New formulation of the multicomponent laminar boundary-layer problem.
Chapman-Enskog method modified for formulation of multicomponent laminar boundary layer problem for numerical solution
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Chapman-Enskog method modified for formulation of multicomponent laminar boundary layer problem for numerical solution
Multicomponent reacting laminar boundary layer in chemical equilibrium solved using Stefan-Maxwell relations
Additional matrix elements necessary for third approximation to viscosity of multicomponent gas mixtures
Control section design of multicomponent microforce measurement system, noting amplifier and servomotor
Multicomponent diffusion theory in glasses and application to tektites
Multicomponent fuels combustion in air, deriving simplified flame sheet model
Reentry vehicle with multicomponent gas mixture injection, calculating heat and mass transfer correlations for stagnation point flow
Radiation resistance of small filamentary loop antenna in cold collisionless uniform multicomponent magnetoplasma, assuming uniform current distribution along loop
Multicomponent diffusion process calculation using eigenvalues of Onsager diffusion matrix
Numerical solutions are presented for the viscous shocklayer equations where the chemistry is treated as being either frozen, equilibrium, or nonequilibrium. Also the effects of the diffusion model, surface catalyticity, and mass injection on surface transport and flow parameters are considered. The equilibrium calculations for air species using multicomponent: diffusion provide solutions previously unavailable. The viscous shock-layer equations are solved by using an implicit finite-difference scheme. The flow is treated as a mixture of inert and thermally perfect species. Also the flow is assumed to be in vibrational equilibrium. All calculations are for a 45 deg hyperboloid. The flight conditions are those for various altitudes and velocities in the earth's atmosphere. Data are presented showing the effects of the chemical models; diffusion models; surface catalyticity; and mass injection of air, water, and ablation products on heat transfer; skin friction; shock stand-off distance; wall pressure distribution; and tangential velocity, temperature, and species profiles.
With the use of a power integral formulation, a study is made of the vlf/elf radiation patterns of arbitrarily oriented electric and magnetic dipoles in a cold lossless multicomponent magnetoplasma. Expressions for the ray patterns are initially developed that apply for arbitrary values of driving frequency, static magnetic-field strength, plasma density, and composition. These expressions are subsequently specialized to vlf/elf radiation in a plasma modeled on the magnetosphere. A series of representative pattern plots are presented for frequencies between the proton and electron gyrofrequencies. These patterns illustrate the fact that focusing effects that arise from the geometrical properties of the refractive index surface tend to dominate the radiation distribution over the entire range from the electron gyrofrequency to 4.6 times the proton gyrofrequency. It is concluded that focusing effects should be of significant importance in the design of a vlf/elf satellite transmitting system in the magnetosphere.
A study is made of the input impedance Z of a small strip-loop antenna with arbitrary orientation in a cold collisionless uniform multicomponent magnetoplasma. Assuming a uniform current distribution, an integral expression for Z is derived which is valid for arbitrary values of driving frequency, plasma composition and density, loop orientation angle, and static magnetic field strength. The integral expression is evaluated numerically for the VLF/ELF range in a plasma modeled upon the inner magnetosphere. Approximate closed-form expressions for Z are also developed. It is found that the loop VLF/ELF input reactance is essentially identical to its free space self inductance. Also the loop radiation resistance is found to be a strong function of the loop orientation angle for frequencies near the lower-hybrid-resonance frequency or below the proton gyrofrequency.
Hypersonic flow of a chemically nonequilibrium multicomponent mixture past an axisymmetric blunt body is considered on the basis of the exact Navier-Stokes and chemical rate equations. The flowfield, characterized by a sharp shock and a boundary layer, is solved numerically in the region between the shock and the body. The governing equations are first formulated in generalized orthogonal coordinates, and then recast in computational coordinates in which both the shock and the body are two straight lines and one coordinate is stretched to allow higher space resolution near the body. The thermodynamic and transport properties are obtained from the most rigorous theories and reliable data for each component and for the mixture itself. A time-marching second-order finite-difference method is used to solve the equations.
Numerical solutions of the viscous-shock-layer equation where the chemistry is treated as being either frozen, equilibrium, or nonequilibrium are presented. Also the effects of the diffusion model, surface catalysis, and mass injection on surface transport and flow parameters are considered. The flow is treated as a mixture of five inert and thermally perfect species. The viscous-shock-layer equations are solved by using an implicit-difference scheme. All calculations are for hyperboloids with included angles of 20 and 45. The flight conditions are those for various altitudes and velocities in the earth's atmosphere. Data are presented to show the effects of the chemical models; diffusion models; surface catalysis; and mass injection of air on heat transfer; skin friction; shock standoff distance; wall pressure distribution; and tangential velocity, temperature, and species profiles. The results show that an equilibrium analysis can substantially overpredict the heat-transfer rates for flow conditions experienced by earth-orbital entry vehicles. Moreover, at such conditions surface catalysis significantly influences heat-transfer and flow-field properties. If a binary rather than a multicomponent diffusion model is assumed, negligible errors in most flow properties result. Quantitative results are presented that show the effect of mass injection on flow properties within and downstream of the injection region.
In view of experimental considerations, we give a model-independent argument that the novel tricritical points in multicomponent fluid mixtures, where three phases simultaneously become critical, are points on the boundary of a single two-dimensional surface of critical points. This result is corroborated by the Landau model suggested by Griffiths. The relationship between these tricritical points and the complex 'higher-order' critical points proposed to exist in certain magnetic systems is elucidated.
The slip conditions for a multicomponent mixture with diffusion, wall-catalyzed atom recombination and thermal radiation are derived, and simplified expressions for engineering applications are presented. The gas mixture may be in chemical nonequilibrium with finite-rate catalytic recombination occurring on the wall. These boundary conditions, which are used for rarefied flow regime flow field calculations, are shown to be necessary for accurate predictions of skin friction and heat transfer coefficients in the rarefied portion of the space shuttle trajectory.
The use of adiabatic relations in the calculation of planetary atmospheres requires knowledge of the ratio of specific heats of a mixture of gases under various pressure and temperature conditions. It is shown that errors introduced by simple averaging of the ratio of specific heats in a multicomponent atmosphere can be roughly 0.4%. Therefore, the gamma-averaging error can become important when integrating through the atmosphere to a large depth.
The effects of molecular angular momentum (spin polarization) on the thermal conductivity of a multicomponent gas mixture are considered. The Wang Chang-Uhlenbeck approach to the kinetic theory of gases with internal states is used. Formal results are obtained for the thermal conductivity of a gas mixture of uniform composition. These results are given in terms of the quantum mechanical degeneracy-averaged cross section.