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All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

QES-Plume v1.0: a Lagrangian dispersion model

Low-cost simulations providing accurate predictions of transport of airborne material in urban areas, vegetative canopies, and complex terrain are demanding because of the small-scale heterogeneity of the features influencing the mean flow and turbulence fields. Common models used to predict turbulent transport of passive scalars are based on the Lagrangian stochastic dispersion model. The Quick Environmental Simulation (QES) tool is a low-computational-cost framework developed to provide high-resolution wind and concentration fields in a variety of complex atmospheric-boundary-layer environments. Part of the framework, QES-Plume, is a Lagrangian dispersion code that uses a time-implicit integration scheme to solve the generalized Langevin equations which require mean flow and turbulence fields. Here, QES-Plume is driven by QES-Winds, a 3D fast-response model that computes mass-consistent wind fields around buildings, vegetation, and hills using empirical parameterizations, and QES-Turb, a local-mixing-length turbulence model. In this paper, the particle dispersion model is presented and validated against analytical solutions to examine QES-Plume’s performance under idealized conditions. In particular, QES-Plume is evaluated against a classical Gaussian plume model for an elevated continuous point-source release in uniform flow, the Lagrangian scaling of dispersion in isotropic turbulence, and a non-Gaussian plume model for an elevated continuous point-source release in a power-law boundary-layer flow. In these cases, QES-Plume yields a maximum relative error below 6 % when compared with analytical solutions. In addition, the model is tested against wind-tunnel data for a uniform array of cubical buildings. QES-Plume exhibits good agreement with the experiment with 99 % of matched zeros and 59 % of the predicted concentrations falling within a factor of 2 of the experimental concentrations. Furthermore, results also emphasize the importance of using high-quality turbulence models for particle dispersion in complex environments. Finally, QES-Plume demonstrates excellent computational performance.

58 GEOSCIENCES↗
NASA NTRS2002

Graphite Ablation and Thermal Response Simulation Under Arc-Jet Flow Conditions

The Two-dimensional Implicit Thermal Response and Ablation program, TITAN, was developed and integrated with a Navier-Stokes solver, GIANTS, for multidimensional ablation and shape change simulation of thermal protection systems in hypersonic flow environments. The governing equations in both codes are demoralized using the same finite-volume approximation with a general body-fitted coordinate system. Time-dependent solutions are achieved by an implicit time marching technique using Gauess-Siedel line relaxation with alternating sweeps. As the first part of a code validation study, this paper compares TITAN-GIANTS predictions with thermal response and recession data obtained from arc-jet tests recently conducted in the Interaction Heating Facility (IHF) at NASA Ames Research Center. The test models are graphite sphere-cones. Graphite was selected as a test material to minimize the uncertainties from material properties. Recession and thermal response data were obtained from two separate arc-jet test series. The first series was at a heat flux where graphite ablation is mainly due to sublimation, and the second series was at a relatively low heat flux where recession is the result of diffusion-controlled oxidation. Ablation and thermal response solutions for both sets of conditions, as calculated by TITAN-GIANTS, are presented and discussed in detail. Predicted shape change and temperature histories generally agree well with the data obtained from the arc-jet tests.

Chen, Y.-K.↗
NASA NTRS1996

Biomass accumulation in hydroponically grown sweetpotato in a controlled environment: a preliminary study

In the development of a plant growth model, the assumptions made and the general equations representing an understanding of plant growth are gradually refined as more information is acquired through experimentation. One such experiment that contributed to sweetpotato model development consisted of measuring biomass accumulation of sweetpotato grown in hydroponic culture in a plant growth chamber. Plants were started from fifteen centimeter long 'TU-82-155' sweetpotato vine cuttings spaced 25 cm apart in each of 18 rectangular growing channels (0.15 by 0.15 by 1.2m) in a system designed to use the nutrient film technique (NFT). Each channel contained four plants. The 3.5m by 5.2m plant growth chamber environmental parameters included an 18h photoperiod, 500 micromoles m-2 s-1 of photosynthetic photon flux (PPF), and a diurnal light/dark temperature of 28 degrees C/22 degrees C. The relative humidity was 80 +/- 5% and the CO2 partial pressure was ambient (350 ppm). The nutrient solution contained in 30L reservoirs was a modified half Hoagland's solution with a 1:2.4 N:K ratio and a pH of 6.2. Solution replenishment occurred when the electrical conductivity (EC) level dropped below 1050. Plants were harvested at 15 days after planting (DAP) and weekly thereafter until day 134. By 57 DAP, stems and fibrous roots had acquired 90% of their total dry biomass, while leaves had reached 84% of their maximum dry biomass. Beginning at 64 DAP dry biomass accumulation in the storage roots dominated the increase in dry biomass for the plants. Dry weight of storage roots at 120 DAP was 165 g/plant or 1.1 kg/m2. Resulting growth curves were consistent with the physiological processes occurring in the plant. Results from this study will be incorporated in a plant growth model for use in conjunction with controlled life support systems for long-term manned space missions.

Biomass↗
NASA NTRS1992

Gross-fragmentation of meteoroids and bulk density of Geminids from photographic fireball records

The explicit solution of the drag and ablation equations of a single nonfragmenting meteoroid moving in any actual atmosphere was published several years ago. The solution yields the theoretical relation of l, the distance flown by the meteoroid in its trajectory, as a function of time, t, assuming that the height, h, is a known function of l. The photographic records of meteors and fireballs are coded by time marks, using a rotating shutter or a similar device to break the moving image. Time is, thus, the independent variable and for each time mark on a meteoroid trajector, the observed distance along the trajectory, l sub obs, as well as the double- or multiple- station photographs of the same meteoroid. Applying this solution to all available Prairie Network (PN) fireball-records, we recognized that the majority of them gave good solutions with standard deviations somewhat bigger than the intrinsic geometrical precision of the data. We also noticed that, on an average, previous methods of evaluation of the meteoroid velocities (interpolation polynomials, numerical differenciation of the observed l sub obs) used up to only several tens of percent of the intrinsic precision of the PN observational data. When residuals of these solutions, i.e. l sub obs - l sub com, were represented as a function of time for about 75 percent of solutions. The remaining 25 percent of residuals showed systematic changes with time exceeding one standard deviation. We tried to explain these systematic time course of residuals by using different meteoroids first computed theoretically and then analyzed by the same model as the natural PN fireballs were. The conclusion of these model computations is that systematic time changes of residuals in the nonfragmenting model exceeding one standard of deviation are caused by sudden gross fragmentation at one or more trajectory points. Thus, we generalized the explicit solution of the drag and ablation equations of a single nonfragmenting meteoroid by allowing for one or more points, where sudden gross fragmentation can occur. Using this generalized solution, the distances along the meteoroid trajectory can be computed for any choice of input parameters and compared with the observed distances flown by the meteoroid. For the most precise and long fireball trajectories, the least-squares solution can, thus, yield the initial velocities, the ablation coefficients, the dynamical masses, the positions of gross-fragmentation points, and the terminal mass. At a gross-fragmentation point, the ratio of the main mass to all the remaining fragments can be compared with the dynamic mass determined from our gross-fragmentation model and, thus, the meteoroid bulk density can be evaluated. We applied the gross-fragmentation model to sever PN fireballs showing time changes of residuals, and we recognized that, in all these cases, the new computed bulk densities of meteoroids resulted higher in comparison with the meteoroid densities determined with the non-gross-fragmentation model. Other aspects of the study are discussed.

Ceplecha, Zdenek↗
DOE OSTI2021

nn-PINNs: Non-Newtonian physics-informed neural networks for complex fluid modeling

Time- and rate-dependent material functions in non-Newtonian fluids in response to different deformation fields pose a challenge in integrating different constitutive models into conventional computational fluid dynamic platforms. Considering their relevance in many industrial and natural settings alike, robust data-driven frameworks that enable accurate modeling of these complex fluids are of great interest. The main goal is to solve the coupled Partial Differential Equations (PDEs) consisting of the constitutive equations that relate the shear stress to the deformation and fully capture the behavior of the fluid under various flow protocols with different boundary conditions. Here, in this work, we present non-Newtonian physics-informed neural networks (nn-PINNs) for solving systems of coupled PDEs adopted for complex fluid flow modeling. The proposed nn-PINN method is employed to solve the constitutive models in conjunction with conservation of mass and momentum by benefiting from Automatic Differentiation (AD) in neural networks, hence avoiding the mesh generation step. nn-PINNs are tested for a number of different complex fluids with different constitutive models and for several flow protocols. These include a range of Generalized Newtonian Fluid (GNF) empirical constitutive models, as well as some phenomenological models with memory effects and thixotropic timescales. nn-PINNs are found to obtain the correct solution of complex fluids in spatiotemporal domains with good accuracy compared to the ground truth solution. We also present applications of nn-PINNs for complex fluid modeling problems with unknown boundary conditions on the surface, and show that our approach can successfully recover the velocity and stress fields across the domain, including the boundaries, given some sparse velocity measurements.

42 ENGINEERING↗
DOE OSTI2024

Superluminal matter waves

The Dirac equation has resided among the greatest successes of modern physics since its emergence as the first quantum mechanical theory fully compatible with special relativity. This compatibility ensures that the expectation value of the velocity is less than the vacuum speed of light. Here, we show that the Dirac equation admits free-particle solutions where the peak amplitude of the wave function can travel at any velocity, including those exceeding the vacuum speed of light, despite having a subluminal velocity expectation value. The solutions are constructed by superposing basis functions with correlations in momentum space. These arbitrary velocity wave functions feature a near-constant profile and may impact quantum mechanical processes that are sensitive to the local value of the probability density as opposed to expectation values.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS2001

Computational Relativistic Astrophysics Using the Flowfield-Dependent Variation Theory

Theoretical models, observations and measurements have preoccupied astrophysicists for many centuries. Only in recent years, has the theory of relativity as applied to astrophysical flows met the challenges of how the governing equations can be solved numerically with accuracy and efficiency. Even without the effects of relativity, the physics of magnetohydrodynamic flow instability, turbulence, radiation, and enhanced transport in accretion disks has not been completely resolved. Relativistic effects become pronounced in such cases as jet formation from black hole magnetized accretion disks and also in the study of Gamma-Ray bursts (GRB). Thus, our concern in this paper is to reexamine existing numerical simulation tools as to the accuracy and efficiency of computations and introduce a new approach known as the flowfield-dependent variation (FDV) method. The main feature of the FDV method consists of accommodating discontinuities of shock waves and high gradients of flow variables such as occur in turbulence and unstable motions. In this paper, the physics involved in the solution of relativistic hydrodynamics and solution strategies of the FDV theory are elaborated. The general relativistic astrophysical flow and shock solver (GRAFSS) is introduced, and some simple example problems for Computational Relativistic Astrophysics (CRA) are demonstrated.

Richardson, G. A.↗
DOE OSTI2023

Separability of the Dirac equation in the STU black hole spacetime: Pairwise-equal charge case study

We study the separability of the Dirac equation in the background of four dimensional charged rotating asymptotically flat black hole solution of supergravity and the low energy string theory known as STU black hole. In particular, we analyze in detail the separability conditions in the pairwise equal charge STU black hole space-time. While in the latter case the minimally coupled Dirac equation is not separable, the introduction of a specific torsion term ensures the separability. The source of the torsion is the Kalb-Ramond field, which is an integral part of string theory, but further aspects of its properties and coupling to fermionic fields remain to be studied. To derive the torsion, two different approaches are used in conformally related frames, showing that the torsion is not unique. The correspondingly modified Dirac equations in the Einstein and string frames are shown to be separable. Furthermore, the massless radial and angular wave equations are examined; they show close similarity with corresponding equations for the standard Kerr background. A generalization of the Teukolsky equation for the pairwise equal case is conjectured. We also briefly analyze a technically sophisticated radial equation in the massive case.

Dirac equation↗
NASA NTRS1991

Progress in the development of PDF turbulence models for combustion

A combined Monte Carlo-computational fluid dynamic (CFD) algorithm was developed recently at Lewis Research Center (LeRC) for turbulent reacting flows. In this algorithm, conventional CFD schemes are employed to obtain the velocity field and other velocity related turbulent quantities, and a Monte Carlo scheme is used to solve the evolution equation for the probability density function (pdf) of species mass fraction and temperature. In combustion computations, the predictions of chemical reaction rates (the source terms in the species conservation equation) are poor if conventional turbulence modles are used. The main difficulty lies in the fact that the reaction rate is highly nonlinear, and the use of averaged temperature produces excessively large errors. Moment closure models for the source terms have attained only limited success. The probability density function (pdf) method seems to be the only alternative at the present time that uses local instantaneous values of the temperature, density, etc., in predicting chemical reaction rates, and thus may be the only viable approach for more accurate turbulent combustion calculations. Assumed pdf's are useful in simple problems; however, for more general combustion problems, the solution of an evolution equation for the pdf is necessary.

Hsu, Andrew T.↗
NASA NTRS2002

Elliptic Grid Generation of Spiral-Bevel Pinion Gear Typical of OH-58 Helicopter Transmission

This paper discusses the source term treatment in the numerical solution of elliptic partial differential equations for an interior grid generation problem in generalized curvilinear coordinates. The geometry considered is that of a planar cross-section of a generic spiral-bevel gear tooth typical of a pinion in the OH-58 helicopter transmission. The source terms used are appropriate for an interior grid domain where all the boundaries are prescribed via a combination of Dirichlet and Neumann boundary conditions. New constraints based on the Green's Theorem are derived which uniquely determine the coefficients in the source terms. These constraints are designed for boundary clustered grids where gradients in physical quantities need to be resolved adequately. However, it is seen that the present formulation works satisfactorily for mild clustering also. Thus, a fully automated elliptic grid generation technique is made possible where there is no need for a parametric study of these parameters since the new relations fix these free parameters uniquely.

Kaul, Upender K.↗
NASA NTRS1985

Dynamic Creep Buckling: Analysis of Shell Structures Subjected to Time-dependent Mechanical and Thermal Loading

The objective of the present research is to develop a general mathematical model and solution methodologies for analyzing the structural response of thin, metallic shell structures under large transient, cyclic, or static thermomechanical loads. Among the system responses associated with these loads and conditions are thermal buckling, creep buckling, and ratcheting. Thus geometric and material nonlinearities (of high order) can be anticipated and must be considered in developing the mathematical model. A complete, true ab-initio rate theory of kinematics and kinetics for continuum and curved thin structures, without any restriction on the magnitude of the strains or the deformations, was formulated. The time dependence and large strain behavior are incorporated through the introduction of the time rates of metric and curvature in two coordinate systems: fixed (spatial) and convected (material). The relations between the time derivative and the covariant derivative (gradient) were developed for curved space and motion, so the velocity components supply the connection between the equations of motion and the time rates of change of the metric and curvature tensors.

Simitses, G. J.↗
NASA NTRS1995

Computing supernova collapse to neutron stars and black holes

We present a new numerical code for spherical hydrodynamics in general relativity. The code can handle gravitational collapse to a neutron star or to a black hole without the appearance of singularities. Moreover, the variables and equations in the code are very similar to those appearing in traditional Lagrangian supernova codes. Any such existing code can thus be easily adapted to treat collapse where the final fate is uncertain and may be either a neutron star or a black hole. The code is based on the formulation of Hernandez & Misner, in which retarded time is used as coordinate. This prevents the computational grid from penetrating inside any black hole that may form. We present the equations and a complete finite difference scheme for the adiabatic evolution of a fluid that obeys a gamma-law equation of state. We summarize the results of several testbed calculations performed to check our code. We also give the transformation of the analytic Oppenheimer-Snyder solution for homogeneous dust collapse to our coordinate system.

Baumgarte, Thomas W.↗
DOE OSTI2024

Perturbations of Gibbons-Maeda black holes in Einstein-Maxwell-dilaton theories

The study of perturbations around black hole backgrounds in general relativity and Einstein-Maxwell theory has a long history, going back to the work of Regge and Wheeler in the 1950s. As part of a broader investigation of perturbations around black holes in supergravity, we describe here our results for the perturbations around the Gibbons-Maeda static charged black holes in a class of Einstein-Maxwell-Dilaton theories. Our analysis follows the general strategy developed by Chandrasekhar and Xanthopoulos for the perturbations of the Reissner-Nordström black hole. Here, the analysis is considerably more involved, because of the presence of the dilaton field, which couples to the other polar modes. We nonetheless find that the problem is completely solvable, in the sense that one can separate variables and eventually describe all the perturbations in terms of diagonalised second-order radial equations. We are able to prove the mode stability of all the Gibbons-Maeda black hole solutions. Published by the American Physical Society 2024

Pope, C. N. (ORCID:0000000284012564)↗
DOE OSTI2022

Twistor space origins of the Newman-Penrose map

Recently, we introduced the “Newman-Penrose map”, a novel correspondence between a certain class of solutions of Einstein’s equations and self-dual solutions of the vacuum Maxwell equations, which we showed was closely related to the classical double copy. Here, we give an alternative definition of this correspondence in terms of quantities that are defined naturally on twistor space, and a shear-free null geodesic congruence on Minkowski space whose twistorial character is articulated by the Kerr theorem. The advantage of this reformulation is that it is purely geometrical in nature, being manifestly invariant under both spacetime diffeomorphisms and projective transformations on twistor space. While the original formulation of the map may be more convenient for most explicit calculations, the twistorial formulation we present here may be of greater theoretical utility.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1993

Analyzing Martian winds and tracer concentrations using Mars Observer data

During the courses of a day, the Mars Observer spacecraft will acquire globally distributed profiles of the martian atmosphere. It is highly desirable that this data be assembled into synoptic weather maps (complete specifications of the atmospheric pressure, temperature, and winds at a given time), which can in turn be used as starting points in the study of many meteorological phenomena. Unfortunately, the special nature of the Mars Observer data presents several challenges above and beyond the usual difficult problem of data initialization. Mars Observer atmospheric data will consist almost exclusively of asynoptic vertical profiles of temperatures (or radiances) and pressures, whereas winds are generally in balance with horizontal gradients of these quantities (which will not be observed). It will therefore be necessary to resort to dynamical models to analyze the wind fields. As a rule, data assimilation into atmospheric models can result in the generation of spurious gravity waves, so special steps must be taken to suppress these. In addition, the asynoptic nature of the data will require a four-dimensional (space and time) data assimilation scheme. The problem is to find a full set of meteorological fields (winds and temperatures) such that, when marched forward in time in the model, they achieve a best fit (in the weighted least-squares sense) to the data. The proposed solution is to develop a model especially for the Mars Observer data assimilation problem. Gravity waves are filtered from the model by eliminating all divergence terms from the prognostic divergence equation. This leaves a diagnostic gradient wind relation between the rotational wind and the temperature field. The divergent wind is diagnosed as the wind required to maintain the gradient wind balance in the presence of the diabatic heating. The primitive equations of atmospheric dynamics (with three principal dependent variables) are thus reduced to a simpler system with a single prognostic equation for temperature - the variable that will be best observed. (This balance system was apparently first derived by Charney as a first-order Rossby number expansion of the equations of motion). Experience with a full primitive equation model of the martian atmosphere indicates that a further simplification is possible: at least for short-term integrations, the model can be linearized about the zonally symmetric basic state.

Houben, Howard C.↗
NASA NTRS1989

A highly parallel multigrid-like method for the solution of the Euler equations

We consider a highly parallel multigrid-like method for the solution of the two dimensional steady Euler equations. The new method, introduced as filtering multigrid, is similar to a standard multigrid scheme in that convergence on the finest grid is accelerated by iterations on coarser grids. In the filtering method, however, additional fine grid subproblems are processed concurrently with coarse grid computations to further accelerate convergence. These additional problems are obtained by splitting the residual into a smooth and an oscillatory component. The smooth component is then used to form a coarse grid problem (similar to standard multigrid) while the oscillatory component is used for a fine grid subproblem. The primary advantage in the filtering approach is that fewer iterations are required and that most of the additional work per iteration can be performed in parallel with the standard coarse grid computations. We generalize the filtering algorithm to a version suitable for nonlinear problems. We emphasize that this generalization is conceptually straight-forward and relatively easy to implement. In particular, no explicit linearization (e.g., formation of Jacobians) needs to be performed (similar to the FAS multigrid approach). We illustrate the nonlinear version by applying it to the Euler equations, and presenting numerical results. Finally, a performance evaluation is made based on execution time models and convergence information obtained from numerical experiments.

Tuminaro, Ray S.↗
NASA NTRS1994

A combined algorithm for minimum time slewing of flexible spacecraft

The use of Pontryagin's Maximum Principle for the large-angle slewing of large flexible structures usually results in the so-called two-point boundary-value problem (TPBVP), in which many requirements (e.g., minimum time, small flexible amplitude, and limited control powers, etc.) must be satisfied simultaneously. The successful solution of this problem depends largely on the use of an efficient numerical computational algorithm. There are many candidate algorithms available for his problem (e.g., quasilinearization, gradient, and shooting, etc.). In this paper, a proposed algorithm, which combines the quasilinearization method with a time shortening technique and a shooting method, is applied to the minimum-time, three-dimensional, and large-angle maneuver of flexible spacecraft, particularly the orbiting Spacecraft Control Laboratory Experiment (SCOLE) configuration. Theoretically, the nonlinear TPBVP can be solved only through the shooting method to find the 'exact' switching times for the bang-bang controls. However, computationally, a suitable guess for the missing initial costates is crucial because the convergence range of the unknown initial costates is usually narrow, especially for systems with high dimensions and when a multi-bang-bang control strategy is needed. On the other hand, the problems of near minimum time attitude maneuver of general rigid spacecraft and fast slewing of flexible spacecraft have been examined by the authors through a numerical approach based on the quasilinearization algorithm with a time shortening technique. Computational results have demonstrated its broad convergence range and insensitivity to initial costate choices. Consequently, a combined approach is naturally suggested here to solve the minimum time slewing problem. That is, in the computational process, the quasilinearization method is used first to obtain a near minimum time solution. Then, the acquired converged initial costates from the quasilinearization approach are transformed (tailored) to and used as the initial costate guess for starting the shooting method. Finally, the shooting method takes over the remaining calculations until the minimum-time solution converges. The nonlinear equations of motion of the SCOLE are formulated by using Lagrange's equations, with the mast modeled as a continuous beam subject to three-dimensional deformations. The numerical results will be presented and some related computational issues will also be discussed.

Bainum, P. M.↗
DOE OSTI2023

Review—Drag Coefficients of Non-Spherical and Irregularly Shaped Particles

Abstract The knowledge of simple and relatively accurate closure equations for the drag coefficients of nonspherical particles is very important for Eulerian multiphase numerical codes that require such inputs for the solution of the momentum equation. However, the existing correlations for the drag coefficients are laden with high uncertainty, which propagates in the numerical results. This review paper examines critically the state of our knowledge of the drag coefficients of nonspherical particles starting with our understanding of the “size” and “shape” of particles. Lengthscales and other parameters that have been used to characterize sizes of nonspherical particles are presented. Shape factors and shape descriptors that have been used in past correlations are also presented together with an appraisal of their applicability. Several correlations that have been developed for the determination of the drag coefficients of nonspherical particles with regular and irregular shapes are also presented together with available information on their accuracy and applicability. Based on the review of the available correlations general recommendations are offered on the use of the correlations as closure equations and inputs in computatioal fluid dynamics (CFD) codes.

Engineering↗