Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Approximate boundary”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 397 records · Page 22
All sourcesNASA NTRSDOE OSTI
NASA NTRS1993

Free-air and Bouguer gravity anomalies and the Martian crustal dichotomy

Free-air and Bouguer gravity anomalies from a 50x50 field, derived from re-analysis of Viking Orbiter and Mariner 9 tracking data and using a 50x50 expansion of the current Mars topography and the GSFC degree 50 geoid as the equipotential reference surface, with the Martian crustal dichotomy are compared. The spherical harmonic topography used has zero mean elevation, and differs from the USGS maps by about 2 km. In this field the dichotomy boundary in eastern Mars lies mostly at -1 to -2 km elevation. Bouguer gravity anomalies are shown on a map of Noachian, Hesperian, and Amazonian age terrains, simplified from current geologic maps. The map is centered at 300 deg W to show the continuity of the dichotomy boundary. Contour interval is 100 mgals. Gravity and topography were compared along approximately 40 profiles oriented parallel to the dichotomy boundary topographic gradient, to determine how the geophysical character of the boundary changes along its length and what this implies for its origin and development.

Frey, Herbert↗
NASA NTRS1989

Inception length to a fully-developed fin-generated shock wave boundary-layer interaction

An experimental study of fin-generated shock wave turbulent boundary-layer interactions confirmed previous observations that, sufficiently far from the fin apex, such interactions become conical. The inception length to conical symmetry was found to increase weakly with Mach number for Mach numbers from 2.5 to 4 and fin angles from 4 to 22 deg. For the range of interactions examined, the inception length was found to depend primarily upon the inviscid shock angle, this angle ranging from 21 to 40 deg. The behavior of the inception length with shock angle can be broadly divided into two categories. For 'weak' interactions with shock angles less than about 35 deg, the inception length decreased as the shock angle increased. For 'strong' interactions with shock angles greater than about 35 deg, the inception region was small and was approximately constant at three boundary-layer thicknesses in length. In the latter, strong interaction case, the inception length was an order of magnitude smaller than that found in the weakest interactions examined, to the extent that strong interactions were practically fully-developed from the apex.

Lu, Frank K.↗
NASA NTRS1992

Ruthenium/Iridium Ratios in the Cretaceous-tertiary Boundary Clay: Implications for Global Dispersal and Fractionation Within the Ejecta Cloud

Ruthenium (Ru) and iridium (Ir) are the least mobile platinum group elements (PGE's) within the Cretaceous-Tertiary (K-T) boundary clay (BC). The Ru/Ir ratio is, therefore, the most useful PGE interelement ratio for distinguishing terrestrial and extraterrestrial contributions to the BC. The Ru/Ir ratio of marine K-T sections (1.77 +/- 0.53) is statistically different from that of the continental sections (0.93 +/- 0.28). The marine Ru/Ir ratios are chondritic (C1 = 1.48 +/- 0.09), but the continental ratios are not. We discovered an inverse correlation of shocked quartz size (or distance from the impact site) and Ru/Ir ratio. This correlation may arise from the difference in Ru and Ir vaporization temperature and/or fractionation during condensation from the ejecta cloud. Postsedimentary alteration, remobilization, or terrestrial PGE input may be responsible for the Ru/Ir ratio variations within the groups of marine and continental sites studied. The marine ratios could also be attained if approximately 15 percent of the boundary metals were contributed by Deccan Trap emissions. However, volcanic emissions could not have been the principal source of the PGE's in the BC because mantle PGE ratios and abundances are inconsistent with those measured in the clay. The Ru/Ir values for pristine Tertiary mantle xenoliths (2.6 +/- 0.48), picrites (4.1 +/- 1.8), and Deccan Trap basalt (3.42 +/- 1.96) are all statistically distinct from those measured in the K-T BC.

Evans, Noreen Joyce↗
NASA NTRS1959

Experimental Investigation of the Pressure Rise Required for the Incipient Separation of Turbulent Boundary Layers in Two-Dimensional Supersonic Flow

An experimental investigation has been made of turbulent boundary-layer separation associated with compression corners, curved surfaces of various radii, and incident shock waves. The purpose of the investigation was to provide design information, and to define significant physical trends, which would aid in the prediction of turbulent separation for various aerodynamic devices, such as compressor blades, flaps, spoilers, and diffusers. A characteristic change in the longitudinal static-pressure distribution (i.e., a change from a curve with one inflection point to a curve with three inflection points) was employed to detect the occurrence of separation. The effects of Reynolds number (10(exp 6) to 10(exp 7) per foot or l.5 x 10(exp 4) to 7.5 x 10(exp 4) based upon boundary-layer thickness) and Mach number (1.6 to 4.2) on the onset of turbulent boundary-layer separation were investigated. The pressure gradient of the boundary-layer flow ahead of the interaction region was essentially zero. The results show a considerable effect of Mach number on the pressure rise for incipient separation for all configurations. For a curved-surface model, the static pressure-rise ratio required to cause separation varied from about 2.5, at a Mach number of 2 to about 16, at a Mach number of 3.5. A substantial effect of Reynolds number on the pressure rise for incipient separation was observed in the upper Mach number range and in the lower Reynolds number range; namely, the pressure rise required for separation decreased with increasing Reynolds number. For low Mach numbers and high Reynolds numbers, there appeared to be no Reynolds number effect. The effects of Mach number and of Reynolds number were similar for all models. Model shape was also found to be an important variable affecting the onset of separation. Large gains were realized in the pressure-rise ratio with no separation when the radius of curvature of the model surface was increased. At a Mach number of 3.4, for instance, the pressure-rise ratio with no separation increased from about 5 to 15 as a result of an increase in the radius of curvature from approximately 0 to 30 boundary-layer thicknesses.

Kuehn, Donald M.↗
NASA NTRS1983

Numerical methods for stiff systems of two-point boundary value problems

Numerical procedures are developed for constructing asymptotic solutions of certain nonlinear singularly perturbed vector two-point boundary value problems having boundary layers at one or both endpoints. The asymptotic approximations are generated numerically and can either be used as is or to furnish a general purpose two-point boundary value code with an initial approximation and the nonuniform computational mesh needed for such problems. The procedures are applied to a model problem that has multiple solutions and to problems describing the deformation of thin nonlinear elastic beam that is resting on an elastic foundation.

Flaherty, J. E.↗
NASA NTRS1994

Cusp/cleft auroral activity in relation to solar wind dynamic pressure, interplanetary magnetic field B(sub z) and B(sub y)

Continuous optical observations of cusp/cleft auroral activities within approximately equal to 09-15 MLT and 70-76 deg magnetic latitude are studied in relation to changes in solar wind dynamic pressure and interplanetary magnetic field (IMF) variability. The observed latitudinal movements of the cusp/cleft aurora in response to IMF B(sub z) changes may be explained as an effect of a variable magnetic field intensity in the outer dayside magnetosphere associated with the changing intensity of region 1 field-aligned currents and associated closure currents. Ground magnetic signatures related to such currents were observed in the present case (January 10, 1993). Strong, isolated enhancements in solar wind dynamic pressure (Delta p/p is greater than or equal to 0.5) gave rise to equatorward shifts of the cusp/cleft aurora, characteristic auroral transients, and distinct ground magnetic signatures of enhanced convection at cleft latitudes. A sequence of auroral events of approximately equal to 5-10 min recurrence time, moving eastward along the poleward boundary of the persistent cusp/cleft aurora in the approximately equal to 10-14 MLT sector, during negative IMF B(sub z) and B(sub y) conditions, were found to be correlated with brief pulses in solar wind dynamic pressure (0.1 is less than Delta p/p is less than 0.5). Simultaneous photometer observations from Ny Alesund, Svalbard, and Danmarkshavn, Greenland, show that the events often appeared on the prenoon side (approximately equal to 10-12 MLT), before moving into the postnoon sector in the case we study here, when IMF B(sub y) is less than 0. In other cases, similar auroral event sequences have been observed to move westward in the prenoon sector, during intervals of positive B(sub y). Thus a strong prenoon/postnoon asymmetry of event occurence and motion pattern related to the IMF B(sub y) polarity is observed. We find that this category of auroral event sequence is stimulated bursts of electron precipitation that originate from magnetosheath plasma that has accessed that dayside magnetosphere in the noon or near-noon sector, possibly at high latitudes, partly governed by the IMF orientation as well as by solar wind dynamic pressure pulses.

Sandholt, P. E.↗
NASA NTRS1997

Factors Influencing Pitot Probe Centerline Displacement in a Turbulent Supersonic Boundary Layer

When a total pressure probe is used for measuring flows with transverse total pressure gradients, a displacement of the effective center of the probe is observed (designated Delta). While this phenomenon is well documented in incompressible flow and supersonic laminar flow, there is insufficient information concerning supersonic turbulent flow. In this study, three NASA Lewis Research Center Supersonic Wind Tunnels (SWT's) were used to investigate pitot probe centerline displacement in supersonic turbulent boundary layers. The relationship between test conditions and pitot probe centerline displacement error was to be determined. For this investigation, ten circular probes with diameter-to-boundary layer ratios (D/delta) ranging from 0.015 to 0.256 were tested in the 10 ft x 10 ft SWT, the 15 cm x 15 cm SWT, and the 1 ft x 1 ft SWT. Reynolds numbers of 4.27 x 10(exp 6)/m, 6.00 x 10(exp 6)/in, 10.33 x 10(exp 6)/in, and 16.9 x 10(exp 6)/m were tested at nominal Mach numbers of 2.0 and 2.5. Boundary layer thicknesses for the three tunnels were approximately 200 mm, 13 mm, and 30 mm, respectively. Initial results indicate that boundary layer thickness, delta, and probe diameter, D/delta play a minimal role in pitot probe centerline offset error, Delta/D. It appears that the Mach gradient, dM/dy, is an important factor, though the exact relationship has not yet been determined. More data is needed to fill the map before a conclusion can be drawn with any certainty. This research provides valuable supersonic, turbulent boundary layer data from three supersonic wind tunnels with three very different boundary layers. It will prove a valuable stepping stone for future research into the factors influencing pitot probe centerline offset error.

Grosser, Wendy I.↗
NASA NTRS2015

The Effect of Backward-Facing Step Height on Instability Growth and Breakdown in Swept Wing Boundary-Layer Transition

A low-speed experiment was performed on a swept at plate model with an imposed pressure gradient to determine the effect of a backward-facing step on transition in a stationary-cross flow dominated flow. Detailed hot-wire boundary-layer measurements were performed for three backward-facing step heights of approximately 36, 45, and 49% of the boundary-layer thickness at the step. These step heights correspond to a subcritical, nearly-critical, and critical case. Three leading-edge roughness configurations were tested to determine the effect of stationary-cross flow amplitude on transition. The step caused a local increase in amplitude of the stationary cross flow for the two larger step height cases, but farther downstream the amplitude decreased and remained below the baseline amplitude. The smallest step caused a slight local decrease in amplitude of the primary stationary cross flow mode, but the amplitude collapsed back to the baseline case far downstream of the step. The effect of the step on the amplitude of the primary cross flow mode increased with step height, however, the stationary cross flow amplitudes remained low and thus, stationary cross flow was not solely responsible for transition. Unsteady disturbances were present downstream of the step for all three step heights, and the amplitudes increased with increasing step height. The only exception is that the lower frequency (traveling crossflow-like) disturbance was not present in the lowest step height case. Positive and negative spikes in instantaneous velocity began to occur for the two larger step height cases and then grew in number and amplitude downstream of reattachment, eventually leading to transition. The number and amplitude of spikes varied depending on the step height and cross flow amplitude. Despite the low amplitude of the disturbances in the intermediate step height case, breakdown began to occur intermittently and the flow underwent a long transition region.

Eppink, Jenna L.↗
NASA NTRS1991

Transformation of two and three-dimensional regions by elliptic systems

A reliable linear system is presented for grid generation in 2-D and 3-D. The method is robust in the sense that convergence is guaranteed but is not as reliable as other nonlinear elliptic methods in generating nonfolding grids. The construction of nonfolding grids depends on having reasonable approximations of cell aspect ratios and an appropriate distribution of grid points on the boundary of the region. Some guidelines are included on approximating the aspect ratios, but little help is offered on setting up the boundary grid other than to say that in 2-D the boundary correspondence should be close to that generated by a conformal mapping. It is assumed that the functions which control the grid distribution depend only on the computational variables and not on the physical variables. Whether this is actually the case depends on how the grid is constructed. In a dynamic adaptive procedure where the grid is constructed in the process of solving a fluid flow problem, the grid is usually updated at fixed iteration counts using the current value of the control function. Since the control function is not being updated during the iteration of the grid equations, the grid construction is a linear procedure. However, in the case of a static adaptive procedure where a trial solution is computed and used to construct an adaptive grid, the control functions may be recomputed at every step of the grid iteration.

Mastin, C. Wayne↗
NASA NTRS1972

Calculation of three-dimensional laminar boundary-layer flows.

Accuracy tests have been made of the approximation, proposed recently by Wang (1971), which reduces the computation of three-dimensional, laminar, compressible, boundary-layer equations to the problem of solving two-dimensional type boundary-layer equations. The tests were made by a comparison of the results achieved using Wang's method with a fully three-dimensional boundary-layer calculation. Results of the comparison are tabulated and are found to be in good agreement.

Fillo, J. A.↗
NASA NTRS1972

Flight-determined characteristics of an air intake system on an F-111A airplane

Flow phenomena of the F-111A air intake system were investigated over a large range of Mach number, altitude, and angle of attack. Boundary-layer variations are shown for the fuselage splitter plate and inlet entrance stations. Inlet performance is shown in terms of pressure recovery, airflow, mass-flow ratio, turbulence factor, distortion factor, and power spectral density. The fuselage boundary layer was found to be not completely removed from the upper portion of the splitter plate at all Mach numbers investigated. Inlet boundary-layer ingestion started at approximately Mach 1.6 near the translating spike and cone. Pressure-recovery distribution at the compressor face showed increasing distortion with increasing angle of attack and increasing Mach number. The time-averaged distortion-factor value approached 1300, which is near the distortion tolerance of the engine at Mach numbers above 2.1.

Hughes, D. L.↗
NASA NTRS1972

Space shuttle: Directional and lateral stability and interference effects of cruise engine location on a 0.015 scale space shuttle

The results are presented that were obtained from a wind tunnel tests to improve space shuttle booster baseline lateral-directional stability, control characteristics, and cruise engine location optimization. Tests were conducted in a 7 x 10-foot transonic wind tunnel. The model employed was a 0.015-scale replica of a space shuttle booster. The three major objectives of this test were to determine the following: (1) force, static stability, and control effectiveness characteristics for varying angles of positive and negative wing dihedral and various combinations of wing tip and centerline dorsal fins; (2) force and static stability characteristics of cruise engines location on the body below the high aerodynamic canard; and (3) control effectiveness for the low-mounted wing configuration. The wing dihedral study was conducted at a cruise Mach number of 0.40 and simulated altitude of 10,000 feet. Portions of the test were conducted to determine the control surfaces stability and control characteristics over the Mach number range of 0.4 to 1.2. The aerodynamic characteristics determined are based on a unit Reynolds number of approximately 2 million per foot. Boundary layer trip strips were employed to induce boundary layer transition.

Buchholz, R. E.↗
NASA NTRS1973

Current distribution on an infinite tubular antenna immersed in a cold collisional magnetoplasma.

Based upon a boundary-value formulation, a new approximate expression is derived for the total axial current on an infinite antenna immersed in an unbounded, cold, collisional magnetoplasma with a dc magnetic field oriented parallel to the antenna. Numerical results are presented for the current distributions over plasma parameters corresponding to each of the eight regions of the Clemmow-Mullaly-Allis diagram and for different values of the collision frequency.

Bhat, B.↗
NASA NTRS1972

Sweep effect on the drag of rows of perpendicular circular cylinders in a laminar boundary layer at supersonic free-stream velocities

Drag measurements were obtained for circular cylinders attached perpendicularly to a flat-plate surface. Measurements were obtained for a single cylinder and for rows of cylinders. The cylinders were alined at various sweep angles relative to the free-stream velocity vector and at spacings appropriate for roughness elements used as boundary layer trips. The drag measurements were obtained for Mach numbers of 3.95 and 4.60, ratios of cylinder height to an undisturbed laminar boundary layer displacement thickness of approximately 1.0 to 3.0, a cylinder height-to-diameter ratio of approximately 2, and sweep angles up to 60. A complete presentation of the experimental results is given. A discussion of the more significant findings, including the most appropriate parameters for correlating the experimental results, is presented.

Lamb, M.↗
NASA NTRS1974

Nonlinear theory of electron neutralization waves in ions beams with dissipation

An analytical theory of nonlinear neutralization waves generated by injection of electrons from a grid in the direction of a homogeneous ion beam of uniform velocity and infinite extension is presented. The electrons are assumed to interact with the ions through the self-consistent space charge field and by strong collective interactions, while diffusion in the pressure gradient is disregarded (zero-temperature approximation). The associated nonlinear boundary-value problem is solved in closed form by means of a von Mises transformation. It is shown that the electron gas moves into the ion space in the form of a discontinuous neutralization wave, which exhibits a periodic field structure (incomplete neutralization). This periodic wave structure is damped out by intercomponent momentum transfer - i.e., after a few relaxation lengths a quasi-neutral plasma results.

Wilhelm, H. E.↗
NASA NTRS1979

Intensity of tropospheric circulation associated with solar magnetic sector boundary transits

The fractional decrease in the vorticity area index associated with transits past the earth of interplanetary magnetic sector boundaries increase as the value of vorticity used to compute the index increases. This suggests that after the boundary transit there is an approximately uniform reduction in all the values of vorticity that are not less than 0.00020/sec. In low altitudes and large absolute vorticities not less than 0.00020/sec the average change in the vorticity area index approaches 50%.

Wilcox, J. M.↗
NASA NTRS1980

An empirical model of the Venusian outer environment. I - The shape of the dayside solar wind-atmosphere interface. II - The shape and location of the bow shock

Solar wind plasma and magnetic field data and ionospheric data obtained from the Pioneer Venus orbiter are discussed. The variation in the magnetic field pressure within the magnetic barrier is shown to be similar to that expected for the solar wind pressure variations along an obstacle's boundary when a more realistic approximation of the shape of the ionosphere is included. Simultaneous solar wind pressure, ionospheric pressure, and magnetic barrier pressure data reveal that the ionospheric pressure below the ionopause is approximately equal to the solar wind pressure. The magnetic barrier pressure is found to be equal to approximately 2/3 to 3/4 of both the solar wind pressure and the ionospheric pressure. Estimates of the hot plasma pressure contribution to the total pressure in the magnetic barrier vary from 1/4 to 1/3. Just below the ionopause the ionospheric pressure deviations from the mean ionospheric pressure are significant, especially below approximately 400 km; they appear to be indicative of the adjustment of the ionospheric structure to changeing solar wind conditions. A first-order model of the ionopause pressure variations as a function of height and solar-zenith angle is proposed. Venera 9 and Venera 10 bow shock crossings are then analyzed for solar zenith angles in the range from approximately 25 deg to approximately 153 deg. A comparison of Venera 9 and Venera 10 bow shock crossings with those observed by the Pioneer Venus orbiter suggests that both the secular variation and the latitudinal asymmetry may be responsible for the closer shock crossings of the Venera 9 and Venera 10 spacecraft.

Vaisberg, O. L.↗