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The purpose of this abstract is to review and assess the application of quantitative models (Gratz numerical correlation model, radiative loss model, yield stress model, surface structure model, and kinematic wave model) of lava flows on Mars. These theoretical models were applied to Martian flow data to aid in establishing the composition of the lava or to determine other eruption conditions such as eruption rate or duration.
A high-speed shear layer is studied using compressibility corrected Reynolds stress turbulence model which employs newly developed model for pressure-strain correlation. MacCormack explicit prediction-corrector method is used for solving the governing equations and the turbulence transport equations. The stiffness arising due to source terms in the turbulence equations is handled by a semi-implicit numerical technique. Results obtained using the new model show a sharper reduction in growth rate with increasing convective Mach number. Some improvements were also noted in the prediction of the normalized streamwise stress and Reynolds shear stress. The computed results are in good agreement with the experimental data.
The roles of pressure-strain and turbulent diffusion models in the numerical calculation of turbulent plane channel flows with second-moment closure models are investigated. Three turbulent diffusion and five pressure-strain models are utilized in the computations. The main characteristics of the mean flow and the turbulent fields are compared against experimental data. All the features of the mean flow are correctly predicted by all but one of the Reynolds stress closure models. The Reynolds stress anisotropies in the log layer are predicted to varying degrees of accuracy (good to fair) by the models. None of the models could predict correctly the extent of relaxation towards isotropy in the wake region near the center of the channel. Results from the directional numerical simulation are used to further clarify this behavior of the models.
The roles of pressure-strain and turbulent diffusion models in the numerical calculation of turbulent plane channel flows with second-moment closure models are investigated. Three turbulent diffusion and five pressure-strain models are utilized in the computations. The main characteristics of the mean flow and the turbulent fields are compared against experimental data. All the features of the mean flow are correctly predicted by all but one of the Reynolds stress closure models. The Reynolds stress anisotropies in the log layer are predicted to varying degrees of accuracy (good to fair) by the models. None of the models could predict correctly the extent of relaxation towards isotropy in the wake region near the center of the channel. Results from the directional numerical simulation are used to further clarify this behavior of the models.
NASTRAN computer program applications in stress analysis performed on Skylab hardware
There has been a recent interest in determining high statistical reliability in risk assessment of aircraft components. The potential consequences are identified of incorrectly assuming a particular statistical distribution for stress or strength data used in obtaining the high reliability values. The computation of the reliability is defined as the probability of the strength being greater than the stress over the range of stress values. This method is often referred to as the stress-strength model. A sensitivity analysis was performed involving a comparison of reliability results in order to evaluate the effects of assuming specific statistical distributions. Both known population distributions, and those that differed slightly from the known, were considered. Results showed substantial differences in reliability estimates even for almost nondetectable differences in the assumed distributions. These differences represent a potential problem in using the stress-strength model for high reliability computations, since in practice it is impossible to ever know the exact (population) distribution. An alternative reliability computation procedure is examined involving determination of a lower bound on the reliability values using extreme value distributions. This procedure reduces the possibility of obtaining nonconservative reliability estimates. Results indicated the method can provide conservative bounds when computing high reliability. An alternative reliability computation procedure is examined involving determination of a lower bound on the reliability values using extreme value distributions. This procedure reduces the possibility of obtaining nonconservative reliability estimates. Results indicated the method can provide conservative bounds when computing high reliability.
Electrochemical kinetic and mass transport model for studying stress corrosion crack propagation in Ti
We consider the applications of stress-strength models in studies involving clinical trials. When studying the effects and side effects of certain procedures (treatments), it is often the case that observations are correlated due to subject effect, repeated measurements and observing many characteristics simultaneously. We develop maximum likelihood estimator (MLE) and uniform minimum variance unbiased estimator (UMVUE) of the reliability which in clinical trial studies could be considered as the chances of increased side effects due to a particular procedure compared to another. The results developed apply to both univariate and multivariate situations. Also, for the univariate situations we develop simple to use lower confidence bounds for the reliability. Further, we consider the cases when both stress and strength constitute time dependent processes. We define the future reliability and obtain methods of constructing lower confidence bounds for this reliability. Finally, we conduct simulation studies to evaluate all the procedures developed and also to compare the MLE and the UMVUE.
A second-order differential Reynolds Stress turbulence model has been applied to the Favre-averaged Navier-Stokes equations for the study of supersonic flows undergoing hydrogen-air chemical reactions. An assumed Beta Probability Density Function is applied to account for the chemical source terms in the conservation equations. An algebraic Reynolds Flux model is used for the fluctuating density-velocity as well as the species mass fraction-velocity correlations. The variances of temperature and species fluctuations are also modelled using an algebraic flux technique. A seven-species, seven-reaction finite rate chemistry mechanism is used to simulate the combustion processes. The resulting formulation is validated by comparison with experimental data on reacting supersonic axisymmetric jets. Results obtained for specific conditions indicate that the effect of chemical reaction on the turbulence is significant.
This paper presents a numerical study of the effects of expansion ratio on two-dimensional separating and reattaching flows in plane backward-facing step geometries with parallel walls. Closure of the Reynolds equations was achieved by four different turbulence models: k-epsilon, 'modified' k-epsilon, algebraic stress, and 'modified' algebraic stress models. The k-epsilon model relates the Reynolds stresses to the mean rate of strain through the definition of an isotropic turbulent viscosity. The more advanced algebraic stress model calculates the stresses from implicit algebraic relationships containing the stresses themselves, the mean rate of strain, and the turbulent kinetic energy and its dissipation rate. 'Modified' versions of the models employ a new dissipation rate equation whose production term was made more sensitive to streamwise curvature effects. A new nonequilibrium wall function treatment proposed by Chieng and Launder (1980) was also incorporated into each model.
A second-order differential Reynolds Stress turbulence model has been applied to the Favre-averaged Navier-Stokes equations for the study of supersonic flows with finite-rate chemistry and radiation. An assumed Beta Probability Density Function is applied to account for the chemical source terms and the radiative flux terms in the conservation equations. A seven-species, seven-reaction finite rate chemistry mechanism is used to simulate the combustion process. The tangent slab approximation is used in radiative flux formulation. A pseudo-gray gas model is used to represent the absorption-emission characteristics of the participating species. The turbulence/radiation interaction is achieved via a new formulation. The resulting formulation is validated by comparison with experimental data on reacting supersonic axisymmetric jets. Results obtained for specific conditions indicate that the effect of chemical reaction on the turbulence is significant. Also, the radiative heat transfer is enhanced by the turbulence.
With the aid of near-wall asymptotic analysis and results of direct numerical simulation, a new near-wall Reynolds stress model (NNWRS) is formulated based on the SSG high-Reynolds-stress model with wall-independent near-wall corrections. Only one damping function is used for flows with a wide range of Reynolds numbers to ensure that the near-wall modifications diminish away from the walls. The model is able to reproduce complicated flow phenomena induced by complex geometry, such as flow recirculation, reattachment and boundary-layer redevelopment in backward-facing step flow and secondary flow in three-dimensional square duct flow. In simple flows, including fully developed channel/pipe flow, Couette flow and boundary-layer flow, the wall effects are dominant, and the NNWRS model predicts less degree of turbulent anisotropy in the near-wall region compared with a wall-dependent near-wall Reynolds Stress model (NWRS) developed by So and colleagues. The comparison of the predictions given by the two models rectifies the misconception that the overshooting of skin friction coefficient in backward-facing step flow prevalent in those near-wall, models with wall normal is caused by he use of wall normal.
The Menter Shear Stress Transport (SST) k . turbulence model is one of the most widely used two-equation Reynolds-averaged Navier-Stokes turbulence models for aerodynamic analyses. The model extends Menter s baseline (BSL) model to include a limiter that prevents the calculated turbulent shear stress from exceeding a prescribed fraction of the turbulent kinetic energy via a proportionality constant, a1, set to 0.31. Compared to other turbulence models, the SST model yields superior predictions of mild adverse pressure gradient flows including those with small separations. In shock - boundary layer interaction regions, the SST model produces separations that are too large while the BSL model is on the other extreme, predicting separations that are too small. In this paper, changing a1 to a value near 0.355 is shown to significantly improve predictions of shock separated flows. Several cases are examined computationally and experimental data is also considered to justify raising the value of a1 used for shock separated flows.
The turbulence models available for the prediction of complex turbulent shear layers are reviewed in this paper, concentrating mainly on three-dimensional flows, flows subjected to curvature and body rotation, separated flows, and vortex flows. A critical review of zero-equation, one-equation, two-equation, algebraic Reynolds stress, and full Reynolds stress models are carried out, with a specific emphasis on their applicability to complex flows. It is concluded that algebraic eddy viscosity models and kappa-epsilon/kappa-omega models, with a constant value of coefficients, are not adequate for complex flows. The models which include a description of stresses, either through an algebraic Reynolds stress model or a full Reynolds stress model, are essential for adequate prediction of these flows. It is recommended that systematic experimental investigations be carried out to isolate various complex interactions in order to understand and model the various effects and to carry out an extension of the present models to include complex flows.
The objective of the present research is to develop improved turbulence models for the computation of complex flows through turbomachinery passages, including the effects of streamline curvature, heat transfer and secondary flows. Advanced turbulence models are crucial for accurate prediction of rocket engine flows, due to existance of very large extra strain rates, such as strong streamline curvature. Numerical simulation of the turbulent flows in strongly curved ducts, including two 180-deg ducts, one 90-deg duct and a strongly concave curved turbulent boundary layer have been carried out with Reynolds stress models (RSM) and algebraic Reynolds stress models (ARSM). An improved near-wall pressure-strain correlation has been developed for capturing the anisotropy of turbulence in the concave region. A comparative study of two modes of transition in gas turbine, the by-pass transition and the separation-induced transition, has been carried out with several representative low-Reynolds number (LRN) k-epsilon models. Effects of blade surface pressure gradient, freestream turbulence and Reynolds number on the blade boundary layer development, and particularly the inception of transition are examined in detail. The present study indicates that the turbine blade transition, in the presence of high freestream turbulence, is predicted well with LRN k-epsilon models employed. The three-dimensional Navier-Stokes procedure developed by the present authors has been used to compute the three-dimensional viscous flow through the turbine nozzle passage of a single stage turbine. A low Reynolds number k-epsilon model and a zonal k-epsilon/ARSM (algebraic Reynolds stress model) are utilized for turbulence closure. An assessment of the performance of the turbulence models has been carried out. The two models are found to provide similar predictions for the mean flow parameters, although slight improvement in the prediction of some secondary flow quantities has been obtained by the ARSM model. It's found that the wake profiles inside the endwall boundary layers are predicted better than those near the mid-span.
The paper presents a brief account of various turbulence models employed in the computation of turbulent flows, and evaluates the application of these models to selected internal flow configurations. The main conclusions of this analysis are: (1) the k-epsilon model is used in a majority of all the two-dimensional flow calculations reported in the literature; (2) modified forms of the k-epsilon model improve the performance for flows with streamline curvature and heat transfer; (3) for flows with swirl, the k-epsilon model performs rather poorly (the algebraic stress model performs better in this case); and (4) for flows with regions of secondary flow (noncircular duct flows), the algebraic stress model performs fairly well. Two important factors in the numerical solution of the model equations, namely false diffusion and inlet boundary conditions, are discussed. The existence of countergradient transport and its implications in turbulence modeling are examined. Finally, some recommendations for improving the model performance are made. The need for detailed experimental data in flows with strong curvature is emphasized.
This viewgraph presentation discusses turbulence modeling requirements, development philosophy, and approach; two major areas of concentration (high speed and low speed turbulence modeling); high speed turbulence modeling; compressibility effects; turbulence models adapted to USA code; M = 9.2 flat plate flow; Mach 7.05 flow over axisymmetric flare; Mach 8.6 flow over cold wall edge; low speed turbulence modeling; turbulence models being assessed; turbulence model deck structure and integration with Navier-Stokes solver; nonlinear algebraic-stress model; rotation modified k-epsilon model; and Reynolds stress model.
The critical state of vortex cores downstream of vortex breakdown has been studied. Base vortical flows were computed using the Reynolds-averaged, axisymmetric Navier-Stokes equations. Standard K - epsilon, RNG and second-order Reynolds stress models were employed. Results indicate that the return to supercriticality is highly dependent on the turbulence model. The K - epsilon model predicted a rapid return of the vortex to supercritical conditions, the location of which showed little sensitivity to changes in the swirl ratio. The Reynolds stress model predicted that the vortex remains subcritical to the end of the domain for each of the swirl ratios employed, and provided results in qualitative agreement with experimental work. The RNG model produced intermediate results, with a downstream movement in the critical location with increasing swirl. Calculations for which area reductions were introduced at the exit in a subcritical flow were also performed using the Reynolds stress model. The structure of the resulting recirculation zone was altered significantly. However, when area reductions were employed within supercritical flows as predicted using the two-equation models, no significant influence on the recirculation zone was noted.