comprehensive study of rough-wall high-speed (M = 2.9) high Reynolds number (Re/m = 1.9e7) turbulent boundary layer flow was performed consisting of experimental, analytical, and numerical methods. Six wall topologies consisting of a smooth and five rough surfaces (two- and three-dimensional machined roughness plates; and 80, 36. and 20 grit sand-grain roughened plates) were studied. A confocal laser scan microscope was used to measure the topography of the sand-grain roughnesses. The experimental measurement techniques included a convention Pitot pressure probe, laser Doppler velocimetry, hot-wire anemometry, color schlieren and laser sheet Mie scattering images. Mean measurements included velocity, Mach number, density, and mass flux. Turbulent measurements included velocity and mass flux turbulence intensities, kinematic Reynolds shear stress, compressible Reynolds shear stress in two planes, and the traverse apparent mass flux. Kinematic turbulent flow statistical properties were found to scale by local mean quantities and displayed a weak dependence on surface roughness. Turbulent flow statistical properties with the explicit appearance of density did not scale by local mean quantities, and had a strong linear dependence on roughness. Surface roughness also had a significant effect on the flow structure size, angles, and energy spectra. A theoretical analysis was performed and a new integral method for the estimation of skin friction was developed. The skin friction estimates were within 4% of compressible semi-empirical relations. A numerical study was performed which used a parabolized Navier-Stokes solver with two algebraic turbulence models and the Rotta model for surface roughness. A new method for the estimation of momentum loss improved the numerical flow predictability. The algebraic turbulence models predicted qualitatively correct profile shapes and accurately predicted the kinematic and compressible Reynolds shear stress levels for all but the near wall region (y/delta
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机译：对粗糙壁高速（M = 2.9）高雷诺数（Re / m = 1.9e7）的综合研究进行了湍流边界层流动，包括实验，分析和数值方法。研究了由光滑表面和五个粗糙表面组成的六种壁拓扑（二维和三维机加工的粗糙板；以及80、36和20粒度的沙粒粗糙板）。共焦激光扫描显微镜用于测量沙粒粗糙度的形貌。实验测量技术包括常规的皮托管压力探头，激光多普勒测速仪，热线风速仪，彩色纹影和激光薄片米氏散射图像。平均值包括速度，马赫数，密度和质量通量。湍流测量包括速度和质量通量湍流强度，运动雷诺剪切应力，两个平面中的可压缩雷诺剪切应力以及横向视在质量通量。运动湍流统计特性被发现按局部均值成比例，并且显示出对表面粗糙度的弱依赖性。具有显式密度的湍流统计特性未按局部均值缩放，并且对粗糙度具有很强的线性依赖性。表面粗糙度对流动结构的尺寸，角度和能谱也有重要影响。进行了理论分析，并开发了一种估计皮肤摩擦的新积分方法。皮肤摩擦估计在可压缩的半经验关系的4％以内。进行了数值研究，该研究使用了抛物线型Navier-Stokes解算器，该解算器具有两个代数湍流模型和用于表面粗糙度的Rotta模型。一种估计动量损失的新方法提高了数值流的可预测性。代数湍流模型可预测定性正确的轮廓形状，并准确预测除了壁附近区域（y / delta）以外的所有运动和可压缩雷诺剪切应力水平
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