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NASA NTRS1977

Similarity laws of lunar and terrestrial volcanic flows

A mathematical model for the terrestrial and lunar volcanic flows is proposed. This mathematical model, which is one-dimensional, steady duct flow of a mixture of a gas and small solid particles (rock), has been analyzed in detail. The similarities and the differences of the essential features of lunar and terrestrial volcanic flows are determined. Numerical results for the equilibrium two-phase flows of lunar and terrestrial volcanics under similar conditions are presented. The main results of the theoretical model are: the lunar crater is much larger than the corresponding terrestrial crater; the exit velocity from the lunar volcanic flow may be higher than the lunar escape velocity but the exit velocity of terrestrial volcanic flow is much less than that of the linear case (this result confirms the hypothesis that Australian tektites came from the moon, as a stream of rock and gas of extremely high speed), and the thermal effects on the lunar volcanic flow are much larger than those in the terrestrial case.

Pai, S. I.↗
NASA NTRS1978

Design of transonic airfoil sections using a similarity theory

A study of the available methods for transonic airfoil and wing design indicates that the most powerful technique is the numerical optimization procedure. However, the computer time for this method is relatively large because of the amount of computation required in the searches during optimization. The optimization method requires that base and calibration solutions be computed to determine a minimum drag direction. The design space is then computationally searched in this direction; it is these searches that dominate the computation time. A recent similarity theory allows certain transonic flows to be calculated rapidly from the base and calibration solutions. In this paper the application of the similarity theory to design problems is examined with the object of at least partially eliminating the costly searches of the design optimization method. An example of an airfoil design is presented.

Nixon, D.↗
NASA NTRS1979

Application of the principle of similarity fluid mechanics

The principle of similarity applied to fluid mechanics is described and illustrated. The concept of transforming the conservation equations by combining similarity principles for thermophysical properties with those for fluid flow is examined. The usefulness of the procedure is illustrated by applying such a transformation to calculate two phase critical mass flow through a nozzle.

Hendericks, R. C.↗
NASA NTRS1979

Design of transonic airfoil sections using a similarity theory

In the present paper, it is shown that numerical optimization is a powerful tool for designing transonic wings and airfoils. Nixon's (1978) similarity theory is extended to cover design optimization problems. Some ground rules for designing shock-free airfoils are proposed and their application is demonstrated by examples. Advantages which accrue from integrating similarity theory into the numerical optimization procedure are noted.

Nixon, D.↗
NASA NTRS1979

Comparisons of the hydraulics of water flows in Martian outflow channels with flows of similar scale on earth

The hydraulics of channelized water flows on Mars and the resulting sediment transport rates are calculated, and similar computations are performed for such terrestrial analogs as the Mississippi River and the catastrophic Lake Missoula floods that formed the Channeled Scabland in eastern Washington State. The morphologies of deep-sea channels formed by catastrophic turbidity currents are compared with the Martian channels, many similarities are pointed out, and the hydraulics of the various flows are compared. The results indicate that the velocities, discharges, bottom shear stresses, and sediment-transport capacity of water flows along the Martian channels would be comparable to those of the oceanic turbidity currents and the Lake Missoula floods. It is suggested that the submarine canyons from which turbidity currents originate are the terrestrial counterparts to the chaotic-terrain areas or craters that serve as sources for many of the Martian channels.

Komar, P. D.↗
NASA NTRS1979

NGC 1275 /3C 84/ - Similar structure in the optical and 3-mm radio variations

Optical and 3.3-mm data for the Seyfert galaxy NGC 1275 (3C 84) are compared. Similarities exist between the variations at the two wavelengths with regard to amplitude, time scale, and interval between events. The question is raised whether these similarities may be the result of a common triggering mechanism.

Epstein, E. E.↗
NASA NTRS1978

Similar explosive eruptions of lunar and terrestrial volcanoes

A mathematical model of one-dimensional, steady duct flow of a mixture of gas and small solid particles (rock), has been applied to the earth and the moon under geometrically and dynamically similar conditions to simulate explosive eruption conditions. Numerical results for equilibrium two-phase flows for lunar and terrestrial explosive eruptions under similar conditions indicate that: (1) a lunar explosive vent is much larger than the corresponding terrestrial vent, (2) the exit velocity from the lunar explosive flow may be higher than the lunar escape velocity, but the exit velocity of terrestrial explosive flow is much less than that of the lunar case (this result supports the hypothesis that Australian tektites came from the moon as a stream of a mixture of rock and gas of extremely high speed), and (3) the thermal effects on the lunar explosive flows are much larger than those of the terrestrial case.

Pai, S. I.↗
NASA NTRS1980

Similarity solutions of a strong shock wave propagation in a mixture of a gas and dusty particles

The similarity solutions of a strong shock wave propagation in a mixture of a gas and small solid particles have been investigated. Similarity solution exists only when the shock is very strong and the surrounding medium is of a constant density and at rest and with negligible counterpressure. The non-dimensional fundamental equations are derived and studied. The results depend on three non-dimensional parameters; i.e. (1) the ratio of the specific heats of the gas, (2) the mass concentration of the solid particles in the mixture and (3) the ratio of the density of the solid to that of initial density of the gas. Numerical solutions for various values of these parameters are presented and discussed. The speeds of the shock wave front and its location with various energy releases are given.

Pai, S. I.↗
NASA NTRS1980

Similarity solutions of some two-space-dimensional nonlinear wave evolution equations

Similarity reductions of the two-space-dimensional versions of the Korteweg-de Vries, modified Korteweg-de Vries, Benjamin-Davis-Ono, and nonlinear Schroedinger equations are presented, and some solutions of the reduced equations are discussed. Exact dispersive solutions of the two-dimensional Korteweg-de Vries equation are obtained, and the similarity solution of this equation is shown to be reducible to the second Painleve transcendent.

Redekopp, L. G.↗
NASA NTRS1981

Sample selection in foreign similarity regions for multicrop experiments

The selection of sample segments in the U.S. foreign similarity regions for development of proportion estimation procedures and error modeling for Argentina, Australia, Brazil, and USSR in AgRISTARS is described. Each sample was chosen to be similar in crop mix to the corresponding indicator region sample. Data sets, methods of selection, and resulting samples are discussed.

Malin, J. T.↗
NASA NTRS1982

Selection of USSR foreign similarity regions

The similarity regions in the United States and Canada were selected to parallel the conditions that affect labeling and classification accuracies in the U.S.S.R. indicator regions. In addition to climate, a significant condition that affects labeling and classification accuracies in the U.S.S.R. is the proportion of barley and wheat grown in a given region (based on sown areas). The following regions in the United States and Canada were determined to be similar to the U.S.S.R. indicator regions: (1) Montana agrophysical unit (APU) 104 corresponds to the Belorussia high barley region; (2) North Dakota and Minnesota APU 20 and secondary region southern Manitoba and Saskatchewan correspond to the Ural RSFSR barley and spring wheat region; (3) Montana APU 23 corresponds to he North Caucasus barley and winter wheat region. Selection criteria included climates, crop type, crop distribution, growth cycles, field sizes, and field shapes.

Disler, J. M.↗
NASA NTRS1983

The continuous similarity model of bulk soil-water evaporation

The continuous similarity model of evaporation is described. In it, evaporation is conceptualized as a two stage process. For an initially moist soil, evaporation is first climate limited, but later it becomes soil limited. During the latter stage, the evaporation rate is termed evaporability, and mathematically it is inversely proportional to the evaporation deficit. A functional approximation of the moisture distribution within the soil column is also included in the model. The model was tested using data from four experiments conducted near Phoenix, Arizona; and there was excellent agreement between the simulated and observed evaporation. The model also predicted the time of transition to the soil limited stage reasonably well. For one of the experiments, a third stage of evaporation, when vapor diffusion predominates, was observed. The occurrence of this stage was related to the decrease in moisture at the surface of the soil. The continuous similarity model does not account for vapor flow. The results show that climate, through the potential evaporation rate, has a strong influence on the time of transition to the soil limited stage. After this transition, however, bulk evaporation is independent of climate until the effects of vapor flow within the soil predominate.

Clapp, R. B.↗
NASA NTRS1982

On two-layer models and the similarity functions for the PBL

An operational Planetary Boundary Layer model which employs similarity principles and two-layer patching to provide state-of-the-art parameterization for the PBL flow is used to study the popularly used similarity functions, A and B. The expected trends with stratification are shown. The effects of baroclinicity, secondary flow, humidity, latitude, surface roughness variation and choice of characteristic height scale are discussed.

Brown, R. A.↗
NASA NTRS1982

Near-wall similarity in three-dimensional turbulent boundary layers. I - Model review. II - Pressure-driven flow results

Eleven proposed models for near-wall similarity for three-dimensional turbulent boundary layer flows are reviewed. Six of these models are comparatively simple scalar models and five are more complex and/or two-component vector models. Ten of the models can be tested as to their validity or predictive capability with the aid of measured mean velocity field, wall pressure field, and direct wall shear stress field (magnitude and direction) data. One of the models cannot be tested owing to its dependence on two parameters that are at present extremely difficult (if not impossible) to measure. Ten three-dimensional near-wall similarity models are then evaluated with direct wall shear, velocity field, and pressure gradient data from a three-dimensional pressure-driven boundary layer flow. In a primary focus of the interval where y+ is between 50 and 300, graphical results suggest that six simpler models and the freestream component of one complex model are adequate for profiles with monotone increasing skew up to about 15 deg.

Pierce, F. J.↗
NASA NTRS1983

Chondrules and other components in C, O, and E chondrites Similarities in their properties and origins

Three types of chondrules are described that are common to H3, LL3, CM2, CO3, and CV3 chondrites. Low- and high-FeO, porphyritic olivine chondrules contain olivine with Fa0.3-8 and Fa5-50 respectively, and can easily be distinguished petrographically. Poikilitic pyroxene chondrules have 1-20 vol pct olivine (Fa0.2-8) enclosed by low-Ca pyroxene (Fs0.5-7), and also occur in E chondrites. These three types formed in separate nebular regions which had dimensions and spacings such that a few percent of the chondrules that collided to form compound chondrules were of different types. Sorting of chondrule precursor material and mixing of chondrule types probably account for most variations in bulk and mineral chemistry among chondrite groups. Metallic Fe,Ni grains containing 0.1-1 percent Cr, Si, and P are present in low-FeO olivine chondrules from all type 2 and least metamorphosed type 3 chondrites. Metal compositions reflect reduction during chondrule formation in the nebula, not nebular condensation. Opaque matrices in type 3 ordinary and carbonaceous chondrites are somewhat similar in composition and mineralogy, and probably have related origins. It is concluded that chondrules in all known chondrite groups share similar nebular origins.

Scott, E. R. D.↗
NASA NTRS1984

Experimental observations of self-similar plasma expansion

The present investigation is concerned with measurements of the plasma potential profile of an expanding plasma, taking into account the demonstration of the self-similar behavior of such a plasma. The obtained experimental results are consistent with self-similar solutions reported by Crow et al. (1975). It is found that the quasi-neutrality condition breaks down early during the experiment. A consideration of the effect of charge separation is, therefore, required. Attention is given to the evolution of the potential profiles of the expanding plasma as a function of time, the accelerated ion fronts, and the sheath formation of the expanding plasma into a floating boundary.

Chan, C.↗
NASA NTRS1984

The reactions of cobalt, iron and nickel in SO-2 atmospheres: Similarities and differences

The reactions of cobalt, iron and nickel in SO2 atmospheres are reviewed and compared. A mixed oxide-sulfide product layer is observed in all cases. Cobalt and nickel exhibits similar behavior. The observed rates are near the sulfidation rates, and the reaction rate is strongly influenced by the outward diffusion of metal through an interconnected sulfide network. A continuous interconnected sulfide is not observed in the oxide-sulfide scales formed on iron, and the reaction rates are more difficult to summarize. The differences and similarities among the three metals are explained in terms of the absence of scale-gas equilibrium and the ratio of the metal diffusivity in the corresponding oxide and sulfide.

Jacobson, N. S.↗