This book introduces the reader to the field of compressible turbulence and compressible turbulent flows across a broad speed range through a unique complimentary treatment of both the theoretical foundations and the measurement and analysis tools currently used. For the computation of turbulent compressible flows, current methods of averaging and filtering are presented so that the reader is exposed to a consistent development of applicable equation sets for both the mean or resolved fields as well as the transport equations for the turbulent stress field. For the measurement of turbulent compressible flows, current techniques ranging from hot-wire anemometry to PIV are evaluated and limitations assessed. Characterizing dynamic features of free shear flows, including jets, mixing layers and wakes, and wall-bounded flows, including shock-turbulence and shock boundary-layer interactions, obtained from computations, experiments and simulations are discussed. - Describes prediction methodologies including the Reynolds-averaged Navier Stokes (RANS) method, scale filtered methods and direct numerical simulation (DNS) - Presents current measurement and data analysis techniques - Discusses the linkage between experimental and computational results necessary for validation of numerical predictions - Meshes the varied results of computational and experimental studies in both free and wall-bounded flows to provide an overall current view of the field

The following grant objectives were delineated in the proposal to NASA: to offer course work in computational fluid dynamics (CFD) and related areas to enable mechanical engineering students at North Carolina A&T State University (N.C. A&TSU) to pursue M.S. studies in CFD, and to enable students and faculty to engage in research in high speed compressible flows. Since no CFD-related activity existed at N.C. A&TSU before the start of the NASA grant period, training of students in the CFD area and initiation of research in high speed compressible flows were proposed as the key aspects of the project. To that end, graduate level courses in CFD, boundary layer theory, and fluid dynamics were offered. This effort included initiating a CFD course for graduate students. Also, research work was performed on studying compressibility effects in high speed flows. Specifically, a modified compressible dissipation model, which included a fourth order turbulent Mach number term, was incorporated into the SPARK code and verified for the air-air mixing layer case. The results obtained for this case were compared with a wide variety of experimental data to discern the trends in the mixing layer growth rates with varying convective Mach numbers. Comparison of the predictions of the study with the results of several analytical models was also carried out. The details of the research study are described in the publication entitled 'Compressibility Effects in Modeling Turbulent High Speed Mixing Layers, ' which is attached to this report. Chandra, Suresh NASA-CR-194547, NAS 1.26:194547 NAG1-1287...

Compressibility, Turbulence and High Speed Flow introduces the reader to the field of compressible turbulence and compressible turbulent flows across a broad speed range, through a unique complimentary treatment of both the theoretical foundations and the measurement and analysis tools currently used. The book provides the reader with the necessary background and current trends in the theoretical and experimental aspects of compressible turbulent flows and compressible turbulence. Detailed derivations of the pertinent equations describing the motion of such turbulent flows is provided and an extensive discussion of the various approaches used in predicting both free shear and wall bounded flows is presented. Experimental measurement techniques common to the compressible flow regime are introduced with particular emphasis on the unique challenges presented by high speed flows. Both experimental and numerical simulation work is supplied throughout to provide the reader with an overall perspective of current trends. - An introduction to current techniques in compressible turbulent flow analysis - An approach that enables engineers to identify and solve complex compressible flow challenges - Prediction methodologies, including the Reynolds-averaged Navier Stokes (RANS) method, scale filtered methods and direct numerical simulation (DNS) - Current strategies focusing on compressible flow control

Compressibility profoundly affects many aspects of turbulence in high-speed flows - most notably stability characteristics, anisotropy, kinetic-potential energy interchange and spectral cascade rate. Many of the features observed in compressible flows are due to the changing nature of pressure. Whereas for incompressible flows pressure merely serves to enforce incompressibility, in compressible flows pressure becomes a thermodynamic variable that introduces a strong coupling between energy, state, and momentum equations. Closure models that attempt to address compressibility effects must begin their development from sound first-principles related to the changing nature of pressure as a flow goes from incompressible to compressible regime. In this thesis, a unified framework is developed for modeling pressure-related compressibility effects by characterizing the role and action of pressure at different speed regimes. Rapid distortion theory is used to examine the physical connection between the various compressibility effects leading to model form suggestions for the pressure-strain correlation, pressure-dilatation and dissipation evolution equation. The pressure-strain correlation closure coefficients are established using fixed point analysis by requiring consistency between model and direct numerical simulation asymptotic behavior in compressible homogeneous shear flow. The closure models are employed to compute high-speed mixing-layers and boundary layers in a differential Reynolds stress modeling solver. The self-similar mixing-layer profile, increased Reynolds stress anisotropy and diminished mixing-layer growth rates with increasing relative Mach number are all well captured. High-speed boundary layer results are also adequately replicated even without the use of advanced thermal-flux models or low Reynolds number corrections. To reduce the computational burden required for differential Reynolds stress calculations, the present compressible pressure-strain correlation model is incorporated into the algebraic modeling framework. The resulting closure is fully explicit, physically realizable, and is a function of mean flow strain rate, rotation rate, turbulent kinetic energy, dissipation rate, and gradient Mach number. The new algebraic model is validated with direct numerical simulations of homogeneous shear flow and experimental data of high-speed mixing-layers. Homogeneous shear flow calculations show that the model captures the asymptotic behavior of direct numerical simulations quite well. Calculations of plane supersonic mixing-layers are performed and comparison with experimental data shows good agreement. Therefore the algebraic model may serve as a surrogate for the more computationally expensive differential Reynolds stress model for flows that permit the weak-equilibrium simplification. The electronic version of this dissertation is accessible from http://hdl.handle.net/1969.1/148160

These proceedings contain the papers presented at the 4th International Symposium on Engineering Turbulence Modelling and Measurements held at Ajaccio, Corsica, France from 24-26 May 1999. It follows three previous conferences on the topic of engineering turbulence modelling and measurements. The purpose of this series of symposia is to provide a forum for presenting and discussing new developments in the area of turbulence modelling and measurements, with particular emphasis on engineering-related problems. Turbulence is still one of the key issues in tackling engineering flow problems. As powerful computers and accurate numerical methods are now available for solving the flow equations, and since engineering applications nearly always involve turbulence effects, the reliability of CFD analysis depends more and more on the performance of the turbulence models. Successful simulation of turbulence requires the understanding of the complex physical phenomena involved and suitable models for describing the turbulent momentum, heat and mass transfer. For the understanding of turbulence phenomena, experiments are indispensable, but they are equally important for providing data for the development and testing of turbulence models and hence for CFD software validation.