摘要:

The linear stability of parallel flow in a concentric annulus to infinitesimal, axially symmetric disturbances is considered. First, the Poiseuille flow in annular cylinders is studied with the ratiokof the outer to inner cylinder as a parameter. The critical Reynolds number is a monotone function of this radius ratio, increasing without bound ask → ∞(Hagen‐Poiseuille flow) from the plane Poiseuille flow limit(k = 1). Second, a one‐parameter family of skewed (variable viscosity) flows in a fixed annulus is studied. The neutral curves for many of these skewed profiles have a second minimum, which for sufficiently skewed profiles, gives the lowest value of the Reynolds number. These two minima are associated with two very different distributions of Reynolds stress. Both distributions are such that on part of the channel the energy is transferred from the disturbance motion to the basic motion and both can be explained by analysis of the Reynolds stress jump condition and the known structure of Reynolds stress near a rigid wall.

ISSN:0031-9171    

DOI:10.1063/1.1691784

出版商:AIP    

年代:1968

数据来源: AIP

摘要:

The steady‐state laminar flow of an incompressible elasticoviscous liquid in an annulus with coaxial porous walls, rotating about a common axis is considered. The rate of fluid injection at one wall is taken to be equal to the rate of fluid suction at the other. The flow phenomenon has been characterized by the nondimensional parametersRc(elastic number),R(cross‐flow Reynolds number),m(ratio of the angular velocities of the cylinders), and &sgr; (radii ratio). A small perturbation method has been used to obtain an approximate solution for the velocity field. The perturbation method is in powers ofRand, thus, valid for sufficiently small |R|, but generalRc. A perturbation method in powers ofRchas also been used to obtain an approximate solution of the velocity field. This solution should be valid for sufficiently small|Rc|but generalR. The effects of the above parameters on the velocity distribution, shear stress at the walls, and the radial pressure variation have been studied.

ISSN:0031-9171    

DOI:10.1063/1.1691786

出版商:AIP    

年代:1968

数据来源: AIP

摘要:

It is shown that the equations for the motion of a tagged fluid particle in a random wave field define a singular perturbation problem, characterized by a nonuniformity at large times. The uniformly valid asymptotic expansion to this problem, the Euler‐Lagrange relationship for random dispersive waves, is obtained. As an application of these general results, an integral representation of the solution is worked out for the case of vertically propagating random acoustic waves in an isothermal atmosphere. It is shown that the nonuniformity of medium leads to a wave generated diffusion process. The time and length scales over which the process is diffusive are determined, and a formula for the diffusion coefficient is presented.

ISSN:0031-9171    

DOI:10.1063/1.1691787

出版商:AIP    

年代:1968

数据来源: AIP

摘要:

It is shown that the direct interaction hypothesis, when applied to the problem of isotropic mixing of a reactant undergoing an isothermal second‐order reaction, fails to preserve, even approximately, an important invariance. Namely, in the absence of molecular diffusion the decay of single‐point statistical functions of the concentration field should be independent of the turbulence.

ISSN:0031-9171    

DOI:10.1063/1.1691788

出版商:AIP    

年代:1968

数据来源: AIP

摘要:

The governing equations of compressible relativistic flow are cast in a form suitable for treating the subsonic, transonic, and supersonic regimes by established aerodynamic techniques. Small disturbance solutions are found which are the relativistic generalizations of the well‐known aerodynamic laws for these flows. A comparison of present results with the nonrelativistic solutions for pressure coefficient shows significant compressible‐relativistic effects for all three flow regimes. In the supersonic regime, the character of the variation of pressure coefficient with Mach number is quite different for the relativistic and nonrelativistic cases. The ultrarelativistic case is found to represent the limit of the compressible‐relativistic effect in the three flow regimes.

ISSN:0031-9171    

DOI:10.1063/1.1691789

出版商:AIP    

年代:1968

数据来源: AIP

摘要:

Results are presented concerning a theoretical and experimental investigation of low‐energy spherical underwater explosions. The theoretical analysis makes use of the explicity hydrodynamic‐shock‐tube solution, a simple incompressible bubble theory, and its modification which accounts for the finite signal propagation times and the low compressibility of the water medium. Experimentally, the low‐energy blasts are generated by exploding glass spheres pressurized with various gases in a water‐filled spherical test chamber under well‐defined conditions. The results are primarily recorded by schlieren optical systems and piezo‐pressure gauges. The experimental phenomena are shown to be in good quantitative agreement with the theoretical predictions within the physical limitations of the relatively small testing facility and the glass fragments. In particular, for the early stages of the explosions the experimental flow results are well described by the modified bubble theory.

ISSN:0031-9171    

DOI:10.1063/1.1691790

出版商:AIP    

年代:1968

数据来源: AIP

摘要:

The approach towards the equilibrium distribution function is investigated for a monatomic gas having an initial distribution function with strong deviations from a Maxwellian. It is assumed that the distribution function can be approximated by a sum of two characteristic distribution functions whose particle densities are functions of time. These functions are eliminated by the solution of the transfer equation forcx4. The result is compared with the exact solution of the Krook equation. The deviation is 3‐15% for the initial distribution functions considered in the present paper. Relaxation constants for a hard‐sphere gas are evaluated for two special initial distribution functions. They cover a range roughly 10% lower than the relaxation times obtained with the linearized Boltzmann equation in a recent paper by Kusˇcˇer and Williams. For an initial distribution function consisting of a superposition of two Maxwellians with different temperatures the relaxation constant is computed from both the momentum equations forcx4andcx6. The difference between the results is only 6.5%.

ISSN:0031-9171    

DOI:10.1063/1.1691791

出版商:AIP    

年代:1968

数据来源: AIP

摘要:

The Enskog dense gas theory is generalized to arbitrary order in gradients of macroscopic field variables. A constitutive relation for the pressure tensor involving products of velocity gradients is presented in an irreducible tensor formulation. The second‐order transport coefficients are evaluated for smooth rigid spheres, and the theory is applied to certain viscometric flows. Expressions are derived for normal stress effects.

ISSN:0031-9171    

DOI:10.1063/1.1691792

出版商:AIP    

年代:1968

数据来源: AIP

摘要:

Forces between unlike molecules are investigated via mutual and thermal diffusion measurements on4He‐85Kr andH2‐85Kr. New experimental results are reported, the thermal diffusion measurements covering the temperature range 77 to 760°K. Above 300°K the measurements are in reasonable accord with those of Ghozlan and Kistemaker, but below 300°K there are substantial discrepancies. Evidence is presented which indicates that the previous results at the lowest temperatures, particularly for He‐Kr, are incorrect. Present measurements support the adequacy of the common potential parameter combination rules forH2‐Kr, but not for He‐Kr; in the latter case the potential well depth &egr;12is apparently smaller than theoretically predicted, a conclusion in accordance with molecular‐beam scattering measurements.

ISSN:0031-9171    

DOI:10.1063/1.1691793

出版商:AIP    

年代:1968

数据来源: AIP

摘要:

Heat conduction through a rarefied gas contained between concentric cylinders is studied analytically. Emphasis is placed on the connection with the experimental determination of thermal accommodation coefficients by the low‐pressure method. The linearized BGK‐model equation is used, based on small relative temperature difference. Two coupled linear integral equations for the perturbed temperature and density are then formulated. An asymptotic analysis is carried out for the case of mean free path much greater than the inner but of the same order as the outer cylinder radius, which corresponds to typical operating conditions for experiments. The lowest‐order deviation of the heat flux from its free‐molecular value is ofO[ln(Kn)/Kn], the same as that obtained by Knudsen iteration. Numerical calculations are performed to find this term. It is found that for a mean free path 20 or more times the inner cylinder radius the relative error introduced by using the free‐molecular value for the heat flux is less than 5%, provided that the ratio of the mean free path to the outer cylinder radius is at least 0.2.

ISSN:0031-9171    

DOI:10.1063/1.1691794

出版商:AIP    

年代:1968

数据来源: AIP