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Two new methods for the numerical solution of conservation laws (the Euler equations in particular) are presented: a uniformly second-order accurate upwind scheme and a third-order accurate centered scheme. Results of these schemes are shown for problems 1, 2, and 5 of this workshop's benchmark problems.
The objective of this study is to investigate the complex three-dimensional flowfield of an oxygen safety pressure relieve valve during an incident, with a computational fluid dynamic (CFD) analysis. Specifically, the analysis will provide a flow pattern that would lead to the expansion of the eventual erosion pattern of the hardware, so as to combine it with other findings to piece together a most likely scenario for the investigation. The CFD model is a pressure based solver. An adaptive upwind difference scheme is employed for the spatial discretization, and a predictor, multiple corrector method is used for the velocity-pressure coupling. The computational result indicated vortices formation near the opening of the valve which matched the erosion pattern of the damaged hardware.
A preconditioned Krylov subspace method (GMRES) is used to solve the linear systems of equations formed at each time-integration step of the unsteady, two-dimensional, compressible Navier-Stokes equations of fluid flow. The Navier-Stokes equations are cast in an implicit, upwind finite-volume, flux-split formulation. Several preconditioning techniques are investigated to enhance the efficiency and convergence rate of the implicit solver based on the GMRES algorithm. The superiority of the new solver is established by comparisons with a conventional implicit solver, namely line Gauss-Seidel relaxation (LGSR). Computational test results for low-speed (incompressible flow over a backward-facing step at Mach 0.1), transonic flow (trailing edge flow in a transonic turbine cascade), and hypersonic flow (shock-on-shock interactions on a cylindrical leading edge at Mach 6.0) are presented. For the Mach 0.1 case, overall speedup factors of up to 17 (in terms of time-steps) and 15 (in terms of CPU time on a CRAY-YMP/8) are found in favor of the preconditioned GMRES solver, when compared with the LGSR solver. The corresponding speedup factors for the transonic flow case are 17 and 23, respectively. The hypersonic flow case shows slightly lower speedup factors of 9 and 13, respectively. The study of preconditioners conducted in this research reveals that a new LUSGS-type preconditioner is much more efficient than a conventional incomplete LU-type preconditioner.
A multiblock, laminar heating analysis for the shuttle orbiter at three trajectory points ranging from Mach 24.3 to Mach 12.86 on reentry is described. The analysis is performed using the Langley Aerothermodynamic Upwind Relaxation Algorithm with a seven species chemical nonequilibrium model. A finite-catalytic-wall model appropriate for shuttle tiles at a radiative equilibrium wall temperature is applied. Computed heating levels are generally in good agreement with the flight data, although a few rather large discrepancies remain unexplained. The multiblock relaxation strategy partitions the flowfield into manageable blocks requiring a fraction of the computational resources (time and memory) required by a full domain approach. In fact, the computational cost for a solution at even a single trajectory point would be prohibitively expensive at the given resolution without the multiblock approach. Converged blocks are reassembled to enable a fully coupled converged solution over the entire vehicle, starting from a nearly converged initial condition.
Computational fluid dynamics models for the thermodynamics and transport properties used in an equilibrium version of the Langley aerothermodynamics upwind relaxation algorithm (LAURA) for Mars atmospheric entries are described. In addition, the physical models used in a nonequilibrium version of LAURA for Mars-entry flows are described. Uncertainties exist in defining constants used in the transport properties for the equilibrium model and in many of the physical models for the nonequilibrium version. Solutions from the two codes using the best available constants are examined at the Mars-entry conditions characteristics of the Mars environmental survey mission. While the flowfields are near thermal equilibrium, chemical nonequilibrium effects are present in the entry cases examined. Convective heating at the stagnation point for these flows (assuming fully catalytic wall boundary conditions) is approximately 100 W/cm(exp 2). Radiative heating is negligible.
A high accuracy convection scheme using a sequential solution technique has been developed and applied to simulate the longitudinal combustion instability and its active control. The scheme has been devised in the spirit of the Total Variation Diminishing (TVD) concept with special source term treatment. Due to the substantial heat release effect, a clear delineation of the key elements employed by the scheme, i.e., the adjustable damping factor and the source term treatment has been made. By comparing with the first-order upwind scheme previously utilized, the present results exhibit less damping and are free from spurious oscillations, offering improved quantitative accuracy while confirming the spectral analysis reported earlier. A simple feedback type of active control has been found to be capable of enhancing or attenuating the magnitude of the combustion instability.
Local orography governs the triggering of cloud formation and the enhancement of processes such as condensation and hydrometeor nucleation and growth in mountainous regions. Intense, lengthy precipitation events are typical upwind of the topographic divide, with sharply decreasing magnitude and duration on the lee side. Differences in mean annual precipitation of several hundred percent between windward slopes of orographic barriers and adjacent valleys or lee side slopes are not unusual. Because much of the streamflow in areas such as the western United States is derived from mountainous areas that are remote and often poorly instrumented, modeling of orographic precipitation has important implications for water resources management. Models of orographically induced precipitation differ by their treatment of atmospheric dynamics and by the extent to which they rely on bulk parameterization of cloud and precipitation physics. Adiabatic ascent and a direct proportionality between efficiency and orographically magnified updrafts are the most frequent assumptions in orographic precipitation modeling. Space-time discretization (i.e., resolution) is a major issue because of the high spatial variability of orographic precipitation. For a specific storm, relative errors as large as 50 to 100% are common in the forecast/hindcast of precipitation intensity and can be even larger in the case of catastrophic storms. When monthly or seasonal timescales are used to evaluate model performance, the magnitude of such errors decreases dramatically, reaching values as low as 10 to 15%. Current research is focusing on the development of data assimilation techniques to incorporate radar and satellite observations, and on the development of aggregation and disaggregation methodologies to address the implications of modeling a multiscale problem at restricted spatial and temporal resolutions.
A new technique for estimating surface fluxes of trace gases, the mixed-layer gradient technique, is used to calculate isoprene and terpene emissions from forests. The technique is applied to tethered balloon measurements made over the Amazon forest and a pine-oak forest in Alabama at altitudes up to 300 m. The observations were made during the dry season Amazon Boundary Layer Experiment (ABLE 2A) and the Rural Oxidants in the Southern Environment 1990 experiment (ROSE I). Results from large eddy simulations of scalar transport in the clear convective boundary layer are used to infer fluxes from the balloon profiles. Profiles from the Amazon give a mean daytime emission of 3630 +/- 1400 micrograms isoprene sq m/h, where the uncertainty represents the standard deviation of the mean of eight flux estimates. Twenty profiles from Alabama give emissions of 4470 +/- 3300 micrograms isoprene sq m/h, 1740 +/- 1060 micrograms alpha-pinene sq m/h, and 790 +/- 560 micrograms beta-pinene sq m/h, respectively. These results are in agreement with emissions derived from chemical budgets. The emissions may be overestimated because of uncertainty about how to incorporate the effects of the canopy on the mixed-layer gradients. The large variability in these emission estimates is probably due to the relatively short sampling times of the balloon profiles, though spatially heterogeneous emissions may also play a role. Fluxes derived using this technique are representative of an upwind footprint of several kilometers and are independent of hydrocarbon oxidation rate and mean advection.
A new multigrid method with adaptive unstructured grids is presented. The three-dimensional Euler equations are solved on tetrahedral grids that are adaptively refined or coarsened locally. The multigrid method is employed to propagate the fine grid corrections more rapidly by redistributing the changes-in-time of the solution from the fine grid to the coarser grids to accelerate convergence. A new approach is employed that uses the parent cells of the fine grid cells in an adapted mesh to generate successively coaser levels of multigrid. This obviates the need for the generation of a sequence of independent, nonoverlapping grids as well as the relatively complicated operations that need to be performed to interpolate the solution and the residuals between the independent grids. The solver is an explicit, vertex-based, finite volume scheme that employs edge-based data structures and operations. Spatial discretization is of central-differencing type combined with a special upwind-like smoothing operators. Application cases include adaptive solutions obtained with multigrid acceleration for supersonic and subsonic flow over a bump in a channel, as well as transonic flow around the ONERA M6 wing. Two levels of multigrid resulted in reduction in the number of iterations by a factor of 5.
A field containing 11 star and incipient star dunes occurs on Mars at 8.8 deg S, 270.9 deg W. Examples of linear dunes are found in a crater at 59.4 deg S, 343 deg W. While rare, dune varieties that form in bi- and multidirectional wind regimes are not absent from the surface of Mars. The occurence of both of these dune fields offers new insight into the nature of martian wind conditions and sand supply. The linear dunes appears to have formed through modification of a formerly transverse aeolian deposit, suggesting a relatively recent change in local wind direction. The 11 dunes in the star dune locality show a progressive change from barchan to star form as each successive dune has traveled up into a valley, into a more complex wind regime. The star dunes corroborate the model of N. Lancaster (1989), for the formation of star dunes by projection of transverse dunes into a complex, topographically influenced wind regime. The star dunes have dark streaks emanating from them, providing evidence that the dunes were active at or near the time the relevant image was obtained by the Viking 1 orbiter in 1978. The star and linear dunes described here are located in different regions on the martian surface. Unlike most star and linear dunes on Earth, both martian examples are isolated occurrences; neither is part of a major sand sea. Previously published Mars general circulation model results suggest that the region in which the linear dune field occurs should be a bimodal wind regime, while the region in which the star dunes occur should be unimodal. The star dunes are probably the result of localized complication of the wind regime owing to topographic confinement of the dunes. Local topographic influence on wind regime is also evident in the linear dune field, as there are transverse dunes in close proximity to the linear dunes, and their occurrence is best explained by funneling of wind through a topographic gap in the upwind crater wall.
The effect of the porous leading edge of an airfoil on the blade-vortex interaction noise, which dominates the far-field acoustic spectrum of the helicopter, is investigated. The thin-layer Navier-Stokes equations are solved with a high-order upwind-biased scheme and a multizonal grid system. The Baldwin-Lomax turbulence model is modified for considering transpiration on the surface. The amplitudes of the propagating acoustic wave in the near field are calculated directly from the computation. The porosity effect on the surface is modeled in two ways: (1) imposition of prescribed transpiration velocity distribution and (2) calculation of transpiration velocity distribution by Darcy's law. Results show leading-edge transpiration can suppress pressure fluctuations at the leading edge during blade-vortex interaction and consequently reduce the amplitude of propagating noise by 30% at a maximum in the near field.
We describe a numerical code to solve the equations for ideal magnetohydrodynamics (MHD). It is based on an explicit finite difference scheme on an Eulerian grid, called the total variation diminishing (TVD) scheme, which is a second-order-accurate extension of the Roe-type upwind scheme. We also describe a non-linear Riemann solver for ideal MHD, which includes rarefractions as well as shocks. The numerical code and the Riemann solver have been used to test each other. Extensive tests encompassing all the possible ideal MHD structures with planar symmetries (i.e., one-dimensional flows) are presented. These include those for which the field structure is two dimensional (i.e., those flows often called '1 + 1/2 dimensional') as well as those for which the magnetic field plane rotates (i.e., those flows often called '1 + 1/2 + 1/2 dimensional'). Results indicate that the code can resolve strong fast, slow, and magnetosonic shocks within two to four cells, but more cells are required if shocks become weak. With proper steepening, we could resolve rotational discontinuities within three to five cells. However, without successful implementation of steepening, contact discontinuities are resolved with approximately 10 cells and tangential discountinuities are resolved with approximately 15 cells. Out tests confirm that slow compound structures with tow-dimensional magnetic fields are composed of intermediate shocks (so-called 2-4 intermediate shocks) followed by slow rarefaction waves. Finally, tests demostrate that in two-dimensional magnetohydrodynamics, fast compound structures, which are composed of intermediate shocks (so-called 1-3 intermediate shocks) preceeded by fast rarefaction waves, are also possible.
The ability of one- and two-equation turbulence models to predict unsteady separated flows over airfoils is evaluated. An implicit, factorized, upwind-biased numerical scheme is used for the integration of the compressible, Reynolds-averaged Navier-Stokes equations. The turbulent eddy viscosity is obtained from the computed mean flowfield by integration of the turbulent field equations. One- and two-equation turbulence models are first tested for a separated airfoil flow at fixed angle of incidence. The same models are then applied to compute the unsteady flowfields about airfoils undergoing oscillatory motion at low subsonic Mach numbers. Experimental cases where the flow has been tripped at the leading-edge and where natural transition was allowed to occur naturally are considered. The more recently developed turbulence models capture the physics of unsteady separated flow significantly better than the standard kappa-epsilon and kappa-omega models. However, certain differences in the hysteresis effects are observed. For an untripped high-Reynolds-number flow, it was found necessary to take into account the leading-edge transitional flow region to capture the correct physical mechanism that leads to dynamic stall.
An experimental and computational study was carried out to investigate the parallel head-on blade-vortex interaction (BVI) and its noise generation mechanism. A shock tube, with an enlarged test section, was used to generate a compressible starting vortex which interacted with a target airfoil. The dual-pulsed holographic interferometry (DPHI) technique and airfoil surface pressure measurements were employed to obtain quantitative flow data during the BVI. A thin-layer Navier-Stokes code (BV12D), with a high-order upwind-biased scheme and a multizonal grid, was also used to simulate numerically the phenomena occurring in the head-on BVI. The detailed structure of a convecting vortex was studied through independent measurements of density and pressure distributions across the vortex center. Results indicate that, in a strong head-on BVI, the opposite pressure peaks are generated on both sides of the leading edge as the vortex approaches. Then, as soon as the vortex passes by the leading edge, the high-pressure peak suddenly moves toward the low-peak-reducing in magnitude as it moves--simultaneously giving rise to the initial sound wave. In both experiment and computation, it is shown that the viscous effect plays a significant role in head-on BVIs.
Explicit and implicit time integration algorithms for the two-dimensional Euler equations on unstructured grids are presented. Both cell-centered and cell-vertex finite volume upwind schemes utilizing Roe's approximate Riemann solver are developed. For the cell-vertex scheme, a four-stage Runge-Kutta time integration, a fourstage Runge-Kutta time integration with implicit residual averaging, a point Jacobi method, a symmetric point Gauss-Seidel method and two methods utilizing preconditioned sparse matrix solvers are presented. For the cell-centered scheme, a Runge-Kutta scheme, an implicit tridiagonal relaxation scheme modeled after line Gauss-Seidel, a fully implicit lower-upper (LU) decomposition, and a hybrid scheme utilizing both Runge-Kutta and LU methods are presented. A reverse Cuthill-McKee renumbering scheme is employed for the direct solver to decrease CPU time by reducing the fill of the Jacobian matrix. A comparison of the various time integration schemes is made for both first-order and higher order accurate solutions using several mesh sizes, higher order accuracy is achieved by using multidimensional monotone linear reconstruction procedures. The results obtained for a transonic flow over a circular arc suggest that the preconditioned sparse matrix solvers perform better than the other methods as the number of elements in the mesh increases.
The Galileo Ultravilet Spectrometer Experiment (UVS) obtained a partial celestial sphere map of interplanetary Lyman-alpha (IP L alpha) on 13-14 December 1990 during the first Earth encounter. The Galileo spacecraft was near the downwind axis of the local interstellar medium flow. These UVS measurements sampled the downwind, anti-sunward hemisphere. The data were modeled using a hot model of the interplanetary hydrogen density distribution with the goal of studying multiple scattering effects in the inner solar system. The derived ratio in the downwind direction of the observed brightness and a single scattering model brightness, both normalized to unity in the upwind direction, is 1.82 +/- 0.2. This brightness ratio requires a multiple scattering correction which is 36% larger than can be accounted for by theoretical calculations. The hot model may require: (1) a temperature perturbation of the interstellar wind velocity distribution or (2) an additional downstream source of interplanetary hydrogen. However, a more likely exlanation which affects the hot model is the latitude dependence of the radiation pressure. This dependence, based on the known solar L alpha flux latitude variation at solar maximum, causes a downwind brightness enhancement by preferential focusing of H-atoms with trajectory planes containing the solar poles. This result implies that radiation pressure near the solar poles is nearly independent of solar cycle and is insufficient to lead to a net repulsion of hydrogen atoms by the sun, as can occur near the ecliptic plane during the solar maximum. In addition, the UVS performed 13 observations of IP L alpha while in cruise between Venus and the Earth in 3 directions fixed in ecliptic coordinates.
The intracluster medium (ICM) within merging clusters of galaxies is likely to be in a violent or turbulent dynamical state which may have a significant effect on the evolution of cluster radio sources. We present results from a recent gas + N-body simulation of a cluster merger, suggesting that mergers can result in long-lived, supersonic bulk flows, as well as shocks, within a few hundred kiloparsecs of the core of the dominant cluster. These results have motivated our new two-dimensional and three-dimensional simulations of jet propagation in such environments. The first set of simulations models the ISM/ICM transition as a contact discontinuity with a strong velocity shear. A supersonic (M(sub j) = 6) jet crossing this discontinuity into an ICM with a transverse, supersonic wind bends continuously, becomes 'naked' on the upwind side, and forms a distended cocoon on the downwind side. In the case of a mildly supersonic jet (M(sub j) = 3), however, a shock is driven into the ISM and ISM material is pulled along with the jet into the ICM. Instabilities excited at the ISM/ICM interface result in the jet repeatedly pinching off and reestablishing itself in a series of 'disconnection events.' The second set of simulations deals with a jet encountering a shock in the merging cluster environment. A series of relatively high-resolution two-dimensional calculations is used to confirm earlier analysis predicting that the jet will not disrupt when the jet Mach number is greater than the shock Mach number. A jet which survives the encounter with the shock will decrease in radius and disrupt shortly thereafter as a result of the growth of Kelvin-Helmholtz instabilities. We also find, in disagreement with predictions, that the jet flaring angle decreases with increasing jet density. Finally, a three-dimensional simulation of a jet crossing an oblique shock gives rise to a morphology which resembles a wide-angle tailed radio source with the jet flaring at the shock and disrupting to form a long, turbulent tail which is dragged downstream by the preshock wind.
The steady three-dimensional thermocapillary motion with a deformable free surface is studied numerically in both normal and zero gravity environments. Flow configurations consist of a square cavity heated from the side. In the analysis, the free surface is allowed to deform and the grid distribution is adapted to the surface deformation. The divergence-free condition is satisfied by using a dual time-stepping approach in the numerical scheme. Convective flux derivatives are evaluated using a third-order accurate upwind-biased flux-split differencing technique. The numerical solutions at the midplane of the square cavity are compared with the results from two-dimensional calculations. In addition, numerial results for cases under zero and normal gravity conditions are compared. Significantly different flow structures and surface deformation have been observed. The comparison of calculated results will be compared with experimental data in the updated version of this paper.