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

对五种不同叶型和/或展宽比的跨声速叶栅激波/边界层干扰激波振荡进行了实验研究。利用纹影光学设备和线性图像传感器测量了尾流激波的位移。在压比略低于设计条件的一定范围内，所有叶栅都检测到了固有频率的尾流激波振荡。五种叶栅的固有频率从300赫兹到1100赫兹，取决于叶片型线和出口马赫数。位移幅值小于弦长的1%。纵横比对固有频率的影响可以忽略不计。为了验证这一推论，用n-…方法进行了数值模拟进一步发展了求解非定常流动N-S方程的隐式迎风松弛格式。二维雷诺平均的N-S方程在空间上用格心有限体积格式离散，在时间上用欧拉隐式方法离散。无粘通量的计算采用基于Roe近似黎曼解的TVD格式的高精度迎风格式，粘性通量的计算采用中心差分方法。湍流模型采用Baldwin和Lomax的代数湍流模型。为了简化网格的生成，采用了一种复合带状网格系统的带状方法，其中周期边界被视为带状边界。提出了一种用Roe近似黎曼求解器计算无粘通量的新的时间线性化方法。该方法不引入近似因式分解，采用逐点松弛法求解未因式方程。为了获得准确的时间解，在每个时间步长执行30次内迭代。数值结果表明，周期不稳定与高频和低频重叠。较高的是来自叶片尾缘的卡曼涡脱落，较低的是与实验检测到的固有频率振荡相对应。较少

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