Results for “computational fluid dynamics simulation” — Page 75

NASA NTRSDate not supplied

Summary of the 5th Propulsion Aerodynamics Workshop Nozzle Test Case: Heated Nozzle Exhaust Passing Over A Film-Cooled Plate

This paper summarizes findings from the fifth AIAA Propulsion Aerodynamics Workshop nozzle test case. The experimental configuration examined by workshop participants was a subsonic nozzle with a square exit blowing a heated exhaust over a film-cooled plate. Computational fluid dynamics solutions were obtained and compared to experimental measurements of flow velocities and temperatures, as well as plate surface temperatures. The heated nozzle operated with a Mach 0.3 exit flow at a static temperature ratio of 2.7. Cooling air blowing ratios of 0, 1, and 2 were considered. Computational meshes for the flow domain were provided for participants. Workshop participants from eight separate organizations represented government, industry, and academia. A variety of flow solutions were obtained: Most of the flow solutions employed a Reynolds-averaged Navier-Stokes (RANS) approach, but scale-resolving simulations were used in some cases, including wall-modeled large-eddy simulation (LES), and a few hybrid RANS-LES approaches. One Lattice-Boltzmann solver was employed. For heat transfer to the test article, many participants used a conjugate heat transfer approach. Effects of mesh sensitivity, flow solution approach, and wall heat transfer approach are considered. In general, a fully three-dimensional conjugate heat transfer approach enabled better prediction of surface temperatures than simpler wall temperature boundary treatments. Also, the scale resolving approaches provided better prediction of static temperatures in the flow immediately above the plate consisting of the hot jet exhaust boundary layer interacting with the cooling film. Comparisons of plate surface friction drag and heat transfer obtained from the computations are also presented.

nozzle↗

NASA NTRSDate not supplied

Summary of the 5th Propulsion Aerodynamics Workshop Nozzle Test Case: Heated Nozzle Exhaust Passing Over A Film-Cooled Plate

This paper summarizes findings from the fifth AIAA Propulsion Aerodynamics Workshop nozzle test case. The experimental configuration examined by workshop participants was a subsonic nozzle with a square exit blowing a heated exhaust over a film-cooled plate. Computational fluid dynamics solutions were obtained and compared to experimental measurements of flow velocities and temperatures, as well as plate surface temperatures. The heated nozzle operated with a Mach 0.3 exit flow at a static temperature ratio of 2.7. Cooling air blowing ratios of 0, 1, and 2 were considered. Computational meshes for the flow domain were provided for participants. Workshop participants from eight separate organizations represented government, industry, and academia. A variety of flow solutions were obtained: Most of the flow solutions employed a Reynolds-averaged Navier-Stokes (RANS) approach, but scale-resolving simulations were used in some cases, including wall-modeled large-eddy simulation (LES), and a few hybrid RANS-LES approaches. One Lattice-Boltzmann solver was employed. For heat transfer to the test article, many participants used a conjugate heat transfer approach. Effects of mesh sensitivity, flow solution approach, and wall heat transfer approach are considered. In general, a fully three-dimensional conjugate heat transfer approach enabled better prediction of surface temperatures than simpler wall temperature boundary treatments. Also, the scale resolving approaches provided better prediction of static temperatures in the flow immediately above the plate consisting of the hot jet exhaust boundary layer interacting with the cooling film. Comparisons of plate surface friction drag and heat transfer obtained from the computations are also presented.

nozzle↗

NASA NTRS1992

Analysis of film cooling in rocket nozzles

Progress during the reporting period is summarized. Analysis of film cooling in rocket nozzles by computational fluid dynamics (CFD) computer codes is desirable for two reasons. First, it allows prediction of resulting flow fields within the rocket nozzle, in particular the interaction of the coolant boundary layer with the main flow. This facilitates evaluation of potential cooling configurations with regard to total thrust, etc., before construction and testing of any prototype. Secondly, CFD simulation of film cooling allows for assessment of the effectiveness of the proposed cooling in limiting nozzle wall temperature rises. This latter objective is the focus of the current work. The desired objective is to use the Finite Difference Navier Stokes (FDNS) code to predict wall heat fluxes or wall temperatures in rocket nozzles. As prior work has revealed that the FDNS code is deficient in the thermal modeling of boundary conditions, the first step is to correct these deficiencies in the FDNS code. Next, these changes must be tested against available data. Finally, the code will be used to model film cooling of a particular rocket nozzle. The third task of this research, using the modified code to compute the flow of hot gases through a nozzle, is described.

Woodbury, Keith A.↗

NASA NTRS1999

Inlet-Compressor Analysis using Coupled CFD Codes

Propulsion performance and operability are key factors in the development of a successful aircraft. For high-speed supersonic aircraft, mixed-compression inlets offer high performance but are susceptible to an instability referred to as unstart. An unstart occurs when a disturbance originating in the atmosphere or the engine causes the shock system to be expelled from the inlet. This event can have adverse effects on control of the aircraft, which is unacceptable for a passenger plane such as the high speed civil transport (HSCT). The ability to predict the transient response of such inlets to flow perturbations is, therefore, important to the proper design of the inlet and the control measures used to prevent unstart. Computational fluid dynamics (CFD) is having an increasing role in the analysis of individual propulsion components. Isolated inlet studies are relatively easy to perform, but a major uncertainty is the boundary condition used at the inlet exit to represent the engine - the so-called compressor face boundary condition. A one-dimensional (1-D) Euler inlet simulation showed that the predicted inlet unstart tolerance to free-stream pressure perturbations can vary by as much as a factor of about six, depending on the boundary condition used. Obviously a thorough understanding of dynamic interactions between inlets and compressors/fans is required to provide the proper boundary condition. To aid in this understanding and to help evaluate possible boundary conditions, an inlet-engine experiment was conducted at the University of Cincinnati. The interaction of acoustic pulses, generated in the inlet, with the engine were investigated. Because of the availability of experimental data for validation, it was decided to simulate the experiment using CFD. The philosophy here is that the inlet-engine system is best simulated by coupling (existing) specialized CFD component-codes. The objectives of this work were to aid in a better understanding of inlet-compressor interaction physics and the formulation of a more realistic compressor-face boundary condition for time-accurate CFD simulations of inlets. Previous simulations have used 1-D Euler engine simulations in conjunction with 1-D Euler and axisymmetric Euler inlet simulations. This effort is a first step toward CFD simulation of an entire engine by coupling multidimensional component codes.

Cole, Gary↗

NASA NTRS2013

Aerodynamic Reconstruction Applied to Parachute Test Vehicle Flight Data Analysis

The aerodynamics, both static and dynamic, of a test vehicle are critical to determining the performance of the parachute cluster in a drop test and for conducting a successful test. The Capsule Parachute Assembly System (CPAS) project is conducting tests of NASA's Orion Multi-Purpose Crew Vehicle (MPCV) parachutes at the Army Yuma Proving Ground utilizing the Parachute Test Vehicle (PTV). The PTV shape is based on the MPCV, but the height has been reduced in order to fit within the C-17 aircraft for extraction. Therefore, the aerodynamics of the PTV are similar, but not the same as, the MPCV. A small series of wind tunnel tests and computational fluid dynamics cases were run to modify the MPCV aerodynamic database for the PTV, but aerodynamic reconstruction of the flights has proven an effective source for further improvements to the database. The acceleration and rotational rates measured during free flight, before parachute inflation but during deployment, were used to con rm vehicle static aerodynamics. A multibody simulation is utilized to reconstruct the parachute portions of the flight. Aerodynamic or parachute parameters are adjusted in the simulation until the prediction reasonably matches the flight trajectory. Knowledge of the static aerodynamics is critical in the CPAS project because the parachute riser load measurements are scaled based on forebody drag. PTV dynamic damping is critical because the vehicle has no reaction control system to maintain attitude - the vehicle dynamics must be understood and modeled correctly before flight. It will be shown here that aerodynamic reconstruction has successfully contributed to the CPAS project.

Cassady, Leonard D.↗

NASA NTRS2016

Effect of Dietary Countermeasures and Impact of Gravity on Renal Calculi Size Distributions Predicted by PBE-System and PBE-CFD Models

Renal stone disease is not only a concern on earth but can conceivably pose a serious risk to the astronauts health and safety in Space. In this work, two different deterministic models based on a Population Balance Equation (PBE) analysis of renal stone formation are developed to assess the risks of critical renal stone incidence for astronauts during space travel. In the first model, the nephron is treated as a continuous mixed suspension mixed product removal crystallizer and the PBE for the nucleating, growing and agglomerating renal calculi is coupled to speciation calculations performed by JESS. Predictions of stone size distributions in the kidney using this model indicate that the astronaut in microgravity is at noticeably greater but still subcritical risk and recommend administration of citrate and augmented hydration as effective means of minimizing and containing this risk. In the second model, the PBE analysis is coupled to a Computational Fluid Dynamics (CFD) model for flow of urine and transport of Calcium and Oxalate in the nephron to predict the impact of gravity on the stone size distributions. Results presented for realistic 3D tubule and collecting duct geometries, clearly indicate that agglomeration is the primary mode of size enhancement in both 1g and microgravity. 3D numerical simulations seem to further indicate that there will be an increased number of smaller stones developed in microgravity that will likely pass through the nephron in the absence of wall adhesion. However, upon reentry to a 1g (Earth) or 38g (Mars) partial gravitational fields, the renal calculi can lag behind the urinary flow in tubules that are adversely oriented with respect to the gravitational field and grow agglomerate to large sizes that are sedimented near the wall with increased propensity for wall adhesion, plaque formation, and risk to the astronauts.

Renal Stones↗

NASA NTRSDate not supplied

Large Vehicle Lunar Landing Surface Interaction and In-Situ Resource Based Risk Mitigation: Landing & Launch Pads

A key capability required for the exploration of planetary bodies is the ability to land on the surface. Previous work performed by NASA and other institutions has primarily focused on landing small spacecraft on planetary surfaces and the associated small-to-medium thrusters required for the soft landing. In the case of human exploration—particularly the establishment of long duration exploration and habitation outposts—the ability to land large landers, such as the SpaceX Starship, is necessary. These larger landing systems require the use of more powerful engines, with higher engine exhaust temperatures and higher landing loads. Understanding the excavation of material by the engines, as well as the potential for the landing legs to sink into the subsurface, is key in ensuring reliable and safe landings. A further improvement in landing reliability can be achieved by constructing landing / launch pads, especially with in-situ resources. Some material excavation by the plume is inevitable, leaving at least a portion of the surface scoured and uneven under the lander and ejecting regolith particles and rocks at very high velocities. One possible solution would be to robotically build landing / launch pads (ideally autonomously) at the destination using in-situ materials. In this case, the first one or few landers will need to land on unimproved surfaces at higher risk; however, they would bring the required equipment to build the landing pads with mostly local resources, thus increasing the reliability of safe landing for subsequent larger landers. A number of methods to build in-situ landing and launch pads have already been developed. These methods include no or some addition of required binder additives to the local regolith material, different processing approaches and result in varying landing pad strengths. A sub-scale rocket engine plume, was used to simulate some of the conditions of a landing on the Moon to assess the effectiveness of various materials for an in-situ built landing pad, The GO2/GCH4 rocket engine fired on 1m2 area coupons of representative pad materials. The results will allow continued development towards materials that satisfy the landing pad properties required for the effective risk reduction and increased reliability for landing people and equipment on the lunar surface. This work contained two parts: (1) computer modeling of a large rocket engine plume interacting with regolith on the Moon, using the Granular Gas Flow Solver (GGFS) provided by CFD Research Corporation as well as other computational fluid dynamics codes (CFD) such as Loci/CHEM. (2) Developing landing/launch pad materials that could be used for in-situ construction on the lunar surface in the future, to mitigate the calculated effects of a large vehicle rocket engine landing and launching on the Moon. The resulting computed values of plume impingement surface temperature, stagnation pressure, gas velocity, shear stress and heat flux were then matched as closely as possible in the Earth’s atmosphere in a sub-scale rocket engine GO2/CH4 test which was provided by Masten Space Systems in Mojave, California. The rocket engine was mounted on a test stand with vertical translation capabilities so that the landing operations of a lander could be simulated (Figure 1).The pad materials test coupons were placed at the surface of a large bin containing simulated lunar basalt regolith and subjected to a test firing as shown in Figure 2. The results of this testing will be presented with related findings, analysis and discussion.

Plume Surface Interaction↗

NASA NTRS1998

Inlet-Compressor Analysis Using Coupled CFD Codes

Propulsion performance and operability are key factors in the development of a successful aircraft. For high-speed supersonic aircraft, mixed-compression inlets offer high performance but are susceptible to an instability referred to as unstart. An unstart occurs when a disturbance originating in the atmosphere or the engine causes the shock system to be expelled from the inlet. This event can have adverse effects on control of the aircraft, which is unacceptable for a passenger plane such as the high speed civil transport (HSCT). The ability to predict the transient response of such inlets to flow perturbations is, therefore, important to the proper design of the inlet and the control measures used to prevent unstart. Computational fluid dynamics (CFD) is having an increasing role in the analysis of individual propulsion components. isolated inlet studies are relatively easy to perform, but a major uncertainty is the boundary condition used at the inlet exit to represent the engine - the so-called compressor face boundary condition. A one-dimensional (I-D) Euler inlet simulation (ref. 1) showed that the predicted inlet unstart tolerance to free-stream pressure perturbations can vary by as much as a factor of about six, depending on the boundary condition used. Obviously, a thorough understanding of dynamic interactions between inlets and compressors/fans is required to provide the proper boundary condition.

Cole, Gary↗

NASA NTRS2019

Kestrel Results at Liftoff Conditions for a Space Launch System Configuration in Proximity to the Launch Tower

Aerodynamic data books for Space Launch System vehicles require databases for the integrated forces and moments and section loads during liftoff and transition to the ascent phase of flight. While the force and moment database can be generated from wind tunnel results, computational analyses are necessary to provide the extensive surface information required to generate proper lineloads. Of the two flight regimes, the liftoff problem is the more costly and complex situation to simulate, as it requires modeling of the vehicle in proximity to the launch tower. The effects of massive separation on the leeward pressure fields of both the tower and vehicle are not well captured with RANS methods, necessitating the use of more advanced methods, such as Delayed Detached Eddy Simulation, in conjunction with computational grids sufficiently refined to resolve the wakes. Details on the computational setup for employing the Kestrel flow solver to address the liftoff problem are presented. The methodology involves the use of independent unstructured near-body grids for the vehicle and the tower, overset by a solution adaptive Cartesian off-body grid. Results from the simulations are compared to experimental results from a test in the NASA Langley Research Center 14- by 22-Foot Subsonic Tunnel.

Computational fluid dynamics↗

NASA NTRSDate not supplied

Aerodynamic Loading on Crew Access Arm

An aerodynamic database for the crew access arm during deployment is generated. While initial attempts used data derived from wind tunnel testing, limitations lead to the use of computational fluid dynamics to improve analysis. This computational data compared favorably to the experimental data increasing confidence in both. Further analysis lead to simplification showing the ability to build the database with a single relative wind variable which takes into account both arm deployment angle and wind direction. Eventually geometric simplifications and conservative results lead to the use of simulations of the CAA alone to build the database.Finally these static conditions are then compared to a dynamic simulation where the CAA rotates into position to test the quasi-steady state assumptions used to generate the database. The dynamic case showed an increase in the moment of interest but within acceptable bounds for now.

SLS↗

NASA NTRSDate not supplied

Ground Wind Loads on the Space Launch System’s Mobile Launcher Crew Access Arm

An aerodynamic database for the crew access arm during deployment is generated. While initial attempts used data derived from wind tunnel testing, limitations lead to the use of computational fluid dynamics to improve analysis. This computational data compared favorably to the experimental data increasing confidence in both. Further analysis lead to simplification showing the ability to build the database with a single relative wind variable which takes into account both arm deployment angle and wind direction. Eventually geometric simplifications and conservative results lead to the use of simulations of the CAA alone to build the database.Finally these static conditions are then compared to a dynamic simulation where the CAA rotates into position to test the quasi-steady state assumptions used to generate the database. The dynamic case showed an increase in the moment of interest but within acceptable bounds for now.

SLS↗

NASA NTRSDate not supplied

Uncertainty Quantification Methodology for Sonic Boom Loudness of a Low-Boom Supersonic Concept

This paper presents a comprehensive analysis of uncertainty quantification for sonic boom loudness metrics associated with the X-59 aircraft during its acoustic validation phase. The study focuses on employing advanced methodologies to characterize uncertainties in key sonic boom parameters predicted from a database derived from a computational fluid dynamics (CFD) solver. These methodologies include creating a polynomial chaos expansion (PCE) surrogate model, which is then used to run a Monte Carlo analysis to obtain 95% uncertainty intervals for sonic boom loudness parameters across the full carpet. Atmospheric uncertainties are rigorously considered, leveraging weather models based on historical data near Edwards Air Force Base to simulate potential flight conditions. The findings include preliminary uncertainty results for the full carpet during the validation phase of the Quesst mission. Additionally, a sensitivity study reveals that the primary sources of uncertainty are humidity and cruise weight.

Laura M. White↗

NASA NTRS2018

High-Fidelity Computational Aerodynamics of the Elytron 4S UAV

High-fidelity Computational Fluid Dynamics (CFD) have been carried out for the Elytron 4S Unmanned Aerial Vehicle (UAV), also known as the converticopter "proto12". It is the scaled wind tunnel model of the Elytron 4S, an Urban Air Mobility (UAM) concept, a tilt-wing, box-wing rotorcraft capable of Vertical Take-Off and Landing (VTOL). The three-dimensional unsteady Navier-Stokes equations are solved on overset grids employing high-order accurate schemes, dual-time stepping, and a hybrid turbulence model using NASA's CFD code OVERFLOW. The Elytron 4S UAV has been simulated in airplane mode and in helicopter mode.

High-Fidelity↗

NASA NTRS2013

Characterization of Aerodynamic Interactions with the Mars Science Laboratory Reaction Control System Using Computation and Experiment

On August 5 , 2012, the Mars Science Laboratory (MSL) entry capsule successfully entered Mars' atmosphere and landed the Curiosity rover in Gale Crater. The capsule used a reaction control system (RCS) consisting of four pairs of hydrazine thrusters to fly a guided entry. The RCS provided bank control to fly along a flight path commanded by an onboard computer and also damped unwanted rates due to atmospheric disturbances and any dynamic instabilities of the capsule. A preliminary assessment of the MSL's flight data from entry showed that the capsule flew much as predicted. This paper will describe how the MSL aerodynamics team used engineering analyses, computational codes and wind tunnel testing in concert to develop the RCS system and certify it for flight. Over the course of MSL's development, the RCS configuration underwent a number of design iterations to accommodate mechanical constraints, aeroheating concerns and excessive aero/RCS interactions. A brief overview of the MSL RCS configuration design evolution is provided. Then, a brief description is presented of how the computational predictions of RCS jet interactions were validated. The primary work to certify that the RCS interactions were acceptable for flight was centered on validating computational predictions at hypersonic speeds. A comparison of computational fluid dynamics (CFD) predictions to wind tunnel force and moment data gathered in the NASA Langley 31-Inch Mach 10 Tunnel was the lynch pin to validating the CFD codes used to predict aero/RCS interactions. Using the CFD predictions and experimental data, an interaction model was developed for Monte Carlo analyses using 6-degree-of-freedom trajectory simulation. The interaction model used in the flight simulation is presented.

Schoenenberger, Mark↗

NASA NTRSDate not supplied

Simulation and Regression Modeling of X-59 Low-Boom Carpets Across America

The NASA X-59 aircraft is predicted to produce a significantly quieter cruise sonic boom than traditional N-wave-producing aircraft. A propagation simulation study was undertaken to quantify loudness levels, exposure size, and variability of the X-59 low-boom carpet using realistic atmospheric profiles across the contiguous United States of America (CONUS). Near-field pressure data of the X-59 in supersonic cruise from NASA’s fully unstructured Navier–Stokes three-dimensional (known as FUN3D) computational fluid dynamics code were propagated using NASA’s PCBoom code, which solves an enhanced Burgers equation along acoustic rays. Atmospheric profiles from the National Oceanic and Atmospheric Administration’s Climate Forecast System Version 2 database were used for propagation at 138 locations across the CONUS. Carpets at each location were generated for aircraft headings in the four cardinal directions. Over one million X-59 carpets were generated in total. The effects of the heading, season, geography, and climate zone on boom levels and exposure size are presented. Multiple linear regression models were developed to estimate carpet width and loudness metrics across the CONUS. These results inform regulators and mission planners on expected variations in boom levels and carpet extent from atmospheric variations. Understanding potential carpet variability is important when planning community noise surveys using the X-59.

X-59↗

NASA NTRSDate not supplied

Coupling a Computational Fluid Dynamics Model to a Spacecraft Thermal System Model for the DraMS Instrument Thermal Analysis

The Dragonfly Mass Spectrometer (DraMS) is an instrument on the Dragonfly mission, which will spend 7 years in deep space cruise before landing and operating on the surface of Titan. Vacuum thermal analyses are required for deep space cruise, and convection analyses are required for the Titan surface operations. Model exchanges across multiple thermal teams are needed for all phases of the mission. For DraMS, Thermal Desktop® (TD) has been the main thermal analytical tool of choice due to its capability in modeling complex thermal systems with relatively low computational power and for its availability across thermal teams. However, TD does not have computational fluid dynamics (CFD) capability and struggles to accurately capture complex convective behavior. DraMS has fans operating in tandem and gas flow behaviors are not easily predicted due to its complex flow paths. CFD software, such as Fluent, can model and predict such complex flow behaviors, but CFD models are computationally expensive, and its workflow processes are not tailored towards simulating large and complex systems. Therefore, a coupled modeling approach was chosen for DraMS: A TD model was used for simulating all the conductive, radiative, and source terms, while a Fluent CFD model was added on, as needed, to the TD model to provide the convective boundary conditions using the System Coupling software. The coupling software allows the TD and Fluent models to communicate data and arrive at a co-solved and co-converged solution. Furthermore, Thermal Iso-value Exchange (TIE) method was developed to facilitate and improve the TD-Fluent data exchange process. This paper will discuss the analytical studies that were done to verify the accuracy and usability of the coupled approach and the challenges associated, which lead to the development of the TIE approach. DraMS thermal design and co-solved analysis results will also be discussed.

Heat transfer↗

NASA NTRSDate not supplied

Coupling a Computational Fluid Dynamics (CFD) Model to a Spacecraft Thermal System Model for the DraMS Instrument Thermal Analysis

The Dragonfly Mass Spectrometer (DraMS) is an instrument on the Dragonfly mission, which will spend 7 years in deep space cruise before landing and operating on the surface of Titan. Vacuum thermal analyses are required for deep space cruise, and convection analyses are required for the Titan surface operations. Model exchanges across multiple thermal teams are needed for all phases of the mission. For DraMS, Thermal Desktop (TD) has been the main thermal analytical tool of choice due to its capability in modeling complex thermal systems with relatively low computational power and for its availability across thermal teams. However, TD does not have computational fluid dynamics (CFD) capability and struggles to accurately capture complex convective behavior. DraMS has fans operating in tandem and gas flow behaviors are not easily predicted due to its complex flow paths. CFD software, such as Fluent, can model and predict such complex flow behaviors, but CFD models are computationally expensive, and its workflow processes are not tailored towards simulating large and complex systems. Therefore, a coupled modeling approach was chosen for DraMS: A TD model was used for simulating all the conductive, radiative, and source terms, while a Fluent CFD model was added on, as needed, to the TD model to provide the convective boundary conditions using the System Coupling software. The coupling software allows the TD and Fluent models to communicate data and arrive at a co-solved and co-converged solution. Furthermore, Thermal Iso-value Exchange (TIE) method was developed to facilitate and improve the TD-Fluent data exchange process. This paper will discuss the analytical studies that were done to verify the accuracy and usability of the coupled approach and the challenges associated, which lead to the development of the TIE approach. DraMS thermal design and co-solved analysis results will also be discussed.

heat transfer↗

NASA NTRS2011

Large Eddy Simulation Study for Fluid Disintegration and Mixing

A new modeling approach is based on the concept of large eddy simulation (LES) within which the large scales are computed and the small scales are modeled. The new approach is expected to retain the fidelity of the physics while also being computationally efficient. Typically, only models for the small-scale fluxes of momentum, species, and enthalpy are used to reintroduce in the simulation the physics lost because the computation only resolves the large scales. These models are called subgrid (SGS) models because they operate at a scale smaller than the LES grid. In a previous study of thermodynamically supercritical fluid disintegration and mixing, additional small-scale terms, one in the momentum and one in the energy conservation equations, were identified as requiring modeling. These additional terms were due to the tight coupling between dynamics and real-gas thermodynamics. It was inferred that if these terms would not be modeled, the high density-gradient magnitude regions, experimentally identified as a characteristic feature of these flows, would not be accurately predicted without the additional term in the momentum equation; these high density-gradient magnitude regions were experimentally shown to redistribute turbulence in the flow. And it was also inferred that without the additional term in the energy equation, the heat flux magnitude could not be accurately predicted; the heat flux to the wall of combustion devices is a crucial quantity that determined necessary wall material properties. The present work involves situations where only the term in the momentum equation is important. Without this additional term in the momentum equation, neither the SGS-flux constant-coefficient Smagorinsky model nor the SGS-flux constant-coefficient Gradient model could reproduce in LES the pressure field or the high density-gradient magnitude regions; the SGS-flux constant- coefficient Scale-Similarity model was the most successful in this endeavor although not totally satisfactory. With a model for the additional term in the momentum equation, the predictions of the constant-coefficient Smagorinsky and constant-coefficient Scale-Similarity models were improved to a certain extent; however, most of the improvement was obtained for the Gradient model. The previously derived model and a newly developed model for the additional term in the momentum equation were both tested, with the new model proving even more successful than the previous model at reproducing the high density-gradient magnitude regions. Several dynamic SGS-flux models, in which the SGS-flux model coefficient is computed as part of the simulation, were tested in conjunction with the new model for this additional term in the momentum equation. The most successful dynamic model was a "mixed" model combining the Smagorinsky and Gradient models. This work is directly applicable to simulations of gas turbine engines (aeronautics) and rocket engines (astronautics).

Bellan, Josette↗