摘要:

A method has been proposed for finding steady solutions of hydrodynamics problems, which represent extrema of energy on isovortical sheets. Here the method is generalized in the form of an algorithm to search for uniformly translating or rotating solutions. It is argued that asymmetric solutions of symmetric systems are not necessarily stable: The energy‐momentum extremum has the topology of a curve on the sheet, and therefore a perturbed state might drift away along neighboring curves. If that were the case, and if the drift would just be a displacement with uniform velocity, in physical space, then it might be able to prove stability in a metric that shifts position and compares shapes (as it has been done with the Korteweg–de Vries soliton). These concepts are exemplified using very simple, finite dimension, cases.

ISSN:0899-8213    

DOI:10.1063/1.857696

出版商:AIP    

年代:1990

数据来源: AIP

摘要:

Higher‐order terms in thek‐&egr; model for the anisotropic representation (AR) of the Reynolds stresses are investigated. Second‐order terms in AR have been introduced to express the anisotropy of the Reynolds stresses, however they include no direct influence on the eddy viscosity. This Letter focuses on third‐order AR in particular, by incorporating new additional eddy viscosity terms. The proposed model was tested in plane channel flow, and compared to a numerical database generated using a large eddy simulation technique. It was found that third‐order AR may be used as an alternative method to reduce the magnitude of the eddy viscosity in the buffer layer region by acting similarly to the Van Driest damping function, commonly used ink‐&egr; models. The relationship of AR to the algebraic stress model is also discussed.

ISSN:0899-8213    

DOI:10.1063/1.857697

出版商:AIP    

年代:1990

数据来源: AIP

摘要:

The fluid‐dynamic and solid‐body interactions among a suspension of perfectly elastic particles settling in a viscous gas are studied. The Reynolds number of the particles, Re≡&rgr;fUa/&mgr;, is small but their Stokes number St≡mU¯/(6&pgr;&mgr;a2) is large, indicating that particle inertia and viscous forces in the fluid are important. Here, &rgr;fis the density of the fluid,mis the mass of a particle,U¯ is the average velocity of the particles,ais their radius, and &mgr; is the fluid viscosity. Equations for the particle velocity distribution and averages of the fluid and particle velocities are derived. For very large Stokes numbers, St≫&fgr;−3/2, where &fgr; is the particle volume fraction, solid‐body collisions lead to a nearly Maxwellian velocity distribution. On the other hand, at smaller Stokes numbers, St≪&fgr;−3/2, fluid‐dynamic interactions play a more important role in determining the particle velocity distribution and the distribution is not Maxwellian. The amount of energy contained in the particle velocity fluctuations is determined by a balance involving fluid‐dynamic interactions, even in the case where the solid‐body collisions lead to a nearly Maxwellian velocity distribution. The viscous interactions are found to be similar to those in a fixed bed at high Stokes numbers, St≫&fgr;−3/4, where the particles do not respond quickly to changes in the local fluid velocity. A stability analysis of the averaged equations indicates that the suspension is unstable to particle density waves for St≫&fgr;−3/2. The inertia of the particles is destabilizing, while the energy introduced into the fluctuating motions of the particles by viscous flow interactions is stabilizing.

ISSN:0899-8213    

DOI:10.1063/1.857698

出版商:AIP    

年代:1990

数据来源: AIP

摘要:

The basic approach toward a theoretical understanding of slow viscous flows in two dimensions is through solutions of the biharmonic equation; however, when the fluid is unbounded some of the solutions corresponding to locally generated flows lead to paradoxical behavior(e.g., Jeffery [Proc. R. Soc. London Ser. A101, 169 (1922)]). Here one case in detail (the source–sink flow in front of a circular cylinder) is described, and then whether such a flow is possible as either (a) the limit of a bounded flow in two dimensions as the radius of the outer boundary grows without bound, or (b) the limit of an unbounded three‐dimensional flow as lengths in the third dimension grow without bound, or (c) the limit of an impulsively started two‐dimensional unbounded flow as time grows without bound is considered. In each case it is found that the formal limit does exist, but that the error is only as small asO[(ln &mgr;)−1] when the appropriate parameter &mgr;→∞. This indicates that such locally generated unbounded flows are not realistically attainable.

ISSN:0899-8213    

DOI:10.1063/1.857699

出版商:AIP    

年代:1990

数据来源: AIP

摘要:

Generalized Taylor dispersion theory is herein extended to circumstances for which the transport of dissolved or suspended chemically reactive (as well as inert) solutes is affected by carrier‐solvent flow fields and/or external forces that are time periodic in both their globalandlocal microscale spaces (and possess commensurate frequencies). The local‐space‐ and time‐averaged solute transport process is characterized by three time‐independent, but frequency‐dependent microscale phenomenological coefficients—K¯*,U¯*, and cf6D*, representing the mean chemical reaction rate, velocity vector, and dispersivity dyadic of the solute, respectively. These macroscale transport coefficients are expressed in terms of time‐periodic eigenfunctions and corresponding eigenvalues using a recently developed solution scheme. This scheme permits the analysis of phenomena involving time‐periodic transport coefficients on a par with that for the classical case of time‐independent microscale phenomenological coefficients.The analysis generalizes to time‐periodiclocal‐spacephenomena a previous treatment, in which only theglobal‐spacecoefficients were allowed to vary periodically with time. This greatly enlarges the scope of potential applications of the analysis. In addition to the time‐averaged phenomenological coefficientsK¯*,U¯*, and CF6D*, comparable instantaneous coefficients are defined governing the local‐space‐averagedinstantaneoussolute concentration. In contrast with their time‐averaged counterparts,K¯*,U¯*, and CF6D*, the latter instantaneous transport coefficients are shown to depend upon the initial solute distribution within the local space. Because of coupling between the local‐ and global‐space transport processes in oscillatory flows and/or oscillatory external force fields,allharmonics of the resulting global‐space solute velocity field contribute to the mean convective solute transport. This phenomenon may result, for example, in zero solvent–nonzero solute net macroscale transport (or vice versa). The driving frequency of the local‐space time‐periodic transport process may be used to parametrically control the macroscale solute reactivity rate coefficient, as well as the solute’s mean velocity and dispersivity about that mean. A companion paper (Part II) [Phys. Fluids A2, 1744 (1990)], provides an example, albeit for the nonreactive case.

ISSN:0899-8213    

DOI:10.1063/1.857700

出版商:AIP    

年代:1990

数据来源: AIP

摘要:

The general theory of Taylor dispersion phenomena in time‐periodic flows, developed in Part I [Phys. Fluids A2, 1731 (1990)], is used to analyze convective–diffusive transport processes for noninteracting neutrally buoyant Brownian particles suspended in a plane Poiseuille flow within a duct bounded laterally by two parallel plates, and subject to the influence of transverse oscillating forces acting upon the suspended particles. The mean axial particle velocity and Taylor–Aris dispersivity are calculated in the large transverse Peclet number limit (‘‘large particle’’ limit), corresponding to circumstances for which particle transport is dominated by convection over diffusion. Effects arising from the externally imposed oscillatory frequency and amplitude are described in terms of a single dimensionless parameter, one whose magnitude may be manipulated to control the axial solute flux. Increasing the dimensionless oscillation periodT¯ significantly decreases the axial dispersivity, whereas the functional dependence of the mean axial particle velocity uponT¯ exhibits a maximum. Physicochemical phenomena arising from the oscillatory force thereby furnish a novel field‐flow fractionation (FFF) scheme for separating Brownian particles of different sizes.

ISSN:0899-8213    

DOI:10.1063/1.857701

出版商:AIP    

年代:1990

数据来源: AIP

摘要:

A wellbore (radiusb) filled with Newtonian fluid (viscosity &eegr;), contains a cylindrical drill string [radiusa=b(1−&egr;)] that touches the wall of the wellbore. Lubrication theory is applied to the fluid‐filled annular gap between cylinder and wall, while Darcy’s law is assumed valid within the rock surrounding the wellbore. The force required to lift the cylinder away from the wall with velocityUisF=bB&pgr;A−3/5, whereB=12&eegr;U/b&egr;3andA=12k/b2&egr;3≪1. The couple required to rotate the cylinder (in a rolling motion) with angular velocity &ohgr; isT=0.75Db2&pgr;A−1/5, whereD=12&eegr;&ohgr;&egr;−3. The effect of a filter cake of permeabilitykcand thicknessg≪bis also considered. SettingK=gk/bkc, the force required to lift the cylinder becomesF=0.72bB&pgr;(K/A)3/4, and the couple isT=0.8Db2&pgr;(K/A)1/4.

ISSN:0899-8213    

DOI:10.1063/1.857702

出版商:AIP    

年代:1990

数据来源: AIP

摘要:

A model of a computer hard disk drive was constructed and measurements of the air flow in the unobstructed space between a pair of disks were obtained. The disks were centrally clamped to a common hub, and rotated within an axisymmetric (cylindrical) enclosure or shroud. Measurements of the circumferential velocity component were made at five radial locations and three rotation rates (&OHgr;=300, 1200, and 3600 rpm) using a laser‐Doppler velocimeter. The resulting mean and rms circumferential velocity profiles are presented and discussed. The data show that the circumferential velocity component profiles are fairly uniform in the axial direction in the space between the disks, except near the shroud where the flow is strongly sheared. The circumferential velocity peaks at a critical radius. Between the hub and the critical radius location the flow is in solid body rotation. Between the critical radius and the shroud the circumferential velocity decreases to zero, gradually at first and then very quickly as the shroud is approached. Analysis based on simplified force balance considerations facilitates the interpretation of the experimental observations and leads to improved understanding of the complex flow phenomena. Numerical calculations of the present configuration assuming axisymmetric steady flow were performed by Changetal. (submitted to Int. J. Heat Mass Transfer). These calculations show reasonable agreement with the averaged velocity data but, for the reasons discussed, fail to reproduce features of the rms distribution associated with nonturbulent flow unsteadiness.

ISSN:0899-8213    

DOI:10.1063/1.857703

出版商:AIP    

年代:1990

数据来源: AIP

摘要:

The response of a confined compressible perfect gas to an uneven time‐dependent volumetric heat source is studied. The low Mach number compressible Navier–Stokes equations are solved numerically by means of the pressure implicit with splitting of operators (P.I.S.O.) algorithm in the case where the characteristic time of the thermal perturbation is small compared to the diffusion time and large compared to the acoustic time. A comparison is made with first‐order asymptotic results previously obtained. The asymptotic analysis is then carried out up to the second order in the bulk. It is shown that: (a) a flow is generated from one side of the cavity to the other, confirming the asymptotic results previously obtained; (b) a flow towards the walls is found in thermal boundary layers because of a sink effect due to the lower temperature in these regions; (c) comparison with analytical results in the bulk is quite satisfactory except for the velocity where some differences are shown; (d) the second‐order asymptotic analysis shows that this approximation in the bulk is a mechanical perturbation caused by the contraction of the fluid layers near the boundaries; (e) the matching between analytical results and numerical results is improved by more than 50% when considering a second‐order solution; (f) this analysis validates both numerical code and scaling laws.

ISSN:0899-8213    

DOI:10.1063/1.857704

出版商:AIP    

年代:1990

数据来源: AIP

摘要:

The dynamic properties of two vaporizing droplets moving in tandem and interacting through hydrodynamic forces are presented for the intermediate Reynolds number range of droplet motion [Re=O(100)]. The problem is relevant for dense spray applications. Depending upon certain initial parameters, the droplets can collide or separate. The behaviors of the droplets are influenced by the mass and heat transport associated with the evaporation of droplets in air. Droplet‐drag coefficient, Nusselt number, droplet mass, droplet Reynolds number, and droplet spacing histories are reported for a limited number of cases following the introduction of two droplets of different radii,a’1,0anda’2,0, at a given initial spacing,a’0, into a hot, convective fluid, which is characterized by uniform free‐stream conditions. A finite‐difference solution of the coupled two‐phase, unsteady Navier–Stokes equations in cylindrical coordinates on a body‐fitted coordinate system is adjusted continually to accommodate the changing boundary shapes resulting from the droplet movement and evaporation.The interactions are significant for initial Reynolds number range of 50 to 200 and for initial droplet spacings of 2 to 15 droplet diameters. Drag coefficients and Nusselt numbers can differ significantly from the values for isolated droplets. Droplet collision is likely for the initially equal‐sized droplets. Droplets moving in tandem collide for larger values of the ratio of the aft initial droplet diameter to the lead initial droplet diameter. A bifurcation value of this parameter is found above which increased separation of the droplets occurs. The bifurcation value increases as initial droplet spacing increases. This value depends only very weakly on the initial Reynolds number. For spacings above two diameters, the lead droplet behaves like an isolated droplet while drag coefficients for the aft droplet are significantly lower. Vaporization rate significantly affects the drag coefficients. For droplets within a few diameters of each other, the Nusselt number for the downstream droplet exhibits an entirely different character as the hot side on the droplet moves aft. Correlations of drag coefficients are reported for droplets of identical initial size. A general understanding is obtained about the modifications of droplet heating, vaporization, and drag due to the proximity of the two droplets.

ISSN:0899-8213    

DOI:10.1063/1.857705

出版商:AIP    

年代:1990

数据来源: AIP