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NASA NTRS1997

CMOTT Turbulence Module for NPARC

This is a user's manual of the CMOTT turbulence module, version 2.0, developed for the NPARC code. The module is written in a self-contained manner so that the user can use any turbulence model in the module without concern as to how it is implemented and solved. Three two-equation turbulence models have been built into the module: Chien, Shih-Lumley and CMOTT models, and all of them have both the low Reynolds number and wall function options. Unlike Chien's model, both the Shih-Lumley and CMOTT models do not involve the dimensionless wall distance y(sup +) in the low Reynolds number approach, an advantage for separated flow calculations. The Van Driest transformation is used so that the wall functions can be applied to both incompressible and compressible flows. The manual gives the details of the turbulence models used and their numerical implementation. It also gives two application examples, one for subsonic and the other for transonic flow, for demonstration. The module can be easily linked to the NPARC code for practical applications.

Zhu, J.↗

NASA NTRS1998

Transition Heat Transfer Modeling Based on the Characteristics of Turbulent Spots

While turbulence models are being developed which show promise for simulating the transition region on a turbine blade or vane, it is believed that the best approach with the greatest potential for practical use is the use of models which incorporate the physics of turbulent spots present in the transition region. This type of modeling results in the prediction of transition region intermittency which when incorporated in turbulence models give a good to excellent prediction of the transition region heat transfer. Some models are presented which show how turbulent spot characteristics and behavior can be employed to predict the effect of pressure gradient and Mach number on the transition region. The models predict the spot formation rate which is needed, in addition to the transition onset location, in the Narasimha concentrated breakdown intermittency equation. A simplified approach is taken for modeling turbulent spot growth and interaction in the transition region which utilizes the turbulent spot variables governing transition length and spot generation rate. The models are expressed in terms of spot spreading angle, dimensionless spot velocity, dimensionless spot area, disturbance frequency and Mach number. The models are used in conjunction with a computer code to predict the effects of pressure gradient and Mach number on the transition region and compared with VKI experimental turbine data.

Simon, Fred↗

NASA NTRS1985

Fundamental study of flow field generated by rotorcraft blades using wide-field shadowgraph

The vortex trajectory and vortex wake generated by helicopter rotors are visualized using a wide-field shadowgraph technique. Use of a retro-reflective Scotchlite screen makes it possible to investigate the flow field generated by full-scale rotors. Tip vortex trajectories are visible in shadowgraphs for a range of tip Mach number of 0.38 to 0.60. The effect of the angle of attack is substantial. At an angle of attack greater than 8 degrees, the visibility of the vortex core is significant even at relatively low tip Mach numbers. The theoretical analysis of the sensitivity is carried out for a rotating blade. This analysis demonstrates that the sensitivity decreases with increasing dimensionless core radius and increases with increasing tip Mach number. The threshold value of the sensitivity is found to be 0.0015, below which the vortex core is not visible and above which it is visible. The effect of the optical path length is also discussed. Based on this investigation, it is concluded that the application of this wide-field shadowgraph technique to a large wind tunnel test should be feasible. In addition, two simultaneous shadowgraph views would allow three-dimensional reconstruction of vortex trajectories.

Parthasarathy, S. P.↗

NASA NTRS1980

Buoyancy effects on flames spreading down thermally thin fuels

Experiments show that buoyancy influences the downward spread rate of flames consuming thermally thin fuel beds. For index cards (0.0098 cm half-thickness) and adding-machine tape (0.0043 cm half-thickness), an increase in the buoyancy level causes the spread rate to drop until no flame propagation is possible. A dimensionless spread rate is found to correlate with a Damkoehler number. As the Damkoehler number increases with decreasing buoyancy level brought about by an increase in pressure or a decrease in gravity, the dimensionless spread rate approaches unity. It is also found that a small change in orientation with respect to the vertical is equivalent to a change in the magnitude of gravity in the direction of spread, and power-law relations between the dimensional spread rate and pressure are only valid over a small pressure range.

Altenkirch, R. A.↗

NASA NTRS1988

Fluid spray simulation with two-fluid nozzles

Two-phase interacting flow inside a two-fluid fuel atomizer was investigated and a correction of aerodynamic and liquid-surface forces with characteristic drop diameter was obtained for liquid-jet breakup in Mach 1 gas flow. Nitrogen gas mass-flux was varied from 6 to 50 g/sq cm sec by using four differently sized two-fluid atomizers with nozzle diameters varyig from 0.32 to 0.56 cm. The correlation was derived by using the acoustic gas velocity, V sub c, as a basic parameter in defining and evaluating the dimensionless product of the Weber (We) and Reynolds (Re) numbers. By using the definition of WeRe, it was found that the ratio of orifice diameter to Sauter mean drop diameter could be correlated with the dimensionless ratio WeRe and the gas to liquid density ratio.

Ingebo, Robert D.↗

NASA NTRS1989

Fuel spray simulation with two-fluid nozzles

Two-phase interacting flow inside a two-fluid fuel atomizer was investigated and a correction of aerodynamic and liquid-surface forces with characteristic drop diameter was obtained for liquid-jet breakup in Mach 1 gas flow. Nitrogen gas mass-flux was varied from 6 to 50 g/sq cm sec by using four differently sized two-fluid atomizers with nozzle diameters varying from 0.32 to 0.56 cm. The correlation was derived by using the acoustic gas velocity, V sub c, as a basic parameter in defining and evaluating the dimensionless product of the Weber (We) and Reynolds (Re) numbers. By using the definition of WeRe, it was found that the ratio of orifice diameter to Sauter mean drop diameter could be correlated with the dimensionless ratio WeRe and the gas to liquid density ratio.

Ingebo, Robert D.↗

NASA NTRS1954

Variation of Local Liquid-Water Concentration About and Ellipsoid of Fineness Ratio 5 Moving in a Droplet Field

Trajectories of water droplets about an ellipsoid of revolution with a fineness ratio of 5 (which often approximates the shape of an aircraft fuselage or missile) were computed with the aid of a differential analyzer. Analyses of these trajectories indicate that the local concentration of liquid water at various points about an ellipsoid in flight through a droplet field varies considerably and under some conditions may be several times the free-stream concentration. Curves of the local concentration factor as a function of spatial position were obtained and are presented in terms of dimensionless parameters Re(sub 0) (free-stream Reynolds number) and K (inertia), which contain flight and atmospheric conditions. These curves show that the local concentration factor at any point is very sensitive to change in the dimensionless parameters Re(sub 0) and K. These data indicate that the expected local concentration factors should be considered when choosing the location of, or when determining antiicing heat requirements for, water- or ice-sensitive devices that protrude into the stream from an aircraft fuselage or missile. Similarly, the concentration factor should be considered when choosing the location on an aircraft of instruments that measure liquid-water content or droplet-size distribution in the atmosphere.

Dorsch, Robert G.↗

NASA NTRS1985

Wide-field shadowgraph flow visualization of tip vortices generated by a helicopter rotor

The vortex trajectory and vortex wake generated by helicopter rotors were visualized using a wide-field shadowgraph technique. Use of a retro-reflective Scotchlite screen made it possible to investigate the flow field generated by full-scale tail rotors. Tip vortex trajectories were visible in shadowgraphs for a range for tip Mach number of 0.38 - 0.60. The effect of the angle of attack was substantial. At an angle of attack greater than 8 degrees, the visibility of the vortex core was significant even at relatively low tip Mach numbers. The theoretical analysis of the visibility was carried out for a rotating blade. This analysis demonstrated that the visibility decreases with increasing dimensionless core radius (ro/c) and increases with increasing tip Mach number. Based on this investigation, it is concluded that the wide-field shadowgraph flow visualization technique should be feasible to study the flow field generated by a large main rotor in a wind tunnel and in an outdoor full-scale test stand. Of note is that the shadowgraph technique could easily be used with other on-going tests such as aerodynamic performance study, noise measurements, velocity measurements with LDV or hot-wire anemometer, local pressure measurement on the rotor surface, etc.

Parthasarathy, S. P.↗

NASA NTRS1987

Gravity and conduction driven melting in a sphere

In the Stefan and Neumann problems fundamentally characterizing melting, unmolten portions of a solid undergoing phase changes within spherical containers are assumed to remain stationary. An approach to these issues that is related to the theories of lubrication and film condensation is presently employed in conjunction with an approximate, closed-form solution of melting within spheres. It is shown that a group of dimensionless parameters containing Prandtl, Archimides and Stefan numbers can describe the melting process. Also given are the results of fundamental heat transfer experiments performed on the melting of a phase-change medium in a spherical shell.

Bahrami, P. A.↗

NASA NTRS1991

Enhancement of the no-vent fill process

This paper presents an analytical and experimental evaluation of an enhanced techniques for no-vent fill. The method entails injecting liquid through the top of the receiver vessel, thereby increasing surface area and agitation of the ullage/liquid interface. Both of these factors promote condensation induced ullage collapse, and reduce compressive impedance to the incoming liquid. The enhanced process was analyzed by modifying the surface area algorithm of an existing tank thermodynamic code to model a downward-pointing, conical jet impringing on a steadily rising liquid surface. Transient pressure and temperature measurements from several tests with Freon-114 were input into the revised model to calculate condensation rate as a function of fill level. By expressing these rates in dimensionless form (i.e., in terms of Stanton number and Prandtl number), an empirical correlation similar to the submerged jet model of Brown and Sonin (1989) was derived. This provided a basis for developing an expression which relates top fill to bottom fill performance.

Vaughan, David A.↗

NASA NTRS2005

Experimental Investigation of Oscillatory Flow Pressure and Pressure Drop Through Complex Geometries

A series of experiments have been performed to investigate the oscillatory flow pressure and pressure drop through complex geometries. These experiments were conducted at the CSU-SLRE facility which is a horizontally opposed, two-piston, single-acting engine with a split crankshaft driving mechanism. Flow through a rectangular duct, with no insert (obstruction), was studied first. Then four different inserts were examined: Abrupt, Manifold, Diverging Short and Diverging Long. The inserts were mounted in the center of the rectangular duct to represent different type of geometries that could be encountered in Stirling machines. The pressure and pressure drop of the oscillating flow was studied for: 1) different inserts, 2) different phase angle between the two pistons of the engine (zero, 90 lead, 180, and 90 lag), and 3) for different piston frequencies (5, 10, 15, and 20 Hz). It was found that the pressure drop of the oscillatory flow increases with increasing Reynolds number. The pressure drop was shown to be mainly due to the gas inertia for the case of oscillatory flow through a rectangular duct with no insert. On the other hand, for the cases with different inserts into the rectangular duct, the pressure drop has three sources: inertia, friction, and local losses. The friction pressure drop is only a small fraction of the total pressure drop. It was also shown that the dimensionless pressure drop decreases with increasing kinetic Reynolds number.

Ibrahim, Mounir B.↗

NASA NTRS2002

Solutal Convection Around Growing Protein Crystal and Diffusional Purification in Space

This work theoretically addressed two subjects: 1) onset of convection, 2) distribution of impurities. Onset of convection was considered analytically and numerically. Crystal growth was characterized by slow surface incorporation kinetics, i.e. growth kinetic coefficient beta (cm/s) small as compared to the typical bulk diffusion rate, D(sub 1)/h, where D(sub 1) is diffusivity of major crystallizing protein and h is the crystal size. Scaling type analysis predicted two laws on how the convection rate, v, essentially the Peclet number, Pe exactly equal to vh/D(sub 1), depends on dimensionless kinetic coefficient a exactly equal to beta h/D(sub 1). Namely: Pe = C(sub 2/5)(aRa(sup 2/5)) and Pe = C(sub 1) aRa. Here, Reynolds number Ra = rho(sub 1)(sup 0)gh(sup 3)(rho(sub p) - rho(sub w))/rho(sup p)rho(sub 1)vD(sub 1), v being solution viscosity. The constants C(sub 2/5), exactly equal to 0.28 and C(sub 1) exactly equal to 10(exp -2) found from the full scale computer simulation for a cylindrical crystal inside big cylindrical vessel. The linear boundary conditions connecting protein and impurity concentration at the interface with the flux to/from the interface was applied. No-slip condition for Navier-Shocker equations was employed. With these conditions, flow and concentration distributions were calculated. Validity of the Pe(Ra) dependencies follows for wide range of parameters for which numerical calculations have been accomplished and presented by various points.

Chernov, A. A.↗

NASA NTRS2011

Correlation of Water Frost Porosity in Laminar Flow over Flat Surfaces

A dimensionless correlation has been proposed for water frost porosity expressing its dependence on frost surface temperature and Reynolds number for laminar forced flow over a flat surface. The correlation is presented in terms of a dimensionless frost surface temperature scaled with the cold plate temperature, and the freezing temperature. The flow Reynolds number is scaled with reference to the critical Reynolds number for laminar-turbulent transition. The proposed correlation agrees satisfactorily with the simultaneous measurements of frost density and frost surface temperature covering a range of plate temperature, ambient air velocity, humidity, and temperature. It is revealed that the frost porosity depends primarily on the frost surface and the plate temperatures and the flow Reynolds number, and is only weakly dependent on the relative humidity. The results also point out the general character of frost porosity displaying a decrease with an increase in flow Reynolds number.

Kandula, Max↗

NASA NTRS1975

Amplitude effects on the dynamic performance of a hydrostatic gas thrust bearing

The Reynolds' equation is applied to a strip gas thrust bearing to analyze amplitude disturbance effects on its dynamic performance. The Reynolds' equation is numerically approximated using finite difference techniques. The time dependent load carrying capacity is represented by a Fourier series up to and including the third harmonics. Design curves for the load capacity and the linear stiffness and damping are presented as a function of inlet location, restrictor coefficient, supply pressure, amplitude of oscillation, and squeeze number. For the range of amplitudes investigated the dimensionless load capacity, stiffness and damping does not exhibit an appreciable change in magnitude; thus, only one design curve is needed to represent each relationship. A design methodology is presented.

Stiffler, A. K.↗

NASA NTRS1977

Dirac cosmology

The large numbers hypothesis (LNH) linking the magnitude of large dimensionless ratios in physics (on the order of 10 to the 40th power) to cosmic time is examined. The LNH is checked against evidence on 3K background radiation of the universe and the (log N, log S)-relation for radio galaxies. Earlier criticisms of LNH by Gamow and Teller are examined, and alternative hypotheses put forth by Dicke and Carter (1974) are discussed. The discussion covers: continuous (additive or multiplicative) creation of matter, the Einstein metric and the atomic metric, and general cosmological and local astronomical implications of LNH. LNH is also viewed in relation to solar evolution and pulsar physics.

Canuto, V.↗

NASA NTRS1991

Thermocapillary flow and natural convection in a melt column with an unknown melt/solid interface

A vertical melt column set up between an upper heating rod and a lower sample rod, i.e., the so-called half-zone system, is a convenient experimental tool for studying convection in the melt in floating-zone crystal growth. In order to help understand the convection observed in the melt column, a computer model has been developed to describe steady state, axisymmetrical thermocapillary flow and natural convection in the melt. The governing equations and boundary conditions are expressed in general non-orthogonal curvilinear coordinates in order to accurately treat the unknown melt/solid interface as well as all other physical boundaries in the system. The effects of key dimensionless variables on the following items are discussed: (1) convection and temperature distribution in the melt; (2) the shape of the melt/solid interface; (3) the height of the melt column. These dimensionless variables are the Grashof, Marangoni and Prandtl numbers.

Lan, C. W.↗

NASA NTRS1983

Correlating downward flame spread rates for thick fuel beds

Flame spread rates are presented for polymethylmethacrylate fuel beds as a function of gravitational acceleration and ambient pressure and oxygen concentration. The data are correlated by plotting a dimensionless spread rate that is a measure of the heat transferred forward of the flame, required to sustain the flame, compared to the maximum possible forward heat transfer against a Damkoehler number. The latter parameter indicates the approach of the flame to its maximum temperature, where the maximum possible forward heat transfer occurs, such that the dimensionless spread rate approaches unity at large Damkoehler number. Surface regression effects on the flame spread process are incorporated into the dimensionless spread rate, and the final correlation is independent of bed thickness.

Altenkirch, R. A.↗

NASA NTRS1986

Numerical modeling of physical vapor transport in a vertical cylindrical ampoule, with and without gravity

Numerical modeling has been performed of the fluid dynamics in a prototypical physical vapor transport crystal growing situation. Cases with and without gravity have been computed. Dependence of the flows upon the dimensionless parameters aspect ratio and Peclet, Rayleigh, and Schmidt numbers is demonstrated to a greater extent than in previous works. Most notably, it is shown that the effects of thermally-induced buoyant convection upon the mass flux on the growth interface crucially depend upon the temperature boundary conditions on the sidewall (e.g., whether adiabatic or of a fixed profile, and in the latter case the results depend upon the shape of the profile assumed).

Miller, T. L.↗