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At least 235 records · Page 13

Addressing CFM Modeling Gaps for Application into NASA’S Future Cutting Edge Missions

NASA, the US industry, and international partners are crafting frameworks to enable sustaining lunar missions. The ongoing programs, led by the agency, and prominent industry players, encompass plans for the sustained use of cryogenic propellants in lunar landers and in-space propellant refueling depots. NASA’s proactive funding initiatives have fueled the advancement of predictive computational models tailored to enhance the storage and transfer of cryogenic propellant. This paper aims to spotlight the latest advancements in this arena and delve into the collaborative efforts surrounding predictive model development within internal NASA programs as well as current and previous collaborations with industry and international partners. The paper presents an overview of recent advancements in cryogenic fluid management model development, along with their correlation with recent microgravity and large-scale cryogenic ground tests. The tests include key experiments such as the ISS Zero-Boil-Off Tank (ZBOT) series of experiments and the (Robotic Refueling Mission 3) RRM3 test during which liquid methane was stored on-orbit for an extended period of five months. The paper also highlights the anchoring of propellant tank pressurized drain tests involving sloshing that were conducted with liquid methane propellant during the Apollo/Saturn Era. Additionally, the paper discusses model anchoring against more recent sloshing tests carried out with liquid hydrogen propellant. Notable large-scale tests, such as a liquid oxygen propellant transfer test conducted by SpaceX were also used to help correlate a two-phase propellant transfer model using the valuable data measured during the test. The paper further showcases model correlations against a substantial oxygen liquefaction test undertaken by NASA to validate In-Situ-Resource-Utilization (ISRU) technologies that will prove pivotal for a sustained lunar presence.

Low-gravity fluid modeling↗

Voltage waveform tailoring for high aspect ratio plasma etching of SiO 2 using Ar/CF 4 /O 2 mixtures: Consequences of low fundamental frequency biases

The use of non-sinusoidal waveforms in low pressure capacitively coupled plasmas intended for microelectronics fabrication has the goal of customizing ion and electron energy and angular distributions to the wafer. One such non-sinusoidal waveform uses the sum of consecutive harmonics of a fundamental sinusoidal frequency, f 0 , having a variable phase offset between the fundamental and even harmonics. In this paper, we discuss results from a computational investigation of the relation between ion energy and DC self-bias when varying the fundamental frequency f 0 for capacitively coupled plasmas sustained in Ar/CF 4 /O 2 and how those trends translate to a high aspect ratio etching of trenches in SiO 2 . The fundamental frequency, f 0 , was varied from 1 to 10 MHz and the relative phase from 0° to 180°. Two distinct regimes were identified. Average ion energy onto the wafer is strongly correlated with the DC self-bias at high f 0 , with there being a maximum at φ = 0° and minimum at φ = 180°. In the low frequency regime, this correlation is weak. Average ion energy onto the wafer is instead dominated by dynamic transients in the applied voltage waveforms, with a maximum at φ = 180° and minimum at φ = 0°. The trends in ion energy translate to etch properties. In both, the high and low frequency regimes, higher ion energies translate to higher etch rates and generally preferable final features, though behaving differently with phase angle.

36 MATERIALS SCIENCE↗

AI Driven Optimization of Public Transit

This project explores the application of AI-driven methods to optimize public transit operations for the Chattanooga Area Regional Transportation Authority (CARTA). By leveraging data analytics, machine learning, and predictive modeling, the initiative seeks to enhance system efficiency, improve rider experience, and support sustainability goals. This research, supported by the National Science Foundation and the U.S. Department of Energy, integrates real-time transit data with advanced computational tools to inform decision-making, optimize routes, and balance operational demands. The work exemplifies a forward-looking model for mid-sized cities aiming to modernize mobility systems through intelligent technology integration.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Performance of the OVERFLOW-MLP and LAURA-MLP CFD Codes on the NASA Ames 512 CPU Origin System

The shared memory Multi-Level Parallelism (MLP) technique, developed last year at NASA Ames has been very successful in dramatically improving the performance of important NASA CFD codes. This new and very simple parallel programming technique was first inserted into the OVERFLOW production CFD code in FY 1998. The OVERFLOW-MLP code's parallel performance scaled linearly to 256 CPUs on the NASA Ames 256 CPU Origin 2000 system (steger). Overall performance exceeded 20.1 GFLOP/s, or about 4.5x the performance of a dedicated 16 CPU C90 system. All of this was achieved without any major modification to the original vector based code. The OVERFLOW-MLP code is now in production on the inhouse Origin systems as well as being used offsite at commercial aerospace companies. Partially as a result of this work, NASA Ames has purchased a new 512 CPU Origin 2000 system to further test the limits of parallel performance for NASA codes of interest. This paper presents the performance obtained from the latest optimization efforts on this machine for the LAURA-MLP and OVERFLOW-MLP codes. The Langley Aerothermodynamics Upwind Relaxation Algorithm (LAURA) code is a key simulation tool in the development of the next generation shuttle, interplanetary reentry vehicles, and nearly all "X" plane development. This code sustains about 4-5 GFLOP/s on a dedicated 16 CPU C90. At this rate, expected workloads would require over 100 C90 CPU years of computing over the next few calendar years. It is not feasible to expect that this would be affordable or available to the user community. Dramatic performance gains on cheaper systems are needed. This code is expected to be perhaps the largest consumer of NASA Ames compute cycles per run in the coming year.The OVERFLOW CFD code is extensively used in the government and commercial aerospace communities to evaluate new aircraft designs. It is one of the largest consumers of NASA supercomputing cycles and large simulations of highly resolved full aircraft are routinely undertaken. Typical large problems might require 100s of Cray C90 CPU hours to complete. The dramatic performance gains with the 256 CPU steger system are exciting. Obtaining results in hours instead of months is revolutionizing the way in which aircraft manufacturers are looking at future aircraft simulation work. Figure 2 below is a current state of the art plot of OVERFLOW-MLP performance on the 512 CPU Lomax system. As can be seen, the chart indicates that OVERFLOW-MLP continues to scale linearly with CPU count up to 512 CPUs on a large 35 million point full aircraft RANS simulation. At this point performance is such that a fully converged simulation of 2500 time steps is completed in less than 2 hours of elapsed time. Further work over the next few weeks will improve the performance of this code even further.The LAURA code has been converted to the MLP format as well. This code is currently being optimized for the 512 CPU system. Performance statistics indicate that the goal of 100 GFLOP/s will be achieved by year's end. This amounts to 20x the 16 CPU C90 result and strongly demonstrates the viability of the new parallel systems rapidly solving very large simulations in a production environment.

Taft, James R.↗

Application of the CATNLF Design Method to a Transonic Transport Empennage Using CDISC

A novel Crossflow Attenuated Natural Laminar Flow (CATNLF) design method has been developed to achieve laminar flow on aircraft empennage at transonic flight conditions. This approach has been applied to the design of a nonlifting vertical tail using CDISC, a knowledgebased aerodynamic design tool developed at the NASA Langley Research Center. A horizontal tail was also designed using an enhanced CATNLF design approach for low-lift components. CDISC was coupled with USM3D-ME, a Navier-Stokes computational fluid dynamics solver. Stability and transition software was used to determine the laminar extent on the surfaces. Results indicate laminar flow can be sustained at midcruise conditions to about x/c=0.40 on the vertical tail and as much as x/c=0.65 on the horizontal tail lower surface. Transonic longitudinal off-design analysis indicates minimal change in the laminar extent. However, nonzero sideslip angles at transonic conditions can cause premature transition relative to the midcruise condition.

Brent W. Pomeroy↗

EUREICA: Efficient UltRa Endpoint IoT-enabled Coordinated Architecture

The electricity grid has evolved from a physical system to a cyber-physical system with digital devices that perform measurement, control, communication, computation, and actuation. The increased penetration of distributed energy resources (DERs) that include renewable generation, flexible loads, and storage provides extraordinary opportunities for improvements in efficiency and sustainability. However, they can introduce new vulnerabilities in the form of cyberattacks, which can cause significant challenges in ensuring grid resilience. The purpose of this project was to develop a framework ((Efficient, Ultra-REsilient, IoT-Coordinated Assets, or EUREICA)for achieving grid resilience through suitably coordinated assets including a network of Internet of Things (IoT) devices, and a local electricity market (LEM) to identify trustable assets and carry out this coordination. Situational Awareness (SA) of locally available DERs with the ability to inject power or reduce consumption is enabled by the market, together with a monitoring procedure for their trustability and commitment. Experiments conducted during this project demonstrated that, with this SA, a variety of cyberattacks can be mitigated using local trustable resources without stressing the bulk grid. The demonstrations were carried out using a variety of high-fidelity co-simulation platforms, real-time hardware-in-the-loop validation, and a utility-friendly simulator.

14 SOLAR ENERGY↗

Techno-Economic Analysis of Recycling Strategies for Catalyst and Acid During Catalytic Graphitization

With the aim of meeting the urgent demand for active anode materials (AAM) in energy storage systems, bio-based graphite (biographite) emerges as an affordable solution to de-risk the turbulent supply chain of critical minerals. Anode grade biographite requires high crystallinity and purity, which can be achieved by catalytic graphitization with iron, followed by acid washing. Therefore, a well-conceived process integration that recycles catalyst can be the starting point to commercialization. This study evaluates closed-loop catalyst recovery, and byproducts valorization scenarios through a technoeconomic framework to help understand the scale-up potential of biographite. For the acid washing, three reactors in series meet the required biographite purity at 99.95%. Iron and acid recovery can reduce material consumption and waste generation by ~95%, albeit at the expense of ~80% increase in capital costs. Recovery scenarios present similar capital and operational expenses, yielding minimum selling prices (MSP) near $6 kg-1 of biographite. Monte Carlo methodology reveals that feedstock price accounts for ~60% of MSP variance, followed by plant capacity ~20%. The likelihood of reaching a competitive profit margin of 30% in the U.S. AAM market sits at 85% average for recovery scenarios, and 103% when iron oxide is sold as byproduct. Additionally, an IRR >= 15% can be achieved for half of Monte Carlo simulations, representing promising early-stage results. Biographite production offers a strategic pathway to stabilize the anode market beyond China by integrating established technologies for a scalable, economically viable, and sustainable process. The role of catalyst recovery and byproducts utilization is critical for advancing the biomaterials industry.

97 MATHEMATICS AND COMPUTING↗

Autonomous sensor suite for evaluating fish-turbine interactions and environmental impacts in marine renewable energy and hydropower

Marine renewable energy (MRE) harnesses ocean-based resources such as waves, tides, currents, and thermal or salinity gradients for sustainable power generation. It has the potential to complement existing renewable resources, support remote communities, and contribute to decarbonization efforts. However, understanding the hydrodynamic forces created by MRE devices and their impacts on marine life is critical for responsible deployment. Here, to address these concerns, advanced sensor devices, including the Marine Sensor Fish (MSF), Sensor Fish Mini (SF Mini), and Flexible Sensor Fish (FSF), were developed to measure interactions between aquatic organisms and MRE systems. This paper details the design, manufacturing, calibration, and field deployment of these sensor suites, highlighting their ability to capture key physical stressors such as shear forces, pressure changes, and collision impacts. The MSF successfully evaluated turbine interactions at a tidal turbine in the Salish Sea, capturing data on turbulence, collision impact, and pressure gradients. The SF Mini validated hydrodynamic conditions in scaled hydraulic models, supporting computational fluid dynamics simulations. The FSF, with its flexible silicone body, measured species-specific impacts in turbulent environments. This research demonstrates the potential of Sensor Fish technology to advance sustainable marine energy systems by reducing biological impacts and informing environmentally sustainable designs.

Ecological impacts↗

Deep Learning for Subsurface Flow: A Comparative Study of U‐Net, Fourier Neural Operators, and Transformers in Underground Hydrogen Storage

Subsurface flow research is essential for the sustainable management of natural resources and the environment. Deep learning (DL) has significantly advanced this field by developing efficient and accurate surrogate models to replace computationally expensive physics‐based simulations. These surrogate models are commonly used to predict the spatiotemporal evolution of state variables, such as gas saturation and reservoir pressure, in heterogeneous geological formations. Despite the various DL models applied to this task, there is a lack of studies systematically comparing their performance. This absence of comparative analysis leads to somewhat arbitrary DL model selection in subsurface flow research, resulting in suboptimal performance and potentially inaccurate predictions. To bridge this gap, we conduct a systematic comparison study of three popular DL architectures—U‐Net, Fourier Neural Operators (FNO), and Segmentation Transformer (SETR)—in surrogate modeling of underground hydrogen storage (UHS). We focus on UHS due to its promise of enhancing clean energy resilience and its cyclic operational conditions that represent common scenarios in various subsurface applications. We evaluate the models based on accuracy, training cost, and inference speed. The comparison shows that U‐Net achieves the highest accuracy, followed by SETR and FNO. Despite its lower accuracy, FNO has the highest inference speed. SETR offers competitive accuracy with the least training memory usage, demonstrating the potential of transformers in learning subsurface flow. Our results provide guidance for selecting DL models for surrogate modeling in a wide range of subsurface flow problems.

42 ENGINEERING↗

Quantum Theory, Quantum Materials, Quantum Computing

The Sanibel Symposium series is renowned amongst materials theorists, quantum chemists, and condensed matter physicists as meetings driving progress on theory, mod eling, and simulation of materials and their molecular and nano-scale constituents. The Symposia are highly unusual (perhaps unique) in their priority emphasis on theory and computation, in having no parallel sessions, in cultivating well-attended Hot-Topic contributed oral sessions, and accessible poster sessions. These provide highly visible, influential platforms for cross-fertilization among specialist investigators, hence are strong contributors to the advance of quantum information sciences (QIS) research of strategic importance to the Office of Basic Energy Sciences (BES). As part of a five-year plan to highlight QIS challenges and opportunities and foster progress on them, each of the pre ceding three Sanibel Symposia had a thematic focus, Quantum Theory, Quantum Materi als, Quantum Computing, as a major program component. Emphasis was on quantum materials and their molecular constituents. The award for 2024 was for year four of that sustained thematic focus.

36 MATERIALS SCIENCE↗

Numerical simulation of unsteady viscous flows

Most unsteady viscous flows may be grouped into two categories, i.e., forced and self-sustained oscillations. Examples of forced oscillations occur in turbomachinery and in internal combustion engines while self-sustained oscillations prevail in vortex shedding, inlet buzz, and wing flutter. Numerical simulation of these phenomena was achieved due to the advancement of vector processor computers. Recent progress in the simulation of unsteady viscous flows is addressed.

Hankey, Wilbur L.↗

Unsteady, Transonic Flow Around Delta Wings Undergoing Coupled and Natural Modes Response: A Multidisciplinary Problem

The unsteady, three-dimensional Navier-Stokes equations coupled with the Euler equations of rigid-body dynamics are sequentially solved to simulate and analyze the aerodynamic response of a high angle of attack delta wing undergoing oscillatory motion. The governing equations of fluid flow and dynamics of the multidisciplinary problem are solved using a time-accurate solution of the laminar, unsteady, compressible, full Navier- Stokes equations with the implicit, upwind, Roe flux-difference splitting, finite-volume scheme and a four-stage Runge-Kutta scheme, respectively. The primary model under consideration consists of a 65 deg swept, sharp-edged, cropped delta wing of zero thickness at 20 deg angle of attack. In a freestream of Mach 0.85 and Reynolds number of 3.23 x 10(exp 6), the flow over the upper surface of the wing develops a complex shock system which interacts with the leading-edge primary vortices producing vortex breakdown. The effect of the oscillatory motion of the wing on the vortex breakdown and overall aerodynamic response is detailed to provide insight to the complicated physics associated with unsteady flows and the phenomenon of wing rock. Forced sinusoidal single and coupled mode rolling and pitching motion is presented for the wing in a transonic freestream. The Reynolds number, frequency of oscillation, and the phase angle are varied. Comparison between the single and coupled mode forced rolling and pitching oscillation cases illustrate the effects of coupling the motion. This investigation shows that even when coupled, forced rolling oscillation at a reduced frequency of 2(pi) eliminates the vortex breakdown which results in an increase in lift. The coupling effect for in phase forced oscillations show that the lift coefficient of the pitching-alone case and the rolling-moment coefficient of the rolling-alone case dominate the resulting response. However, with a phase lead in the pitching motion, the coupled motion results in a non-periodic response of the rolling moment. The second class of problems involve releasing the wing in roll to respond to the flowfield. Two models of sharp-edged delta wings, the previous 65 deg swept model and an 80 deg swept, sharp-edged delta wing, are used to observe the aerodynamic response of a wing free to roll in a transonic and subsonic freestream, respectively. These cases demonstrate damped oscillations, self-sustained limit cycle oscillations, and divergent rolling oscillations. Ultimately, an active control model using a mass injection system was applied on the surface of the wing to suppress the self-sustained limit cycle oscillation known as wing rock. Comparisons with experimental investigations complete this study, validating the analysis and illustrating the complex details afforded by computational investigations.

Menzies, Margaret Anne↗

Aero-Thermo-Structural Design Optimization of Internally Cooled Turbine Blades

A set of robust and computationally affordable inverse shape design and automatic constrained optimization tools have been developed for the improved performance of internally cooled gas turbine blades. The design methods are applicable to the aerodynamics, heat transfer, and thermoelasticity aspects of the turbine blade. Maximum use of the existing proven disciplinary analysis codes is possible with this design approach. Preliminary computational results demonstrate possibilities to design blades with minimized total pressure loss and maximized aerodynamic loading. At the same time, these blades are capable of sustaining significantly higher inlet hot gas temperatures while requiring remarkably lower coolant mass flow rates. These results suggest that it is possible to design internally cooled turbine blades that will cost less to manufacture, will have longer life span, and will perform as good, if not better than, film cooled turbine blades.

Dulikravich, G. S.↗

Large Scale Experiments on Spacecraft Fire Safety

Full scale fire testing complemented by computer modelling has provided significant know how about the risk, prevention and suppression of fire in terrestrial systems (cars, ships, planes, buildings, mines, and tunnels). In comparison, no such testing has been carried out for manned spacecraft due to the complexity, cost and risk associated with operating a long duration fire safety experiment of a relevant size in microgravity. Therefore, there is currently a gap in knowledge of fire behaviour in spacecraft. The entire body of low-gravity fire research has either been conducted in short duration ground-based microgravity facilities or has been limited to very small fuel samples. Still, the work conducted to date has shown that fire behaviour in low-gravity is very different from that in normal-gravity, with differences observed for flammability limits, ignition delay, flame spread behaviour, flame colour and flame structure. As a result, the prediction of the behaviour of fires in reduced gravity is at present not validated. To address this gap in knowledge, a collaborative international project, Spacecraft Fire Safety, has been established with its cornerstone being the development of an experiment (Fire Safety 1) to be conducted on an ISS resupply vehicle, such as the Automated Transfer Vehicle (ATV) or Orbital Cygnus after it leaves the ISS and before it enters the atmosphere. A computer modelling effort will complement the experimental effort. Although the experiment will need to meet rigorous safety requirements to ensure the carrier vehicle does not sustain damage, the absence of a crew removes the need for strict containment of combustion products. This will facilitate the possibility of examining fire behaviour on a scale that is relevant to spacecraft fire safety and will provide unique data for fire model validation. This unprecedented opportunity will expand the understanding of the fundamentals of fire behaviour in spacecraft. The experiment is being developed by an international topical team that is collaboratively defining the experiment requirements and performing supporting analysis, experimentation and technology development. This paper presents the objectives, status and concept of this project.

Urban, David L.↗

Large Scale Experiments on Spacecraft Fire Safety

Full scale fire testing complemented by computer modelling has provided significant knowhow about the risk, prevention and suppression of fire in terrestrial systems (cars, ships, planes, buildings, mines, and tunnels). In comparison, no such testing has been carried out for manned spacecraft due to the complexity, cost and risk associated with operating a long duration fire safety experiment of a relevant size in microgravity. Therefore, there is currently a gap in knowledge of fire behaviour in spacecraft. The entire body of low-gravity fire research has either been conducted in short duration ground-based microgravity facilities or has been limited to very small fuel samples. Still, the work conducted to date has shown that fire behaviour in low-gravity is very different from that in normal gravity, with differences observed for flammability limits, ignition delay, flame spread behaviour, flame colour and flame structure. As a result, the prediction of the behaviour of fires in reduced gravity is at present not validated. To address this gap in knowledge, a collaborative international project, Spacecraft Fire Safety, has been established with its cornerstone being the development of an experiment (Fire Safety 1) to be conducted on an ISS resupply vehicle, such as the Automated Transfer Vehicle (ATV) or Orbital Cygnus after it leaves the ISS and before it enters the atmosphere. A computer modelling effort will complement the experimental effort. Although the experiment will need to meet rigorous safety requirements to ensure the carrier vehicle does not sustain damage, the absence of a crew removes the need for strict containment of combustion products. This will facilitate the possibility of examining fire behaviour on a scale that is relevant to spacecraft fire safety and will provide unique data for fire model validation. This unprecedented opportunity will expand the understanding of the fundamentals of fire behaviour in spacecraft. The experiment is being developed by an international topical team that is collaboratively defining the experiment requirements and performing supporting analysis, experimentation and technology development. This paper presents the objectives, status and concept of this project.

Urban, David↗

Unmanned Vehicle Material Flammability Test

Microgravity combustion phenomena have been an active area of research for the past 3 decades however, there have been very few experiments directly studying spacecraft fire safety under low-gravity conditions. Furthermore, none of these experiments have studied sample and environment sizes typical of those expected in a spacecraft fire. All previous experiments have been limited to samples of the order of 10 cm in length and width or smaller. Terrestrial fire safety standards for all other habitable volumes on earth, e.g. mines, buildings, airplanes, ships, etc., are based upon testing conducted with full-scale fires. Given the large differences between fire behavior in normal and reduced gravity, this lack of an experimental data base at relevant length scales forces spacecraft designers to base their designs using 1-g understanding. To address this question a large scale spacecraft fire experiment has been proposed by an international team of investigators. This poster presents the objectives, status and concept of this collaborative international project to examine spacecraft material flammability at realistic scales. The concept behind this project is to utilize an unmanned spacecraft such as Orbital Cygnus vehicle after it has completed its delivery of cargo to the ISS and it has begun its return journey to earth. This experiment will consist of a flame spread test involving a meter scale sample ignited in the pressurized volume of the spacecraft and allowed to burn to completion while measurements are made. A computer modeling effort will complement the experimental effort. Although the experiment will need to meet rigorous safety requirements to ensure the carrier vehicle does not sustain damage, the absence of a crew removes the need for strict containment of combustion products. This will facilitate the examination of fire behavior on a scale that is relevant to spacecraft fire safety and will provide unique data for fire model validation. This will be the first opportunity to examine microgravity flame behavior at scales approximating a spacecraft fire.

Combustion↗

Large-Scale Spacecraft Fire Safety Tests

An international collaborative program is underway to address open issues in spacecraft fire safety. Because of limited access to long-term low-gravity conditions and the small volume generally allotted for these experiments, there have been relatively few experiments that directly study spacecraft fire safety under low-gravity conditions. Furthermore, none of these experiments have studied sample sizes and environment conditions typical of those expected in a spacecraft fire. The major constraint has been the size of the sample, with prior experiments limited to samples of the order of 10 cm in length and width or smaller. This lack of experimental data forces spacecraft designers to base their designs and safety precautions on 1-g understanding of flame spread, fire detection, and suppression. However, low-gravity combustion research has demonstrated substantial differences in flame behavior in low-gravity. This, combined with the differences caused by the confined spacecraft environment, necessitates practical scale spacecraft fire safety research to mitigate risks for future space missions. To address this issue, a large-scale spacecraft fire experiment is under development by NASA and an international team of investigators. This poster presents the objectives, status, and concept of this collaborative international project (Saffire). The project plan is to conduct fire safety experiments on three sequential flights of an unmanned ISS re-supply spacecraft (the Orbital Cygnus vehicle) after they have completed their delivery of cargo to the ISS and have begun their return journeys to earth. On two flights (Saffire-1 and Saffire-3), the experiment will consist of a flame spread test involving a meter-scale sample ignited in the pressurized volume of the spacecraft and allowed to burn to completion while measurements are made. On one of the flights (Saffire-2), 9 smaller (5 x 30 cm) samples will be tested to evaluate NASAs material flammability screening tests. The first flight (Saffire-1) is scheduled for July 2015 with the other two following at six-month intervals. A computer modeling effort will complement the experimental effort. Although the experiment will need to meet rigorous safety requirements to ensure the carrier vehicle does not sustain damage, the absence of a crew removes the need for strict containment of combustion products. This will facilitate the first examination of fire behavior on a scale that is relevant to spacecraft fire safety and will provide unique data for fire model validation.

Combustion↗

A rational approach to the use of Prandtl's mixing length model in free turbulent shear flow calculations

Prandtl's basic mixing length model was used to compute 22 test cases on free turbulent shear flows. The calculations employed appropriate algebraic length scale equations and single values of mixing length constant for planar and axisymmetric flows, respectively. Good agreement with data was obtained except for flows, such as supersonic free shear layers, where large sustained sensitivity changes occur. The inability to predict the more gradual mixing in these flows is tentatively ascribed to the presence of a significant turbulence-induced transverse static pressure gradient which is neglected in conventional solution procedures. Some type of an equation for length scale development was found to be necessary for successful computation of highly nonsimilar flow regions such as jet or wake development from thick wall flows.

Rudy, D. H.↗