摘要:

A numerical computation of the laminar boundary layer on a fixed circular disk of radiusawhose axis is concentric with that of a vortex having circulation&Ggr;is described. The computations were started at the edge of the disk and continued inward toward the axis until the properties of the terminal flow became evident. A two‐layer asymptotic expansion was formulated for the solution of the boundary‐layer equations near the axis, and the terminal‐flow properties revealed by the analysis are shown to be in excellent agreement with the numerical results. The structure of the terminal boundary layer consists of an inner layer next to the surface with thicknessO[(&ngr;/&Ggr;)1/2r]in which the flow is primarily radial, and an outer layer with thicknessO[(&ngr;/&Ggr;)1/2a]of predominantly inviscid nature in which the flow recovers to the external potential vortex. The mass flux in the outer layer does not vanish asr→0, indicating that the boundary layer must erupt from the surface atr=0in the manner envisioned by Moore.

ISSN:0031-9171    

DOI:10.1063/1.1693691

出版商:AIP    

年代:1971

数据来源: AIP

摘要:

The vaporization rate of chromium metal into an atmosphere of cold helium gas was measured in a rotating disk flow geometry. Gas conditions were 1 atm pressure and temperatures of 300 and 600°K. The disk temperature was varied from 1630 to 1760°K. At the lowest disk temperatures, the rates appeared to approach the values predicted by isothermal convection‐diffusion theory. At higher temperatures, the measured rates were considerably greater than those predicted by simple mass transfer considerations and were reduced when the helium temperature was increased. These observations suggest that condensation of metal vapor in the boundary layer was accelerating the vaporization rate. At the highest disk temperature investigated, the observed rate was a factor of 10 greater than the rate predicted from isothermal rotating disk theory. A difference of this magnitude is expected for kinetically unhindered condensation in the boundary layer (i.e., the metal partial pressure follows the temperature profile according to the vapor pressure curve).

ISSN:0031-9171    

DOI:10.1063/1.1693692

出版商:AIP    

年代:1971

数据来源: AIP

摘要:

The quantity which is here called the fundamental derivative has been defined as the nondimensional form&Ggr;≡12&rgr;3c4(∂2&Ugr;/∂P2)s. The relation of&Ggr;to other thermodynamic variables is discussed. It is already known that the existence of conventional compression shocks requires&Ggr;>0. It is shown that other dynamic behavior of compressible fluids is fixed by the sign of&Ggr;. Particular emphasis is given to phenomena corresponding to negative&Ggr;. These phenomena include the area variation of a transonic passage, the form of a Prandtl‐Meyer wave, the behavior of adiabatic flow with friction, and nonlinear wave propagation. Formulas and numerical values are given for&Ggr;in various substances.

ISSN:0031-9171    

DOI:10.1063/1.1693693

出版商:AIP    

年代:1971

数据来源: AIP

摘要:

Kinetic equations are presented which successfully incorporate the effects of atomic line radiation on the spatial and time evolution of the velocity distributions of a radiating gas. The equations are applied to the steady‐state optical excitation of a free molecular slab of two level atoms in a model of the optically excited laser amplifier. Iteration on the coupled kinetic equations and equation of radiative transfer is used to construct a first approximation to the velocity distributions in the optically thick limit. This corresponds to integral iteration in kinetic theory. By performing certain quadratures over the first‐order velocity distribution for particles in the excited or upper lasing state, it is possible to calculate the inversion density as well as all the radiative properties of the gas. An asymptotic theory is given for the density in the limit of weak external radiation and for two wall reflectance conditions. Also an interesting bimodal behavior of the emission profile is seen. The lineshape of the emitted radiation is constant in the line core for about one Doppler width, then it reaches a sharp peak before a Gaussian decay in the far wings.

ISSN:0031-9171    

DOI:10.1063/1.1693694

出版商:AIP    

年代:1971

数据来源: AIP

摘要:

A development is given of a thermodynamical theory of fluid suspensions of deformable particles. Assuming particles are spherical when undeformed and become ellipsoidal when sheared, linear constitutive equations are extracted from the general theory and restrictions on the material coefficients which appear in these linear constitutive equations are deduced by thermodynamical considerations. Applying this linear theory to steady shear flow of solutions for which particle interactions are negligible, it is found, solely by use of the thermodynamical restrictions on material coefficients, that the theory qualitatively predicts observed behavior in steady shear flow of dilute solutions of random coiling macromolecules, such as solutions of polyisobutylene. In particular, the resulting expressions for apparent viscosityt21/Kand normal stress differencet11 − t22are exactly those known to characterize experimental results forK≤103sec−1. For low shear ratesK, the predicted value for the second normal stress differencet22−t33in terms oft11−t22is exactly as measured experimentally. It is suggested that consideration of particle interaction effects will be necessary to accurately predictt22−t33at higher shear rates.

ISSN:0031-9171    

DOI:10.1063/1.1693695

出版商:AIP    

年代:1971

数据来源: AIP

摘要:

The artificial viscosity method is used to calculate the flow following the detonation of a centrally initiated pentolite sphere in fresh water at sea level, up to the time the main shock in the water is 100 charge radii from the center. Pressure, particle velocity, and temperature versus distance at various times are obtained; also peak pressures, time constants, and pressure versus time at fixed positions. Partial steam formation in the water close to the gas bubble is shown to be possible but unimportant at the distances covered. The partition and distribution of kinetic and internal energies in the water and the gas sphere, and the energy dissipated by shock heating, are found. The calculated dissipated energy is 33% of the total energy released in the detonation when the shock front is 10 charge radii from the center, and 40.5% when the shock front is 100 charge radii from the center.

ISSN:0031-9171    

DOI:10.1063/1.1693696

出版商:AIP    

年代:1971

数据来源: AIP

摘要:

A physical model is presented for the structure of an electric‐current‐carrying discontinuity moving into nonconducting gas and leaving nonconducting gas behind. The model assumes a normal shock wave followed by a porous current sheet. A three‐fluid analysis (electrons, neutrals, and singly charged ions) is made for the case where the component of magnetic field normal to the plane of the discontinuity is zero. All the dependent variables can be computed as functions of displacement in the streamwise direction, as demonstrated in two specific examples. The model admits finite‐strength current sheets as solutions, with the electron and ion density diminishing to zero upstream and downstream of the sheet. As seen moving with the discontinuity, the impressed electric field and the induced electric field are additive on both sides of the discontinuity. This is in contrast to the case for magnetohydrodynamic shock waves, where these two fields cancel on both sides; and to gas‐ionizing shock waves, where the two fields cancel on the downstream side. In the frame of reference moving with the discontinuity, the discontinuity dissipates electrical energy and decelerates the gas. A new jump relation is found which may be described as a “sheet Ohm's law.” The fact that one and only one such relation exists, implies that a current‐carrying discontinuity moving through nonconducting gas is unstable and cannot be part of a unique flow solution unless the discontinuity moves supersonically with respect to the upstream gas and subsonically with respect to the downstream gas.

ISSN:0031-9171    

DOI:10.1063/1.1693697

出版商:AIP    

年代:1971

数据来源: AIP

摘要:

Momentum coupling between two interpenetrating plasmas in the presence of a weak magnetic field has been studied experimentally. A coaxial plasma gun ionizes and accelerates aluminum (0.4 mg to 10 cm/&mgr;sec) into a low‐pressure background gas which has been preionized by ultraviolet radiation from the gun. A steady magnetic field is applied parallel to the aluminum flow with maximum amplitude such that (1) the ratio of dynamic (aluminum) pressure to magnetic pressure, is of order103, (2) the ion gyroradius is much larger than over‐all flow scale, and (3) the Alfve´n Mach number is greater than 10. Under these conditions, the field should have no direct influence on the deceleration rate of the aluminum plasma. Streak camera photographs show little momentum transfer between the two plasmas when no field is applied (verifying collisionless conditions) and almost complete transfer when field is applied. Magnetic field probes show that the applied field has been pushed aside by the aluminum plasma creating a field free bubble region. The scale length of the electron density gradients has been measured with a holographic interferometer indicating momentum transfer lengths less than 1 cm and thus two orders of magnitude less than the ion gyroradius.

ISSN:0031-9171    

DOI:10.1063/1.1693698

出版商:AIP    

年代:1971

数据来源: AIP

摘要:

A model for the high‐beta spherical expansion of a plasma in a background magnetic field and ambient plasma is applied to laser‐created plasmas. An analytic solution for the magnetic field configuration during early phases of the expansion is obtained and is found to be stable to small amplitude disturbances propagating in arbitrary directions with respect to the background magnetic field. The electrons are treated as an inertialess fluid throughout the analysis.

ISSN:0031-9171    

DOI:10.1063/1.1693699

出版商:AIP    

年代:1971

数据来源: AIP

摘要:

The dynamical formation and structure of the plasma focus has been studied with a two‐dimensional numerical fluid model. The extremely high kinetic energy densities obtained in the numerical fluid experiment as the result of adiabatic compression and viscous heating agree well with experiment. Three features in the plasma focus are isolated: an anode cold source, a hot pinch region, and an axial shock. The anomalously long lifetime of the plasma focus is shown to be the result of axial flow, with stabilization of magnetohydrodynamic modes through the ion stress tensor in the intermediate collisionless, collision‐dominated regime. Estimates of the neutron yield based on the numerical fluid experiment concur with experimental yields, and are the result of thermally reacting deuterons in the hot pinch region. The plasma parameters of interest determined from the hot pinch region suggest that the ion distribution function will not have a simple Maxwellian form and this in particular may account for the discrepancy with experiment on the anisotropy in space of the neutron yield.

ISSN:0031-9171    

DOI:10.1063/1.1693700

出版商:AIP    

年代:1971

数据来源: AIP