摘要:

The reversible two‐fluid equations of helium II are shown to possess two integrals of circulation. The first, which expresses conservation of circulation in the superfluid, is well known, but the second, which expresses conservation of the line integral of&rgr;n(un− us)/(&rgr;s)around a circuit moving with the normal fluid, appears to be new.

ISSN:0031-9171    

DOI:10.1063/1.1691851

出版商:AIP    

年代:1968

数据来源: AIP

摘要:

Measurements have been made of the logarithmic decrement and period of disks of radius 3‐8.5 cm performing torsional oscillations at amplitudes in the range 0.01‐1.6 rad in fluids of kinematic viscosity 0.29‐3.06 centistokes. Both the logarithmic decrement and period were observed to depend on the amplitude of oscillation in qualitative agreement with a thory due to Rosenblat which predicts amplitude effects due to secondary flow. The amplitude effects were smaller than predicted and were dependent on the radius of the disk but were relatively insensitive to kinematic viscosity, disk thickness, or distance to the outer boundary. Below 0.2 rad the period was constant within 0.001% and below 0.3 rad the logarithmic decrement was constant within 0.3%; empirical correlations are presented for the data at higher amplitudes.

ISSN:0031-9171    

DOI:10.1063/1.1691852

出版商:AIP    

年代:1968

数据来源: AIP

摘要:

Similarity solutions of the boundary‐layer equations representing the flow of jets in an external stream and tailored pressure gradients were obtained. These solutions apply to jets in coflowing and counterflowing streams. A number of analytical solutions not previously published were obtained. Of particular interest are the solutions for small‐increment jets which imply that a Gaussian velocity profile exists far downstream from the origin of the jet, even in arbitrary pressure gradient. The solutions were extended to turbulent flow using the hypothesis of a constant eddy viscosity, which in turn, was modified to account for intermittency. The theoretical predictions were compared with the measurements of Gartshore in self‐preserving wakes and the agreement between theory and experiment is good.

ISSN:0031-9171    

DOI:10.1063/1.1691853

出版商:AIP    

年代:1968

数据来源: AIP

摘要:

The impulsive piston problem is examined for an early period before nonlinear effects acquire significance. It is assumed that the velocity of the piston is well below the mean thermal speed, that specular reflection occurs at its surface, and that the linearized isothermal Bhatnagar‐Gross‐Krook equation governs the gas dynamics. With the aid of Fourier and Laplace transforms an exact solution to this equation and also asymptotic solutions for times short and long as compared to a mean free time are derived. At the earliest times a “relative steepening” of the density profile near the isothermal sound speed is observed. Much later a Navier‐Stokes shock‐type profile is achieved, but, in addition, a careful analysis predicts the presence of a “transient Knudsen layer” near the piston joined smoothly to an extremely weak “kinetic precursor disturbance” far ahead of the shock. Discussion is given to the influence of the chosen kinetic model equation and boundary condition on these results.

ISSN:0031-9171    

DOI:10.1063/1.1691854

出版商:AIP    

年代:1968

数据来源: AIP

摘要:

A set of kinetic equations for polyatomic gases is obained by extending the 13‐moment approximation of Grad to solve the inelastic Boltzmann equation of Wang Chang, Uhlenbeck, and de Boer. It is expected that the resulting 17‐moment approximation (the four additional moments are the internal temperature and the internal heat flux vector) will be applicable to a wider class of physical problems than the “normal”‐type Chapman‐Enskog solutions to the inelastic Boltzmann equation. In particular, the kinetic equations should prove quite useful in the study of shock structure and sound propagation in polyatomic gases. As examples, the 17‐moment approximation is applied to near equilibrium and relaxation type flows; and all the essential features of the Wang Changet al.analysis are recovered, such as those involving temperature equilibration, volume viscosity, and the extension of the Navier‐Stokes equations to polyatomic gases. In addition, corrections to the Navier‐Stokes equations are derived involving terms which are second order in the transport coefficients. Possible generalizations and extensions of the 17‐moment approximation are also discussed.

ISSN:0031-9171    

DOI:10.1063/1.1691855

出版商:AIP    

年代:1968

数据来源: AIP

摘要:

Rigorous bounds on the permeability of a porous medium to Knudsen flow are formulated by applying the variational procedure of DeMarcus. The bounds are expressed in terms of certain averages characterizing the random‐pore geometry. Explicit calculations are given for a model pore structure generated from randomly overlapped spheres.

ISSN:0031-9171    

DOI:10.1063/1.1691856

出版商:AIP    

年代:1968

数据来源: AIP

摘要:

Approximate formulas for computing the thermal conductivity of a polyatomic gas developed by Eucken, Hirschfelder, Mason and Monchick, and Saxena are compared with experimental data and the results of calculations for models of polyatomic molecules. It is found that due to the scatter in the experimental results, comparison with the model calculations is the most severe test of the approximate formulas. On this basis, the Mason and Monchick formulas are found to be the most accurate. A modification of the Mason‐Monchick computational scheme is considered, and it is found that this modification leads to results which are in even better agreement with both the model calculations and laboratory data.

ISSN:0031-9171    

DOI:10.1063/1.1691857

出版商:AIP    

年代:1968

数据来源: AIP

摘要:

For two important classes of inviscid and relaxing gases, namely for real gases with several internal degrees of freedom and for diatomic dissociating gases, the frozen shock in steady one‐dimensional compression flow is always weaker than the equilibrium shock.

ISSN:0031-9171    

DOI:10.1063/1.1691859

出版商:AIP    

年代:1968

数据来源: AIP

摘要:

A closed analytical model for compressible magnetohydrodynamic boundary layers is formulated by using transport equations for the turbulent fluctuations of species mass density, velocity, and temperature, and thus avoidinga priorirelations between turbulent fluxes and mean flow quantities. The equations for both the mean and the fluctuating motion are simplified according to the boundary‐layer approximation, and closure of the system is achieved by the introduction of “universal turbulence structure parameters” that only relate turbulent correlations among themselves. This model accounts for convection and diffusion of turbulent fluxes as well as for the effect of turbulence suppression by applied magnetic fields. It is shown that if convection, diffusion, and electromagnetic effects were omitted in the equations of fluctuating motion, the latter would reduce to algebraic forms defining the concepts of mixing length, turbulent Prandtl number, and turbulent Schmidt number in terms of turbulence structure parameters.

ISSN:0031-9171    

DOI:10.1063/1.1691860

出版商:AIP    

年代:1968

数据来源: AIP

摘要:

Flow in a magnetic annular shock tube is analyzed, in which both the driving and applied magnetic fields vary with time. First, one‐dimensional flow is solved by the hypersonic similarity method for the case in which both fields are proportional to a power of time. Second, the local similarity approximation is described to treat more general case in which the fields are smooth functions of time. Third, a purely numerical integration using Lax's finite difference method is carried out for a flow with a sinusoidal driving magnetic field, in which a typical nonsimilar nature of the solution appears in some parts as well as locally similar ones in other parts of the flow. Next, some experiments on a magnetic annular shock tube using air as the working gas, are described with special interest paid to the effect of unsteady azimuthal magnetic field on the flow, and comparisons with theoretical predictions are reported.

ISSN:0031-9171    

DOI:10.1063/1.1691861

出版商:AIP    

年代:1968

数据来源: AIP