Weakly Compressible Descriptions of Turbulence in Compressible Flows

Abstract

Public reoomna Duraen for tnis collection of information is estimated to average 1 hour per response inciuaing the time or reviewing the aata neeaeo ana completing and reviewing this collection of information. Sena comments regarding this burden estimate or any reducing this ouraen to Department of Defense. Washington Heaaguaners Services. Directorate for Informs «on Operations anORept mmJv)7 Respondents should be aware that notwithstanding any other provision of law no person snail be subject to any penai. 222024302 Resoonaents snould be aware that notwithstanomg any --. _" ".,,. .",,,-.""o-cc cuirenllv vaiig OMB control numper PLEASE DO NOT RETURN YOUR FORM TO THE ABOVE ApPReSS AFRL-SR-BL-TR-01- REPORT DATE (DD-MM-YYYY) 02-01-2001 REPORT TYPE Final Techr TITLE AND SUBTITLE Weakly Compressible Descriptions of Turbulence in Comoressible Flows AUTHOR(S)Roben D. Moser PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES)University of Illinois at Urbana-Champaign, Urbana, IL 61801 V.'eakiv compressible asymptotics and direct numerical simulation are used to investigate tr.e effects of compressibility on high speed turbulent shear layers. The asymptotic analysis leads -z a decomposition procedure that can be used to approximately determine the acoustic and r.cr.accustic components of a compressible flow. In boundary layers, it is found that the acoustic fluctuations are only weakly coupled to the nor.acoustic, so equations describing only the nonacoustic fluctuations (incompressible, variable density) would provide a good description of the turbulence. SPONSORING / MONITORING AGENCY NAME(S) AND ADDRESS(ES)AFOSR 07015 Motivation and ObjectivesA large fraction of the effort in turbulence research, including numerical simulations, experiments, theory and modeling, has been directed toward incompressible turbulence. This is largely due to the simplifications that the incompressible assumption allows, and to the belief that turbulence is in essence an incompressible phenomenon. However, many of the flows of technological interest are compressible (e.g. external aerodynamics, propulsion systems) leading to the requirement that our understanding of incompressible turbulence be translated to these compressible flows. An example of this is that most commonly used turbulence models for compressible flows are modifications of models developed for incompressible flows (e.g. the k-e model).Fortunately, in many flows the small-scale turbulence is nearly incompressible, albeit with non-constant density, even though the flow itself is highly compressible. For example, in much of the literature on compressible boundary layers (see the review by Spina et al., 1994), differences relative to an incompressible boundary layer (up to M = 5, say) are understood as being caused by variations in the mean density across the layer. This has long been appreciated and is the basis of the Van Driest (Van Driest 1951, 1956) transformation and the Morkovin hypothesis (Morkovin 1961).These observations suggest that a formulation based on low Mach number ...