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At least 289 records · Page 16

Line relaxation methods for the solution of 2D and 3D compressible flows

An implicit finite element based algorithm for the compressible Navier-Stokes equations is outlined, and the solution of the resulting equation by a line relaxation on general meshes of triangles or tetrahedra is described. The problem of generating and adapting unstructured meshes for viscous flows is reexamined, and an approach for both 2D and 3D simulations is proposed. An efficient approach appears to be the use of an implicit/explicit procedure, with the implicit treatment being restricted to those regions of the mesh where viscous effects are known to be dominant. Numerical examples demonstrating the computational performance of the proposed techniques are given.

Hassan, O.↗

2D axisymmetric analysis of SRM ignition transient

To analyze ignition transient of Space Shuttle solid rocket motor, a transient two-dimensional numerical model based on turbulent compressible Navier-Stokes equations in a generalized coordinate system was developed. One-dimensional numerical models (Peretz et al., 1973; Han, 1992; Pardue and Han, 1992) with empirical correlations data obtained from steady turbulent boundary layer flows agrees reasonably well with test rocket data by adjusting a few parameters. However, a 1D model can not provide a physical insight into the complex multidimensional thermal fields and flowfields in the chamber and the converging-diverging rocket nozzle. As an interim step, a 2D model was developed and compared with test data. A modified version of SIMPLE algorithm was used for the numerical model, and the standard k-epsilon model with a wall function was used for turbulence closure. Transient flowfields and thermal fields in the combustion chamber and the attached nozzle were obtained for a selected rocket geometry and propellant. Transient behaviors of the flow and thermal fields were analyzed, and were found to be in good agreement with physical expectations.

Bai, S. D.↗

Flow transitions in a 2D directional solidification model

Flow transitions in a Two Dimensional (2D) model of crystal growth were examined using the Bridgman-Stockbarger me thod. Using a pseudo-spectral Chebyshev collocation method, the governing equations yield solutions which exhibit a symmetry breaking flow tansition and oscillatory behavior indicative of a Hopf bifurcation at higher values of Ra. The results are discussed from fluid dynamic viewpoint, and broader implications for process models are also addressed.

Larroude, Philippe↗

Phase transitions and 2D spherical convection in a large icy satellite

Three ice phase transitions, based on experimental and theoretical results, were incorporated into a 2D spherical convection model. These phase transitions are the exothermic Ice 1-2, the endothermic Ice 2-6, and the exothermic Ice 6-8 phase transitions. The fluid is assumed isoviscous and the anelastic liquid formulation was used. The object is an icy satellite whose physical characteristics resemble those of Ganymede or Callisto. Structural models, similar to those of Mueller and McKinnon, with different core sizes, i.e. with different degree of differentiation were studied. The shells, i.e. the mantle of the satellite, is heated both internally and from below to account for the decaying radiogenic heating and the heat flow from the solid core. The lower boundary of the mantle is rigid and isothermal, the upper boundary is isothermal. Calculations with rigid and shear stress free upper boundary are carried out in order to assess the role of the different boundary conditions. Two different Rayleigh numbers, depending on the assumed value of the viscosity, were used in the calculations and the thermal evolution of the satellite was studied. The suit of calculations presented demonstrates that phase transition cannot be ignored when the thermal evolution of a large icy satellite has to be studied. The importance of the construction of the realistic phase diagram for ice was also documented. On the other hand the degree of differentiation, simulated with the structures with different core's radius does not seem to drastically influence the overall behavior of the convective activity. Within the limits of our simulations, the post-accretional evolution seems to be independent on the degree of primordial differentiation.

Forni, O.↗

The 2D and 3D hypersonic flows with unstructured meshes

Viewgraphs on 2D and 3D hypersonic flows with unstructured meshes are presented. Topics covered include: mesh generation, mesh refinement, shock-shock interaction, velocity contours, mesh movement, vehicle bottom surface, and adapted meshes.

Rajiv Thareja↗

Impact of stratospheric aircraft on calculations of nitric acid trihydrate cloud surface area densities using NMC temperatures and 2D model constituent distributions

A parameterization of NAT (nitric acid trihydrate) clouds is developed for use in 2D models of the stratosphere. The parameterization uses model distributions of HNO3 and H2O to determine critical temperatures for NAT formation as a function of latitude and pressure. National Meteorological Center temperature fields are then used to determine monthly temperature frequency distributions, also as a function of latitude and pressure. The fractions of these distributions which fall below the critical temperatures for NAT formation are then used to determine the NAT cloud surface area density for each location in the model grid. By specifying heterogeneous reaction rates as functions of the surface area density, it is then possible to assess the effects of the NAT clouds on model constituent distributions. We also consider the increase in the NAT cloud formation in the presence of a fleet of stratospheric aircraft. The stratospheric aircraft NO(x) and H2O perturbations result in increased HNO3 as well as H2O. This increases the probability of NAT formation substantially, especially if it is assumed that the aircraft perturbations are confined to a corridor region.

Considine, David B.↗

Effect of open hole on tensile failure properties of 2D triaxial braided textile composites and tape equivalents

The unnotched and notched (open hole) tensile strength and failure mechanisms of two-dimensional (2D) triaxial braided composites were examined. The effect of notch size and notch position were investigated. Damage initiation and propagation in notched and unnotched coupons were also examined. Theory developed to predict the normal stress distribution near an open hole and failure for tape laminated composites was evaluated for its applicability to triaxial braided textile composite materials. Four fiber architectures were considered with different combinations of braid angle, longitudinal and braider yam size, and percentage of longitudinal yarns. Tape laminates equivalent to textile composites were also constructed for comparison. Unnotched tape equivalents were stronger than braided textiles but exhibited greater notch sensitivity. Notched textiles and tape equivalents have roughly the same strength at large notch sizes. Two common damage mechanisms were found: braider yams cracking and near notch longitudinal yarn splitting. Cracking was found to initiate in braider yarns in unnotched and notched coupons, and propagate in the direction of the braider yarns until failure. Longitudinal yarn splitting occurred in three of four architectures that were longitudinally fiber dominated. Damage initiation stress decreased with increasing braid angle. No significant differences in prediction of near notch stress between measured and predicted stress were weak for textiles with large braid angle. Notch strength could not be predicted using existing anisotropic theory for braided textiles due to their insensitivity to notch.

Norman, Timothy L.↗

Electron excitation cross sections for the 2s(2)2p(3)4S(O) -- 2s(2)2p(3)2D(O) (forbidden) and 4S(O) -- 2s2p(4) 4P (resonance) transitions in O II

Experimental and theoretical excitation cross sections are reported for the first forbidden transition 4S(O) -- 2S(2)2p(3) 2D(O) (lambda-lambda 3726, 3729) and the first allowed (resonance) transition 4S(O) -- 2s2p(4) 4P(lambda-833) in O II. Use is made of electron energy loss and merged-beams methods. The electron energy range covered is 3.33 (threshold) to 15 eV for the S -- D transition, and 14.9 (threshold) to 40 eV for the S -- P transition. Care was taken to assess and minimize the metastable fraction of the O II beam. An electron mirror was designed and tested to reflect inelastically backscattered electrons into the forward direction to account for the full range of polar scattering angles. Comparisons are made between present experiments and 11-state R-matrix calculations. Calculations are also presented for the 4S(O) -- 2s(2)2p(3)2P(O) (lambda-2470) transition.

Zuo, M.↗

Comparative Results from a CFD Challenge Over a 2D Three-Element High-Lift Airfoil

A high-lift workshop was held in May of 1993 at NASA Langley Research Center. A major part of the workshop centered on a blind test of various computational fluid dynamics (CFD) methods in which the flow about a two- dimensional (2D) three-element airfoil was computed without prior knowledge of the experimental data. The results of this 'blind' test revealed: (1) The Reynolds Averaged Navier-Stokes (RANS) methods generally showed less variability among codes than did potential/Euler solvers coupled with boundary-layer solution techniques. However, some of the coupled methods still provided excellent predictions. (2) Drag prediction using coupled methods agreed more closely with experiment than the RANS methods. Lift was more accurately predicted than drag for both methods. (3) The CFD methods did well in predicting lift and drag changes due to changes in Reynolds number, however, they did not perform as well when predicting lift and drag increments due to changing flap gap, (4) Pressures and skin friction compared favorably with experiment for most of the codes. (5) There was a large variability in most of the velocity profile predictions. Computational results predict a stronger siat wake than measured suggesting a missing component in turbulence modeling, perhaps curvature effects.

Klausmeyer, Steven M.↗

The Wavelet Element Method: Realization and Additional Features in 2D and 3D - Part 2

The Wavelet Element Method (WEM) provides a construction of multiresolution systems and biorthogonal wavelets on fairly general domains. These are split into subdomains that are mapped to a single reference hypercube. Tensor products of scaling functions and wavelets defined on the unit interval are used on the reference domain. By introducing appropriate matching conditions across the interelement boundaries, a globally continuous biorthogonal wavelet basis on the general domain is obtained. This construction does not uniquely define the basis functions but rather leaves some freedom for fulfilling additional features. In this paper we detail the general construction principle of the WEM to the 1D, 2D and 3D cases. We address additional features such as symmetry, vanishing moments and minimal support of the wavelet functions in each particular dimension. The construction is illustrated by using biorthogonal spline wavelets on the interval.

Canuto, Claudio↗

Electron Excitation Cross Sections for the S II Transitions: 3s(exp 2)3p(exp 3) 4S(exp o) approaches 3s(exp 2)3p(exp 3) 2D(exp o), 2P(exp o), and 3s3p(exp 4) 4P

Experimental and theoretical collisional excitation cross sections are reported for the transitions 3s(exp 2)3p(exp 3)4S(exp o) approaches 3s(exp 2)3p(exp 3) 2D(exp o), 2P(exp o), and 3s3P(exp 4) 4P in S II. The transition wavelengths (energies) are 6716 A (1.85 eV), 4069 A (3.05 eV), and 1256 A (9.87 eV), respectively. In the experiments, use is made of the energy-loss merged-beams method. The metastable fraction of the S II beam was assessed and minimized. The contribution of elastically scattered electrons was reduced by the use of a lowered solenoidal magnetic field and a modulated radio-frequency voltage on the analyzing plates and by retarding grids to reject the elastically scattered electrons with larger Larmor radii. For each transition, comparisons are made among experiments, the new 19 state R-matrix calculation, and three other close-coupling calculations.

Liao, C.↗

A 2D Microphysical Analysis of Aerosol Nucleation in the Polar Winter Stratosphere: Implications for H2SO4 Photolysis and Nucleation Mechanisms

Each spring a layer of small particles forms between 20 and 30 km in the polar regions. Results are presented from a 2D microphysical model of sulfate aerosol, which provide the first self-consistent explanation of the observed "CN layer." Photochemical conversion of sulfuric acid to SO2 in the upper stratosphere and mesosphere is necessary for this layer to form. Recent laboratory measurements of H2SO4 and SO3 photolysis rates are consistent with such conversion, though an additional source of SO2 may be required. Nucleation throughout the polar winter extends the top of the aerosol layer to higher altitudes, despite strong downward transport of ambient air. This finding may be important to heterogeneous chemistry at the top of the aerosol layer in polar winter and spring.

Mills, Michael J.↗

Doubled CO2 Effects on NO(y) in a Coupled 2D Model

Changes in temperature and ozone have been the main focus of studies of the stratospheric impact of doubled CO2. Increased CO2 is expected to cool the stratosphere, which will result in increases in stratospheric ozone through temperature dependent loss rates. Less attention has been paid to changes in minor constituents which affect the O3 balance and which may provide additional feedbacks. Stratospheric NO(y) fields calculated using the GSFC 2D interactive chemistry-radiation-dynamics model show significant sensitivity to the model CO2. Modeled upper stratospheric NO(y) decreases by about 15% in response to CO2 doubling, mainly due to the temperature decrease calculated to result from increased cooling. The abundance of atomic nitrogen, N, increases because the rate of the strongly temperature dependent reaction N + O2 yields NO + O decreases at lower temperatures. Increased N leads to an increase in the loss of NO(y) which is controlled by the reaction N + NO yields N2 + O. The NO(y) reduction is shown to be sensitive to the NO photolysis rate. The decrease in the O3 loss rate due to the NO(y) changes is significant when compared to the decrease in the O3 loss rate due to the temperature changes.

Rosenfield, J. E.↗

HOTCFGM-2D: A Coupled Higher-Order Theory for Cylindrical Structural Components with Bi-Directionally Components with Bi-Directionally Graded Microstructures

The objective of this two-year project was to develop and deliver to the NASA-Glenn Research Center a two-dimensional higher-order theory, and related computer codes, for the analysis and design of cylindrical functionally graded materials/structural components for use in advanced aircraft engines (e.g., combustor linings, rotor disks, heat shields, brisk blades). To satisfy this objective, two-dimensional version of the higher-order theory, HOTCFGM-2D, and four computer codes based on this theory, for the analysis and design of structural components functionally graded in the radial and circumferential directions were developed in the cylindrical coordinate system r-Theta-z. This version of the higher-order theory is a significant generalization of the one-dimensional theory, HOTCFGM-1D, developed during the FY97 for the analysis and design of cylindrical structural components with radially graded microstructures. The generalized theory is applicable to thin multi-phased composite shells/cylinders subjected to steady-state thermomechanical, transient thermal and inertial loading applied uniformly along the axial direction such that the overall deformation is characterized by a constant average axial strain. The reinforcement phases are uniformly distributed in the axial direction, and arbitrarily distributed in the radial and circumferential direction, thereby allowing functional grading of the internal reinforcement in the r-Theta plane. The four computer codes fgmc3dq.cylindrical.f, fgmp3dq.cylindrical.f, fgmgvips3dq.cylindrical.f, and fgmc3dq.cylindrical.transient.f are research-oriented codes for investigating the effect of functionally graded architectures, as well as the properties of the multi-phase reinforcement, in thin shells subjected to thermomechanical and inertial loading, on the internal temperature, stress and (inelastic) strain fields. The reinforcement distribution in the radial and circumferential directions is specified by the user. The thermal and inelastic properties of the individual phases can vary with temperature. The inelastic phases are presently modeled by the power-law creep model generalized to multi-directional loading (within fgmc3dq.cylindrical.f and fgmc3dq.cylindrical.transient.f for steady-state and transient thermal loading, respectively), and incremental plasticity and GVIPS unified viscoplasticity theories (within the steady-state loading versions fgmp3dq.cylindrical.f and fgmgvips3dq.cylindrical.f).

Pindera, Marek-Jerzy↗

Generation and Radiation of Acoustic Waves from a 2D Shear Layer

A thin free shear layer containing an inflection point in the mean velocity profile is inherently unstable. Disturbances in the flow field can excite the unstable behavior of a shear layer, if the appropriate combination of frequencies and shear layer thicknesses exists, causing instability waves to grow. For other combinations of frequencies and thicknesses, these instability waves remain neutral in amplitude or decay in the downstream direction. A growing instability wave radiates noise when its phase velocity becomes supersonic relative to the ambient speed of sound. This occurs primarily when the mean jet flow velocity is supersonic. Thus, the small disturbances in the flow, which themselves may generate noise, have generated an additional noise source. It is the purpose of this problem to test the ability of CAA to compute this additional source of noise. The problem is idealized such that the exciting disturbance is a fixed known acoustic source pulsating at a single frequency. The source is placed inside of a 2D jet with parallel flow; hence, the shear layer thickness is constant. With the source amplitude small enough, the problem is governed by the following set of linear equations given in dimensional form.

Dahl, Milo D.↗

Toward an Efficient Icing CFD Process Using an Interactive Software Toolkit: Smagglce 2D

Two-dimensional CID analysis for iced airfoils can be a labor-intensive task. The software toolkit SmaggIce 2D is being developed to help streamline the CID process and provide the unique features needed for icing. When complete, it will include a combination of partially automated and fully interactive tools for all aspects of the tasks leading up to the flow analysis: geometry preparation, domain decomposition. block boundary demoralization. gridding, and linking with a flow solver. It also includes tools to perform ice shape characterization, an important aid in determining the relationship between ice characteristics and their effects on aerodynamic performance. Completed tools, work-in-progress, and planned features of the software toolkit are presented here.

Vickerman, Mary B.↗

Analysis of 2D Torus and Hub Topologies of 100Mb/s Ethernet for the Whitney Commodity Computing Testbed

A variety of different network technologies and topologies are currently being evaluated as part of the Whitney Project. This paper reports on the implementation and performance of a Fast Ethernet network configured in a 4x4 2D torus topology in a testbed cluster of 'commodity' Pentium Pro PCs. Several benchmarks were used for performance evaluation: an MPI point to point message passing benchmark, an MPI collective communication benchmark, and the NAS Parallel Benchmarks version 2.2 (NPB2). Our results show that for point to point communication on an unloaded network, the hub and 1 hop routes on the torus have about the same bandwidth and latency. However, the bandwidth decreases and the latency increases on the torus for each additional route hop. Collective communication benchmarks show that the torus provides roughly four times more aggregate bandwidth and eight times faster MPI barrier synchronizations than a hub based network for 16 processor systems. Finally, the SOAPBOX benchmarks, which simulate real-world CFD applications, generally demonstrated substantially better performance on the torus than on the hub. In the few cases the hub was faster, the difference was negligible. In total, our experimental results lead to the conclusion that for Fast Ethernet networks, the torus topology has better performance and scales better than a hub based network.

Pedretti, Kevin T.↗

Advecting Procedural Textures for 2D Flow Animation

This paper proposes the use of specially generated 3D procedural textures for visualizing steady state 2D flow fields. We use the flow field to advect and animate the texture over time. However, using standard texture advection techniques and arbitrary textures will introduce some undesirable effects such as: (a) expanding texture from a critical source point, (b) streaking pattern from the boundary of the flowfield, (c) crowding of advected textures near an attracting spiral or sink, and (d) absent or lack of textures in some regions of the flow. This paper proposes a number of strategies to solve these problems. We demonstrate how the technique works using both synthetic data and computational fluid dynamics data.

Kao, David↗