摘要:

The minimum Reynolds number,ReNc, below which all the two‐dimensional and monochromatic wave disturbances decay, is studied numerically for a thermally stratified plane Poiseuille flow. TheReNcis found to be sensitive to the change of Prandtl numberP. Under unstable stratification with Rayleigh number just below critical,ReNc&bartil;1000 is found forP≤10−3. ©1996 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.868905

出版商:AIP    

年代:1996

数据来源: AIP

摘要:

Our aim is to explore, both experimentally and theoretically, the cumulative effects of small particle–liquid density difference, where the particles are used as tracers in recirculating flow. As an example we take a flow field generated in a differentially heated cavity. The main flow structure in such a cavity consists in one or two spiraling motions. Long‐term observations of such structures with the help of tracers (small particles) indicated that accumulation of the particles may set in at some flow regions. For theoretical insight into the phenomenon, a simple analytical model of recirculating (rotating) flow was studied. It was assumed that particles are spherical and rigid, and their presence does not affect the flow field. The particle Reynolds number is negligibly small, hence only the effects of particle–liquid density difference are of importance. Besides buoyancy, the effects of Saffman’s force and the inertial forces are also taken into account when calculating particle trajectories. Both cases were analyzed, particles with density slightly higher and lower than the fluid. It was found that in our case the inertial forces are egligible. In the numerical experiment trajectories of particles were investigated. The particles were allocated at random in the flow field obtained by numerical solution of the natural convection in the differentially heated cavity. In the experimental part, behavior of a dilute particle suspension in the convective cell was explored. In the model‐analytical study of a simple spiraling motion, it was found that due to the interaction of the recirculating convective flow field and the gravity‐buoyancy force, the particles may be trapped in some flow regions, whereas the rest of the flow field becomes particle‐free. This prediction agrees fairly well with the numerical and experimental findings. ©1996 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.868913

出版商:AIP    

年代:1996

数据来源: AIP

摘要:

We examine thermal convection in a rotating spherical shell with central gravity and a spatially non‐uniformly heated outer surface at two values of the Prandtl number:Pr=7.0, appropriate for water at room temperature, andPr=0.7, appropriate for air at standard temperature and pressure, by numerical calculation. Four calculations are performed in a sequence: the onset of convection with homogeneous temperature boundary condition, nonlinear boundary‐forced steady convection, stability of the forced steady convection to infinitesimal disturbances, and time stepping of subsequent secondary convection. Unlike our previous study of the infinite Prandtl number limit [J. Fluid Mech.250, 209 (1993)] inertial terms in the equation of motion for moderate Prandtl numbers play a key role in the dynamics. The effects of an inhomogeneous temperature boundary condition on nonlinear convection are illustrated by varying the wavelength and strength of the imposed boundary temperature. It is shown that even a slight inhomogeneity in the thermal boundary condition can lock azimuthally drifting convection and make it stationary, or modify the normal drifting convection rolls to a vacillating structure. In the infinite Prandtl number case, when inertial forces are absent from the equation of motion, resonance occurs when the wavelengths of boundary forcing and natural convection coincide. Fluid inertia destroys this resonance for finite Prandtl number fluids. The same effect reduces in size the stability region where steady convection is locked to the boundary, and steady convection becomes unstable to time‐dependent convection. The period of the secondary convection is close to that obtained with uniform temperature boundaries but the spatial structure is dramatically changed, exhibiting vacillations between the wavelength of the boundary temperature and that of the natural convection. ©1996 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.868914

出版商:AIP    

年代:1996

数据来源: AIP

摘要:

The influence of the velocity profile on transient (algebraic) growth of three‐dimensional disturbances in channel flow is investigated. Only streamwise‐independent perturbations are considered and the effect of a single forcing Orr–Sommerfeld mode is studied. This restriction is motivated by previous investigations, which show that the largest possible (global optimal) energy growth of a disturbance is generally obtained for streamwise‐independent perturbations. Analytic solutions for the energy growth on starting profiles for plane Couette and plane Poiseuille flow are deduced and the findings reveal that the most favorable profiles for transient growth are indeed the fully developed ones. An isoperimetric method to compute optimal profiles is then presented with the purpose to increase the energy growth compared to the fully developed profiles. These profiles are dependent on the spanwise wave number, as well as the perturbation growth time. A numerical investigation show that significant energy magnification can take place on such a profile, even at short growth times of the perturbation. It is further established that these profiles are stable only for low Reynolds number. ©1996 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.868906

出版商:AIP    

年代:1996

数据来源: AIP

摘要:

Flow past an inclined flat plate at an angle of attack of 30° and a Reynolds number of 30 000 is investigated experimentally. The velocity field in the wake is measured with a laser doppler anemometer (LDA) in the region from one plate breadth downstream to three and a half‐plate breadths downstream. Controlled forcing is applied to the wake by vibrating the plate in the across‐wind direction at a frequency in the middle of the lock‐in range. The forcing serves to enhance the regularity and two‐dimensionality of vortex shedding from the plate. It also facilitates phase‐locked averaging of the LDA data. The LDA bursts are sorted according to their arrival instants relative to a particular phase of the vortex shedding cycles. The phase‐averaged velocity results reveal large‐scale vortical structures in the wake. Dynamical properties of these structures such as coherent vorticity and Reynolds stress production are discussed. The wake is found to be strongly asymmetric. The flow dynamics in the wake are dominated by a train of counterclockwise vortices shed from the trailing edge of the plate. The development, shedding and subsequent convection of these vortices are studied by following the consecutive phases of the shedding cycle. ©1996 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.868907

出版商:AIP    

年代:1996

数据来源: AIP

摘要:

The probability density functions (PDFs) of the velocity and the velocity difference field induced by a distribution of a large number of discrete vortex elements are investigated numerically and analytically. Tails of PDFs of the velocity and velocity difference induced by a single vortex element are found. Treating velocities induced by different vortex elements as independent random variables, PDFs of the velocity and velocity difference induced by all vortex elements are found using limit distribution theorems for stable distributions. Our results generalize and extend the analysis by Takayasu [Prog. Theor. Phys.72, 471 (1984)]. In particular, we are able to treat general distributions of vorticity, and obtain results for velocity differences and velocity derivatives of arbitrary order. The PDF for velocity differences of a system of singular vortex elements is shown to be Cauchy in the case of small separationr, both in 2 and 3 dimensions. A similar type of analysis is also applied to non‐singular vortex blobs. We perform numerical simulations of the system of vortex elements in two dimensions, and find that the results compare favorably with the theory based on the independence assumption. These results are related to the experimental and numerical measurements of velocity and velocity difference statistics in the literature. In particular, the appearance of the Cauchy distribution for the velocity difference can be used to explain the experimental observations of Tong and Goldburg [Phys. Lett. A127, 147 (1988); Phys. Rev. A37, 2125, (1988); Phys. Fluids31, 2841 (1988)] for turbulent flows. In addition, for intermediate values of the separation distance, near exponential tails are found. ©1996 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.868908

出版商:AIP    

年代:1996

数据来源: AIP

摘要:

The statistical properties of the velocity fluctuation components at moderateRe&lgr;are studied in homogeneous and non‐homogeneous turbulence by an experimental technique. Measurements are performed by means of a hot‐wire anemometer with X‐probe downstream of a screen for several positions,x/M=9 up to 109, whereMis the screen mesh size, withRe&lgr;ranging from 37 to 82. The homogeneity of the flow is analyzed by means of velocity measurements in different transverse positions and a direct evaluation of the local isotropy of the flow is performed by means of velocity spectra. The scaling properties of the statistical moments of the structure functions up to the order of six, are investigated in the extreme positions by means of the extended self‐similarity (ESS) method and the intermittency exponents are detected for both homogeneous and non‐homogeneous flow conditions. A comparison of the longitudinal and transverse intermittency exponents as functions of the position is then performed and discussed in addition to the analysis of the transition from the anomalous to a regular scaling for small spatial separation. ©1996 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.868909

出版商:AIP    

年代:1996

数据来源: AIP

摘要:

A study of Lagrangian chaos, Eulerian chaos, and mixing enhancement in converging–diverging channel flows, using spectral element direct numerical simulations, is presented. The time‐dependent, incompressible Navier–Stokes and continuity equations are solved for laminar, transitional, and chaotic flow regimes for 100≤Re≤850. Classical fluid dynamics representations and dynamical system techniques characterize Eulerian flows, whereas Lagrangian trajectories and finite‐time Lagrangian Lyapunov exponents identify Lagrangian chaotic flow regimes and quantify mixing enhancement. Classical representations demonstrate that the flow evolution to an aperiodic chaotic regime occurs through a sequence of instabilities, leading to three successive supercritical Hopf bifurcations. Poincare´ sections and Eulerian Lyapunov exponent evaluations verify the first Hopf bifurcation at 125<Re<150 and the onset of Eulerian chaos at Re≊550. Lagrangian trajectories and finite‐time Lagrangian Lyapunov exponents reveal the onset of Lagrangian chaos, its relation with the appearance of the first Hopf bifurcation, the interplay between Lagrangian and Eulerian chaos, and the coexistence of Lagrangian chaotic flows with Eulerian nonchaotic velocity fields. Last, Lagrangian and Eulerian Lyapunov exponents are used to demonstrate that the onset of Eulerian chaos coincides with the spreading of a strong Lagrangian chaotic regime from the vortex region to the whole fluid domain. ©1996 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.868910

出版商:AIP    

年代:1996

数据来源: AIP

摘要:

Particle transport in fully‐developed turbulent channel flow has been investigated using large eddy simulation (LES) of the incompressible Navier–Stokes equations. Calculations were performed at channel flow Reynolds numbers, Re&tgr;, of 180 and 644 (based on friction velocity and channel half width); subgrid‐scale stresses were parametrized using the Lagrangian dynamic eddy viscosity model. Particle motion was governed by both drag and gravitational forces and the volume fraction of the dispersed phase was small enough such that particle collisions were negligible and properties of the carrier flow were not modified. Material properties of the particles used in the simulations were identical to those in the DNS calculations of Rouson and Eaton [Proceedingsofthe7thWorkshoponTwo‐PhaseFlowPredictions(1994)] and experimental measurements of Kulicketal. [J. Fluid Mech.277, 109 (1994)]. Statistical properties of the dispersed phase in the channel flow at Re&tgr;=180 are in good agreement with the DNS; reasonable agreement is obtained between the LES at Re&tgr;=644 and experimental measurements. It is shown that the LES correctly predicts the greater streamwise particle fluctuation level relative to the fluid and increasing anisotropy of velocity fluctuations in the dispersed phase with increasing values of the particle time constant. Analysis of particle fluctuation levels demonstrates the importance of production by mean gradients in the particle velocity as well as the fluid‐particle velocity correlation. Preferential concentration of particles by turbulence is also investigated. Visualizations of the particle number density field near the wall and along the channel centerline are similar to those observed in DNS and the experiments of Fessleretal. [Phys. Fluids6, 3742 (1994)]. Quantitative measures of preferential concentration are also in good agreement with Fessleretal. [Phys. Fluids6, 3742 (1994)]. ©1996 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.868911

出版商:AIP    

年代:1996

数据来源: AIP

摘要:

Direct numerical simulations (DNS) of passive scalar mixing in isotropic turbulence is used to study, analyze, and, subsequently, model the role of small (subgrid) scales in the mixing process. In particular, we attempt to model the dissipation of the large‐scale (supergrid) scalar fluctuations caused by the subgrid scales by decomposing it into two parts: (i) the effect due to the interaction among the subgrid scales,E≫&fgr;; and, (ii) the effect due to interaction between the supergrid and the subgrid scales,E≳<&fgr;. Model comparison with DNS data shows good agreement. ©1996 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.868894

出版商:AIP    

年代:1996

数据来源: AIP