摘要:

In this paper, the rapid simple shearing flow of a dry cohesionless soft‐ferromagnetic metal powder is studied in an externally applied magnetic field. An annular shear‐cell apparatus was used to test the powder. Dry metal powder is contained in the annular channel. The powder is rapidly sheared by rotating one of the shear transmission surfaces while the other shear transmission surface remains fixed. Various magnetic fields are applied to the metal powder during the shearing motion. At present this field effect on the flow is not well understood. The shear stress and normal stress on the stationary surface are measured as a function of the following parameters: fractional solids content, shear rate, shear‐cell gap thickness, and the magnitude and direction of the magnetic field strength. Both the fractional solids content and the shear‐cell gap thickness are kept at prescribed values during stress measurements. The shear stress and normal stress are observed to increase with the application of a magnetic field. A framework is developed that explains the magnetic field effect in shear flow applications.

ISSN:0031-9171    

DOI:10.1063/1.866213

出版商:AIP    

年代:1987

数据来源: AIP

摘要:

Generation of ripples by wind blowing over a viscous fluid was investigated by G. I. Taylor [TheScientificPapersofG.I.Taylor(Cambridge U. P., Cambridge, 1963), Vol. 3, No. 25] with linear stability analysis. Taylor considered the case of temporally growing disturbances in a low density gas and applied his results to explain the process of atomization of a liquid jet injected into a low density gas. Taylor’s analysis is extended here to investigate the case of a spatially growing disturbance in a dense gas. Taylor showed that temporal disturbances of wavelength shorter than the capillary length are stable. The same is found for the spatial disturbances. Each type of disturbance possesses a maximum growth rate with a specific wavelength and frequency. The atomized droplet size corresponding to the maximum growth rate is shown in both theories to decrease inversely as the square of the jet velocity. While the maximum growth rate increases as the square root of the gas‐to‐liquid density ratio whenA2exceeds 1 for the temporal disturbances, the same dependence on the density ratio does not hold for spatial disturbances untilA2exceeds 100, whereA2is a flow parameter representing the ratio of surface force to the viscous force. WhenA2exceeds 100 the growth rates predicted by two theories deviate significantly only at air pressure higher than 10 atm for most liquids at room temperature.However, for all parameters, the spray angle changes along the jet axis according to the spatial theory, but remains constant according to the temporal theory. It is shown that the viscous force in the liquid may be increased relative to the surface tension force to the point that no discernable spray angle may be observed in practice. Then an intact jet without atomization may result. It is shown that the onset of atomization is primarily caused by the pressure fluctuation which resonates the capillary waves. The results on the interfacial amplification rate suggest that a sufficiently large initial amplitude at the nozzle exit is essential for the onset of atomization.

ISSN:0031-9171    

DOI:10.1063/1.866214

出版商:AIP    

年代:1987

数据来源: AIP

摘要:

Some physically significant consequences of recent advances in the theory of homogeneous statistical solutions of Navier–Stokes equations are presented. Invariance properties of families of those solutions are discussed and used to derive rigorously certain previously conjectured results, e.g., the Kolmogorov spectrum. Others include a reinterpretation of the von Karman–Howarth–Dryden equation that leads to the conditions for the existence of an inertial subrange. Further an application of Poincare´’s inequality produces a different view of intermittency. It is also suggested how a measurement of the two‐point triple velocity correlation could yield an accurate value of Kolmogorov’s constant.

ISSN:0031-9171    

DOI:10.1063/1.866215

出版商:AIP    

年代:1987

数据来源: AIP

摘要:

The fixed‐point form of hydrodynamic equations emerging from renormalization group analysis of strong turbulence is analyzed using perturbation expansion in powers of the renormalized coupling constant (Reynolds number) Re*∝&egr;1/2. In the second order of &egr; expansion, transport equations are derived for energy and variance of a passive scalar which are identical to the inertial‐range form of the eddy‐damped quasinormal Markovian approximation (EDQNM), but without adjustable parameters which must be determined from experiment. The energy and scalar variance spectra are predicted to beEk=1.617&egr;¯2/3k−5/3, and &THgr;k=1.146N¯ &egr;¯−1/3k−5/3, where &egr;¯ andN¯ are, respectively, the dissipation rate of energy and scalar variance. This level of agreement with experiment has in the past proved difficult to obtain from renormalized perturbation theory applied to thebarehydrodynamic equations, without introduction of parameters that must be adjusted to different values for different dynamical fields. The fidelity of the present method, which emphasizes in a particular way the distant interactions inkspace, may be related to the degree of nonlocality of the bare dynamics as manifested by possible generic Beltramization tendencies in strong turbulence.

ISSN:0031-9171    

DOI:10.1063/1.866216

出版商:AIP    

年代:1987

数据来源: AIP

摘要:

A direct numerical simulation of the three‐dimensional Navier–Stokes equation at high Reynolds numbers is performed by the spectral method with 3×3403effective modes (853independent degrees of freedom) starting from a high‐symmetric flow. Kolmogorov’s [C. R. (Dokl.) Acad. Sci. URSS30, 301 (1941)] similarity forms of the energy spectra (the one‐dimensional longitudinal and lateral energy spectra as well as the three‐dimensional one) in the universal range are observed in a decaying period after the enstrophy takes the maximum value. During this period the energy decays exponentially in time and the microscale Reynolds number changes from 100 to 60. At the lower part of the universal range Kolmogorov’s inertial range spectrumE(k,t)=A&egr;(t)2/3k−5/3is observed over nearly one decade of the wavenumber, where the Kolmogorov constantA≊1.8. At the higher part of the universal range, on the other hand, it has an exponential tail with an algebraic correction,E(k,t)/[&egr;(t)&ngr;5]1/4=B(k/kd(t))mexp[−&bgr;(k/kd(t))], R)], whereB≊8.4,m≊−1.6, &bgr;≊4.9, andkd(t)=[&egr;(t)/&ngr;3]1/4is the energy dissipation wavenumber.

ISSN:0031-9171    

DOI:10.1063/1.866137

出版商:AIP    

年代:1987

数据来源: AIP

摘要:

Velocity fluctuations are measured in both the intermittent and irrotational regions outside the turbulent/nonturbulent interface of a self‐preserving wake. In the outer part of the intermittent region, there is a tendency for all the predictions of the theory of Phillips [Proc. Cambridge Philos. Soc.51, 220 (1955)] to be satisfied by the nonturbulent data. At larger distances from the interface, the level of the velocity fluctuations becomes comparable with the background turbulence but the organized motion induced by coherent structures within the wake can still be identified. The contribution of this motion to the normal stresses satisfies irrotationality and homogeneity and the amplitude of this motion decays in a manner consistent with Phillips’ theory.

ISSN:0031-9171    

DOI:10.1063/1.866138

出版商:AIP    

年代:1987

数据来源: AIP

摘要:

In applications to turbulent reactive flows, the probability density function approach requires a model for molecular diffusivity. The objective of the present work is to develop a consistent model for passive scalars in turbulent flows, improving the calculation of the velocity‐scalar correlation coefficient. This is done by using the Langevin model for the velocity and by adjusting two model parameters of a velocity‐biased mixing model for the scalar, which are determined by reference to homogeneous isotropic turbulent flows with a uniform mean cross‐stream scalar gradient. Calculated and measured profiles are in good agreement.

ISSN:0031-9171    

DOI:10.1063/1.866139

出版商:AIP    

年代:1987

数据来源: AIP

摘要:

Some studies of forced and unforced plane turbulent mixing layers have been conducted using two experimental and two computational approaches. The present paper contains an overall comparison and discussion of the measured and computed results. The experimental results include flow‐visualization data using the smoke‐laser technique and mean flow and turbulence measurements obtained with hot X wires and a two‐component laser‐Doppler velocimeter (LDV). The mean flow and turbulence results indicate that the two experimental techniques agree reasonably well for this shear flow. Two‐dimensional computations of the measured mixing layers have also been conducted in a coordinated effort; one method uses the inviscid discrete vortex technique for a spatially developing layer and the other is based on an approximation to the Reynolds‐averaged Navier–Stokes equations. The vortex method was found to give excellent results for the forced mixing layer while the Reynolds‐averaged computations, with a modified turbulence model, were particularly successful at capturing the near‐field viscous behavior that included the splitter plate wake.

ISSN:0031-9171    

DOI:10.1063/1.866140

出版商:AIP    

年代:1987

数据来源: AIP

摘要:

As a result of the increasing inefficiency in the transfer of energy in collisions between species with a decreasing ratio of molecular masses, the Knudsen number range of validity of the Chapman–Enskog (CE) theory for binary gas mixtures decreases linearly with the molecular mass ratio. To remedy the situation, a two‐fluid CE theory uniformly valid in the molecular mass ratio is constructed here. The analysis extends previous two‐fluid theories to allow for arbitrary potentials of intermolecular interaction and arbitrary mass ratios. The treatment differs from the CE formulation in that the mean velocities and temperatures of the two gases are not required to be identical to lowest order. To first order, the streaming terms of the Boltzmann equation are thus computed in terms of the derivatives of the two‐fluid hydrodynamic quantities, rather than the mean mixture properties as in the CE theory. As a result, associated with the nonconservation of momentum and energy for each species alone, two new ‘‘driving forces’’ appear in the first‐order integral equations. The amount of momentum and energy transferred per unit time between the species appear in the theory as free constants, which allow satisfying the constraint that all hydrodynamic information be contained within the lowest‐order two‐fluid Maxwellians. Simultaneously, this constraint fixes the rate of momentum and energy interchange in terms of the two‐fluid hydrodynamic quantities and their gradients. The driving forced12of the CE theory is directly related to the rate of interspecies momentum transfer, and the corresponding CE functionsD1andD2appear here unmodified.But the physical interpretation ofd12is very different in the two pictures. On the CE side there is only one momentum equation, whiled12provides constitutive information fixing the diffusion flux (velocity differences) in the mass conservation equation. Here, the similar constitutive information associated tod12is used to couple two different momentum equations. Although the CE theory captures some of the two‐velocity aspects of the problem, no CE analog exists with the functionsE1andE2associated here with temperature differences, which now require solving new integral equations. Finally, the presence of two velocities and two temperatures leads to four coefficients of viscosity and of thermal conductivity for the two stress tensors and heat flux vectors. Also, two thermal diffusion factors enter now into the expression ford12. Although all these new coefficients arise as portions of the overall CE transport coefficients, their independent optimal determination requires new developments. The corresponding variational formulation is presented here and used to first order to obtain explicit expressions for all two‐fluid transport coefficients by means of Sonine polynomials as trial functions.

ISSN:0031-9171    

DOI:10.1063/1.866141

出版商:AIP    

年代:1987

数据来源: AIP

摘要:

In several studies of rarefied gas dynamics and particle transport, not only the diffusion coefficient, but also a detailed description of the Chapman–Enskog solution for diffusion is required. The case of diffusion of a trace species in a background gas is considered for arbitrary molecular mass ratio, and accurate results are reported for the Chapman–Enskog solution obtained by solving numerically an integral equation of Pidduck.

ISSN:0031-9171    

DOI:10.1063/1.866142

出版商:AIP    

年代:1987

数据来源: AIP