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At least 271 records · Page 15
All sourcesNASA NTRSDOE OSTI
NASA NTRS1995

The space-time solution element method: A new numerical approach for the Navier-Stokes equations

This paper is one of a series of papers describing the development of a new numerical method for the Navier-Stokes equations. Unlike conventional numerical methods, the current method concentrates on the discrete simulation of both the integral and differential forms of the Navier-Stokes equations. Conservation of mass, momentum, and energy in space-time is explicitly provided for through a rigorous enforcement of both the integral and differential forms of the governing conservation laws. Using local polynomial expansions to represent the discrete primitive variables on each cell, fluxes at cell interfaces are evaluated and balanced using exact functional expressions. No interpolation or flux limiters are required. Because of the generality of the current method, it applies equally to the steady and unsteady Navier-Stokes equations. In this paper, we generalize and extend the authors' 2-D, steady state implicit scheme. A general closure methodology is presented so that all terms up through a given order in the local expansions may be retained. The scheme is also extended to nonorthogonal Cartesian grids. Numerous flow fields are computed and results are compared with known solutions. The high accuracy of the scheme is demonstrated through its ability to accurately resolve developing boundary layers on coarse grids. Finally, we discuss applications of the current method to the unsteady Navier-Stokes equations.

Scott, James R.↗
DOE OSTI2022

The kinetic origin of the fluid helicity—A symmetry in the kinetic phase space

Helicity, a topological degree that measures the winding and linking of vortex lines, is preserved by ideal (barotropic) fluid dynamics. In the context of the Hamiltonian description, the helicity is a Casimir invariant characterizing a foliation of the associated Poisson manifold. Casimir invariants are special invariants that depend on the Poisson bracket, not on the particular choice of the Hamiltonian. The total mass (or particle number) is another Casimir invariant, whose invariance guarantees the mass (particle) conservation (independent of any specific choice of the Hamiltonian). In a kinetic description (e.g., that of the Vlasov equation), the helicity is no longer an invariant (although the total mass remains a Casimir of the Vlasov’s Poisson algebra). The implication is that some “kinetic effect” can violate the constancy of the helicity. To elucidate how the helicity constraint emerges or submerges, we examine the fluid reduction of the Vlasov system; the fluid (macroscopic) system is a “sub-algebra” of the kinetic (microscopic) Vlasov system. In the Vlasov system, the helicity can be conserved if a special helicity symmetry condition holds. To put it another way, breaking helicity symmetry induces a change in the helicity. We delineate the geometrical meaning of helicity symmetry and show that for a special class of flows (the so-called epi-two-dimensional flows), the helicity symmetry is written as ∂γ = 0 for a coordinate γ of the configuration space.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1992

Evidence for a black hole in the X-ray binary Nova Muscae 1991

Optical photometry and spectroscopy of the X-ray Nova Muscae 1991 in quiescence reveal an orbital period of 10.398 +/- 0.014 hr and an absorption-line velocity curve consistent with a sinusoidal modulation at a half-amplitude of 409 +/- 18 km/s. The spectral type of the secondary star is in the range K0 V to K4 V. The value of the mass function, 3.1 +/- 0.4 solar mass, is a conservative lower limit on the mass of the compact primary and suggests that the primary is a black hole. Further considerations of the binary inclination angle and the mass of the secondary strengthen the black hole model. The folded light curves in the I band and the B + V band resemble ellipsoidal variations, with an additional brightening near one of the maxima in the B + V band. The orbital period is 1.4 percent shorter than the photometric period observed during outburst, as expected if the outburst modulations are analogs of 'superhumps' in dwarf novae. In quiescence, the optical properties of the X-ray binary Nova Muscae 1991 bear a striking resemblance to the black hole binary A0620-00, which extends the basis of similarity that was demonstrated during outburst at X-ray and optical wavelengths.

Remillard, Ronald A.↗
NASA NTRS1993

Modeling of Non-Spherical Droplet Dynamics

A two-dimensional time-dependent computer code based on the modified Arbitrary Lagrangian Eulerian (ALE) technique, has been developed to simulate non-spherical droplet dynamics and evaporation under convective flows at real rocket combustion chamber conditions. The equations of mass, momentum, energy and species are simultaneously solved for both liquid and gas phases with an accurate dynamic interface tracking. The jump boundary conditions across the deforming droplet surface are obtained by applying the integral forms of conservation of mass, momentum, and energy. At each time step, the interface geometry and flow properties at the droplet surface are implicitly solved by satisfying the interface boundary conditions. A Lagrangian technique was developed to track the arbitrarily moving interface between the liquid droplet and the external gas. An elliptic grid generator is adopted to dynamically reconstruct grids both inside and outside the droplet surface. This code has been used to study droplet oscillation, droplet deformation/breakup, nonspherical droplet evaporation in both low and high pressure convective flows. This presentation briefly describes the numerical algorithm for modeling of the nonspherical droplet dynamics and demonstrates the representative simulation results of nonspherical droplet evaporation at low and high pressure convective flows. Potential applications of this code to rocket combustor design and performance predictions are discussed.

Deng, Zheng-Tao↗
NASA NTRS1989

Interaction of surface radiation with convection in crystal growth by physical vapor transport

Growth of single crystals from vapor in closed ampoules is governed by an intricate interplay between mass, momentum and heat transfer processes. The objective of this study is to examine and isolate the effects of surface radiation heat transfer on the vapor transport process using a mathematical model. The model consists of a set of coupled nonlinear partial differential equations for conservation of mass, momentum, energy and species, and the integrodifferential equations which represent radiative exchange. It depends on five important physical parameters. These are Grashof number, Prandtl number, Schmidt number, aspect ratio and the radiation-conduction number. The effects of these dimensionless groupings are systematically investigated. From the cases examined, it is concluded that surface radiation can change the flow structure appreciably. This is especially true in microgravity environment where radiation competes primarily with conduction in modifying the thermal profiles. The numerical results also show that in the presence of radiation, the top heating configuration (source on top) is no longer stable and that near the growing crystal, radiation-induced vortices can introduce significant nonuniformities in the growth flux.

Kassemi, Mohammad↗
NASA NTRS1998

Nuclear modules for space electric propulsion

Analysis of interplanetary cargo and piloted missions requires calculations of the performances and masses of subsystems to be integrated in a final design. In a preliminary and scoping stage the designer needs to evaluate options iteratively by using fast computer simulations. The Oak Ridge National Laboratory (ORNL) has been involved in the development of models and calculational procedures for the analysis (neutronic and thermal hydraulic) of power sources for nuclear electric propulsion. The nuclear modules will be integrated into the whole simulation of the nuclear electric propulsion system. The vehicles use either a Brayton direct-conversion cycle, using the heated helium from a NERVA-type reactor, or a potassium Rankine cycle, with the working fluid heated on the secondary side of a heat exchanger and lithium on the primary side coming from a fast reactor. Given a set of input conditions, the codes calculate composition. dimensions, volumes, and masses of the core, reflector, control system, pressure vessel, neutron and gamma shields, as well as the thermal hydraulic conditions of the coolant, clad and fuel. Input conditions are power, core life, pressure and temperature of the coolant at the inlet of the core, either the temperature of the coolant at the outlet of the core or the coolant mass flow and the fluences and integrated doses at the cargo area. Using state-of-the-art neutron cross sections and transport codes, a database was created for the neutronic performance of both reactor designs. The free parameters of the models are the moderator/fuel mass ratio for the NERVA reactor and the enrichment and the pitch of the lattice for the fast reactor. Reactivity and energy balance equations are simultaneously solved to find the reactor design. Thermalhydraulic conditions are calculated by solving the one-dimensional versions of the equations of conservation of mass, energy, and momentum with compressible flow.

Difilippo, F. C.↗
NASA NTRS1992

On recontamination and directional-bias problems in Monte Carlo simulation of PDF turbulence models

Turbulent combustion can not be simulated adequately by conventional moment closure turbulent models. The probability density function (PDF) method offers an attractive alternative: in a PDF model, the chemical source terms are closed and do not require additional models. Because the number of computational operations grows only linearly in the Monte Carlo scheme, it is chosen over finite differencing schemes. A grid dependent Monte Carlo scheme following J.Y. Chen and W. Kollmann has been studied in the present work. It was found that in order to conserve the mass fractions absolutely, one needs to add further restrictions to the scheme, namely alpha(sub j) + gamma(sub j) = alpha(sub j - 1) + gamma(sub j + 1). A new algorithm was devised that satisfied this restriction in the case of pure diffusion or uniform flow problems. Using examples, it is shown that absolute conservation can be achieved. Although for non-uniform flows absolute conservation seems impossible, the present scheme has reduced the error considerably.

Hsu, Andrew T.↗
NASA NTRS1971

Transpiration and film cooling boundary layer computer program. Volume 2: Computer program and user's manual

A finite difference turbulent boundary layer computer program which allows for mass transfer wall cooling and equilibrium chemistry effects is presented. The program is capable of calculating laminar or turbulent boundary layer solutions for an arbitrary ideal gas or an equilibrium hydrogen oxygen system. Either two dimensional or axisymmetric geometric configurations may be considered. The equations are solved, in nondimension-alized physical coordinates, using the implicit Crank-Nicolson technique. The finite difference forms of the conservation of mass, momentum, total enthalpy and elements equations are linearized and uncoupled, thereby generating easily solvable tridiagonal sets of algebraic equations. A detailed description of the computer program, as well as a program user's manual is provided. Detailed descriptions of all boundary layer subroutines are included, as well as a section defining all program symbols of principal importance. Instructions are then given for preparing card input to the program and for interpreting the printed output. Finally, two sample cases are included to illustrate the use of the program.

Gloss, R. J.↗
NASA NTRS1999

Semiempirical Two-Dimensional Magnetohydrodynamic Model of the Solar Corona and Interplanetary Medium

We have developed a two-dimensional semiempirical MHD model of the solar corona and solar wind. The model uses empirically derived electron density profiles from white-light coronagraph data measured during the Skylub period and an empirically derived model of the magnetic field which is fitted to observed streamer topologies, which also come from the white-light coronagraph data The electron density model comes from that developed by Guhathakurta and coworkers. The electron density model is extended into interplanetary space by using electron densities derived from the Ulysses plasma instrument. The model also requires an estimate of the solar wind velocity as a function of heliographic latitude and radial component of the magnetic field at 1 AU, both of which can be provided by the Ulysses spacecraft. The model makes estimates as a function of radial distance and latitude of various fluid parameters of the plasma such as flow velocity V, effective temperature T(sub eff), and effective heat flux q(sub eff), which are derived from the equations of conservation of mass, momentum, and energy, respectively. The term effective indicates that wave contributions could be present. The model naturally provides the spiral pattern of the magnetic field far from the Sun and an estimate of the large-scale surface magnetic field at the Sun, which we estimate to be approx. 12 - 15 G. The magnetic field model shows that the large-scale surface magnetic field is dominated by an octupole term. The model is a steady state calculation which makes the assumption of azimuthal symmetry and solves the various conservation equations in the rotating frame of the Sun. The conservation equations are integrated along the magnetic field direction in the rotating frame of the Sun, thus providing a nearly self-consistent calculation of the fluid parameters. The model makes a minimum number of assumptions about the physics of the solar corona and solar wind and should provide a very accurate empirical description of the solar corona and solar wind Once estimates of mass density rho, flow velocity V, effective temperature T(sub eff), effective heat flux q(sub eff), and magnetic field B are computed from the model and waves are assumed unimportant, all other plasma parameters such as Mach number, Alfven speed, gyrofrequency, etc. can be derived as a function of radial distance and latitude from the Sun. The model can be used as a planning tool for such missions as Slar Probe and provide an empirical framework for theoretical models of the solar corona and solar wind The model will be used to construct a semiempirical MHD description of the steady state solar corona and solar wind using the SOHO Large Angle Spectrometric Coronagraph (LASCO) polarized brightness white-light coronagraph data, SOHO Extreme Ultraviolet Imaging Telescope data, and Ulysses plasma data.

Sittler, Edward C., Jr.↗
DOE OSTI2024

A Particle Method for the Multispecies Landau Equation

Abstract The multispecies Landau collision operator describes the two-particle, small scattering angle or grazing collisions in a plasma made up of different species of particles such as electrons and ions. Recently, a structure preserving deterministic particle method (Carrillo et al. in J. Comput. Phys. 7:100066, 2020) has been developed for the single species spatially homogeneous Landau equation. This method relies on a regularization of the Landau collision operator so that an approximate solution, which is a linear combination of Dirac delta distributions, is well-defined. Based on a weak form of the regularized Landau equation, the time dependent locations of the Dirac delta functions satisfy a system of ordinary differential equations. In this work, we extend this particle method to the multispecies case, and examine its conservation of mass, momentum, and energy, and decay of entropy properties. We show that the equilibrium distribution of the regularized multispecies Landau equation is a Maxwellian distribution, and state a critical condition on the regularization parameters that guarantees a species independent equilibrium temperature. A convergence study comparing an exact multispecies Bobylev-Krook-Wu (BKW) solution to the particle solution shows approximately 2nd order accuracy. Important physical properties such as conservation, decay of entropy, and equilibrium distribution of the particle method are demonstrated with several numerical examples.

Mathematics↗
NASA NTRS1990

Upward ion flow in ionospheric holes on Venus

The nature of ion flow within two ionospheric holes on the nightside of Venus was investigated using ion composition measurements made by the ion mass spectrometer on the Pioneer Venus Orbiter. A comparison of the altitude profiles of the observed ion densities with those expected under diffusive equilibrium conditions indicates that the major ions O(+), NO(+), and O2(+), as well as the minor ions H(+) and He(+) flow upward and away from Venus along the axes of the holes. This result agrees with a quantitative evaluation of the ion flow speeds appearing in expressions derived from the equations for conservation of mass and momentum of the ions and electrons. The analysis shows that all ion species flow upward in the holes because the upward force produced by the plasma pressure gradient exceeds all downward forces. However, the nature of the ion source required to maintain such flow is not known.

Hartle, R. E.↗
DOE OSTI2022

A numerical approach for detecting switch-like bistability in mass action chemical reaction networks with conservation laws

Theoretical analysis of signaling pathways can provide a substantial amount of insight into their function. One particular area of research considers signaling pathways capable of assuming two or more stable states given the same amount of signaling ligand. This phenomenon of bistability can give rise to switch-like behavior, a mechanism that governs cellular decision making. Investigation of whether or not a signaling pathway can confer bistability and switch-like behavior, without knowledge of specific kinetic rate constant values, is a mathematically challenging problem. Recently a technique based on optimization has been introduced, which is capable of finding example parameter values that confer switch-like behavior for a given pathway. Although this approach has made it possible to analyze moderately sized pathways, it is limited to reaction networks that presume a uniterminal structure. It is this limited structure we address by developing a general technique that applies to any mass action reaction network with conservation laws. In this paper we developed a generalized method for detecting switch-like bistable behavior in any mass action reaction network with conservation laws. The method involves (1) construction of a constrained optimization problem using the determinant of the Jacobian of the underlying rate equations, (2) minimization of the objective function to search for conditions resulting in a zero eigenvalue, (3) computation of a confidence level that describes if the global minimum has been found and (4) evaluation of optimization values, using either numerical continuation or directly simulating the ODE system, to verify that a bistability region exists. The generalized method has been tested on three motifs known to be capable of bistability. We have developed a variation of an optimization-based method for the discovery of bistability, which is not limited to uniterminal chemical reaction networks. Successful completion of the method provides an S-shaped bifurcation diagram, which indicates that the network acts as a bistable switch for the given optimization parameters.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

A consistent and conservative model and its scheme for N -phase- M -component incompressible flows

Here, we propose a consistent and conservative model for multiphase and multicomponent incompressible flows, where there can be arbitrary numbers of phases and components. Each phase has a background fluid called the pure phase, each pair of phases is immiscible, and components are dissolvable in some specific phases. The model is developed based on the multiphase Phase-Field model including the contact angle boundary condition, the diffuse domain approach, and the analyses on the proposed consistency conditions for multiphase and multicomponent flows. The model conserves the mass of individual pure phases, the amount of each component in its dissolvable region, and thus the mass of the fluid mixture, and the momentum of the flow. It ensures that no fictitious phases or components can be generated and that the summation of the volume fractions from the Phase-Field model is unity everywhere so that there is no local void or overfilling. It satisfies a physical energy law and it is Galilean invariant. A corresponding numerical scheme is developed for the proposed model, whose formal accuracy is 2nd-order in both time and space. It is shown to be consistent and conservative and its solution is demonstrated to preserve the Galilean invariance and energy law. Numerical tests indicate that the proposed model and scheme are effective and robust to study various challenging multiphase and multicomponent flows.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1985

The Southern Hemisphere circulation during the FGGE and its representativeness

An analysis of the global redistribution of mass during the FGGE year indicates that the global circulation was highly anomalous in several respects, especially from April to July 1979. For the 56 to year period 1924-1980, sea-level pressures over the northern hemisphere during the FGGE year were second highest in spring and highest in summer. In April and June, the anomalies were 1-in-100-year events. At the same time, sea-level pressure deficits and an exceptionally deep circumpolar trough were recorded over the Southern Hemisphere. Such compensation between the hemispheres, through the constraint of conservation of mass, provides support for the highly typical nature of the circulation analyzed to exist over the Southern Hemisphere throughout the FGGE year. The Southern Hemisphere circulation was characterized by an exceptionally deep circumpolar trough, an increase in westerlies from 40 deg to 70 deg S, and a decrease in westerlies to the north. In winter, the subtropical jet was weaker and the polar jet stronger than normal, so that a pronounced double jet structure prevailed. In summer, the jet was shifted south by 3 deg latitude. A southward shift in storm tracks accompanied these changes year round in a manner consistent with theory.

Trenberth, K. E.↗
DOE OSTI2021

Analytical solution for the cumulative wake of wind turbines in wind farms

This paper solves an approximate form of conservation of mass and momentum for a turbine in a wind farm array. The solution is a fairly simple explicit relationship that predicts the streamwise velocity distribution within a wind farm with an arbitrary layout. As this model is obtained by solving flow-governing equations directly for a turbine that is subject to upwind turbine wakes, no ad hoc superposition technique is needed to predict wind farm flows. A suite of large-eddy simulations (LES) of wind farm arrays is used to examine self-similarity as well as validity of the so-called conservation of momentum deficit for turbine wakes in wind farms. The simulations are performed with and without the presence of some specific turbines in the wind farm. This allows us to systematically study some of the assumptions made to develop the analytical model. A modified version of the conservation of momentum deficit is also proposed to provide slightly better results at short downwind distances, as well as in the far wake of turbines deep inside a wind farm. Model predictions are validated against the LES data for turbines in both full-wake and partial-wake conditions. While our results highlight the limitation in capturing the flow speed-up between adjacent turbine columns, the model is overall able to acceptably predict flow distributions for a moderately sized wind farm. Finally, the paper employs the new model to provide insights on the accuracy of common wake superposition methods.

17 WIND ENERGY↗
NASA NTRS1946

Some Effects of Compressibility on the Flow Through Fans and Turbines

The laws of conservation of mass, momentum, and energy are applied to the compressible flow through a two-dimensional cascade of airfoils. A fundamental relation between the ultimate upstream and downstream flow angles, the inlet Mach number, and the pressure ratio across the cascade is derived. Comparison with the corresponding relation for incompressible flow shows large differences. The fundamental relation reveals two ranges of flow angles and inlet Mach numbers, for which no ideal pressure ratio exists. One of these nonideal operating ranges is analogous to a similar type in incompressible flow. The other is characteristic only of compressible flow. The effect of variable axial-flow area is treated. Some implications of the basic conservation laws in the case of nonideal flow through cascades are discussed.

Perl, W.↗
NASA NTRSDate not supplied

Recent Advancements in the PATO Material Response Code

Introduction: Predicting the complicated multiphysics phenomena during atmospheric entry requires high-fidelity modeling tools to refine estimates of mission risks during entry. To this end, new capabilities are being added to the Porous-material Analysis Toolbox based on OpenFOAM (PATO). PATO is an open-source software for Computational Material Response (CMR) of reactive porous materials submitted to high-temperature environments. The objective of this work is to highlight current efforts to add to and improve upon the modeling capabilities of PATO. These include efforts to loosely couple PATO with other discipline specialized codes including hypersonic Computational Fluid Dynamics (CFD), to assess the interaction effects between pyrolysis gas blowing and the boundary layer, and Computational Solid Mechanics (CSM), to address modeling of mechanical erosion. Other refinements include surface phenomena modeling capabilities to address the effects of silicone-based coatings applied to the TPS during flight preparation, and a unified multiphase solver for a mixed porous-material and plain-fluid domain. Coupling CMR with CFD (CMR/CFD): A loose coupling between PATO and the Data Parallel Line Relaxation (DPLR) CFD code has been achieved by making use of a blowing boundary condition at the heatshield surface available in DPLR. Starting with heat flux estimates with no pyrolysis gas blowing at the surface, blowing gases are computed by the CMR and passed to the CFD such that aerothermal properties of the environment can be recomputed for a new CMR computation. This leads to an iterative process which is supplemented with an estimate of the radiative heat flux using the Nonequilibrium air radiation (NEQAIR) program. The entire iterative process is illustrated in Figure 1. This coupling strategy has been utilized in computing the MSL material response. The goal is to compare the coupled CMR/CFD results with material response results obtained using traditional blowing corrections. Coupling CMS with CMR: A mechanical erosion model is currently being implemented in PATO to account for the additional mass removal induced by high shear conditions. The modeling process at each timestep consists of updating the mechanical properties as a function of temperature and computing the stress tensor and displacement fields of the material. Then, a failure criteria model determines the regions in which the stress exceeds the ultimate strength values resulting in mesh movement to account for mass removal. This model allows the material response simulation to compute the recession due to both oxidation and shear-induced erosion. The model is demonstrated by computing material response of sphere-cone arc jet samples. Surface Modeling Capabilities: NuSil, a silicone-based coating, was sprayed onto the MSL and Mars 2020 heatshields to mitigate shedding of phenolic dust. To better understand the effects of the NuSil coating on the material response, a novel model has been implemented in PATO. In this model, the equilibrium of the charred NuSil surface is modeled as pure silica, and a constant offset, inspired by the classical spallation model, is added to the the char blowing rate and wall enthalpy to reproduce HyMETS experimental results. The model has also been used to estimate the 3D material response of the MSL heatshield. Unified Solver: In addition to the iterative loose coupling approach mentioned above, a multiphase unified solver is being developed to couple the environment (plain-fluid phase) and the porous-material phase. The solver is based on the volume averaged conservation of mass, momentum, and energy for the macroscale with closure models which include microscale effects through effective physicochemical properties. The unified solver has been used to compute flow through a porous plug and solve the Beavers and Joseph problem. Since the strong coupling between phases is inherent to this solver, modeling assumptions present in other coupling methods of material response are mitigated. This strategy also makes it feasible to capture the competition between surface and volume ablation in the same computational domain, which is usually not possible with other coupling approaches.

Material Response↗