, Reynolds-averaged Navier-Stokes equations are discretized in space using a cell-centered finite volume formulation and in time using the Euler implicit method. The inviscid fluxes are evaluated using a highly accurate upwind scheme based on a TVD formulation with the Roe's approximate Riemann solver, and the viscous fluxes are determined in a central differencing manner. The algebraic turbulence model of Baldwin and Lomax is employed. To simplify grid generations, a zonal approach with a composite zonal grid system is implemented, in which periodic boundaries are treated as zonal boundaries. A new time-linearization of the inviscid fluxes evaluated by the Roe's approximate Riemann solver is presented in detail. No approximate factorization is introduced, and unfactored equations are solved by pointwise relaxation method. To obtain time-accurate solutions, 30 inner iterations are performed at each time step. The numerical results showed periodic unsteadiness overlapped with higher and lower frequency. The higher one is come from the Karman vortex shedding from a blade trailing edge, and the lower one corresponds to the experimentally detected oscillation with inherent frequency. Less