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NASA NTRS1986

Computation of turbulent rotating channel flow with an algebraic Reynolds stress model

An Algebraic Reynolds Stress Model has been implemented to modify the Kolmogorov-Prandtl eddy viscosity relation to produce an anisotropic turbulence model. The eddy viscosity relation becomes a function of the local turbulent production to dissipation ratio and local turbulence/rotation parameters. The model is used to predict fully-developed rotating channel flow over a diverse range of rotation numbers. In addition, predictions are obtained for a developing channel flow with high rotation. The predictions are compared with the experimental data available. Good predictions are achieved for mean velocity and wall shear stress over most of the rotation speeds tested. There is some prediction breakdown at high rotation (rotation number greater than .10) where the effects of the rotation on turbulence become quite complex. At high rotation and low Reynolds number, the laminarization on the trailing side represents a complex effect of rotation which is difficult to predict with the described models.

Warfield, M. J.↗

NASA NTRS1989

The relaxation of a turbulent boundary layer in an adverse pressure gradient

Reattached turbulent boundary layer relaxation downstream of a wall fence is investigated. An adverse pressure gradient is imposed upon it which is adjusted to bring the boundary layer into equilibrium. The pressure gradient is adjusted so as to bring the Clauser parameter G down to a value of about 11.4 and then maintain it constant. In the region from the reattachment point to 2 or 3 reattachment lengths downstream, the boundary layer recovers from the initial major effects of reattachment. Farther downstream, where G is constant, the pressure-gradient parameter changes very slowly and profiles of non-dimensionalized eddy viscosity appear self-similar. However, pressure gradient and eddy viscosity are both roughly twice as large as expected on the basis of previous equilibrium turbulent boundary layer studies.

Cutler, Andrew D.↗

NASA NTRS2016

Reference Solutions for Benchmark Turbulent Flows in Three Dimensions

A grid convergence study is performed to establish benchmark solutions for turbulent flows in three dimensions (3D) in support of turbulence-model verification campaign at the Turbulence Modeling Resource (TMR) website. The three benchmark cases are subsonic flows around a 3D bump and a hemisphere-cylinder configuration and a supersonic internal flow through a square duct. Reference solutions are computed for Reynolds Averaged Navier Stokes equations with the Spalart-Allmaras turbulence model using a linear eddy-viscosity model for the external flows and a nonlinear eddy-viscosity model based on a quadratic constitutive relation for the internal flow. The study involves three widely-used practical computational fluid dynamics codes developed and supported at NASA Langley Research Center: FUN3D, USM3D, and CFL3D. Reference steady-state solutions computed with these three codes on families of consistently refined grids are presented. Grid-to-grid and code-to-code variations are described in detail.

Diskin, Boris↗

NASA NTRS1979

Numerical simulation of supersonic cone flow at high angle of attack

A conical symmetry assumption is applied to the full Navier-Stokes equations resulting in an equation set containing time and two coordinate directions as independent variables. The set is integrated by use of a finite difference technique for the particular case of sharp cones at incidence. Solutions are obtained and compared with experiment for auxiliary conditions corresponding to both laminar and turbulent flows. Closure for the turbulent flow case is provided by use of a scalor eddy viscosity model based on the mixing length hypothesis. Modifications to the eddy viscosity model were found which led to excellent surface pressure and surface flow direction agreement for turbulent flow at low supersonic Mach numbers. It is apparent that further work on the turbulence model is necessary for agreement at higher supersonic Mach numbers.

Mcrae, D. S.↗

NASA NTRS1982

Turbulence modeling for computational aerodynamics

The status of turbulence modeling for external aerodynamic flows is reviewed, and closure concepts for the compressible form of the Reynolds-averaged Navier-Stokes equations are briefly outlined to establish a framework for comparison. The importance of experimental requirements for developing and verifying turbulence models is emphasized. Attention is then given to three important flow categories: attached flows, separating and reattaching flows, and trailing-edge flows. Examples of comparisons between experiments and computations for twoand three-dimensional flows are presented to illustrate the status of modeling. It is shown that, for most two-dimensional attached flows, eddy viscosity concepts will probably be adequate. For attached three-dimensional flows, however, eddy-viscosity and Reynolds-stress models are both deficient, failing to predict the proper surface shear-stress in rapidly skewing boundary layers, regardless of whether they are pressure driven or strain driven.

Marvin, J. G.↗

NASA NTRS1994

A dynamic localization model with stochastic backscatter

The modeling of subgrid scales in large-eddy simulation (LES) has been rationalized by the introduction of the dynamic localization procedure. This method allows one to compute rather than prescribe the unknown coefficients in the subgrid-scale model. Formally, the LES equations are supposed to be obtained by applying to the Navier-Stokes equations a 'grid filter' operation. Though the subgrid stress itself is unknown, an identity between subgrid stresses generated by different filters has been derived. Although preliminary tests of the Dynamic Localization Model (DLM) with k-equation have been satisfactory, the use of a negative eddy viscosity to describe backscatter is probably a crude representation of the physics of reverse transfer of energy. Indeed, the model is fully deterministic. Knowing the filtered velocity field and the subgrid-scale energy, the subgrid stress is automatically determined. We know that the LES equations cannot be fully deterministic since the small scales are not resolved. This stems from an important distinction between equilibrium hydrodynamics and turbulence. In equilibrium hydrodynamics, the molecular motions are also not resolved. However, there is a clear separation of scale between these unresolved motions and the relevant hydrodynamic scales. The result of molecular motions can then be separated into an average effect (the molecular viscosity) and some fluctuations. Due to the large number of molecules present in a box with size of the order of the hydrodynamic scale, the ratio between fluctuations and the average effect should be very small (as a result of the 'law of large numbers'). For that reason, the hydrodynamic balance equations are usually purely deterministic. In turbulence, however, there is no clear separation of scale between small and large eddies. In that case, the fluctuations around a deterministic eddy viscosity term could be significant. An eddy noise would then appear through a stochastic term in the subgrid-scale model and could be the source of backscatter.

Carati, Daniele↗

NASA NTRS1990

An Improved K-Epsilon Model for Near-Wall Turbulence and Comparison with Direct Numerical Simulation

An improved k-epsilon model for low Reynolds number turbulence near a wall is presented. The near-wall asymptotic behavior of the eddy viscosity and the pressure transport term in the turbulent kinetic energy equation is analyzed. Based on this analysis, a modified eddy viscosity model, having correct near-wall behavior, is suggested, and a model for the pressure transport term in the k-equation is proposed. In addition, a modeled dissipation rate equation is reformulated. Fully developed channel flows were used for model testing. The calculations using various k-epsilon models are compared with direct numerical simulations. The results show that the present k-epsilon model performs well in predicting the behavior of near-wall turbulence. Significant improvement over previous k-epsilon models is obtained.

Shih, T. H.↗

NASA NTRS1991

An improved k-epsilon model for near wall turbulence

An improved k-epsilon model for low Reynolds number turbulence near a wall is presented. In the first part of this work, the near-wall asymptotic behavior of the eddy viscosity and the pressure transport term in the turbulent kinetic energy equation are analyzed. Based on these analyses, a modified eddy viscosity model with the correct near-wall behavior is suggested, and a model for the pressure transport term in the k-equation is proposed. In addition, a modeled dissipation rate equation is reformulated, and a boundary condition for the dissipation rate is suggested. In the second part of the work, one of the deficiencies of the existing k-epsilon models, namely, the wall distance dependency of the equations and the damping functions, is examined. An improved model that does not depend on any wall distance is introduced. Fully developed turbulent channel flows and turbulent boundary layers over a flat plate are studied as validations for the proposed new models. Numerical results obtained from the present and other previous k-epsilon models are compared with data from direct numerical simulation. The results show that the present k-epsilon model, with added robustness, performs as well as or better than other existing models in predicting the behavior of near-wall turbulence.

Shih, T. H.↗

NASA NTRS2001

Modeling of Turbulent Flow in Electromagnetically Levitated Metal Droplets

This article details an effort to improve the understanding and prediction of turbulent flow inside a droplet of molten metal levitated in an electromagnetic field. It is shown that the flow field in a test case, a nickel droplet levitated under microgravity conditions, is in the transitional regime between laminar and turbulent flow. Past research efforts have used laminar, enhanced viscosity, and k-epsilon turbulence models to describe the flow. The method highlighted in our study is the renormalization group (RNG) algorithm. We show that an accurate description of the turbulent eddy viscosity is critical in order to obtain realistic velocity fields, and that the turbulent eddy viscosity cannot be uniform in levitated droplets. The RNG method does not impose isotropic length or time scales on the flow field, thus allowing such nonuniform features to be captured. A number of other materials processing applications exhibit similarly complex flow characteristics, such as highly recirculating, transitional, and free surface flows, for which this modeling approach may prove useful.

Berry, S.↗

NASA NTRS1982

Features of a reattaching turbulent shear layer subject to an adverse pressure gradient

Experimental data have been obtained in an incompressible turbulent flow over a rearward-facing step with superimposed adverse pressure gradient. Mean velocities, Reynolds stresses and triple-products measured by a laser Doppler velocimeter are presented for two cases of adverse pressure gradient. Mixing lengths, eddy viscosities, production, convection, turbulent diffusion, and dissipation terms are extracted from the data. These data are compared with various mixing length and eddy-viscosity turbulence models. Numerical calculations incorporating the k-epsilon and the algebraic-stress turbulence models are compared with the data. When determining quantities of engineering interest, the modified algebraic-stress model (ASM) is a significant improvement over the unmodified ASM and the unmodified k-epsilon model

Driver, D. M.↗

NASA NTRS1985

Features of a reattaching turbulent shear layer in divergent channel flow

Experimental data have been obtained in an incompressible turbulent flow over a rearward-facing step in a diverging channel flow. Mean velocities, Reynolds stresses, and triple products that were measured by a laser Doppler velocimeter are presented for two cases of tunnel wall divergence. Eddy viscosities, production, convection, turbulent diffusion, and dissipation (balance of kinetic energy equation) terms are extracted from the data. These data are compared with various eddy-viscosity turbulence models. Numerical calculations incorporating the k-epsilon and algebraic-stress turbulence models are compared with the data. When determining quantities of engineering interest, the modified algebraic-stress model (ASM) is a significant improvement over the unmodified ASM and the unmodified k-epsilon model; however, like the others, it dramatically overpredicts the experimentally determined dissipation rate.

Driver, D. M.↗

NASA NTRS1981

On the OLP prediction of the unstable modes of the flat plate turbulent boundary layer

The Orr et al. (OLP) stability analysis is reformulated to yield profiles from hot-wire velocity covariance data in the boundary layer of a flow over a flat plate. The proper orthogonal decomposition theorem (PODT) is used to maximize the mean square of the inner product of the velocity vector with a deterministic candidate vector function in Hilbert space. The OLP formulation couples the PODT for the eddy viscosity with a global extremum principle for the disturbance kinetic energy. Derivation of the governing equations is described analytically, as are the extraction of the mean velocity profile and the eddy viscosity. Finally, techniques for characterizing the dominant mode of the velocity field are introduced and applied to three-dimensional flow over a flat plate. Good agreement is found between the predictions, using laboratory data, and the measured energy and three-dimensional structures of the dominant eddies.

Wadia, A. R.↗

NASA NTRS1973

Study of the far wake vortex field generated by a rectangular airfoil in a water tank

Underwater towing experiments were carried out with a rectangular airfoil of aspect ratio 5.3 at 4 and 8 deg angles of attack and at chord-based Reynolds numbers between 2 x 100,000 and 7.5 x 100,000. Quantitative measurements by means of the hydrogen bubble technique indicated lower peak swirl velocities in the range of 100 to 1000 lenghts downstream than have been measured in wind tunnel of flight tests. The maximum circumferential velocity decayed whereas the turbulent eddy viscosity increased. This behavior and other known rates of vortex decay are explained in terms of an analytical solution for the vortex problem with time varying eddy viscosity. It is shown that this case corresponds to nonequilibrium turbulent vortex flow.

Lezius, D. K.↗

NASA NTRS1992

Nonequilibrium algebraic turbulence modeling considerations for transonic airfoils and wings

The nonequilibrium algebraic turbulence model of Johnson and King has been applied successfully to both airfoils and wings. However, in wing applications a different expression for the outer 'equilibrium' eddy viscosity has been used because of apparent difficulties in determining the boundary-layer thickness. It is shown in this paper, that this expression does not give eddy viscosity levels for two-dimensional flows that are consistent with Clauser's correlation for equilibrium turbulent boundary layers. And as a consequence, results in inferior predictions when used in airfoil calculations. The objective of this paper is to develop a formulation applicable to wing flows which reduces to the proper form in the two-dimensional case. This necessitates, in part, finding a better way of estimating the boundary-layer thickness from the computed flowfield.

Johnson, D. A.↗

NASA NTRS1980

Stellar convection. III - Convection at large Rayleigh numbers

The results of a numerical, three-dimensional study of convection in a self-gravitating sphere of Boussinesq fluid with a Rayleigh number of 10-billion and a Prandtl number of 1 are presented. The velocity and temperature are computed by using spectral methods in the horizontal and finite-differencing in the radial directions. An eddy viscosity and diffusivity are needed to model the subresolution flow. For Rayleigh numbers much less than 10-billion the flows do not have well-defined inertial ranges, and an eddy viscosity and diffusivity cannot be assigned in this self-consistent manner. By computing the energy spectra as well as the detailed energy budgets as a function of wavenumber, it is shown that for Rs = 10-billion there is an inertial range for the modes corresponding to spherical harmonics with l greater than 6.

Marcus, P. S.↗

NASA NTRS1991

Single Doppler radar and lidar studies of the dynamics of mixed layers and overlying stable regions

Some examples of profiles of PBL quantities retrieved from Doppler radar and lidar observations are shown, and the extent to which the deduced quantities agree with the traditional eddy viscosity concept is examined. It is found in one case that the concept of 'top down bottom up' diffusion introduced by Wyngaard (1983) is more pertinent than that of the eddy viscosity. In another case it is found that, in stable layers with sufficiently large Richardson number, the momentum fluxes could be counter-gradient. In this latter case the use of a negative turbulence diffusion coefficient would result in an ill-posed differential equation, thus confusing the 'diffusion problem'.

Xu, Mei↗

NASA NTRS1973

Turbulent jet mixing at high supersonic speeds.

The results of three related studies of turbulent jet mixing are presented and discussed. The major effort was the collection of mean-flow data at a much higher free stream Mach number than was previously available. The effects of initial swirl in the injectant were found to be minimal. Numerical predictions of the non-swirling experimental case obtained using an eddy viscosity approximation are found to be in reasonable agreement with the data. Lastly, an approximate analysis of the decay of the swirling velocity is developed. This analysis is based upon an eddy viscosity model for transport in the circumferential direction adapted from wing-tip vortex work.

Schetz, J. A.↗

NASA NTRS1988

Numerical solutions of the complete Navier-Stokes equations

The physical phenomena within supersonic flows that sustain chemical reactions are investigated. An earlier study to develop accurate physical models for supersonic reacting flowfields focused on 2-D laminar shear layers. The objective is to examine the mixing and subsequent combustion within turbulent reacting shear layers. To conduct this study, a computer program has been written to solve the axisymmetric Reynolds averaged Navier-Stokes equations. The numerical method uses a cell-centered finite volume approach and a Runge Kutta time stepping scheme. The Reynolds averaged equations are closed using the eddy viscosity concept. Several zero-equation models have been tested by making calculations for an H2-air nonreacting coaxial jet flow. Comparisons made with experimental data show that Cohen's eddy viscosity model provides best agreement. The finite rate chemistry model used in the study of 2-D laminar shear layers is incorporated into the computer program and data is compared from a recent experiment performed at NASA Langley.

Hassan, H. A.↗