摘要:

An integral representation is obtained for the velocity and pressure fields produced by the horizontal motion of two‐dimensional bodies below (or on) the free surface of a viscous liquid. This allows consideration of viscous and free surface effects to be incorporated in one model for the prediction of forces on the body. The integral representation is used to consider the simple physical example of the motion of a horizontal flat plate. This illustrates the interaction of viscous and free surface effects since the plate experiences skin friction drag plus drag due to the generation of surface waves by the viscous boundary layer.

ISSN:0031-9171    

DOI:10.1063/1.1692251

出版商:AIP    

年代:1969

数据来源: AIP

摘要:

Numerical solutions have been obtained for incompressible Newtonian flow around a circular cylinder for Reynolds numbers of 1, 2, 4, 10, 15, 30, 50, 100, and 500. The results are presented in the form of vorticity and stream function distributions. The solutions allow detailed characterization of the vortex rings. Drag coefficients, pressure distributions, and vortex dimensions are compared with experimental data and with available theoretical predictions for Reynolds numbers up to 50. The agreement with both experimental data and previous theoretical solutions is considered to be excellent.

ISSN:0031-9171    

DOI:10.1063/1.1692253

出版商:AIP    

年代:1969

数据来源: AIP

摘要:

An exact similarity solution is given for the flow of a fluid‐particle suspension over an infinitely large disk rotating at a constant velocity. Numerical solutions of the resulting ordinary differential equations provide velocity distributions for both fluid and solid phases and density distributions for the solid. The boundary‐layer thicknesses of the particle cloud and the fluid are found to be approximately equal. In addition to its intrinsic value as a solution to a physical problem, the results provide a convenient basis for judging the accuracy of approximate techniques.

ISSN:0031-9171    

DOI:10.1063/1.1692261

出版商:AIP    

年代:1969

数据来源: AIP

摘要:

Mean‐flow measurements have been made in the supersonic wake of a very slender, two‐dimensional body at zero incidence and heat transfer rate. Excellent correlation of the lateral distribution of axial velocity is obtained when the lateral distance is divided by the transverse wake scale which is formed from the measured velocity defect. The latter is found to decay as the inverse square root of distance for the entire range of about 1850 virtual model thicknesses mapped; thus, the transverse scale increases as the square root of distance. In the latter half of this range the lateral distribution of static temperature also appears to correlate in the same lateral coordinate, and the temperature defect also decays as the inverse square root of distance. It is demonstrated that these results are accurately predictable from a basic similarity analysis beginning with Townsend's measured velocity decay on the axis; the turbulent Reynolds number of 13.0 agrees closely with Townsend's 12.5. The corresponding Prandtl number found lies in the range from 0.65 to 0.70.

ISSN:0031-9171    

DOI:10.1063/1.1692273

出版商:AIP    

年代:1969

数据来源: AIP

摘要:

A theory of homogeneous turbulence in an incompressible fluid is formulated. The field variablev(r, t)is expanded in terms of a complete set of an ideal random basis, the first term of which is Gaussian. Since the ideal basis follows the actual fluid motion, there should be no incorrect relation between large and small eddies.

ISSN:0031-9171    

DOI:10.1063/1.1692291

出版商:AIP    

年代:1969

数据来源: AIP

摘要:

Three statistical theories of turbulence are applied to thermal convection between infinite slippery plates in the limit of infinite Prandtl number. The range of Rayleigh numberRinvestigated is657 ≤ R ≤ 1.25 × 104. The theories, which are compared in a series of numerical calculations, are the direct interaction approximation, the quasilinear approximation, and the quasinormal approximation. The direct interaction approximation gives results for the evolution Nusselt number in good agreement with some simple exact solutions to the problem. The flow predicted by this method is very persistent. Turbulence first appears just at criticalRand its intensity gradually increases with increasingR. The quasinormal approximation gives satisfactory results forR ≲ 2000, but some of the initial value problems lead to an unphysical negative temperature autocorrelation spectrum for largerR. In none of the initial value problems forR > 2 × 103did the quasinormal procedure yield a sensible stationary state. The quasilinear approximation appears to upperbound the heat transport given by both the other approximations predicting about 8% larger heat transport than the direct interaction approximation.

ISSN:0031-9171    

DOI:10.1063/1.1692293

出版商:AIP    

年代:1969

数据来源: AIP

摘要:

The flow of a laminar stream containing a periodic fluctuation of the mass fraction of a chemical species over a flat plate was considered. The fluctuation of the chemical species is assumed to be continuously generated at a point uptream of the plate, and the surface of the plate is assumed to possess a finite catalyticity for the first‐order surface reaction of the chemical species. When the wavelength in the inviscid stream is long compared with the distance along the surface, the out‐of‐phase fluctuation in the boundary layer was found to increase with the Damkohler number, beginning with a finite value when the Damkohler number is zero, and only decrease for very large values of Damkohler number. Thus, the off‐phase fluctuation in the boundary layer, particularly near the surface, is maximum for a given fluctuation in the free stream when the surface Damkohler number is finite. When the wavelength in the inviscid stream is very small as compared with the distance along the surface, the fluctuation is confined to the outer portion of the boundary layer. In the limit of the continuously decreasing wavelength (continuously increasing frequency), the momentum boundary‐layer edge becomes a singular line across which no fluctuation can penetrate. The regular and the singular perturbation techniques have been employed for the analysis.

ISSN:0031-9171    

DOI:10.1063/1.1692294

出版商:AIP    

年代:1969

数据来源: AIP

摘要:

For the case of a binary mixture it is shown that it is possible to formulate the calculation of the coefficients of viscosity, thermal conductivity, thermal diffusivity, and diffusion in terms of variational principles. These are such that a first‐order error in the trial function representing the departure of the distribution functions from their local thermal equilibrium values leads to a second‐order error in the transport coefficients. For those coefficients which are intrinsically positive the variational method reduces to an absolute maximum principle.

ISSN:0031-9171    

DOI:10.1063/1.1692295

出版商:AIP    

年代:1969

数据来源: AIP

摘要:

It is shown that the transport coefficients for an almost‐Lorentzian mixture(m&bgr;/m&agr; ≪ 1, n&bgr;/n&agr; < 1)can be computed as a perturbation to the coefficients for a true Lorentzian mixture, which are known exactly. This method of computation is found to be much more efficient than the usual Chapman‐Enskog method. Application to partially ionized gases is discussed.

ISSN:0031-9171    

DOI:10.1063/1.1692296

出版商:AIP    

年代:1969

数据来源: AIP

摘要:

The theory of nonisothermal, nonstationary diffusion in a two‐bulb geometry is corrected and extended. Two major corrections to simple theory are necessary: one for the variation with time of the thermal diffusion ratio, and one for the deviations from a quasistationary state in the connecting tube. All previous treatments of the second correction contain inadequacies serious enough to necessitate revision of many reported diffusion coefficients

ISSN:0031-9171    

DOI:10.1063/1.1692297

出版商:AIP    

年代:1969

数据来源: AIP