| The objective of this research is to identify systematically the compressibility effects in supersonic boundary layers. In addition to variable-mean-density (temperature) effects, argued by Morkovin to be the main difference between incompressible and compressible boundary layers, there are also compressibility effects due to turbulent fluctuations. Compressible turbulent boundary-layer fluctuations can be represented as a sum of four components, arising from different physical phenomena: incompressible, thermal, pseudosound, and acoustic. The role of these flow components in the supersonic compressible boundary-layer dynamics has been studied in this work, and compressibility effects due to these components have been identified.; First, the role of the acoustic component of fluctuations in the supersonic boundary-layer dynamics was examined. Two decoupled systems of governing equations, for the nonacoustic (incompressible and thermal) and acoustic components of fluctuations, were derived in the limit of small turbulence Mach number, and a procedure for numerical decomposition, based on the nonacoustic equations, was developed to evaluate directly the interaction of the nonacoustic flow with acoustics. The results indicate that the system of nonacoustic equations provides an accurate description of the evolution of the nonacoustic fluctuations in a turbulent boundary layer, up to at least Ma = 6. Further, to at least Ma = 6, the acoustic fluctuations do not contribute to the evolution of turbulent kinetic energy or the components of the Reynolds stress tensor.; Second, since it has been determined that the acoustic (and pseudosound) component of the flow does not have much influence on the dynamics of the supersonic boundary layer; the fluctuating thermal component was studied as the only source of compressibility effects in the boundary layer. An approach to the study of thermal compressibility effects and a possible way to draw a parallel between incompressible and compressible modeling were developed. It has been proposed that the thermal component of the fluctuations can be treated as a perturbation about a variable-mean-density incompressible flow. In this way, terms linear in thermal variables, which can give rise to compressibility, are easily identified. The numerical decomposition procedure was extended to decompose the nonacoustic component of the flow into the incompressible and thermal parts, so that thermal terms can be evaluated directly and compared with leading-order incompressible terms to verify their importance. For the turbulence model development, it has been assumed that the leading-order incompressible problem is known, and a way of reducing the modeling of important thermal terms to this known problem was provided. By this approach, extended incompressible models for the turbulent kinetic energy equation and the Reynolds stress transport equation were derived. It was found that most of the thermal compressibility effects are due directly to density fluctuations. The only exceptions are the thermal contribution to the production of turbulent kinetic energy and the Reynolds stress due to fluctuating thermal divergence. |
