摘要:

Oscillatory Marangoni convection in silicon–oil liquid bridges, sustained by two circular coaxial disks with prescribed time‐dependent temperature profiles and bounded by cylindrical free surfaces, is investigated by direct three‐dimensional (3‐D) and time‐dependent simulation of the model equations, using finite difference methods explicit in time and a staggered spatial mesh in cylindrical coordinates. It is shown that, for low enough values of the dimensionless rate of ramping, the time‐dependent nature of the boundary conditions becomes unimportant and the computed critical Marangoni numbers approach the values obtained with steady stability analyses. For typical microgravity experiments, involving unsteady boundary conditions, the computed critical Marangoni numbers and the oscillation frequencies agree with available experimental data of sounding rockets and Spacelab experiments. The 3‐D thermo‐fluid‐dynamic oscillatory regime structures are depicted, discussed, and compared with previous experimental and theoretical analyses, providing physical explanations of the onset of instability and coherent pictures of the flow organization when oscillatory conditions are established. Immediately after the onset of instability, the oscillatory flow can be described by a standing wave and a pulsating temperature distribution. When the oscillatory disturbances become large, the azimuthal velocity causes the rotation of ‘‘temperature spots’’ along the free surface of the liquid bridge so that the time‐dependent temperature and velocity fields can be properly described by the dynamic model of an azimuthally traveling wave. ©1996 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.869070

出版商:AIP    

年代:1996

数据来源: AIP

摘要:

Stability of the flow of incompressible viscous fluid in a circular pipe is studied numerically. A perturbation consisting of finite‐amplitude two‐dimensional and infinitesimal three‐dimensional parts is imposed on the basic flow. The temporal evolution of the perturbation is analyzed by direct numerical calculation of the Navier–Stokes equations. The two‐dimensional disturbances are independent of the streamwise coordinate and initially take the form of streamwise rolls. It is shown that the nonlinear development of two‐dimensional perturbations results in substantial spanwise modulation of the streamwise velocity component manifesting itself as a formation of streaks and the occurrence of inflection points. The modulated mean flow is found to be highly unstable to the three‐dimensional perturbations which are localized spatially near these points. An instability mechanism that includes the modulation of the flow by growing two‐dimensional disturbances and the inflectional instability of the modulated flow to three‐dimensional perturbations is proposed. ©1996 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.869071

出版商:AIP    

年代:1996

数据来源: AIP

摘要:

The stability of a two‐dimensional flow in a symmetric channel with a suddenly expanded part is investigated numerically and analyzed by using the method of the nonlinear stability theory. From results of the numerical simulation, it is shown that the flow is steady, symmetric and unique at very low Reynolds numbers, while the symmetric flow loses its stability at a critical Reynolds number resulting in an appearance of asymmetric flow. The transition from the steady symmetric flow to the steady asymmetric one is found to occur due to the symmetry breaking pitchfork bifurcation when the aspect ratio, the ratio of the length of the expanded part to its width, is large. It is also found that the bifurcated flow becomes symmetric again when the Reynolds number is increased and the resultant symmetric flow loses its stability becoming periodic in time as the Reynolds number is further increased. On the other hand, when the aspect ratio is small there occurs no pitchfork bifurcation and the direct transition from the steady symmetric flow to a periodic flow occurs due to a Hopf bifurcation. The critical aspect ratio is found to be about 2.3. The critical Reynolds numbers for these bifurcations are evaluated. ©1996 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.869072

出版商:AIP    

年代:1996

数据来源: AIP

摘要:

The spin‐up from rest to a state of solid‐body rotation in a tank with one or more stepwise changes in depth is studied experimentally. Since flow across the steps is counteracted by the rotation acquired by the fluid in the course of the spin‐up process, eventually the flow is forced into a cellular pattern determined by the position of the steps. However, if the initial flow field has little resemblance with the quasisteady pattern imposed by the topography, most of the energy of the flow may be dissipated before the organization into the preferred pattern is complete. ©1996 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.869073

出版商:AIP    

年代:1996

数据来源: AIP

摘要:

Convection in a cavity with a free surface and heated from the side is studied by a combination of flow visualization and particle image velocimetry. In these experiments, buoyancy and thermocapillarity are of comparable importance in driving the convection. The Prandtl number of the working fluid, the cavity aspect ratio, and the ratio of Rayleigh to Marangoni numbers are all held fixed; the primary experimentally varied parameter is the imposed temperature difference, which varied from 0.3 to 20 °C, resulting in a range of Marangoni numbers between 6×103and 4.2×105. For low Marangoni numbers, the flow is steady and two dimensional, as expected. The global nature of the flow is in good agreement with available numerical simulations of combined thermocapillary‐buoyancy driven convection. At higher Marangoni number, Ma>1.5×105, we observe a transition to steady three‐dimensional convection. The nature of this transition is typical of an imperfect bifurcation, and the flow structure is investigated both qualitatively and quantitatively. It is concluded that for the parameter values studied the first unstable mode consists of steady three‐dimensional, approximately cubical, vortical structures that are periodic along the axis of the cavity. The three‐dimensional flows observed by visualizations are in remarkable agreement with the recent numerical computations of Mundrane and Zebib [Phys. Fluids A5, 810 (1993)]. ©1996 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.869095

出版商:AIP    

年代:1996

数据来源: AIP

摘要:

The enhancement of momentum and heat transfer caused by stationary streamwise vortices due to a Coriolis instability in a rotating straight channel is examined. It is shown that the changes in skin friction and Nusselt number depend on changes in the spanwise averaged mean flow and temperature distributions. Hot wire anemometry was used to experimentally determine the streamwise velocity and temperature distributions in a cross stream plane 68 channel widths downstream of the inlet. A technique to accurately compensate the velocity readings for the varying temperature in the channel was developed. It is shown that the streamwise vortices give rise to disturbance profiles which are close to those obtained from linear theory for small rotation numbers and that in this region there is no enhancement of either the averaged momentum or heat transfer. However, even for a disturbance amplitude in the streamwise velocity of the order of 20%, the disturbances are close to linear (both the disturbance distribution and growth rate). In this weakly non‐linear region the changes in the mean flow and temperature distributions could be estimated by using the linear eigenfunctions of the disturbances where the amplitude was taken from the measurements. In the fully non‐linear (saturated) region the Nusselt number on both the stable and unstable side of the channel was almost twice that at no rotation, however, the skin friction was almost unaffected on the stable side. This shows that the Reynolds analogy between momentum and heat transfer is not valid in this flow situation. ©1996 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.869074

出版商:AIP    

年代:1996

数据来源: AIP

摘要:

Experiments on the oscillatory behavior of axisymmetric buoyant plumes of helium and helium‐air mixtures are reported for a range of nozzle diameters (3.6 cm<d<20 cm), source velocities, and plume densities. Measurements include pulsation frequencies as determined from total pressure fluctuations along the plume centerline in addition to the phase resolved laser Doppler velocity measurements. These nonreacting buoyant plumes are found to exhibit periodic oscillations of plume boundaries which subsequently evolve into toroidal vortices within one‐half diameter above the nozzle exit. These oscillations and vortices are similar to those observed in pool fires, although their frequency scaling is somewhat different. The frequency relationship is well represented by the expressionS=0.8Ri0.381, where the Strouhal number isS=fd/V0and the Richardson number is defined as Ri1=[(&rgr;∞−&rgr;p)gd]/&rgr;∞V20. Parametersf, V0, &rgr; are frequency, source velocity, and density and subscriptspand ∞ refer to the plume fluid and ambient, respectively. Between Ri1=100 and 500, a transition in the frequency scaling is observed as evidenced by more turbulent and vigorously mixing plumes beyond this transition. In this region,S=2.1Ri0.281. This change in scaling can be explained by the effect of turbulent mixing on local plume density and the resulting modification of the convection speed of the toroidal vortices. These results provide a consistent basis for the mechanism of the observed instability which is quite different than other types of flow instabilities. Additionally, the phase resolved velocity field of a pulsating buoyant plume reveals a strong buoyant acceleration along the plume centerline followed by a deceleration in the region of the toroidal vortex formation. The strong upward acceleration is also accompanied by significant radial inflow toward the plume centerline determining the entrainment characteristics of these pulsating buoyant plumes. ©1996 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.869075

出版商:AIP    

年代:1996

数据来源: AIP

摘要:

The destabilization of the rotating disk flow subject to a forcing is experimentally investigated. An isolated roughness element of size of order &dgr; (the constant boundary layer thickness) is placed under the linear threshold of the cross‐flow instability in order to create a hydrodynamic pattern of finite amplitude and localized in space. The experimental neutral stability curve is first established. The resulting double parabolic curve exhibits two minima: one of which is due to the amplification of fundamental modes, the other one is linked to the emergence of superharmonic modes. Dispersion curves determined by means of two‐point measurements appear to be shifted away from those measured in the natural case (without forcing). We show that this discrepancy is due to the presence of weak nonlinear effects which can be described by a Ginzburg–Landau amplitude equation. Lastly, we present an original method that enables to determine both components of the group velocity vector using the measured dispersion relations and wave packet propagation angle. ©1996 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.869076

出版商:AIP    

年代:1996

数据来源: AIP

摘要:

Drag reduction on an impulsively started circular cylinder by surface suction has been investigated with a joint numerical and experimental study. Two suction slots entraining mass with various rates were located symmetrically in a range of angles downstream of the points of zero shear stress. The Reynolds number Re of this study was between 500 and 2000, while the suction coefficientM˙varied from 0 to 0.08. Analysis based on the force contributed by fluid elements with nonvanishing vorticity [Chang, Proc. R. Soc. London Ser. A437, 517 (1992)] has provided a clear view of the physical mechanism causing the drag reduction. For the impulsive flow with surface suction, the initial drag reduction is due to the strengthening of the front boundary layer, while the slender vortices in the near wake due to suction then become the dominant factor in reduction of the drag force in later stages. Close agreements were found between the experimental and numerical results, including streakline flow visualization and surface vorticity measurements on the top of the cylinder. In addition, a parametric study on the slot location, the suction angle, and the width of the suction slot has also been carried out in detail. ©1996 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.869097

出版商:AIP    

年代:1996

数据来源: AIP

摘要:

Often in oil reservoirs a layer of water lies under the layer of oil. The suction pressure due to a distribution of oil wells will cause the oil‐water interface to rise up towards the wells. A three‐dimensional boundary integral formulation is presented for calculating the steady interface shape when the oil wells are represented by point sinks. Sophisticated integration techniques are implemented in an effort to obtain accurate results. In particular, the efficiency of various integration methods are compared for this problem, includingQUADPACKroutines, adaptive methods based on the IMT rule, the Kronrod rule, the method of degenerate quadrilaterals, and the Gauss‐Rational rule for infinite integrals. Numerical results for various general multi‐sink distributions are discussed, as are some further results for the axisymmetric single well problem. ©1996 American Institute of Physics.

ISSN:1070-6631    

DOI:10.1063/1.869077

出版商:AIP    

年代:1996

数据来源: AIP