Search NASA⌕ Search

SEARCH · Search NASA

Results for “RANS simulations”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 163 records · Page 9

Effect of Spatial Filtering in Implicit Large-Eddy Simulations of Separated Flows

The relatively high Reynolds number of turbulent flows encountered in various applications puts these problems well beyond the reach of direct numerical simulation (DNS) at present. Meanwhile, lower-fidelity Reynolds-averaged Navier-Stokes (RANS) calculations are known to be not accurate enough in complex problems, such as smooth-body flow separation and other flows involving highly-unsteady phenomena. Hence, given the current infeasibility of DNS and the unsatisfactory performance of RANS, intermediate techniques such as large-eddy simulation (LES) and hybrid RANS-LES, whose fidelity lie between RANS and DNS, have received much attention for application to various problems of practical importance. Modeling of the effect of missing scales on resolved scales, also known as subgrid-scale (SGS) modeling, is an important subject for LES. SGS models can be broadly categorized as explicit or implicit approaches. The explicit approach is based on an SGS model that explicitly appears in the governing equations expressed in the form of so-called “filtered Navier-Stokes equations”, which describe the evolution of the turbulence scales resolved by the LES grid. The effect of the scales unresolved by the grid is represented by the SGS model. The implicit modeling approach, on the other hand, does not employ an explicit model but instead treats the intrinsic dissipation of the numerical discretization scheme as an implicit SGS model. An LES without an explicit SGS model is commonly termed as an implicit LES (ILES). The relative merits of one SGS modeling approach over another is a subject of ongoing debate. We have opted to employ an ILES methodology, based on high-order compact finite-difference and spatial filtering schemes, in our recent investigations of separated flow problems [1, 2]. Further discussion of our preference of ILES over explicit LES is provided in Uzun and Malik [2]. The spatial filtering operation, described in the next section, is treated as an implicit SGS model for the ILES. Some observations made during the course of our recent investigations, which pointed out to excessive numerical dissipation in certain parts of the flowfield, prompted us to take a closer look at the potential effect of the spatial filter on ILES predictions. This technical note is therefore devoted to spatial filter effects in the context of a high Reynolds number, transonic shock-induced separated flow.

Ali Uzun↗

Numerical Simulation of Forced and Free-to-Roll Delta-Wing Motions

The three-dimensional, Reynolds-averaged, Navier-Stokes (RANS) equations are used to numerically simulate nonsteady vortical flow about a 65-deg sweep delta wing at 30-deg angle of attack. Two large-amplitude, high-rate, forced-roll motions, and a damped free-to-roll motion are presented. The free-to-roll motion is computed by coupling the time-dependent RANS equations to the flight dynamic equation of motion. The computed results are in good agreement with the forces, moments, and roll-angle time histories. Vortex breakdown is present in each case. Significant time lags in the vortex breakdown motions relative to the body motions strongly influence the dynamic forces and moments.

Chaderjian, Neal M.↗

Simulations of Turbulent Momentum and Scalar Transport in Confined Swirling Coaxial Jets

This paper presents the numerical simulations of confined three dimensional coaxial water jets. The objectives are to validate the newly proposed nonlinear turbulence models of momentum and scalar transport, and to evaluate the newly introduced scalar APDF and DWFDF equation along with its Eulerian implementation in the National Combustion Code (NCC). Simulations conducted include the steady RANS, the unsteady RANS (URANS), and the time-filtered Navier-Stokes (TFNS) with and without invoking the APDF or DWFDF equation. When the APDF or DWFDF equation is invoked, the simulations are of a hybrid nature, i.e., the transport equations of energy and species are replaced by the APDF or DWFDF equation. Results of simulations are compared with the available experimental data. Some positive impacts of the nonlinear turbulence models and the Eulerian scalar APDF and DWFDF approach are observed.

Shih, Tsan-Hsing↗

The NASA Low-Pressure Turbine Flow Physics Program

An overview of the NASA Lewis Low-Pressure Turbine (LPT) Flow Physics Program will be presented. The program was established in response to the aero-engine industry's need for improved LPT efficiency and designs. Modern jet engines have four to seven LPT stages, significantly contributing to engine weight. In addition, there is a significant efficiency degradation between takeoff and cruise conditions, of up to 2 points. Reducing the weight and part count of the LPT and minimizing the efficiency degradation will translate into fuel savings. Accurate prediction methods of LPT flows and losses are needed to accomplish those improvements. The flow in LPT passages is at low Reynolds number, and is dominated by interplay of three basic mechanisms: transition, separation and wake interaction. The affecting parameters traditionally considered are Reynolds number, freestream turbulence intensity, wake frequency parameter, and the pressure distribution (loading). Three-dimensional effects and additional parameters, particularly turbulence characteristics like length scales, spectra and other statistics, as well as wake turbulence intensity and properties also play a role. The flow of most interest is on the suction surface, where large losses are generated as the flow tends to separate at the low Reynolds numbers. Ignoring wakes, a common flow scenario, there is laminar separation, followed by transition on the separation bubble and turbulent reattachment. If transition starts earlier the separation will be eliminated and the boundary layer will be attached leading to the well known bypass transition issues. In contrast, transition over a separation bubble is closer to free shear layer transition and was not investigated as well, particularly in the turbine environment. Unsteadiness created by wakes complicates the picture. Wakes induce earlier transition, and the calmed regions trailing the induced turbulent spots can delay or eliminate separation via shear stress modification. Three-dimensional flow physics and geometry will have strong effects. Altogether a very complex and challenging problem emerges. The objective of the program is to provide improved models and physical understanding of the complex flow, which are essential for accurate prediction of flow and losses in the LPT. Experimental, computational and analytical work as complementing and augmenting approaches are used. The program involves industry, universities and research institutes, and other government laboratories. It is characterized by strong interaction among participants, quick dissemination of results, and responsiveness to industry's needs. The presentation will describe the work elements. Highlighting some activities in progress are experiments on simulated blade suction surface in low-speed wind tunnels, on curved wall, and on a flat-plate, both with pressure gradient. In the area of computation, assessment of existing models is performed using RANS (Reynolds Averaged Navier Stokes) simulations. Laminar flow DNS was completed. Analytical studies of instability and receptivity in attached and separated flows were started. In the near future the program is moving to include wake effects and development of improved modeling. Experimental work in preparation stages are: (1) Addition of wakes to the curved tunnel experiment; (2) Low-speed rotating rig experiment on GE90 engine LPT; and (3) Transonic cascade. In the area of computation, it is expected to move from model assessment towards development of improved models. In addition, a new project of Large Eddy Simulation (LES) of LPT is to begin and will provide numerical data bases. It is planned to implement the emerging improved models in a multistage turbomachinery code and to validate against the GE90 engine LPT.

Ashpis, David E.↗

Simulations of Turbulent Momentum and Scalar Transport in Non-Reacting Confined Swirling Coaxial Jets

This paper presents the numerical simulations of confined three-dimensional coaxial water jets. The objectives are to validate the newly proposed nonlinear turbulence models of momentum and scalar transport, and to evaluate the newly introduced scalar APDF and DWFDF equation along with its Eulerian implementation in the National Combustion Code (NCC). Simulations conducted include the steady RANS, the unsteady RANS (URANS), and the time-filtered Navier-Stokes (TFNS); both without and with invoking the APDF or DWFDF equation. When the APDF (ensemble averaged probability density function) or DWFDF (density weighted filtered density function) equation is invoked, the simulations are of a hybrid nature, i.e., the transport equations of energy and species are replaced by the APDF or DWFDF equation. Results of simulations are compared with the available experimental data. Some positive impacts of the nonlinear turbulence models and the Eulerian scalar APDF and DWFDF approach are observed.

combustors↗

The Sensitivity of West African Squall Line Water Budgets to Land Cover

This study used a two-dimensional coupled land/atmosphere (cloud-resolving) model to investigate the influence of land cover on the water budgets of squall lines in the Sahel. Study simulations used the same initial sounding and one of three different land covers, a sparsely vegetated semi-desert, a grassy savanna, and a dense evergreen broadleaf forest. All simulations began at midnight and ran for 24 hours to capture a full diurnal cycle. In the morning, the latent heat flux, boundary layer mixing ratio, and moist static energy in the boundary layer exhibited notable variations among the three land covers. The broadleaf forest had the highest latent heat flux, the shallowest, moistest, slowest growing boundary layer, and significantly more moist static energy per unit area than the savanna and semi-desert. Although all simulations produced squall lines by early afternoon, the broadleaf forest had the most intense, longest-lived squall lines with 29% more rainfall than the savanna and 37% more than the semi-desert. The sensitivity of the results to vegetation density, initial sounding humidity, and grid resolution was also assessed. There were greater differences in rainfall among land cover types than among simulations of the same land cover with varying amounts of vegetation. Small changes in humidity were equivalent in effect to large changes in land cover, producing large changes in the condensate and rainfall. Decreasing the humidity had a greater effect on rainfall volume than increasing the humidity. Reducing the grid resolution from 1.5 km to 0.5 km decreased the temperature and humidity of the cold pools and increased the rain volume.

Mohr, Karen I.↗

OVERFLOW Analysis of Supersonic Retropropulsion Testing on a Blunt Mars Entry Vehicle Concept

Supersonic retropropulsion (SRP) flow over a Hypersonic Inflatable Aerodynamic Decelerator (HIAD) blunt-body vehicle was simulated using the Overflow Computational Fluid Dynamics (CFD) solver. Two nozzle configurations were tested (1E and 1F) as a subset of the seven total configurations in the Descent System Study (DSS) testing campaign. A generalized, Adaptive Mesh Refinement (AMR) shock capturing and plume refinement technique was developed and calibrated for producing automatic and unique grid systems optimized for any given testing condition. Solution independence from grid resolution was determined by successively increasing grid refinement until asymptotic convergence of the mean aerodynamic loads was observed. Overflow Reynolds-averaged Navier-Stokes (RANS) solutions produced realistic SRP flow phenomena, including Mach disk normal shocks contained in high-thrust plumes and bow shock triple-points. Solutions for the 1E nozzle configuration were steady. Conversely, a subset of the 1F test conditions were unsteady and exhibited periodic, non-sinusoidal expansions and contractions of the streamwise-oriented plume, resulting in unsteady aerodynamic loads on the vehicle. Initial investigations into the effect of turbulence modeling fidelity demonstrated significant differences between the aerodynamic loads simulated with RANS and Detached Eddy Simulation (DES). Multiple flow mechanisms were identified as root causes of these differences, including bow shock shape augmentation and reduced entrainment due to reduced turbulence in the DES simulations. Initial comparisons of pitching moment control authority and aerodynamic drag performance between the tested nozzle configurations demonstrated that the 1E configuration may be more advantageous for the Mars Entry, Descent, and Landing (EDL) task.

Supersonic Retropropulsion↗

OVERFLOW Analysis of Supersonic Retropropulsion Testing on a Blunt Mars Entry Vehicle Concept

Supersonic retropropulsion (SRP) flow over a Hypersonic Inflatable Aerodynamic Decelerator (HIAD) blunt-body vehicle was simulated using the Overflow Computational Fluid Dynamics (CFD) solver. Two nozzle configurations were tested (1E and 1F) as a subset of the seven total configurations in the Descent System Study (DSS) testing campaign. A generalized, Adaptive Mesh Refinement (AMR) shock capturing and plume refinement technique was developed and calibrated for producing automatic and unique grid systems optimized for any given testing condition. Solution independence from grid resolution was determined by successively increasing grid refinement until asymptotic convergence of the mean aerodynamic loads was observed. Overflow Reynolds-averaged Navier-Stokes (RANS) solutions produced realistic SRP flow phenomena, including Mach disk normal shocks contained in high-thrust plumes and bow shock triple-points. Solutions for the 1E nozzle configuration were steady. Conversely, a subset of the 1F test conditions were unsteady and exhibited periodic, non-sinusoidal expansions and contractions of the streamwise-oriented plume, resulting in unsteady aerodynamic loads on the vehicle. Initial investigations into the effect of turbulence modeling fidelity demonstrated significant differences between the aerodynamic loads simulated with RANS and Detached Eddy Simulation (DES). Multiple flow mechanisms were identified as root causes of these differences, including bow shock shape augmentation and reduced entrainment due to reduced turbulence in the DES simulations. Initial comparisons of pitching moment control authority and aerodynamic drag performance between the tested nozzle configurations demonstrated that the 1E configuration may be more advantageous for the Mars Entry, Descent, and Landing (EDL) task.

Supersonic Retropropulsion↗

Noise of Embedded High Aspect Ratio Nozzles

A family of high aspect ratio nozzles were designed to provide a parametric database of canonical embedded propulsion concepts. Nozzle throat geometries with aspect ratios of 2:1, 4:1, and 8:1 were chosen, all with convergent nozzle areas. The transition from the typical round duct to the rectangular nozzle was designed very carefully to produce a flow at the nozzle exit that was uniform and free from swirl. Once the basic rectangular nozzles were designed, external features common to embedded propulsion systems were added: extended lower lip (a.k.a. bevel, aft deck), differing sidewalls, and chevrons. For the latter detailed Reynolds-averaged Navier-Stokes (RANS) computational fluid dynamics (CFD) simulations were made to predict the thrust performance and to optimize parameters such as bevel length, and chevron penetration and azimuthal curvature. Seventeen of these nozzles were fabricated at a scale providing a 2.13 inch diameter equivalent area throat." ! The seventeen nozzles were tested for far-field noise and a few data were presented here on the effect of aspect ratio, bevel length, and chevron count and penetration. The sound field of the 2:1 aspect ratio rectangular jet was very nearly axisymmetric, but the 4:1 and 8:1 were not, the noise on their minor axes being louder than the major axes. Adding bevel length increased the noise of these nozzles, especially on their minor axes, both toward the long and short sides of the beveled nozzle. Chevrons were only added to the 2:1 rectangular jet. Adding 4 chevrons per wide side produced some decrease at aft angles, but increased the high frequency noise at right angles to the jet flow. This trend increased with increasing chevron penetration. Doubling the number of chevrons while maintaining their penetration decreased these effects. Empirical models of the parametric effect of these nozzles were constructed and quantify the trends stated above." Because it is the objective of the Supersonics Project that future design work be done more by physics-based computations and less by experiments, several codes under development were evaluated against these test cases. Preliminary results show that the RANS-based code JeNo predicts the spectral directivity of the low aspect ratio jets well, but has no capability to predict the non-axisymmetry. An effort to address this limitations, used in the RANS-based code of Leib and Goldstein, overpredicted the impact of aspect ratio. The broadband shock noise code RISN, also limited to axisymmetric assumptions, did a good job of predicting the spectral directivity of underexpanded 2:1 cold jet case but was not as successful on high aspect ratio jets, particularly when they are hot. All results are preliminary because the underlying CFD has not been validated yet. An effort using a Large Eddy Simulation code by Stanford University predicted noise that agreed with experiments to within a few dB.

Bridges, James E.↗

Exploring Unstructured Mesh Adaptation for Hybrid Reynolds-Averaged Navier–Stokes/Large Eddy Simulation

Mesh adaptation methods for the Reynolds-averaged Navier–Stokes (RANS) equations are rapidly maturing and beginning to impact the design of aerospace vehicles. RANS turbulence modeling improvements have slowed and may stagnate. Wall-modeled large eddy simulation (LES) and hybrid RANS/LES (HRLES) may provide an improved modeling capability but require specialized expertise to construct appropriate meshes and are considered be too ex-pensive for routine practical use. The realization of the CFD Vision 2030 Study includes improving geometry linkage, mesh generation/adaptation, and turbulence modeling/resolving methods for automated management of errors and uncertainties of physics-based, predictive modeling that can set the stage for ensuring a vehicle is in compliance with a regulation or specification (i.e., certification or qualification by analysis). An exploration of mesh adaptation for HRLES is performed to document synergies and challenges between mesh adaptation and HRLES. Vortex breakdown over a delta wing is examined to show the improvement of HRLES over RANS turbulence modeling approaches. A high lift configuration is shown to demonstrate complex geometry capability. Research and development opportunities are identified to advocate for continuing investments that may allow HRLES to enter routine practical use as a tool for aerospace vehicle analysis and design.

Michael A Park↗

Time Accurate CFD Simulations of the Orion Launch Abort Vehicle in the Transonic Regime

Significant asymmetries in the fluid dynamics were calculated for some cases in the CFD simulations of the Orion Launch Abort Vehicle through its abort trajectories. The CFD simulations were performed steady state and in three dimensions with symmetric geometries, no freestream sideslip angle, and motors firing. The trajectory points at issue were in the transonic regime, at 0 and +/- 5 angles of attack with the Abort Motors with and without the Attitude Control Motors (ACM) firing. In some of the cases the asymmetric fluid dynamics resulted in aerodynamic side forces that were large enough that would overcome the control authority of the ACMs. MSFC's Fluid Dynamics Group supported the investigation into the cause of the flow asymmetries with time accurate CFD simulations, utilizing a hybrid RANS-LES turbulence model. The results show that the flow over the vehicle and the subsequent interaction with the AB and ACM motor plumes were unsteady. The resulting instantaneous aerodynamic forces were oscillatory with fairly large magnitudes. Time averaged aerodynamic forces were essentially symmetric.

Rojahn, Josh↗

Time Accurate CFD Simulations of the Orion Launch Abort Vehicle in the Transonic Regime

Significant asymmetries in the fluid dynamics were calculated for some cases in the CFD simulations of the Orion Launch Abort Vehicle through its abort trajectories. The CFD simulations were performed steady state with symmetric boundary conditions and geometries. The trajectory points at issue were in the transonic regime, at 0 and 5 angles of attack with the Abort Motors with and without the Attitude Control Motors (ACM) firing. In some of the cases the asymmetric fluid dynamics resulted in aerodynamic side forces that were large enough that would overcome the control authority of the ACMs. MSFC s Fluid Dynamics Group supported the investigation into the cause of the flow asymmetries with time accurate CFD simulations, utilizing a hybrid RANS-LES turbulence model. The results show that the flow over the vehicle and the subsequent interaction with the AB and ACM motor plumes were unsteady. The resulting instantaneous aerodynamic forces were oscillatory with fairly large magnitudes. Time averaged aerodynamic forces were essentially symmetric.

Ruf, Joseph↗

Simulations of Turbulent Momentum and Scalar Transport in Confined Swirling Coaxial Jets

This paper presents the numerical simulations of confined three-dimensional coaxial water jets. The objectives are to validate the newly proposed nonlinear turbulence models of momentum and scalar transport, and to evaluate the newly introduced scalar APDF and DWFDF equation along with its Eulerian implementation in the National Combustion Code(NCC). Simulations conducted include the steady RANS, the unsteady RANS (URANS), and the time-filtered Navier-Stokes (TFNS); both without and with invoking the APDF or DWFDF equation.

combustors↗

Performance Characteristics of a Boundary Layer Ingesting Inlet - Distortion Tolerant Fan Through CFD Code Coupling

A method of constructing a high-fidelity simulation using two NASA CFD codes, Launch Ascent and Vehicle Aerodynamics (LAVA), which is the general-purpose solver, and a turbomachinery specific code NASA-TURBO (TURBO), will be presented. Validation of the code coupling is performed through comparison to experimental data obtained in the 2017 wind tunnel test of NASA’s Boundary Layer Ingesting Inlet - Distortion Tolerant Fan (BLI2DTF). For the simulation, the external flow field is computed by LAVA utilizing a steady-state Reynolds-averaged Navier-Stokes (RANS) methodology. Data from LAVA is exchanged with TURBO, which simulated the propulsor utilizing an unsteady-RANS methodology. A sensitivity analysis is performed using averaged and instantaneous data transfer between the two codes, as well as varying the amount of simulation time TURBO computes between updates. The results of the coupled simulations appear to replicate the BLI2DTF experiment correctly. Static pressure taps leading into and around the nacelle, total pressure ratio and efficiency of the propulsor, and profiles of total temperature, pressure, and Mach number at the rear measurement plane, aft of the propulsor, are in good agreement with experimental data. These results provide confidence that the coupled simulation is behaving in a physically realizable manner.

CFD↗

Optimal Design of Passive Flow Control for a Boundary-Layer-Ingesting Offset Inlet Using Design-of-Experiments

This research will investigate the use of Design-of-Experiments (DOE) in the development of an optimal passive flow control vane design for a boundary-layer-ingesting (BLI) offset inlet in transonic flow. This inlet flow control is designed to minimize the engine fan-face distortion levels and first five Fourier harmonic half amplitudes while maximizing the inlet pressure recovery. Numerical simulations of the BLI inlet are computed using the Reynolds-averaged Navier-Stokes (RANS) flow solver, OVERFLOW, developed at NASA. These simulations are used to generate the numerical experiments for the DOE response surface model. In this investigation, two DOE optimizations were performed using a D-Optimal Response Surface model. The first DOE optimization was performed using four design factors which were vane height and angles-of-attack for two groups of vanes. One group of vanes was placed at the bottom of the inlet and a second group symmetrically on the sides. The DOE design was performed for a BLI inlet with a free-stream Mach number of 0.85 and a Reynolds number of 2 million, based on the length of the fan-face diameter, matching an experimental wind tunnel BLI inlet test. The first DOE optimization required a fifth order model having 173 numerical simulation experiments and was able to reduce the DC60 baseline distortion from 64% down to 4.4%, while holding the pressure recovery constant. A second DOE optimization was performed holding the vanes heights at a constant value from the first DOE optimization with the two vane angles-of-attack as design factors. This DOE only required a second order model fit with 15 numerical simulation experiments and reduced DC60 to 3.5% with small decreases in the fourth and fifth harmonic amplitudes. The second optimal vane design was tested at the NASA Langley 0.3- Meter Transonic Cryogenic Tunnel in a BLI inlet experiment. The experimental results showed a 80% reduction of DPCP(sub avg), the circumferential distortion level at the engine fan-face.

Allan, Brian G.↗

Optimal Design of Passive Flow Control for a Boundary-Layer-Ingesting Offset Inlet Using Design-of-Experiments

This research will investigate the use of Design-of-Experiments (DOE) in the development of an optimal passive flow control vane design for a boundary-layer-ingesting (BLI) offset inlet in transonic flow. This inlet flow control is designed to minimize the engine fan face distortion levels and first five Fourier harmonic half amplitudes while maximizing the inlet pressure recovery. Numerical simulations of the BLI inlet are computed using the Reynolds-averaged Navier-Stokes (RANS) flow solver, OVERFLOW, developed at NASA. These simulations are used to generate the numerical experiments for the DOE response surface model. In this investigation, two DOE optimizations were performed using a D-Optimal Response Surface model. The first DOE optimization was performed using four design factors which were vane height and angles-of-attack for two groups of vanes. One group of vanes was placed at the bottom of the inlet and a second group symmetrically on the sides. The DOE design was performed for a BLI inlet with a free-stream Mach number of 0.85 and a Reynolds number of 2 million, based on the length of the fan face diameter, matching an experimental wind tunnel BLI inlet test. The first DOE optimization required a fifth order model having 173 numerical simulation experiments and was able to reduce the DC60 baseline distortion from 64% down to 4.4%, while holding the pressure recovery constant. A second DOE optimization was performed holding the vanes heights at a constant value from the first DOE optimization with the two vane angles-of-attack as design factors. This DOE only required a second order model fit with 15 numerical simulation experiments and reduced DC60 to 3.5% with small decreases in the fourth and fifth harmonic amplitudes. The second optimal vane design was tested at the NASA Langley 0.3-Meter Transonic Cryogenic Tunnel in a BLI inlet experiment. The experimental results showed a 80% reduction of DPCPavg, the circumferential distortion level at the engine fan face.

Allan, Brian G.↗

LES, DNS and RANS for the analysis of high-speed turbulent reacting flows

The objective of this research is to continue our efforts in advancing the state of knowledge in Large Eddy Simulation (LES), Direct Numerical Simulation (DNS), and Reynolds Averaged Navier Stokes (RANS) methods for the analysis of high-speed reacting turbulent flows. In the first phase of this research, conducted within the past six months, focus was in three directions: RANS of turbulent reacting flows by Probability Density Function (PDF) methods, RANS of non-reacting turbulent flows by advanced turbulence closures, and LES of mixing dominated reacting flows by a dynamics subgrid closure. A summary of our efforts within the past six months of this research is provided in this semi-annual progress report.

Givi, Peyman↗

LES, DNS and RANS for the analysis of high-speed turbulent reacting flows

The purpose of this research is to continue our efforts in advancing the state of knowledge in large eddy simulation (LES), direct numerical simulation (DNS), and Reynolds averaged Navier Stokes (RANS) methods for the computational analysis of high-speed reacting turbulent flows. In the second phase of this work, covering the period 1 Sep. 1993 - 1 Sep. 1994, we have focused our efforts on two research problems: (1) developments of 'algebraic' moment closures for statistical descriptions of nonpremixed reacting systems, and (2) assessments of the Dirichlet frequency in presumed scalar probability density function (PDF) methods in stochastic description of turbulent reacting flows. This report provides a complete description of our efforts during this past year as supported by the NASA Langley Research Center under Grant NAG1-1122.

Givi, Peyman↗