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NASA NTRS1996

Multigrid Techniques for Highly Indefinite Equations

A multigrid method for the solution of finite difference approximations of elliptic PDE's is introduced. A parallelizable version of it, suitable for two and multi level analysis, is also defined, and serves as a theoretical tool for deriving a suitable implementation for the main version. For indefinite Helmholtz equations, this analysis provides a suitable mesh size for the coarsest grid used. Numerical experiments show that the method is applicable to diffusion equations with discontinuous coefficients and highly indefinite Helmholtz equations.

Shapira, Yair↗

NASA NTRS2000

A Two Colorable Fourth Order Compact Difference Scheme and Parallel Iterative Solution of the 3D Convection Diffusion Equation

A new fourth order compact difference scheme for the three dimensional convection diffusion equation with variable coefficients is presented. The novelty of this new difference scheme is that it Only requires 15 grid points and that it can be decoupled with two colors. The entire computational grid can be updated in two parallel subsweeps with the Gauss-Seidel type iterative method. This is compared with the known 19 point fourth order compact differenCe scheme which requires four colors to decouple the computational grid. Numerical results, with multigrid methods implemented on a shared memory parallel computer, are presented to compare the 15 point and the 19 point fourth order compact schemes.

Zhang, Jun↗

NASA NTRS2011

A Maximum Likelihood Approach to Determine Sensor Radiometric Response Coefficients for NPP VIIRS Reflective Solar Bands

Optical sensors aboard Earth orbiting satellites such as the next generation Visible/Infrared Imager/Radiometer Suite (VIIRS) assume that the sensors radiometric response in the Reflective Solar Bands (RSB) is described by a quadratic polynomial, in relating the aperture spectral radiance to the sensor Digital Number (DN) readout. For VIIRS Flight Unit 1, the coefficients are to be determined before launch by an attenuation method, although the linear coefficient will be further determined on-orbit through observing the Solar Diffuser. In determining the quadratic polynomial coefficients by the attenuation method, a Maximum Likelihood approach is applied in carrying out the least-squares procedure. Crucial to the Maximum Likelihood least-squares procedure is the computation of the weight. The weight not only has a contribution from the noise of the sensor s digital count, with an important contribution from digitization error, but also is affected heavily by the mathematical expression used to predict the value of the dependent variable, because both the independent and the dependent variables contain random noise. In addition, model errors have a major impact on the uncertainties of the coefficients. The Maximum Likelihood approach demonstrates the inadequacy of the attenuation method model with a quadratic polynomial for the retrieved spectral radiance. We show that using the inadequate model dramatically increases the uncertainties of the coefficients. We compute the coefficient values and their uncertainties, considering both measurement and model errors.

Lei, Ning↗

NASA NTRS2015

An Update to the NASA Reference Solar Sail Thrust Model

An optical model of solar sail material originally derived at JPL in 1978 has since served as the de facto standard for NASA and other solar sail researchers. The optical model includes terms for specular and diffuse reflection, thermal emission, and non-Lambertian diffuse reflection. The standard coefficients for these terms are based on tests of 2.5 micrometer Kapton sail material coated with 100 nm of aluminum on the front side and chromium on the back side. The original derivation of these coefficients was documented in an internal JPL technical memorandum that is no longer available. Additionally more recent optical testing has taken place and different materials have been used or are under consideration by various researchers for solar sails. Here, where possible, we re-derive the optical coefficients from the 1978 model and update them to accommodate newer test results and sail material. The source of the commonly used value for the front side non-Lambertian coefficient is not clear, so we investigate that coefficient in detail. Although this research is primarily designed to support the upcoming NASA NEA Scout and Lunar Flashlight solar sail missions, the results are also of interest to the wider solar sail community.

Heaton, Andrew F.↗

NASA NTRS1990

Experimental investigation of rotor-stator interaction in a centrifugal pump with several vaned diffusers

Steady and unsteady diffuser vane pressure measurements have been conducted with a two-dimensional test impeller, in an experimental investigation of rotor-stator interaction within a centrifugal pump having several vaned diffusers, under conditions of different flow coefficients and different radial gaps between the impeller blade trailing edge and the diffuser vane leading edge. The largest pressure fluctuations on the diffuser vanes and the impeller blades were found to be of the same order of magnitude as the total pressure rise across the pump. Increasing the number of diffuser vanes was found to result in a significant decrease of impeller blade pressure fluctuations.

Arndt, N.↗

NASA NTRS1990

Modeling of the SiC chemical vapor deposition process and comparison with experimental results

A model of the NASA Lewis SiC CVD process is described, and the results presented. A key feature of the model is the direct coupling of gas-phase chemical kinetics with diffusion. A deposition chemistry model using reactive sticking coefficients for each gas-phase species provides the diffusion boundary conditions. SiC deposition rates predicted by the model agree reasonably well with experimentally observed rates.

Annen, K. D.↗

NASA NTRS1943

Experimental Investigation of a Model of a Two-Stage Turboblower

In the present paper an investigation is made of two stages of a multistage turboblower having a vaneless diffuser behind the impeller and guide vanes at the inlet to the nest stage. The method employed was that of investigating the performance of the successive elements of the blower (the impeller, vaneless diffuser, ets.) whereby the kinematics of the flow through the blower could be followed and the pressure at the different points computed. The character of the flow and the physical significance of the loss coefficients could thereby be determined so as to secure the best agreement of the computed with the actual performance of the blower. Since the tests were carried out for various delivery volumes, the dependence of the coefficients on a number of factors (angle of attack, velocities, etc.) could be obtained. The distribution of the losses that occur during the transformation of dynamic pressure at the impeller exit into static pressure could be found and likewise the range within which the friction coefficient varies in the vaneless diffuser. With the aid of factors having a certain physical significance, the centrifugal blower could be computed on the basis of a more or less schematical consideration of the phenomena occuring during the air flow through it, and the use of arbitrary factors and recourse to the geometrical similtude law thus avoided. The present investigation largely summarizes all the previous work af the CHI Blower Section on the different elements of a centrifugal blower. Some considerations on the analysis of model test data for application to full-scale are presented in the appendix.

Dovjik, s.↗

NASA NTRS1993

The telegraph equation in charged particle transport

We present a new derivation of the telegraph equation which modifies its coefficients. First, an infinite order partial differential equation is obtained for the velocity space solid angle-averaged phase-space distribution of particles which underwent at least a few collisions. It is shown that, in the lowest order asymptotic expansion, this equation simplifies to the well-known diffusion equation. The second-order asymptotic expansion for isotropic small-angle scattering results in a modified telegraph equation with a signal propagation speed of v(5/11) exp 1/2 instead of the usual v/3 exp 1/2. Our derivation of a modified telegraph equation follows from an expansion of the Boltzmann equation in the relevant smallness parameters and not from a truncation of an eigenfunction expansion. This equation is consistent with causality. It is shown that, under steady state conditions in a convecting plasma, the telegraph equation may be regarded as a diffusion equation with a modified transport coefficient, which describes a combination of diffusion and cosmic-ray inertia.

Gombosi, T. I.↗

NASA NTRS2013

Modeling Analysis for NASA GRC Vacuum Facility 5 Upgrade

A model of the VF5 test facility at NASA Glenn Research Center was developed using the direct simulation Monte Carlo Hypersonic Aerothermodynamics Particle (HAP) code. The model results were compared to several cold flow and thruster hot fire cases. The main uncertainty in the model is the determination of the effective sticking coefficient -- which sets the pumping effectiveness of the cryopanels and oil diffusion pumps including baffle transmission. An effective sticking coefficient of 0.25 was found to provide generally good agreement with the experimental chamber pressure data. The model, which assumes a cold diffuse inflow, also fared satisfactorily in predicting the pressure distribution during thruster operation. The model was used to assess other chamber configurations to improve the local effective pumping speed near the thruster. A new configuration of the existing cryopumps is found to show more than 2x improvement over the current baseline configuration.

cryopumping↗

NASA NTRS1988

Venus - Surface electromagnetic properties

Pioneer Venus high-angle radar imaging data are used here to correct values of the specular power reflection coefficient for the effects of diffusely scattering small-scale surface roughness. A value of 5.0 + or - 0.9 is found for the average dielectric permittivity of the rolling plains and lowlands, suggesting that most of the Venus surface is overlain by at most only a few cm of soil or dust. The unexpectedly high values of power reflection coefficient are confirmed by observations of correspondingly low values of radiothermal emission. Thus there can be little doubt that most of the highlands contain significant amounts of a conducting mineral near the surface.

Pettengill, Gordon H.↗

NASA NTRS1996

Design, Construction and Testing of Annular Diffusers for High Speed Civil Transportation Combustor Applications

A theoretical and an experimental design study of subsonic flow through curved-wall annular diffusers has been initiated under this award in order to establish the most pertinent design parameters and hence performance characteristics for such devices, an the implications of their application in the design of engine components in the aerospace industries. The diffusers under this study are expected to contain appreciable regions of stall and the effects of swirl on their performance are being studied. The experimental work involves the application of Computer Aided Design software tool to the development of a suitable annular diffuse geometry and the subsequent downloading of such data to a CNC machine at Central State University (CSU). Two experimental run segments have been completed so far during FY-95 involving flow visualization and diffuser performance evaluation based on Kinetic Energy Dissipation. The method of calculation of the performance of diffusers based on pressure recovery coefficient has been shown to have some shortcomings and so the kinetic energy dissipation approach has been introduced in the run segment two with some success. The application of the discretized, full Navier Stokes and Continuity equations to the numerical study of the problem described above for the time-mean flow is expected to follow. Various models of turbulence are being evaluated for adoption throughout the study and comparisons would be made with experimental data where they exist. Assessment of diffuser performance based on the dissipated mechanical energy would also be made. The result of the investigations are expected to indicate that more cost effective component design of such devices as diffusers which normally contain complex flows can still be achieved.

Okhio, Cyril B.↗

NASA NTRS1981

Effects of free-stream turbulence on diffuser performance

An experimental evaluation of the effects of free-stream turbulence on the performance of a subsonic two-dimensional diffuser has been made. Increases of the diffuser's static pressure recovery coefficient of 11.3 and 23.9 percent at total included divergence angles of 12 and 20 degrees respectively were obtained when the value of the inlet integral free-stream scale of turbulence in the flow direction was at least 7.2 times larger than the inlet boundary layer displacement thickness, when the inlet total free-stream turbulence intensity was at least 3.5 percent, and when the axes of upstream rods used to generate turbulence were perpendicular to the flow and parallel to the diverging walls of the diffuser. It is hypothesized that a larger scale of turbulence with the specified eddy axis orientation transmits the free-stream energy to the walls more effectively and, when coupled with large turbulence intensities, are mechanisms which act to decrease the distortion and delay separation within the diffuser.

Hoffmann, J. A.↗

NASA NTRS1980

Effects of free-stream turbulence on diffuser performance

An experimental evaluation of the effects of free stream turbulence on the performance of a subsonic two dimensional diffuser was made. The diffuser's static pressure recovery coefficient was increased 11.4 and 21.1 percent at total. Divergence angles of 12 and 20 degrees respectively were obtained when the value of the inlet integral free stream scale of turbulence in the flow direction was at least 7.5 times larger than the inlet boundary layer displacement thickness, and when the inlet total free stream turbulence intensity was at least 3.5 percent. It is hypothesized that a larger scale of turbulence transmits the free stream energy to the wall more effectively and when coupled with large turbulence intensities, acts to decrease the distortion and delay separation within the diffuser.

Hoffmann, J. A.↗

NASA NTRS1987

Experimental evaluation of two turning vane designs for fan drive corner of 0.1-scale model of NASA Lewis Research Center's proposed altitude wind tunnel

Two turning vane designs were experimentally evaluated for corner 2 of a 0.1 scale model of the NASA Lewis Research Center's proposed Altitude Wind Tunnel (AWT). Corner 2 contained a simulated shaft fairing for a fan drive system to be located downstream of the corner. The corner was tested with a bellmouth inlet followed by a 0.1 scale model of the crossleg diffuser designed to connect corners 1 and 2 of the AWT. Vane A was a controlled-diffusion airfoil shape; vane B was a circular-arc airfoil shape. The A vanes were tested in several arrangements which included the resetting of the vane angle by -5 degrees or the removal of the outer vane. The lowest total pressure loss for vane A configuration was obtained at the negative reset angle. The loss coefficient increased slightly with the Mach number, ranging from 0.165 to 0.175 with a loss coefficient of 0.170 at the inlet design Mach number of 0.24. Removal of the outer vane did not alter the loss. Vane B loss coefficients were essentially the same as those for the reset vane A configurations. The crossleg diffuser loss coefficient was 0.018 at the inlet design Mach number of 0.33.

Boldman, Donald R.↗

NASA NTRS1975

Analysis of liquid rocket combustion chamber turbulence levels from diffusion data

The intensity of turbulence and the Lagrangian correlation coefficient in a liquid-rocket combustion chamber have been analytically determined from an analysis of experimental diffusion data obtained in a small rocket engine which operated at 300-psia chamber pressure and produced approximately 250 pounds thrust. Results of gas-sample measurements obtained by Orsat and gas-chromatograph techniques to determine helium-concentration profiles were analyzed on the basis of Taylor's (1921) turbulent diffusion theory to obtain turbulence flow-field parameters. The results of the analysis indicate that turbulent diffusion in a combustion chamber can be adequately modeled by the one-dimensional Taylor theory, which assumes that the intensity of turbulence is a function only of axial distance in the chamber and that the Lagrangian correlation coefficient is expressed by a power law. The results indicate a higher intensity of turbulence and lower correlation than previously expected.

Smith, L. O., Jr.↗

NASA NTRS1972

Investigation of bubbles in arterial heat pipes

The behavior of gas occlusions in arterial heat pipes has been studied experimentally and theoretically. Specifically, the gas-liquid system properties, solubility and diffusivity, have been measured from -50 to 100 C for helium and argon in ammonia, Freon-21 (CHC12F), and methanol. Properties values obtained were then used to experimentally test models for gas venting from a heat pipe artery under isothermal conditions (i.e., no-heat flow), although the models, as developed, are also applicable to heat pipes operated at power, with some minor modifications. Preliminary calculations indicated arterial bubbles in a stagnant pipe require from minutes to days to collapse and vent. It has been found experimentally that a gas bubble entrapped within an artery structure has a very long lifetime in many credible situations. This lifetime has an approximately inverse exponential dependence on temperature, and is generally considerably longer for helium than for argon. The models postulated for venting under static conditions were in general quantitative agreement with experimental data. Factors of primary importance in governing bubble stability are artery diameter, artery wall thickness, noncondensible gas partial pressure, and the property group (the Ostwald solubility coefficient multiplied by the gas/liquid diffusivity).

Saaski, E. W.↗

NASA NTRS1972

Thermal conductivity of earth materials at high temperatures.

The total thermal conductivity (lattice plus radiative) of several important earth materials is measured in the temperature range from 500 to 1900 K. A new technique is used in which a CO2 laser generates a low-frequency temperature wave at one face of a small disk-shaped sample, and an infrared detector views the opposite face to detect the phase of the emerging radiation. Phase data at several frequencies yield the simultaneous determination of the thermal diffusivity and the mean extinction coefficient of the material. The lattice, radiative, and total thermal conductivities are then calculated. Results for single-crystal and polycrystalline forsterite-rich olivines and an enstatite indicate that, even in relatively pure large-grained material, the radiative conductivity does not increase rapidly with temperature. The predicted maximum total thermal conductivity at a depth of 400 km in an olivine mantle is 0.020 cal/cm/sec/deg C, which is less than twice the surface value.

Schatz, J. F.↗

NASA NTRS1983

Inlet free-stream turbulence effects on diffuser performance

The performance of a subsonic two dimensional diffuser was experimentally evaluated as a function of inlet free-stream turbulence parameters. Anisotropic inlet free-stream turbulence with the eddy axis perpendicular to the flow and parallel to the diverging walls of the diffuser appears to be more effective at transmitting energy to the diverging walls of the diffuser, thereby improving diffuser performance, as compared to isotropic turbulence or anisotropic turbulence with the eddy axis perpendicular to the diverging walls of the diffuser. The pressure recovery of the diffuser was found to be strongly dependent upon the inlet free-stream total turbulence intensity, was independent of eddy size for large eddy dimensions, and was dependent upon eddy size for small eddy dimensions. The improvement in the diffuser's static pressure recovery coefficient at a total included divergence angle of 20 deg, compared to the low inlet turbulence case, was found to be as much as 21 times larger than the pressure loss across the turbulence generators.

Hoffman, J. A.↗