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At least 289 records · Page 16

The Pore Formation and Mobility Investigation: A Summary of Conducted Research on the International Space Station

The Pore Formation and Mobility Investigation (PFMI) is being conducted in the Microgravity Science Glovebox (MSG) aboard the International Space Station (ISS) with the goal of understanding bubble generation and interactions during controlled directional solidification processing. Through the course of the experiments, beginning in September 2002, a number of key factors pertinent to solidification processing of materials in a microgravity environment have been directly observed, measured, and modeled. Though most experiments ran uninterrupted, on four separate occasions malfunctions to the PFMI hardware and software were experienced that required crew intervention, including in-space repair. Fortunately, each repair attempt was successful and restored the PFMI apparatus to a fully functional condition. Based on PFMI results and lessons learned, the intent of this presentation is to draw attention to the role ISS experiments/hardware can play in providing insight to potential fabrication processing techniques and repair scenarios that might arise during long duration space transport and/or on the lunar/Mars surface.

Grugel, R. N.↗

A Hybrid RANS/LES Approach for Predicting Jet Noise

Hybrid acoustic prediction methods have an important advantage over the current Reynolds averaged Navier-Stokes (RANS) based methods in that they only involve modeling of the relatively universal subscale motion and not the configuration dependent larger scale turbulence. Unfortunately, they are unable to account for the high frequency sound generated by the turbulence in the initial mixing layers. This paper introduces an alternative approach that directly calculates the sound from a hybrid RANS/LES flow model (which can resolve the steep gradients in the initial mixing layers near the nozzle lip) and adopts modeling techniques similar to those used in current RANS based noise prediction methods to determine the unknown sources in the equations for the remaining unresolved components of the sound field. The resulting prediction method would then be intermediate between the current noise prediction codes and previously proposed hybrid noise prediction methods.

Goldstein, Marvin E.↗

Preliminary Evaluation of GEOS-5 Aerosol and CO Distributions Forecast During TC4

The NASA Tropical Composition, Cloud, and Climate Coupling (TC4) Mission was based out San Jose, Costa Rica during July and August 2007. During TC4 the NASA Global Modeling and Assimilation Office (GMAO) ran twice-daily 0.5 x 0.666 global 5-day forecasts of the Goddard Earth Observing System atmospheric general circulation model and data assimilation system (GEOS-5). This implementation of GEOS-5 contained an aerosol and carbon monoxide (CO) model to provide online forecast tropospheric distributions of dust, sea salt, sulfate, and carbonaceous aerosols and CO for both the planning of flights and for science. Here we provide a description of the aerosol and CO modeling system and give a preliminary evaluation of forecast tracer distributions. Our comparisons to satellite observations of aerosol and CO show qualitatively similar simulated distributions of tracers to those observed. During TC4 copious amounts of dust were observed in the Caribbean. The model generally reproduced the observations of the timing of dust events and the vertical structure in the lower atmosphere. However, the model simulations had too much aerosol at high altitudes relative to airborne Cloud Physics Lidar observations. The results were similar for biomass burning aerosol and CO tracers, where the model showed higher simulated concentrations of these tracers at aircraft flight altitude than observations.

Colarco, Peter R.↗

Jet Surface Interaction Scrubbing Noise from High Aspect-Ratio Rectangular Jets

Concepts envisioned for the future of civil air transport consist of unconventional propulsion systems in the close proximity of the airframe. Distributed propulsion system with exhaust configurations that resemble a high aspect ratio rectangular jet are among geometries of interest. Nearby solid surfaces could provide noise shielding for the purpose of reduced community noise. Interaction of high-speed jet exhaust with structure could also generate new sources of sound as a result of flow scrubbing past the structure, and or scattered noise from sharp edges. The present study provides a theoretical framework to predict the scrubbing noise component from a high aspect ratio rectangular exhaust in proximity of a solid surface. The analysis uses the Greens function (GF) to the variable density Pridmore-Brown equation in a transversely sheared mean flow. Sources of sound are defined as the auto-covariance function of second-rank velocity fluctuations in the jet plume, and are modeled using a RANS-based acoustic analogy approach. Acoustic predictions are presented in an 8:1 aspect ratio rectangular exhaust at three subsonic Mach numbers. The effect of nearby surface on the scrubbing noise component is shown on both reflected and shielded sides of the plate.

Propulsion Noise↗

Overview of the Inaugural Space Health Impacts for the NASA Experience (SHINE) Training Program – Virtual Space Radiation Curriculum

The Space Radiation Element part of NASA Human Research Program initiated a virtual, annual space radiation curriculum. The SHINE space radiation curriculum aims to educate participants not only in the scientific aspects of space radiation but also in the agency’s risk management strategies. SHINE combines weekly seminars by speakers from NASA, other government agencies, academia, and industry, with networking sessions designed to foster collaboration between participants and interactions with NASA scientists. A total of 59 applications were received from which 25 participants were selected. The 25 participants, with citizenship from a total of 8 countries, are composed of 5 graduate students, 4 postdocs, 11 scientists and 5 professors/medical doctors. Participants have a wide range of expertise including molecular and cellular biology, microbiology, botany, physiology, engineering, physics, aerospace medicine, planetary science, biostatistics, and modeling. The inaugural course ran weekly from February 2023 to August 2023 and was comprised of lectures, less formal coffee hours and office hours. The topics covered ranged from space environments to health effects to granting opportunities. The second annual SHINE training program is scheduled from February to August 2024. In addition, a separate competitive practicum session, to allow participants to gain hands-on radiation experience, will be held Fall 2024 at the NASA Space Radiation Laboratory (NSRL).

Janice A. Zawask↗

Overview of The Inaugural Space Health Impacts for the NASA Experience (SHINE) Training Program - Virtual Space Radiation Curriculum

The Space Radiation Element part of NASA Human Research Program initiated a virtual, annual space radiation curriculum. The SHINE space radiation curriculum aims to educate participants not only in the scientific aspects of space radiation but also in the agency’s risk management strategies. SHINE combines weekly seminars by speakers from NASA, other government agencies, academia, and industry, with networking sessions designed to foster collaboration between participants and interactions with NASA scientists. A total of 59 applications were received from which 25 participants were selected. The 25 participants, with citizenship from a total of 8 countries, are composed of 5 graduate students, 4 postdocs, 11 scientists and 5 professors/medical doctors. Participants have a wide range of expertise including molecular and cellular biology, microbiology, botany, physiology, engineering, physics, aerospace medicine, planetary science, biostatistics, and modeling. The inaugural course ran weekly from February 2023 to August 2023 and was comprised of lectures, less formal coffee hours and office hours. The topics covered ranged from space environments to health effects to granting opportunities. The second annual SHINE training program is scheduled from February to August 2024. In addition, a separate competitive practicum session, to allow participants to gain hands-on radiation experience, will be held Fall 2024 at the NASA Space Radiation Laboratory (NSRL).

SHINE↗

Jet Surface Interaction-Scrubbing Noise

Generation of sound due to scrubbing of a jet flow past a nearby solid surface is investigated within the framework of the generalized acoustic analogy theory. The analysis applies to the boundary layer noise generated at and near a wall, and excludes the scattered noise component that is produced at the leading or the trailing edge. While compressibility effects are relatively unimportant at very low Mach numbers, frictional heat generation and thermal gradient normal to the surface could play important roles in generation and propagation of sound in high speed jets of practical interest. A general expression is given for the spectral density of the far-field sound as governed by the variable density Pridmore- Brown equation. The propagation Green's function should be solved numerically starting with the boundary conditions on the surface and subject to specified mean velocity and temperature profiles between the surface and the observer. The equivalent sources of aerodynamic sound are associated with non-linear momentum flux and enthalpy flux terms that appear in the linearized Navier-Stokes equations. These multi-pole sources should be modeled and evaluated with input from a Reynolds-Averaged Navier-Stokes (RANS) solver with an appropriate turbulence model.

Khavaran, Abbas↗

Toward Verification of the γ-Reθt Transition Model in OVERFLOW and FUN3D

The results of an ongoing assessment of the transition modeling capability in NASA's OVERFLOW and FUN3D programs are presented, with a focus on the Langtry-Menter γ-Reθt transition model in combination with the shear-stress transport (SST) turbulence model. While the effect of numerics and boundary conditions on the accuracy and iterative convergence of RANS solutions for fully turbulent flows has been well documented, especially in the context of canonical flow configurations, the same cannot be said for transport-equation-based transition models coupled with RANS-based turbulence models. Given the criticality of transition modeling for new aircraft design and optimization, there has been a renewed focus on the accuracy of such transition models and their inconsistent implementation across different flow solvers as seen from the AIAA and NATO-AVT workshops. In this work, we aim to establish the verification of such models via these two well established CFD codes with different numerics. The goal is to produce high-quality data, such as grids, solutions, and other auxiliary data, that may be utilized for code verification by others in the CFD community. As a first step, the work reported here is focused on the Langtry-Menter transition model as applied to two simple 2D configurations, namely the flat plate, and the NLF-0416, respectively. The paper also highlights how the boundary conditions and baseline turbulence model can affect the solutions from the SST-based Langtry-Menter transition model. A preliminary evaluation of the automatic mesh adaption capabilities of these solvers and potential benefits for flow configurations involving a mix of laminar, transitional, and fully turbulent flows is also reported.

CFD Modeling↗

Numerical Study of High-Temperature Jet Flow Using RANS/LES and PANS Formulations

Two multi-scale-type turbulence models are implemented in the PAB3D solver. The models are based on modifying the Reynolds Averaged Navier-Stokes (RANS) equations. The first scheme is a hybrid RANS/LES model utilizing the two-equation (k(epsilon)) model with a RANS/LES transition function dependent on grid spacing and the computed turbulence length scale. The second scheme is a modified version of the Partially Averaged Navier-Stokes (PANS) model, where the unresolved kinetic energy parameter (f(sub k)) is allowed to vary as a function of grid spacing and the turbulence length scale. This parameter is estimated based on a novel two-stage procedure to efficiently estimate the level of scale resolution possible for a given flow on a given grid for Partial Averaged Navier-Stokes (PANS). It has been found that the prescribed scale resolution can play a major role in obtaining accurate flow solutions. The parameter f(sub k) varies between zero and one and equal to one in the viscous sub layer, and when the RANS turbulent viscosity becomes smaller than the LES viscosity. The formulation, usage methodology, and validation examples are presented to demonstrate the enhancement of PAB3D's time-accurate and turbulence modeling capabilities. The accurate simulations of flow and turbulent quantities will provide valuable tool for accurate jet noise predictions. Solutions from these models are compared to RANS results and experimental data for high-temperature jet flows. The current results show promise for the capability of hybrid RANS/LES and PANS in simulating such flow phenomena.

Abdol-Hamid, Khaled S.↗

Computations of Flow over a Hump Model Using Higher Order Method with Turbulence Modeling

Turbulent separated flow over a two-dimensional hump is computed by solving the RANS equations with k - omega (SST) turbulence model for the baseline, steady suction and oscillatory blowing/suction flow control cases. The flow equations and the turbulent model equations are solved using a fifth-order accurate weighted essentially. nonoscillatory (WENO) scheme for space discretization and a third order, total variation diminishing (TVD) Runge-Kutta scheme for time integration. Qualitatively the computed pressure distributions exhibit the same behavior as those observed in the experiments. The computed separation regions are much longer than those observed experimentally. However, the percentage reduction in the separation region in the steady suction case is closer to what was measured in the experiment. The computations did not predict the expected reduction in the separation length in the oscillatory case. The predicted turbulent quantities are two to three times smaller than the measured values pointing towards the deficiencies in the existing turbulent models when they are applied to strong steady/unsteady separated flows.

Balakumar, P.↗

Multiphysics Computational Analysis of a Perforated Plate Cooling Flow

A multiphysics analysis of a film cooling flow was conducted using a computational fluid dynamics (CFD) solver in conjunction with a conjugate heat transfer (CHT) solver. The film cooling problem consisted of a square nozzle producing a heated subsonic jet over a perforated plate with three sections of 45 cooling holes each. Results from the multiphysics analysis were compared to a CFD-only approach and experimental results. Reynolds-averaged Navier-Stokes (RANS) computations were employed first, with and without the CHT solver. The multiphysics approach provided much closer agreement with experimentally measured plate temperatures than the CFD-only approach. Comparisons of computed velocities and temperatures were also made with experimental data. Hybrid RANS-large eddy simulation calculations employing the Delayed Detached Eddy Simulation (DDES) approach were also conducted within the multiphysics framework. The DDES approach was unable to resolve turbulent structures in the near wall regions. Hence, the RANS part of the DDES model was used in near wall regions, and produced surface temperatures along with velocity and temperature profiles close to the wall that were very similar to the RANS results. The DDES approach did resolve structures in the outer portion of the boundary layer especially near the end of the plate where the boundary layer was thicker. The key result was the improved surface temperatures produced by the multiphysics approach employing CHT over the fluid-only approach.

Computational Fluid Dynamics↗

Numerical simulation of involute-plate research reactor flow behavior using RANS, LES and DNS

This paper investigates the flow behavior of involute-plate research reactors by performing Reynolds-Averaged Navier Stokes simulation (RANS), Large Eddy Simulation (LES) and Direct Numerical Simulation (DNS) of the channel flow between fuel plates. By modeling turbulence with different numerical approaches, this study provides data with three levels of fidelity. For the RANS simulation, three widely used turbulence models, i.e., k-ε, k-ω, Reynolds Stress Turbulence model (RST) are applied by using the commercial CFD code STAR-CCM +. For LES and DNS, the open-source CFD code, Nek5000, is used given its outstanding scalability on High Performance Computer (HPC) and high-order technique. The results from RANS simulations are compared with that from LES and DNS for benchmarking. Both macroscale parameters and turbulence statistics, such as velocity magnitude, lateral velocity and turbulence kinetic energy, are presented and analyzed. The results from RANS simulation achieve good agreement with LES and DNS on velocity and turbulence kinetic energy prediction. The RST turbulence model predicts the most similar flow pattern of lateral velocity as compared to LES and DNS. The Lambda-2 (λ2) criterion with a reasonable threshold is used to demonstrate the instantaneous vortices distribution in the involute channel from both LES and DNS calculation. The DNS simulation captures more detailed turbulence especially near the corner, which explains the discrepancy between LES and DNS results near the corner. The normalized RMS error are defined and calculated to assess the performance of those turbulence models. The RST model captures the anisotropic feature of turbulence, which enable it to outperform other turbulence models for predicting the flow behavior in an involute channel. Although some discrepancies are found between LES and DNS results in the corner, the overall deviations between LES and DNS are found to be small. In conclusion, given that the computational cost of DNS calculation is an order of magnitude higher, using LES data for benchmarking RANS model is a cost-effective approach.

DNS↗

An Initial Investigation of the Effects of Turbulence Models on the Convergence of the RK/Implicit Scheme

A three-stage Runge-Kutta (RK) scheme with multigrid and an implicit preconditioner has been shown to be an effective solver for the fluid dynamic equations. This scheme has been applied to both the compressible and essentially incompressible Reynolds-averaged Navier-Stokes (RANS) equations using the algebraic turbulence model of Baldwin and Lomax (BL). In this paper we focus on the convergence of the RK/implicit scheme when the effects of turbulence are represented by either the Spalart-Allmaras model or the Wilcox k-! model, which are frequently used models in practical fluid dynamic applications. Convergence behavior of the scheme with these turbulence models and the BL model are directly compared. For this initial investigation we solve the flow equations and the partial differential equations of the turbulence models indirectly coupled. With this approach we examine the convergence behavior of each system. Both point and line symmetric Gauss-Seidel are considered for approximating the inverse of the implicit operator of the flow solver. To solve the turbulence equations we use a diagonally dominant alternating direction implicit (DDADI) scheme. Computational results are presented for three airfoil flow cases and comparisons are made with experimental data. We demonstrate that the two-dimensional RANS equations and transport-type equations for turbulence modeling can be efficiently solved with an indirectly coupled algorithm that uses the RK/implicit scheme for the flow equations.

Swanson, R. C.↗

Transient Efficiency, Flexibility, and Reliability Optimization of Coal-Fired Power Plants - Final Report

This program developed an advanced model-based monitoring and model-predictive control algorithms for a coal fired power plant (CFPP), and deployed these algorithms in a real-time platform to demonstrate performance benefits for transient flexibility and plant operation efficiency. More specifically, the objectives were successfully achieved through a combination of (i) developing a high-fidelity transient plant model in Apros, which was used as a high-fidelity plant simulation between $100-50\% TMCR$ where TMCR denotes the turbine maximum continuous rating, i.e., baseload, (ii) developing a very fast physics-based reduced-order model (ROM) of the plant, which ran more than $100\times$ faster than real-time, enabling its use as real-time embedded model for model-based estimation (MBE) and model predictive control (MPC) (iii) implementing a real-time MBE based on ROM using a robust unscented Kalman filter (UKF) to continuously tune the ROM to match the measurements from high-fidelity Apros plant model despite significant plant-model mismatch, and thus, obtain a Digital Twin of the plant (iv) designing and implementing a real-time MPC with dual objectives of transient plant load tracking with high ramp rates and minimizing coal consumption, i.e., improving plant efficiency in the baseload-partload operation range of $100-50\% TMCR$. Each key element above was developed and tested individually, and has been reported in corresponding Topical Reports. Finally, all the individual elements were integrated in an overall closed-loop system, that was successfully tested in desktop Simulink test harness simulations with ROM or high-fidelity model as the plant. Thereafter, the Simulink implementation was used to auto-generate C-code and deploy as real-time Docker microservice containers in Linux, and validate that they can run in real-time in the hardware-in-the loop (HIL) setup and produce the same results as in Simulink. The results of the integrated simulation tests in Simulink as well as the real-time HIL deployment are documented in this final report, showing good load tracking for load ramps at $3-4\%/min$ ramp rates, and achieving up to $5.5\%$ reduction in coal relative to baseline operation at $50\% TMCR$ load. The desktop and HIL simulations show successful performance of the overall model based estimation and control solution and achieve the key objectives of the program for flexible, efficient and reliable operation of subcritical coal fired power plants.

20 FOSSIL-FUELED POWER PLANTS↗

Transient Efficiency, Flexibility, and Reliability Optimization of Coal-Fired Power Plants - Final Program Review

This program developed an advanced model-based monitoring and model-predictive control algorithms for a coal fired power plant (CFPP), and deployed these algorithms in a real-time platform to demonstrate performance benefits for transient flexibility and plant operation efficiency. More specifically, the objectives were successfully achieved through a combination of (i) developing a high-fidelity transient plant model in Apros, which was used as a high-fidelity plant simulation between $100-50\% TMCR$ where TMCR denotes the turbine maximum continuous rating, i.e., baseload, (ii) developing a very fast physics-based reduced-order model (ROM) of the plant, which ran more than $100\times$ faster than real-time, enabling its use as real-time embedded model for model-based estimation (MBE) and model predictive control (MPC) (iii) implementing a real-time MBE based on ROM using a robust unscented Kalman filter (UKF) to continuously tune the ROM to match the measurements from high-fidelity Apros plant model despite significant plant-model mismatch, and thus, obtain a Digital Twin of the plant (iv) designing and implementing a real-time MPC with dual objectives of transient plant load tracking with high ramp rates and minimizing coal consumption, i.e., improving plant efficiency in the baseload-partload operation range of $100-50\% TMCR$. Each key element above was developed and tested individually, and has been reported in corresponding Topical Reports. Finally, all the individual elements were integrated in an overall closed-loop system, that was successfully tested in desktop Simulink test harness simulations with ROM or high-fidelity model as the plant. Thereafter, the Simulink implementation was used to auto-generate C-code and deploy as real-time Docker microservice containers in Linux, and validate that they can run in real-time in the hardware-in-the loop (HIL) setup and produce the same results as in Simulink. The results of the integrated simulation tests in Simulink as well as the real-time HIL deployment are documented in this final report, showing good load tracking for load ramps at $3-4\%/min$ ramp rates, and achieving up to $5.5\%$ reduction in coal relative to baseline operation at $50\% TMCR$ load. The desktop and HIL simulations show successful performance of the overall model based estimation and control solution and achieve the key objectives of the program for flexible, efficient and reliable operation of sub-critical coal fired power plants.

20 FOSSIL-FUELED POWER PLANTS↗

Computations of Flow Over a Hump Model Using Higher Order Method With Turbulence Modeling

Turbulent separated flow over a two-dimensional hump is computed by solving the RANS equations with k-omega (SST) turbulence model for the baseline, steady suction and oscillatory blowing/suction flow control cases. The flow equations and the turbulent model equations are solved using a fifth-order accurate weighted essentially nonoscillatory (WENO) scheme for space discretization and a third order, total variation diminishing (TVD) Runge-Kutta scheme for time integration. Qualitatively the computed pressure distributions exhibit the same behavior as they are observed in the experiments. The computed separation regions are much longer than that are observed. However, the percentage reduction in the separation region in the steady suction case is closer to that was measured in the experiment. The computations did not predict the expected reduction in the separation length in the oscillatory case. The predicted turbulent quantities are two to three times smaller than that are measured and it points towards the deficiencies in the existing turbulent models when they are applied to strong steady/unsteady separated flows.

Balakumar, Ponnampalam↗

RANS Simulation of Variable Density Turbulent Round Jets with Coflow using xRAGE Hydrodynamic Code and BHR Turbulence Models

This work for the fiscal year 2023 (FY23) is a continuation of previous efforts to evaluate the BHR turbulence models for their ability to accurately simulate variable density turbulent round jets with coflow. As before, RANS simulations are carried out using the xRAGE hydrodynamic code. The following are some of the previous findings. Israel showed that i) the symmetry boundary conditions for the BHR models in axisymmetric simulations were in error, ii) three grids of different resolutions did not lead to converging solutions, and iii) BHR 3.1 simulation exhibited instabilities and did not reach a steady state. Saenz and Rauenzahn derived and implemented into xRAGE the correct BHR boundary conditions at the symmetry axis. Cline conducted sensitivity studies with various parameters including the BHR models (versions 2, 3.1 and 4), gravity, material pressure, specific heat, initial turbulent kinetic energy and initial turbulent length scale, and found that the largest factor impacting on simulation results was the BHR model version, followed by the initial turbulent length scale. In addition, freeze boundary conditions at the exit and the side wall of the computational domain were used to remove anomalous flow behavior. Cline adjusted the inlet jet velocity, initial turbulent kinetic energy and initial turbulent length scale to obtain the best reasonable match with the experimental data of Charonko and Prestridge. It was found that the BHR 2 and 3.1 models performed in a similar manner, but the BHR 2 model produced much lower levels of density-specific-volume covariance and turbulent kinetic energy. The main focus for the FY23 is to study the effects of computational parameters related to the boundary conditions, mesh, domain size and timestep size. The reasoning behind this is that, unless simulation results can be shown to be reasonably independent from the aforementioned computational parameters, it would be difficult to attribute any discrepancies between simulation and experimental results to turbulence models. This important aspect has largely been overlooked in the previous years, and therefore will be studied comprehensively here. Additionally, effects of varying the initial turbulent length scale will be examined because it was previously identified as a major factor affecting the flow fields.

42 ENGINEERING↗

Large-Eddy Simulation Code Developed for Propulsion Applications

A large-eddy simulation (LES) code was developed at the NASA Glenn Research Center to provide more accurate and detailed computational analyses of propulsion flow fields. The accuracy of current computational fluid dynamics (CFD) methods is limited primarily by their inability to properly account for the turbulent motion present in virtually all propulsion flows. Because the efficiency and performance of a propulsion system are highly dependent on the details of this turbulent motion, it is critical for CFD to accurately model it. The LES code promises to give new CFD simulations an advantage over older methods by directly computing the large turbulent eddies, to correctly predict their effect on a propulsion system. Turbulent motion is a random, unsteady process whose behavior is difficult to predict through computer simulations. Current methods are based on Reynolds-Averaged Navier- Stokes (RANS) analyses that rely on models to represent the effect of turbulence within a flow field. The quality of the results depends on the quality of the model and its applicability to the type of flow field being studied. LES promises to be more accurate because it drastically reduces the amount of modeling necessary. It is the logical step toward improving turbulent flow predictions. In LES, the large-scale dominant turbulent motion is computed directly, leaving only the less significant small turbulent scales to be modeled. As part of the prediction, the LES method generates detailed information on the turbulence itself, providing important information for other applications, such as aeroacoustics. The LES code developed at Glenn for propulsion flow fields is being used to both analyze propulsion system components and test improved LES algorithms (subgrid-scale models, filters, and numerical schemes). The code solves the compressible Favre-filtered Navier- Stokes equations using an explicit fourth-order accurate numerical scheme, it incorporates a compressible form of Smagorinsky s model for the subgrid-scale turbulence, and it uses generalized curvilinear coordinates to allow analysis of a wide range of geometries. The code runs in parallel on shared memory multiprocessor computers and is written in Fortran 90 with dynamic memory allocation. A sample result for a Mach-1.4 round jet is presented in the figure. Instantaneous Mach number contours in several cross-planes downstream of the nozzle exit are shown, illustrating how an LES captures the large unsteady three-dimensional turbulent structures present in the jet.

DeBonis, James R.↗