Direct numerical simulation of supersonic turbulent boundary layers TeX Export

@phdthesis{citeulike:3687567, abstract = {The objectives of this research were to develop a method by which the spatially developing compressible turbulent boundary layer could be simulated using a temporally developing numerical simulation and to study the physics of the compressible turbulent boundary layer. We take advantage of the technique developed by Spalart (1987, 1988) for the incompressible case. In this technique, it is recognized that the boundary layer exhibits slow growth in the streamwise direction, so the turbulence can be treated as approximately homogeneous in this direction. The slow growth is accounted for with a coordinate transformation and a multiple scale analysis. The result is a modified system of equations (Navier-Stokes plus some extra terms, which we call "slow growth terms") that are homogeneous in both the streamwise and spanwise directions and represent the state of the boundary layer at a given streamwise location (or, equivalently, a given thickness). The compressible Navier-Stokes equations are solved using a mixed Fourier and B-spline "spectral" method. The dependent variables are expanded in terms of a Fourier representation in the horizontal directions and a B-spline representation in the wall-normal direction. In the wall-normal direction non-reflecting boundary conditions are used at the freestream boundary, and zero-heat-flux no-slip boundary conditions are used at the wall. This combination of splines and Fourier methods produces a very accurate numerical method. Mixed implicit/explicit time discretization is used. Results are presented for a case with a Mach number of 2.5, and a Reynolds number, based on momentum integral thickness and wall viscosity, of \$R\sb{\theta\sp\prime}\$ = 840. The results show that the van Driest transformed velocity satisfies the incompressible scalings and a narrow logarithmic region is obtained. The results for the turbulence intensities compare well with the incompressible simulations of Spalart. Pressure fluctuations are found to be higher than in incompressible flow. Morkovin's strong Reynolds analogy does not agree with the results of the simulation, however, an analogy is found between the rate of turbulent heat transfer and the rate of turbulent momentum transfer. Reynolds stress and turbulent kinetic energy budgets are computed and compared with the budgets from Spalart's incompressible simulations.}, author = {Guarini, Stephen}, citeulike-article-id = {3687567}, citeulike-linkout-0 = {http://proquest.umi.com/pqdweb?did=732826501&Fmt=7&clientId=48776&RQT=309&VName=PQD}, keywords = {aerospace, engineering, materials, mathematics, mechanical}, location = {United States -- California}, posted-at = {2008-11-25 16:42:07}, priority = {2}, school = {Stanford University}, title = {Direct numerical simulation of supersonic turbulent boundary layers}, url = {http://proquest.umi.com/pqdweb?did=732826501&Fmt=7&clientId=48776&RQT=309&VName=PQD}, year = {1998} }

TY - THES ID - citeulike:3687567 L3 - citeulike-article-id:3687567 N2 - The objectives of this research were to develop a method by which the spatially developing compressible turbulent boundary layer could be simulated using a temporally developing numerical simulation and to study the physics of the compressible turbulent boundary layer. We take advantage of the technique developed by Spalart (1987, 1988) for the incompressible case. In this technique, it is recognized that the boundary layer exhibits slow growth in the streamwise direction, so the turbulence can be treated as approximately homogeneous in this direction. The slow growth is accounted for with a coordinate transformation and a multiple scale analysis. The result is a modified system of equations (Navier-Stokes plus some extra terms, which we call "slow growth terms") that are homogeneous in both the streamwise and spanwise directions and represent the state of the boundary layer at a given streamwise location (or, equivalently, a given thickness). The compressible Navier-Stokes equations are solved using a mixed Fourier and B-spline "spectral" method. The dependent variables are expanded in terms of a Fourier representation in the horizontal directions and a B-spline representation in the wall-normal direction. In the wall-normal direction non-reflecting boundary conditions are used at the freestream boundary, and zero-heat-flux no-slip boundary conditions are used at the wall. This combination of splines and Fourier methods produces a very accurate numerical method. Mixed implicit/explicit time discretization is used. Results are presented for a case with a Mach number of 2.5, and a Reynolds number, based on momentum integral thickness and wall viscosity, of $R\sb{\theta\sp\prime}$ = 840. The results show that the van Driest transformed velocity satisfies the incompressible scalings and a narrow logarithmic region is obtained. The results for the turbulence intensities compare well with the incompressible simulations of Spalart. Pressure fluctuations are found to be higher than in incompressible flow. Morkovin's strong Reynolds analogy does not agree with the results of the simulation, however, an analogy is found between the rate of turbulent heat transfer and the rate of turbulent momentum transfer. Reynolds stress and turbulent kinetic energy budgets are computed and compared with the budgets from Spalart's incompressible simulations. CY - United States -- California TI - Direct numerical simulation of supersonic turbulent boundary layers PB - Stanford University KW - aerospace KW - engineering KW - materials KW - mathematics KW - mechanical AU - Guarini, Stephen PY - 1998/// UR - http://proquest.umi.com/pqdweb?did=732826501&Fmt=7&clientId=48776&RQT=309&VName=PQD ER -