Results for “conditional” — Page 92

NASA NTRS1986

The discrete one-sided Lipschitz condition for convex scalar conservation laws

Physical solutions to convex scalar conservation laws satisfy a one-sided Lipschitz condition (OSLC) that enforces both the entropy condition and their variation boundedness. Consistency with this condition is therefore desirable for a numerical scheme and was proved for both the Godunov and the Lax-Friedrichs scheme--also, in a weakened version, for the Roe scheme, all of them being only first order accurate. A new, fully second order scheme is introduced here, which is consistent with the OSLC. The modified equation is considered and shows interesting features. Another second order scheme is then considered and numerical results are discussed.

Brenier, Yann↗

NASA NTRS1987

Numerical study of the effects of boundary conditions on the measurement and calibration of gardon type heat flux sensors

To monitor the high-intensity heat flux conditions that occur in the space shuttle main engine (SSME), it is necessary to use specifically designed heat flux sensors. These sensors, which are of the Gardon-type, are exposed on the measuring face to high-intensity radiative and convective heat fluxes and on the other face to convective cooling. To improve the calibration and measurement accuracy of these gauges, researchers are studing the effect that the thermal boundary conditions have on gauge performance. In particular, they are studying how convective cooling effects the field inside the sensor and the measured heat flux. The first phase of this study involves a numerical study of these effects. Subsequent phases will involve experimental verification. A computer model of the heat transfer around a Garden-type heat flux sensor was developed. Two specific geometries are being considered are: (1) heat flux sensor mounted on a flat-plate; and (2) heat flux sensor mounted at the stagnation point of a circular cylinder. Both of these configurations are representative of the use of heat flux sensors in the components of the SSME. The purpose of the analysis is to obtain a temperature distribution as a function of the boundary conditions.

Krane, M.↗

NASA NTRS1987

Laboratory evaluation and application of microwave absorption properties under simulated conditions for planetary atmospheres

Laboratory measurements were conducted to evaluate properties of atmospheric gases under simulated conditions for the outer planets. A significant addition to this effort was the capability to make such measurements at millimeter wavelengths. Measurements should soon be completed on the millimeter wave absorption from ammonia under Jovian conditions. Also studied will be the feasibility of measuring the microwave and millimeter wave properties of phosphine (PH3) under simulated Jovian conditions. Further analysis and application of the laboratory results to microwave and millimeter wave absorption data for the outer planet, such as Voyager Radio Occultation experiments, will be pursued.

Steffes, Paul G.↗

NASA NTRS1987

High-speed propeller noise predictions - Effects of boundary conditions used in blade loading calculations

The acoustics of an advanced single rotation SR-3 propeller at cruise conditions are studied employing a time-domain approach. The study evaluates the acoustic significance of the differences in blade pressures computed using nonreflecting rather than hard wall boundary conditions in the three-dimensional Euler code solution. The directivities of the harmonics of the blade passing frequency tone and the effects of chordwise loading on tone directivity are examined. The results show that the maximum difference in the computed sound pressure levels due to the use of blade pressure distributions obtained with the nonreflecting rather than the hard wall boundary conditions is about 1.5 dB. The blade passing frequency tone directivity obtained in the present study shows good agreement with jetstar flight data.

Nallasamy, M.↗

NASA NTRS1987

Dynamic optimization problems with bounded terminal conditions

Bounded terminal conditions of nonlinear optimization problems are converted to equality terminal conditions via Valentine's device. In so doing, additional unknown parameters are introduced into the problem. The transformed problems can still be easily solved using the sequential gradient-restoration algorithm (SGRA) via a simple augmentation of the unknown parameter vector pi. Three example problems with bounded terminal conditions are solved to verify this technique.

Lee, A. Y.↗

NASA NTRS1987

A new formulation of electromagnetic wave scattering using an on-surface radiation boundary condition approach

A new formulation of electromagnetic wave scattering by convex, two-dimensional conducting bodies is reported. This formulation, called the on-surface radiation condition (OSRC) approach, is based upon an expansion of the radiation condition applied directly on the surface of a scatterer. It is now shown that application of a suitable radiation condition directly on the surface of a convex conducting scatterer can lead to substantial simplification of the frequency-domain integral equation for the scattered field, which is reduced to just a line integral. For the transverse magnetic case, the integrand is known explicitly. For the transverse electric case, the integrand can be easily constructed by solving an ordinary differential equation around the scatterer surface contour. Examples are provided which show that OSRC yields computed near and far fields which approach the exact results for canonical shapes such as the circular cylinder, square cylinder, and strip. Electrical sizes for the examples are ka = 5 and ka = 10. The new OSRC formulation of scattering may present a useful alternative to present integral equation and uniform high-frequency approaches for convex cylinders larger than ka = 1. Structures with edges or corners can also be analyzed, although more work is needed to incorporate the physics of singular currents at these discontinuities. Convex dielectric structures can also be treated using OSRC.

Kriegsmann, Gregory A.↗

NASA NTRS1987

Euler analysis of the three-dimensional flow field of a high-speed propeller - Boundary condition effects

The results of an investigation of the effects of far field boundary conditions on the solution of the three dimensional Euler equations governing the flow field of a high speed single rotation propeller are presented. The results show that the solutions obtained with the nonreflecting boundary conditions are in good agreement with experimental data. The specification of nonreflecting boundary conditions is effective in reducing the dependence of the solution on the location of the far field boundary. Details of the flow field within the blade passage and the tip vortex are presented. The dependence of the computed power coefficient on the blade passage and the tip vortex are presented. The dependence of the computed power coefficient on the blade setting angle is examined.

Nallasamy, M.↗

NASA NTRS1987

Protostellar formation in rotating interstellar clouds. VI - Nonuniform initial conditions

The collapse and fragmentation of rotating protostellar clouds is explored, starting from nonuniform density and nonuniform rotation initial conditions. Whether binary fragmentation occurs during the first dynamic collapse phase depends strongly on the initial density profile. Exponential clouds are only somewhat more resistant to fragmentation than uniform-density clouds, but power-law clouds do not undergo fragmentation for likely values of a relevant parameter. Because binary fragments start from profiles intermediate between uniform density and exponential clouds, minimum protostellar mass for population I stars should be increased to approximately 0.02 solar mass. The axisymmetric Terey et al. (1984) model should be stable with respect to nonaxisymmetric perturbations. Considering the observed binary frequency, collapse from power-law initial conditions appears to be less common than collapse from more uniform initial conditions.

Boss, Alan P.↗

NASA NTRS1987

Free-edge delamination: Laminate width and loading conditions effects

The width and loading conditions effects on free-edge stress fields in composite laminates are investigated using a three-dimensional finite element analysis. This analysis includes a special free-edge region refinement or superelement with progrssive substructuring (mesh refinement) and finite thickness interply layers. The different loading conditions include in-plane and out-of-plane bending, combined axial tension and in-plane shear, twisting, uniform temperature and uniform moisture. Results obtained indicate that: axial tension causes the smallest magnitude of interlaminar free edge stress compared to other loading conditions; free-edge delamination data obtained from laboratory specimens cannot be scaled to structural components; and composite structural components are not likely to delaminate.

Murthy, P. L. N.↗

NASA NTRS1987

High speed propeller performance and noise predictions at takeoff/landing conditions

The performance and noise of a high speed SR-7A model propeller under takeoff/landing conditions are considered. The blade loading distributions are obtained by solving the three-dimensional Euler equations and the sound pressure levels are computed using a time domain approach. At the nominal takeoff operating point, the blade sections near the hub are lightly or negatively loaded. The chordwise loading distributions are distinctly different from those of cruise conditions. The noise of the SR-7A model propeller at takeoff is dominated by the loading noise, similar to that at cruise conditions. The waveforms of the acoustic pressure signature are nearly sinusoidal in the plane of the propeller. The computed directivity of the blade passing frequency tone agrees fairly well with the data at nominal takeoff blade angle.

Nallasamy, M.↗

NASA NTRS1988

Noise of a model counterrotation propeller with reduced aft rotor diameter at simulated takeoff/approach conditions (F7/A3)

A model high-speed advanced counterrotation propeller, F7/A3, was tested in the NASA Lewis Research Center 9 by 15 foot Anechoic Wind Tunnel at simulated takeoff/approach conditions of 0.2 Mach number. Acoustic measurements were taken with an axially translating microphone probe, and with a polar microphone probe which was fixed to the propeller nacelle and could take both sideline and circumferential acoustic surveys. Aerodynamic measurements were also made to establish propeller operating conditions. The propeller was run at two setting angles (front angle/rear angle) of 36.4/43.5 and 41.1/46.4 degrees, forward rotor tip speeds from 165 to 259 m/sec, rotor spacings from 8.48 to 14.99 cm based on pitch change axis separation, and angles of attack to 16 degrees. The aft rotor diameter was 85 percent of the forward rotor diameter to reduce tip vortex-aft rotor interaction as a major interaction noise source. Results are compared with equal diameter F7/A7 data which was previously obtained under similar operating conditions. The aft rotor-alone tone was 7 dB lower for the reduced diameter aft rotor, due to reduced tip speed at constant rpm. Interaction tone levels for the F7/A3 propeller were higher at minimum row spacing and lower at maximum spacing.

Woodward, Richard P.↗

NASA NTRS1988

Aircraft and ground vehicle friction correlation test results obtained under winter runway conditions during joint FAA/NASA Runway Friction Program

Aircraft and ground vehicle friction data collected during the Joint FAA/NASA Runway Friction Program under winter runway conditions are discussed and test results are summarized. The relationship between the different ground vehicle friction measurements obtained on compacted snow- and ice-covered conditions is defined together with the correlation to aircraft tire friction performance under similar runway conditions.

Yager, Thomas J.↗

NASA NTRS1988

Liquid sprays and flow studies in the direct-injection diesel engine under motored conditions

A two dimensional, implicit finite difference method of the control volume variety, a two equation model of turbulence, and a discrete droplet model were used to study the flow field, turbulence levels, fuel penetration, vaporization, and mixing in diesel engine environments. The model was also used to study the effects of engine speed, injection angle, spray cone angle, droplet distribution, and intake swirl angle on the flow field, spray penetration and vaporization, and turbulence in motored two-stroke diesel engines. It is shown that there are optimum conditions for injection, which depend on droplet distribution, swirl, spray cone angle, and injection angle. The optimum conditions result in good spray penetration and vaporization and in good fuel mixing. The calculation presented clearly indicates that internal combustion engine models can be used to assess, at least qualitatively, the effects of injection characteristics and engine operating conditions on the flow field and on the spray penetration and vaporization in diesel engines.

Nguyen, Hung Lee↗

NASA NTRS1988

Noise of a model counterrotation propeller with reduced aft rotor diameter at simulated takeoff/approach conditions (F7/A3)

A model high-speed advanced counterrotation propeller, F7/A3, was tested in the NASA Lewis Research Center 9 by 15 foot Anechoic Wind Tunnel at simulated takeoff/approach conditions of 0.2 Mach number. Acoustic measurements were taken with an axially translating microphone probe, and with a polar microphone probe which was fixed to the propeller nacelle and could take both sideline and circumferential acoustic surveys. Aerodynamic measurements were also made to establish propeller operating conditions. The propeller was run at two setting angles (front angle/rear angle) of 36.4/43.5 and 41.1/46.4 degrees, forward rotor tip speeds from 165 to 259 m/sec, rotor spacings from 8.48 to 14.99 cm based on pitch change axis separation, and angles of attack to 16 degrees. The aft rotor diameter was 85 percent of the forward rotor diameter to reduce tip vortex-aft rotor interaction as a major interaction noise source. Results are compared with equal diameter F7/A7 data which was previously obtained under similar operating conditions. The aft rotor-alone tone was 7 dB lower for the reduced diameter aft rotor, due to reduced tip speed at constant rpm. Interaction tone levels for the F7/A3 propeller were higher at minimum row spacing and lower at maximum spacing.

Woodward, Richard P.↗

NASA NTRS1988

High speed propeller performance and noise predictions at takeoff/landing conditions

The performance and noise of a high speed SR-7A model propeller under takeoff/landing conditions are considered. The blade loading distributions are obtained by solving the three-dimensional Euler equations and the sound pressure levels are computed using a time domain approach. At the nominal takeoff operating point, the blade sections near the hub are lightly or negatively loaded. The chordwise loading distributions are distinctly different from those of cruise conditions. The noise of the SR-7A model propeller at takeoff is dominated by the loading noise, similar to that at cruise conditions. The waveforms of the acoustic pressure signature are nearly sinusoidal in the plane of the propeller. The computed directivity of the blade passing frequency tone agrees fairly well with the data at nominal takeoff blade angle.

Nallasamy, M.↗

NASA NTRS1988

Latitudinal electron precipitation patterns during large and small IMF magnitudes for northward IMF conditions

It is demonstrated that there are distinct differences in the electron precipitation patterns (or the polar cap size), geomagnetic activity, and field-aligned currents in the highest-latitude region for small and large IMF B(z) values when the IMF B(z) component is positive. First, during periods of weakly northward IMF, there is a distinct area in the highest-latitude region in which the electron precipitation is absent except for the polar rain. By contrast, during strongly northward IMF, the entire polar region is often filled with burst-type soft electron precipitations. Second, geomagnetic disturbances and field-aligned-current intensities in the highest-latitude region are less during a weak IMF B(z) condition than those during a strongly northward IMF B(z) condition. Geomagnetic activity in the auroral zone for both conditions is absent or very weak.

Makita, K.↗

NASA NTRS1987

Numerical tests of a modified full implicit continuous Eulerian (FICE) scheme with projected normal characteristic boundary conditions for MHD flows

A numerical method has been developed based on a modified full implicit continuous Eulerian (FICE) scheme and projected normal characteristic boundary conditions for simulating MHD flows which undergo a long process of evolution. An astrophysical flow is chosen for illustration of this procedure, and numerical tests are made to verify the computational stability and physically realistic solution. Three computational tests have been accomplished; they are tests of solving methods, characteristic boundary condition, and time steps. The tests show that the program from the modified FICE scheme with proper boundary conditions and time steps can be made numerically stable for a time long enough to obtain physically plausible solutions.

Wu, S. T.↗

NASA NTRS1988

Some observations on boundary conditions for numerical conservation laws

Four choices of outflow boundary conditions are considered for numerical conservation laws. All four methods are stable for linear problems, for which examples are presented where either a boundary layer forms or the numerical scheme, together with the boundary condition, is unstable due to the formation of a reflected shock. A simple heuristic argument is presented for determining the suitability of the boundary condition.

Kamowitz, David↗