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NASA NTRS2026

Development of a One-Domain Volume-Averaged Navier–Stokes Solver

The interaction between a high-enthalpy flow and a thermal protection material is inherently multiscale and multiphysics. In conventional aerothermal analyses, the external flow and material response are generally modeled using separate computational domains coupled through boundary conditions at the material surface. Although this approach has supported many practical applications, it requires assumptions about the location and behavior of the interface and may become difficult to apply when material decomposition, internal reactions, and surface recession substantially alter the porous structure. This report presents the development of a one-domain formulation in which the free-fluid and porous-material regions are represented within a single computational domain. The formulation is based on the volume-averaged Navier–Stokes (VANS) equations, derived from the governing equations for reacting, compressible flow and condensed material. Volume averaging transfers the influence of the unresolved material microstructure to the macroscale equations through effective transport properties, interfacial source terms, and dispersion fluxes. Particular attention is given to regions in which porosity and permeability vary rapidly, including the diffuse transition between a porous material and the surrounding fluid. The resulting equations are implemented in the Porous-material Analysis Toolbox based on OpenFOAM (PATO). The report describes the pressure–velocity coupling strategy used by the solver, examines spatial filtering techniques for deriving effective properties, and evaluates the influence of a smoothly varying interface permeability. Numerical demonstrations include canonical porous-flow configurations, a flow-tube configuration representative of FiberForm® permeability experiments, and the oxidation of a porous carbon material. The purpose of this work is to establish a mathematical and computational foundation for a unified treatment of flow and thermal protection material response. The present formulation is intended to support the progressive inclusion of additional physical processes, including multicomponent transport, finite-rate gas–surface chemistry, pyrolysis, internal oxidation, and material recession. It also provides a framework for connecting pore-scale simulations and microstructural characterization with macroscale aerothermal-response calculations. This report is intended for researchers and engineers working in computational fluid dynamics, porous-media transport, material response, and thermal protection system modeling. It documents both the theoretical development and the initial numerical assessment of the one-domain approach, while identifying the closure of effective and dispersion terms as an important subject for continued investigation.

Ablation↗
NASA NTRSDate not supplied

Improvements in Simulating a Mach 0.80 Transonic Truss-Braced Wing Configuration using the Spalart-Allmaras and k-ω SST Turbulence

Teams from the NASA Ames Research Centers (ARC) and Langley Research Center (LaRC) have been working on validating their computational fluid dynamics (CFD) results for the Boeing Mach 0.80 Transonic Truss-Braced Wing (TTBW) configuration. Experimental data used for the validation were gathered from a test conducted of a 4.5% scale Mach 0.80 TTBW model in the NASA Ames Research Center 11-by 11-Foot Transonic Wind Tunnel. The CFD simulations were initially run with both LAVA and USM3D Mixed Element solvers utilizing the Spalart-Allmaras (SA) turbulence model. A discrepancy was observed between CFD and experimental loads and moments ranging on average from 0.047 to 0.063 for lift coefficient, 16.5 to 27 in drag counts, and -0.02 to -0.032 for pitching moment, varying with the solver used. With introducing the refactored version of LAVA these values dropped to 0.034 to 0.047 for lift coefficient, 7.74 to 16.5 in drag counts, and lastly -0.012 to -0.02 for pitching moment. Based on findings from Boeing, who observed an improved comparison to experimental data when using the k-ω Shear Stress Transport (SST) turbulence model, the NASA teams conducted simulations with SST to investigate turbulence modeling sensitivities. OVERFLOW and USM3D V6 solvers were used for the comparison of SST and SA simulations. CFD results using the SST turbulence model demonstrate an improvement in matching with experimental CL values, reducing the discrepancies seen by 0.021-0.055 (62-93% reduction in discrepancy respective to the OVERFLOW and USM3D V6). The SST model has varying effects on CD, based on the solver / grid paradigm; for USM3D this prediction is only improved at higher angles of attack (above the cruise design point) resulting in a reduced discrepancy of 8.8–25 drag counts However, at the mid-to-low angles of attack, SST increases the CD discrepancy by 4-55 counts, increasing at lower angles of attack. For OVERFLOW this discrepancy only exists at the low angles of attack and maxes out at 10 counts of drag. Above α = 1.5° OVERFLOW SST reduces discrepancy by 9.3 drag counts on average.

AATT↗
NASA NTRS2003

Numerical Models of Human Circulatory System under Altered Gravity: Brain Circulation

A computational fluid dynamics (CFD) approach is presented to model the blood flow through the human circulatory system under altered gravity conditions. Models required for CFD simulation relevant to major hemodynamic issues are introduced such as non-Newtonian flow models governed by red blood cells, a model for arterial wall motion due to fluid-wall interactions, a vascular bed model for outflow boundary conditions, and a model for auto-regulation mechanism. The three-dimensional unsteady incompressible Navier-Stokes equations coupled with these models are solved iteratively using the pseudocompressibility method and dual time stepping. Moving wall boundary conditions from the first-order fluid-wall interaction model are used to study the influence of arterial wall distensibility on flow patterns and wall shear stresses during the heart pulse. A vascular bed modeling utilizing the analogy with electric circuits is coupled with an auto-regulation algorithm for multiple outflow boundaries. For the treatment of complex geometry, a chimera overset grid technique is adopted to obtain connectivity between arterial branches. For code validation, computed results are compared with experimental data for steady and unsteady non-Newtonian flows. Good agreement is obtained for both cases. In sin-type Gravity Benchmark Problems, gravity source terms are added to the Navier-Stokes equations to study the effect of gravitational variation on the human circulatory system. This computational approach is then applied to localized blood flows through a realistic carotid bifurcation and two Circle of Willis models, one using an idealized geometry and the other model using an anatomical data set. A three- dimensional anatomical Circle of Willis configuration is reconstructed from human-specific magnetic resonance images using an image segmentation method. The blood flow through these Circle of Willis models is simulated to provide means for studying gravitational effects on the brain circulation under auto-regulation.

Kim, Chang Sung↗
NASA NTRS2009

Unsteady Full Annulus Simulations of a Transonic Axial Compressor Stage

Two recent research endeavors in turbomachinery at NASA Glenn Research Center have focused on compression system stall inception and compression system aerothermodynamic performance. Physical experiment and computational research are ongoing in support of these research objectives. TURBO, an unsteady, three-dimensional, Navier-Stokes computational fluid dynamics code commissioned and developed by NASA, has been utilized, enhanced, and validated in support of these endeavors. In the research which follows, TURBO is shown to accurately capture compression system flow range-from choke to stall inception-and also to accurately calculate fundamental aerothermodynamic performance parameters. Rigorous full-annulus calculations are performed to validate TURBO s ability to simulate the unstable, unsteady, chaotic stall inception process; as part of these efforts, full-annulus calculations are also performed at a condition approaching choke to further document TURBO s capabilities to compute aerothermodynamic performance data and support a NASA code assessment effort.

Herrick, Gregory P.↗
NASA NTRS1992

Numerical simulation of jet noise

Jet noise and jet-induced structural loads have become key issues in the design of commercial and military aircraft. Computational Fluid Dynamics (CFD) can be of use in predicting the underlying jet shear-layer instabilities and, in conjunction with classical acoustic theory, jet noise. The computational issues involved in the resolution of high Reynolds number unsteady jet flows are addressed in this paper. Once these jet flows can be accurately resolved, it should be possible to use acoustic theory to extract, for example, the far-field jet noise. An assessment of future work and computational resources required for directly computing far-field jet noise is also presented.

Van Dalsem, W. R.↗
NASA NTRS2018

A Higher-Order Space-Time Finite-Element Method for Moving-Body and Fluid-Structure Interaction Problems

We present a high-order finite-element method for moving body and fluid/structure interaction problems. Our solution strategy is based on a space-time discontinuous Galerkin (DG) spectral-element discretization which extends to arbitrary order of accuracy. The space-time DG discretization is a natural choice for moving body and fluid-structure interaction problems as moving surfaces are incorporated simply by considering curved space-time elements whose space-time faces align with the moving body. We present a discontinuous-Galerkin in time discretization for six-degree of motion modeling of rigid bodies, and a continuous-Galerkin discretization for equations of linear elasticity to generate curved space-time meshes. Numerical results for several simple 2D test cases are presented in order to verify the implementation of the different models. Finally we present a preliminary dynamic simulation of a parachute.

High-Order↗
NASA NTRS1993

Navier-Stokes simulations of the Shuttle Orbiter aerodynamic characteristics with emphasis on pitch trim and bodyflap

An analysis of the longitudinal aerodynamics of the Shuttle Orbiter in the hypersonic flight regime is made through the use of computational fluid dynamics (CFD). Particular attention is given to establishing the cause of the 'pitching moment anomaly' which occurred on the Orbiter's first flight and to computing the aerodynamics of a complete Orbiter configuration at flight conditions. Data from ground based facilities as well as Orbiter flight data are used to validate the computed results. Analysis shows that the 'pitching moment anomaly' is a real gas chemistry effect which cannot be simulated in ground-based facilities. Computed flight aerodynamics for the Orbiter are within 5 percent of the measured flight values and trim bodyflap deflections are predicted to within 10 percent.

Weilmuenster, K. J.↗
NASA NTRS1999

Simulation of Unsteady Hypersonic Combustion Around Projectiles in an Expansion Tube

The temporal evolution of combustion flowfields established by the interaction between wedge-shaped bodies and explosive hydrogen-oxygen-nitrogen mixtures accelerated to hypersonic speeds in an expansion tube is investigated. The analysis is carried out using a fully implicit, time-accurate, computational fluid dynamics code that we developed recently for solving the Navier-Stokes equations for a chemically reacting gas mixture. The numerical results are compared with experimental data from the Stanford University expansion tube for two different gas mixtures at Mach numbers of 4.2 and 5.2. The experimental work showed that flow unstart occurred for the Mach 4.2 cases. These results are reproduced by our numerical simulations and, more significantly, the causes for unstart are explained. For the Mach 5.2 mixtures, the experiments and numerical simulations both produced stable combustion. However, the computations indicate that in one case the experimental data were obtained during the transient phase of the flow; that is, before steady state had been attained.

Yungster, S.↗
NASA NTRS2001

Development of an Unstructured Mesh Code for Flows About Complete Vehicles

This report describes the research work undertaken at the Massachusetts Institute of Technology, under NASA Research Grant NAG4-157. The aim of this research is to identify effective algorithms and methodologies for the efficient and routine solution of flow simulations about complete vehicle configurations. For over ten years we have received support from NASA to develop unstructured mesh methods for Computational Fluid Dynamics. As a result of this effort a methodology based on the use of unstructured adapted meshes of tetrahedra and finite volume flow solvers has been developed. A number of gridding algorithms, flow solvers, and adaptive strategies have been proposed. The most successful algorithms developed from the basis of the unstructured mesh system FELISA. The FELISA system has been extensively for the analysis of transonic and hypersonic flows about complete vehicle configurations. The system is highly automatic and allows for the routine aerodynamic analysis of complex configurations starting from CAD data. The code has been parallelized and utilizes efficient solution algorithms. For hypersonic flows, a version of the code which incorporates real gas effects, has been produced. The FELISA system is also a component of the STARS aeroservoelastic system developed at NASA Dryden. One of the latest developments before the start of this grant was to extend the system to include viscous effects. This required the development of viscous generators, capable of generating the anisotropic grids required to represent boundary layers, and viscous flow solvers. We show some sample hypersonic viscous computations using the developed viscous generators and solvers. Although this initial results were encouraging it became apparent that in order to develop a fully functional capability for viscous flows, several advances in solution accuracy, robustness and efficiency were required. In this grant we set out to investigate some novel methodologies that could lead to the required improvements. In particular we focused on two fronts: (1) finite element methods and (2) iterative algebraic multigrid solution techniques.

Peraire, Jaime↗
NASA NTRS2007

Nonlinear Aeroelastic Analysis Using a Time-Accurate Navier-Stokes Equations Solver

A method to simulate limit cycle oscillation (LCO) due to control surface freeplay using a modified CFL3D, a time-accurate Navier-Stokes computational fluid dynamics (CFD) analysis code with structural modeling capability, is presented. This approach can be used to analyze aeroelastic response of aircraft with structural behavior characterized by nonlinearity in the force verses displacement curve. A limited validation of the method, using very low Mach number experimental data for a three-degrees-of-freedom (pitch/plunge/flap deflection) airfoil model with flap freeplay, is also presented.

Kuruvila, Geojoe↗
NASA NTRS2009

Cryogenic Fluid Storage Technology Development: Recent and Planned Efforts at NASA

Recent technology development work conducted at NASA in the area of Cryogenic Fluid Management (CFM) storage is highlighted, including summary results, key impacts, and ongoing efforts. Thermodynamic vent system (TVS) ground test results are shown for hydrogen, methane, and oxygen. Joule-Thomson (J-T) device tests related to clogging in hydrogen are summarized, along with the absence of clogging in oxygen and methane tests. Confirmation of analytical relations and bonding techniques for broad area cooling (BAC) concepts based on tube-to-tank tests are presented. Results of two-phase lumped-parameter computational fluid dynamic (CFD) models are highlighted, including validation of the model with hydrogen self pressurization test data. These models were used to simulate Altair representative methane and oxygen tanks subjected to 210 days of lunar surface storage. Engineering analysis tools being developed to support system level trades and vehicle propulsion system designs are also cited. Finally, prioritized technology development risks identified for Constellation cryogenic propulsion systems are presented, and future efforts to address those risks are discussed.

Moran, Matthew E.↗
NASA NTRS2018

Numerical Simulation of Dynamic Stall Using Near-Body Adaptive Mesh Refinement

Time-dependent Reynolds-averaged Navier-Stokes simulations have been carried out for a NACA 0012 airfoil and a flexible UH-60A rotor undergoing dynamic stall. The OVERFLOW computational fluid dynamics (CFD) code is used to explore the use of near-body adaptive mesh refinement (NB-AMR) for the first time on a flexible helicopter rotor in forward flight. Emphasis is placed on understanding the temporal and spatial convergence of the solutions, their numerical efficiency and stability, and establishing a grid-converged solution. Some of the remaining differences between CFD and flight-test measurements are discussed. Time-dependent flow visualization is used to provide an improved understanding of the physical mechanisms involved with two-dimensional and three-dimensional dynamic stall, and the NB-AMR process.

Near-Body↗
NASA NTRSDate not supplied

Updated Noise Dose Range of NASA’s X-59 Aircraft Estimated from Propagation Simulations

A follow-on study to Doebler and Loubeau, “The noise dose range of the X-59 estimated from propagation simulations,” JASA 150(4), A208 (2021); doi:10.1121/10.0008134 is described. In the previous work, propagation simulations of NASA’s X-59 sonic thump were conducted using two near-field pressure solutions from NASA’s Cart3D computational fluid dynamics (CFD) code. The near-fields were propagated through realistic atmospheric profiles from the Climate Forecast System Version 2 database across the USA, and Perceived Level statistics of the thumps were presented. The current work repeats the previous analyses, instead using near-field CFD solutions from NASA’s Fully Unstructured Navier-Stokes (FUN3D) code for the same aircraft conditions (Mach 1.4 at 53,200 feet and Mach 1.3 at 43,000 feet), which achieve the minimum and maximum cruise loudness. NASA and contractors in the X-59 development and community noise testing project mutually agreed upon using FUN3D for generating near-field pressures. Sonic thump loudness statistics using the FUN3D near-fields are similar to those of Cart3D. The min loudness condition is about 1 dB (PL) greater when using the FUN3D solution, and the max loudness condition results are nearly identical. Understanding the X-59’s dose range for various flight and atmospheric conditions is important for planning X-59 community noise surveys.

X-59↗
NASA NTRSDate not supplied

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↗
NASA NTRS1973

Computer program for the prediction of reorientation flow dynamics

Program uses Navier-Stokes and continuity equations for incompressible, viscous fluid as the basic equations governing reorientation flow dynamics. Program can simulate curved as well as straight-walled boundaries; has ability to calculate both free-surface and confined flows; and can be used in either cylindrical or plane geometry.

Betts, W. S., Jr.↗
NASA NTRS1994

Direct numerical simulation of sheared turbulent flow

The summer assignment to study sheared turbulent flow was divided into three phases which were: (1) literature survey, (2) computational familiarization, and (3) pilot computational studies. The governing equations of fluid dynamics or Navier-Stokes equations describe the velocity, pressure, and density as functions of position and time. In principle, when combined with conservation equations for mass, energy, and thermodynamic state of the fluid a determinate system could be obtained. In practice the Navier-Stokes equations have not been solved due to the nonlinear nature and complexity of these equations. Consequently, the importance of experiments in gaining insight for understanding the physics of the problem has been an ongoing process. Reasonable computer simulations of the problem have occured as the computational speed and storage of computers has evolved. The importance of the microstructure of the turbulence dictates the need for high resolution grids in extracting solutions which contain the physical mechanisms which are essential to a successful simulation. The recognized breakthrough occurred as a result of the pioneering work of Orzag and Patterson in which the Navier-Stokes equations were solved numerically utilizing a time saving toggling technique between physical and wave space, known as a spectral method. An equally analytically unsolvable problem, containing the same quasi-chaotic nature as turbulence, is known as the three body problem which was studied computationally as a first step this summer. This study was followed by computations of a two dimensional (2D) free shear layer.

Harris, Vascar G.↗