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

本文对五种不同叶型和展弦比的跨音速涡轮机叶栅进行了激波/边界层干扰引起的激波振荡实验研究。尾流激波的位移是通过纹影光学设备和线性图像传感器测量的。在比设计压比稍低的一定压比范围内，所有叶栅都出现了具有固有频率的尾流激波振荡。五个叶栅的固有频率范围从300 Hz到1100 Hz，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。从这一事实推断，振荡的原因可以用二维考虑来解释，而不能用三维考虑来解释。为了验证这一推论，用一个非线性的数值模拟方法进行了数值模拟。 ...更多信息 本文发展了求解非定常N-S方程的隐式迎风松弛格式。二维的，雷诺平均的Navier-Stokes方程离散在空间中使用一个细胞中心的有限体积配方和时间使用欧拉隐式方法。无粘通量的评估使用一个高精度的迎风格式的基础上的TVD制定与Roe的近似黎曼求解器，和粘性通量的中心差分方式确定。采用Baldwin和Lomax的代数湍流模型。为了简化网格生成，分区方法与复合分区网格系统的实施，其中周期性边界被视为分区边界。详细介绍了一种新的时间线性化的无粘通量的Roe的近似黎曼求解器评估。不引入近似因式分解，用逐点松弛法求解未因式分解的方程组。为了获得时间精确的解决方案，在每个时间步执行30次内部迭代。数值结果表明，周期性非定常现象与高、低频重叠。较高的一个是来自卡门涡脱落的叶片后缘，和较低的一个对应的实验检测到的振动与固有频率。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