Low-velocity Side Research Articles

Dynamics of a two-dimensional upflowing mixing layer seeded with bubbles: Bubble dispersion and effect of two-way coupling

The evolution and structure of a spatially evolving two-dimensional mixing layer seeded with small bubbles are numerically investigated. The one-way coupling approach is first employed to show that characteristics of bubble dispersion are dominated by the possibility for sufficiently small bubbles to be captured in the core of the vortices. A stability analysis of the ordinary differential equation system governing bubble trajectories reveals that this entrapment process is governed by the presence of stable fixed points advected by the mean flow. Two-way coupling simulations are then carried out to study how the global features of a two-dimensional flow are affected by bubble-induced disturbances. The local interaction mechanism between the two phases is first analyzed using detailed simulations of a single bubbly vortex. The stability of the corresponding fixed point is found to be altered by the collective motion of bubbles. For trapped bubbles, the interphase momentum transfer yields periodic sequences of entrapment, local reduction of velocity gradients, and eventually escape of bubbles. Similar mechanisms are found to take place in the spatially evolving mixing layer. The presence of bubbles is also found to enhance the destabilization of the inlet velocity profile and to shorten the time required for the rollup phenomenon to occur. The most spectacular effects of small bubbles on the large-scale flow are a global tilting of the mixing layer centerline towards the low-velocity side and a strong increase of its spreading rate. In contrast, no significant modification of the flow is observed when the bubbles are not captured in the large-scale vortices, which occurs when the bubble characteristics are such that the drift parameter defined in the text exceeds a critical value. These two contrasted behaviors agree with available experimental results.

Rubber friction on smooth surfaces

We study the sliding friction for viscoelastic solids, e.g., rubber, on hard flat substrate surfaces. We consider first the fluctuating shear stress inside a viscoelastic solid which results from the thermal motion of the atoms or molecules in the solid. At the nanoscale the thermal fluctuations are very strong and give rise to stress fluctuations in the MPa-range, which is similar to the depinning stresses which typically occur at solid-rubber interfaces, indicating the crucial importance of thermal fluctuations for rubber friction on smooth surfaces. We develop a detailed model which takes into account the influence of thermal fluctuations on the depinning of small contact patches (stress domains) at the rubber-substrate interface. The theory predicts that the velocity dependence of the macroscopic shear stress has a bell-shaped form, and that the low-velocity side exhibits the same temperature dependence as the bulk viscoelastic modulus, in qualitative agreement with experimental data. Finally, we discuss the influence of small-amplitude substrate roughness on rubber sliding friction.

Vortexing Flow Patterns in a Water Model of Slab Continuous Casting Mold

A water model experiment was conducted to observe the vortexing flow in the steel slab continuous casting mold, the snake- shaped Plexiglas mold was designed to simulate the actual caster. The camera was used to record the flow patterns, which were visualized by injecting the black sesames into water. The changes of shape of single vortex and two vortices with time have been observed during experiments. A numerical model has been developed to analyze the vortexing flow, which may be produced by moving the submerged entry nozzle from center to off-center in the slab continuous casting of steel. According to the numerical results, the vortexing flow is resulted from three-dimensional biased flow in the mold. A vortex is located at the low velocity side adjacent to the submerged entry nozzle. The vortex strength depends on the local horizontal velocity of fluid and decreases gradually with distance from the free surface. The vortexing zone size depends on the biased distance of the submerged entry nozzle, and intensity of the vortexing flow depends on the casting speed of the continuous caster.

Three-dimensionality of mode transition in vortex-induced vibrations of a circular cylinder

End lift forces and hot-wire anemometry in the wake of a flexibly-mounted rigid cylinder, undergoing vortex-induced vibrations within a uniform flow, show that the spanwise correlation undergoes a sharp reduction near conditions of maximum amplitude. Peak lift force and motion amplitudes occur on the low-velocity side of this low-correlation region; the region is bounded above by the advent of frequency lock-in. Certain aspects of this correlation loss are interpreted in the context of other free- and forced-vibration tests, and highlight the sensitivity of three-dimensional effects to the physical parameters.

On uniform planar shear flow around a circular cylinder at subcritical Reynolds number

An experimental investigation was conducted of a circular cylinder immersed in a uniform planar shear flow, where the approach velocity varies across the diameter of the cylinder. The study was motivated by some apparent discrepancies between numerical and experimental studies of the flow, and the general lack of experimental data, particularly in the subcritical Reynolds number regime. Of interest was the effect of shear on the vortex-shedding frequency and the mean aerodynamic forces, including the direction and origin of the steady mean lift force experienced by the cylinder, which has been the subject of contradictory results in the literature and for which measurements have rarely been reported. The circular cylinder was tested at Reynolds numbers from Re=4.0×10 4 to 9.0×10 4, and the dimensionless shear parameter ranged from K=0.02 to 0.07, which corresponds to a flow with low to moderate shear. The results from both the present and previous studies show that low to moderate shear causes a small increase in the Strouhal number, an increase in the mean base pressure coefficient, a reduction in the mean drag force coefficient, and a small mean lift force directed towards the low-velocity side. These effects are consistent with a narrowing, or reduction in width, of the cylinder near wake, which is supported by an asymmetric mean static pressure distribution on the surface of the cylinder.

Discrete Particle Simulation and Visualized Research of the Gas−Solid Flow in an Internally Circulating Fluidized Bed

In this paper, the DEM (discrete element method) is used to simulate the gas−solid flow of a two-dimensional internally circulating fluidized bed. Eulerian and Lagrangian methods are used to deal with gas-field and discrete particles, respectively. The gas flow is determined by the local average Navier−Stokes equation, the motion of individual particle is obtained by solving Newton's second law of motion, and particle collisions are taken into account. The simulated results indicate that there is particle circulation from the high-velocity region to the low-velocity region in internally circulating fluidized beds with uneven air distributions; therefore, the mixing characteristics of the bed material are good. Through visualization experiments, we confirm that there is transverse movement of bubbles from the high-velocity side to the low-velocity side in internally circulating fluidized beds. Thus, particles in the trailing vortex of bubbles also move transversely. This is an important factor that results in particle circulation in internally circulating fluidized beds.

The Ursa Major Cluster of Galaxies. V. HiRotation Curve Shapes and the Tully‐Fisher Relations

The Tully-Fisher relations for a complete sample of spirals in the Ursa Major cluster is investigated. The merits of combining B, R, I and K' photometry with HI rotation curves (RCs) have been exploited. In addition to the corrected HI global profile widths W_{R,I}^i, the HI RCs allow direct measurements of the maximum rotation Vmax and the amplitudes Vflat of the outer flat parts. The dynamical state of the gas disks could also be determined in detail. For large galaxy samples, the M^{b,i}_R - Log(W_{R,I}^i) correlation in conjunction with strict selection criteria is preferred for distance determinations with a 7% accuracy. Galaxies with rising RCs at the last measured point lie systematically on the low velocity side of the TF-relation. Galaxies with partly declining RCs (Vmax>Vflat) tend to lie on the high velocity side when using W_{R,I}^i or Vmax. These trends are eliminated when Vflat is used. The M^{b,i}_B - Log(2Vflat) residuals correlate consistently with morphology, color, surface brightness and gas mass fraction. These correlations are absent for the near-IR M^{b,i}_K' - Log(2Vflat) residuals. The tightest correlation (Xred=1.1) is found for the M^{b,i}_K' - Log(2Vflat) relation with a slope of -11.3 +/- 0.5 and a total scatter of 0.26^m with a most likely intrinsic scatter of zero. The tightness of the near-IR correlation is preserved when converting it into a baryonic TF-relation which has a slope of -10.0 for (Mgas/L_K')=1.6 while a zero intrinsic scatter remains most likely. The tightness of the near-IR and baryonic correlations suggests that the TF-relation reflects a correlation between the dark matter halo mass, indicated by Vflat, and the total baryonic mass Mbar where Mbar~Vflat^4. The distribution of the baryons inside halos of similar mass is irrelevant for this relation.

Modeling of biased flow phenomena associated with the effects of static magnetic-field application and argon gas injection in slab continuous casting of steel

Biased flow occurs frequently in the slab continuous casting process and leads to downgraded steel quality. A mathematical model has been developed to analyze the three-dimensional biased flow phenomena associated with the effects of static magnetic-field application and argon gas injection in the slab continuous casting process. By moving the submerged entry nozzle (SEN) from center to off-center, the biased flow and vortexing flow in the mold can be reproduced in the numerical simulation. The existence of a vortexing flow is shown to result from three-dimensional biased flow in the mold. A vortex is located at the low-velocity side adjacent to the SEN. The vortex strength depends on the local horizontal velocity of molten steel and decreases gradually with distance from the free surface. The vortexing-zone size depends on the biased distance of the SEN, and the intensity of the vortexing flow depends on the casting speed of the continuous caster. Only when the location and strength of the magnetic field are properly chosen, can the vortexing flow be suppressed by a static magnetic-field application. The effect of argon gas injection on the vortexing flow is not remarkable. The combination of magnetic-field application and argon gas injection can correct the biased flow and suppress the vortexing flow by suppressing the surface velocity and removing the downward velocity near the SEN in the mold.

The effects of shear flow on the unsteady wakes behind a sphere at moderate Reynolds numbers

Numerical simulations to investigate the effects of shear flow on wakes behind a sphere were carried out using a three-dimensional finite element method. The time-dependent Navier–Stokes equations were solved by a modified explicit time integration scheme. The Reynolds number, defined by the sphere diameter and oncoming velocity at its center, ranged from 20 to 500. Linear shear is assumed, and the dimensionless shear rate, defined as the vertical gradient of oncoming shear flow, was varied from 0.0 to 0.2. Extensive comparisons were made between the present computed results and available experimental and numerical investigations, and showed that they are in close agreement. Computed lift force was directed toward the low velocity side for Re>50 whereas it was toward the high velocity side for Re<50. In addition, drag forces showed slight increases compared to those in a uniform flow. The Reynolds number, at which vortex shedding begins, was found to be lower than that in a uniform flow and was a function of the shear rate. Vortex shedding frequency also increases with the Reynolds number and the shear rate. The irregularity of the vortex shedding and the oscillation of the vortex detachment location appearing in uniform and low shear flows at Re=500 vanishes when high shear was present.

A finite difference solution of the shear flow over a circular cylinder

The incompressible viscous shear flow past a circular cylinder is analyzed by solving two-dimensional Navier-Stokes equations and pressure Poisson equation using a finite difference method. The shear flow is calculated for Reynolds numbers from 80 to 1000, and shear parameters up to 0.25. The numerical results indicate that the vortex shedding persists at the shear parameters up to 0.25 for the present Reynolds number range. The Strouhal number and the drag coefficient decrease as the shear parameter increases. There is a transverse force acting from the high velocity side toward the low velocity side in the shear flow.

Drag and lift forces on a rotating sphere in a linear shear flow

The drag and lift forces acting on a rotating rigid sphere in a homogeneous linear shear flow are numerically studied by means of a three-dimensional numerical simulation. The effects of both the fluid shear and rotational speed of the sphere on the drag and lift forces are estimated for particle Reynolds numbers of 1[les ]Rep[les ]500.The results show that the drag forces both on a stationary sphere in a linear shear flow and on a rotating sphere in a uniform unsheared flow increase with increasing the fluid shear and rotational speed. The lift force on a stationary sphere in a linear shear flow acts from the low-fluid-velocity side to the high-fluid-velocity side for low particle Reynolds numbers of Rep&lt;60, whereas it acts from the high-velocity side to the low-velocity side for high particle Reynolds numbers of Rep&gt;60. The change of the direction of the lift force can be explained well by considering the contributions of pressure and viscous forces to the total lift in terms of flow separation. The predicted direction of the lift force for high particle Reynolds numbers is also examined through a visualization experiment of an iron particle falling in a linear shear flow of a glycerin solution. On the other hand, the lift force on a rotating sphere in a uniform unsheared flow acts in the same direction independent of particle Reynolds numbers. Approximate expressions for the drag and lift coefficients for a rotating sphere in a linear shear flow are proposed over the wide range of 1[les ]Rep[les ]500.

Rotation Curve Shapes and the Tully-Fisher Relations

The scatter in the K’–band Tully–Fisher relation (TFr) is larger than can be expected from observational uncertainties when using the widths of global HI profiles of a volume limited, complete sample without any morphological selection criteria. This poster shows, however, that the observed scatter can be explained when considering the shapes of the galaxy rotation curves (RCs). Using Vmax from the RCs, it turns out that galaxies with rising RCs tend to lie on the low–velocity side of the TFr and those with declining RCs tend to lie on the high velocity side. The scatter in the K’–Vflat TFr is consistent with the measurement uncertainties.

Acoustic Excitation of Dual Diffusion Flames with Coherent Structure Behind a Rear-Facing Semicircular Cylinder

In this paper two types of dual diffusion flames formed behind a rear-facing semicircular fuel nozzle are experimentally investigated; one is the plane diffusion flame consisting of an ordinary laminar diffusion flame on the lower-velocity side of the fuel nozzle and a lifted flame on the higher-velocity side, the other the bluffbody stabilized wake flame composed of two lifted flames on both sides of the fuel nozzle. The CAPLA(computer-aided phase-locked averaging) method is combined with the acoustic excitation to examine not only effects of the acoustic excitation on the flame structure, but also phase characteristics of the formation processes of organized eddies and eddy-flames. The acoustic excitation at a constant frequency of 300 Hz is applied by a flat loudspeaker flush-mounted on the higher-velocity side wall of the combustion tunnel. According to flash shadowgraphs of the flames the acoustic excitation is found to make the outline of eddy-flames clear with increasing the excitation intensity due to the rapid and clear formation of organized eddies, leaving general features of the flames almost unvaried. Frequency spectra of fluctuating temperature for two kinds of flames show that, at the maximum excitation intensity applied, only a fundamental peak at 300 Hz and some of its harmonics can be observed without exhibiting any white noise character. Therefore, it is confirmed that the acoustic excitation is very useful in the phase-locked-averaging measurements of turbulent flames. The phase-averaged two-dimensional temperature profiles at eight consecutive phases obtained for two kinds of flames demonstrate clearly the entire process from the formation of an initial organized eddy to the establishment of an eddy-flame. As a result, the organized eddy-flame in the plane diffusion flame is found to have an average lifetime of about three times the period of the organized eddy formation of 1/300 sec, while the lifetime of the organized eddy-flame in the bluflbody stabilized wake flame is about twice the period of the organized eddy formation.

Gas Kinetic Approach to Two-Dimensional Traffic Flow

The kinetics of cars in two-dimensional traffic flow is described in terms of Boltzmann-like gas kinetic equations. Paveri-Fontana's gas kinetic equation for one-dimensional traffic flow is extended to two-dimensional traffic. The desired velocity is taken into account in the gas kinetic equations. A discrete version of the kinetic equations is used to numerically solve the equations. The velocity distributions are calculated by a numerical method. The steady-state velocity distributions are derived numerically for different accelerations and densities. It is shown that the velocity distribution of east-bound cars deviates to the low-velocity side with increasing density of north-bound cars. It is also found that the velocity distribution deviates to the high-velocity side with increasing acceleration under the condition of constant density.

Evolution of a thermal mixing layer in uniformly sheared turbulent flow

The present study is concerned with scalar mixing in uniformly sheared turbulent flow, in which Reynolds stresses and integral length scales grow nearly exponentially. For this purpose, the high-velocity half of a uniformly sheared, turbulent air stream was heated electrically to a nearly uniform temperature, slightly above that in the other half, thus generating a thermal mixing layer between the heated and unheated streams. Measurements show that the mean temperature field reached a quasiasymptotic state, in which, to a first approximation, it maintained an error-function-like profile with a width that grew almost linearly within the range of measurements. The effects of shear were, however, manifested by an asymmetry of the mean temperature profile, indicating deeper penetration of the layer into the lower velocity side. Measurements of the evolution of rms temperature fluctuations, heat fluxes, third-order covariances, and length scales are also reported. Simple theoretical predictions of the evolution of the thermal mixing layer width and of temperature fluctuation statistics are also presented and shown to agree well with the measurements.

Flow About a Circular Cylinder in and Near a Turbulent Plane Mixing Layer

This paper deals with an experimental study of the fluid forces, surface pressure, and vortex-shedding frequency of a circular cylinder placed in and near a turbulent plane mixing layer with zero velocity ratio. These characteristics are given as functions of the cylinder diameter d divided by the local mixing-layer width δ and the nondimensional transverse coordinate of the center of the cylinder in a Reynolds number range 5500–46000. For the cylinder d/δ = 2.2–2.3 the r.m.s. lift attained a maximum 40 percent higher than that in the uniform flow when a part of the cylinder surface was near an intermittently turbulent edge on the high-velocity side of the mixing layer; the time-mean resultant force attained a sharp maximum as high as 80 percent of that in the uniform flow when the axis of the cylinder was located at the center of the mixing layer. The former maximum was interpreted in terms of a vortex-body interaction while the latter maximum was found to be associated with a large delay of the boundary-layer separation on the low-velocity side of the cylinder.

Heating of upflowing auroral H+ and O+ Beams: Results from quasi‐linear theory

Particle measurements at 3 RE in the auroral zone revealed the existence of simultaneous upgoing hydrogen and oxygen beams on auroral field lines. The observed beam distributions were broad, indicating that significant heating took place near or below the satellite. The most interesting features that were noted in the distribution functions included extended parallel O+ high energy and H+ low energy tails, and a perpendicular broadening of the O+ distribution. The purpose of the present work was to carry out an analysis of the mechanisms that could produce such heating, and to base this analysis as fully as possible on plasma and wave parameters measured by the Dynamics Explorer 1 (DE 1) satellite. An analysis of Maxwellian fits to the observed distribution functions showed that an oblique slow hydrogen acoustic mode was weakly unstable at frequencies between the oxygen and hydrogen gyrofrequencies. The location of wave‐particle resonant and nonresonant regions in velocity space suggested qualitatively that H+ undergoes weak parallel heating on the low velocity side of the beam and that O+ is heated in the perpendicular direction on the high velocity side of the beam at satellite altitude. Energy is transferred from parallel motion of H+ to perpendicular motion of O+ during this process. Calculations of diffusion time scales for both H+ and O+ showed quantitatively that resonant diffusion within 1 RE of the satellite is sufficiently fast to explain the perpendicular O+ heating and a substantial portion of the parallel H+ heating. Some additional parallel diffusion of both species must have taken place below the satellite. Nonresonant diffusion and interactions of ions with a parallel H+ acoustic wave, which may be unstable below the satellite, could be responsible for this additional heating. These processes transfer energy from parallel motion of H+ to parallel motion of O+. The presence of a third ion species also could have modified the parallel heating rate. These latter possibilities could not be studied in detail with the available data.

The interaction of turbulence and pressure gradients in a baffle-stabilized premixed flame

Simultaneous measurements of time-resolved velocity and temperature have been obtained by laser-Doppler anemometry and numerically compensated fine-wire thermocouples in the near wake of a premixed flame stabilized on a disk baffle located on the axis, and at the exit, of a confining pipe. The diameter of the disk was 0.056 m, the diameter of the pipe was 0.080 m, the volumetric equivalence ratio with natural gas as the fuel was 0.79 and the Reynolds number, based on pipe diameter and upstream pipe bulk velocity of 9 m/s, was 46 800. The purpose of the measurements is to quantify the relative magnitudes of terms involving the mean pressure gradient and Reynolds stresses in the balance of turbulent kinetic energy and heat flux in a strongly sheared, high-Reynolds-number, reacting flow. The latter term has been associated with non-gradient diffusion in other flows. Source terms involving the mean pressure gradient are large in the conservation of turbulent heat flux but not in the conservation of Reynolds stress. The ‘thin-flame’ model of burning suggests that the sign and magnitude of the heat flux is closely related to the conditioned mean velocities. The mean axial velocity of the reactants is larger (by up to 0.27 of the reference velocity) than that of the products on the low-velocity side of the shear layer that surrounds the recirculation bubble but the reverse is true on the high-velocity side. These observations are related to the sign of the axial pressure gradient, which is associated with the streamline curvature, and the consequent preferential acceleration of the low-density products. Generally, the Reynolds stresses of the products are higher than those of the reactants and, in contrast to previously reported measurements, the contribution to the unconditioned stresses by the difference in the mean velocity between products and reactants, the so-called ‘intermittent’ contribution, is small. This is a consequence of the high Reynolds number of our flow.

Numerical study on viscous shear flow past a circular cylinder using integro-differential formulation

Numerical solutions of the unsteady Navier-Stokes equations are presented for the two dimensional flow about a cylinder immersed in a simple shear flow by using the integrodifferential formulation. Selected numerical results for Reynolds numbers 40 and 80 shear parametersK=0.1 and 0.2 are presented and compared with finite-difference results. Plots of streamlines and equi-vorticity lines and time histories of lift, drag, stagnation point and separation angles are given. It was found that two separation bubbles exist periodically behind the lowvelocity side of the cylinder; a main bubble and a secondary one, while there is only one bubble behind the high-velocity side. Numerical results showed that the lift force acts in the direction towards the low-velocity side of the free stream and its magnitude varies periodically with the nondimensional time. In addition, the magnitude of the lift force is approximately proportional to the shear parameterK.

The effects of highly exothermic chemical reaction on a two-dimensional mixing layer

An experimental study of the effect of a highly exothermic chemical reaction on a two-stream mixing layer was performed. One stream was lean premixed cold reactants, while the other stream was hot combustion products that acted as an ignition source for the reactants. Results were obtained for a cold to hot side velocity ratio of 15:5 m/s and cold side equivalence ratios ranging from 0 to 0.8. The effect of increasing the energy release was to cause an increase in the acceleration of fluid on the hot, low-velocity side and, thus, an increase in the growth rate of the layer, movement of the centerline position toward the low-velocity side, earlier interaction of the layer with the wall, and a more rapid decay of the Reynolds stresses from their peak values. The large vortex structures that dominated this flowfield were not qualitatively affected by the exothermic reaction. The layer continued to grow by subharmonic combination until wall effects became important. For equivalence ratios less than the lean flammability limit, chemical reaction was restricted to the region of fluid-dynamic mixing. For equivalence ratios greater than the lean flammability limit, however, the reaction zone extended into the irrotational portion of the reactant stream.