Engineering topics

Gatski, T. B.

Publications and source records attributed to Gatski, T. B..

At least 19 records

NASA NTRS2006

Summary of the 2004 CFD Validation Workshop on Synthetic Jets and Turbulent Separation Control

A computational fluid dynamics (CFD) validation workshop for synthetic jets and turbulent separation control (CFDVAL2004) was held in Williamsburg, Virginia in March 2004. Three cases were investigated: synthetic jet into quiescent air, synthetic jet into a turbulent boundary layer crossflow, and flow over a hump model with no-flow-control, steady suction, and oscillatory control. This paper is a summary of the CFD results from the workshop. Although some detailed results are shown, mostly a broad viewpoint is taken, and the CFD state-of-the-art for predicting these types of flows is evaluated from a general point of view. Overall, for synthetic jets, CFD can only qualitatively predict the flow physics, but there is some uncertainty regarding how to best model the unsteady boundary conditions from the experiment consistently. As a result, there is wide variation among CFD results. For the hump flow, CFD as a whole is capable of predicting many of the particulars of this flow provided that tunnel blockage is accounted for, but the length of the separated region compared to experimental results is consistently overpredicted.

Rumsey, C. L.↗

NASA NTRS2004

Summary of the 2004 CFD Validation Workshop on Synthetic Jets and Turbulent Separation Control

A CFD validation workshop for synthetic jets and turbulent separation control (CFDVAL2004) was held in Williamsburg, Virginia in March 2004. Three cases were investigated: synthetic jet into quiescent air, synthetic jet into a turbulent boundary layer crossflow, and flow over a hump model with no-flow-control, steady suction, and oscillatory control. This paper is a summary of the CFD results from the workshop. Although some detailed results are shown, mostly a broad viewpoint is taken, and the CFD state-of-the-art for predicting these types of flows is evaluated from a general point of view. Overall, for synthetic jets, CFD can only qualitatively predict the flow physics, but there is some uncertainty regarding how to best model the unsteady boundary conditions from the experiment consistently. As a result. there is wide variation among CFD results. For the hump flow, CFD as a whole is capable of predicting many of the particulars of this flow provided that tunnel blockage is accounted for, but the length of the separated region compared to experimental results is consistently overpredicted.

Rumsey, C. L.↗

NASA NTRS2003

Analysis of Extensive Cross-Flow Separation using Higher-Order RANS Closure Models

The turbulent flow fields associated with the incompressible flow over a 6:1 prolate spheroid at high angle of attack, and the supersonic flow over an ogive cylinder are studied. Both these flows are characterized by large separation and vortical flow regions and therefore provide a challenging database for comparison of turbulent closure models. Of interest is the ability to predict the effects of separation and associated vortical motion common to both flows. Two turbulent models are investigated that each represent the class of linear eddy-viscosity models (LEVMs) and explicit algebraic stress models (EASMs). Since the EASM accounts for anisotropic effects, the in- fluence of these effects on flow field predictions can be assessed. The EASM model is shown to both improve the separation location prediction and pressure trough under the secondary vortex on the 6:1 prolate spheroid at high angle of attack and high Reynolds number, and improve the prediction of the separation location on a supersonic ogive cylinder.

Morison, J. H.↗

NASA NTRS2003

Analysis of Extensive Cross-Flow Separation using Higher-Order RANS Closure Models

The turbulent flow fields associated with the incompressible flow over a 6:1 prolate spheroid at high angle of attack, and the supersonic flow over an ogive cylinder are studied. Both these flows are characterized by large separation and vortical flow regions and therefore provide a challenging database for comparison of turbulent closure models. Of interest is the ability to predict the effects of separation and associated vortical motion common to both flows. Two turbulent models are investigated that each represent the class of linear eddy-viscosity models (LEVMs) and explicit algebraic stress models (EASMs). Since the EASM accounts for anisotropic effects, the influence of these effects on flow field predictions can be assessed. The EASM model is shown to both improve the separation location prediction and pressure trough under the secondary vortex on the 6:l prolate spheroid at high angle of attack and high Reynolds number, and improve the prediction of the separation location on a supersonic ogive cylinder.

Morrison, J. H.↗

NASA NTRS2002

Numerical Simulation of a Spatially Evolving Supersonic Turbulent Boundary Layer

The results from direct numerical simulations of a spatially evolving, supersonic, flat-plate turbulent boundary-layer flow, with free-stream Mach number of 2.25 are presented. The simulated flow field extends from a transition region, initiated by wall suction and blowing near the inflow boundary, into the fully turbulent regime. Distributions of mean and turbulent flow quantities are obtained and an analysis of these quantities is performed at a downstream station corresponding to Re(sub x)= 5.548 x10(exp 6) based on distance from the leading edge.

Gatski, T. B.↗

NASA NTRS2002

Elliptic Relaxation of a Tensor Representation for the Redistribution Terms in a Reynolds Stress Turbulence Model

A formulation to include the effects of wall proximity in a second-moment closure model that utilizes a tensor representation for the redistribution terms in the Reynolds stress equations is presented. The wall-proximity effects are modeled through an elliptic relaxation process of the tensor expansion coefficients that properly accounts for both correlation length and time scales as the wall is approached. Direct numerical simulation data and Reynolds stress solutions using a full differential approach are compared for the case of fully developed channel flow.

Carlson, J. R.↗

NASA NTRS2002

Modeling Disturbance Dynamics in Transitional and Turbulent Boundary Layers

The dynamics of an ensemble of linear disturbances in boundary-layer flows at various Reynolds numbers is studied through an analysis of the transport equations for the mean disturbance kinetic energy and energy dissipation rate. Effects of adverse and favorable pressure-gradients on the disturbance dynamics are also included in the analysis. Unlike the fully turbulent regime where nonlinear phase scrambling of the fluctuations affects the flow field even in proximity to the wall, the early stage transition regime fluctuations studied here are influenced across the boundary layer by the solid boundary. In addition, the dominating dynamics in the disturbance kinetic energy equation is governed by the energy production, pressure-transport and viscous diffusion - also in contrast to the fully turbulent regime. For the disturbance dissipation rate, a dynamic balance exists between the destruction and diffusion of dissipation.

Grosch, C. E.↗

NASA NTRS2002

Properties of the Residual Stress of the Temporally Filtered Navier-Stokes Equations

The development of a unifying framework among direct numerical simulations, large-eddy simulations, and statistically averaged formulations of the Navier-Stokes equations, is of current interest. Toward that goal, the properties of the residual (subgrid-scale) stress of the temporally filtered Navier-Stokes equations are carefully examined. Causal time-domain filters, parameterized by a temporal filter width 0 less than Delta less than infinity, are considered. For several reasons, the differential forms of such filters are preferred to their corresponding integral forms; among these, storage requirements for differential forms are typically much less than for integral forms and, for some filters, are independent of Delta. The behavior of the residual stress in the limits of both vanishing and in infinite filter widths is examined. It is shown analytically that, in the limit Delta to 0, the residual stress vanishes, in which case the Navier-Stokes equations are recovered from the temporally filtered equations. Alternately, in the limit Delta to infinity, the residual stress is equivalent to the long-time averaged stress, and the Reynolds-averaged Navier-Stokes equations are recovered from the temporally filtered equations. The predicted behavior at the asymptotic limits of filter width is further validated by numerical simulations of the temporally filtered forced, viscous Burger's equation. Finally, finite filter widths are also considered, and a priori analyses of temporal similarity and temporal approximate deconvolution models of the residual stress are conducted.

Pruett, C. D.↗

NASA NTRS2001

Turbulence Modeling: A NASA Perspective

This paper presents turbulence modeling from NASA's perspective. The topics include: 1) Hierarchy of Solution Methods; 2) Turbulence Modeling Focus; 3) Linear Eddy Viscosity Models; and 4) Nonlinear Eddy Viscosity Algebraic Stress Models.

Gatski, T. B.↗

NASA NTRS2001

Turbulence Modeling Effects on the Prediction of Equilibrium States of Buoyant Shear Flows

The effects of turbulence modeling on the prediction of equilibrium states of turbulent buoyant shear flows were investigated. The velocity field models used include a two-equation closure, a Reynolds-stress closure assuming two different pressure-strain models and three different dissipation rate tensor models. As for the thermal field closure models, two different pressure-scrambling models and nine different temperature variance dissipation rate, Epsilon(0) equations were considered. The emphasis of this paper is focused on the effects of the Epsilon(0)-equation, of the dissipation rate models, of the pressure-strain models and of the pressure-scrambling models on the prediction of the approach to equilibrium turbulence. Equilibrium turbulence is defined by the time rate (if change of the scaled Reynolds stress anisotropic tensor and heat flux vector becoming zero. These conditions lead to the equilibrium state parameters. Calculations show that the Epsilon(0)-equation has a significant effect on the prediction of the approach to equilibrium turbulence. For a particular Epsilon(0)-equation, all velocity closure models considered give an equilibrium state if anisotropic dissipation is accounted for in one form or another in the dissipation rate tensor or in the Epsilon(0)-equation. It is further found that the models considered for the pressure-strain tensor and the pressure-scrambling vector have little or no effect on the prediction of the approach to equilibrium turbulence.

Zhao, C. Y.↗

NASA NTRS1999

Predicting Turbulent Convective Heat Transfer in Three-Dimensional Duct Flows

The performance of an explicit algebraic stress model is assessed in predicting the turbulent flow and forced heat transfer in straight ducts, with square, rectangular, trapezoidal and triangular cross-sections, under fully developed conditions over a range of Reynolds numbers. Iso-thermal conditions are imposed on the duct walls and the turbulent heat fluxes are modeled by gradient-diffusion type models. At high Reynolds numbers (>/= 10(exp 5)), wall functions are used for the velocity and temperature fields; while at low Reynolds numbers damping functions are introduced into the models. Hydraulic parameters such as friction factor and Nusselt number are well predicted even when damping functions are used, and the present formulation imposes minimal demand on the number of grid points without any convergence or stability problems. Comparison between the models is presented in terms of the hydraulic parameters, friction factor and Nusselt number, as well as in terms of the secondary flow patterns occurring within the ducts.

Rokni, M.↗

NASA NTRS1999

Towards a Rational Model for the Triple Velocity Correlations of Turbulence

This paper presents a rational approach to modelling the triple velocity correlations that appear in the transport equations for the Reynolds stresses. All existing models of these correlations have largely been formulated on phenomenological grounds and are defective in one important aspect: they all neglect to allow for the dependence of these correlations on the local gradients of mean velocity. The mathematical necessity for this dependence will be demonstrated in the paper. The present contribution lies in the novel use of Group Representation Theory to determine the most general tensorial form of these correlations in terms of all the second- and third-order tensor quantities that appear in the exact equations that govern their evolution. The requisite representation did not exist in the literature and therefore had to be developed specifically for this purpose by Professor G. F. Smith. The outcome of this work is a mathematical framework for the construction of algebraic, explicit, and rational models for the triple velocity correlations that are theoretically consistent and include all the correct dependencies. Previous models are reviewed, and all are shown to be an incomplete subset of this new representation, even to lowest order.

Younis, B. A.↗

NASA NTRS1999

Asymptotic Behavior of Ensemble-Averaged Linear Disturbances in Homogeneous Shear Flow

In order to expand the predictive capability of single-point turbulence closure models too account for the early-stage transition regime, a methodology for the formulation and calibration of model equations for the ensemble-averaged disturbance kinetic energy and energy dissipation rate is presented. The calibration is based on homogeneous shear flow where disturbances can be described by rapid distort,ion theory (RDT). The relationship between RDT and linear stability theory is exploit,c d in order to obtain a closed set, of modeled equations. The linear disturbance equations are solved directly so that, the numerical simulation yields a database from which the closure coefficient,s in the ensemble-averaged disturbance equations can he determined.

Thacker, W. D.↗

NASA NTRS1999

Predicting Buoyant Shear Flows Using Anisotropic Dissipation Rate Models

This paper examines the modeling of two-dimensional homogeneous stratified turbulent shear flows using the Reynolds-stress and Reynolds-heat-flux equations. Several closure models have been investigated-, the emphasis is placed on assessing the effect of modeling the dissipation rate tensor in the Reynolds-stress equation. Three different approaches are considered: one is an isotropic approach while the other two are anisotropic approaches. The isotropic approach is based on Kolmogorov's hypothesis and a dissipation rate equation modified to account for vortex stretching. One of the anisotropic approaches is based on an algebraic representation of the dissipation rate tensor, while another relies on solving a modeled transport equation for this tensor. In addition, within the former anisotropic approach, two different algebraic representations are examined one is a function of the Reynolds-stress anisotropy tensor, and the other is a function of' the mean velocity gradients. The performance of these closure models is evaluated against experimental and direct numerical simulation data of pure shear flows. pure buoyant flows and buoyant shear flows. Calculations have been carried out over a range of Richardson numbers (Ri) and two different Prandtl numbers (Pr); thus the effect of Pr on the development of counter-gradient heat flux in a stratified shear flow can be assessed. At low Ri, the isotropic model performs well in the predictions of stratified shear flows; however, its performance deteriorates as Ri increases. At high Ri, the transport equation model for the dissipation rate tensor gives the best result. Furthermore, the results also lend credence to the algebraic dissipation rate model based on the Reynolds stress anisotropy tensor. Finally, it is found that Pr has an effect on the development of counter-gradient heat flux. The calculations show that, under the action of shear, counter-gradient heat flux does not occur even at Ri = 1 in an air flow.

So, R. M. C.↗

NASA NTRS1999

Modeling the Dynamics of Ensemble-Averaged Linear Disturbances in Homogeneous Shear Flow

In order to expand the predictive capability of single-point turbulence closure models to account for the early-stage transition regime, a methodology for the formulation and calibration of model equations for the ensemble-averaged disturbance kinetic energy and energy dissipation rate is presented. The calibration is based on homogeneous shear flow where disturbances can be described by rapid distortion theory (RDT). The relationship between RDT and linear stability theory is exploited in order to obtain a closed set of modeled equations. The linear disturbance equations are solved directly so that the numerical simulation yields a database from which the closure coefficients in the ensemble-averaged disturbance equations can be determined. Key words: transition/turbulence modeling, homogeneous shear, rapid distortion theory.

Thacker, W. D.↗

NASA NTRS1999

Computation of Turbulent Wake Flows in Variable Pressure Gradient

Transport aircraft performance is strongly influenced by the effectiveness of high-lift systems. Developing wakes generated by the airfoil elements are subjected to strong pressure gradients and can thicken very rapidly, limiting maximum lift. This paper focuses on the effects of various pressure gradients on developing symmetric wakes and on the ability of a linear eddy viscosity model and a non-linear explicit algebraic stress model to accurately predict their downstream evolution. In order to reduce the uncertainties arising from numerical issues when assessing the performance of turbulence models, three different numerical codes with the same turbulence models are used. Results are compared to available experimental data to assess the accuracy of the computational results.

Duquesne, N.↗

NASA NTRS1997

Time Evolution of Modeled Reynolds Stresses in Planar Homogeneous Flows

The analytic expression of the time evolution of the Reynolds stress anisotropy tensor in all planar homogeneous flows is obtained by exact integration of the modeled differential Reynolds stress equations. The procedure is based on results of tensor representation theory, is applicable for general pressure-strain correlation tensors, and can account for any additional turbulence anisotropy effects included in the closure. An explicit solution of the resulting system of scalar ordinary differential equations is obtained for the case of a linear pressure-strain correlation tensor. The properties of this solution are discussed, and the dynamic behavior of the Reynolds stresses is studied, including limit cycles and sensitivity to initial anisotropies.

Jongen, T.↗

NASA NTRS1997

Predicting NonInertial Effects with Algebraic Stress Models which Account for Dissipation Rate Anisotropies

Three types of turbulence models which account for rotational effects in noninertial frames of reference are evaluated for the case of incompressible, fully developed rotating turbulent channel flow. The different types of models are a Coriolis-modified eddy-viscosity model, a realizable algebraic stress model, and an algebraic stress model which accounts for dissipation rate anisotropies. A direct numerical simulation of a rotating channel flow is used for the turbulent model validation. This simulation differs from previous studies in that significantly higher rotation numbers are investigated. Flows at these higher rotation numbers are characterized by a relaminarization on the cyclonic or suction side of the channel, and a linear velocity profile on the anticyclonic or pressure side of the channel. The predictive performance of the three types of models are examined in detail, and formulation deficiencies are identified which cause poor predictive performance for some of the models. Criteria are identified which allow for accurate prediction of such flows by algebraic stress models and their corresponding Reynolds stress formulations.

Jongen, T.↗