摘要:

The structure of a plane shock wave is studied by an extension to the gas dynamics of the two‐fluid model already introduced in the superfluidity theory. The classical form is used for the linearization of two Boltzmann equations, and restricted to the first approximation. This is different from Mott‐Smith's solutions which cannot be derived by linearization from a single Boltzmann equation, and as a result has to be introduced arbitrarily. Six equations of change for conservative quantities (mass, momentum, energy) are obtained which makes possible the solution of the wave problem without having to introduce other equations of change. Calculations are made using the elastic‐sphere model. Comparison with observations made on argon gives very satisfactory results. The solutions tend asymptotically to a stationary solution corresponding to a Mach number equal to infinity, and to a shock wave thickness 11.4 times the mean free path ahead of the shock for all monatomic gases. This establishes the possibility of coexistence of two fluids in nonequilibrium, even thermal, in shock waves with large gradients.

ISSN:0031-9171    

DOI:10.1063/1.1706628

出版商:AIP    

年代:1962

数据来源: AIP

摘要:

Collision integrals (transport cross sections) for atomic and molecular interactions of importance in high‐temperature air are calculated based on accurate force laws which have recently become available. The tabulations include the collision integrals for diffusion, viscosity, and thermal conductivity, and the collision integral ratiosA*,B*, andC* needed for mixture calculations, and cover the range from 1000° to 15 000°K for the major interactions N&sngbnd;N, O&sngbnd;O, N&sngbnd;O, N&sngbnd;N2, O&sngbnd;O2, O&sngbnd;N2, N2&sngbnd;N2, O2&sngbnd;O2, and N2&sngbnd;O2. Average potential energy functions, but no collision integrals, are given for the minor interactions O&sngbnd;NO, O2&sngbnd;NO, N2&sngbnd;NO, and NO&sngbnd;NO. The calculations all refer to atoms and molecules in their ground states only. Calculational errors are estimated to be about 5% over the temperature range, but may occasionally rise as high as 10%. The relative magnitudes of the average collision integrals are discussed briefly for their bearing on the qualitative behavior of the corresponding gas mixtures, and on the assessment of the errors involved in some approximations commonly used in calculations of transport properties of air.

ISSN:0031-9171    

DOI:10.1063/1.1706629

出版商:AIP    

年代:1962

数据来源: AIP

摘要:

The classical problem of heat and mass transfer from single spheres at low values of the Reynolds number, where the velocity field is given by Stokes' formula, is considered. It is shown, by the use of a singular perturbation technique, how an expansion may be derived for the Nusselt number Nu in terms of the Pe´clet number Pe which yields an accurate expression for the rate of transfer of energy or matter in the range 0 ≦ Pe ≦ 1. It is also established, by studying both the Pe → 0 and Pe → ∞ asymptotes, that the functional relation between Nu and Pe as obtained with the Stokes velocity profile is less sensitive to an increase in the Reynolds number than the familiar Stokes law for the drag coefficient.

ISSN:0031-9171    

DOI:10.1063/1.1706630

出版商:AIP    

年代:1962

数据来源: AIP

摘要:

The dynamical equations which describe the behavior of isotropic turbulence in two dimensions are derived on the basis of the hypothesis that fourth‐order cumulants of the velocity field are zero. The equations are then integrated numerically as an initial‐value problem for an inviscid fluid. The result shows that the calculated rate of energy transfer is greater toward the larger scales than the smaller scales. The most remarkable feature revealed by the computation is that the energy‐spectrum function assumes negative values during the course of time for medium‐sized eddies. Truncation errors which arise from finite difference approximations in numerical integration are examined. From this result, it is concluded that the hypothesis of zero fourth‐order cumulants does not always guarantee positive energy, at least, for a turbulent flow in two dimensions.

ISSN:0031-9171    

DOI:10.1063/1.1706631

出版商:AIP    

年代:1962

数据来源: AIP

摘要:

Two problems are considered, each of which represents a class of flows. In the first problem the motion is induced by passage of electric current through an incompressible viscous electrically conducting fluid contained in an insulated axisymmetric tube. The solution is obtained in closed form by assuming small Reynolds numbers such that the electromagnetic forces are balanced by viscous forces. In the second problem incompressible inviscid electrically conducting fluid flows through an axisymmetric tube and the flow is modified due to passage of electric current. The complete solution of the resultant rotational flow is obtained in closed form for small changes in tube diameter. At appreciable rates of current flow the fluid in the central part of a contracting tube behaves as if the tube were expanding; the opposite is true for an expanding tube. This is shown to be the case quite generally even when the assumption of small magnetic Reynolds number is dropped. Further, at large rates of current flow there may develop a secondary flow.

ISSN:0031-9171    

DOI:10.1063/1.1706632

出版商:AIP    

年代:1962

数据来源: AIP

摘要:

An idealized theory of flame propagation is formulated to explain the effects of tube diameter, mixture composition, and direction of motion in a gravity field on the flame shape and ``speed of uniform motion'' of a flame front propagating through a stationary air‐fuel mixture contained in a long tube. The effect of local flame curvature on flame speed and viscous effects within the fluid are considered, for it is believed that both play major roles in the production of a steady flame of finite amplitude. Ideally it is possible to match the present theory (valid far from a real wall) to a theory that accounts for the flame shape of the ``quenched'' portion of the flame close to the wall. This matching is only discussed qualitatively.

ISSN:0031-9171    

DOI:10.1063/1.1706633

出版商:AIP    

年代:1962

数据来源: AIP

摘要:

Experiments are described concerning the interface instability which arises when an argon‐bromine mixture falls under gravity into air or into helium. Existing theories which include viscosity effects fail to explain the observed amplitude growth rate, but it is shown that approximate inclusion of diffusion effects allows calculation of all features of early perturbation growth accurately to within experimental error.

ISSN:0031-9171    

DOI:10.1063/1.1706634

出版商:AIP    

年代:1962

数据来源: AIP

摘要:

The calculation of the development of a spherical explosion in sea water, due to the symmetrical detonation of a charge of pentaerythritol tetranitrate, is carried up to the stage when the second blast wave converges as an implosive wave on the center and is reflected. Continuing earlier calculations by the authors, the complete field of disturbance is determined by the Eulerian approach, using the method of characteristics and boundary‐fitting techniques, up to the characteristic ray originating from the center at the time of implosion. At this ray the main shock has traveled approximately 7 charge radii from the center. The implosive phase of the second shock motion is a well‐known similarity phenomenon, and a variety of methods for treating this are discussed.

ISSN:0031-9171    

DOI:10.1063/1.1706635

出版商:AIP    

年代:1962

数据来源: AIP

摘要:

The problem of flute instabilities earlier discussed by Rosenbluth and Longmire and by the author is reconsidered. The theory is extended to include the influence of a mass velocity in the unperturbed state as well as compression and expansion effects arising from the inhomogeneity of the magnetic field. According to the latter effects, surfaces of constant density will not move with the fluid velocity. A description of the dynamics of density perturbations is made in terms of the fluid equations under the assumption of negligible Ohmic and viscous dissipation. Adiabatic and isothermal changes of state are discussed for a plasma with adiabatic and isothermal distributions of pressure and density in the unperturbed state. The plasma is found to be stable against flute disturbances of any wavelength, not only for cusped geometry, but also for mirror geometry under certain conditions. This is the case when the characteristic lengthB/|∇B| of the magnetic field is less than twice the characteristic lengthN/|∇N| of the unperturbed density distribution. The approximations of the present theory exclude a treatment of perturbations which extend across the whole plasma body. The compression mechanism which is responsible for the stabilization is a zero‐order effect which is independent of the assumptions of isotropy and of the special forms of the unperturbed density and pressure distributions.

ISSN:0031-9171    

DOI:10.1063/1.1706636

出版商:AIP    

年代:1962

数据来源: AIP

摘要:

Perturbations of a plasma torus which are independent of azimuth are not covered by the general theory. A method for treating these special modes is presented, uniqueness theorems proved, and a rapidly converging numerical scheme for computation is given. It is also shown that these modes have the same behavior in a torus of infinite aspect ratio as do the corresponding ones in a cylinder; therefore the infinitely thin torus is stable against these modes.

ISSN:0031-9171    

DOI:10.1063/1.1706637

出版商:AIP    

年代:1962

数据来源: AIP