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

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At least 361 records · Page 20

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

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

Supersonic Retropropulsion↗

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

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

Supersonic Retropropulsion↗

A Benchmark Example for Delamination Propagation Predictions Based on the Calibrated End-Loaded Split Specimen

A benchmark example based on the Calibrated End-Loaded Split (C-ELS) specimen is developed and used to assess the performance of recently developed delamination propagation capabilities in the Abaqus/Standard finite element code. The C-ELS specimen has the advantage of a longer region of stable delamination propagation compared to the existing mode II benchmark case. The new benchmark example may therefore provide a better assessment tool by enabling more stable crack growth in regions further away from the boundary conditions or load application. First, a benchmark result is created manually using two-dimensional finite element models of the C-ELS specimen with different delamination lengths. Second, the performance of the delamination propagation capabilities in the Abaqus/Standard finite element code are assessed by comparing the results to the benchmark case. Two examples with different starter delamination lengths are studied. A shorter starter length is chosen to create a scenario with unstable delamination propagation. A longer delamination causes stable delamination propagation. Detailed results from three-dimensional analyses with aligned and mis-aligned meshes and two levels of mesh refinement are provided for several permutations of numerical input parameters. In general, good agreement can be achieved between the results obtained from the quasi-static propagation analysis and the benchmark analysis. However, particular non-default settings are found to be most reliable, accurate, and numerically efficient. Numerical artifacts including anomalous unreleased nodes in the crack wake and zig-zag crack fronts occur, and further development of the Abaqus/Standard VCCT propagation may be required. Use of the benchmark case to assess the continuous improvements in one finite element code illustrates the value of establishing benchmark solutions.

delamination↗

Current Capabilities of AFRL’s Spacecraft Simulation Tool

Assessment of spacecraft integration issues is typically accomplished with a combination of numerical tools developed to simulate different regions with different key physics. For instance, a detailed study of spacecraft with an electric propulsion device requires a device model, a plume model, and a spacecraft charging model. AFRL’s in-house spacecraft simulation tool, TURF, is now capable of performing all of these calculations in one simulation. In addition, the plume simulation capability has been expanded significantly to improve speed and accuracy. Other upgrades in TURF include adaptive mesh refinement (AMR) and dynamic load balancing. All of these upgrades are covered in this paper by providing detailed descriptions or pointing to relevant references. This paper also presents three example simulations demonstrating its multi-physics multi-scale capability.

spacecraft simulation↗

Predicting Orion Launch Abort Acoustics

Computational fluid dynamics (CFD) scale-resolving simulations were performed to help assess the Orion launch abort system’s vibro-acoustic environment in collaboration with the Orion Loads and Dynamics team at the Johnson Space Center (JSC). The primary objectives are to establish best practices and to validate CFD predictions for surface fluctuating pressure spectra with ground, wind tunnel, and flight test data. Excellent agreement is obtained between CFD predictions by the Cartesian adaptive mesh refinement (AMR) module of the Launch, Ascent, and Vehicle Aerodynamics (LAVA) solver and measurements from a ground test representative of the start of a pad abort scenario, and with measurements from a wind tunnel test case corresponding to a transonic, high total angle of attack ascent abort scenario. A simplified (static and at rest) simulation of a pad abort flight test shows good agreement with the flight data, whereas a more costly simulation where the vehicle is accelerating relative to the ground from rest to Mach 0.4 shows consistent over-prediction of the spectra. Simulation results for a supersonic ascent abort flight test are in reasonable agreement with the measurements, but show larger excursions in regions where non-linear interactions between the plume turbulence, shocks, and turbulent boundary layer are strongest – likely due to CFD modeling assumptions, the effect of which are discussed. Overall, the CFD results demonstrate that scale-resolving simulation methodologies like the one presented can help characterize full-scale launch abort vehicle near-field noise and can complement wind tunnel, ground and flight tests by providing trends and reducing uncertainty for scenarios that cannot or are not planned to be tested.

Orion↗

Development of a C-ELS Specimen-Based Numerical Benchmark for Mode II Delamination and Assessment of Two VCCT-Based Propagation Strategies

A finite element (FE) benchmark example inspired by the calibrated end-loaded split (C-ELS) specimen is developed and used to assess the performance of delamination propagation capabilities based on linear elastic fracture mechanics (LEFM). The C-ELS specimen has the advantage of a longer region of stable delamination propagation compared to the existing mode II benchmark case. The new benchmark example may therefore provide a better assessment tool by enabling more stable crack growth in regions further away from the boundary conditions or load application. First, a benchmark result is created manually using two-dimensional finite element models of the C-ELS specimen with different delamination lengths. Second, the performance of the virtual crack closure technique (VCCT) delamination propagation capabilities in the Abaqus/Standard®1 FE code and the recently developed Progressive Release eXplicit-VCCT (PRX-VCCT) method are assessed by comparing the results to the benchmark case. Two examples with different starter delamination lengths are studied. A shorter starter length is chosen to create a scenario with unstable delamination propagation. A longer delamination encourages stable delamination propagation. Detailed results from three-dimensional analyses with aligned and misaligned meshes and two levels of mesh refinement are provided. In general, good agreement can be achieved between the results obtained from the quasi-static propagation analysis and the benchmark analysis. Numerical artifacts including anomalous unreleased nodes in the crack wake and zig-zag crack fronts occur for propagation analyses using Abaqus/Standard VCCT. In comparison, continuous, smooth, delamination fronts are observed for PRX-VCCT. The use of the benchmark case to assess different VCCT-based propagation strategies illustrates the value of establishing benchmark cases.

Composite Materials↗

Fluid-Structure Interaction Simulations of the ASPIRE SR03 Supersonic Parachute Flight Test

Research into parachute performance continues to be a source of significant investment from the National Aeronautics and Space Administration to mitigate risks and to enable a variety of exploration missions, including landing on Mars as well as returning to Earth. The cost of flight tests to certify any changes to the current state-of-the-art parachute designs limits the development of next generation parachute systems. Fluid-structure interaction simulations could help accelerate this process once validated. The Launch, Ascent, and Vehicle Aerodynamics team is developing the capability to perform such fluid-structure interaction simulations by coupling a higher-order Cartesian immersed boundary computational fluid dynamics solver with adaptive mesh refinement to a finite element structural dynamics solver in space and time. We continue the effort to validate this tool with the Advanced Supersonic Parachute Inflation Research Experiments SR03 flight test featuring a strengthened parachute akin to the Mars 2020 mission that landed the Perseverance rover on Mars, and a higher freestream dynamic pressure prior to inflation. The effect of the flow conditions’ angle of attack and of the initial parachute shape are quantified. The impact of relaxing modeling assumptions with regards to radial stiffeners on the parachute canopy is also investigated. Results demonstrate improvements in agreement with the pull force recorded during the SR03 flight test as the initial conditions of the flow and parachute are brought closer to those experienced in flight, and further improved when the radial stiffener modeling assumptions are relaxed.

ESM↗

Fluid-Structure Interaction Simulations of the ASPIRE SR03 Supersonic Parachute Flight Test

Research into parachute performance continues to be a source of significant investment from the National Aeronautics and Space Administration to mitigate risks and to enable a variety of exploration missions, including landing on Mars as well as returning to Earth. The cost of flight tests to certify any changes to the current state-of-the-art parachute designs limits the development of next generation parachute systems. Fluid-structure interaction simulations could help accelerate this process once validated. The Launch, Ascent, and Vehicle Aerodynamics team is developing the capability to perform such fluid-structure interaction simulations by coupling a higher-order Cartesian immersed boundary computational fluid dynamics solver with adaptive mesh refinement to a finite element structural dynamics solver in space and time. We continue the effort to validate this tool with the Advanced Supersonic Parachute Inflation Research Experiments SR03 flight test featuring a strengthened parachute akin to the Mars 2020 mission that landed the Perseverance rover on Mars, and a higher freestream dynamic pressure prior to inflation. The effect of the flow conditions’ angle of attack and of the initial parachute shape are quantified. The impact of relaxing modeling assumptions with regards to radial stiffeners on the parachute canopy is also investigated. Results demonstrate improvements in agreement with the pull force recorded during the SR03 flight test as the initial conditions of the flow and parachute are brought closer to those experienced in flight, and further improved when the radial stiffener modeling assumptions are relaxed.

ESM↗

Recent Progress on Rans-Based Transition Model Verification

The current efforts to assess and improve the Reynolds-averaged Navier-Stokes (RANS)-coupled transition models in the NASA FUN3D and OVERFLOW codes are summarized in this study. The first AIAA Transition Modeling Workshop and the NATO AVT-313 Transition Workshop both emphasized the need for code verification for transport equations based transition models as a top priority. We discuss the methods used for the model verification, the resulting grid families, the flow solutions, and other supporting information collected with at least two established NASA flow solvers, namely, FUN3D and OVERFLOW. These results, which will be uploaded onto the NASA Turbulence Modeling Resource, should assist other members of the computational fluid dynamics (CFD) community in verifying their own implementations of various transition models, such as the Langtry-Menter (LM2009) model, the one-equation γ model, and Coder’s amplification factor transport (AFT) model. Grid convergence is assessed using both global and local flow metrics of interest such as lift and drag as well as local skin-friction coefficients. We also explore the anisotropic unstructured metric-based adaptive mesh refinement library known as refine with the NASA FUN3D solver to determine if this capability can achieve the same accuracy as handcrafted structured grids with a significantly smaller node count and to learn the characteristics of the resulting grid distribution, especially in the vicinity of the transition zone.

Transition↗

Optimizing the Resolution of Hydrodynamic Simulations for MCRaT Radiative Transfer Calculations

Despite their discovery about half a century ago, the Gamma-ray burst (GRB) prompt emission mechanism is still not well understood. Theoretical modeling of the prompt emission has advanced considerably due to new computational tools and techniques. One such tool is the PLUTO hydro dynamics code, which is used to numerically simulate GRB outflows. PLUTO uses Adaptive Mesh Refinement to focus computational efforts on the portion of the grid that contains the simulated jet. Another tool is the Monte Carlo Radiation Transfer (MCRaT) code, which predicts electromagnetic signatures of GRBs by conducting photon scatterings within a jet using PLUTO. The effects of the underlying resolution of a PLUTO simulation with respect to MCRaT post-processing radiative transfer results have not yet been quantified. We analyze an analytic spherical outflow and a hydrodynamically simulated GRB jet with MCRaT at varying spatial and temporal resolutions and quantify how decreasing both resolutions affect the resulting mock observations. We find that changing the spatial resolution changes the hydrodynamic properties of the jet, which directly affect the MCRaT mock observable peak energies. We also find that decreasing the temporal resolution artificially decreases the high energy slope of the mock observed spectrum, which increases both the spectral peak energy and the luminosity. We show that the effects are additive when both spatial and temporal resolutions are modified. Our results allow us to understand how decreased hydrodynamic temporal and spatial resolutions affect the results of post-processing radiative transfer calculations, allowing for the optimization of hydrodynamic simulations for radiative transfer codes.

Jose Arita-Escalante↗

Recent Progress on RANS-Based Transition Model Verification

The current efforts to assess and improve the Reynolds-averaged Navier-Stokes (RANS)-coupled transition models in the NASA FUN3D and OVERFLOW codes are summarized in this study. The first AIAA Transition Modeling Workshop and the NATO AVT-313 Transition Workshop both emphasized the need for code verification for transport equations based transition models as a top priority. We discuss the methods used for the model verification, the resulting grid families, the flow solutions, and other supporting information collected with at least two established NASA flow solvers, namely, FUN3D and OVERFLOW. These results, which will be uploaded onto the NASA Turbulence Modeling Resource, should assist other members of the computational fluid dynamics (CFD) community in verifying their own implementations of various transition models, such as the Langtry-Menter (LM2009) model, the one-equation γ model, and Coder’s amplification factor transport (AFT) model. Grid convergence is assessed using both global and local flow metrics of interest such as lift and drag as well as local skin-friction coefficients. We also explore the anisotropic unstructured metric-based adaptive mesh refinement library known as refine with the NASA FUN3D solver to determine if this capability can achieve the same accuracy as handcrafted structured grids with a significantly smaller node count and to learn the characteristics of the resulting grid distribution, especially in the vicinity of the transition zone.

RANS↗

CFD Modeling & Validation of Single Bubble Growth During Cavitation in Zero Gravity

Cryogenic Fluid Management (CFM) in zero gravity represents a vital area of research as NASA pursues future long-duration space missions. Success of these missions relies heavily on the ability to store and transfer the cryogenic liquid fuels efficiently and safely. In the Zero Boil-Off Tank (ZBOT-1) Experiment in 2018, unexpected and intense phase change occurred at the screened Liquid Acquisition Device (LAD) during tank pressure control that was later attributed to cavitation. The cavitation ultimately resulted in pump failure. Since cryogen cavitation during storage and transfer of propellants in microgravity has been a source of serious concern for the aerospace community, a series of drop tower experiments with liquid methane were also performed at the University of Bremen to carefully study cavitation from a single bubble nucleus in an engineered micron-sized wall cavity. As the test cell is depressurized during the 10-second drop, cavitation causes bubble growth from the nucleus. Here, in a collaboration between the Case Western Reserve University and University of Bremen, we present a two-phase Computational Fluid Dynamics (CFD) model of bubble growth from a single wall cavity during depressurization in microgravity. Both 2D axisymmetric and 3D parametric simulation case studies are performed to show the evolution of the bubble growth. The model uses a Volume of Fluid (VOF) approach with and without adaptive mesh refinement and adaptive time stepping to capture the growth dynamics using an explicit formulation with algebraic reconstruction of the interface. CFD results show good agreement with corresponding experiment. Based on the velocity, temperature, and volume fraction fields generated by the validation case studies, detailed discussion and analysis of fluid flow and heat transfer during bubble growth process are presented to delineate the intricacies of the cavitation process. Strengths and shortcomings of the present numerical approach in capturing this phenomenon are also highlighted.

Two Phase Flow↗

Ground Tests on the BOLT Geometry at Mach 7: Cross-Facility Comparison and Stability Analysis

Transition measurements have been obtained through two experimental campaigns conducted independently by the German Aerospace Center and the French Aerospace Lab with the French Alternative Energies and Atomic Energy Commission on subscale models of the BOLT-1 flight experiment geometry. This paper details a cross-facility comparison of measurements obtained at Mach 7, as well as subsequent computational analysis. Infrared (IR) thermography measurements obtained by both campaigns have facilitated a global comparison of the transition front across facilities at analagous conditions, which are found to be in good agreement. High-frequency surface pressure fluctuation data demonstrate significant amplification of instabilities with Mack-mode characteristics in the outboard regions of the acreage. These measurements are compared to stability analyses of varying fidelity. The computational methods employed to characterize the boundary-layer transition phenomena include the traditional line-marching implementation of the Parabolized Stability Equations (PSE), 2D eigenvalue analysis coupled with PSE, and Adaptive Mesh Refinement Wavepacket Tracking. While the 2D eigenvalue analysis is found to predict instabilities, which correlate in terms of frequency and acreage location to the experimental measurements, the predicted amplification for these instabilities is lower than would typically be expected for transition. Line-marching results for traveling crossflow produce the best match to the experimental transition front, with a consistent transition N factor of approximately 3-3.5.

Boundary Layer Transition↗

Computational Techniques to Generate Space Launch System Aerodynamic Databases

This document describes the reasoning and trade studies used to evaluate tools for constructing the aerodynamic lineload databases for the liftoff and transition phases of flight for the Space Launch System. Three computational fluid dynamics codes (USM3D, FUN3D, Kestrel) were investigated with various turbulence models, as well as detached eddy simulation variants for the launch vehicle in free air and in proximity to the tower. Decisions were made mostly based on results from brief developmental studies performed in response to specific, unforeseen challenges that were encountered in the analysis of a given configuration. The need to develop databases in a timely manner, as well as accurately capture the expected leeward-wake flowfield characteristics, led to the selection of the Kestrel flow solver with its delayed detached eddy simulation method, the Spalart-Allmaras turbulence model, and the adaptive mesh refinement capability in the off-body Cartesian grid region.

Karen A. Deere↗

Development of a Combined Cohesive and Virtual Crack-Closure Technique Approach to Represent R-Curves

Resistance curve (R-curve) effects due to fiber bridging, crack migration, and other blunting mechanisms are common in composite laminates. These mechanisms can dramatically increase the resistance to crack propagation but can be challenging to simulate. Delamination with R-curves can be analyzed using cohesive zone modeling (CZM) or the virtual crack closure technique (VCCT). Large fracture process zones can be simulated with CZM, but they require highly refined meshes. Coarser meshes can be used with VCCT, but this method is only applicable to small fracture process zones with R-curves defined as functions of position. Therefore, a technique with the computational efficiency of VCCT and the natural ability of cohesive elements to represent large fracture process zones is desirable. An approach is proposed that starts as a CZM in which the cohesive traction separation law (TSL) is separated into high-strength (HS) and low-strength (LS) components. The HS part, which is responsible for the mesh requirements of the CZM analysis, is replaced by VCCT. The combined method is evaluated by analyzing the response of double cantilevered beam specimens. Two specimen layup configurations, [0/90/90/0] 3s and [0/90/90/0] 9s , are evaluated. The R-curve response from each configuration is determined and applied to the constitutive properties of models built with CZM and with VCCT. The results and computational efficiency of the CZM, VCCT, and combined approaches are compared. The results are indicative that a combined cohesive/VCCT approach can enable progressive failure analyses to retain the computational efficiency of VCCT with the ability of the cohesive elements to capture R-curve effects.

Virtual Crack-Closure Technique↗

Comparison of OVERFLOW Computational and Experimental Results for a Blunt Mars Entry Vehicle Concept during Supersonic Retropropulsion

Simulations of unsteady supersonic retropropulsion (SRP) flow over a Hypersonic Inflatable Aerodynamic Decelerator (HIAD) blunt-body vehicle were performed using the OVERFLOW Computational Fluid Dynamics (CFD) solver. High-fidelity flow solver techniques, including Detached Eddy Simulation (DES) turbulence modeling and Adaptive Mesh Refinement (AMR), were employed to obtain improved realism in CFD predictions. Simulation conditions and geometry configurations were designed to match specific runs in the Descent System Study (DSS) wind tunnel testing (WTT) campaign. The accuracy of each simulation is assessed by direct comparison to experimental data. Comparisons of computational predictions of the SRP flowfield and bow shock shape to experimental schlieren imaging show reasonable prediction of mean shock shape, with approximately 10% similarity in shock standoff distance for selected conditions, as well as similarity in local, time-varying fluctuations of the shock-plume interaction. Comparisons of discrete measurements of surface pressure coefficient (Cp) indicate CFD accuracy within approximately 10% of the experiment across the majority of the model heatshield, with larger variations at some of the heatshield edge locations with stronger flow unsteadiness. Simulated unsteadiness of these chaotic flows, which were highly dynamic and multi-modal, was shown to be within 20-40% of experimentally-measured pressure standard deviation (SD) for the majority of the sampled locations.

Supersonic Retropropulsion↗

Comparison of OVERFLOW Computational and Experimental Results for a Blunt Mars Entry Vehicle Concept during Supersonic Retropropulsion

Simulations of unsteady supersonic retropropulsion (SRP) flow over a Hypersonic Inflatable Aerodynamic Decelerator (HIAD) blunt-body vehicle were performed using the OVERFLOW Computational Fluid Dynamics (CFD) solver. High-fidelity flow solver techniques, including Detached Eddy Simulation (DES) turbulence modeling and Adaptive Mesh Refinement (AMR), were employed to obtain improved realism in CFD predictions. Simulation conditions and geometry configurations were designed to match specific runs in the Descent System Study (DSS) wind tunnel testing (WTT) campaign. The accuracy of each simulation is assessed by direct comparison to experimental data. Comparisons of computational predictions of the SRP flowfield and bow shock shape to experimental schlieren imaging show reasonable prediction of mean shock shape, with approximately 10% similarity in shock standoff distance for selected conditions, as well as similarity in local, time-varying fluctuations of the shock-plume interaction. Comparisons of discrete measurements of surface pressure coefficient (Cp) indicate CFD accuracy within approximately 10% of the experiment across the majority of the model heatshield, with larger variations at some of the heatshield edge locations with stronger flow unsteadiness. Simulated unsteadiness of these chaotic flows, which were highly dynamic and multi-modal, was shown to be within 20-40% of experimentally-measured pressure standard deviation (SD) for the majority of the sampled locations.

Supersonic Retropropulsion↗

Investigation of Physical Mechanisms for Jet Noise Reduction by Plug Nozzle Porosity

This paper presents the results of a computational study on porous-plug nozzles for their eventual application in reducing takeoff noise levels for supersonic civil transport. The study explores a wide range of porous-plug geometries, encompassing variations in hole size, plug length and porosity. Computational fluid dynamics (CFD) analyses are employed in concert with an advanced automated mesh refinement (AMR) scheme, Sketch-to-Solution (S2S), to investigate porous plug nozzle design strategies that may diminish shock strength, broad-band shock noise (BBSN), flow separation, and other undesirable characteristics associated with high takeoff noise levels. A selected subset of the porous-plug nozzles that were analyzed computationally were manufactured at subscale using stereolithography 3D printing. These nozzles were tested experimentally, obtaining far-field noise spectral data and schlieren flow visualization pictures. Detailed comparisons between CFD predictions and experimental results were conducted. These comparisons focus on gaining a better understanding of the underlying physical mechanisms responsible for noise reduction with the porous plugs relative to corresponding solid plugs.

computational fluid dynamics↗