The Turbulent Boundary Layer in a Compressible Fluid


Book Description

The first object of the paper is to develop a transformation which reduces the boundary-layer equations for compressible two-dimensional mean turbulent motion to incompressible form. The second object is to apply this transformation to the special case of the adiabatic turbulent boundary layer on a smooth wall. The transformation represents at every stage a genuine kinematic and dynamic correspondence between two real flows, both of which are capable of being observed experimentally. Since the mean pressure and mean velocity can then be measured in either flow, the mean acceleration of the fluid can in principle be determined, and the shearing stress can be adequately and accurately defined as the stress which is necessary to account for this acceleration. This formulation leads to a general transformation valid for laminar or turbulent flow in wakes and boundary layers, without regard to the state or energy equations or the viscosity law for the compressible fluid, and without regard to the boundary conditions on surface pressure or temperature in the event that a surface is involved. (Author).







Analysis of Turbulent Boundary Layers


Book Description

Analysis of Turbulent Boundary Layers focuses on turbulent flows meeting the requirements for the boundary-layer or thin-shear-layer approximations. Its approach is devising relatively fundamental, and often subtle, empirical engineering correlations, which are then introduced into various forms of describing equations for final solution. After introducing the topic on turbulence, the book examines the conservation equations for compressible turbulent flows, boundary-layer equations, and general behavior of turbulent boundary layers. The latter chapters describe the CS method for calculating two-dimensional and axisymmetric laminar and turbulent boundary layers. This book will be useful to readers who have advanced knowledge in fluid mechanics, especially to engineers who study the important problems of design.







The Influence of Surface Roughness on Supersonic High Reynolds Number Turbulent Boundary Layer Flow


Book Description

A comprehensive study of rough-wall high speed (M=2.9) high Reynolds number (Re/m = 1.9. 10 to the 7th power) 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.




An Experimental Investigation of the Compressible Turbulent Boundary Layer with a Favorable Pressure Gradient


Book Description

The paper describes the results of a detailed experimental investigation of a two-dimensional turbulent boundary layer in a favorable pressure gradient where the free-stream Mach number varied from 3.8 to 4.6 and the ratio of wall to adiabatic-wall temperature has a nominal value of 0.82. Detailed profile measurements were made with pressure and temperature probes; skin friction was measured directly with a shear balance. The velocity- and temperature-profile results were compared with zero pressure gradient and incompressible results. The skin-friction data were correlated with momentum-thickness Reynolds number and pressure-gradient parameter. (Author).




Compressible Turbulent Boundary Layer Computations for Flow with Longitudinal Curvature


Book Description

A numerical study has been performed using a finite-difference boundary layer computer program that includes corrections to the equations of motion for longitudinal curvature and allows the static pressure to be specified as a known function of x and y. Calculations with and without the corrections for longitudinal curvature and pressure gradient normal to be the local surface have been compared to experimental measurements of a supersonic turbulent boundary layer flow over a surface with concave longitudinal curvature. Substantially improved agreement with experimental measurements is obtained for the calculations including corrections for wall curvature and pressure gradient normal to the local surface for density profile, skin friction coefficient, and boundary-layer integral properties.




Theoretical Analysis of Stationary Potential Flows and Boundary Layers at High Speed


Book Description

Summary: The present report consists of two parts. The first part deals with the two-dimensional stationary flow in the presence of local supersonic zones. A numerical method of integration of the equation of gas dynamics is developed. Proceeding from solutions at great distance from the body the flow pattern is calculated step by step. Accordingly the related body form is obtained at the end of the calculation. The second part treats the relationship between the displacement thickness of laminar and turbulent boundary layers and the pressure distribution at high speeds. The stability of the boundary layer is investigated, resulting in basic differences in the behavior of subsonic and supersonic flows. Lastly, the decisive importance of the boundary layer for the pressure distribution, particularly for thin profiles, is demonstrated.




Experimental Investigation of High-Speed Boundary Layers with Wall Roughness


Book Description

A comprehensive investigation of the influence of surface roughness on the mean and turbulent flow properties of a high-speed turbulent boundary layer flow was performed. Six wall topologies, including a smooth and five rough surfaces consisting of three random sand-grain plates and two uniformly machined plates (k = 0 - 1.7 mm), were tested at three high Reynolds number (Re/m = 2 x lO (exp 7) Mach numbers (0.22, 0.65 and 2.75) . Mean flow measurements included surveys of the velocity and density. Turbulence quantities included measurements of the kinematic velocity turbulence intensities, mass flux turbulence intensities, kinematic Reynolds shear stress, compressible Reynolds shear stress, density-transverse-velocity fluctuation correlation, velocity spectra, auto-correlations, micro- and integral-scales and turbulent structure angles. Numerical simulations included evaluating three algebraic turbulence models with a boundary layer program. A three-year program was performed.