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At least 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1989

Numerical simulation of viscous vortex rings

Vortex interactions and their role in turbulent flow are examined. The objectives are twofold. First, to use the existing axisymmetric code to study the annihilation process of colliding vortex rings and determine the relevance of this problem to similar 3-D phenomena. The second objective is to extend the code to three dimensions. The code under development is unique in that it can compute flows in a truly infinite domain (i.e., without periodic boundary conditions or approximations from truncating the domain). Because of this, the far field sound can be computed, and therefore, contribute to improved models of turbulence generated noise for this class of flows. Issues which can be addressed by the code include: effects of viscosity on mode selection in azimuthal breakdown of vortex rings (i.e., the Widnall instability); reconnection, the associated production of small scales, and the time scale of the process.

Stanaway, Sharon Kay↗
NASA NTRS1988

Interaction and merging of vortex filaments

The asymptotic solutions of Navier-Stokes equations for vortex filaments of finite strength with small effective vortical cores are summarized with special emphasis placed on the physical meaning and the practical limit to the applicability of the asymptotic solution. Finite-difference solutions of Navier-Stokes equations for the marging of the filament(s) are described with a focus on the development of the approximate boundary conditions for the computational domain. An efficiency study employing a model problem is used to assess the advantages of the present approximate boundary condition method over previously used techniques. Applications of the present method are presented for the motion and decay of a 3:1 elliptic vortex ring, and for the merging process of a pair of coaxial vortex rings. A numerical procedure for the problem of local merging of vortex filaments, which requires the asymptotic analysis as well as the numerical Navier-Stokes solver, is also presented.

Liu, C. H.↗
NASA NTRS1987

Approximation techniques for domain identification in two-dimensional parabolic systems under boundary observations

The identification of the geometrical structure of the system boundary for a two-dimensional diffusion system is considered. The domain identification treated is converted into an optimization problem based on a fit-to-data criterion and theoretical convergence results for approximate identification techniques are discussed. Results of numerical experiments to demonstrate the efficiency of the theoretical ideas are reported.

Banks, H. T.↗
NASA NTRS1984

Navier-Stokes calculations for unsteady three-dimensional vortical flows in unbounded domains

Finite-difference Navier-Stokes calculations for unsteady, three-dimensional, incompressible, viscous flows induced by initial vorticity distributions are presented and discussed in this paper. The initial vorticity distributions are assumed to be embedded in a flow field of infinite extent that is quiescent at infinity. These vorticity distributions are typical of vortex rings and other closed vortical tubes or structures. Such structures are important elements in fluid flows such as jets, atmospheric convection and the far-field wakes of aircraft; studies of their interaction may aid in an understanding of complex fluid flows. The calculations employ a method recently proposed by Ting to approximate the infinite-domain boundary value problem with a finite boundary computational domain, and this method is shown to yield accurate three-dimensional results for reasonable expenditures of computer time. Because of the efficiency of the boundary condition technique and the resulting Navier-Stokes code, a 16-bit minicomputer with virtual memory was capable of performing the calculations for the unsteady motion of two obliquely colliding vortex rings. The results of these calculations are presented in the paper.

Chamberlain, J. P.↗
NASA NTRS2014

Simulations of Emerging Magnetic Flux. II. The Formation of Unstable Coronal Flux Ropes and the Initiation of Coronal Mass Ejections

We present results from three-dimensional magnetohydrodynamic simulations of the emergence of a twisted convection zone flux tube into a pre-existing coronal dipole field. As in previous simulations, following the partial emergence of the sub-surface flux into the corona, a combination of vortical motions and internal magnetic reconnection forms a coronal flux rope. Then, in the simulations presented here, external reconnection between the emerging field and the pre-existing dipole coronal field allows further expansion of the coronal flux rope into the corona. After sufficient expansion, internal reconnection occurs beneath the coronal flux rope axis, and the flux rope erupts up to the top boundary of the simulation domain (approximately 36 Mm above the surface).We find that the presence of a pre-existing field, orientated in a direction to facilitate reconnection with the emerging field, is vital to the fast rise of the coronal flux rope. The simulations shown in this paper are able to self-consistently create many of the surface and coronal signatures used by coronal mass ejection (CME) models. These signatures include surface shearing and rotational motions, quadrupolar geometry above the surface, central sheared arcades reconnecting with oppositely orientated overlying dipole fields, the formation of coronal flux ropes underlying potential coronal field, and internal reconnection which resembles the classical flare reconnection scenario. This suggests that proposed mechanisms for the initiation of a CME, such as "magnetic breakout," are operating during the emergence of new active regions.

corona↗
NASA NTRS1988

Motion, decay and merging of vortex filaments

The asymptotic solutions of Navier-Stokes equations for vortex filaments of finite strength with small effective vortical cores are summarized. Emphases are placed on the physical meaning and the practical limit to the applicability of the asymptotic solution. Finite-difference solutions of Navier-Stokes equations for the merging of the filament(s) are described. It is focused on the development of the approximate boundary conditions for the computational domain.

Liu, C. H.↗
NASA NTRS1993

On the accurate long-time solution of the wave equation in exterior domains: Asymptotic expansions and corrected boundary conditions

We consider the solution of scattering problems for the wave equation using approximate boundary conditions at artificial boundaries. These conditions are explicitly viewed as approximations to an exact boundary condition satisfied by the solution on the unbounded domain. We study the short and long term behavior of the error. It is provided that, in two space dimensions, no local in time, constant coefficient boundary operator can lead to accurate results uniformly in time for the class of problems we consider. A variable coefficient operator is developed which attains better accuracy (uniformly in time) than is possible with constant coefficient approximations. The theory is illustrated by numerical examples. We also analyze the proposed boundary conditions using energy methods, leading to asymptotically correct error bounds.

Hagstrom, Thomas↗
NASA NTRS1981

Microstructure of Al2O3 scales formed on NiCrAl alloys

The structure of transient scales formed on pure and Y or Zr-doped Ni-15Cr-13Al alloys oxidized for 0.1 hr at 1100 C was studied by the use of transmission electron microscopy. Crystallographically oriented scales were found on all three alloys, but especially for the Zr-doped NiCrAl. The oriented scales consisted of alpha-(Al,Cr)2O3, Ni(Al,Cr)2O4 and gamma-Al2O3. They were often found in intimate contact with each other such that the close-packed planes and directions of one oxide phase were aligned with those of another. The prominent structural features of the oriented scales were approximately equal to micrometer subgrains; voids, antiphase domain boundaries and aligned precipitates were also prevalent. Randomly oriented alpha-Al2O3 was also found and was the only oxide ever observed at the immediate oxide metal interface. These approximately 0.15 micrometer grains were populated by intragranular voids which decreased in size and number towards the oxide metal interface. A sequence of oxidation was proposed in which the composition of the growing scale changed from oriented oxides rich in Ni and Cr to oriented oxides rich in Al. At the same time the structure changed from cubic spinels to hexagonal corundums with apparent precipitates of one phase in the matrix of the other. Eventually randomly oriented pure alpha-Al2O3 formed as the stable oxide with an abrupt transition: there was no gradual loss of orientation, no gradual compositional change or no gradual decrease in precipitate density.

Smialek, J. L.↗
NASA NTRS1997

Multilevel methods for elliptic problems on unstructured grids

Multilevel methods on unstructured grids for elliptic problems are reviewed. The advantages of these techniques are the flexible approximation of the boundaries of complicated physical domains and the ability to adapt the grid to the resolution of fine scaled structures. Multilevel methods, which include multigrid methods and domain decomposition methods, depend on the correct splitting of appropriate finite element spaces. The standard splittings used in the structured grid case cannot be directly extended to unstructured grids due to their requirement for a hierarchical grid structure. Issues related to the application of multilevel methods to unstructured grids are discussed, including how the coarse spaces and transfer operators are defined and how different types of boundary conditions are treated. An obvious way to generate a coarse mesh is to regrid the physical domain several times. Several alternatives are proposed and discussed: node nested coarse spaces, agglomerated coarse spaces and algebraically generated coarse spaces.

Chan, Tony F.↗
NASA NTRS2016

Acoustic Radiation From a Mach 14 Turbulent Boundary Layer

Direct numerical simulations (DNS) are used to examine the turbulence statistics and the radiation field generated by a high-speed turbulent boundary layer with a nominal freestream Mach number of 14 and wall temperature of 0:18 times the recovery temperature. The flow conditions fall within the range of nozzle exit conditions of the Arnold Engineering Development Center (AEDC) Hypervelocity Tunnel No. 9 facility. The streamwise domain size is approximately 200 times the boundary-layer thickness at the inlet, with a useful range of Reynolds number corresponding to Re 450 􀀀 650. Consistent with previous studies of turbulent boundary layer at high Mach numbers, the weak compressibility hypothesis for turbulent boundary layers remains applicable under this flow condition and the computational results confirm the validity of both the van Driest transformation and Morkovin's scaling. The Reynolds analogy is valid at the surface; the RMS of fluctuations in the surface pressure, wall shear stress, and heat flux is 24%, 53%, and 67% of the surface mean, respectively. The magnitude and dominant frequency of pressure fluctuations are found to vary dramatically within the inner layer (z/delta 0.< or approx. 0.08 or z+ < or approx. 50). The peak of the pre-multiplied frequency spectrum of the pressure fluctuation is f(delta)/U(sub infinity) approx. 2.1 at the surface and shifts to a lower frequency of f(delta)/U(sub infinity) approx. 0.7 in the free stream where the pressure signal is predominantly acoustic. The dominant frequency of the pressure spectrum shows a significant dependence on the freestream Mach number both at the wall and in the free stream.

Zhang, Chao↗
NASA NTRS1980

Boundary conditions for the numerical solution of elliptic equations in exterior regions

Elliptic equations in exterior regions frequently require a boundary condition at infinity to ensure the well-posedness of the problem. Examples of practical applications include the Helmholtz equation and Laplace's equation. Computational procedures based on a direct discretization of the elliptic problem require the replacement of the condition on a finite artificial surface. Direct imposition of the condition at infinity along the finite boundary results in large errors. A sequence of boundary conditions is developed which provides increasingly accurate approximations to the problem in the infinite domain. Estimates of the error due to the finite boundary are obtained for several cases. Computations are presented which demonstrate the increased accuracy that can be obtained by the use of the higher order boundary conditions. The examples are based on a finite element formulation but finite difference methods can also be used.

Bayliss, A.↗
NASA NTRS1980

Comments on numerical solution of boundary value problems of the Laplace equation and calculation of eigenvalues by the grid method

The mathematics involved in numerically solving for the plane boundary value of the Laplace equation by the grid method is developed. The approximate solution of a boundary value problem for the domain of the Laplace equation by the grid method consists of finding u at the grid corner which satisfies the equation at the internal corners (u=Du) and certain boundary value conditions at the boundary corners.

Lyusternik, L. A.↗
NASA NTRS1993

Multigrid direct numerical simulation of the whole process of flow transition in 3-D boundary layers

A new technology was developed in this study which provides a successful numerical simulation of the whole process of flow transition in 3-D boundary layers, including linear growth, secondary instability, breakdown, and transition at relatively low CPU cost. Most other spatial numerical simulations require high CPU cost and blow up at the stage of flow breakdown. A fourth-order finite difference scheme on stretched and staggered grids, a fully implicit time marching technique, a semi-coarsening multigrid based on the so-called approximate line-box relaxation, and a buffer domain for the outflow boundary conditions were all used for high-order accuracy, good stability, and fast convergence. A new fine-coarse-fine grid mapping technique was developed to keep the code running after the laminar flow breaks down. The computational results are in good agreement with linear stability theory, secondary instability theory, and some experiments. The cost for a typical case with 162 x 34 x 34 grid is around 2 CRAY-YMP CPU hours for 10 T-S periods.

Liu, Chaoqun↗
NASA NTRS1987

The terminal area simulation system. Volume 1: Theoretical formulation

A three-dimensional numerical cloud model was developed for the general purpose of studying convective phenomena. The model utilizes a time splitting integration procedure in the numerical solution of the compressible nonhydrostatic primitive equations. Turbulence closure is achieved by a conventional first-order diagnostic approximation. Open lateral boundaries are incorporated which minimize wave reflection and which do not induce domain-wide mass trends. Microphysical processes are governed by prognostic equations for potential temperature water vapor, cloud droplets, ice crystals, rain, snow, and hail. Microphysical interactions are computed by numerous Orville-type parameterizations. A diagnostic surface boundary layer is parameterized assuming Monin-Obukhov similarity theory. The governing equation set is approximated on a staggered three-dimensional grid with quadratic-conservative central space differencing. Time differencing is approximated by the second-order Adams-Bashforth method. The vertical grid spacing may be either linear or stretched. The model domain may translate along with a convective cell, even at variable speeds.

Proctor, F. H.↗
NASA NTRS1986

Multigrid-sinc methods

A Galerkin method using Whittaker cardinal or 'sinc' functions as basis functions is described for the solution of boundary-value problems. When the solution is analytic in the interior of the domain, the error of approximation using 2N + 1 points is O(e exp /-gamma sq rt N/) even if derivatives of the solution are singular at the boundaries. A multigrid method with overall complexity O(N log N) is used to solve the discrete equations. This paper contains a description of the multigrid-sinc algorithm along with some preliminary numerical results for two-point boundary-value problems.

Schaffer, Steve↗
NASA NTRS1980

Analytic and approximate boundary-fitted coordinate systems for fluid flow simulation

A method for constructing a direct functional relation between the computational and physical domains such that boundaries in the computational domain map into boundaries in the physical domain is presented. This method which is called the 'two-boundary technique' is based on generating functions that represent two disconnected boundaries in the physical domain and an independent function which connects one boundary with another to generate grids. The suggested connecting functions are simple linear and cubic parametric polynomials with parameters based on position and derivatives at the disconnected boundaries. The boundaries can be defined by analytical, approximate, and tension spline functions; the grid density in specified regions is controlled by embedding contraction functions in either the boundary representation or the connecting function.

Smith, R. E.↗
NASA NTRS1992

Estimation of unknown variable parameters in moving boundary problems

The problem of estimating unknown variable parameters appearing in moving boundary problems is considered; these are specifically nonlinear diffusion equations defined on a moving spatial domain. A spline-based approximation method that results in a sequence of computationally tractable approximate parameter estimation problems has been developed. A convergence result is proved for a certain class of these moving boundary problems. The paper is concluded with a set of representative numerical examples.

Murphy, K. A.↗
NASA NTRS1994

Subband And Transform Compression Of Video Signals

Class of hierarchical subband coders developed primarily for compression of image data at video rates. Offers good performance with limited computational complexity and with flexibility inherent in subband decomposition. Particular subband decomposition chosen for coders appears to hide large quantitative errors effectively, largely because decomposition occurs along two-dimensional spatial-frequency-domain boundaries resembling spatial-frequency-domain curves of constant sensitivity of human visual system. Curves found approximately diamond-shaped: thus, low-pass filtering for reduction of data ideally involves nonrectangular passbands.

Sauer, Ken↗