摘要:

We use an advection hypothesis to analyze the decay of centerline velocity of a circular jet issuing into a counterflowing stream. Working in the Lagrangian frame, we follow the locations and velocity gradients of jet fluid particles along the jet central axis while the particles are being advected backwards by the counterflow. The spatial velocity gradient along the jet centerline is thus obtained and subsequently integrated to describe the spatial decay of axial velocities. Laser-doppler velocity measurements are performed in the laboratory and the data are well predicted by our analytical expression of centerline velocity decay. Looking from another view, our treatment supports that the effect of an external axial flow stream on the jet flow field can be represented by a certain degree of stretching or contracting of the jet in the axial direction. ©1998 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.869589

出版商:AIP    

年代:1998

数据来源: AIP

摘要:

An algebraic preclosure theory for the Reynolds stress⟨u′u′⟩is developed based on asmoothing approximationwhich compares the space–time relaxation of a convective-diffusive Green’s function with the space–time relaxation of turbulent correlations. The formal preclosure theory relates the Reynolds stress to three distinct statistical properties of the flow: (1) a relaxation time&tgr;Rassociated with the temporal structure of the turbulence; (2) the spatial gradient of the mean field; and, (3) a prestress correlation related to fluctuations in the instantaneous Reynolds stress and the pressure field. Closure occurs by using anisotropicmodel for the prestress. For simple shear flows, the theory predicts the existence of a nonzero primary normal stress difference and aneddyviscosity coefficient which depends on the temporal relaxation of the turbulent structure and a characteristic time scale associated with the mean field. The asymptotic state of homogeneously sheared turbulence shows that&tgr;RS∼1,whereSrepresents the mean shear rate. The Reynolds stress model and a set of recalibratedk−&egr;transport equations predict that the relaxation of homogeneously sheared turbulence to an asymptotic state requires development distances larger than20×⟨uz⟩(0)/S,a theoretical result consistent with experimental observations. ©1998 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.869590

出版商:AIP    

年代:1998

数据来源: AIP

摘要:

An analytical study of isotropic scalar fluctuations decay in isotropic turbulence is undertaken. From a fixed-point analysis, the existence of two complete self-preserving regimes is demonstrated. One of them relates to the final period of decay whereas the other one corresponds to the decay at large Reynolds and Pe´clet numbers. In both cases, the scalar-to-velocity timescale ratio is constant. In the final period, its asymptotic value is determined by the values of the coefficients of velocity and scalar enstrophy destruction. At large Reynolds and Pe´clet numbers, it depends on the latter as well as on the values of the mixed-derivative and velocity derivative skewness coefficients. A model for the approach to full self-preservation of scalar fluctuations decay is proposed. This model accounts for non-equilibrium resulting from initial unbalanced vortex stretching. In the conditions of experiments on temperature fluctuations decay in grid-turbulence, it displays a transient regime, extending over the region of measurements, during which the decay exponent is not constant but slowly varying. ©1998 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.869591

出版商:AIP    

年代:1998

数据来源: AIP

摘要:

The structure of the small scale velocity field is studied in an approximately homogeneous shear flow (constant mean shear) over the Reynolds number range156⩽R&lgr;⩽390.The shear was generated in a wind tunnel using screens of various solidity and a series of straightening channels in the manner of Tavoularis and Corrsin [J. Fluid Mech.104, 311 (1981)]. We show there is significant skewness (of order 1) of the derivative of the longitudinal velocity in the direction of the mean gradient, and thus that for these Reynolds numbers the flow is anisotropic at the small scales. The skewness slowly decreases withR&lgr;and is described by the empirical fit:S∂u/∂y=15.4R&lgr;−0.6.Thus, even if this downward trend continues, our results imply that anisotropy at the third moment continues to very highR&lgr;.We also show that, over theR&lgr;range investigated, the kurtosis of∂u/∂ydecreases (due to the diminishing effect of the structures that cause the skewness), implying that there will be a transition in this quantity, since it must increase as intermittency becomes more pronounced at higherR&lgr;.Transverse (as well as longitudinal) structure functions of the longitudinal velocity are studied up to the fifth moment. It is shown that the third order transverse structure function has a scaling range. Thus, the anisotropy exists at inertial as well as dissipation scales. The results are compared and contrasted with those of a passive scalar (for which it is known that persistent anisotropy exists at the third moment and above). ©1998 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.869592

出版商:AIP    

年代:1998

数据来源: AIP

摘要:

This paper presents a general procedure for including added effects, such as turbulent dissipation rate anisotropies, into algebraic stress formulations in both inertial and noninertial frames of reference. Explicit algebraic stress models, which assume an isotropic turbulent dissipation rate, have been developed previously and extended for application to noninertial frames. Independently, anisotropic dissipation rate models have also been developed. Recently, an algebraic, anisotropic dissipation rate model has been developed and used in conjunction with a full Reynolds stress closure. Unfortunately, in the theoretical formulations used previously for explicit algebraic models, the combination of the algebraic stress and algebraic dissipation rate models only appeared possible for inertial frames. The alternative procedure outlined here remedies this problem and allows for the construction of a composite model for both inertial and noninertial frames. This new composite model formulation is tested in homogeneous shear with and without rotation, and in strongly rotating channel and pipe flows using different types of anisotropic dissipation rate models. ©1998 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.869593

出版商:AIP    

年代:1998

数据来源: AIP

摘要:

Direct numerical simulations (DNS) of bubble-laden isotropic decaying turbulence are performed using the two-fluid approach (TF) instead of the Eulerian–Lagrangian approach (EL). The motivation for the study is that EL requires considerable computational resources, especially for the case of two-way coupling, where the instantaneous trajectories of a large number of individual bubbles need to be computed. The TF formulation is developed by spatially averaging the instantaneous equations of the carrier flow and bubble phase over a scale of the order of the Kolmogorov length scale, which, in our case, is much larger than the bubble diameter. On that scale, the bubbles are treated as a continuum (without molecular diffusivity) characterized by the bubble phase velocity field and concentration (volume fraction). The bubble concentration,C, is assumed small enough(C⩽10−3)to neglect the bubble–bubble interactions. As a test case, direct simulation of a bubble-laden Taylor–Green vortex with one-way coupling is performed with a bubble response time of the order of the flow time scale (inverse of the mean vorticity). This simple flow allows a direct examination of the effects of the preferential accumulation of bubbles in the high-enstrophy regions of the flow on the accuracy of the two-fluid formulation. The temporal development of the maximum bubble concentration obtained from DNS agrees well with the analytical solution. DNS of the bubble-laden decaying turbulence are also performed for both cases of one-way and two-way coupling. Here, the bubble diameter and response time are much smaller than the Kolmogorov length and time scales, respectively. In this case, as expected, the effects of the preferential accumulation of the bubbles are not pronounced. The results also show that the bubble-laden flow is analogous to a stratified flow with an effective density=(1−C)&rgr;f.Thus, due to the two-way interaction between the bubbles and carrier flow, the turbulence decay is enhanced with stable stratification, and reduced with unstable stratification.©1998 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.869594

出版商:AIP    

年代:1998

数据来源: AIP

摘要:

In this paper we present new results for the dynamics of a problem for the interaction of a compressible gas flow with a movable rigid surface. Compressible lubrication theory is applied to describe the dynamics of the vertical motion of air bearing sliders used in computer hard disk drives. In the limit of large bearing number we show this problem can be reduced to a nonlinear integrodifferential equation. Linear stability analysis and perturbation methods show that over the range of possible slider positions there is an infinite sequence of Hopf bifurcations yielding stable large amplitude periodic orbits. The dynamics of near-crash behavior and interaction with a moving disk surface are also addressed. ©1998 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.869595

出版商:AIP    

年代:1998

数据来源: AIP

摘要:

The linear stability of viscous compressible plane Couette flow is not well understood even though the stability of incompressible Couette flow has been studied extensively and has been shown to be stable to linear disturbances. In this paper, the viscous linear stability of supersonic Couette flow for a perfect gas governed by Sutherland viscosity law was studied using two global methods to solve the linear stability equations. The two methods are a fourth-order finite-difference method and a spectral collocation method. Two families of wave modes, modes I and II, were found to be unstable at finite Reynolds numbers, where mode II is the dominant instability among the unstable modes. These two families of wave modes are acoustic modes created by sustained acoustic reflections between a wall and a relative sonic line when the mean flow in the local region is supersonic with respect to the wave velocities. The effects of viscosity on the stability of the two families of acoustic modes were studied by comparing the viscous results at finite Reynolds numbers with the inviscid results published by Duck, Erlebacher, and Hussaini [J. Fluid Mech.258(1994)]. It was shown that viscosity plays a destabilizing role in both mode I and mode II stability for supersonic Couette flow in a range of Reynolds numbers and wavenumbers. The effects of compressibility, three-dimensionality, and wall cooling on the two wave families were also studied. The stability of supersonic Couette flow was found to be different from that of the unbounded boundary layers in many aspects because of the effects of additional boundary conditions at the upper wall. ©1998 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.869596

出版商:AIP    

年代:1998

数据来源: AIP

摘要:

Unstable concentration gradients inherent in traveling chemical waves can give rise to buoyancy-driven convection, altering the speed of the wave. When an excitable Belousov–Zhabotinsky reaction system is confined within a sufficiently narrow, vertical two-dimensional channel, convection arises at a symmetry-breaking bifurcation point. The observed linear rate of change of wave speed with the bifurcation parameter is a necessary consequence of theZ2symmetry present. ©1998 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.869597

出版商:AIP    

年代:1998

数据来源: AIP

摘要:

A model of dissociation of diatomic molecules in intermolecular collisions, for use in Direct Simulation Monte Carlo (DSMC) calculations, has been proposed by Lord. This model, is a development of the exact available energy or vibrationally linked chemistry model of Bird, which models dissociation and chemical reactions directly via Borgnakke–Larsen type energy redistributions between translation and internal modes, dissociation being assumed to occur whenever the vibrational energy of a molecule exceeds its dissociation energy. The model employs the correct energy level scheme of a Morse oscillator and has been shown to yield equilibrium dissociation rate constants forN2which are in excellent agreement with published values. A shortcoming of the model, however, is that it is purely classical, the molecular vibrational energy being assumed to be continuously distributed. Although this is not a serious defect for the prediction of dissociation, since the dissociation energy is normally many times the largest vibrational energy level spacing, it means that the model is unsuitable for describing vibrational energy exchange at lower collision energies where quantization effects are significant and must be taken into account in a way which satisfies detailed balance at equilibrium. The present paper describes a quantized extension of the earlier model which satisfies this requirement and can therefore be used in conjunction with it. It is shown that the two models become identical at high collision energies. ©1998 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.869598

出版商:AIP    

年代:1998

数据来源: AIP