摘要:

The turbulence characteristics of an axisymmetric wake shed by a very slender body at Mach 3 have been measured with the hot‐wire anemometer. The region covered began at transition, located immediately downstream of the model, and ended about 100 virtual (momentum) wake diameters downstream. By using computer‐aided corrections to the anemometer frequency response, maps of the temperature and axial velocity fluctuations, their cross correlations, spectral density, and autocorrelation macroscales were obtained as a function of the axial and radial coordinates. Beyond 40 wake diameters from the virtual origin, dynamic equilibration forces these distributions into seemingly selfpreserving forms. These forms are identical with their incompressible counterparts except for a coordinate transformation already suggested by the dynamic equilibrium hypothesis and the Reynolds analogy typical of adiabatic flows. The density macroscale is numerically smaller than that of the velocity, although they both approximate the transverse wake scale. Away from the axis, both the fluctuation magnitudes and their spectral densities are apparently disorted by signals associated with the intermittent boundary, which is thought to be weakly periodic with a wavelength on the order of the wake diameter.

ISSN:0031-9171    

DOI:10.1063/1.1692209

出版商:AIP    

年代:1968

数据来源: AIP

摘要:

A theory of unsteady long waves in a stratified fluid over a channel of arbitrary cross section is proposed. The results obtained are general enough to meet any practical purpose, but rather simple in application. A formula is first derived to determine the wave speed in relation to any given density profile, current speed, and cross section of the channel. The wave form is then prescribed by a set of three time‐dependent equations, depending upon the relationship among the longitudinal length, wave amplitude, and time scales. The theory predicts the occurrence of various types of internal waves at the depth where the rate of change of the density profile is the largest in the increasing direction of depth, and with slight modification, the method developed is applied to the case of a fluid with infinite height or a fixed boundary, where density stratification plays an indispensable role.

ISSN:0031-9171    

DOI:10.1063/1.1692210

出版商:AIP    

年代:1968

数据来源: AIP

摘要:

For general centered self‐similar unsteady flows separated by a shock wave from an unsteady ambient medium, the profile distributions of physical variables are, in general, obtainable by purely numerical means only. However, one integral of motion based on mass and energy conservation relations is found to exist universally, except in the singular case where the ambient density decay exponent falls on the geometry expansion index. This work formally derives and presents this integral in closed form.

ISSN:0031-9171    

DOI:10.1063/1.1692211

出版商:AIP    

年代:1968

数据来源: AIP

摘要:

The mass spectrometer has frequently been employed to study chemical kinetics and ionization processes. The difficulty encountered is the sampling process, i.e., the transfer of a sample of gaseous or ionized species from a high‐temperature and high‐pressure reactive region, into the operating pressure of a mass spectrometer,10−5mm Hg, with the fewest reactions and changes of composition. The sampling process in the shock tube is further complicated by the nonsteady, nonuniform, cool, and dense end‐wall thermal layer. A detailed study of ions (or gaseous species) diffusing through the thermal layer and expanding through an orifice to a free‐molecular jet, and the reactions which occur during the process, is carried out using a simplified model. The agreement between the simplified model results and the experimental results promises the possibility of obtaining quantitative measurement by this sampling process.

ISSN:0031-9171    

DOI:10.1063/1.1692212

出版商:AIP    

年代:1968

数据来源: AIP

摘要:

Monochromatic radiation propagating in a direction opposite to that of a uniform, one‐dimensional shock wave is absorbed throughout the region behind the shock front. Euler's equations for unsteady flow with energy addition and the macroscopic equation for radiative transfer neglecting emission are used to describe the motion. Behind the shock front it is assumed that the energy added to a fluid element during heating is small compared with its initial internal energy. Then, the mathematical method of strained coordinates (Poincare´‐Lighthill‐Kuo technique) can be applied, and it is found that the radiation is exponentially attenuated behind the shock wave. The absorbed radiation accelerates the shock wave and generates a secondary shock front. The time at which the secondary shock wave appears is inversely proportional to both the intensity of the radiation and the absorption coefficient. The asymptotic constant velocity of the secondary shock wave is found to equal the speed of a rearward propagating acoustic wave plus a correction proportional to the radiation intensity.

ISSN:0031-9171    

DOI:10.1063/1.1692213

出版商:AIP    

年代:1968

数据来源: AIP

摘要:

A closure at the third‐order moment is presented for the problem of the decay of reactants which obey a second‐order equation, and whose initial description is given stochastically. The closure satisfies prescribed realizability conditions for all possible initial assignments of the mean, the mean square fluctuations, and third‐order moments of the concentration field. The closure is applied in two typical examples, and in each case the results agree satisfactorily with exact stochastic solutions.

ISSN:0031-9171    

DOI:10.1063/1.1692214

出版商:AIP    

年代:1968

数据来源: AIP

摘要:

Numerical techniques have been used to study natural convection in a fluid subjected to axial rotation. Axisymmetrical flows were studied in two different geometries for a variety of rotational speeds. For case I(R1 = 1.0, R2 = 2.5, H = 3.0), the computed flow patterns were qualitatively compared with those which would be expected from the basic rules of physics, and good agreement was obtained. Rotational speeds between&OHgr; = 0,and&OHgr; = 20were studied for a Grashoff number of 3000. Increased rotational speed was found to decrease the over‐all heat transfer rate. For case II(R1 = 1.0, R2 = 4.0, H = 1.0), rotational speeds of&OHgr; = 0.0to&OHgr; = 40.0were studied at a Grashoff number of 400. At low rotational speeds, a single convection cell was found, however, at higher rotational speeds, the single cell became unstable, and changed to a two‐celled pattern. This transition resulted in a slight increase in the over‐all heat transfer rate.

ISSN:0031-9171    

DOI:10.1063/1.1692215

出版商:AIP    

年代:1968

数据来源: AIP

摘要:

In spherical regions, an arbitrary solenoidal velocity field can be developed into a series of toroidal and poloidal fields. These fundamental vector fields, expressed in terms of spherical Bessel functions and spherical harmonics, have certain orthogonality properties which prove useful in treating convective flow problems within spheres. The utility of this velocity field representation is demonstrated by considering the stability of a nonuniformly heated fluid in a spherical cavity. A variational principle is presented, equivalent to the eigenvalue problem for the critical Rayleigh number (the stability criterion). This principle forms the basis for an approximate method of determining upper bounds to the critical Rayleigh number. It is found that a class of three‐dimensional disturbances is more unstable than either the simplest poloidal (axisymmetric) disturbance mode or the simplest toroidal (two‐dimensional) disturbance mode. The numerical results are compared with previously published analyses.

ISSN:0031-9171    

DOI:10.1063/1.1692216

出版商:AIP    

年代:1968

数据来源: AIP

摘要:

The stability of a fluid layer with adverse time‐dependent density gradients is examined by two computational techniques. The most direct solution, that of integrating the time‐dependent equations, is compared with the results obtained by invoking the often used quasistationary state approximation. It is seen that this latter approximation is not valid if the instability stems from a sudden change in the concentration or temperature at one surface of the fluid layer. The particular problem studied here is that of a liquid film resting on an impermeable wall with gas absorption into the liquid. In this case the system evolves from one stable state to another with the essential problem being to assess the stability of the system during its evolution between these stable states. It is shown that a single critical Rayleigh number does not exist as in the usual case with linear time‐independent density gradients, but that the critical Rayleigh number depends, to some extent, on intangible factors such as the initial perturbation magnitude and the mode of observation.

ISSN:0031-9171    

DOI:10.1063/1.1692217

出版商:AIP    

年代:1968

数据来源: AIP

摘要:

The problem of heat and mass transfer from small spheres and cylinders freely suspended in a shear flow is considered in the limit of Reynolds number Re → 0. Asymptotic formulas are derived which relate the Nusselt number Nu to the Pe´clet number Pe in the limit Pe → 0, and for the case of the cylinder, Pe → ∞. At high Pe, the Nusselt number is found to approach a constant value, whereas, at low Pe it is shown to increase withPe12for the sphere and with—(log Pe)−1for the cylinder. These results indicate the existence of a fundamental difference at high Pe between the shear flow problem studied here and the corresponding classical problem of uniform flow at infinity.

ISSN:0031-9171    

DOI:10.1063/1.1692218

出版商:AIP    

年代:1968

数据来源: AIP