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Gatski, T. B.

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

At least 37 records · Page 2
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NASA NTRS1992

On explicit algebraic stress models for complex turbulent flows

Explicit algebraic stress models that are valid for three-dimensional turbulent flows in noninertial frames are systematically derived from a hierarchy of second-order closure models. This represents a generalization of the model derived by Pope who based his analysis on the Launder, Reece, and Rodi model restricted to two-dimensional turbulent flows in an inertial frame. The relationship between the new models and traditional algebraic stress models -- as well as anistropic eddy visosity models -- is theoretically established. The need for regularization is demonstrated in an effort to explain why traditional algebraic stress models have failed in complex flows. It is also shown that these explicit algebraic stress models can shed new light on what second-order closure models predict for the equilibrium states of homogeneous turbulent flows and can serve as a useful alternative in practical computations.

Gatski, T. B.↗
NASA NTRS1992

Development of turbulence models for shear flows by a double expansion technique

Turbulence models are developed by supplementing the renormalization group (RNG) approach of Yakhot and Orszag with scale expansions for the Reynolds stress and production of dissipation terms. The additional expansion parameter (eta) is the ratio of the turbulent to mean strain time scale. While low-order expansions appear to provide an adequate description of the Reynolds stress, no finite truncation of the expansion for the production of dissipation term in powers of eta suffices - terms of all orders must be retained. Based on these ideas, a new two-equation model and Reynolds stress transport model are developed for turbulent shear flows. The models are tested for homogeneous shear flow and flow over a backward facing step. Comparisons between the model predictions and experimental data are excellent.

Yakhot, V.↗
NASA NTRS1991

Development of turbulence models for shear flows by a double expansion technique

Turbulence models are developed by supplementing the renormalization group (RNG) approach of Yakhot and Orszag with scale expansions for the Reynolds stress and production of dissipation terms. The additional expansion parameter (eta) is the ratio of the turbulent to mean strain time scale. While low-order expansions appear to provide an adequate description of the Reynolds stress, no finite truncation of the expansion for the production of dissipation term in powers of eta suffices - terms of all orders must be retained. Based on these ideas, a new two-equation model and Reynolds stress transport model are developed for turbulent shear flows. The models are tested for homogeneous shear flow and flow over a backward facing step. Comparisons between the model predictions and experimental data are excellent.

Yakhot, V.↗
NASA NTRS1990

Assessment and application of Reynolds stress closure models to high-speed compressible flows

The paper presents results from the development of higher order closure models for the phenomological modeling of high-speed compressible flows. The work presented includes the introduction of an improved pressure-strain correlationi model applicable in both the low- and high-speed regime as well as modifications to the isotropic dissipation rate to account for dilatational effects. Finally, the question of stiffness commonly associated with the solution of two-equation and Reynolds stress transport equations in wall-bounded flows is examined and ways of relaxing these restrictions are discussed.

Gatski, T. B.↗
NASA NTRS1990

The structure and dynamics of bubble-type vortex breakdown

A unique discrete form of the Navier-Stokes equations for unsteady, three-dimensional, incompressible flow has been used to study vortex breakdown numerically. A Burgers-type vortex was introduced along the central axis of the computational domain, and allowed to evolve in space and time. By varying the strength of the vortex and the free stream axial velocity distribution, using a previously developed Rossby number criterion as a guide, the location and size of the vortex breakdown region was controlled. While the boundaries of the vortex breakdown bubble appear to be nominally symmetric, the internal flow field is not. Consequently, the mechanisms for mixing and entrainment required to sustain the bubble region are different from those suggested by earlier axisymmetric models. Results presented in this study, for a Reynolds number of 200, are in good qualitative agreement with higher Reynolds number experimental observations, and a variety of plots have been presented to help illuminate the fluid physics.

Spall, R. E.↗
NASA NTRS1989

The numerical solution of the Navier-Stokes equations for 3-dimensional, unsteady, incompressible flows by compact schemes

The present numerical method for the solution of unsteady, incompressible three-dimensional flow Navier-Stokes equations using velocity-vorticity variables and irregular Cartesian grids proceeds by solving: (1) equations of Cauchy-Riemann type for the velocity; and (2) transport-diffusion equations for the vorticity, whose solenoidal vorticity components are generated by a Poisson equation for an appropriate scalar potential. Iterations are used to solve the finite difference equations, facilitating the use of vector and parallel-computing methods; numerical experiments have verified the method's second-order spatial and temporal accuracy.

Gatski, T. B.↗
NASA NTRS1989

An analysis of curvature effects for the control of wall-bounded shear flows

The Reynolds stress transport equations are used to predict the effects of simultaneous and sequential combinations of distortions on turbulent boundary layers. The equations are written in general orthogonal curvilinear coordinates, with the curvature terms expressed in terms of the principal radii of curvature of the respective coordinate surfaces. Results are obtained for the cases of two-dimensional and three-dimensional flows in the limit where production and pressure-strain redistribution dominate over diffusion effects.

Gatski, T. B.↗
NASA NTRS1987

A criterion for vortex breakdown

A criterion for the onset of vortex breakdown is proposed. Based upon previous experimental, computational, and theoretical studies, an appropriately defined local Rossby number is used to delineate the region where breakdown occurs. In addition, new numerical results are presented which further validate this criterion. A number of previous theoretical studies concentrating on inviscid standing-wave analyses for trailing wing-tip vortices are reviewed and reinterpreted in terms of the Rossby number criterion. Consistent with previous studies, the physical basis for the onset of breakdown is identified as the ability of the flow to sustain such waves. Previous computational results are reviewed and re-evaluated in terms of the proposed breakdown criterion. As a result, the cause of breakdown occurring near the inflow computational boundary, common to several numerical studies, is identified. Finally, previous experimental studies of vortex breakdown for both leading edge and trailing wing-tip vortices are reviewed and quantified in terms of the Rossby number criterion.

Spall, R. E.↗
NASA NTRS1987

Numerical simulation of three-dimensional unsteady vortex flow using a compact vorticity-velocity algorithm

A numerical algorithm is presented which is used to solve the unsteady, fully three-dimensional, incompressible Navier-Stokes equations in vorticity-velocity variables. A discussion of the discrete approximation scheme is presented as well as the solution method used to solve the resulting algebraic set of difference equations. Second order spatial and temporal accuracy is verified through solution comparisons with exact results obtained for steady three-dimensional stagnation point flow and unsteady axisymmetric vortex spin-up. In addition, results are presented for the problem of unsteady bubble-type vortex breakdown with emphasis on internal bubble dynamics and structure.

Gatski, T. B.↗
NASA NTRS1987

On a criterion for vortex breakdown

A criterion for the onset of vortex breakdown is proposed. Based upon previous experimental, computational, and theoretical studies, an appropriately defined local Rossby number is used to delineate the region where breakdown occurs. In addition, new numerical results are presented which further validate this criterion. A number of previous theoretical studies concentrating on inviscid standing-wave analyses for trailing wing-tip vortices are reviewed and reinterpreted in terms of the Rossby number criterion. Consistent with previous studies, the physical basis for the onset of breakdown is identified as the ability of the flow to sustain such waves. Previous computational results are reviewed and re-evaluated in terms of the proposed breakdown criterion. As a result, the cause of breakdown occurring near the inflow computational boundary, common to several numerical studies, is identified. Finally, previous experimental studies of vortex breakdown for both leading edge and trailing wing-tip vortices are reviewed and quantified in terms of the Rossby number criterion.

Spall, R. E.↗
NASA NTRS1987

A numerical simulation of vortex breakdown

A numerical simulation of vortex breakdown using the time-dependent Navier-Stokes equations is performed. Unlike previous studies, the numerical algorithm, formulated in terms of the velocity and vorticity, is not restricted by axisymmetry conditions. The vortex is parameterized in terms of the Reynolds number and Rossby number. The resulting breakdown structure is analyzed using contour plots of velocity, vorticity and pressure as well as axial, radial, and swirl velocity profiles at various streamwise locations. The relationship of these results to experimentally observed structures and previous numerical results is discussed.

Spall, R. E.↗
NASA NTRS1985

Drag characteristics of unsteady, perturbed boundary layer flows

A series of time-dependent numerical computations have been performed for the flow of an unsteady boundary layer over an embedded cavity, which is aligned normal to the flow direction. The unsteady flow is the result of the imposition of a Stuart vortex, at the inflow boundary of the computational domain, onto an otherwise unperturbed two-dimensional laminar boundary layer flow. This produces a strongly vortical, but spatially monochromatic, motion at inflow which is allowed to evolve downstream through the time-dependent numerical solution of appropriate conservation equations. As the imposed vortex evolves over the solid boundary, a weaker induced vortical motion is produced and together these perturbing motions interact with the fluid motion in the embedded cavity. An analysis of the pertinent dynamic variables as well as the time-dependent drag characteristics for this type of non-planar geometry is performed; with particular emphasis on the relative contribution of both pressure drag and frictional drag at various times in the evolution process.

Gatski, T. B.↗
NASA NTRS1985

Vortex motion in wall-bounded viscous flow

A factor of general interest in a broad class of wall-bounded flows is the dynamic evolution of vortical structures through the flow. The structures are three-dimensional, and an overall mathematical description of such entities has not yet been formulated. One of the objectives of the present investigation is concerned with the establishment of a framework, based on first principles, which may form a basis for more detailed analytical studies. Another aim is related to the establishment of boundary and initial conditions in numerical experiments. The mathematical framework employed involves the method of matched asymptotic expansions, and an inner solution field is constructed which consists of a two-dimensional vortical structure. The outer solution field is taken to be an otherwise undisturbed laminar two-dimensional parallel or self-similar viscous flowfield.

Gatski, T. B.↗
NASA NTRS1984

A numerical study of the two- and three-dimensional unsteady Navier-Stokes equations in velocity-vorticity variables using compact difference schemes

A compact finite-difference approximation to the unsteady Navier-Stokes equations in velocity-vorticity variables is used to numerically simulate a number of flows. These include two-dimensional laminar flow of a vortex evolving over a flat plate with an embedded cavity, the unsteady flow over an elliptic cylinder, and aspects of the transient dynamics of the flow over a rearward facing step. The methodology required to extend the two-dimensional formulation to three-dimensions is presented.

Gatski, T. B.↗
NASA NTRS1984

A numerical study of the 2- and 3-dimensional unsteady Navier-Stokes equations in velocity-vorticity variables using compact difference schemes

A compact finite-difference approximation to the unsteady Navier-Stokes equations in velocity-vorticity variables is used to numerically simulate a number of flows. These include two-dimensional laminar flow of a vortex evolving over a flat plate with an embedded cavity, the unsteady flow over an elliptic cylinder, and aspects of the transient dynamics of the flow over a rearward facing step. The methodology required to extend the two-dimensional formulation to three-dimensions is presented.

Gatski, T. B.↗
NASA NTRS1984

Embedded shear layer computations for increased drag reduction

One of the most promising methods of minimizing drag is the reduction of skin friction by injection of low momentum fluid into the near-wall region of turbulent boundary layer flows. This method could be made more effective by limiting the spread rate of the resulting mixing region. In order to achieve a better understanding of how this goal might be achieved, numerical investigations of the relevant fluid dynamic processes governing these regions have been conducted. A compact finite-difference algorithm has been applied to the complete form of the governing conservation equations for a two-dimensional laminar mixing layer. The ability of this computational approach to model successfully the formation and interaction of the large scale vortical structures which dominate such flow fields is verified in the present study. Parameters which affect the spread rate of the mixing region are also identified. In addition, the relative importance of viscous and momentum transport effects in the vortex interactions is determined.

Gatski, T. B.↗