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NASA NTRS1992

The remarkable ability of turbulence model equations to describe transition

This paper demonstrates how well the k-omega turbulence model describes the nonlinear growth of flow instabilities from laminar flow into the turbulent flow regime. Viscous modifications are proposed for the k-omega model that yield close agreement with measurements and with Direct Numerical Simulation results for channel and pipe flow. These modifications permit prediction of subtle sublayer details such as maximum dissipation at the surface, k approximately y(exp 2) as y approaches 0, and the sharp peak value of k near the surface. With two transition specific closure coefficients, the model equations accurately predict transition for an incompressible flat-plate boundary layer. The analysis also shows why the k-epsilon model is so difficult to use for predicting transition.

Wilcox, David C.↗
NASA NTRS1993

Propagation velocity of perturbations in turbulent channel flow

A database obtained from direct numerical simulation of a turbulent channel flow is analyzed to extract the streamwise component of the propagation velocity V of velocity, vorticity, and pressure fluctuations from their space-time correlations. A surprising result is that V is approximately the same as the local mean velocity for most of the channel, except for the near-wall region. For y(+) less than 15, V is virtually constant, implying that perturbations of all flow variables propagate like waves near the wall. In this region V is 55 percent of the centerline velocity Uc for velocity and vorticity perturbations and 75 percent of U sub c for pressure perturbations. This is equal to U at y(+) = 15 for velocity and vorticity perturbations, and equal to U at y(+) = 20 for pressure perturbations, indicating that the dynamics of the nearwall turbulence is controlled by turbulence structures present near y(+) about 15-20. Scale dependence of V is also examined by analyzing the bandpass-filtered flow fields. This paper contains comprehensive documentation on the propagation velocities, which should prove useful in the evaluation of Taylor's hypothesis.

Kim, John↗
NASA NTRS1993

Spanwise scale selection in plane mixing layers

Direct numerical simulations of temporally evolving plane mixing layers undergoing as many as three pairings have been examined for evidence of spanwise scale change. All simulations were begun from a few low-wavenumber disturbances, usually derived from linear stability theory, in addition to the mean velocity. The amplitude of the initial three-dimensional disturbances varied from infinitesimal to large enough to trigger a rapid transition to turbulence. The time required for a change of characteristic spanwise scale with infinitesimal three-dimensional disturbances was found to be very long, requiring three or more pairings to complete a doubling of the spanwise scale. Stronger three-dimensionality can produce more rapid scale changes, but it is also likely to trigger transition to turbulence. No evidence was found for a change from an organized array of rib vortices at one spanwise scale to a similar array at a larger spanwise scale.

Rogers, Michael M.↗
NASA NTRS1992

Reactant conversion in homogeneous turbulence - Mathematical modeling, computational validations, and practical applications

The presently obtained closed-form analytical expressions, which predict the limiting rate of mean reactant conversion in homogeneous turbulent flows under the influence of a binary reaction, are derived via the single-point pdf method based on amplitude mapping closure. With this model, the maximum rate of the mean reactant's decay can be conveniently expressed in terms of definite integrals of the parabolic cylinder functions. The results obtained are shown to be in good agreement with data generated by direct numerical simulations.

Madnia, C. K.↗
NASA NTRS1993

Effective equations and the inverse cascade theory for Kolmogorov flows

We study the two-dimensional Kolmogorov flows in the limit as the forcing frequency goes to infinity. Direct numerical simulation indicates that the low frequency energy spectrum evolves to a universal kappa (exp -4) decay law. We derive effective equations governing the behavior of the large scale flow quantities. We then present numerical evidence that with smooth initial data, the solution to the effective equation develops a kappa (exp -4) type singularity at a finite time. This gives a convenient explanation for the kappa (exp -4) decay law exhibited by the original Kolmogorov flows.

Weinan, E.↗
NASA NTRS1993

Perspective - Systematic study of Reynolds stress closure models in the computations of plane channel flows

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.

Demuren, A. O.↗
NASA NTRS1993

The rollup of a vortex layer near a wall

The behavior of an inviscid vortex layer of non-zero thickness near a wall is studied, both through direct numerical simulation of the two-dimensional vorticity equation at high Reynolds numbers, and using an approximate ordinary nonlinear integro-differential equation which is satisfied in the limit of a thin layer under long-wavelength perturbations. For appropriate initial conditions the layer rolls up and breaks into compact vortices which move along the wall at constant speed. Because of the effect of the wall, they correspond to equilibrium counter-rotating vortex dipoles. This breakup can be related to the disintegration of the initial conditions of the approximate nonlinear dispersive equation into solitary waves. The study is motivated by the formation of longitudinal vortices from vortex sheets in the wall region of a turbulent channel.

Jimenez, Javier↗
NASA NTRS1993

A Reynolds stress model for near-wall turbulence

The paper formulates a tensorially consistent near-wall second-order closure model. Redistributive terms in the Reynolds stress equations are modeled by an elliptic relaxation equation in order to represent strongly nonhomogeneous effects produced by the presence of walls; this replaces the quasi-homogeneous algebraic models that are usually employed, and avoids the need for ad hoc damping functions. The model is solved for channel flow and boundary layers with zero and adverse pressure gradients. Good predictions of Reynolds stress components, mean flow, skin friction, and displacement thickness are obtained in various comparisons to experimental and direct numerical simulation data. The model is also applied to a boundary layer flowing along a wall with a 90-deg, constant-radius, convex bend.

Durbin, P. A.↗
NASA NTRS1993

Degrees of locality of energy transfer in the inertial range

Measured raw transfer interactions from which local energy transfer is argued to result are summed in a way that directly indicates the scale disparity (s) of contributions to the net energy flux across the spectrum. It is found that the dependence upon s closely follows the s exp -4/3 form predicted by classical arguments. As a result, it is concluded that direct numerical simulation measurements lend support to the classical Kolmogorov phenomenology of local interactions and local transfer in an inertial range.

Zhou, YE↗
NASA NTRS1993

New time scale based k-epsilon model for near-wall turbulence

A k-epsilon model is proposed for wall bonded turbulent flows. In this model, the eddy viscosity is characterized by a turbulent velocity scale and a turbulent time scale. The time scale is bounded from below by the Kolmogorov time scale. The dissipation equation is reformulated using this time scale and no singularity exists at the wall. The damping function used in the eddy viscosity is chosen to be a function of R(sub y) = (k(sup 1/2)y)/v instead of y(+). Hence, the model could be used for flows with separation. The model constants used are the same as in the high Reynolds number standard k-epsilon model. Thus, the proposed model will be also suitable for flows far from the wall. Turbulent channel flows at different Reynolds numbers and turbulent boundary layer flows with and without pressure gradient are calculated. Results show that the model predictions are in good agreement with direct numerical simulation and experimental data.

Yang, Z.↗
NASA NTRS1993

Multigrid methods and high order finite difference for flow in transition - Effects of isolated and distributed roughness elements

The high order finite difference and multigrid methods have been successfully applied to direct numerical simulation (DNS) for flow transition in 3D channels and 3D boundary layers with 2D and 3D isolated and distributed roughness in a curvilinear coordinate system. A fourth-order finite difference technique on stretched and staggered grids, a fully-implicit time marching scheme, a semicoarsening multigrid method associated with line distributive relaxation scheme, and a new treatment of the outflow boundary condition, which needs only a very short buffer domain to damp all wave reflection, are developed. These approaches make the multigrid DNS code very accurate and efficient. This makes us not only able to do spatial DNS for the 3D channel and flat plate at low computational costs, but also able to do spatial DNS for transition in the 3D boundary layer with 3D single and multiple roughness elements. Numerical results show good agreement with the linear stability theory, the secondary instability theory, and a number of laboratory experiments.

Liu, C.↗
NASA NTRS1992

Requirements for facilities and measurement techniques to support CFD development for hypersonic aircraft

The design of a hypersonic aircraft poses unique challenges to the engineering community. Problems with duplicating flight conditions in ground based facilities have made performance predictions risky. Computational fluid dynamics (CFD) has been proposed as an additional means of providing design data. At the present time, CFD codes are being validated based on sparse experimental data and then used to predict performance at flight conditions with generally unknown levels of uncertainty. This paper will discuss the facility and measurement techniques that are required to support CFD development for the design of hypersonic aircraft. Illustrations are given of recent success in combining experimental and direct numerical simulation in CFD model development and validation for hypersonic perfect gas flows.

Sellers, William L., III↗
NASA NTRS1993

Isotropy of the small scales of turbulence at low Reynolds number

Spectral local isotropy tests are applied to direct numerical simulation data, mainly at the centerline of a fully developed turbulent channel flow. Despite the small Reynolds number of the simulation, the high-wavenumber behavior of velocity and vorticity spectra is consistent with local isotropy. This consistency is verified by the relationship between streamwise wavenumber spectra and spanwise wavenumber spectra. The high-wavenumber behavior of the pressure spectrum is also consistent with local isotropy and compares favorably with the calculation of Batchelor (1951), which assumes isotropy and joint normality of the velocity field at two points in space. The latter assumption is validated by the shape but not the magnitude of the quadruple correlation of the streamwise velocity fluctuation at small separations. There is only partial support for local spectral isotropy away from the centerline as the magnitude of the mean strain rate increases.

Kim, J.↗
NASA NTRS1993

The compositional structure and the effects of exothermicity in a nonpremixed planar jet flame

Results are presented of direct numerical simulation (DNS) of a randomly perturbed compressible, spatially developing two-dimensional planar jet under the influence of a finite rate chemical reaction of the type F + O yields product. The objectives of the simulations are to assess the compositional structure of the flame and to determine the influence of reaction exothermicity by means of statistical sampling of the DNS generated data. It is shown that even with this idealized kinetics model the simulated results exhibit features in accord with experimental data. These results indicate that the Damkohler number is an important parameter in determining the statistical composition of the reacting field and that the results are not very sensitive to the mechanism by which this parameter is varied. It is demonstrated that as the intensity of mixing is increased and the effect of finite rate chemistry is more pronounced, the magnitudes of the ensemble mean and variance of the product mass fraction decrease and those of the reactants' mass fraction increase. Also, at higher mixing rates the joint probability density functions of the reactants' mass fractions shift towards higher values within the composition domain, indicating a lower reactedness.

Steinberger, C. J.↗
NASA NTRS1993

On the measurement of lateral velocity derivatives in turbulent flows

Direct numerical simulation data for the lateral velocity derivative delta(u)/delta(y) at the centerline of a fully developed turbulent channel flow provide reasonable support for Wyngaard's analysis of the error involved in measuring this quantity using parallel hot wires. Numerical data in the wall region of the channel flow also provide a useful indication of how to select the separation between the wires. Justification for this choice is obtained by comparing several measured statistics of delta(u)/delta(y) with the corresponding numerical data.

Antonia, R. A.↗
NASA NTRS1993

Spectral response of a bilinear oscillator

An approximate analytical procedure is presented to estimate the response power spectral density of a randomly excited spring/mass/damper system having a bilinear spring. The approximate expression for the response spectrum is developed by representing the nonlinear oscillator as a linear system having a natural frequency that depends on the envelope of the random response. This approximate representation of the system leads to estimates of the response spectrum that agree extremely well with those obtained by direct numerical simulation of the governing equation.

Miles, R. N.↗
NASA NTRS1990

Flow over a rearward facing step

The characteristics of flow over a rearward facing step is discussed in a paper presented by NASA Lewis Research Center personnel. The objective is to obtain data which will be used for validation of Direct Numerical Simulations being developed at NASA Langley and Ames. Two phases of the work are identified as a study of large scale structures in the flow using hot-wire/cold wire techniques and the development of a statistical data base for using three-component laser velocimetry.

Kjelgaard, Scott O.↗
NASA NTRS1991

Single and double point modeling of homogeneous turbulence

Investigations carried out for revisiting homogeneous turbulent flows in the presence of mean shear, rotation, or external compression are summarized. The simplest and most concise RDT (Rapid Distortion Theory) formulation, which includes a comprehensive linear stability analysis, is used for this purpose. Such a linear approach could be extended by a generalized EDQNM (Eddy Damped Quasi-Normal Markovian) to two point closure in order to model non-linear interactions, especially when pure Coriolis effects are present. The results are discussed in connection with databases obtained by DNS (Direct Numerical Simulations), including previous Center for Turbulence Research (CTR) results and new calculations in progress. The main goal is to contribute to and significantly improve on the rational one-point closure models in progress at the CTR and at Ecole Centrale de Lyon (ECL).

Cambon, C.↗