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

Assessment of closure coefficients for compressible-flow turbulence models

A critical assessment is made of the closure coefficients used for turbulence length scale in existing models of the transport equation, with reference to the extension of these models to compressible flow. It is shown that to satisfy the compressible 'law of the wall', the model coefficients must actually be functions of density gradients. The magnitude of the errors that result from neglecting this dependence on density varies with the variable used to specify the length scale. Among the models investigated, the k-omega model yields the best performance, although it is not completely free from errors associated with density terms. Models designed to reduce the density-gradient effect to an insignificant level are proposed

Energy-balance climate models

An introductory survey of the global energy balance climate models is presented with an emphasis on analytical results. A sequence of increasingly complicated models involving ice cap and radiative feedback processes are solved and the solutions and parameter sensitivities are studied. The model parameterizations are examined critically in light of many current uncertainties. A simple seasonal model is used to study the effects of changes in orbital elements on the temperature field. A linear stability theorem and a complete nonlinear stability analysis for the models are developed. Analytical solutions are also obtained for the linearized models driven by stochastic forcing elements. In this context the relation between natural fluctuation statistics and climate sensitivity is stressed

An assessment and application of turbulence models for hypersonic flows

The current approach to the Accurate Computation of Complex high-speed flows is to solve the Reynolds averaged Navier-Stokes equations using finite difference methods. An integral part of this approach consists of development and applications of mathematical turbulence models which are necessary in predicting the aerothermodynamic loads on the vehicle and the performance of the propulsion plant. Computations of several high speed turbulent flows using various turbulence models are described and the models are evaluated by comparing computations with the results of experimental measurements. The cases investigated include flows over insulated and cooled flat plates with Mach numbers ranging from 2 to 8 and wall temperature ratios ranging from 0.2 to 1.0. The turbulence models investigated include zero-equation, two-equation, and Reynolds-stress transport models

Calculations of Supersonic and Hypersonic Flows using Compressible Wall Functions

The present paper presents a numerical procedure to calculate supersonic and hypersonic flows using the compressible law of the wall. The turbulence models under consideration include the Launder-Reece-Rodi-Gibson Reynolds-stress model and the k-epsilon model. The models coupled with the proposed wall function technique have been tested in both separated and unseparated flows. The flows include (1) an insulated flat plate flow over a range of Mach numbers, (2) a Mach 5 flat plate flow with cold wall conditions, (3) a two dimensional supersonic compression corner flow, (4) a hypersonic flow over an axisymmetric flare, and (5) a hypersonic flow over a 2-D compression corner. Results indicate that the wall function technique gives improved predictions of skin friction and heat transfer in separated flows compared with models using wall dampers. Predictions of the extent of separation are not improved over the wall damper models except with the Reynolds-stress model for the supersonic compression corner flow case

Foster Parents\u27 Reasons for Fostering and Foster Family Utilization

Better utilization of foster families might be linked to parents\u27 reasons for fostering. This study used data from the National Survey of Current and Former Foster Parents to examine relationships between reasons for fostering and types of services and length of service foster parents provide. Top reasons for fostering were child-centered. The least endorsed reasons were self-oriented. Those who fostered to help children with special problems were more likely to have a child placed, had more children, and had fostered more types of special needs children. Parents who fostered because their children were grown were more likely to have a child placed, had more children, and were more likely to intend to continue fostering. Conversely, parents who wanted to be loved or who wanted companionship fostered fewer children. Implications for improving foster family utilization are discussed

A method to quantitatively evaluate Hamaker constant using the jump-into-contact effect in Atomic Force microscopy

We find that the jump-into-contact of the cantilever in the atomic force microscope (AFM) is caused by an inherent instability in the motion of the AFM cantilever. The analysis is based on a simple model of the cantilever moving in a nonlinear force field. We show that the jump-into-contact distance can be used to find the interaction of the cantilever tip with the surface. In the specific context of the attractive van der Waals interaction, this method can be realized as a new method of measuring the Hamaker constant for materials. The Hamaker constant is determined from the deflection of the cantilever at the jump-into-contact using the force constant of the cantilever and the tip radius of curvature, all of which can be obtained by measurements. The results have been verified experimentally on a sample of cleaved mica, a sample of Si wafer with natural oxide and a silver film, using a number of cantilevers with different spring constants. We emphasize that the method described here is applicable only to surfaces that have van der Waals interaction as the tip-sample interaction. We also find that the tip to sample separation at the jump-into-contact is simply related to the cantilever deflection at this point, and this provides a method to exactly locate the surface.Comment: 11 pages, 4 figures, 1 tabl