Turbulence modeling for hypersonic flows

Turbulence modeling for high speed compressible flows is described and discussed. Starting with the compressible Navier-Stokes equations, methods of statistical averaging are described by means of which the Reynolds-averaged Navier-Stokes equations are developed. Unknown averages in these equations are approximated using various closure concepts. Zero-, one-, and two-equation eddy viscosity models, algebraic stress models and Reynolds stress transport models are discussed. Computations of supersonic and hypersonic flows obtained using several of the models are discussed and compared with experimental results. Specific examples include attached boundary layer flows, shock wave boundary layer interactions and compressible shear layers. From these examples, conclusions regarding the status of modeling and recommendations for future studies are discussed

Pressure and convective heat-transfer measure- ments in a shock tunnel using several test gases

Pressure and convective heat-transfer measurements on hemisphere-cylinder, blunted 30 degree cone, in shock tunnel using several test gase

A method for solving the nonsimilar laminar boundary-layer equations including foreign gas injection

Solving nonsimilar laminar boundary layer equations including foreign gas injectio

On the period of the coherent structure in boundary layers at large Reynolds numbers

The period of the large coherent structure in a subsonic, compressible, turbulent boundary layer was determined using the autocorrelation of the velocity and pressure fluctuations for Reynolds numbers between 5,000 and 35,000. In low Reynolds number flows the overall correlation period scaled with the outer variables - namely, the free stream velocity and the boundary layer thickness

Turbulence modeling for compressible flows

Material prepared for a course on Applications and Fundamentals of Turbulence given at the University of Tennessee Space Institute, January 10 and 11, 1977, is presented. A complete concept of turbulence modeling is described, and examples of progess for its use in computational aerodynimics are given. Modeling concepts, experiments, and computations using the concepts are reviewed in a manner that provides an up-to-date statement on the status of this problem for compressible flows

Modeling of turbulent separated flows for aerodynamic applications

Steady, high speed, compressible separated flows modeled through numerical simulations resulting from solutions of the mass-averaged Navier-Stokes equations are reviewed. Emphasis is placed on benchmark flows that represent simplified (but realistic) aerodynamic phenomena. These include impinging shock waves, compression corners, glancing shock waves, trailing edge regions, and supersonic high angle of attack flows. A critical assessment of modeling capabilities is provided by comparing the numerical simulations with experiment. The importance of combining experiment, numerical algorithm, grid, and turbulence model to effectively develop this potentially powerful simulation technique is stressed

Age measurements of the Precambrian rocks of the Death Valley-Mojave Desert region, California

Ar^(40)-K^(40) and Sr^(87)-R^(87) age measurements in the eastern Mojave Desert indicate two separate early Precambrian events (see table). The older event is approximately 1650 m.y. old and is evidenced by pegmatites and associated metamorphic rocks in the Mountain Pass district. Ages were measured on coarse muscovite and potassium feldspar, MP-1 and MP-2, from a pegmatite which cuts across biotite-bearing gneisses, MP-7 and MP-9. These data confirm the widespread areal extent of this ancient metamorphic terrane. Ages of biotite, MP-21 and MP-22, from the shonkinite, which intrudes the metamorphic rocks, at Mountain Pass and the Rb-Sr age of potassium feldspar, MM-3f, from granite in the Marble Mountains suggest a period of igneous intrusion in the 1350 to 1410 m.y. interval. Metamorphic rocks in the central Panamint Range have been mapped and are shown to be stratigraphically early Precambrian. K-Ar ages of approximately 80 m.y. have been measured on biotite, muscovite, and hornblende. The minerals show no memory of a Precambrian age. The early Precambrian rocks show no evidence of a younger period of metamorphism. However, a younger metamorphism can be recognized in the overlying Precambrian(?) Noonday dolomite and Johnnie formation

GW method with the self-consistent Sternheimer equation

We propose a novel approach to quasiparticle GW calculations which does not require the computation of unoccupied electronic states. In our approach the screened Coulomb interaction is evaluated by solving self-consistent linear-response Sternheimer equations, and the noninteracting Green's function is evaluated by solving inhomogeneous linear systems. The frequency-dependence of the screened Coulomb interaction is explicitly taken into account. In order to avoid the singularities of the screened Coulomb interaction the calculations are performed along the imaginary axis, and the results are analytically continued to the real axis through Pade' approximants. As a proof of concept we implemented the proposed methodology within the empirical pseudopotential formalism and we validated our implementation using silicon as a test case. We examine the advantages and limitations of our method and describe promising future directions.Comment: 18 pages, 6 figure