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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.↗

NASA NTRS1993

A research program for improving heat transfer prediction for the laminar to turbulent transition region of turbine vanes/blades

A program sponsored by NASA for the investigation of the heat transfer in the transition region of turbine vanes and blades with the objective of improving the capability for predicting heat transfer is described. The accurate prediction of gas-side heat transfer is important to the determination of turbine longevity, engine performance, and developmental costs. The need for accurate predictions will become greater as the operating temperatures and stage loading levels of advanced turbine engines increase. The present methods for predicting transition shear stress and heat transfer on turbine blades are based on incomplete knowledge and are largely empirical. To meet the objective of the NASA program, a team approach consisting of researchers from government, universities, a research institute, and a small business is presented. The research is divided into the areas of experiments, direct numerical simulations (DNS), and turbulence modeling. A summary of the results to date is given for the above research areas in a high-disturbance environment (bypass transition) with a discussion of the model development necessary for use in numerical codes.

Simon, Frederick F.↗

NASA NTRS1993

Large eddy simulations of time-dependent and buoyancy-driven channel flows

The primary goal of this work has been to assess the performance of the dynamic SGS model in the large eddy simulation (LES) of channel flows in a variety of situations, viz., in temporal development of channel flow turned by a transverse pressure gradient and especially in buoyancy-driven turbulent flows such as Rayleigh-Benard and internally heated channel convection. For buoyancy-driven flows, there are additional buoyant terms that are possible in the base models, and one objective has been to determine if the dynamic SGS model results are sensitive to such terms. The ultimate goal is to determine the minimal base model needed in the dynamic SGS model to provide accurate results in flows with more complicated physical features. In addition, a program of direct numerical simulation (DNS) of fully compressible channel convection has been undertaken to determine stratification and compressibility effects. These simulations are intended to provide a comparative base for performing the LES of compressible (or highly stratified, pseudo-compressible) convection at high Reynolds number in the future.

Cabot, William H.↗

NASA NTRS1993

Large-eddy simulation of turbulent flow with a surface-mounted two-dimensional obstacle

In this paper, we perform a large eddy simulation (LES) of turbulent flow in a channel containing a two-dimensional obstacle on one wall using a dynamic subgrid-scale model (DSGSM) at Re = 3210, based on bulk velocity above the obstacle and obstacle height; the wall layers are fully resolved. The low Re enables us to perform a DNS (Case 1) against which to validate the LES results. The LES with the DSGSM is designated Case 2. In addition, an LES with the conventional fixed model constant (Case 3) is conducted to allow identification of improvements due to the DSGSM. We also include LES at Re = 82,000 (Case 4) using conventional Smagorinsky subgrid-scale model and a wall-layer model. The results will be compared with the experiment of Dimaczek et al.

Yang, Kyung-Soo↗

NASA NTRS1992

A study of the fine scale motions of incompressible time-developing mixing layers

This work is an extension of a project conducted at the previous CTR summer program and was reported by Chen et al. (1990). In that program, the geometry and topology of the dissipating motions in a variety of shear flows was examined. All data was produced by direct numerical simulations (DNS). The partial derivatives of the velocity field were determined at every grid point in the flow and various invariants and related quantities were computed from the velocity gradient tensor. Motions characterized by high rates of kinetic energy dissipation and high enstrophy were of particular interest. Scatter diagrams of the invariants were mapped out and interesting and unexpected patterns were seen. Each type of shear layer produced its own characteristic scatter plot. In the present project, attention is focused on the incompressible plane mixing layer, and the scatter diagrams are replaced with more useful joint probability density contours. Comparison of the topology of the dissipating motions of flows at different Reynolds numbers are made. Also, plane mixing layers at the same Reynolds number but with different initial conditions are compared.

Soria, J.↗

NASA NTRS1992

Effect of finite-rate chemistry and unequal Schmidt numbers on turbulent non-premixed flames modeled with single-step chemistry

The interaction between a quasi-laminar flame and a turbulent flowfield is investigated through direct numerical simulations (DNS) of reacting flow in two- and three-dimensional domains. Effects due to finite-rate chemistry are studied using a single step global reaction A (fuel) + B (oxidizer) yields P (product), and by varying a global Damkoehler number, as a result of which the turbulence-chemistry interaction in the flame is found to generate a wide variety of conditions, ranging from near-equilibrium to near-extinction. Differential diffusion effects are studied by changing the Schmidt number of one reactive species to one-half. It is observed that laminar flamelet response is followed within the turbulent flowfield, except in regions where transient effects seem to dominate.

Chen, J. H.↗

NASA NTRS1993

A representation for the turbulent mass flux contribution to Reynolds-stress and two-equation closures for compressible turbulence

The turbulent mass flux, or equivalently the fluctuating Favre velocity mean, appears in the first and second moment equations of compressible kappa-epsilon and Reynolds stress closures. Mathematically it is the difference between the unweighted and density-weighted averages of the velocity field and is therefore a measure of the effects of compressibility through variations in density. It appears to be fundamental to an inhomogeneous compressible turbulence, in which it characterizes the effects of the mean density gradients, in the same way the anisotropy tensor characterizes the effects of the mean velocity gradients. An evolution equation for the turbulent mass flux is derived. A truncation of this equation produces an algebraic expression for the mass flux. The mass flux is found to be proportional to the mean density gradients with a tensor eddy-viscosity that depends on both the mean deformation and the Reynolds stresses. The model is tested in a wall bounded DNS at Mach 4.5 with notable results.

Ristorcelli, J. R.↗

NASA NTRS1993

Computation of turbulent flows over backward and forward-facing steps using a near-wall Reynolds stress model

Separation and reattachment of turbulent shear layers is observed in many important engineering applications, yet it is poorly understood. This has motivated many studies on understanding and predicting the processes of separation and reattachment of turbulent shear layers. Both of the situations in which separation is induced by adverse pressure gradient, or by discontinuities of geometry, have attracted attention of turbulence model developers. Formulation of turbulence closure models to describe the essential features of separated turbulent flows accurately is still a formidable task. Computations of separated flows associated with sharp-edged bluff bodies are described. For the past two decades, the backward-facing step flow, the simplest separated flow, has been a popular test case for turbulence models. Detailed studies on the performance of many turbulence models, including two equation turbulence models and Reynolds stress models, for flows over steps can be found in the papers by Thangam & Speziale and Lasher & Taulbee). These studies indicate that almost all the existing turbulence models fail to accurately predict many important features of back step flow such as reattachment length, recovery rate of the redeveloping boundary layers downstream of the reattachment point, streamlines near the reattachment point, and the skin friction coefficient. The main objectives are to calculate flows over backward and forward-facing steps using the NRSM and to make use of the newest DNS data for detailed comparison. This will give insights for possible improvements of the turbulence model.

Ko, Sung HO↗

NASA NTRS1993

A large eddy simulation scheme for turbulent reacting flows

The recent development of the dynamic subgrid-scale (SGS) model has provided a consistent method for generating localized turbulent mixing models and has opened up great possibilities for applying the large eddy simulation (LES) technique to real world problems. Given the fact that the direct numerical simulation (DNS) can not solve for engineering flow problems in the foreseeable future (Reynolds 1989), the LES is certainly an attractive alternative. It seems only natural to bring this new development in SGS modeling to bear on the reacting flows. The major stumbling block for introducing LES to reacting flow problems has been the proper modeling of the reaction source terms. Various models have been proposed, but none of them has a wide range of applicability. For example, some of the models in combustion have been based on the flamelet assumption which is only valid for relatively fast reactions. Some other models have neglected the effects of chemical reactions on the turbulent mixing time scale, which is certainly not valid for fast and non-isothermal reactions. The probability density function (PDF) method can be usefully employed to deal with the modeling of the reaction source terms. In order to fit into the framework of LES, a new PDF, the large eddy PDF (LEPDF), is introduced. This PDF provides an accurate representation for the filtered chemical source terms and can be readily calculated in the simulations. The details of this scheme are described.

Gao, Feng↗

NASA NTRS1993

A transport equation for the scalar dissipation in reacting flows with variable density: First results

Although the different regimes of premixed combustion are not well defined, most of the recent developments in turbulent combustion modeling are led in the so-called flamelet regime. The goal of these models is to give a realistic expression to the mean reaction rate (w). Several methods can be used to estimate (w). Bray and coworkers (Libby & Bray 1980, Bray 1985, Bray & Libby 1986) express the instantaneous reaction rate by means of a flamelet library and a frequency which describes the local interaction between the laminar flamelets and the turbulent flowfield. In another way, the mean reaction rate can be directly connected to the flame surface density (Sigma). This quantity can be given by the transport equation of the coherent flame model initially proposed by Marble & Broadwell 1977 and developed elsewhere. The mean reaction rate, (w), can also be estimated thanks to the evolution of an arbitrary scalar field G(x, t) = G(sub O) which represents the flame sheet. G(x, t) is obtained from the G-equation proposed by Williams 1985, Kerstein et al. 1988 and Peters 1993. Another possibility proposed in a recent study by Mantel & Borghi 1991, where a transport equation for the mean dissipation rate (epsilon(sub c)) of the progress variable c is used to determine (w). In their model, Mantel & Borghi 1991 considered a medium with constant density and constant diffusivity in the determination of the transport equation for (epsilon(sub c)). A comparison of different flamelet models made by Duclos et al. 1993 shows the realistic behavior of this model even in the case of constant density. Our objective in this present report is to present preliminary results on the study of this equation in the case of variable density and variable diffusivity. Assumptions of constant pressure and a Lewis number equal to unity allow us to significantly simplify the equation. A systematic order of magnitude analysis based on adequate scale relations is performed on each term of the equation. As in the case of constant density and constant diffusivity, the effects of stretching of the scalar field by the turbulent strain field, of local curvature, and of chemical reactions are predominant. In this preliminary work, we suggest closure models for certain terms, which will be validated after comparisons with DNS data.

Mantel, T.↗

NASA NTRS1993

The production of premixed flame surface area in turbulent shear flow

In the present work, we use three-dimensional Direct Numerical Simulation (DNS) of premixed flames in turbulent shear flow to characterize the effect of a mean shear motion on flame surface production. The shear is uniform in the unburnt gas, and simulations are performed for different values of the mean shear rate, S. The data base is then used to estimate and compare the different terms appearing in the Sigma-equation as a function of S. The analysis gives in particular the relative weights f the turbulent flow and mean flow components, a(sub T) and A(sub T), of the flame surface production term. This comparison indicates whether the dominant effects of a mean flow velocity gradient on flame surface area are implicit and scale with the modified turbulent flow parameters, kappa and epsilon, or explicit and scale directly with the rate of deformation.

Trouve, A.↗

NASA NTRS1993

Direct simulation of isothermal-wall supersonic channel flow

The motivation for this work is the fact that in turbulent flows where compressibility effects are important, they are often poorly understood. A few examples of such flows are those associated with astrophysical phenomena and those found in combustion chambers, supersonic diffusers and nozzles, and over high-speed airfoils. For this project, we are primarily interested in compressibility effects near solid surfaces. Our main objective is an improved understanding of the fundamentals of compressible wall-bounded turbulence, which can in turn be used to cast light upon modeling concepts such as the Morkovin hypothesis and the Van Driest transformation. To this end, we have performed a direct numerical simulation (DNS) study of supersonic turbulent flow in a plane channel with constant-temperature walls. All of the relevant spatial and temporal scales are resolved so that no sub grid scale or turbulence model is necessary. The channel geometry was chosen so that finite Mach number effects can be isolated by comparing the present results to well established incompressible channel data. Here the fluid is assumed to be an ideal gas with constant specific heats, constant Prandtl number, and power-law temperature-dependent viscosity. Isothermal-wall boundary conditions are imposed so that a statistically stationary state may be obtained. The flow is driven by a uniform (in space) body force (rather than a mean pressure gradient) to preserve stream wise homogeneity, with the body force defined so that the total mass flux is constant.

Coleman, Gary N.↗

NASA NTRS1994

Center for modeling of turbulence and transition: Research briefs, 1993

This research brief contains the progress reports of the research staff of the Center for Modeling of Turbulence and Transition (CMOTT) from June 1992 to July 1993. It is also an annual report to the Institute for Computational Mechanics in Propulsion located at Ohio Aerospace Institute and NASA Lewis Research Center. The main objectives of the research activities at CMOTT are to develop, validate, and implement turbulence and transition models for flows of interest in propulsion systems. Currently, our research covers eddy viscosity one- and two-equation models, Reynolds-stress algebraic equation models, Reynolds-stress transport equation models, nonequilibrium multiple-scale models, bypass transition models, joint scalar probability density function models, and Renormalization Group Theory and Direct Interaction Approximation methods. Some numerical simulations (LES and DNS) have also been carried out to support the development of turbulence modeling. Last year was CMOTT's third year in operation. During this period, in addition to the above mentioned research, CMOTT has also hosted the following programs: an eighteen-hour short course on 'Turbulence--Fundamentals and Computational Modeling (Part I)' given by CMOTT at the NASA Lewis Research Center; a productive summer visitor research program that has generated many encouraging results; collaborative programs with industry customers to help improve their turbulent flow calculations for propulsion system designs; a biweekly CMOTT seminar series with speakers from within and without the NASA Lewis Research Center including foreign speakers. In addition, CMOTT members have been actively involved in the national and international turbulence research activities. The current CMOTT roster and organization are listed in Appendix A. Listed in Appendix B are the abstracts of the biweekly CMOTT seminar. Appendix C lists the papers contributed by CMOTT members.

Liou, William W.↗

NASA NTRS1993

The radiated noise from isotropic turbulence revisited

The noise radiated from isotropic turbulence at low Mach numbers and high Reynolds numbers, as derived by Proudman (1952), was the first application of Lighthill's Theory of Aerodynamic Noise to a complete flow field. The theory presented by Proudman involves the assumption of the neglect of retarded time differences and so replaces the second-order retarded-time and space covariance of Lighthill's stress tensor, Tij, and in particular its second time derivative, by the equivalent simultaneous covariance. This assumption is a valid approximation in the derivation of the second partial derivative of Tij/derivative of t exp 2 covariance at low Mach numbers, but is not justified when that covariance is reduced to the sum of products of the time derivatives of equivalent second-order velocity covariances as required when Gaussian statistics are assumed. The present paper removes these assumptions and finds that although the changes in the analysis are substantial, the change in the numerical result for the total acoustic power is small. The present paper also considers an alternative analysis which does not neglect retarded times. It makes use of the Lighthill relationship, whereby the fourth-order Tij retarded-time covariance is evaluated from the square of similar second order covariance, which is assumed known. In this derivation, no statistical assumptions are involved. This result, using distributions for the second-order space-time velocity squared covariance based on the Direct Numerical Simulation (DNS) results of both Sarkar and Hussaini(1993) and Dubois(1993), is compared with the re-evaluation of Proudman's original model. These results are then compared with the sound power derived from a phenomenological model based on simple approximations to the retarded-time/space covariance of Txx. Finally, the recent numerical solutions of Sarkar and Hussaini(1993) for the acoustic power are compared with the results obtained from the analytic solutions.

Lilley, Geoffrey M.↗

NASA NTRS1993

The nonlinear Galerkin method: A multi-scale method applied to the simulation of homogeneous turbulent flows

Using results of Direct Numerical Simulation (DNS) in the case of two-dimensional homogeneous isotropic flows, the behavior of the small and large scales of Kolmogorov like flows at moderate Reynolds numbers are first analyzed in detail. Several estimates on the time variations of the small eddies and the nonlinear interaction terms were derived; those terms play the role of the Reynolds stress tensor in the case of LES. Since the time step of a numerical scheme is determined as a function of the energy-containing eddies of the flow, the variations of the small scales and of the nonlinear interaction terms over one iteration can become negligible by comparison with the accuracy of the computation. Based on this remark, a multilevel scheme which treats differently the small and the large eddies was proposed. Using mathematical developments, estimates of all the parameters involved in the algorithm, which then becomes a completely self-adaptive procedure were derived. Finally, realistic simulations of (Kolmorov like) flows over several eddy-turnover times were performed. The results are analyzed in detail and a parametric study of the nonlinear Galerkin method is performed.

Debussche, A.↗

NASA NTRS1994

A modified restricted Euler equation for turbulent flows with mean velocity gradients

The restricted Euler equation captures many important features of the behavior of the velocity gradient tensor observed in direct numerical simulations (DNS) of isotropic turbulence. However, in slightly more complex flows the agreement is not good, especially in regions of low dissipation. In this paper, it is demonstrated that the Reynolds-averaged restricted Euler equation violates the balance of mean momentum for virtually all homogeneous turbulent flows with only two major exceptions: isotropic and homogeneously-sheared turbulence. A new model equation which overcomes this shortcoming and is more widely applicable is suggested. This modele is derived from the Navier-Stokes equation with a restricted Euler type approximation made on the fluctuating velocity gradient field. Analytical solutions of the proposed modified restricted Euler equation appear to be difficult to obtain. Hence, a strategy for numerically calculating the velocity gradient tensor is developed. Preliminary calculations tend to indicate that the modified restricted Euler equation captures many important aspects of the behavior of the fluctuating velocity gradients in anisotropic homogeneous turbulence.

Girimaji, Sharath S.↗

NASA NTRS1994

Scalability study of parallel spatial direct numerical simulation code on IBM SP1 parallel supercomputer

The implementation and the performance of a parallel spatial direct numerical simulation (PSDNS) code are reported for the IBM SP1 supercomputer. The spatially evolving disturbances that are associated with laminar-to-turbulent in three-dimensional boundary-layer flows are computed with the PS-DNS code. By remapping the distributed data structure during the course of the calculation, optimized serial library routines can be utilized that substantially increase the computational performance. Although the remapping incurs a high communication penalty, the parallel efficiency of the code remains above 40% for all performed calculations. By using appropriate compile options and optimized library routines, the serial code achieves 52-56 Mflops on a single node of the SP1 (45% of theoretical peak performance). The actual performance of the PSDNS code on the SP1 is evaluated with a 'real world' simulation that consists of 1.7 million grid points. One time step of this simulation is calculated on eight nodes of the SP1 in the same time as required by a Cray Y/MP for the same simulation. The scalability information provides estimated computational costs that match the actual costs relative to changes in the number of grid points.

Hanebutte, Ulf R.↗

NASA NTRS1994

Direct numerical simulations of turbulent non-premixed methane-air flames modeled with reduced kinetics

Turbulent non-premixed stoichiometric methane-air flames modeled with reduced kinetics have been studied using the direct numerical simulation approach. The simulations include realistic chemical kinetics, and the molecular transport is modeled with constant Lewis numbers for individual species. The effect of turbulence on the internal flame structure and extinction characteristics of methane-air flames is evaluated. Consistent with earlier DNS with simple one-step chemistry, the flame is wrinkled and in some regions extinguished by the turbulence, while the turbulence is weakened in the vicinity of the flame due to a combination of dilatation and an increase in kinematic viscosity. Unlike previous results, reignition is observed in the present simulations. Lewis number effects are important in determining the local stoichiometry of the flame. The results presented in this work are preliminary but demonstrate the feasibility of incorporating reduced kinetics for the oxidation of methane with direct numerical simulations of homogeneous turbulence to evaluate the limitations of various levels of reduction in the kinetics and to address the formation of thermal and prompt NO(x).

Card, J. M.↗