摘要:

Results are reported of calculations of the Nusselt number for steady two‐dimensional laminar convection in a thin fluid layer between parallel conducting plates. An iterative numerical technique is used to calculate the Nusselt number and the structure of the roll for Rayleigh numbers between 2000 and 22 000 and for Prandtl numbers of 0.5, 1, 2, 6.8, and 200. Comparison with results at Prandtl numbers of 6.8 and ∞ obtained by other investigators using different techniques show good agreement. Discussion is included of the factors affecting accuracy: (1) the zone size in a finite‐difference mesh, (2) the number of iteration cycles, and (3) extrapolation from a sequence of meshes to zero zone size. The conclusion is that extrapolation from a pair of grids using 20 and 30 zones per length scale can yield 1% accuracy over the ranges of parameters considered.

ISSN:0031-9171    

DOI:10.1063/1.1692166

出版商:AIP    

年代:1968

数据来源: AIP

摘要:

Measurements have been made of the onset of instability in rotating Couette flow in order to check some recent numerical results. The case of a very wide gap, a medium gap, and a very narrow clearance ratio have been studied. The accuracy of the results is about ± 2%. The present data and other values available in the literature are compared with the computations of different investigators. With a few exceptions the agreement is found to be excellent. End effects are described and their relative importance is discussed. Methods of scaling the results are evaluated. A simple formula is presented for calculating the onset value when only the inner cylinder rotates.

ISSN:0031-9171    

DOI:10.1063/1.1692167

出版商:AIP    

年代:1968

数据来源: AIP

摘要:

Observations have been made on the onset of instability, and on the waveform both at onset and in the finite amplitude region for flows with closed nonrotationally symmetric streamlines. The effect of placing obstacles in the gap between concentric rotating circular cylinders is shown to depend primarily on the extent to which they modify the mean flow. The case of a square inner cylinder and circular outer cylinder is compared with the case of a circular inner cylinder and square outer cylinder. It is shown that the former arrangement, which is time‐dependent, is much less stable than the latter. It is concluded that the shape of the boundaries in the Taylor double cylinder problem do not influence the stability markedly, other than by defining the clearance ratio, unless they make the problem time‐dependent.

ISSN:0031-9171    

DOI:10.1063/1.1692168

出版商:AIP    

年代:1968

数据来源: AIP

摘要:

A diffusion approximation is derived for the transfer of spectral components of mean‐square fluctuations of a passive scalar quantity advected by an isotropic turbulent flow. This approximation, expected to be most useful for very large Reynolds numbers, preserves nonnegative spectral components and chaotic equilibrium solutions, as well as producing−53power advection range spectra in appropriate circumstances. A comparison is made with some observations of Gibson and Schwarz at a Prandtl number of 7. Cutoff difficulties at large wavenumber make the approximation questionable for Prandtl numbers much greater than 7.

ISSN:0031-9171    

DOI:10.1063/1.1692169

出版商:AIP    

年代:1968

数据来源: AIP

摘要:

Experiments with a circular cylinder in an incompressible, two‐dimensional flow show the influence of the unsteady wake on the flow field and heat transfer near the forward stagnation point. Velocity fluctuations, correlations between velocity fluctuations, fluctuation spectra, and the heat transfer near the forward stagnation point were measured and the influence of the wake determined. The wake induces rmsu′ velocity fluctuations near the forward stagnation point just outside the boundary layer of about 12%. Theu′ fluctuations on opposite sides of the stagnation point have a correlation coefficient of − 1. Energy spectra of the fluctuations show a peak energy density at the cylinder Strouhal frequency. Imposed free‐stream turbulence of 6% intensity increases the fluctuations slightly but reduces the correlations significantly. The wake‐induced velocity fluctuations do not influence the mean heat transfer near the forward stagnation point.

ISSN:0031-9171    

DOI:10.1063/1.1692170

出版商:AIP    

年代:1968

数据来源: AIP

摘要:

A previous study of the laminar boundary layer involving four inert species with widely different molecular weights but with a uniform external stream has been extended to describe such a boundary layer at an axisymmetric stagnation point. The transport properties of the gas mixture are described with reasonable accuracy so as to permit assessment of the importance thereof on the predictions of the boundary‐layer behavior. Comparison of the exact calculations is made with the predictions based on the “cold wall” approximation and on a model based on the inner‐layer solutions for “massive blowing.”

ISSN:0031-9171    

DOI:10.1063/1.1692171

出版商:AIP    

年代:1968

数据来源: AIP

摘要:

The nonequilibrium flow of an ideal dissociating gas past a convex corner is studied. Linearized theory based on the undisturbed flow is reexamined, and it is shown that it does not give a good quantitative description of the variation of flow quantities along the wall, even for relatively small corner angles. The apparent agreement between the results of linear theory and characteristics solutions reported in earlier work is shown to be due to an ambiguous definition of the characteristic relaxation time. It is only when a characteristic relaxation time based on downstream conditions, rather than upstream conditions, is used in the linearized theory that the results agree reasonably with the numerical calculations. The modified linear theory is used to calculate the increase in entropy along the wall, and it is shown that normal gradients in entropy exist even far downstream of the corner. The calculated increase in entropy along the wall is related explicitly to the asymptotic wall values of the other flow variables, and these values are shown to be different from the infinite‐reaction‐rate equilibrium values. The calculated asymptotic values are in good agreement with those obtained from numerical calculations.

ISSN:0031-9171    

DOI:10.1063/1.1692172

出版商:AIP    

年代:1968

数据来源: AIP

摘要:

The low Reynolds number flow of a gas past an infinite heated circular cylinder is studied for the case of variable property flow when the temperature difference between the cylinder and free stream is small. The perturbation to the corresponding incompressible velocity field is calculated by the method of matched asymptotic expansions developed by Kaplun, and Proudman and Pearson. When the temperature difference between the cylinder and free stream is appreciable, a solution for the velocity field is found on the assumption that the viscosity and thermal conductivity of the gas are invariant. This solution possesses the interesting property that the zero‐order solution for the velocity field near the cylinder is a uniformly valid solution of the problem.

ISSN:0031-9171    

DOI:10.1063/1.1692173

出版商:AIP    

年代:1968

数据来源: AIP

摘要:

Equations governing the flow of a compressible or heated rotating jet far downstream from the orifice, in the neighborhood of the axis of symmetry, are solved in the von Mises plane, and expressions for the axial and radial distributions of velocity and enthalpy are derived. Relations for the retransformation to the physical plane are obtained and computed for specific initial conditions.

ISSN:0031-9171    

DOI:10.1063/1.1692174

出版商:AIP    

年代:1968

数据来源: AIP

摘要:

Volume integrals of the quantityE/&OHgr;, whereEis the classical acoustic energy density of Rayleigh and &OHgr; is a frequency variable as measured by an observer moving with the medium, are conserved within the assumptions of geometric acoustics in a moving medium whose undisturbed motion is not necessarily steady. WithAnthe area of a ray tube cut by a wave front, the quantityEaAn/&OHgr;2is constant along a ray. These results generalize classical results of Blokhintsev.

ISSN:0031-9171    

DOI:10.1063/1.1692175

出版商:AIP    

年代:1968

数据来源: AIP