摘要:

A new model is presented for simulating rotational energy relaxation in the direct simulation Monte Carlo method (DSMC) using discrete distributions. The method extends the phenomenological approach generally employed that simulates the distribution as a continuum. The discrete approach simulates the mechanics of relaxation for the rigid rotor model. The theory is developed and combined for use with an existing model for simulating the rate of rotational relaxation. A number of test problems are then considered. Each set of flow conditions is chosen because of the availability of experimental data. Some of the experimental measurements provide rotational energy distributions thus allowing detailed comparison with the numerical simulations. Generally, the comparisons are quite favorable, although it is indicated that more sophisticated models are required to simulate some of the detailed structure of the energy distributions observed experimentally.

ISSN:0899-8213    

DOI:10.1063/1.858531

出版商:AIP    

年代:1993

数据来源: AIP

摘要:

In homopolar motors and generators, large dc electric currents pass through the sliding electrical contacts between rotating copper disks (rotors) and static copper surfaces shrouding the rotor tips (stators). A liquid metal in the small radial gap between the rotor tip and concentric stator surface can provide a low‐resistance, low‐drag electrical contact. Since there is a strong magnetic field in the region of the electrical contacts, there are large electromagnetic body forces on the liquid metal. The primary, azimuthal motion consists of simple Couette flow, plus an electromagnetically driven flow with large extremes of the azimuthal velocity near the rotor corners. The secondary flow involves the radial and axial velocity components, is driven by the centrifugal force associated with the primary flow, and is opposed by the electromagnetic body force, so that the circulation varies inversely as the square of the magnetic‐field strength. Three flow regimes are identified as the angular velocity &OHgr; of the rotor is increased. For small &OHgr;, the primary flow is decoupled from the secondary flow. As &OHgr; increases, the secondary flow begins to convect the azimuthal‐velocity peaks radially outward, which in turn changes the centrifugal force driving the secondary flow. At some critical value of &OHgr;, the flow becomes periodic through the coupling of the primary and secondary flows. The azimuthal‐velocity peaks begin to move radially in and out with an accompanying oscillation in the secondary‐flow strength.

ISSN:0899-8213    

DOI:10.1063/1.858532

出版商:AIP    

年代:1993

数据来源: AIP

摘要:

The impulsive‐source distribution or Green’s function for an unboundedn‐dimensional Euclidean space filled by a material medium which undergoes a time‐dependent homogeneous deformation and which is characterized by a time‐dependent anisotropic diffusion tensor is derived. The special case of time‐independent velocity gradients is considered (motions with constant stretch history), in which the anisotropic diffusivity is assumed to arise from the distortion of the otherwise isotropic medium supporting the diffusion process. Explicit reductions are given for steady simple‐shearing (viscometric) flows. Also, a brief discussion is given of the relevance to general linear Brownian dynamical systems and the associated Taylor dispersion processes.

ISSN:0899-8213    

DOI:10.1063/1.858533

出版商:AIP    

年代:1993

数据来源: AIP

摘要:

Disturbance structures that achieve maximum growth over a specified interval of time have recently been obtained for unbounded constant shear flow making use of closed‐form solutions. Optimal perturbations have also been obtained for the canonical bounded shear flows, the Couette, and plane Poiseuille flows, using numerical solution of the linearized Navier–Stokes equations. In this note it is shown that these optimal perturbations have similar spectra and structure indicating an underlying universality of shear flow dynamics that is not revealed by traditional methods based on modal analysis.

ISSN:0899-8213    

DOI:10.1063/1.858534

出版商:AIP    

年代:1993

数据来源: AIP

摘要:

Experimental data on the mean axial velocity and the intensity of the radial and axial velocity components on the axis of counterflowing turbulent streams are compared with a previously published Reynolds stress theory. Agreement is found to be satisfactory.

ISSN:0899-8213    

DOI:10.1063/1.858535

出版商:AIP    

年代:1993

数据来源: AIP

摘要:

A form of the evolution equation for the dissipation showing the effects of rotation is derived directly from the Navier–Stokes equations. Rotation affects the dissipation if the flow is inhomogeneous or compressible. This is due to the fact that pressure scales with inverse Rossby number and certain pressure correlations usually neglected have to be retained when Re Ro≊1. The term reflecting the effects of rotation on the dissipation is a volume integral of the two‐point velocity correlation similar in structure to the ‘‘rapid‐pressure’’ correlation appearing in the second‐moment equations. Some of its properties are indicated.

ISSN:0899-8213    

DOI:10.1063/1.858536

出版商:AIP    

年代:1993

数据来源: AIP

摘要:

The Smagorinsky subgrid model is revised to properly account for grid anisotropy, using energy equilibrium considerations in isotropic turbulence. For moderate resolution anisotropies, Deardorff’s estimate involving an equivalent grid scale &Dgr;eq=(&Dgr;1&Dgr;2&Dgr;3)1/3is given a rigorous basis. For more general grid anisotropies, the Smagorinsky eddy viscosity is recast as &ngr;T=[cs&Dgr;eqf(a1,a2)]2‖S˜‖, wheref(a1,a2) is a function of the grid aspect ratiosa1anda2, and ‖S˜‖ is the resolved strain rate magnitude. The asymptotic behavior of &ngr;Tat several limits of the aspect ratios are examined. Approximation formulas are developed so thatf(a1,a2) can easily be evaluated in practice, for arbitrary values ofa1anda2. It is argued that these results should be used in conjunction with the dynamic model of Germanoetal. whenever the anisotropy of the test‐filter differs significantly from that of the basic grid.

ISSN:0899-8213    

DOI:10.1063/1.858537

出版商:AIP    

年代:1993

数据来源: AIP