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DOE OSTI2014

Steady fall of isothermal, resistive-viscous, compressible fluid across magnetic field

This is a basic MHD study of the steady fall of an infinite, vertical slab of isothermal, resistive-viscous, compressible fluid across a dipped magnetic field in uniform gravity. This double-diffusion steady flow in unbounded space poses a nonlinear but numerically tractable, one-dimensional (1D) free-boundary problem, assuming constant coefficients of resistivity and viscosity. The steady flow is determined by a dimensionless number μ{sub 1} proportional to the triple product of the two diffusion coefficients and the square of the linear total mass. For a sufficiently large μ{sub 1}, the Lorentz, viscous, fluid-pressure, and gravitational forces pack and collimate the fluid into a steady flow of a finite width defined by the two zero-pressure free-boundaries of the slab with vacuum. The viscous force is essential in this collimation effect. The study conjectures that in the regime μ{sub 1}→0, the 1D steady state exists only for μ{sub 1}∈Ω, a spectrum of an infinite number of discrete values, including μ{sub 1} = 0 that corresponds to two steady states, the classical zero-resistivity static slab of Kippenhahn and Schlüter [R. Kippenhahn and A. Schlüter, Z. Astrophys. 43, 36 (1957)] and its recent generalization [B. C. Low et al., Astrophys. J. 755, 34 (2012)] to admit an inviscid resistive flow. The pair of zero-pressure boundaries of each of the μ{sub 1}→0 steady-state slabs are located at infinity. Computational evidence suggests that the Ω steady-states are densely distributed around μ{sub 1} = 0, as an accumulation point, but are sparsely separated by open intervals of μ{sub 1}-values for which the slab must be either time-dependent or spatially multi-dimensional. The widths of these intervals are vanishingly small as μ{sub 1}→0. This topological structure of physical states is similar to that described by Landau and Liftshitz [L. D. Landau and E. M. Lifshitz, Fluid Mechanics (Addison-Wesley, Reading, MA, 1959)] to explain the onset of hydrodynamic turbulence. The implications of this MHD study are discussed, with an interest in the prominences in the solar atmosphere and the interstellar clouds in the Galaxy.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

NASA NTRS2000

Supercomputing Aspects for Simulating Incompressible Flow

The primary objective of this research is to support the design of liquid rocket systems for the Advanced Space Transportation System. Since the space launch systems in the near future are likely to rely on liquid rocket engines, increasing the efficiency and reliability of the engine components is an important task. One of the major problems in the liquid rocket engine is to understand fluid dynamics of fuel and oxidizer flows from the fuel tank to plume. Understanding the flow through the entire turbo-pump geometry through numerical simulation will be of significant value toward design. One of the milestones of this effort is to develop, apply and demonstrate the capability and accuracy of 3D CFD methods as efficient design analysis tools on high performance computer platforms. The development of the Message Passage Interface (MPI) and Multi Level Parallel (MLP) versions of the INS3D code is currently underway. The serial version of INS3D code is a multidimensional incompressible Navier-Stokes solver based on overset grid technology, INS3D-MPI is based on the explicit massage-passing interface across processors and is primarily suited for distributed memory systems. INS3D-MLP is based on multi-level parallel method and is suitable for distributed-shared memory systems. For the entire turbo-pump simulations, moving boundary capability and efficient time-accurate integration methods are built in the flow solver, To handle the geometric complexity and moving boundary problems, an overset grid scheme is incorporated with the solver so that new connectivity data will be obtained at each time step. The Chimera overlapped grid scheme allows subdomains move relative to each other, and provides a great flexibility when the boundary movement creates large displacements. Two numerical procedures, one based on artificial compressibility method and the other pressure projection method, are outlined for obtaining time-accurate solutions of the incompressible Navier-Stokes equations. The performance of the two methods is compared by obtaining unsteady solutions for the evolution of twin vortices behind a flat plate. Calculated results are compared with experimental and other numerical results. For an unsteady flow, which requires small physical time step, the pressure projection method was found to be computationally efficient since it does not require any subiteration procedure. It was observed that the artificial compressibility method requires a fast convergence scheme at each physical time step in order to satisfy the incompressibility condition. This was obtained by using a GMRES-ILU(0) solver in present computations. When a line-relaxation scheme was used, the time accuracy was degraded and time-accurate computations became very expensive.

Kwak, Dochan↗

NASA NTRS1994

Coupled Marangoni-Benard/Rayleigh-Benard Instability with Temperature Dependent Viscosity

The onset of convection induced by coupled surface tension gradient and buoyancy forces is investigated with temperature dependent viscosity. Both surface tension and viscosity are assumed to vary linearly with temperature. The limiting case, Ma=0, is the buoyancy driven convection problem typically referred to as the Rayleigh-Benard stability problem. The other limiting case, Ra=0, is the surface tension (gradient) driven flow problem referred to as the Marangoni-Benard problem. The equations and boundary conditions obtained from the linear analysis are solved numerically as a generalized eigenvalue problem. Neutral stability curves for different viscosity slopes have been generated for the Marangoni-Benard and Rayleigh-Benard problems. It is shown that the curves can be collapsed to a single curve by appropriately scaling the results for each of the limiting cases. The critical Marangoni number is determined as a function of the slope of the viscosity temperature variation, epsilon, for different values of the Rayleigh number. When the viscosity decreases linearly with temperature, the coupled buoyancy-surface tension problem, including the limiting cases of Ra=0 and Ma=0, is found to be more stable than the constant viscosity case.

Skarda, J. Raymond Lee↗

NASA NTRS2000

Towards Flange-to-Flange Turbopump Simulations for Liquid Rocket Engines

The primary objective of this research is to support the design of liquid rocket systems for the Advanced Space Transportation System. Since the space launch systems in the near future are likely to rely on liquid rocket engines, increasing the efficiency and reliability of the engine components is an important task. One of the major problems in the liquid rocket engine is to understand fluid dynamics of fuel and oxidizer flows from the fuel tank to plume. Understanding the flow through the entire turbopump geometry through numerical simulation will be of significant value toward design. This will help to improve safety of future space missions. One of the milestones of this effort is to develop, apply and demonstrate the capability and accuracy of 3D CFD methods as efficient design analysis tools on high performance computer platforms. The development of the MPI and MLP versions of the INS3D code is currently underway. The serial version of INS3D code is a multidimensional incompressible Navier-Stokes solver based on overset grid technology. INS3D-MPI is based on the explicit massage-passing interface across processors and is primarily suited for distributed memory systems. INS3D-MLP is based on multi-level parallel method and is suitable for distributed-shared memory systems. For the entire turbopump simulations, moving boundary capability and an efficient time-accurate integration methods are build in the flow solver. To handle the geometric complexity and moving boundary problems, overset grid scheme is incorporated with the solver that new connectivity data will be obtained at each time step. The Chimera overlapped grid scheme allows subdomains move relative to each other, and provides a great flexibility when the boundary movement creates large displacements. The performance of the two time integration schemes for time-accurate computations is investigated. For an unsteady flow which requires small physical time step, the pressure projection method was found to be computationally efficient since it does not require any subiterations procedure. It was observed that the artificial compressibility method requires a fast convergence scheme at each physical time step in order to satisfy incompressibility condition. This was obtained by using a GMRES-ILU(0) solver in our computations. When a line-relaxation scheme was used, the time accuracy was degraded and time-accurate computations became very expensive. The current geometry for the LOX boost turbopump has various rotating and stationary components, such as inducer, stators, kicker, hydrolic turbine, where the flow is extremely unsteady. Figure 1 shows the geometry and computed surface pressure of the inducer. The inducer and the hydrolic turbine rotate in different rotational speed.

Kiris, Cetin↗

NASA NTRS1979

Liquid oxygen/liquid hydrogen auxiliary power system thruster investigation

The design, fabrication, and demonstration of a 111 newton (25 lb) thrust, integrated auxiliary propulsion system (IAPS) thruster for use with LH2/LO2 propellants is described. Hydrogen was supplied at a temperature range of 22 to 33 K (40 to 60 R), and oxygen from 89 to 122 K (160 to 220 R). The thruster was designed to operate in both pulse mode and steady-state modes for vehicle attitude control, space maneuvering, and as an abort backup in the event of failure of the main propulsion system. A dual-sleeve, tri-axial injection system was designed that utilizes a primary injector/combustor where 100 percent of the oxygen and 8 percent of the hydrogen is introduced; a secondary injector/combustor where 45 percent of the hydrogen is introduced to mix with the primary combustor gases; and a boundary layer injector that uses the remaining 45 percent of the hydrogen to cool the thrust throat/nozzle design. Hot-fire evaluation of this thruster with a BLC injection distance of 2.79 cm (1.10 in.) indicated that a specific impulse value of 390 sec can be attained using a coated molybdenum thrust chamber. Pulse mode tests indicated that a chamber pressure buildup to 90 percent thrust can be achieved in a time on the order of 48 msec. Some problems were encountered in achieving ignition of each pulse during pulse trains. This was interpreted to indicate that a higher delivered spark energy level ( 100 mJ) would be required to maintain ignition reliability of the plasma torch ignition system under the extra 'cold' conditions resulting during pulsing.

Eberle, E. E.↗

NASA NTRS1985

A method for estimating soil moisture availability

A method for estimating values of soil moisture based on measurements of infrared surface temperature is discussed. A central element in the method is a boundary layer model. Although it has been shown that soil moistures determined by this method using satellite measurements do correspond in a coarse fashion to the antecedent precipitation, the accuracy and exact physical interpretation (with respect to ground water amounts) are not well known. This area of ignorance, which currently impedes the practical application of the method to problems in hydrology, meteorology and agriculture, is largely due to the absence of corresponding surface measurements. Preliminary field measurements made over France have led to the development of a promising vegetation formulation (Taconet et al., 1985), which has been incorporated in the model. It is necessary, however, to test the vegetation component, and the entire method, over a wide variety of surface conditions and crop canopies.

Carlson, T. N.↗

NASA NTRS1991

Transformation of two and three-dimensional regions by elliptic systems

A reliable linear system is presented for grid generation in 2-D and 3-D. The method is robust in the sense that convergence is guaranteed but is not as reliable as other nonlinear elliptic methods in generating nonfolding grids. The construction of nonfolding grids depends on having reasonable approximations of cell aspect ratios and an appropriate distribution of grid points on the boundary of the region. Some guidelines are included on approximating the aspect ratios, but little help is offered on setting up the boundary grid other than to say that in 2-D the boundary correspondence should be close to that generated by a conformal mapping. It is assumed that the functions which control the grid distribution depend only on the computational variables and not on the physical variables. Whether this is actually the case depends on how the grid is constructed. In a dynamic adaptive procedure where the grid is constructed in the process of solving a fluid flow problem, the grid is usually updated at fixed iteration counts using the current value of the control function. Since the control function is not being updated during the iteration of the grid equations, the grid construction is a linear procedure. However, in the case of a static adaptive procedure where a trial solution is computed and used to construct an adaptive grid, the control functions may be recomputed at every step of the grid iteration.

Mastin, C. Wayne↗

NASA NTRS1994

Multilayer Thin Film Polarizer Design for Far Ultraviolet using Induced Transmission and Absorption Technique

Good theoretical designs of far ultraviolet polarizers have been reported using a MgF2/Al/MgF2 three layer structure on a thick Al layer as a substrate. The thicknesses were determined to induce transmission and absorption of p-polarized light. In these designs Al optical constants were used from films produced in ultrahigh vacuum (UHV: 10(exp -10) torr). Reflectance values for polarizers fabricated in a conventional high vacuum (p approx. 10(exp -6 torr)) using the UHV design parameters differed dramatically from the design predictions. Al is a highly reactive material and is oxidized even in a high vacuum chamber. In order to solve the problem other metals have been studied. It is found that a larger reflectance difference is closely related to higher amplitude and larger phase difference of Fresnel reflection coefficients between two polarizations at the boundary of MgF2/metal. It is also found that for one material a larger angle of incidence from the surface normal brings larger amplitude and phase difference. Be and Mo are found good materials to replace Al. Polarizers designed for 121.6 nm with Be at 60 deg and with Mo at 70 deg are shown as examples.

Kim, Jongmin↗

NASA NTRS2015

Analysis of Advanced Thermoelectric Materials and Their Functional Limits

The world's demand for energy is increasing dramatically, but the best energy conversion systems operate at approximately 30% efficiency. One way to decrease energy loss is in the recovery of waste heat using thermoelectric (TE) generators. A TE generator is device that generates electricity by exploiting heat flow across a thermal gradient. The efficiency of a TE material for power generation and cooling is determined by the dimensionless Figure of Merit (ZT): ZT = S(exp. 2)sigmaT/κ: where S is the Seebeck coefficient, sigma is the electrical conductivity, T is the absolute temperature, and κ is the thermal conductivity. The parameters are not physically independent, but intrinsically coupled since they are a function of the transport properties of electrons. Traditional research on TE materials has focused on synthesizing bulk semiconductor-type materials that have low thermal conductivity and high electrical conductivity affording ZT values of 1. The optimization of the σ/κ ratio is difficult to achieve using current material formats, as these material constants are complementary. Recent areas of research are focusing on using nanostructural artifacts that introduce specific dislocations and boundary conditions that scatter the phonons. This disrupts the physical link between thermal (phonon) and electrical (electron) transport. The result is that κ is decreased without decreasing σ. These material formats give ZT values of up to 2 which represent approximately 18% energy gain from waste heat recovery. The next challenge in developing the next generation of TE materials with superior performance is to tailor the interconnected thermoelectric physical parameters of the material system. In order to approach this problem, the fundamental physics of each parameter S, sigma, and κ need to be physically understood in their context of electron/phonon interaction for the construction of new high ZT thermoelectric devices. Is it possible to overcome the physical limit imposed by of the effect of phonon lattice oscillation and energetic electrons towards thermal conductivity? Is the Seebeck coefficient, based on the difference in voltage over temperature gradient ( deltaV/deltaT), an intrinsic parameter of each material? All these parameters were manipulated using nano-bridge and twin-lattice structural concepts at the NASA Langley Research Center. This talk will review the current trend of TE research to optimize the ZT and discuss about new approaches on increasing ZT within functional limits of each parameter.

Kim, Hyun Jung↗

NASA NTRS2021

Evaluation of Stereology for Snow Microstructure Measurement and Microwave Emission Modeling: A Case Study

Reliable microstructure measurement of snow is a requirement for microwave radiative transfer model validation. Snow specific surface area (SSA) can be measured using stereological methods, in which snow samples are cast in the field and photographed in the laboratory. Processing stereology photographs manually by counting intersections of test cycloids with air–ice boundaries reduces the problems in binary segmentation. This paper is a case study to evaluate the repeatability of the manually stereology interpretation by two independent research groups. We further assessed how uncertainty in snow SSA influences simulated brightness temperature(TB) driven by the Microwave Emission Model of Layered Snowpacks (MEMLS), and how stereology compares to Near Infrared (NIR) camera and hand lens. Data was obtained from two alpine snow profiles from Steamboat Springs, Colorado. Results showed that stereological SSA values measured by two groups are highly consistent, and the ground radiometer measured TBat 19 and 37 GHz was successfully predicted (RMSE<3.8 K);simulations using NIR SSA and hand-lens geometric grain size (Dg)measurements have larger errors. This conclusion was not sensitive to uncertainty in the free parameters of TB modeling.

Microwave radiometry↗

DOE OSTI2024

An Efficient Numerical Algorithm for Solving Coupled Time-Dependent Ginzburg-Landau Equation for Superconductivity and Elasticity

A decoupled finite element algorithm is developed for simulating the vortex dynamics on an elastic superconductor which couples the time-dependent Ginzburg- Landau equation with the complex-valued superconducting order parameter and the vector-valued magnetic potential, and the elasticity equation. We present an iterative algorithm for the decoupled system arising from the time and spatial discretization using a combination of preconditioner, algebraic multigrid method (AMG) and preconditioned conjugate gradient method (PCG). The iterative algorithm allows us to perform large-scale three-dimensional simulations of mesoscale pattern formation during superconducting phase transitions with arbitrary elastic boundary conditions. Here, the performance and efficiency of the algorithm are numerically verified by several benchmark problems, exhibiting up to two orders of magnitude improvement depending on the scale of discrete system compared to the exact solver.

Efficiency↗

DOE OSTI2017

Influence of Sedimentation Length on the Convective Stability of a Colloidal Suspension

The convective stability of a colloidal suspension is studied in the case when the vertical dimension of the cavity is less than or comparable with the sedimentation length of nanoparticles. The analysis is carried out within the Boussinesq approximation on the basis of a modified model that takes into account the dependence of a thermodiffusion flow on the local value of impurity concentration. A new parameter of the problem is the ratio of the sedimentation length to the vertical dimension of the cavity. For a quiescent colloidal suspension, exact and approximate (in the case of small concentrations) solutions are obtained that describe the distributions of nanoparticles. A transformation is obtained that allows one to investigate the convective stability of a colloidal suspension stratified in the gravitational field by the Galerkin method with a set of simple trial functions. Instability boundaries and the characteristics of critical perturbations are determined. It is shown that, in the case of negative thermodiffusion, a decrease in the sedimentation length leads to a decrease in the convection threshold and the frequency of neutral oscillations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

NASA NTRS1974

Finite element solution theory for three-dimensional boundary flows

A finite element algorithm is derived for the numerical solution of a three-dimensional flow field described by a system of initial-valued, elliptic boundary value partial differential equations. The familiar three-dimensional boundary layer equations belong to this description when diffusional processes in only one coordinate direction are important. The finite element algorithm transforms the original description into large order systems of ordinary differential equations written for the dependent variables discretized at node points of an arbitrarily irregular computational lattice. The generalized elliptic boundary conditions is piecewise valid for each dependent variable on boundaries that need not explicitly coincide with coordinate surfaces. Solutions for sample problems in laminar and turbulent boundary flows illustrate favorable solution accuracy, convergence, and versatility.

Baker, A. J.↗

NASA NTRS1944

On the general theory of thin airfoils for nonuniform motion

General thin-airfoil theory for a compressible fluid is formulated as boundary problem for the velocity potential, without recourse to the theory of vortex motion. On the basis of this formulation the integral equation of lifting-surface theory for an incompressible fluid is derived with the chordwise component of the fluid velocity at the airfoil as the function to be determined. It is shown how by integration by parts this integral equation can be transformed into the Biot-Savart theorem. A clarification is gained regarding the use of principal value definitions for the integral which occur. The integral equation of lifting-surface theory is used a s the starting point for the establishment of a theory for the nonstationary airfoil which is a generalization of lifting-line theory for the stationary airfoil and which might be called "lifting-strip" theory. Explicit expressions are given for section lift and section moment in terms of the circulation function, which for any given wing deflection is to be determined from an integral equation which is of the type of the equation of lifting-line theory. The results obtained are for airfoils of uniform chord. They can be extended to tapered airfoils. One of the main uses of the results should be that they furnish a practical means for the analysis of the aerodynamic span effect in the problem of wing flutter. The range of applicability of "lifting-strip" theory is the same as that of lifting-line theory so that its results may be applied to airfoils with aspect ratios as low as three.

BIBLIOGRAPHY-WINGS↗

DOE OSTI2018

Quantum formalism for classical statistics

In static classical statistical systems the problem of information transport from a boundary to the bulk finds a simple description in terms of wave functions or density matrices. While the transfer matrix formalism is a type of Heisenberg picture for this problem, we develop here the associated Schrödinger picture that keeps track of the local probabilistic information. The transport of the probabilistic information between neighboring hypersurfaces obeys a linear evolution equation, and therefore the superposition principle for the possible solutions. Operators are associated to local observables, with rules for the computation of expectation values similar to quantum mechanics. We discuss how non-commutativity naturally arises in this setting. Also other features characteristic of quantum mechanics, such as complex structure, change of basis or symmetry transformations, can be found in classical statistics once formulated in terms of wave functions or density matrices. We construct for every quantum system an equivalent classical statistical system, such that time in quantum mechanics corresponds to the location of hypersurfaces in the classical probabilistic ensemble. For suitable choices of local observables in the classical statistical system one can, in principle, compute all expectation values and correlations of observables in the quantum system from the local probabilistic information of the associated classical statistical system. Realizing a static memory material as a quantum simulator for a given quantum system is not a matter of principle, but rather of practical simplicity.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

NASA NTRS2000

Comparison of Analytical and CAA Solution(s): Unsteady Response of a Rectilinear Swept Cascade to an Incident Gust

This problem is aimed at testing the ability of computational aeroacoustic methods to calculate the acoustic pressure field generated as a result of the interaction of a convected harmonic gust with a rectilinear cascade of swept flat plates. All relevant geometric information is the same as the unsteady response of an isolated finite span swept airfoil to an incident gust problem with the exception of the sweep angle alpha, which is now taken to be a variable. Assume a cascade stagger angle of zero (with the x-axis aligned with the chord) and a gap-to-chord ratio of h/c = 1. The mean flow Mach number M(sub 0), gust frequency omega, gust amplitude A, and chordwise wavenumber k(sub x) are the same. But for the cascade problem take k(sub y) = pi and k(sub z) = 0. The appropriate physical scales are also the same, as is the governing equation and boundary conditions. Naturally, the impermeability condition now applies to the entire cascade. For this problem, determine the amplitude of upstream-radiated rms acoustic pressure as a function of the sweep angle at the specified frequency. Specifically, show the variations of rms acoustic pressure amplitude at the upstream location (-5c, 0, l/2) for sweep angle alpha in the range (0.0 deg, 30.0 deg). Use sweep angle increments no larger than 2.5 deg. Express the results in dB using the rms pressure value for alpha = 0.0 deg as the reference level. The appropriate FORTRAN output statement should read "WRITE(IUNIT,*) alpha, 20-log10 (p(sub rms)(alpha)/p(sub rms)(0))".

Envia, Edmane↗

DOE OSTI2013

Divertor with a third-order null of the poloidal field

A concept and preliminary feasibility analysis of a divertor with the third-order poloidal field null is presented. The third-order null is the point where not only the field itself but also its first and second spatial derivatives are zero. In this case, the separatrix near the null-point has eight branches, and the number of strike-points increases from 2 (as in the standard divertor) to six. It is shown that this magnetic configuration can be created by a proper adjustment of the currents in a set of three divertor coils. If the currents are somewhat different from the required values, the configuration becomes that of three closely spaced first-order nulls. Analytic approach, suitable for a quick orientation in the problem, is used. Potential advantages and disadvantages of this configuration are briefly discussed.

36 MATERIALS SCIENCE↗

NASA NTRS1979

Utility of a finite element solution algorithm for initial-value problems

The Galerkin criterion within a finite element Weighted Residuals formulation is employed to establish an implicit solution algorithm for an initial-value partial differential equation. Numerical solutions of a transient parabolic and a hyperbolic equation, obtained using linear, quadratic and two cubic finite element basis functions, are employed to quantize accuracy and confirm and refine theoretical convergence rate estimates. The linear basis algorithm for the hyperbolic equation displays excellent accuracy on a coarse computational grid and a high-order convergence rate with discretization refinement. Good accuracy and a strong convergence rate in surface flux are determined for a nonhomogeneous Neumann boundary constraint applied to a parabolic equation. The results amply demonstrate the impact of the nondiagonal finite element initial-value matrix structure on solution accuracy and/or convergence rate.

Baker, A. J.↗