摘要:

Plane wave solutions for the propagation of sound in a polyatomic gas have been obtained by employing the method of Sirovich and Thurber for polyatomic kinetic models. An asymptotic analysis valid at small frequencies yields the correct continuum limits for the absorption and speed of propagation, and numerical calculations were made for a wide range of frequencies and at several values of the collision number for the relaxation of internal degrees of freedom. Calculations using values of model parameters suitable for nitrogen, oxygen, and air, over a large range of the rarefaction parameter, are in very good agreement with dispersion and absorption measured in these gases.

ISSN:0031-9171    

DOI:10.1063/1.1692298

出版商:AIP    

年代:1969

数据来源: AIP

摘要:

The sharp leading edge problem is studied within the framework of the kinetic theory of gases. The Boltzmann equation with the Bhatnagar‐Gross‐Krook model is used as the governing equation. The method of discrete ordinates developed by Huang is applied. The local distribution functions for the entire flow field have been calculated for the case of supersonic flow,M∞ = 1.5; thus, the complete flow field has been generated for various plate temperature values. The calculated results offer considerable insight into the behavior of a rarefied gas flow as it traverses the complete spectrum of flow regimes from near‐free molecular to continuum, and present a meaningful connection between the near‐free molecule solution at the leading edge and the extended continuum theories in the interaction regimes. Comparison with the existing theories and experimental data show reasonably good agreement in all flow properties. For higher Mach numbers, however, a higher‐order quadrature is necessary. It is felt that the only limitation of the present solution is that of large computer storage requirements.

ISSN:0031-9171    

DOI:10.1063/1.1692299

出版商:AIP    

年代:1969

数据来源: AIP

摘要:

The dynamics of a highly conducting fluid stream coupled by means of a transverse electric or parallel magnetic field to a conducting elastic medium is examined in detail. From the dispersion relation and the Bers‐Briggs criterion, the stability of the infinite length system is described. Eigen‐frequencies and eigenfunctions are computed for the finite length system and good agreement is obtained with an electrohydrodynamic experiment. A physical explanation is given for the overstabilities observed. The close analogy between a limiting case of the field‐coupled system and an electron beam coupled to a traveling wave structure is discussed.

ISSN:0031-9171    

DOI:10.1063/1.1692252

出版商:AIP    

年代:1969

数据来源: AIP

摘要:

The general mathematical problem of magnetohydrodynamic thermal entrance regions is investigated for a parallel plate channel by including the Hall effect, axial heat conduction, Joule heating, and viscous dissipation. The associated eigenvalue problem is solved by the Galerkin method and the results are presented for the temperature development in a channel under uniform wall temperature conditions. It is concluded that the Hall current has considerable effect on the thermal problem and that the axial heat conduction cannot be neglected for low Peclet numbers.

ISSN:0031-9171    

DOI:10.1063/1.1692254

出版商:AIP    

年代:1969

数据来源: AIP

摘要:

The flow of a conducting fluid in a duct in the presence of a magnetic field with a small nonuniformity of the following kind is considered : forx < 0, the field is uniform and parallel to the axis0xof the duct; forx > 0, the field is nonuniform and the curvature of the magnetic lines is small, of order&egr;. A perturbation theory is presented for the case of small magnetic Reynolds numberRmand small Alfve´n numberA. In particular, the flow field is determined to order&egr;and to zero order inRm, and the magnetic field to order&egr; Rm. Downstream, all the perturbations decay algebraically. The upstream perturbations of the flow field initially decay exponentially, with ultimate algebraic decay in the&egr; Rm‐order terms. For the induced magnetic field, the upstream decay is algebraic.

ISSN:0031-9171    

DOI:10.1063/1.1692255

出版商:AIP    

年代:1969

数据来源: AIP

摘要:

The effects of viscosity and finite electrical conductivity of mercury on the axisymmetric instabilities of a current‐carrying annular cylinder of mercury are considered in the context of the experiment of Lehnert and Sjo¨gren. A straightforward numerical method to solve the characteristic value problems is used to determine the real values of growth rates for various values of the wavenumbers and current density ratios, using true as well as hypothetical values of viscosity and electrical conductivity. It is shown that the consideration of neither the viscosity nor the electrical conductivity of mercury is adequate to remove a discrepancy between the experiment and an earlier theory by Jayasimha and Murty. It is shown that other parameters remaining the same, the viscosity of the fluid will have to be 10 times larger, or its electrical conductivity would have to be107times higher to reduce the growth rates to nearly half their values in the absence of viscosity and electrical conductivity.

ISSN:0031-9171    

DOI:10.1063/1.1692256

出版商:AIP    

年代:1969

数据来源: AIP

摘要:

The behavior of a large‐amplitude intermediate magnetohydrodynamic wave in the presence of reflected particles is examined. For reflections off its front side, the wave becomes a spreading expansion wave; for reflections off the back side it steepens to a shock wave, i.e., an entropy increase is produced across the wave.

ISSN:0031-9171    

DOI:10.1063/1.1692257

出版商:AIP    

年代:1969

数据来源: AIP

摘要:

The time evolution of wave correlations (cumulants) in a uniformly turbulent ensemble of weakly nonlinear, dispersive systems is discussed. With closure of the hierarchy for wave correlations appropriate to the inclusion of resonant four‐wave processes, a kinetic equation for the spectral energy density of the waves is derived in situations where the resonant three‐wave decay condition cannot be satisfied. The resulting kinetic equation is a nonlinear integrodifferential equation with driving terms trilinear in the energy density. Some general properties of this equation are discussed including associated conservation relations and the law of increase of entropy.

ISSN:0031-9171    

DOI:10.1063/1.1692258

出版商:AIP    

年代:1969

数据来源: AIP

摘要:

The electrical conductivity of the noble gases—argon, helium, xenon, and krypton—has been calculated for arbitrary degrees of ionization for electron temperatures in the 300‐30 000°K range. A variational method elaborated by Robinson and Bernstein was employed in the calculations, along with the electron‐atom momentum transfer cross‐section values reported by Frost and Phelps. Because of the very low values of the electron‐noble‐gas atom cross sections near the Ramsauer minimum, Coulomb collisions have been found to influence the conductivity for values of fractional ionization as low as10−7. For the same reason electron‐neutral momentum transfer collisions have been found to be unimportant for values of fractional ionization as low as10−5, above which the gas behaves as though it were fully ionized. Two limiting degrees of ionization have been defined for each noble gas above or below which the gas can be considered either completely or weakly ionized, respectively. In addition, the influence of electron‐electron interactions on the electrical conductivity in the partially ionized regime has been established.

ISSN:0031-9171    

DOI:10.1063/1.1692259

出版商:AIP    

年代:1969

数据来源: AIP

摘要:

The problem of electron‐ion temperature relaxation when two semi‐infinite, nonmagnetized plasmas at different initial temperatures were suddenly brought into thermal contact under constant pressure is investigated using the two‐fluid model. No current is assumed to flow across the interface, and charge separation is considered only to the extent of a simple correction on effective thermal conductivity (i.e., no plasma oscillation). Viscous stresses associated with induced fluid motion are also neglected. The asymptotic solution for long time after thermal contact is shown to be identical to that in a single‐temperature plasma, with effective thermal conductivity equal to approximately[1 + (3me/mi)12]times the local electron thermal conductivity. For a time scale shorter than or comparable to the mean electron‐ion collisional energy transfer timeteia self‐similar solution is obtained in the form of a double series in ascending powers of the nondimensional time&tgr; = t/teiand of the initial temperature difference parameter&egr; ≡ (T2−T1)/(T2+T1). It is found that the induced pressure is quite large at early times, suggesting that thermal shock could be a significant source of plasma wave excitation in certain non‐steady problems.

ISSN:0031-9171    

DOI:10.1063/1.1692260

出版商:AIP    

年代:1969

数据来源: AIP