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All sourcesNASA NTRSDOE OSTI
NASA NTRS1991

A Chebyshev spectral collocation method using a staggered grid for the stability of cylindrical flows

A staggered spectral collocation method for the stability of cylindrical flows is developed. In this method the pressure is evaluated at different nodal points than the three velocity components. These modified nodal points do not include the two boundary nodes; therefore the need for the two artificial pressure boundary conditions employed by Khorrami et al. is eliminated. It is shown that the method produces very accurate results and has a better convergence rate than the spectral tau formulation. However, through extensive convergence tests it was found that elimination of the artificial pressure boundary conditions does not result in any significant change in the convergence behavior of spectral collocation methods.

Khorrami, Mehdi R.↗
NASA NTRS1992

Unstructured grid methods for compressible flows

The implementation of the finite element method on unstructured triangular grids is described and the development of centered finite element schemes for the solution of the compressible Euler equation on general triangular and tetrahedral grids is discussed. Explicit and implicit Lax-Wendroff type methods and a method based upon the use of explicit multistep timestepping are considered. In the latter case, the convergence behavior of the method is accelerated by the incorporation of a fully unstructured multigrid procedure. The advancing front method for generating unstructured grids of triangles and tetrahedra is described and the application of adaptive mesh techniques to both steady and transient flow analysis is illustrated.

Morgan, K.↗
NASA NTRS2000

Three-Dimensional Incompressible Navier-Stokes Flow Computations about Complete Configurations Using a Multiblock Unstructured Grid Approach

A multiblock unstructured grid approach is presented for solving three-dimensional incompressible inviscid and viscous turbulent flows about complete configurations. The artificial compressibility form of the governing equations is solved by a node-based, finite volume implicit scheme which uses a backward Euler time discretization. Point Gauss-Seidel relaxations are used to solve the linear system of equations at each time step. This work employs a multiblock strategy to the solution procedure, which greatly improves the efficiency of the algorithm by significantly reducing the memory requirements by a factor of 5 over the single-grid algorithm while maintaining a similar convergence behavior. The numerical accuracy of solutions is assessed by comparing with the experimental data for a submarine with stem appendages and a high-lift configuration.

Sheng, Chunhua↗
NASA NTRS2003

Algorithmic Enhancements to the VULCAN Navier-Stokes Solver

VULCAN (Viscous Upwind aLgorithm for Complex flow ANalysis) is a cell centered, finite volume code used to solve high speed flows related to hypersonic vehicles. Two algorithms are presented for expanding the range of applications of the current Navier-Stokes solver implemented in VULCAN. The first addition is a highly implicit approach that uses subiterations to enhance block to block connectivity between adjacent subdomains. The addition of this scheme allows more efficient solution of viscous flows on highly-stretched meshes. The second algorithm addresses the shortcomings associated with density-based schemes by the addition of a time-derivative preconditioning strategy. High speed, compressible flows are typically solved with density based schemes, which show a high level of degradation in accuracy and convergence at low Mach numbers (M less than or equal to 0.1). With the addition of preconditioning and associated modifications to the numerical discretization scheme, the eigenvalues will scale with the local velocity, and the above problems will be eliminated. With these additions, VULCAN now has improved convergence behavior for multi-block, highly-stretched meshes and also can solve the Navier-Stokes equations for very low Mach numbers.

Litton, D. K.↗
NASA NTRS2003

Comparison of Artificial Compressibility Methods

Various artificial compressibility methods for calculating three-dimensional, steady and unsteady, laminar and turbulent, incompressible Navier-Stokes equations are compared in this work. Each method is described in detail along with appropriate physical and numerical boundary conditions. Analysis of well-posedness and numerical solutions to test problems for each method are provided. A comparison based on convergence behavior, accuracy, stability and robustness is used to establish the relative positive and negative characteristics of each method.

Kiris, Cetin↗
NASA NTRS2004

Evaluation of a Multigrid Scheme for the Incompressible Navier-Stokes Equations

A fast multigrid solver for the steady, incompressible Navier-Stokes equations is presented. The multigrid solver is based upon a factorizable discrete scheme for the velocity-pressure form of the Navier-Stokes equations. This scheme correctly distinguishes between the advection-diffusion and elliptic parts of the operator, allowing efficient smoothers to be constructed. To evaluate the multigrid algorithm, solutions are computed for flow over a flat plate, parabola, and a Karman-Trefftz airfoil. Both nonlifting and lifting airfoil flows are considered, with a Reynolds number range of 200 to 800. Convergence and accuracy of the algorithm are discussed. Using Gauss-Seidel line relaxation in alternating directions, multigrid convergence behavior approaching that of O(N) methods is achieved. The computational efficiency of the numerical scheme is compared with that of Runge-Kutta and implicit upwind based multigrid methods.

Swanson, R. C.↗
NASA NTRS2001

Towards Optimal Multigrid Efficiency for the Navier-Stokes Equations

A fast multigrid solver for the steady incompressible Navier-Stokes equations is presented. Unlike time-marching schemes, this approach uses relaxation of the steady equations. Application of this method results in a discretization that correctly distinguishes between the advection and elliptic parts of the operator, allowing efficient smoothers to be constructed. Numerical solutions are shown for flow over a flat plate and a Karman-Trefftz airfoil. Using collective Gauss-Seidel line relaxation in both the vertical and horizontal directions, multigrid convergence behavior approaching that of O(N) methods is achieved. The computational efficiency of the numerical scheme is compared with that of a Runge-Kutta based multigrid method.

Swanson, R. C.↗
NASA NTRS2004

Comparison of Artificial Compressibility Methods

Various artificial compressibility methods for calculating the three-dimensional incompressible Navier-Stokes equations are compared. Each method is described and numerical solutions to test problems are conducted. A comparison based on convergence behavior, accuracy, and robustness is given.

Kiris, Cetin↗
NASA NTRS2008

Grid Quality and Resolution Issues from the Drag Prediction Workshop Series

The drag prediction workshop series (DPW), held over the last six years, and sponsored by the AIAA Applied Aerodynamics Committee, has been extremely useful in providing an assessment of the state-of-the-art in computationally based aerodynamic drag prediction. An emerging consensus from the three workshop series has been the identification of spatial discretization errors as a dominant error source in absolute as well as incremental drag prediction. This paper provides an overview of the collective experience from the workshop series regarding the effect of grid-related issues on overall drag prediction accuracy. Examples based on workshop results are used to illustrate the effect of grid resolution and grid quality on drag prediction, and grid convergence behavior is examined in detail. For fully attached flows, various accurate and successful workshop results are demonstrated, while anomalous behavior is identified for a number of cases involving substantial regions of separated flow. Based on collective workshop experiences, recommendations for improvements in mesh generation technology which have the potential to impact the state-of-the-art of aerodynamic drag prediction are given.

Mavriplis, Dimitri J.↗
NASA NTRS2023

Implementation and Assessment of Menter’s Galilean-Invariant γ Transition Model in OVERFLOW

With an increased emphasis on greener air transports and sustainable aviation, the modeling of laminar-to-turbulent boundary layer transition is anticipated to have an added significance, particularly in the applications related to laminar flow technology. However, unmanned aerial vehicles, crewed reentry vehicles, and ground-to-flight extrapolation all benefit from transition models. Because no single transition model is ideal for the complete spectrum of applications, it is useful to incorporate a variety of models in general-purpose CFD solvers, such as the NASA OVERFLOW Overset CFD code. While the Langtry-Menter 𝛄 − 𝑹𝒆 𝛉𝒕 model, currently available in OVERFLOW, has been widely used for CFD predictions of flows with laminar, transitional, and turbulent boundary layers, it does not possess the Galilean invariance property, a desirable attribute for rotorcraft applications. To help overcome that limitation, we have recently implemented Menter's baseline version of the SST-based γ transition model, along with a Galilean invariant stationary crossflow extension within OVERFLOW (version 2.3e). An initial assessment of the newly implemented model has been carried out using 2D benchmark cases including flat plates and the NLF-0416 airfoil, addressing several transition scenarios ranging from bypass transition due to freestream turbulence, natural transition via Tollmien-Schlichting instabilities, and transition due to a laminar separation bubble. The crossflow extension has been applied to the infinite swept NLF(2)-0415 wing and the 6:1 prolate spheroid. Wherever possible, the results were obtained on a sequence of meshes to ascertain the grid convergence behavior, which has been evaluated through global metrics such as force coefficients as well as local values of the skin-friction coefficient at selected points near and within the transition region. Overall, the model appears to be correctly implemented and the results show promise for further development using the framework of the γ transition model.

CFD modeling↗
DOE OSTI2025

Serpent - Bison - THM Preliminary Multiphysics Modeling of a Nuclear Thermal Propulsion System Fuel Assembly

This work demonstrates the Monte Carlo neutronic and Thermo-Hydraulic coupling scheme using the Serpent code and MOOSE application Bison and Thermo Hydraulic Module. The coupling scheme is then applied to the reference BWX Technologies Nuclear Ther- mal Propulsion system at he fuel assembly level where it’s used to perform an analysis of the isothermal material coefficients and potential material reactivity worth. A method is developed to isolate which feedback effects should be considered for proceeding with reduced order deterministic neutronic modeling where branch off analysis must be con- ducted. The convergence behavior of the coupling scheme is demonstrated where it fol- lows the standard Picard iteration approach. Verification studies for the method of deduc- ing relevant feedback effects is also demonstrated.

22 - GENERAL STUDIES OF NUCLEAR REACTORS↗
NASA NTRS1978

The behavior of a convergent plate boundary - Crustal deformation in the South Kanto district, Japan

The northwesternmost part of the Sagami trough, a part of the Philippine Sea-Eurasian plate boundary, was ruptured during the great South Kanto earthquake in 1923. Very extensive and frequent geodetic measurements of crustal deformation have been made in the South Kanto district since the 1890's, and these constitute the most complete data set on crustal movements in the world. These data were reanalyzed and interpreted and according to our interpretation indicate the following sequence of events. The coseismic movements were due to oblique thrust and right lateral slip of about 8 m on a fault outcropping at the base of the Sagami trough. This was followed by postseismic deformation resulting from reversed afterslip of 20-60 cm that occurred at an exponentially decaying rate in time. The interseismic deformation is produced by steady subduction at a rate of about 1.8 cm/yr. During subduction the top 10-15 km of the plate boundary is apparently locked, while deeper parts slip aseismically at an irregular rate. No significant precursory deformation was observed. The recurrence time for 1923 type earthquakes is 200-300 years. The Boso and Miura peninsulas are broken into a series of fault-bound blocks that move semi-independently of the surrounding region. The subduction zone itself, where it is exposed on land, is shown to be a wide zone encompassing several faults that are active at different times.

Scholz, C. H.↗
DOE OSTI2024

Non-DNA radiosensitive targets that initiate persistent behavioral deficits in rats exposed to space radiation

Predicting future CNS risks for astronauts during deep-space missions will rely substantially on ground-based rodent data with space-relevant ions and behaviors. For rats, the accumulated evidence indicates that less densely ionizing radiation, such as 4 He and 12 C ions, induce behavior deficits at lower doses than densely ionizing ions, such as 48 Ti and 56 Fe. However, this observation conflicts with standard somatic radiobiology, in which densely ionizing ions are generally more effective than less densely ionizing ions, and where the DNA/nucleus is the accepted target for radiation-induced tumorigenesis, cytogenetic aberrations, genetic mutations, and reproductive cell death. To gain deeper insight into the subcellular nature of the radiation targets for behavior risks, we compared the effects of dose, fluence, and linear energy transfer (LET) of 4 He and 56 Fe particles using existing datasets for four distinct behavioral outcomes in rats: elevated plus maze (EPM-anxiety), novel object recognition (NOR-memory), operant responding (OR-response to environmental stimuli), and attentional set-shifting (ATSET-cognitive flexibility). We confirmed that less densely ionizing particles (except protons) showed ~100-fold lower threshold doses than densely ionizing particles for behavioral deficits (0.1–1 cGy for 4 He vs. 15–100 cGy for 56 Fe). However, when analyzed by fluence the behavioral responses converged, indicating that 4 He and 56 Fe were equally effective on a per-track basis. When analyzed by LET, there were ~100-fold differences in the LET for maximum effectiveness for behavioral deficits and DNA endpoints (~1 vs ~100 keV/μm, respectively). These unique features of radiation-induced behavioral deficits (high sensitivity to particles in the 1-keV/μm range, insensitivity to protons in the 0.2 keV/μm range, and isofluence dependence for particles with LET>1 keV/μm) provide evidence in support of a new hypothesis of sub-micron sized radiosensitive targets for behavioral effects consistent with the thickness of plasma membranes and/or small subcellular structures, smaller than a whole synapse. Like our behavior findings, mouse immature oocyte killing which is known to have a plasma membrane target was also better explained by fluence, rather than dose. In contrast, fluence analyses for DNA/nuclear endpoints in somatic cells (e.g., tumor induction, chromosome aberrations) showed opposite results, suggesting that behavior targets are not DNA. Our findings raise questions regarding the identity of subcellular targets and the multi-cellular functional unit for behavior risks, low-dose susceptibility, and generalizability from rat to other species and astronauts.

63 RADIATION, THERMAL, AND OTHER ENVIRON. POLLUTAN↗
NASA NTRS2006

Apparent Transition Behavior of Widely-Used Turbulence Models

The Spalart-Allmaras and the Menter SST kappa-omega turbulence models are shown to have the undesirable characteristic that, for fully turbulent computations, a transition region can occur whose extent varies with grid density. Extremely fine two-dimensional grids over the front portion of an airfoil are used to demonstrate the effect. As the grid density is increased, the laminar region near the nose becomes larger. In the Spalart-Allmaras model this behavior is due to convergence to a laminar-behavior fixed point that occurs in practice when freestream turbulence is below some threshold. It is the result of a feature purposefully added to the original model in conjunction with a special trip function. This degenerate fixed point can also cause nonuniqueness regarding where transition initiates on a given grid. Consistent fully turbulent results can easily be achieved by either using a higher freestream turbulence level or by making a simple change to one of the model constants. Two-equation kappa-omega models, including the SST model, exhibit strong sensitivity to numerical resolution near the area where turbulence initiates. Thus, inconsistent apparent transition behavior with grid refinement in this case does not appear to stem from the presence of a degenerate fixed point. Rather, it is a fundamental property of the kappa-omega model itself, and is not easily remedied.

Rumsey, Christopher L.↗
NASA NTRS2007

Apparent Transition Behavior of Widely-Used Turbulence Models

The Spalart-Allmaras and the Menter SST k-omega turbulence models are shown to have the undesirable characteristic that, for fully turbulent computations, a transition region can occur whose extent varies with grid density. Extremely fine two-dimensional grids over the front portion of an airfoil are used to demonstrate the effect. As the grid density is increased, the laminar region near the nose becomes larger. In the Spalart-Allmaras model this behavior is due to convergence to a laminar-behavior fixed point that occurs in practice when freestream turbulence is below some threshold. It is the result of a feature purposefully added to the original model in conjunction with a special trip function. This degenerate fixed point can also cause non-uniqueness regarding where transition initiates on a given grid. Consistent fully turbulent results can easily be achieved by either using a higher freestream turbulence level or by making a simple change to one of the model constants. Two-equation k-omega models, including the SST model, exhibit strong sensitivity to numerical resolution near the area where turbulence initiates. Thus, inconsistent apparent transition behavior with grid refinement in this case does not appear to stem from the presence of a degenerate fixed point. Rather, it is a fundamental property of the k-omega model itself, and is not easily remedied.

Rumsey, Christopher L.↗
NASA NTRS1958

Experimental Behavior of Pentaborane-Air Combustion Products During Expansion in a Convergent Divergent Nozzle

In order to evaluate the post combustion behavior of boric oxide, pentaborane-air mixtures, burned to completion at a combustor pressure of 3 atmospheres, were expanded through a 7.1-inch-long convergent-divergent nozzle having a 4-inch-diameter throat and an exit-to-throat area ratio of 1.68. The experimentally determined thrust performance was in good agreement with the ideal equilibrium performance at stagnation temperatures of 3300 deg R and lower. The boric oxide vapor at the combustor exit required about 400 F deg supercooling before any condensed phase was observed. For a given thrust, fuel consumption was as much as 20 percent greater than predicted from vapor-pressure data for combustor outlet temperatures i n the vicinity of 3600 deg R. A similar result could be expected in full-scale engines, since the test combustor provided an unusually long dwell time and a highly turbulent environment. During the expansion process, the vapor (when present) did not condense to the extent predicted for an equilibrium expansion process. Moreover, condensation was observed only i n the form of small, abrupt phase changes i n the subsonic flow near the throat. Friction, due to liquid boric oxide films on the nozzle surfaces, was negligible when the surface temperature was above 800 F.

PENTABORANE↗
NASA NTRS2001

Effect of Under-Resolved Grids on High Order Methods

There has been much discussion on verification and validation processes for establishing the credibility of CFD simulations. Since the early 1990s, many of the aeronautical and mechanical engineering related reference journals mandated that any accepted articles in numerical simulations (without known solutions to compared with) need to perform a minimum of one level of grid refinement and time step reduction. Due to the difficulty in analysis, the effect of under-resolved grids and the nonlinear behavior of available spatial discretizations, are scarcely discussed in the literature. Here, an under-resolved numerical simulation is one where the grid spacing being used is too coarse to resolve the smallest physically relevant scales of the chosen continuum governing equations that are of interest to the numerical modeler. With the advent of new developments in fourth-order or higher spatial schemes, it has become common to regard high order schemes as more accurate, reliable and require less grid points. The danger comes when one tries to perform computations with the coarsest grid possible while still hoping to maintain numerical results sufficiently accurate for complex flows, and especially, data-limited problems. On one hand, high order methods when applies to highly coupled multidimensional complex nonlinear problems might have different stability, convergence and reliability behavior than their well studied low order counterparts, especially for nonlinear schemes such as TVD, MUSCL with limiters, ENO, WENO and discrete Galerkin. On the other hand, high order methods involve more operation counts and systematic grid convergence study can be time consuming and prohibitively expansive. At the same time it is difficult to fully understand or categorize the different nonlinear behavior of finite discretizations, especially at the limits of under-resolution when different types of bifurcation phenomena might occur, depending on the combination of grid spacings, time steps, initial conditions and numerical treatments of boundary conditions.

Yee, H. C.↗
NASA NTRS1974

Segregation behavior in a stationary vertical zone with converging interfaces - Pressure-induced segregation effects

Crystal growth and segregation were investigated in a confined vertical melt zone in which the upper solid-melt interface advanced under destabilizing and the lower interface under stabilizing thermal gradients. A technique reported by Kim et al. (1972) was used in the study. The experimental results are discussed, giving attention to interface morphology and growth rate and questions of dopant segregation. Dopant inhomogeneities formed simultaneously in both advancing interfaces can be explained on the basis of pressure induced segregation effects.

Kim, K. M.↗