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At least 577 records · Page 32

Goertler instability in compressible boundary layers along curved surfaces with suction and cooling

The Goertler instability of the laminar compressible boundary layer flows along concave surfaces is investigated. The linearized disturbance equations for the three-dimensional, counter-rotating streamwise vortices in two-dimensional boundary layers are presented in an orthogonal curvilinear coordinate. The basic approximation of the disturbance equations, that includes the effect of the growth of the boundary layer, is considered and solved numerically. The effect of compressibility on critical stability limits, growth rates, and amplitude ratios of the vortices is evaluated for a range of Mach numbers for 0 to 5. The effect of wall cooling and suction of the boundary layer on the development of Goertler vortices is investigated for different Mach numbers.

El-Hady, N.↗

Data-driven, structure-preserving approximations to entropy-based moment closures for kinetic equations

In this study, we present a data-driven approach for approximating entropy-based closures of moment systems from kinetic equations. The proposed closure learns the entropy function by fitting the map between the moments and the entropy of the moment system, and thus does not depend on the spacetime discretization of the moment system or specific problem configurations such as initial and boundary conditions. With convex and C 2 approximations, this data-driven closure inherits several structural properties from entropy-based closures, such as entropy dissipation, hyperbolicity, and H-Theorem. We construct convex approximations to the Maxwell–Boltzmann entropy using convex splines and neural networks, test them on the plane source benchmark problem for linear transport in slab geometry, and compare the results to the standard, entropy-based systems which solve a convex optimization problem to find the closure. Numerical results indicate that these data-driven closures provide accurate solutions in much less computation time than that required by the optimization routine.

97 MATHEMATICS AND COMPUTING↗

Nature of buoyancy-driven flows in a reduced-gravity environment

The role of buoyancy-driven convection in reduced-gravity environments has been emphasized. It is shown that for some materials-processing experiments the values of the fundamental dimensionless parameters such as Gr or Ra are shifted from the very large (ground-based values) to moderately large (space-based values). As a consequence, in cases where approximate analytical solutions are desired, the accuracy of the usual asymptotic (boundary-layer) analysis in which infinitely large parametric ranges are assumed is reduced. Approximate analytical techniques for refinement of the asymptotic solutions are identified that will extend the accuracy to the moderately large parametric ranges associated with space-based processing.

Kassemi, Siavash A.↗

Numerical simulation of steady transonic flow about airfoils

A computer code has been developed that couples a fast transonic full-potential AF2 solver with both an efficient integral boundary-layer method and a viscous wedge approximation of the shock/boundary-layer interaction. The efficiency of the coupled analysis methods and the method of coupling has resulted in a uniquely efficient analysis tool. The airfoil geometry is modified by the displacement thickness before the shock and the displacement thickness plus the viscous wedge thickness after the shock by considering the viscous effects as an equivalent transpiration boundary condition. The flow about conventional and supercritical airfoils under moderately strong shock situations has been calculated. Comparisons with experimental data indicate that this viscous correction method has improved the accuracy of the full-potential analysis. Furthermore, the computer time required to obtain a converged solution has been reduced.

Lee, S. C.↗

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.↗

The Formation and Erosion History of Mt. Sharp

The Curiosity rover is exploring 155 km diameter Gale crater and Mt. Sharp, Gale's 5 km high central mound (Fig. 1). This study addresses the formation and erosion history of Mt. Sharp. Gale lies on the topographic dichotomy between the southern highlands and the northern plains - a drop of over 2 km [1,2]. Altitude differences between the north and south rim reflect this regional slope, as do altitude differences between the deep annulus north of Mt. Sharp and the southern crater floor. Orbiter and rover images demonstrate that most exposed areas on Mt. Sharp consist of thin, sub-parallel units interpreted as sedimentary layers [3]. Gale is typical of the 50 large martian craters that have been totally or partially filled with such layers [4,5]. In many craters these sediments have been deeply eroded. Central Peak and Peak Ring: The highest point on Mt. Sharp, near the crater's center, is interpreted as a central peak [6]. The peak has a massive lower portion and a thin, smooth capping deposit (Fig. 2). Gale's size is transitional between martian craters with single central peaks and craters with peak rings approximately half the crater's diameter [2,6]. The boundaries of Mt. Sharp, as well as an arc of hills to the southeast of the mountain, closely match a circle approximately 80 km in diameter (Fig. 3). This morphology suggests that the Gale impact may have formed both a central peak and a partial peak ring, which is covered by the sediments of Mt. Sharp in the north and possibly exposed in the arc of eroded hills in the southeast quadrant (Figs. 3,4).

Allen, Carlton C.↗

The receptivity of boundary layers on blunt bodies to oscillations in the free stream

One aspect of the boundary layer receptivity problem is examined, that of the flow induced in the bounday layer on the forward portion of a blunt body by unsteadiness in the mean flow. An approximate solution for the disturbances generated in the boundary layer by a long wavelength sound wave impinging normally on the front of a body in steady motion is also provided.

Grosch, C. E.↗

Interaction of a Boundary Layer with a Turbulent Wake

The objective of this grant was to study the transition mechanisms on a flat-plate boundary layer interacting with the wake of a bluff body. This is a simplified configuration presented and designed to exemplify the phenomena that occur in multi-element airfoils, in which the wake of an upstream element impinges on a downstream one. Some experimental data is available for this configuration at various Reynolds numbers. The first task carried out was the implementation and validation of the immersed-boundary method. This was achieved by performing calculations of the flow over a cylinder at low and moderate Reynolds numbers. The low-Reynolds number results are discussed, which is enclosed as Appendix A. The high-Reynolds number results are presented in a paper in preparation for the Journal of Fluid Mechanics. We performed calculations of the wake-boundary-layer interaction at two Reynolds numbers, Re approximately equal to 385 and 1155. The first case is discussed and a comparison of the two calculations is reported. The simulations indicate that at the lower Reynolds number the boundary layer is buffeted by the unsteady Karman vortex street shed by the cylinder. This is shown: long streaky structures appear in the boundary layer in correspondence of the three-dimensionalities in the rollers. The fluctuations, however, cannot be self-sustained due to the low Reynolds-number, and the flow does not reach a turbulent state within the computational domain. In contrast, in the higher Reynolds-number case, boundary-layer fluctuations persist after the wake has decayed (due, in part, to the higher values of the local Reynolds number Re achieved in this case); some evidence could be observed that a self-sustaining turbulence generation cycle was beginning to be established. A third simulation was subsequently carried out at a higher Reynolds number, Re=3900. This calculation gave results similar to those of the Re=l155 case. Turbulence was established at fairly low Reynolds number, as a consequence of the high level of the free-stream perturbation. An instantaneous flow visualization for that case is shown. A detailed examination of flow statistics in the transitional and turbulent regions, including the evolution of the turbulent kinetic energy (TKE) budget and frequency spectra showed the formation and evolution of turbulent spots characteristic of the bypass transition mechanism. It was also observed that the turbulent eddies achieved an equilibrium, fully developed turbulent states first, as evidenced by the early agreement achieved by the terms in the TKE budget with those observed in turbulent flows. Once a turbulent Reynolds stress profile had been established, the velocity profile began to resemble a turbulent one, first in the inner region and later in the outer region of the wall layer. An extensive comparison of the three cases, including budgets, mean velocity and Reynolds stress profiles and flow visualization, is included. The results obtained are also presented.

Piomelli, Ugo↗

A spectral boundary integral equation method for the 2-D Helmholtz equation

In this paper, we present a new numerical formulation of solving the boundary integral equations reformulated from the Helmholtz equation. The boundaries of the problems are assumed to be smooth closed contours. The solution on the boundary is treated as a periodic function, which is in turn approximated by a truncated Fourier series. A Fourier collocation method is followed in which the boundary integral equation is transformed into a system of algebraic equations. It is shown that in order to achieve spectral accuracy for the numerical formulation, the nonsmoothness of the integral kernels, associated with the Helmholtz equation, must be carefully removed. The emphasis of the paper is on investigating the essential elements of removing the nonsmoothness of the integral kernels in the spectral implementation. The present method is robust for a general boundary contour. Aspects of efficient implementation of the method using FFT are also discussed. A numerical example of wave scattering is given in which the exponential accuracy of the present numerical method is demonstrated.

Hu, Fang Q.↗

Direct simulation of a turbulent boundary layer up to R sub theta = 1410

The turbulent boundary layer on a flat plate, with zero pressure gradient, is simulated numerically at four stations between R sub theta = 225 and R sub theta = 1410. The three-dimensional time-dependent Navier-Stokes equations are solved using a spectral method with up to about 10 to the 7th grid points. Periodic spanwise and streamwise conditions are applied, and a multiple-scale procedure is applied to approximate the slow streamwise growth of the boundary layer. The flow is studied, primarily, from a statistical point of view. The solutions are compared with experimental results. The scaling of the mean and turbulent quantities with Reynolds number is compared with accepted laws, and the significant deviations are documented. The turbulence at the highest Reynolds number is studied in detail. The spectra are compared with various theoretical models. Reynolds-stress budget data are provided for turbulence-model testing.

Spalart, Philippe R.↗

Introduction to the Ulysses encounter with Jupiter

The Ulysses spacecraft encountered Jupiter in February 1992, passing within 6.31 radii of the planet. For approximately 8 days it was inside the Jovian magnetosphere, and for several days before and after that, Ulysses was in the interaction regions formed by the solar wind (the magnetosheath and boundary layer). The inbound trajectory was at an approximately 1000 LT and the outbound trajectory was at 1800 LT, that is, dusk, a unique feature of the flight path. Three regions interior to the magnetosphere were identified as on previous missions both inbound and outbound. In addition, the spacecraft twice penetrated a cusplike region at high latitude in the inner magnetosphere. Following closest approach, Ulysses traversed the Io plasma torus in basically a north-south direction. Although Ulysses is a heliospheric mission, the experiments were suited to an investigation of Jupiter's magnetosphere and have returned much new information. This introduction to the accompanying articles by the Ulysses investigators provides basic information on the experiments, the spacecraft, and the trajectory. In addition, the scientific context of the encounter is reviewed on the basis of the preliminary analyses of the Ulysses observations and a rudimentary comparison with the earlier Pioneer and Voyager results. Some important scientific questions raised by the encounter, along with some tentative answers, are presented.

Smith, Edward J.↗

Effect of boundary conditions on fluctuations of the Bose condensate of interacting atoms

For a gas of trapped interacting atoms forming a Bose condensate, we demonstrate a possibility of a significant influence of the boundary conditions on the statistics of the number of particles in the fundamental mode of the system. The analysis is carried out in the Bogoliubov – Popov low-temperature approximation for model homogeneous cubic traps with periodic or combined periodic and zero boundary conditions. It is shown that the effect of the boundary conditions does not weaken even in the region of parameters corresponding to the relatively strong interaction in the Thomas – Fermi asymptotic case, and does not disappear when proceeding to the thermodynamic limit. (paper)

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Direct simulation of a turbulent boundary layer up to R(sub)(theta)= 1410

The turbulent boundary layer on a flat plate, with zero pressure gradient, is simulated numerically at four stations between R sub theta = 225 and R sub theta = 1410. The three-dimensional time-dependent Navier-Stokes equations are solved using a spectra method with up to about 10 to the 7th power grid points. Periodic spanwise and stream-wise conditions are applied, and a multiple-scale procedure is applied to approximate the slow streamwise growth of the boundary layer. The flow is studied, primarily, from a statistical point of view. The solutions are compared with experimental results. The scaling of the mean and turbulent quantities with Reynolds number is examined and compared with accepted laws, and the significant deviations are documented. The turbulence at the highest Reynolds number is studied in detail. The spectra are compared with various theoretical models. Reynolds-stress budget data are provided for turbulence-model testing.

Spalart, Philippe R.↗

Separation behavior of boundary layers on three-dimensional wings

An inverse boundary layer procedure for calculating separated, turbulent boundary layers at infinitely long, crabbing wing was developed. The procedure was developed for calculating three dimensional, incompressible turbulent boundary layers was expanded to adiabatic, compressible flows. Example calculations with transsonic wings were made including viscose effects. In this case an approximated calculation method described for areas of separated, turbulent boundary layers, permitting calculation of this displacement thickness. The laminar boundary layer development was calculated with inclined ellipsoids.

Stock, H. W.↗

The no boundary density matrix

We discuss a no-boundary proposal for a subregion of the universe. In the classical approximation, this density matrix involves finding a specific classical solution of the equations of motion with no boundary. Beyond the usual no boundary condition at early times, we also have another no boundary condition in the region we trace out. We can find the prescription by starting from the usual Hartle-Hawking proposal for the wavefunction on a full slice and tracing out the unobserved region in the classical approximation. We discuss some specific subregions and compute the corresponding solutions. These geometries lead to phenomenologically unacceptable probabilities, as expected.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Simple approximations for the asymptotic description of the interaction between a normal shock wave and a turbulent boundary layer at transonic speeds

The asymptotic description of the interaction between a normal shock wave and a turbulent boundary layer is reviewed. The layers necessary in a rational analysis of the interaction are discussed with emphasis on the differences from an interaction with a laminar boundary layer, the uncoupling of solutions for the distribution of pressure and skin friction at the wall, and the role of the Reynolds shear stress in these solutions. The accuracy of asymptotic solutions in flows at Reynolds numbers of technical interest is discussed. Solutions for the distribution of pressure and skin friction at the wall and the shape of the shock are considered for the case where the flow is near separation. For the pressure and skin friction, it is possible to write two simplified partial solutions, one valid at the beginning of the interaction and one valid somewhat downstream of the shock wave. A solution composed of these two parts and a linear interpolation between them appears to give good comparison with experiment; one unknown constant, independent of the parameters of the interaction, must be found from experiment. The simplified relations are presented. Comparison of numerical computations with experimental data indicates a possible value for the constant and shows quite satisfactory results.

Adamson, T. C., Jr.↗

Experimental evaluation of heat transfer on a 1030:1 area ratio rocket nozzle

A 1030:1 carbon steel, heat-sink nozzle was tested. The test conditions included a nominal chamber pressure of 2413 kN/sq m and a mixture ratio range of 2.78 to 5.49. The propellants were gaseous oxygen and gaseous hydrogen. Outer wall temperature measurements were used to calculate the inner wall temperature and the heat flux and heat rate to the nozzle at specified axial locations. The experimental heat fluxes were compared to those predicted by the Two-Dimensional Kinetics (TDK) computer model analysis program. When laminar boundary layer flow was assumed in the analysis, the predicted values were within 15% of the experimental values for the area ratios of 20 to 975. However, when turbulent boundary layer conditions were assumed, the predicted values were approximately 120% higher than the experimental values. A study was performed to determine if the conditions within the nozzle could sustain a laminar boundary layer. Using the flow properties predicted by TDK, the momentum-thickness Reynolds number was calculated, and the point of transition to turbulent flow was predicted. The predicted transition point was within 0.5 inches of the nozzle throat. Calculations of the acceleration parameter were then made to determine if the flow conditions could produce relaminarization of the boundary layer. It was determined that if the boundary layer flow was inclined to transition to turbulent, the acceleration conditions within the nozzle would tend to suppress turbulence and keep the flow laminar-like.

Kacynski, Kenneth J.↗

Soft X-ray spectral fits of Geminga with model neutron star atmospheres

The spectrum of the soft X-ray pulsar Geminga consists of two components, a softer one which can be interpreted as thermal-like radiation from the surface of the neutron star, and a harder one interpreted as radiation from a polar cap heated by relativistic particles. We have fitted the soft spectrum using a detailed magnetized hydrogen atmosphere model. The fitting parameters are the hydrogen column density, the effective temperature T(sub eff), the gravitational redshift z, and the distance to radius ratio, for different values of the magnetic field B. The best fits for this model are obtained when B less than or approximately 1 x 10(exp 12) G and z lies on the upper boundary of the explored range (z = 0.45). The values of T(sub eff) approximately = (2-3) x 10(exp 5) K are a factor of 2-3 times lower than the value of T(sub eff) obtained for blackbody fits with the same z. The lower T(sub eff) increases the compatibility with some proposed schemes for fast neutrino cooling of neutron stars (NSs) by the direct Urca process or by exotic matter, but conventional cooling cannot be excluded. The hydrogen atmosphere fits also imply a smaller distance to Geminga than that inferred from a blackbody fit. An accurate evaluation of the distance would require a better knowledge of the ROSAT Position Sensitive Proportional Counter (PSPC) response to the low-energy region of the incident spectrum. Our modeling of the soft component with a cooler magnetized atmosphere also implies that the hard-component fit requires a characteristic temperature which is higher (by a factor of approximately 2-3) and a surface area which is smaller (by a factor of 10(exp 3), compared to previous blackbody fits.

Meyer, R. D.↗