摘要:

The interaction of a near-critical axisymmetric incompressible swirling flow in a straight pipe with small inlet azimuthal vorticity perturbations is studied. Certain flow conditions that may reflect the physical situation are prescribed along the pipe inlet and outlet. It is first demonstrated that under these conditions a regular-expansion solution in terms of the small azimuthal vorticity perturbations has a singular behavior around the critical swirl. This singularity infers that large-amplitude disturbances may be induced by the small perturbations when the incoming flow to the pipe has a swirl level around the critical swirl. In order to understand the nature of flows in this swirl range, a small-disturbance analysis is developed. It shows that under the prescribed inlet/outlet conditions, a small but finite inlet azimuthal vorticity perturbation breaks the transcritical bifurcation of solutions of the Euler equations at the critical swirl into two branches of perturbed solutions. When the azimuthal vorticity perturbations are positive these branches show a regular behavior. However, when they are negative, the perturbed branches fold at limit points near the critical swirl, with a finite gap between the two branches, and no near-columnar equilibrium state can exist for an incoming flow with swirl close to the critical level. The flow must develop large disturbances in this swirl range. Beyond this range, two equilibrium states may exist under the same inlet/outlet conditions. When the negative inlet vorticity perturbations become larger in their size, this special behavior uniformly changes into a branch of single equilibrium state for each incoming swirl. The relevance of the results to the appearance of the axisymmetric vortex breakdown in a pipe and the control of this phenomenon using inlet vorticity perturbations is also discussed. The results suggest that, in general, positive inlet azimuthal vorticity perturbations may be used to delay vortex breakdown to higher swirl levels whereas negative perturbations induce the appearance of vortex breakdown at levels below the critical swirl. ©1998 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.869685

出版商:AIP    

年代:1998

数据来源: AIP

摘要:

A proper orthogonal decomposition (POD) of the flow in a square lid-driven cavity atRe=22,000is computed to educe the coherent structures in this flow and to construct a low-dimensional model for driven cavity flows. Among all linear decompositions, the POD is the most efficient in the sense that it captures the largest possible amount of kinetic energy (for any given number of modes). The first 80 POD modes of the driven cavity flow are computed from 700 snapshots that are taken from a direct numerical simulation (DNS). The first 80 spatial POD modes capture (on average) 95&percent; of the fluctuating kinetic energy. From the snapshots a motion picture of the coherent structures is made by projecting the Navier–Stokes equation on a space spanned by the first 80 spatial POD modes. We have evaluated how well the dynamics of this 80-dimensional model mimics the dynamics given by the Navier–Stokes equations. The results can be summarized as follows. A closure model is needed to integrate the 80-dimensional system atRe=22,000over long times. With a simple closure the energy spectrum of the DNS is recovered. A linear stability analysis shows that the first (Hopf) bifurcation of the 80-dimensional dynamical system takes place atRe=7,819. This number lies about 0.7&percent; above the critical Reynolds number given in Poliashenko and Aidun [J. Comput. Phys.121, 246 (1995)] and differs by about 2&percent; from the first instability found with DNS. In addition to that, the unstable eigenvector displays the correct mechanism: a centrifugal instability of the primary eddy, however, the frequency of the periodic solution after the first bifurcation differs from that of the DNS. The stability of periodic solutions of the 80-dimensional system is analyzed by means of Floquet multipliers. ForRe=11,188−11,500the ratio of the two periods of the stable 2-periodic solution of the 80-dimensional system is approximately the same as the ratio of the two periods of the 2-periodic solution of the DNS atRe=11,000. For slightly higher Reynolds numbers both solutions lose one period. The periodic solutions of the dynamical system atRe=11,800and the DNS atRe=12,000have approximately the same period and have qualitatively the same behavior. ©1998 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.869686

出版商:AIP    

年代:1998

数据来源: AIP

摘要:

The effect of nonuniform seeding on the dispersion of fluid elements and heavy particles has been investigated in two-dimensional, incompressible mixing layers. The cross-stream dispersion of fluid elements can be enhanced using nonuniform seeding with most particles near the saddle point because of the greater lateral extent of streamlines in this region, though the increase in dispersion compared to a uniform seeding occurs only after a few vortex turnover times. Compared to fluid elements, additional mechanisms—ejection from vortex cores, separatrix crossing, and the effect of the initial particle velocity—must be considered in the analysis of nonuniform seeding on heavy particle dispersion. The influences of these additional mechanisms are first investigated in a Stuart vortex. With increasing response time, vortex ejection and separatrix crossing shift the streamwise position maximizing lateral transport towards the vortex core. While changes in the initial particle velocity increase/decrease displacement, lateral dispersion may still be enhanced by appropriate nonuniform seeding of particles near the saddle point. Numerical simulations of the incompressible Navier–Stokes equations are then used to study cross-stream dispersion in a temporally evolving two-dimensional mixing layer. Stokes numbersStin the calculations were 0.05, 1, 10, and 100 whereStis defined as the ratio of the particle response time to the time scale formed using the vorticity thickness of the initial mean flow. Particles were initially distributed nonuniformly at the interface between the two streams or along a line parallel to the interface. Simulation results show that the seeding location maximizing lateral dispersion is both time and Stokes number dependent, with larger increases in dispersion for the interface seeding. For Stokes numbers of order unity cross-stream dispersion exhibits a weak dependence on initial position since particles are efficiently ejected from the vortex core with subsequent motion confined to the nearby region outside the separatrix in one of the freestreams. Simulation results also show that substantial increases in particle dispersion can be obtained using nonuniform seedings relative to that obtained from an initially uniform distribution. ©1998 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.869687

出版商:AIP    

年代:1998

数据来源: AIP

摘要:

There have been many studies of turbulent combustion flows, however the interaction between turbulent motion and the chemical reactions that occur in hypersonic flows has not been studied. In these flows, the rate of product formation depends almost exclusively on the temperature, and small temperature fluctuations may produce large changes in the rate of product formation. To study this process, we perform direct numerical simulations of reacting isotropic turbulence decay under conditions typical of a hypersonic turbulent boundary layer flow. We find that there is a positive feedback between the turbulence and exothermic reactions. That is, positive temperature fluctuations increase the reaction rate, thereby increasing the heat released by the reaction, which further increases the temperature. Simultaneously, the pressure increases causing localized expansions and compressions that feed the turbulent kinetic energy. The Reynolds stress budget shows that the feedback occurs through the pressure-strain term. We also find that the strength of the feedback depends on how much heat is released, the rate at which it is released, and the turbulent Mach number. The feedback process is negative for endothermic reactions, and temperature fluctuations are damped. ©1998 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.869688

出版商:AIP    

年代:1998

数据来源: AIP

摘要:

Static pressure fluctuations measured in the atmospheric surface layer over a grass covered forest clearing are studied in the context of Townsend’s 1961 hypothesis regarding the effect of the outer region on the inner region. It is shown that large-scale pressure features are actively straining the inertial-scale pressure fluctuations, thus invalidating the direct extension of Kolmogorov’s 1941 hypothesis to the spectral scaling of pressure within the inertial subrange. A parameter describing the large scale pressure fluctuations is added to the set of variables responsible for inertial-range pressure differences and dimensional analysis is employed to derive an improved scaling law for pressure spectra which more closely matches these and previous experimental results. An examination of the Poisson equation for pressure is conducted and found to support the dimensional and experimental results. ©1998 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.869689

出版商:AIP    

年代:1998

数据来源: AIP

摘要:

A new explanation of the well documented effects of mild streamline curvature on the anisotropy of sheared turbulence has been developed. Its main underlying assumption is that the mean streamline curvature has no direct effect on the production and dynamics of each individual turbulent eddy, which is produced with the structure of purely sheared turbulence, and is subsequently convected downstream while retaining its initial anisotropy relative to fixed inertial coordinates. The local Reynolds stress anisotropy accumulates the contributions of all surviving eddies produced upstream, which, because the mean shear keeps changing direction, have different anisotropies, when viewed in terms of the local curvilinear coordinates; thus, the local anisotropy is influenced by the history of flow curvature only indirectly. A model developed to demonstrate the validity of the hypothesis requires only the specification of the turbulence anisotropies in a fully developed, rectilinear, reference flow (e.g., a rectilinear uniformly sheared flow), the geometrical features of the flow under study, and a dimensionless mean eddy lifetime. It predicts accurately the observed asymptotic turbulence structure of uniformly sheared flow subjected to prolonged, constant curvature and the exponential adjustment of this structure to stepwise changes in flow curvature. Predictions of the shear stress anisotropy in a curved mixing layer are also in good agreement with published data. In all these cases, the present model makes better predictions than two popular Reynolds stress models and a rapid distortion model. ©1998 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.869690

出版商:AIP    

年代:1998

数据来源: AIP

摘要:

The interactions of flows generated by ionic discharges with wall turbulence are not only of interest for turbulence control, but also for devices of industrial importance, such as wire-plate electrostatic precipitators (ESPs). Under conditions of uniform discharge, in wire-plate ESPs, arrays of regular, spanwise vortices are found in the absence of a through-flow. These arise from ionic discharges from the spanwise wires placed between the grounded plates on each side. The interactions of such electrohydrodynamic (EHD) flows with a turbulent through-flow are still poorly understood. Direct numerical simulation (DNS) is an attractive method for investigating such problems since the details of the interactions can be unraveled, and the results are directly applicable to industrial-scale systems because their Reynolds numbers are typically quite low. In this study, pseudospectral channel flow simulations were performed with the electrohydrodynamic effects being modeled by a spatially varying body-force term in the equations of fluid motion. The interactions between EHD flows and wall structures were elucidated by examining the instantaneous structure of the flow field. Results indicate that the mean flow, the EHD flows, and the turbulence field undergo significant modifications caused by mutual interaction. First, it is found that EHD flows reduce drag, allowing larger flow rates for a given pressure drop. Second, the EHD flows themselves appear weakened by the presence of the through-flow, particularly in the central region of the channel. The EHD flows affect the turbulence field by both increasing dissipation and turbulence production, the overall turbulence level being determined by the balance between the increased dissipation and production. Even though high EHD flow intensities may increase streamwise and wall-normal turbulence intensities, the Reynolds stress is reduced, consistent with the observed reduction in drag. From a mechanistic viewpoint, there are indications that EHD flows of the type investigated here reduce drag by decreasing the relative importance of the positive Reynolds stress contributions, i.e., second (ejections) and fourth (sweeps) quadrant events, compared to the negative Reynolds stress contributions, i.e., first and third quadrant events. ©1998 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.869691

出版商:AIP    

年代:1998

数据来源: AIP

摘要:

We consider the resistive steady states of a uniformly conducting magnetofluid inside a toroidal boundary. The problem becomes tractable in the limit of slow flow: i.e., low Reynolds number, which may be in turn justified when the viscous Lundquist number is small. Previous calculations are extended to apprehend the toroidal component of the necessary flow. The emerging pattern is one of helical vortices which seem likely to be ubiquitous in toroidal geometry, and which disappear in the “straight-cylinder approximation.” ©1998 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.869692

出版商:AIP    

年代:1998

数据来源: AIP

摘要:

A recent analysis of the stability of spherical bubble oscillations shows that the high order shape modes are parametrically unstable with respect to small but finite perturbations [Z. C. Feng and L. G. Leal, J. Fluid Mech.266, 209 (1994)]. Using a heuristic approach it is shown here that the acoustic radiation due to the liquid compressibility plays an important role in stabilization of the high frequency modes and overall stability of the bubble spherical shape. ©1998 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.869693

出版商:AIP    

年代:1998

数据来源: AIP

摘要:

Receptivity and stability of a two-dimensional laminar wall jet is considered. The wall jet and the disturbance source examined in a direct numerical simulation by S. Wernz and H. F. Fasel (AIAA Paper 96-0079) are chosen for the analysis. The disturbances are introduced by blowing and suction through a slot in the wall. The disturbances of two frequencies (28 and 56 Hz) are considered. Because two eigenmodes may be unstable in the wall-jet flow, both of them are taken into account for each frequency. Therefore, the linear receptivity problem is solved for two pairs of eigenmodes, and their development and interaction downstream from the source are analyzed. The analysis allows one to explain the behavior of the fundamental and subharmonic disturbances observed in the numerical simulation. ©1998 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.869694

出版商:AIP    

年代:1998

数据来源: AIP