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At least 703 records · Page 39

Heating of minor ions by the coronal slow shock

The coronal slow shock has been predicted to exist embedded in large coronal holes at 4-10 solar radii. In this paper, a three-fluid model is used to study the jumps in minor ion properties across a slow shock such as the coronal slow shock. The jump conditions are formulated in the de Hoffmann-Teller frame of reference. The Rankine-Hugoniot solution determines the MHD flow and the magnetic field across the shocks. For each minor ion species, the fluid equations for the conservation of mass, momentum, and energy can be solved to determine the velocity and the temperature of the ions across the shock. Also obtained is a similarity solution for heavy ions. The results show that, on the downstream side of the slow shock, the ion temperatures are nearly proportional to the ion masses for He, O, Si, and Fe, in agreement with observed ion temperatures in the inner solar wind. This indicates that the possibly existing coronal slow shock can be responsible for the observed heating of minor ions in the solar wind.

Whang, Y. C.↗

Heat Transfer from Radiatively Heated Material in a Low Reynolds Number Microgravity Environment

A mathematical model of the transient three-dimensional heat transfer between a slowly moving ambient gas stream and a thermally thick or thin flat surface heated by external radiation in a microgravity environment is presented. The problem is motivated in part by fire safety issues in spacecraft. The gas phase is represented by variable property convection-diffusion energy and mass conservation equations valid at low Reynolds numbers. The absence of gravity and low Reynolds number together permit the flow to be represented by a self-consistent velocity potential determined by the ambient velocity and the thermal expansion in the gas. The solid exchanges energy with the gas by conduction/convection and with the surroundings by surface absorption and re-emission of radiation. Heat conduction in the solid is assumed to be one dimensional at each point on the surface as a consequence of the limited times (of order of 10 seconds) of interest in these simulations. Despite the apparent simplicity of the model, the results show a complex thermally induced flow near the heated surface. The thermal exchange between the gas and solid produces an outward sourcelike flow upstream of the center of the irradiated area and a sinklike flow downstream. The responses of the temperature fields and the associated flows to changes in the intensity of the external radiation and the ambient velocity are discussed.

Yamashita, H.↗

Effect of magnetic field geometry on the wave signature of the pickup of interstellar neutrals

By using the technique of Johnstone et al. (1991), the asymptotic wave spectrum induced by the pickup of interstellar ions in the heliosphere is derived. This approach is independent of quasi-linear theory. The asymptotic wave spectrum is calculated from the standard resonance condition by assuming that the asymptotic ion distribution is bispherical and by using conservation of energy. The calculation places no restriction on either the ratio of Alfven speed to solar wind flow speed or the particle pitch angle. Spectra for various geometries (relative orientations of the magnetic field and solar wind velocity) are calculated. Absolute upper limits to the expected wave enhancements are calculated. These upper limits are compared to the background fluctuation spectrum extrapolated from 0.87 AU, assuming a spectral index of -5/3 and radial dependences of -2 and -3. The heliocentric radial distances at which the peaks in the various geometry-dependent wave spectra are expected to be observable above the background are identified. Peaks due to pickup hydrogen at the proton gyrofrequency are found to be always stronger relative to the background in parallel than in perpendicular geometries. The parallel-geometry excitations consist only of sunward propagating waves. In perpendicular geometries a peak also occurs, this time near 0.1 of the proton gyrofrequency (corresponding to the peak calculated by Lee and Ip (1987)). However, the steep spectral dependence of the ambient wave field makes it unlikely that this peak will be observed inside 20 AU. A similar result holds for the case of pickup-helium induced excitation at the helium gyrofrequency. Inside 10 AU, peaks at these lower frequencies tend to be obscured by the steep frequency dependence (proportional to -5/3) of the ambient spectrum and then are only observable in parallel geometries.

Williams, L. L.↗

Computation of Gust-Cascade Interaction Using the CE/SE Method

The problem 2 in Category 3 of the 4th Computational Aeroacoustic(CAA) Workshop is solved using the space-time conservation element and solution element (CE/SE) method. This problem models rotor-stator interaction in a 2D cascade. It involves complex geometries and flow physics including vortex shedding and acoustic radiation. The parallel version of the 2D nonlinear Euler solver is used with an unstructured triangular mesh to solve this problem. The Giles approach is incorporated with the CE/SE method to handle non-equal pitches of the rotor and stator. Validation on the Giles approach is performed using Problem 3.1 in the 2nd CAA Workshop. The space-time CE/SE method is a finite volume method with second-order accuracy in both space and time. The flux conservation is enforced in both space and time instead of space only. It has low numerical dissipation and dispersion errors. It uses simple non-reflecting boundary conditions and is compatible with unstructured meshes. It is simple, flexible, and generate reasonably accurate solutions. The CE/SE method has been successfully applied to solve numerous practical problems, especially aeroacoustic problems. Some preliminary numerical results of the benchmark problem 3.2 of the 4th CAA Workshop are shown. The steady-state pressure contour is plotted. The mean pressure distribution on the blade surface is compared with Turbo solution showing a good agreement. The sound pressure level versus the rotor harmonic n at the six designated positions on the blade surface, three locations at inlet plane, and three locations at the outlet plane are plotted. It can be seen that the acoustic response exists only at the excitation frequencies (n = 1,2,3). On the blade surface, the acoustic wave at n = 1 is dominant, while at the inlet and outlet planes, the sound pressure level at n = 2 becomes the largest, which is similar to the results presented. The distribution of sound pressure level at different spatial modes along the z- direction is plotted for n = 1,2,3, respectively. It shows that the spatial modes m = -32 and 22 at n = 1 exponentially decay, and the spatial modes m = 10 at n = 2, m = -42 and 12 at n = 3 propagate both upstream and downstream, which agrees with the prediction based on the linearized theory. Some oscillations are observed, which needs to be investigated further. In the final paper, the numerical results will be compared with a frequency-domain solver LINFLUX solution if it is available.

Wang, X.-Y.↗

Entropy Stable h/p-Nonconforming Discretization with the Summation-by-Parts Property for the Compressible Euler and Navier–Stokes Equations

In this paper, we extend the entropy conservative/stable algorithms presented by Del Rey Fernandez and coauthors for the compressible Euler and Navier-Stokes equations on nonconforming p-refined/coarsened curvilinear grids to h/p refinement/coarsening. The main difficulty in developing nonconforming algorithms is the construction of appropriate coupling procedures across nonconforming interfaces. Here, we utilize a computationally simple and efficient approach based upon using decoupled interpolation operators. The resulting scheme is entropy conservative/stable and elementwise conservative. Numerical simulations of the isentropic vortex and viscous shock propagation con firm the entropy conservation/stability and accuracy properties of the method (achieving ~ p + 1 convergence), which are comparable to those of the original conforming scheme. Simulations of the Taylor{Green vortex at R(e) = 1,600 and turbulent flow past a sphere at R(e(infinity)) = 2,000 show the robustness and stability properties of the overall spatial discretization for unstructured grids. Finally, to demonstrate the entropy conservation property of a fully-discrete explicit entropy stable algorithm with h=p refinement/coarsening, we present the time evolution of the entropy function obtained by simulating the propagation of the isentropic vortex using a relaxation Runge-Kutta scheme.

Nonconforming interfaces↗

A compressible Navier-Stokes solver with two-equation and Reynolds stress turbulence closure models

This report outlines the development of a general purpose aerodynamic solver for compressible turbulent flows. Turbulent closure is achieved using either two equation or Reynolds stress transportation equations. The applicable equation set consists of Favre-averaged conservation equations for the mass, momentum and total energy, and transport equations for the turbulent stresses and turbulent dissipation rate. In order to develop a scheme with good shock capturing capabilities, good accuracy and general geometric capabilities, a multi-block cell centered finite volume approach is used. Viscous fluxes are discretized using a finite volume representation of a central difference operator and the source terms are treated as an integral over the control volume. The methodology is validated by testing the algorithm on both two and three dimensional flows. Both the two equation and Reynolds stress models are used on a two dimensional 10 degree compression ramp at Mach 3, and the two equation model is used on the three dimensional flow over a cone at angle of attack at Mach 3.5. With the development of this algorithm, it is now possible to compute complex, compressible high speed flow fields using both two equation and Reynolds stress turbulent closure models, with the capability of eventually evaluating their predictive performance.

Navier-Stoke solver↗

Thermoacoustic convection of fluids in low gravity

The heat flow in a confined perfect gas in low gravity is investigated, including the effects of conduction and thermal convection. Buoyancy-driven flow is neglected, due to the low-gravity environment, but the effect of thermoacoustic motion due to fluid compressibility is included. One-dimensional mathematical models are constructed from the conservation equations for a compressible, viscous, heat-conducting fluid. A conservative, time-dependent finite-difference method is used to generate numerical solutions on a digital computer. Problems for flat plates and cylindrical segments are solved for specified thermal boundary conditions. Numerical results are given which indicate that thermoacoustic convection can significantly increase the transient heat flow over conduction model predictions for cases where a confined gas is rapidly heated.

Spradley, L. W.↗

Space Shuttle Main Engine performance analysis

For a number of years, NASA has relied primarily upon periodically updated versions of Rocketdyne's power balance model (PBM) to provide space shuttle main engine (SSME) steady-state performance prediction. A recent computational study indicated that PBM predictions do not satisfy fundamental energy conservation principles. More recently, SSME test results provided by the Technology Test Bed (TTB) program have indicated significant discrepancies between PBM flow and temperature predictions and TTB observations. Results of these investigations have diminished confidence in the predictions provided by PBM, and motivated the development of new computational tools for supporting SSME performance analysis. A multivariate least squares regression algorithm was developed and implemented during this effort in order to efficiently characterize TTB data. This procedure, called the 'gains model,' was used to approximate the variation of SSME performance parameters such as flow rate, pressure, temperature, speed, and assorted hardware characteristics in terms of six assumed independent influences. These six influences were engine power level, mixture ratio, fuel inlet pressure and temperature, and oxidizer inlet pressure and temperature. A BFGS optimization algorithm provided the base procedure for determining regression coefficients for both linear and full quadratic approximations of parameter variation. Statistical information relative to data deviation from regression derived relations was also computed. A new strategy for integrating test data with theoretical performance prediction was also investigated. The current integration procedure employed by PBM treats test data as pristine and adjusts hardware characteristics in a heuristic manner to achieve engine balance. Within PBM, this integration procedure is called 'data reduction.' By contrast, the new data integration procedure, termed 'reconciliation,' uses mathematical optimization techniques, and requires both measurement and balance uncertainty estimates. The reconciler attempts to select operational parameters that minimize the difference between theoretical prediction and observation. Selected values are further constrained to fall within measurement uncertainty limits and to satisfy fundamental physical relations (mass conservation, energy conservation, pressure drop relations, etc.) within uncertainty estimates for all SSME subsystems. The parameter selection problem described above is a traditional nonlinear programming problem. The reconciler employs a mixed penalty method to determine optimum values of SSME operating parameters associated with this problem formulation.

Santi, L. Michael↗

Numerical Simulation of Shock-Induced Combustion Past Blunt Bodies Using Shock-Fitting Technique

Two-dimensional axisymmetric, reacting viscous flow over blunt projectiles is computed to study shock induced combustion at Mach 5.11 and Mach 6.46 in hydrogen-air mixture. A finite-difference, shock-fitting method is used to solve the complete set of Navier Stokes and species conservation equations. In this approach, the bow shock represents a boundary of the computational domain and is treated as a discontinuity across which Rankine-Hugoniot conditions are applied. All interior details of the flow such as compression waves, reaction front, and the wall boundary layer are captured automatically in the solution. Since shock-fitting approach reduces the amount of artificial dissipation, all the intricate details of the flow are captured much more clearly than has been possible with the shock-capturing approach. This has allowed an improved understanding of the physics of shock-induced combustion over blunt projectiles and the numerical results can now be explained more readily with one dimensional wave-interaction model than before.

Ahuja, J. K.↗

CAS2D: FORTRAN program for nonrotating blade-to-blade, steady, potential transonic cascade flows

An exact, full-potential-equation (FPE) model for the steady, irrotational, homentropic and homoenergetic flow of a compressible, homocompositional, inviscid fluid through two dimensional planar cascades of airfoils was derived, together with its appropriate boundary conditions. A computer program, CAS2D, was developed that numerically solves an artificially time-dependent form of the actual FPE. The governing equation was discretized by using type-dependent, rotated finite differencing and the finite area technique. The flow field was discretized by providing a boundary-fitted, nonuniform computational mesh. The mesh was generated by using a sequence of conforming mapping, nonorthogonal coordinate stretching, and local, isoparametric, bilinear mapping functions. The discretized form of the FPE was solved iteratively by using successive line overrelaxation. The possible isentropic shocks were correctly captured by adding explicitly an artificial viscosity in a conservative form. In addition, a three-level consecutive, mesh refinement feature makes CAS2D a reliable and fast algorithm for the analysis of transonic, two dimensional cascade flows.

Dulikravich, D. S.↗

Quasi 1-D Analysis of a Circular, Compressible, Turbulent Jet Laden with Water Droplets

Recent experimental studies indicate that presence of small amount of liquid droplets reduces the Overall Sound Pressure Level (OASPL) of a jet. Present study is aimed at numerically investigating the effect of liquid particles on the overall flow quantities of a heated, compressible round jet. The jet is assumed perfectly expanded. A quasi-1D model was developed for this purpose which uses area-averaged quantities that satisfy integral conservation equations. Special attention is given to represent the early development region since it is acoustically important. Approximate velocity and temperature profiles were assumed in this region to evaluate entrainment rate. Experimental correlations were used to obtain spreading rate of shear layer. The base flow thus obtained is then laden with water droplets at the exit of the nozzle. Mass, momentum and energy coupling between the two phases is represented using empirical relations. Droplet size and mass loading are varied to observe their effect on flow variables.

Source record↗

A longitudinally-patched grid approach with applications to high speed flows

The combined use of an implicit, upwind finite-volume scheme with an 'equivalent' gamma formulation (for real gas effects) and with a three-dimensional conservative patched grid formulation is discussed. Results are presented over a wide Mach number range on both single and patched grids.

Walters, R. W.↗

Pulsed electromagnetic gas acceleration

Experimental data were combined with one-dimensional conservation relations to yield information on the energy deposition ratio in a parallel-plate accelerator, where the downstream flow was confined to a constant area channel. Approximately 70% of the total input power was detected in the exhaust flow, of which only about 20% appeared as directed kinetic energy, thus implying that a downstream expansion to convert chamber enthalpy into kinetic energy must be an important aspect of conventional high power MPD arcs. Spectroscopic experiments on a quasi-steady MPD argon accelerator verified the presence of A(III) and the absence of A(I), and indicated an azimuthal structure in the jet related to the mass injection locations. Measurements of pressure in the arc chamber and impact pressure in the exhaust jet using a piezocrystal backed by a Plexiglas rod were in good agreement with the electromagnetic thrust model.

Jahn, R. G.↗

Blood flow and oxygen uptake during exercise

A model is developed for predicting oxygen uptake, muscle blood flow, and blood chemistry changes under exercise conditions. In this model, the working muscle mass system is analyzed. The conservation of matter principle is applied to the oxygen in a unit mass of working muscle under transient exercise conditions. This principle is used to relate the inflow of oxygen carried with the blood to the outflow carried with blood, the rate of change of oxygen stored in the muscle myoglobin, and the uptake by the muscle. Standard blood chemistry relations are incorporated to evaluate venous levels of oxygen, pH, and carbon dioxide.

Mitchell, J. W.↗

Numerical computation of transonic flows with shock waves

Some recent developments in numerical methods for calculating solutions to the transonic potential flow equation are reviewed, including (1) the construction of the stable coordinate independent difference schemes; (2) the use of conservation form to insure proper shock jump conditions; (3) analysis of the relaxation method by the time dependent analogy; (4) accelerated iterative schemes.

Jameson, A.↗

An alternative approach to the numerical simulation of steady inviscid flow

A numerical procedure for the efficient simulation of steady inviscid flow is described and its utility demonstrated. Application of the surrogate equation technique allows the formulation of stable, fully conservative, type dependent finite difference equations for use in obtaining numerical solutions to systems of first order partial differential equations, such as the steady state Euler equations or their various approximations. Computational results are presented for the full Euler equations and for the transonic disturbance equations. For the latter case, a computational efficiency greater than that obtained by means of the standard perturbation potential approach is indicated.

Johnson, G. M.↗

Solution of the two-dimensional Euler equations with generalized coordinate transformation using flux vector splitting

An implicit finite difference code using flux vector splitting has been developed for solving the two-dimensional inviscid gas dynamics equations. The method is spatially second-order acurate, fully conservative, and uses body-conforming generalized coordinates for treating complex geometries. Numerical results have been obtained for transonic flow over a circular cylinder and airfoils. Steady results for a half cylinder (top and bottom symmetry-imposed) range from critical flow to a strong shock case with rotationally induced flow separation. Full cylinder solutions at freestream Mach number values of 0.5, however, show unsteady oscillation. A perturbation form of the method has also been developed and used to compute both fore and aft inviscid flow separation about a cylinder for a nonuniform incoming stream.

Buning, P. G.↗

Transonic viscous and inviscid solutions using a composite velocity procedure

Solutions for transonic viscous and inviscid flows using a composite velocity procedure are presented. The velocity components of the compressible Navier-Stokes equations are written in terms of a multiplicative composite consisting of a viscous or rotational velocity and an inviscid, irrotational, potential like function. For viscous flows, the governing equations are solved using a coupled strongly implicit procedure and the outer inviscid flow corresponds to an irrotational, potential flow. Further investigation of the inviscid flow solution is made so that the correct rotational flow solution may be obtained for the transonic case. The Euler equations are solved for the inviscid flow calculations. Solutions to the full potential equation are recovered unless the axial momentum equation is written in full conservation form.

Gordnier, R. E.↗