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NASA NTRS1958

A Method for Calculation of Hydrodynamic Lift for Submerged and Planing Rectangular Lifting Surfaces

A method is presented for the calculation of lift coefficients for rectangular lifting surfaces of aspect ratios from 0.125 to 10 operating at finite depths beneath the water surface, including the zero depth or planing condition. Theoretical values are compared with experimental values obtained at various depths of submergence with lifting surfaces of aspect ratios from 0.125 to 10. The method can also be applied to hydrofoils with dihedral. Lift coefficients computed by this method are in good agreement with existing experimental data for aspect ratios from 0.125 to 10 and dihedral angles up to 10 degrees.

Wadlin, Kenneth L↗

NASA NTRS1959

A Method for Calculation of Hydrodynamic Lift for Submerged and Planing Rectangular Lifting Surfaces

Wadlin, Kenneth L.↗

NASA NTRS2011

Sub-Scale Testing and Development of the J-2X Fuel Turbopump Inducer

In the early stages of the J-2X upper stage engine program, various inducer configurations proposed for use in the fuel turbopump (FTP) were tested in water. The primary objectives of this test effort were twofold. First, to obtain a more comprehensive data set than that which existed in the Pratt & Whitney Rocketdyne (PWR) historical archives from the original J-2S program, and second, to supplement that data set with information regarding the cavitation induced vibrations for both the historical J-2S configuration as well as those tested for the J-2X program. The J-2X FTP inducer, which actually consists of an inducer stage mechanically attached to a kicker stage, underwent 4 primary iterations utilizing sub-scaled test articles manufactured and tested in PWR's Engineering Development Laboratory (EDL). The kicker remained unchanged throughout the test series. The four inducer configurations tested retained many of the basic design features of the J-2S inducer, but also included variations on leading edge blade thickness and blade angle distribution, primarily aimed at improving suction performance at higher flow coefficients. From these data sets, the effects of the tested design variables on hydrodynamic performance and cavitation instabilities were discerned. A limited comparison of impact to the inducer efficiency was determined as well.

Sargent, Scott R.↗

NASA NTRS1985

Heat transfer and fluid mechanics measurements in transitional boundary layer flows

Experimental results are presented to document hydrodynamic and thermal development of flat-plate boundary layers undergoing natural transition. Local heat transfer coefficients, skin friction coefficients and profiles of velocity, temperature and Reynolds normal and shear stresses are presented. A case with no transition and transitional cases with 0.68% and 2.0% free-stream disturbance intensities were investigated. The locations of transition are consistent with earlier data. A late-laminar state with significant levels of turbulence is documented. In late-transitional and early-turbulent flows, turbulent Prandtl number and conduction layer thickness values exceed, and the Reynolds analogy factor is less than, values previously measured in fully turbulent flows.

Wang, T.↗

NASA NTRS1985

Heat transfer and fluid mechanics measurements in transitional boundary layer flows

Experimental results are presented to document hydrodynamic and thermal development of flat-plate boundary layers undergoing natural transition. Local heat transfer coefficients, skin friction coefficients and profiles of velocity, temperature and Reynolds normal and shear stresses are presented. A case with no transition and transitional cases with 0.68 percent and 2.0 percent free-stream disturbance intensities were investigated. The locations of transition are consistent with earlier data. A late-laminar state with significant levels of turbulence is documented. In late-transitional and early-turbulent flows, turbulent Prandtl number and conduction layer thickness values exceed, and the Reynolds analogy factor is less than, values previously measured in fully turbulent flows.

Wang, T.↗

NASA NTRS1926

Inertia Factors of Ellipsoids for Use in Airship Design

This report is based on a study made by the writer as a member of the Special Committee on Design of Army Semirigid Airship RS-1 appointed by the National Advisory Committee for Aeronautics. The increasing interest in airships has made the problem of the potential flow of a fluid about an ellipsoid of considerable practical importance. In 1833 George Green, in discussing the effect of the surrounding medium upon the period of a pendulum, derived three elliptic integrals, in terms of which practically all the characteristics of this type of motion can be expressed. The theory of this type of motion is very fully given by Horace Lamb in his "Hydrodynamics," and applications to the theory of airships by many other writers. Tables of the inertia coefficients derived from these integrals are available for the most important special cases. These tables are adequate for most purposes, but occasionally it is desirable to know the values of these integrals in other cases where tabulated values are not available. For this reason it seems worth while to assemble a collection of formulae which would enable them to be computed directly from standard tables of elliptic integrals, circular and hyperbolic functions and logarithms without the need of intermediate transformations. Some of the formulae for special cases (elliptic cylinder, prolate spheroid, oblate spheroid, etc.) have been published before, but the general forms and some special cases have not been found in previous publications. (author)

Tuckerman, L. B.↗

NASA NTRS1988

Heat conduction in cooling flows

It has been suggested that electron conduction may significantly reduce the accretion rate (and star foramtion rate) for cooling flows in clusters of galaxies. A numerical hydrodynamics code was used to investigate the time behavior of cooling flows with conduction. The usual conduction coefficient is modified by an efficiency factor, mu, to realize the effects of tangled magnetic field lines. Two classes of models are considered, one where mu is independent of position and time, and one where inflow stretches the field lines and changes mu. In both cases, there is only a narrow range of initial conditions for mu in which the cluster accretion rate is reduced while a significant temperature gradient occurs. In the first case, no steady solution exists in which both conditions are met. In the second case, steady state solutions occur in which both conditions are met, but only for a narrow range of initial values where mu = 0.001.

Bregman, Joel N.↗

NASA NTRS2002

Static and Dynamic Effects of Lateral Carrier Diffusion in Semiconductor Lasers

Electron and hole diffusions in the plane of semiconductor quantum wells play an important part in the static and dynamic operations of semiconductor lasers. It is well known that the value of diffusion coefficients affects the threshold pumping current of a semiconductor laser. At the same time, the strength of carrier diffusion process is expected to affect the modulation bandwidth of an AC-modulated laser. It is important not only to investigate the combined DC and AC effects due to carrier diffusion, but also to separate the AC effects from that of the combined effects in order to provide design insights for high speed modulation. In this presentation, we apply a hydrodynamic model developed by the present authors recently from the semiconductor Bloch equations. The model allows microscopic calculation of the lateral carrier diffusion coefficient, which is a nonlinear function of the carrier density and plasma temperature. We first studied combined AC and DC effects of lateral carrier diffusion by studying the bandwidth dependence on diffusion coefficient at a given DC current under small signal modulation. The results show an increase of modulation bandwidth with decrease in the diffusion coefficient. We simultaneously studied the effects of nonlinearity in the diffusion coefficient. To clearly identify how much of the bandwidth increase is a result of decrease in the threshold pumping current for smaller diffusion coefficient, thus an effective increase of DC pumping, we study the bandwidth dependence on diffusion coefficient at a given relative pumping. A detailed comparison of the two cases will be presented.

Li, Jian-Zhong↗

NASA NTRS1995

Non-parabolic hydrodynamic formulations for the simulation of inhomogeneous semiconductor devices

Hydrodynamic models are becoming prevalent design tools for small scale devices and other devices in which high energy effects can dominate transport. Most current hydrodynamic models use a parabolic band approximation to obtain fairly simple conservation equations. Interest in accounting for band structure effects in hydrodynamic device simulation has begun to grow since parabolic models can not fully describe the transport in state of the art devices due to the distribution populating non-parabolic states within the band. This paper presents two different non-parabolic formulations of the hydrodynamic model suitable for the simulation of inhomogeneous semiconductor devices. The first formulation uses the Kane dispersion relationship (hk)(exp 2)/2m = W(1 + alpha(W)). The second formulation makes use of a power law ((hk)(exp 2)/2m = xW(sup y)) for the dispersion relation. Hydrodynamic models which use the first formulation rely on the binomial expansion to obtain moment equations with closed form coefficients. This limits the energy range over which the model is valid. The power law formulation readily produces closed form coefficients similar to those obtained using the parabolic band approximation. However, the fitting parameters (x,y) are only valid over a limited energy range. The physical significance of the band non-parabolicity is discussed as well as the advantages/disadvantages and approximations of the two non-parabolic models. A companion paper describes device simulations based on the three dispersion relationships: parabolic, Kane dispersion, and power low dispersion.

Smith, Arlynn W.↗

NASA NTRS1996

Non-Parabolic Hydrodynamic Formulations for the Simulation of Inhomogeneous Semiconductor Devices

Hydrodynamic models are becoming prevalent design tools for small scale devices and other devices in which high energy effects can dominate transport. Most current hydrodynamic models use a parabolic band approximation to obtain fairly simple conservation equations. Interest in accounting for band structure effects in hydrodynamic device simulation has begun to grow since parabolic models cannot fully describe the transport in state of the art devices due to the distribution populating non-parabolic states within the band. This paper presents two different non-parabolic formulations or the hydrodynamic model suitable for the simulation of inhomogeneous semiconductor devices. The first formulation uses the Kane dispersion relationship ((hk)(exp 2)/2m = W(1 + alphaW). The second formulation makes use of a power law ((hk)(exp 2)/2m = xW(exp y)) for the dispersion relation. Hydrodynamic models which use the first formulation rely on the binomial expansion to obtain moment equations with closed form coefficients. This limits the energy range over which the model is valid. The power law formulation readily produces closed form coefficients similar to those obtained using the parabolic band approximation. However, the fitting parameters (x,y) are only valid over a limited energy range. The physical significance of the band non-parabolicity is discussed as well as the advantages/disadvantages and approximations of the two non-parabolic models. A companion paper describes device simulations based on the three dispersion relationships; parabolic, Kane dispersion and power law dispersion.

Smith, A. W.↗

NASA NTRS1985

Mechanics of a gaseous film barrier to lubricant wetting of elastohydrodynamically lubricated conjunctions

Two analytical models, one based on simple hydrodynamic lubrication and the other on soft elastohydrodynamic lubrication, are presented and compared to delineate the dominant physical parameters that govern the mechanics of a gaseous film between a small droplet of lubricant and the outer race of a ball bearing. Both models are based on the balance of gravity forces, air drag forces, and air film lubrication forces and incorporate a drag coefficient C sub D and a lubrication coefficient C sub L to be determined from experiment. The soft elastohydrodynamic lubrication (EHL) model considers the effects of droplet deformation and solid-surface geometry; the simpler hydrodynamic lubrication (HL) model assumes that the droplet remains essentially spherical. The droplet's angular position depended primarily on the ratio of gas inertia to droplet gravity forces and on the gas Reynolds number and weakly on the ratio of droplet gravity forces to surface tension forces (Bond number) and geometric ratios for the soft EHL. An experimental configuration in which an oil droplet is supported by an air film on the rotating outer race of a ball bearing within a pressure-controlled chamber produced measurements of droplet angular position as a function of outer-race velocity droplet size and type, and chamber pressure.

Prahl, J. M.↗

NASA NTRS1975

Design and application of squeeze film dampers for turbomachinery stabilization

The steady-state transient response of the squeeze film damper bearing was investigated. Both the steady-state and transient equations for the hydrodynamic bearing forces are derived; the steady-state equations were used to determine the damper equivalent stiffness and damping coefficients. These coefficients are used to find the damper configuration which will provide the optimum support characteristics based on a stability analysis of the rotor-bearing system. The effects of end seals and cavitated fluid film are included. The transient analysis of rotor-bearing systems was conducted by coupling the damping and rotor equations and integrating forward in time. The effects of unbalance, cavitation, and retainer springs are included. Methods of determining the stability of a rotor-bearing system under the influence of aerodynamic forces and internal shaft friction are discussed.

Gunter, E. J.↗

NASA NTRS1991

Generalized hydrodynamic transport in lattice-gas automata

The generalized hydrodynamics of two-dimensional lattice-gas automata is solved analytically in the linearized Boltzmann approximation. The dependence of the transport coefficients (kinematic viscosity, bulk viscosity, and sound speed) upon wave number k is obtained analytically. Anisotropy of these coefficients due to the lattice symmetry is studied for the entire range of wave number, k. Boundary effects due to a finite mean free path (Knudsen layer) are analyzed, and accurate comparisons are made with lattice-gas simulations.

Luo, Li-Shi↗

NASA NTRS1993

Steady flow on to a conveyor belt - Causal viscosity and shear shocks

Some hydrodynamical consequences of the adoption of a causal theory of viscosity are explored. Causality is introduced into the theory by letting the coefficient of viscosity go to zero as the flow velocity approaches a designated propagation speed for viscous signals. Consideration is given to a model of viscosity which has a finite propagation speed of shear information, and it is shown that it produces two kinds of shear shock. A 'pure shear shock' corresponds to a transition from a superviscous to a subviscous state with no discontinuity in the velocity. A 'mixed shear shock' has a shear transition occurring at the same location as a normal adiabatic or radiative shock. A generalized version of the Rankine-Hugoniot conditions for mixed shear shocks is derived, and self-consistent numerical solutions to a model 2D problem in which an axisymmetric radially infalling stream encounters a spinning star are presented.

Syer, D.↗

NASA NTRS1967

Hydrodynamics of tire hydroplaning.

Tire hydroplaning, noting lift force on planing surface and pressure distribution

LIFT COEFFICIENT↗

NASA NTRS1951

Aerodynamic Characteristics of a Flying-Boat Hull Having a Length-Beam Ratio of 15, TED No. NACA 2206

An investigation was made in the Langley 300 MPH 7- by 10-foot tunnel to determine the aerodynamic characteristics of a flying-boat hull of a length-beam ratio of 15 in the presence of a wing. The investigation was an extension of previous tests made on hulls of length-beam ratios of 6, 9, and 12; these hulls were designed to have approximately the same hydrodynamic performance with respect to spray and resistance characteristics. Comparison with the previous investigation at lower length-beam ratios indicated a reduction in minimum drag coefficients of 0.0006 (10 peroent)with fixed transition when the length-beam ratio was extended from 12 to 15. As with the hulls of lower length-beam ratio, the drag reduction with a length-beam ratio of 15 occurred throughout the range of angle of attack tested and the angle of attack for minimum drag was in the range from 2deg to 3deg. Increasing the length-beam ratio from 12 to 15 reduced the hull longitudinal instability by an mount corresponding to an aerodynamic-center shift of about 1/2 percent of the mean aerodynamic chord of the hypothetical flying boat. At an angle of attack of 2deg, the value of the variation of yawing-moment coefficient with angle of yaw for a length-beam ratio of 15 was 0.00144, which was 0.00007 larger than the value for a length-beam ratio of 12.

Riebe, John M.↗

NASA NTRS2023

Formation of the Lyman Continuum during Solar Flares

The Lyman continuum (LyC; <911.12 Å) forms at the top of the chromosphere in the quiet Sun, making LyC a powerful tool for probing the chromospheric plasma during solar flares. To understand the effects of nonthermal energy deposition in the chromosphere during flares, we analyzed LyC profiles from a grid of field-aligned radiative-hydrodynamic models generated using the RADYN code as part of the F-CHROMA project. The spectral response of LyC, the temporal evolution of the departure coefficient of hydrogen, b 1 , and the color temperature, T c , in response to a range of nonthermal electron distribution functions, were investigated. The LyC intensity was seen to increase by 4–5.5 orders of magnitude during solar flares, responding most strongly to the nonthermal electron flux of the beam. Generally, b 1 decreased from 10 2 –10 3 to closer to unity during solar flares, indicating a stronger coupling to local conditions, while T c increased from 8–9 to 10–16 kK. T c was found to be approximately equal to the electron temperature of the plasma when b1 was at a minimum. Both optically thick and optically thin components of LyC were found to be in agreement with the interpretation of recent observations. The optically thick layer forms deeper in the chromosphere during a flare compared to quiescent periods, whereas the optically thin layers form at higher altitudes due to chromospheric evaporation, in low-temperature, high-density regions propagating upward. We put these results in the context of current and future missions.

Solar flares↗

NASA NTRS1996

Comparison of Code Predictions to Test Measurements for Two Orifice Compensated Hydrostatic Bearings at High Reynolds Numbers

Rotordynamic coefficients obtained from testing two different hydrostatic bearings are compared to values predicted by two different computer programs. The first set of test data is from a relatively long (L/D=1) orifice compensated hydrostatic bearing tested in water by Texas A&M University (TAMU Bearing No.9). The second bearing is a shorter (L/D=.37) bearing and was tested in a lower viscosity fluid by Rocketdyne Division of Rockwell (Rocketdyne 'Generic' Bearing) at similar rotating speeds and pressures. Computed predictions of bearing rotordynamic coefficients were obtained from the cylindrical seal code 'ICYL', one of the industrial seal codes developed for NASA-LeRC by Mechanical Technology Inc., and from the hydrodynamic bearing code 'HYDROPAD'. The comparison highlights the difference the bearing has on the accuracy of the predictions. The TAMU Bearing No. 9 test data is closely matched by the predictions obtained for the HYDROPAD code (except for added mass terms) whereas significant differences exist between the data from the Rocketdyne 'Generic' bearing the code predictions. The results suggest that some aspects of the fluid behavior in the shorter, higher Reynolds Number 'Generic' bearing may not be modeled accurately in the codes. The ICYL code predictions for flowrate and direct stiffness approximately equal those of HYDROPAD. Significant differences in cross-coupled stiffness and the damping terms were obtained relative to HYDROPAD and both sets of test data. Several observations are included concerning application of the ICYL code.

Keba, John E.↗