摘要:

The thermodynamic equilibrium of rotating liquid He II is investigated on the basis of the macroscopic Landau theory. After reviewing the classical theory of rotating fluids, it is shown that for He II the normal fluid component is in solid body rotation while the superfluid flow can be irrotational except for a set of vortex lines or vortex sheets which must be stationary in a reference frame rotating with the normal fluid. Therefore, an array of quantized vortex lines which rotate with the normal fluid can be considered to be in thermal equilibrium. The number and positions of the lines is determined by thermodynamic stability requirements. The dissipative effects must have the property that they vanish in equilibrium and that they drive the system to the state of equilibrium. It is further shown that the equations proposed by Khalatnikov fulfill these requirements.

ISSN:0031-9171    

DOI:10.1063/1.1692335

出版商:AIP    

年代:1969

数据来源: AIP

摘要:

The thermal diffusion factor for 50%4He‐3Hegaseous mixtures has been measured from room temperature to about 55°K. The experiments were done using a two‐bulb type apparatus and in some cases the method of successive separations. From room temperature to about 80°K the present data agree well with earlier investigations. Below 80°K the agreement is only qualitative. The present data compare well with values based on quantum theoretical calculations using the Morse‐VDDpotential but do not agree with values based on the Lennard‐Jones 12‐6 potential.

ISSN:0031-9171    

DOI:10.1063/1.1692336

出版商:AIP    

年代:1969

数据来源: AIP

摘要:

In the Stratford‐Townsend model of a strongly retarded two‐dimensional incompressible turbulent boundary layer, the velocity profile in the wall region, often termed the modified law of the wall, is obtained from an extended mixing length hypothesis together with the assumption of a linear total stress distribution normal to the wall. Here, the equations of motion are solved using a similarity assumption and a linear stress distribution. It is found that for certain flows Townsend's modified law of the wall is quite compatible with the similarity solution. In addition, it emerges from the present analysis that, under certain circumstances, a linear velocity profile satisfies the conditions arising from inserting a linear stress distribution into the equations of motion even better than Townsend's profiles, at least in the region not too close to the wall. It is found that a simple observed change from the conventional assumption of a mixing length varying linearly with distance from the wall allows this linear velocity profile to be predicted and, when the profile is compared with measurements, good agreement is obtained.

ISSN:0031-9171    

DOI:10.1063/1.1692337

出版商:AIP    

年代:1969

数据来源: AIP

摘要:

The location of the boundary‐layer separation point on a circular cylinder has been investigated experimentally for a stationary cylinder and for a cylinder which is performing vortex‐excited oscillations. The results for the stationary cylinder are in close agreement with published data. For the vibrating cylinder, the range of angular displacement of the separation point was found to depend upon the vibration amplitude and frequency, and the peak displacement occurred at a different frequency from that which gave the peak cylinder amplitude. As the frequency of the wake motion increases beyond that which gives that maximum range in the location of the separation point, the range of the motion of the separation point decreases. For given cylinder and wake frequencies, the higher the cylinder amplitude, the greater the motion of the wake. The phase shift of the actual wake was found to be close to 180 deg behind that of an ideal wake which aligns itself behind the relative velocity vector of the flow. The phase shift was found to be independent of cyclinder amplitude.

ISSN:0031-9171    

DOI:10.1063/1.1692338

出版商:AIP    

年代:1969

数据来源: AIP

摘要:

A theoretical study is made of the convection near a heated vertical plate in a dc electric field. Electrical forces are produced by a bulk charge density in an electric field. This charge density occurs because the temperature gradients produce gradients in conductivity in a fluid with Ohmic electrical properties. To find the effect of the electrical forces, a set of boundary‐layer equations is developed and then integrated over the boundary layer. This integration produces ordinary differential equations when profiles are assumed for the temperature, velocity, and electric field. These profiles each have the same boundary‐layer thickness. Both numerical and analytical solutions are found for these equations. The analytical solutions are for special cases and approximate the numerical solutions. The results are approximate expressions for the temperature, velocity, electric field, and heat transfer from the plate.

ISSN:0031-9171    

DOI:10.1063/1.1692339

出版商:AIP    

年代:1969

数据来源: AIP

摘要:

The combined effects of a thermal gradient and a dc electric field upon a poorly conducting fluid are used to induce steady convection. A vertically directed temperature gradient is used to establish an electrical conductivity gradient over the rectangular cross section of a liquid‐filled channel. Then a static potential, which varies either linearly or periodically along the channel, is imposed on electrodes that form the channel top. A similar potential, spatially shifted in the longitudinal (horizontal) direction, is applied at the bottom of the channel. These electrodes make physical and electrical contact with the fluid, which typically has a mean electrical conductivity of10−10 mho/m. Because of the conductivity gradient, the vertical component of the resulting electric field induces free charges in the bulk, and these charges are then pulled in the horizontal direction by the longitudinal component of the electric field. An analytical model is used to predict the distribution of potential, electric stress, and velocity. It is assumed that effects of convection on the charge distribution can be ignored (electric Reynolds number small). An experiment is described in which the periodic potential distribution is closed on itself in a re‐entrant channel to achieve fully developed flow. Experiment and theory compare favorably with discrepancies largely attributable to finite electric Reynolds number effects.

ISSN:0031-9171    

DOI:10.1063/1.1692340

出版商:AIP    

年代:1969

数据来源: AIP

摘要:

The instability with respect to infinitesimal, antisymmetrical disturbances of a viscous, laminar, plane jet is investigated for an incompressible fluid. The minimum critical Reynolds number is found to be 4.03 when the unperturbed flow is assumed to be parallel and 12.4 when some corrections for nonparallelism are made. In the actual jet flow it does not appear that a small two‐dimensional disturbance in itself leads to transition, because as it propagates downstream the disturbance leaves the unstable region in the&agr;‐Rplane, and then proceeds to damp out.

ISSN:0031-9171    

DOI:10.1063/1.1692342

出版商:AIP    

年代:1969

数据来源: AIP

摘要:

The propagation of infinitesimal sound waves in a liquid containing gas bubbles is considered. Relative motion of gas bubbles and liquid is explicitly allowed for, and it is shown that a significant error in the speed of waves may arise if the relative motion and fluctuations of mass fraction are neglected. The structure of steady shock waves is also derived.

ISSN:0031-9171    

DOI:10.1063/1.1692343

出版商:AIP    

年代:1969

数据来源: AIP

摘要:

The rarefaction shock is found to be impossible practically in an equilibrium van der Waals-Maxwell fluid, in and across all phase regions, although numerical tables seem to indicate the opposite result. The existence of this type of shock depends explicitly on the constant-volume specific heat, as well as the pressure equation of state. The form of specific heat assumed here includes contributions from translation, rotation, and vibration energies of the molecule; Einstein functions are used to represent the latter. In particular, the vaporizing expansion wave in the saturated liquid phase cannot be discontinuous. Metastable states of supersaturation are not considered. Despite the results for this theoretical model, the necessary conditions for the rarefaction shock are found to be satisfied, in principle, for a small region near the critical point of a real two-phase fluid (steam).

ISSN:0031-9171    

DOI:10.1063/1.1692344

出版商:AIP    

年代:1969

数据来源: AIP

摘要:

The concept of parasitic eigenvalues in the numerical solution of sets of ordinary differential equations is introduced. The use of an implicit method is proposed for the solution of sets of differential equations containing such parasitic eigenvalues. These ideas are then applied to the integration of the equations which govern the one‐dimensional flow of a chemically reactive gas. In particular, results are presented for the flow downstream of a normal shock wave and for the flow in a converging‐diverging nozzle. The conditions are delineated under which the more complicated computations required by the implicit method appear justified.

ISSN:0031-9171    

DOI:10.1063/1.1692345

出版商:AIP    

年代:1969

数据来源: AIP