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A comparison is made of the boundary-layer flow computed by the approximate method developed by K. Pohlhausen with the exact solutions which have been published for several special cases. A modification of Pohlhausen's method has been developed which extends the range of application at the expense of some decrease in the accuracy of the approximations.
The structure and stability of flames in dusty mixtures is investigated. The presence of the dust leads to significant transport of energy by radiation and the fundamental goal of the analysis is to explore to what extent this displaces the classical non-hydrodynamical stability boundaries of the plane degradation. An approximate description of the radiative transport permits analysis for arbitrary values of both the planck length and the Boltzman number. It is shown that the pulsating/traveling-wave instability usually associated with values of Lewis number (L(sub e)) bigger than 1 is stongly enhanced by the presence of radiation and can be present even if L(sub e) is less than 1. On the other hand radiation tends to supress the cellular instability normally associated with values of L(sub e) less than 1. The latter is consisitent with preliminary experimental observations of Abbud-Madrid and Ronney.
An experimental study is conducted to examine the crossplane structure and streamwise decay of vortices shed from airfoil-type vortex generators. The vortex generators are set in a counter-rotating array spanning the full circumference of a straight pipe. The span of the vortex generators above the duct surface, h, is approximately equal to the local turbulent boundary layer thickness, delta. Measurement of three-component mean flow velocity in downstream crossplanes are used to characterize the structure of the shed vortices. Measurements in adjacent crossplanes (closely spaced along the streamwise coordinate) characterize the interaction and decay of the embedded vortices. A model constructed by the superposition of Oseen vortices is compared to the data for one test case.
A passive tracer to represent dissolved silicate concentrations, with biologically realistic uptake kinetics, is successfully incorporated into a three-dimensional, eddy-resolving, ocean circulation model of the Indian Ocean. Hypotheses are tested to evaluate physical processes which potentially affect the availability of silicate for diatom production in the Arabian Sea. An alternative mechanism is offered to the idea that open ocean upwelling is primarily responsible for the high, vertical nutrient flux and consequent large-scale phytoplankton bloom in the northwestern Arabian Sea during the southwest monsoon. Model results show that dissolved silicate in surface waters available for uptake by diatoms is primarily influenced by the intensity of nearshore upwelling from soutwest monsoonal wind forcing and by the offshore advective transport of surface waters. The upwelling, which in the model occurs within 200 +/- 50 km of the coast, appears to be a result of a combination of coastal upwelling, Elkman pumping, and divergence of the coastal flow as it turns offshore. Localized intensifications of silicate concentrations appear to be hydrodynamically driven and geographically correlated to coastal topographic features. The absence of diatoms in sediments of the eastern Arabian Basin is consistent with modeled distributional patterns of dissolved silicate resulting from limited westward advection of upwelled coastal waters from the western continental margin of India and rapid uptake of available silicate by diatoms. Concentrations of modeled silicate become sufficiently low to become unavailable for diatom production in the eastern Arabian Sea, a region between 61 deg E and 70 deg E at 8 deg N on the south, with the east and west boundaries converging on the north at approximately 67 deg E, 20 deg N.
Electric field data from the Geotail spacecraft provide an opportunity to extend the observations of spiky fields made by International Sun Earth Explorer-1 (ISEE-1) to a region of the magnetosphere where quasistatic electric field measurements have not previously been msde, to examine their possible importance in the dynamics of the middle and distant tail, and to test some hypotheses about their formation. In this paper, examples of large fields in the plasma sheet and its boundary at radial distances up to approximately 90 R(sub E) are presented. It is shown that three different types of large electric fields can occur: (1) spiky fields; (2) 'DC' fields; and (3) waves at frequencies comparable to the lower hybrid frequency. There is usually a gradation between (1) and (3), and often large electric field spikes are embedded in regions of lower amplitude waves. The waves tend to occur in short (few to 10's of seconds) packets whose start and stop times are not always correlated with changes in the magnetic field and/or density (as indicated by the spacecraft potential). The peak frequency is often less than but comparable to the lower hybrid frequency in agreement with theories of lower hybrid drift waves in the magnetotail. The largest spikes are not always associated with the largest changes in the spacecraft potential and/or magnetic field. It is suggested that the spiky fields may represent the nonlinear development of the waves.
A computational investigation was conducted to support the development of a semi-span model test capability in the NASA LaRC's National Transonic Facility. This capability is required for the testing of high-lift systems at flight Reynolds numbers. A three-dimensional Navier-Stokes solver was used to compute the low-speed flow over both a full-span configuration and a semi-span configuration. The computational results were found to be in good agreement with the experimental data. The computational results indicate that the stand-off height has a strong influence on the flow over a semi-span model. The semi-span model adequately replicates the aerodynamic characteristics of the full-span configuration when a small stand-off height, approximately twice the tunnel empty sidewall boundary layer displacement thickness, is used. Several active sidewall boundary layer control techniques were examined including: upstream blowing, local jet blowing, and sidewall suction. Both upstream tangential blowing, and sidewall suction were found to minimize the separation of the sidewall boundary layer ahead of the semi-span model. The required mass flow rates are found to be practicable for testing in the NTF. For the configuration examined, the active sidewall boundary layer control techniques were found to be necessary only near the maximum lift conditions.
The goal of this paper is the implementation of hybrid V-cycle hierarchical multilevel methods for the indefinite discrete systems which arise when a mixed finite element approximation is used to solve elliptic boundary value problems. By introducing a penalty parameter, the perturbed indefinite system can be reduced to a symmetric positive definite system containing the small penalty parameter for the velocity unknown alone. We stabilize the hierarchical spatial decomposition approach proposed by Cai, Goldstein, and Pasciak for the reduced system. We demonstrate that the relative condition number of the preconditioner is bounded uniformly with respect to the penalty parameter, the number of levels and possible jumps of the coefficients as long as they occur only across the edges of the coarsest elements.
An experimental investigation was conducted in the Langley 8-Foot Transonic Pressure Tunnel to determine the flow characteristics of rectangular cavities with varying relative dimensions at subsonic and transonic speeds. Cavities were tested with width-to-depth ratios of 1, 4, 8, and 16 for length-to-depth ratios l/h of 1 through 17.5. The maximum cavity depth was 2.4 in., and the turbulent boundary layer approaching the cavity was approximately 0.5 in. thick. Unsteady- and mean static-pressure measurements were made at free-stream Mach numbers from 0.20 to 0.95 at a unit Reynolds number per foot of approximately 3 x 10(exp 6); however, only unsteady-pressure results are presented in this paper. Results indicate that as l/h increases, cavity flows changed from resonant to nonresonant with resonant amplitudes decreasing gradually. Resonant spectra are obtained largely in cavities with mean static-pressure distributions characteristic of open and transitional flows. Resonance sometimes occurred for closed flow. Increasing cavity width or decreasing cavity depth while holding l/h fixed had the effect of increasing resonant amplitudes and sometimes induced resonance. The effects due to changes in width are more pronounced. Decreasing Mach number has the effect of broadening the resonances.
Bulk growth of wide band gap II-VI semiconductors by physical vapor transport (PVT) has been developed and refined over the past several years at NASA Marshall Space Flight Center. Results from a modeling study of PVT crystal growth of ZnSe are reported in this paper. The PVT process is numerically investigated using a two-dimensional formulation of the governing equations and associated boundary conditions. Both the incompressible Boussinesq approximation and a compressible model are tested to determine the influence of gravity on the process and to discern the differences between the two approaches. The influence of a residual gas is included in the models. The results show that both the incompressible and compressible approximations provide comparable results and the presence of a residual gas tends to measurably reduce the mass flux in the system. Detailed flow, thermal and concentration profiles are provided. The simulations show that the Stefan flux dominates the system flow field and the subtle gravitational effects can be gauged by subtracting this flux from the calculated profiles. Shear flows, due to solutal buoyancy, of the order of 50 microns/s for the liorizont,-d growth orientation and 10 microns/s for the vertical orientation are predicted. Whether these flows can fully account for the observed gravity related growth morphological effects and inhomogeneous solute and dopant distributions is a matter of conjecture. A template for future modeling efforts in this area is suggested which incorporates a mathematical approach to the tracking of the growth front based on energy of formation concepts.
Crystal growth from the vapor phase has various advantages over melt growth. The main advantage is from a lower processing temperature which makes the process more amenable in instances where the melting temperature of the crystal is high. Other benefits stem from the inherent purification mechanism in the process due to differences in the vapor pressures of the native elements and impurities, and the enhanced interfacial morphological stability during the growth process. Further, the implementation of PVT growth in closed ampoules affords experimental simplicity with minimal needs for complex process control which makes it an ideal candidate for space investigations in systems where gravity tends to have undesirable effects on the growth process. Bulk growth of wide band gap II-VI semiconductors by physical vapor transport has been developed and refined over the past several years at NASA MSFC. Results from a modeling study of PVT crystal growth of ZnSe are reported in this paper. The PVT process is numerically investigated using both two-dimensional and fully three-dimensional formulation of the governing equations and associated boundary conditions. Both the incompressible Boussinesq approximation and the compressible model are tested to determine the influence of gravity on the process and to discern the differences between the two approaches. The influence of a residual gas is included in the models. The results show that both the incompressible and compressible approximations provide comparable results and the presence of a residual gas tends to measurably reduce the mass flux in the system. Detailed flow, thermal and concentration profiles will be provided in the final manuscript along with computed heat and mass transfer rates. Comparisons with the 1-D model will also be provided. The effect of gravity on the process from numerical computations shows subtle effects although experimental evidence from vertically and horizontally grown samples show dramatic evidence of gravitational effects. The shortcomings of the problem formulation will be discussed and a framework will be provided leading up towards a more comprehensive model of PVT systems.
Crystal growth from the vapor phase has various advantages over melt growth. The main advantage is from a lower processing temperature which makes the process more amenable in instances where the melting temperature of the crystal is high. Other benefits stem from the inherent purification mechanism in the process due to differences in the vapor pressures of the native elements and impurities, and the enhanced interfacial morphological stability during the growth process. Further, the implementation of Physical Vapor Transport (PVT) growth in closed ampoules affords experimental simplicity with minimal needs for complex process control which makes it an ideal candidate for space investigations in systems where gravity tends to have undesirable effects on the growth process. Bulk growth of wide band gap II-VI semiconductors by physical vapor transport has been developed and refined over the past several years at NASA MSFC. Results from a modeling study of PVT crystal growth of ZnSe arc reported in this paper. The PVI process is numerically investigated using both two-dimensional and fully three-dimensional formulation of the governing equations and associated boundary conditions. Both the incompressible Boussinesq approximation and the compressible model are tested to determine the influence of gravity on the process and to discern the differences between the two approaches. The influence of a residual gas is included in the models. The preliminary results show that both the incompressible and compressible approximations provide comparable results and the presence of a residual gas tends to measurably reduce the mass flux in the system. Detailed flow, thermal and concentration profiles will be provided in the final manuscript along with computed heat and mass transfer rates. Comparisons with the 1-D model will also be provided.
Mosquito Lagoon is a shallow, bar-built estuary located on the east central Florida Coast, primarily within the KSC boundary. The lagoon and watershed cover approximately 327 sq km (79422 acres) .The Lagoon occupies 159 sq km (37853 acres). Water depths average approximately 1m. The lagoon volume is approximately 1.6 x 10(exp 8)cu m. Water quality in Mosquito Lagoon is good. Salinity data typically range between 20 ppt and 35 ppt. The lowest value recorded was 4.5 ppt and the highest value was 37 ppt. Water temperatures fluctuate 2 - 3 C over a 24 h period. Cold front passage can rapidly alter water temperatures by 5 - 10 C or more in a short period of time. The highest temperature was 33.4 C and the lowest temperature was 8.8 C after a winter storm. Dissolved oxygen concentrations ranged from a low of 0.4 mg/l to a high of 15.3 mg/l. Extended periods of measurements below the Florida Department of Environmental Protection criteria of 4.0 mg/l were observed in fall and spring months suggesting high system respiration and oxygen demand. Metals such as antimony, arsenic, molybdenum and mercury were report as below detection limits for all samples. Cadmium, copper, chromium, silver, and zinc were found to be periodically above the Florida Department of Environmental Protection criteria for Class II and Class III surface waters.
Observations of auroral hiss obtained from the Voyager 1 encounter with Jupiter have been reanalyzed. The Jovian auroral hiss was observed near the inner boundary of the warm Io torus and has a low-frequency cutoff caused by propagation near the resonance cone. A simple ray tracing procedure using an offset tilted dipole of the Jovian magnetic field is used to determine possible source locations. The results obtained are consistent with two sources located symmetrically with respect to the centrifugal equator along an L shell (L approximately = 5.59) that is coincident with the boundary between the hot and cold regions of the Io torus and is located just inward of the ribbon feature observed from Earth. The distance of the sources from the centrifugal equator is approximately 0.58 +/- 0.01 R(sub J). Based on the similarity to terrestrial auroral hiss, the Jovian is auroral hiss is believed to be generated by beams of low energy (approximately tens to thousands of eV) electrons. The low-frequency cutoff of the auroral hiss suggests that the electrons are accelerated near the inferred source region, possibly by parallel electric fields similar to those existing in the terrestrial auroral regions. A field-aligned current is inferred to exist at L shells just inward of the plasma ribbon. A possible mechanism for driving this current is discussed.
The problems of sidewall boundary-layer effects in airfoil testing is treated by considering the changes in the flow area due to boundary-layer thinning under the influence of the airfoil flowfield. Using von Karman's momentum integral equation, it is shown that the sidewall boundary-layer thickness in the region of the airfoil can reduce to about half the undisturbed value under the conditions prevailing in testing of supercritical airfoils. A Mach number correction due to this increased width of the flow passage is proposed. Using the small disturbance approximation, the effect of the sidewall boundary-layers is shown to be equivalent to a change in the test Mach number and also in the airfoil thickness. Comparison of the results of this approach with other similarity rules and correlation of the experimental data demonstrate the applicability of the analysis presented from low speeds to transonic speeds.
A theoretical and experimental investigation at subcavitation speeds was made of the effect of the free-water surface and rigid boundaries on the lift and drag of an aspect-ratio-10 hydrofoil at both subcritical and supercritical speeds and of an aspect ratio-4 hydrofoil at supercritical speeds. Approximate theoretical solutions for the effects of the free-water surface and rigid boundaries on drag at subcritical speeds are developed. An approximate theoretical solution for the effects of these boundaries on drag at subcritical speeds is also presented. The agreement between theory and experiment at both supercritical and subcritical speeds is satisfactory for engineering calculations of hydrofoil characteristics from aerodynamic data. The experimental investigation indicated no appreciable effect of the limiting speed of wave propagation on lift-curve slope or angle of zero lift. It also showed that the increase in drag as the critical speed is approached from the supercritical range is gradual. The result is contrary to the abrupt increase at the critical speed predicted by theory.
A one-way wave equation is a partial differential which, in some approximate sense, behaves like the wave equation in one direction but permits no propagation in the opposite one. The construction of such equations can be reduced to the approximation of the square root of (1-s sup 2) on -1, 1 by a rational function r(s) = p sub m (s)/q sub n(s). Those rational functions r for which the corresponding one-way wave equation is well-posed are characterized both as a partial differential equation and as an absorbing boundary condition for the wave equation. We find that if r(s) interpolates the square root of (1-s sup 2) at sufficiently many points in (-1,1), then well-posedness is assured. It follows that absorbing boundary conditions based on Pade approximation are well-posed if and only if (m, n) lies in one of two distinct diagonals in the Pade table, the two proposed by Engquist and Majda. Analogous results also hold for one-way wave equations derived from Chebyshev or least-squares approximation.
A two-part study of the buckling and postbuckling of laminated anisotropic plates with bending-extensional coupling is presented. The first part involves the development and application of a modified Rayleigh-Ritz analysis technique. Modifications made to the classical technique can be grouped into three areas. First, known symmetries of anisotropic panels are exploited in the selection of approximation functions. Second, a reduced basis technique based on these same symmetries is applied in the linear range. Finally, geometric boundary conditions are enforced via an exterior penalty function approach, rather than relying on choice of approximation functions to satisfy these boundary conditions. Numerical results are presented for both the linear and nonlinear range, with additional studies made to determine the effect of variation in penalty parameter and number of basis vectors. In the second part, six panels possessing anisotropy and bending-extensional coupling are tested. Detailed comparisons are made between experiment and finite element results in order to gain insight into the postbuckling and failure characteristics of such panels. The panels are constructed using two different lamination sequences, and panels with three different aspect ratios were constructed for each lamination sequence.
The study concerns the influence of the three-dimensional cross flows on the compressible turbulent boundary layer development and flow separation prediction around V/STOL engine inlets at high incidence. The governing equations for the three-dimensional boundary layer flow with small-cross approximation are solved numerically on an intrinsic streamline coordinate system. Results are presented to illustrate the effects of small cross-flow, compressibility and streamline curvatures on the flow. Comparisons of the results with the wind tunnel data for scaled model and with data obtained from another existing compressible axisymmetric turbulent boundary layer scheme are included in the analysis.