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NASA NTRS1992

Turbulence modeling and experiments

The best way of verifying turbulence is to do a direct comparison between the various terms and their models. The success of this approach depends upon the availability of the data for the exact correlations (both experimental and DNS). The other approach involves numerically solving the differential equations and then comparing the results with the data. The results of such a computation will depend upon the accuracy of all the modeled terms and constants. Because of this it is sometimes difficult to find the cause of a poor performance by a model. However, such a calculation is still meaningful in other ways as it shows how a complete Reynolds stress model performs. Thirteen homogeneous flows are numerically computed using the second order closure models. We concentrate only on those models which use a linear (or quasi-linear) model for the rapid term. This, therefore, includes the Launder, Reece and Rodi (LRR) model; the isotropization of production (IP) model; and the Speziale, Sarkar, and Gatski (SSG) model. Which of the three models performs better is examined along with what are their weaknesses, if any. The other work reported deal with the experimental balances of the second moment equations for a buoyant plume. Despite the tremendous amount of activity toward the second order closure modeling of turbulence, very little experimental information is available about the budgets of the second moment equations. Part of the problem stems from our inability to measure the pressure correlations. However, if everything else appearing in these equations is known from the experiment, pressure correlations can be obtained as the closing terms. This is the closest we can come to in obtaining these terms from experiment, and despite the measurement errors which might be present in such balances, the resulting information will be extremely useful for the turbulence modelers. The purpose of this part of the work was to provide such balances of the Reynolds stress and heat flux equations for the buoyant plume.

Shabbir, Aamir↗
NASA NTRS1992

Near-wall reconstruction of higher order moments and length scales using the POD

An analysis of the near-wall behavior of the proper orthogonal decomposition (POD) eigenfunctions derived from direct numerical simulation (DNS) of channel flow is performed. Consistent with previous studies, a low order multi-mode reconstruction of the kinetic energy and Reynolds shear stress suffices. A similar reconstruction of the isotropic dissipation rate is shown to be insufficient, however. An analysis is performed of the multi-mode composition of the dissipation rate in the near-wall region, and it is shown that a significant number of higher-order modes are required to achieve the correct asymptotic consistency in the near-wall region. In an attempt to avoid this problem, a length scale definition is proposed in terms of an integration of the correlation tensor which factors in the presence of the wall. The wall is accounted for by only integrating out to 2y(+) and not over the entire domain. Viscous and inviscid estimates for the dissipation were used in the near-wall and core regions respectively, in conjunction with this length scale representation to obtain an estimate of the dissipation throughout the domain. The resulting dissipation exhibits the proper behavior near the wall and in the inertial layer. A 1 POD mode estimate of the length scale is computed and found to agree quite well with the length scale obtained when the entire correlation tensor is used.

Glauser, Mark N.↗
NASA NTRS1993

Numerical Simulation of a High Mach Number Jet Flow

The recent efforts to develop accurate numerical schemes for transition and turbulent flows are motivated, among other factors, by the need for accurate prediction of flow noise. The success of developing high speed civil transport plane (HSCT) is contingent upon our understanding and suppression of the jet exhaust noise. The radiated sound can be directly obtained by solving the full (time-dependent) compressible Navier-Stokes equations. However, this requires computational storage that is beyond currently available machines. This difficulty can be overcome by limiting the solution domain to the near field where the jet is nonlinear and then use acoustic analogy (e.g., Lighthill) to relate the far-field noise to the near-field sources. The later requires obtaining the time-dependent flow field. The other difficulty in aeroacoustics computations is that at high Reynolds numbers the turbulent flow has a large range of scales. Direct numerical simulations (DNS) cannot obtain all the scales of motion at high Reynolds number of technological interest. However, it is believed that the large scale structure is more efficient than the small-scale structure in radiating noise. Thus, one can model the small scales and calculate the acoustically active scales. The large scale structure in the noise-producing initial region of the jet can be viewed as a wavelike nature, the net radiated sound is the net cancellation after integration over space. As such, aeroacoustics computations are highly sensitive to errors in computing the sound sources. It is therefore essential to use a high-order numerical scheme to predict the flow field. The present paper presents the first step in a ongoing effort to predict jet noise. The emphasis here is in accurate prediction of the unsteady flow field. We solve the full time-dependent Navier-Stokes equations by a high order finite difference method. Time accurate spatial simulations of both plane and axisymmetric jet are presented. Jet Mach numbers of 1.5 and 2.1 are considered. Reynolds number in the simulations was about a million. Our numerical model is based on the 2-4 scheme by Gottlieb & Turkel. Bayliss et al. applied the 2-4 scheme in boundary layer computations. This scheme was also used by Ragab and Sheen to study the nonlinear development of supersonic instability waves in a mixing layer. In this study, we present two dimensional direct simulation results for both plane and axisymmetric jets. These results are compared with linear theory predictions. These computations were made for near nozzle exit region and velocity in spanwise/azimuthal direction was assumed to be zero.

Hayder, M. Ehtesham↗
NASA NTRS1992

Research in computational fluid dynamics and analysis of algorithms

Recently, higher-order compact schemes have seen increasing use in the DNS (Direct Numerical Simulations) of the Navier-Stokes equations. Although they do not have the spatial resolution of spectral methods, they offer significant increases in accuracy over conventional second order methods. They can be used on any smooth grid, and do not have an overly restrictive CFL dependence as compared with the O(N(exp -2)) CFL dependence observed in Chebyshev spectral methods on finite domains. In addition, they are generally more robust and less costly than spectral methods. The issue of the relative cost of higher-order schemes (accuracy weighted against physical and numerical cost) is a far more complex issue, depending ultimately on what features of the solution are sought and how accurately they must be resolved. In any event, the further development of the underlying stability theory of these schemes is important. The approach of devising suitable boundary clusters and then testing them with various stability techniques (such as finding the norm) is entirely the wrong approach when dealing with high-order methods. Very seldom are high-order boundary closures stable, making them difficult to isolate. An alternative approach is to begin with a norm which satisfies all the stability criteria for the hyperbolic system, and look for the boundary closure forms which will match the norm exactly. This method was used recently by Strand to isolate stable boundary closure schemes for the explicit central fourth- and sixth-order schemes. The norm used was an energy norm mimicking the norm for the differential equations. Further research should be devoted to BC for high order schemes in order to make sure that the results obtained are reliable. The compact fourth order and sixth order finite difference scheme had been incorporated into a code to simulate flow past circular cylinders. This code will serve as a verification of the full spectral codes. A detailed stability analysis by Carpenter (from the fluid Mechanics Division) and Gottlieb gave analytic conditions for stability as well as asymptotic stability. This had been incorporated in the code in form of stable boundary conditions. Effects of the cylinder rotations had been studied. The results differ from the known theoretical results. We are in the middle of analyzing the results. A detailed analysis of the effects of the heating of the cylinder on the shedding frequency had been studied using the above schemes. It has been found that the shedding frequency decreases when the wire was heated. Experimental work is being carried out to affirm this result.

Gottlieb, David↗
NASA NTRS1993

Large eddy simulations and direct numerical simulations of high speed turbulent reacting flows

The primary objective of this research is to extend current capabilities of Large Eddy Simulations (LES) and Direct Numerical Simulations (DNS) for the computational analyses of high speed reacting flows. Our efforts in the first two years of this research have been concentrated on a priori investigations of single-point Probability Density Function (PDF) methods for providing subgrid closures in reacting turbulent flows. In the efforts initiated in the third year, our primary focus has been on performing actual LES by means of PDF methods. The approach is based on assumed PDF methods and we have performed extensive analysis of turbulent reacting flows by means of LES. This includes simulations of both three-dimensional (3D) isotropic compressible flows and two-dimensional reacting planar mixing layers. In addition to these LES analyses, some work is in progress to assess the extent of validity of our assumed PDF methods. This assessment is done by making detailed companions with recent laboratory data in predicting the rate of reactant conversion in parallel reacting shear flows. This report provides a summary of our achievements for the first six months of the third year of this program.

Givi, P.↗
NASA NTRS1993

Time accurate simulations of compressible shear flows

The objectives of this research are to employ direct numerical simulation (DNS) to study the phenomenon of mixing (or lack thereof) in compressible free shear flows and to suggest new means of enhancing mixing in such flows. The shear flow configurations under investigation are those of parallel mixing layers and planar jets under both non-reacting and reacting nonpremixed conditions. During the three-years of this research program, several important issues regarding mixing and chemical reactions in compressible shear flows were investigated.

Givi, Peyman↗
NASA NTRS1993

Large-eddy simulation of turbulent flow in a channel with a surface-mounted two-dimensional obstacle using a dynamic subgrid-scale model

We apply the dynamic subgrid-scale model (DSGSM) to large-eddy simulation (LES) of turbulent channel flow with a square rib mounted on one wall. The Reynolds number (Re) is 3210 based on the mean velocity above the obstacle and the obstacle height. Near-wall structures are resolved with the no-slip boundary condition. The results show better agreement with direct numerical simulation (DNS) than LES with a fixed model constant, verifying the value of the DSGSM for simulating complex turbulent flows.

Yang, Kyung-Soo↗
NASA NTRS1993

One-equation near-wall turbulence modeling with the aid of direct simulation data

The length scales appearing in the relations for the eddy viscosity and dissipation rate in one-equation models were evaluated from direct numerical (DNS) simulation data for developed channel and boundary-layer flow at two Reynolds numbers each. To prepare the ground for the evaluation, the distribution of the most relevant mean-flow and turbulence quantities is presented and discussed, also with respect to Reynolds-number influence and to differences between channel and boundary-layer flow. An alternative model is tested as near wall component of a two-layer model by application to developed-channel, boundary-layer and backward-facing-step flows.

Rodi, W.↗
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.↗