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Evaluation of Heat Transfer Coefficient from Velocity Distribution in Boundary Layer

This paper describes a method of evaluating heat transfer coefficient from a velocity distribution in the boundary layer. The power law velocity profile and universal velocity distribution in a smooth pipe have been used to evaluate the wall shear stress, and the heat transfer coefficient was evaluated from the wall shear stress using the Chilton-Colburn analogy. The predicted pressure drop was compared with the pressure drop computed by the Colebrook equation, and the predicted heat transfer coefficient was compared with the heat transfer coefficient calculated by the Dittus-Boelter equation. The accuracy of pressure drop prediction was within 1%, and the accuracy of heat transfer coefficient prediction was within 8%. This method has the potential to use a Navier-Stokes based CFD solution to evaluate the heat transfer coefficient in nodal or network flow codes.

Heat Transfer Coefficient

Evaluation of Heat Transfer Coefficient from Velocity Distribution in Boundary Layer

This paper describes a method of evaluating heat transfer coefficient from a velocity distribution in the boundary layer. The power law velocity profile and universal velocity distribution in a smooth pipe have been used to evaluate the wall shear stress, and the heat transfer coefficient was evaluated from the wall shear stress using the Chilton-Colburn analogy. The predicted pressure drop was compared with the pressure drop computed by the Colebrook equation, and the predicted heat transfer coefficient was compared with the heat transfer coefficient calculated by the Dittus-Boelter equation. The accuracy of pressure drop prediction was within 1%, and the accuracy of heat transfer coefficient prediction was within 8%. This method has the potential to use a Navier-Stokes based CFD solution to evaluate the heat transfer coefficient in nodal or network flow codes.

Heat Transfer Coefficient

Electron Velocity Distribution Function in Magnetic Clouds in the Solar Wind

We present a study of the kinetic properties of the electron velocity distribution functions within magnetic clouds, since they are the dominant thermal component. The study is based on high time resolution data from the GSFC WIND/SWE electron spectrometer and the Berkeley 3DP electron plasma instruments. Recent studies on magnetic clouds have shown observational evidence of anti-correlation between the total electron density and electron temperature, which suggest a polytrope law P(sub e) = alpha(Nu(sub e) (sup gamma)) for electrons with the constant gamma approximates 0.5 < 1. This anti-correlation and small polytropic gamma-values is interpreted in the context of the presence of highly non-Maxwellian electron distributions (i.e. non-thermal) within magnetic clouds. These works suggested that the non-thermal electrons can contribute as much as 50% of the total electron pressure within magnetic clouds. We have revisited some of the magnetic cloud events previously studied and attempted to quantify the nature of the non-thermal electrons by modeling the electron velocity distribution function using a kappa distribution function to characterize the kinetic non-thermal effects. If non-thermal tail effects are the source for the anti-correlation between the moment electron temperature and density and if the kappa distribution is a reasonable representative model of non-thermal effects, then the electron velocity distribution within magnetic clouds should show indication for small K-values when gamma < 1.

Nieves-Chinchil, Teresa

Real-time three-dimensional color Doppler echocardiography for characterizing the spatial velocity distribution and quantifying the peak flow rate in the left ventricular outflow tract

Quantification of flow with pulsed-wave Doppler assumes a "flat" velocity profile in the left ventricular outflow tract (LVOT), which observation refutes. Recent development of real-time, three-dimensional (3-D) color Doppler allows one to obtain an entire cross-sectional velocity distribution of the LVOT, which is not possible using conventional 2-D echo. In an animal experiment, the cross-sectional color Doppler images of the LVOT at peak systole were derived and digitally transferred to a computer to visualize and quantify spatial velocity distributions and peak flow rates. Markedly skewed profiles, with higher velocities toward the septum, were consistently observed. Reference peak flow rates by electromagnetic flow meter correlated well with 3-D peak flow rates (r = 0.94), but with an anticipated underestimation. Real-time 3-D color Doppler echocardiography was capable of determining cross-sectional velocity distributions and peak flow rates, demonstrating the utility of this new method for better understanding and quantifying blood flow phenomena.

NASA Discipline Cardiopulmonary

Non-gyrotropic proton and alpha-particle velocity distributions in the solar wind: TAUS observations and stability analysis

Ion velocity distribution functions have been measured with high time resolution by the TAUS plasma instrument on the PHOBOS mission to Mars in 1989. The unambiguous separation of protons and alpha-particles by TAUS enabled us to study the nonthermal features of their distributions separately and to analyze the stability of the distributions against excitation of waves in the cyclotron-frequency domain. Typical nonthermal features include temperature anisotropies, with T(sub perpendicular) larger than T(sub parallel), and ion beam populations drifting along the local magnetic field direction. Also, distinctly non-gyrotropic alpha-particle velocity distributions were sometimes found. Non-gyrotropy strongly changes the wave dispersion and gives rise to new growing modes, related to the coupling of the standard wave modes existing in gyrotropic plasma. It is found that for the measured non-gyrotropic ion distributions the right-hand polarized wave can also be excited by a temperature anistropy instead of the usual beam drift.

Astudillo, H. F.

Auroral ion velocity distributions using a relaxation model.

Calculation of ion velocity distributions for a weakly-ionized plasma subjected to crossed electric and magnetic fields for application to the auroral ionosphere. By replacing the Boltzmann collision integral with a simple relaxation model, an exact solution to Boltzmann's equation could be obtained. This solution has the advantage over a series expansion in that all the higher-order velocity moments are inherent in it. The exact solution is particularly advantageous when studying large departures of the distribution from its Maxwellian form, because these departures are caused by the higher velocity moments. In general, however, a simple relaxation model can only be used to obtain qualitative information on the distribution function. Consequently, it is possible to determine when the higher-order velocity moments affect the ion velocity distribution and the nature of their effect, but it is not possible to obtain accurate quantitative results.

St-Maurice, J.-P.

Validation of MCDS by comparison of predicted with experimental velocity distribution functions in rarefied normal shocks

Velocity distribution functions in normal shock waves in argon and helium are calculated using Monte Carlo direct simulation. These are compared with experimental results for argon at M = 7.18 and for helium at M = 1.59 and 20. For both argon and helium, the variable-hard-sphere (VHS) model is used for the elastic scattering cross section, with the velocity dependence derived from a viscosity-temperature power-law relationship in the way normally used by Bird (1976).

Pham-Van-diep, Gerald C.

Background and Pickup Ion Velocity Distribution Dynamics in Titan's Plasma Environment: 3D Hybrid Simulation and Comparison with CAPS T9 Observations

In this report we discuss the ion velocity distribution dynamics from the 3D hybrid simulation. In our model the background, pickup, and ionospheric ions are considered as a particles, whereas the electrons are described as a fluid. Inhomogeneous photoionization, electron-impact ionization and charge exchange are included in our model. We also take into account the collisions between the ions and neutrals. The current simulation shows that mass loading by pickup ions H(+); H2(+), CH4(+) and N2(+) is stronger than in the previous simulations when O+ ions are introduced into the background plasma. In our hybrid simulations we use Chamberlain profiles for the atmospheric components. We also include a simple ionosphere model with average mass M = 28 amu ions that were generated inside the ionosphere. The moon is considered as a weakly conducting body. Special attention will be paid to comparing the simulated pickup ion velocity distribution with CAPS T9 observations. Our simulation shows an asymmetry of the ion density distribution and the magnetic field, including the formation of the Alfve n wing-like structures. The simulation also shows that the ring-like velocity distribution for pickup ions relaxes to a Maxwellian core and a shell-like halo.

Lipatov, A. S.

Determination of Non-Thermal Velocity Distributions from SERTS Linewidth Observations

Non-thermal velocities obtained from the measurement of coronal Extreme Ultraviolet (EUV) linewidths have been consistently observed in solar EUV spectral observations and have been theorized to result fro m many plausible scenarios including wave motions, turbulence, or magnetic reconnection. Constraining these velocities can provide a physical limit for the available energy resulting from unresolved motions in the corona. We statistically determine a series of non-thermal velocity distributions from linewidth measurements of 390 emission lines from a wide array of elements and ionization states observed during the Solar Extreme Ultraviolet Research Telescope and Spectrograph 1991-1997 flights covering the spectral range 174-418 A and a temperature range from 80,000 K to 12.6 MK. This sample includes 248 lines from active regions, 101 lines from quiet-Sun regions, and 41 lines were observed from plasma off the solar limb. We find a strongly peaked distribution corresponding to a non-thermal velocity of 19-22 km/s in all three of the quiet-Sun, active region, and off-limb distributions. For the possibility of Alfven wave resonance heating, we find thai velocities in the core of these distributions do not provide sufficient energy, given typical densities and magnetic field strengths for the coronal plasma, to overcome the estimated coronal energy losses required to maintain the corona at the typical temperatures working as the sole mechanism. We find that at perfect efficiency 50%-60% of the needed energy flux can be produced from the non-thermal velocities measured.

Coyner, Aaron J.

Theoretical surface velocity distributions on acoustic splitter geometries for an engine inlet

The potential-flow velocity distributions on several splitter geometries in an engine inlet and their variation with different splitter leading-edge shapes and distances from the inlet highlight were analyzed. The velocity distributions on the inner and outer surfaces of the splitters are presented for low-speed and cruise conditions. At zero incidence angle, the splitter with the 4-to-1 elliptical leading edge had lower peak velocities and velocity gradients than the splitter with the 2-to-1 elliptical leading edge. The velocity gradients decreased as the distance from the inlet highlight to the splitter leading edge was increased. For a given distance, the peak velocity on the splitter inner surface increased with increasing inlet incidence angle. At an incidence angle of 50 deg, the velocity level and gradients on the inner surface of the splitter in the forward position were sufficiently severe to suggest local separation.

Albers, J. A.

Method of designing cascade blades with prescribed velocity distributions in compressible potential flows

By use of the assumption that the pressure-volume relation is linear, a solution to the problem of designing a cascade for a given turning and with a prescribed velocity distribution along the blade in a potential flow of a compressible perfect fluid was obtained by a method of correspondence between potential flows of compressible and incompressible fluids. The designing of an isolated airfoil with a prescribed velocity distribution along the airfoil is considered as a special case of cascade. If the prescribed velocity distribution is not theoretically attainable, the method provides a means of modifying the distribution so as to obtain a physically significant blade shape. Numerical examples are included.

Costello, George R

Stationary Plasma Thruster Ion Velocity Distribution

A nonintrusive velocity diagnostic based on laser induced fluorescence of the 5d4F(5/2)-6p4D(5/2) singly ionized xenon transition was used to interrogate the exhaust of a 1.5 kW Stationary Plasma Thruster (SPT). A detailed map of plume velocity vectors was obtained using a simplified, cost-effective, nonintrusive, semiconductor laser based scheme. Circumferential velocities on the order of 250 m/s were measured which implied induced momentum torques of approximately 5 x 10(exp -2) N-cm. Axial and radial velocities were evaluated one mm downstream of the cathode at several locations across the width of the annular acceleration channel. Radial velocities varied linearly with radial distance. A maximum radial velocity of 7500 m/s was measured 8 mm from the center of the channel. Axial velocities as large as 16,500 m/s were measured.

Manzella, David H.