摘要:

A simple model is formulated following classical lines and used to investigate the decay of line vortices in which both self‐induced and ambient turbulence may exist. The effect of molecular viscosity is included, since it may be important at certain times and in certain regions of the vortices. Circulation overshoot, predicted for the first time by Saffman, is also predicted by this model when self‐induced turbulence is taken into account. This occurs even if no trace of overshoot is present initially. Experimental data of Focke, which exhibit overshoot, are used to test the model. The presence of a logarithmic portion in the circulation profiles of turbulent vortices is discussed critically.

ISSN:0031-9171    

DOI:10.1063/1.861075

出版商:AIP    

年代:1975

数据来源: AIP

摘要:

The flow properties of liquid helium are such that the motions of vortex rings and line vortices can be calculated from hydrodynamic potential theory. The two‐dimensional (line vortex) case allows a relatively simple method of calculating vortex motion: The ’’Routh path function’’ yields a solution through conformal mapping. Using this method, the case of a rectilinear vortex pair approaching a slit in a wall is analyzed. Criteria for their just passing through are found.

ISSN:0031-9171    

DOI:10.1063/1.861076

出版商:AIP    

年代:1975

数据来源: AIP

摘要:

Experimental results are presented describing the character of the secondary flow developed within a curved pipe for which the primary (axial) flow is driven by an oscillating pressure gradient. The comparison between previous theory and experiment is excellent.

ISSN:0031-9171    

DOI:10.1063/1.861077

出版商:AIP    

年代:1975

数据来源: AIP

摘要:

The use of the Wiener–Hermite expansion for the turbulence problem is reviewed. The expansion is known to give good results for lower Reynolds’ number flows, up to a fluctuation Reynolds’ number of 20 using more recent time‐dependent bases. The use and meaning of these bases is discussed. A new development in Wiener–Hermite expansion is used to calculate Burgers’ model: It is known that these expansions are not unique; by taking advantage of this arbitrariness, a renormalization is presented and used to improve the convergence of the expansion. The procedure involves calculation for turbulence using a time‐dependent base for a short time. The calculation is then stopped and the resulting functions are adjusted in such a way as to minimize the non‐Gaussian part of the energy, at the same time preserving the last value of the transfer function. Following this, the calculation is resumed using these new, adjusted values for the functions; then the process is repeated. For the first time it was possible to obtain the equilibrium formk−2, of the energy spectrum for Burgers’ model of turbulence. The calculation proceeds, holding the non‐Gaussian part of the energy to but a few percent. Good results are obtained up to fluctuation Reynolds’ numbers of 100.

ISSN:0031-9171    

DOI:10.1063/1.861078

出版商:AIP    

年代:1975

数据来源: AIP

摘要:

The anomalous behavior of Pitot tubes in the turbluent pipe flow of a dilute polymer solution is investigated and discussed. Pitot tube error is measured using an alternative optical means of local velocity measurement. Unlike previous research in this field a strict control is kept on the state of degradation of the solutions and Pitot tube error is measured directly whilst the tube is under test. Errors which occurred in total head pressure measurement were found to be negative and in some cases were as high as 40%. Factors which influence the Pitot tube accuracy are identified and a dynamical similarity argument is used to express the error as a function of these. Pitot tube error is attributed to the polymer solutions storing energy viscoelastically at the tube tip. A critical review of explanations previously put forward for Pitot error with reference to the results is included in the discussion. The polymer used was polyox WSR‐301.

ISSN:0031-9171    

DOI:10.1063/1.861079

出版商:AIP    

年代:1975

数据来源: AIP

摘要:

The effects of polydispersity in drag reduction were studied by testing two narrow molecular weight distribution polystyrene samples individually and in mixtures. The results indicate that the largest molecules in the distribution determine the value of the onset point and that this value decreases with increasing molecular weight. Above the onset point the magnitude of the drag reduction effect is shown to be a complex function of both molecular weight and polydispersity.

ISSN:0031-9171    

DOI:10.1063/1.861080

出版商:AIP    

年代:1975

数据来源: AIP

摘要:

Accurate semi‐analytic solutions to the inverse blunt‐body problem have been obtained using a method of series expansion. Rational fractions are used for series summation and analytic continuation. Angles of incidence up to 30° and Mach numbers as low as 2 have been considered. The maximum entropy streamline will not wet the body surface in asymmetric flow. It may pass either above or below the stagnation streamline. Limit lines appear in the supersonic portion of the flow field, both in the shock layer and in its upstream analytic continuation.

ISSN:0031-9171    

DOI:10.1063/1.861081

出版商:AIP    

年代:1975

数据来源: AIP

摘要:

There are numerous problems of two‐dimensional viscous, compressible or incompressible steady‐state flows where the governing hydrodynamic equations are difficult to solve even numerically due to their elliptic‐hyperbolic character and the complex geometry of the flow configuration. For such problems, a finite‐element numerical technique has been developed whereby the steady‐state hydrodynamic equations and the associated boundary conditions are solved taking into full account the nonlinear convective terms, viscous terms, heat conduction terms, and variable fluid properties. The numerical technique is based upon a general formulation for the system of hydrodynamic equations making use of the method of weighted residuals, applied over discrete, distorted finite elements of the flow domain where the unknown fluid variables are expressed continuously in terms of polynomial approximating functions and nodal parameters. This process results in a set of nonlinear algebraic equations for the nodal parameters which are solved iteratively by using a multi‐dimensional Newton–Raphson scheme. To assess its accuracy, the method is applied to problems of compressible and incompressible viscous flow and heat transfer in diverging channels with plane walls, and also to a problem of normal shock wave in one‐dimensional flow. The results in all cases are in satisfactory agreement with existing analytical solutions and experimental data. Furthermore, the numerical scheme appears to be stable.

ISSN:0031-9171    

DOI:10.1063/1.861082

出版商:AIP    

年代:1975

数据来源: AIP

摘要:

The onset of convection in a horizontal, isotropic, water‐saturated porous medium is considered. The temperature difference between the top and bottom is as large as 250 °C. The effects of an eightfold variation in kinematic viscosity are included. The critical Rayleigh number is found to be substantially reduced from the classical value although the associated wavenumber is nearly the same. Neutral mode streamline and isotherm patterns are considerably distorted in the vertical direction in distinction to the symmetric patterns found in the constant viscosity classical calculation.

ISSN:0031-9171    

DOI:10.1063/1.861083

出版商:AIP    

年代:1975

数据来源: AIP

摘要:

The hypothesis, proposed by Probstein and Gold, that cross‐hatching results from the differential deformation of an inelastic material at its surface, has been used in this analysis. Wall pressure and wall shear stress perturbations leading to the deformation were calculated with the linearized small perturbation theory. The supersonic boundary layer was composed of an inviscid outer layer and a viscous sublayer. Both laminar and turbulent mean velocity and Mach number profiles were used in the calculation. In contrast to the work of Probstein and Gold the viscous sublayer was included and wall pressure perturbations were also considered. The essential result is the prediction of the pattern cant angle, which was not possible with the inviscid analysis. The theory qualitatively confirms the experimentally observed features of cross‐hatching, similarly seen by Probstein and Gold. For instance, for cross‐hatching to occur, the boundary layer must be supersonic and turbulent, whilst the inelastic body material must be of the Maxwell type. Theory and experiment also show that the pattern is charcterized by a cant angle equal to the local Mach angle, by a wavelength inversely proportional to the static pressure and directly proportional to the viscosity of the material.

ISSN:0031-9171    

DOI:10.1063/1.861084

出版商:AIP    

年代:1975

数据来源: AIP