Measurement of bubble size, velocity and concentration in flashing flow behind a sudden constriction

In the present paper the results of investigations in flashing flow behind a sudden constriction in vertical upflow are described. Flow visualization, laser-Doppler and phase-Doppler anemometry have been used to measure local bubble and fluid velocities, local bubble sizes and void fractions. The measurements were performed in the midplane of a two-dimensional channel with a 2:1 stepwise constriction.It was found that bubble nucleation takes place in the recirculation zone immediately behind the constriction, which is the location of the lowest static pressure. These bubbles are transported downstream by the mean flow field, while undergoing further growth. No additional nucleation was observed downstream of the recirculation zone. A periodic, cloudwise behaviour of the bubble formation was found which could be explained by the interaction between the bubble growth and the mean flow field. This interaction results in strong disturbances of the mean flow field, which show up as an increase of the fluctuating bubble velocity by a factor of 3 compared to single-phase measurements in a region of 10 step heights behind the constriction. However, these fluctuations appear more like a periodic change in the mean velocity rather than a higher turbulence level. The measured arithmetic mean bubble diameters rise from approx. 50 μm in the recirculation region to about 70–80 μm 50 step heights downstream. Maximum local bubble number density and void fraction were found to be 160001/cm³ and 0.8%, respectively.     

A model of stress dissipation in second-moment closures

The paper presents a modified expression for the dissipation rate tensor _ij in the second-moment closure models, which employs the dissipation flatness parameterE and the turbulenceRe number. The expression reproduced the distribution among the three diagonal components of _ij in agreement with the direct numerical simulation of a plane channel flow ofMansour, Kim and Moin, 1988. Implemented in a low-Re-number differentialRe-stress model the relationship yielded predictions of dissipative components better than other models, albeit spoiled by still unsatisfactory modelling of the equation for the energy dissipation rate . on leave from Mainski Fakultet, University of Sarajevo, Bosnia Hercegovina.     

Vortex-induced oscillations at low Reynolds numbers: Hysteresis and vortex-shedding modes

Results are presented for the numerical simulation of vortex-induced vibrations (VIVs) of a cylinder at low Reynolds numbers (Re). A stabilized space–time finite-element formulation is utilized to solve the incompressible flow equations in primitive variables. The cylinder, of low nondimensional mass (m^*=10), is free to vibrate in, both, the transverse and in-line directions. To investigate the effect of Re and reduced natural frequency, F_n, two sets of computations are carried out. In the first set of computations the Reynolds number is fixed (=100) and the reduced velocity (U^*=1/F_n) is varied. Hysteresis, in the response of the cylinder, is observed at the low- as well as high-end of the range of reduced velocity for synchronization/lock-in. In the second set of computations, the effect of Reynolds number (50Re500) is investigated for a fixed reduced velocity (U^*=4.92). The effect of the Reynolds number is found to be very significant for VIVs. While the vortex-shedding mode at low Re is 2S (two single vortices shed per cycle), at Re300 and larger, the P+S mode of vortex shedding (a single vortex and one pair of counter-rotating vortices are released in each cycle of shedding) is observed. This is the first time that the P+S mode has been observed for a cylinder undergoing free vibrations. This change of vortex-shedding mode is hysteretic in nature and results in a very large increase in the amplitude of in-line oscillations. Since the flow ceases to remain two-dimensional beyond Re200, it remains to be seen whether the P+S mode of shedding can actually be observed in reality for free vibrations.     

Optical Analysis and Qualitative Discrimination of Vortex-Flame Interaction in a Plane Premixed Shear Layer

To obtain practical schemes of vortex–flame interactions, a series of organized eddies formed in the plane premixed shear layer is investigated, instead of a single vortex ring or a single vortex tube. The plane premixed shear layer is first formed between two parallel uniform propane–air mixture streams. For getting clear qualitative pictures of vortex–flame interactions in the plane premixed shear layer, two extreme ignition points are assigned; one is assigned at the center of an organized eddy where the vortex motion plays an important role, the other at the midpoint between two adjacent organized eddies where the rolling-up motion prevails. A premixed flame is initiated by an electric discharge at one of the two assigned points and propagates either in the large scale organized eddy or along the interface between two uniform mixture streams. Propagation and deformation processes of the flame are observed using the simultaneously two-directional and high-speed Schlieren photography. The tangential velocity of organized eddy and the equivalence ratio of premixed shear flow are varied as two main parameters. The outline of propagating flame after the midpoint ignition is numerically analyzed by superposing the flame propagation having a constant burning velocity on the vortex flow field simulated with the discrete vortex method. The results obtained show that there exists another type of vortex–flame interaction in the plane shear layer in addition to the vortex bursting, and that it is caused by the rolling-up motion particular to the coherent structure in the plane shear layer and is simply named the vortex boosting. It is qualitatively concluded therefore that, in the ordinary turbulent premixed flames formed in the plane premixed shear layer, these two fundamental vortex-flame interactions get tangled with each other to augment the propagation velocity. An empirical expression which qualitatively takes into account of the effects of both vortex and chemical properties is finally proposed.     

Constitutive relations for the interaction force in multicomponent particulate flows

In the mechanics of multiphase (or multicomponent) mixtures, one of the outstanding issues is the formulation of constitutive relations for the interaction force. In this paper, we give a brief review of the various relations proposed for this interaction force. The review is tilted toward presenting the works of those who have used the mixture theory (or the theory of interacting continua) to derive or to propose a relationship for the interaction (or diffusive) force. We propose a constitutive relation which is general and frame-indifferent and thus suitable for use in many flow conditions. At the end, we provide an alternative approach for finding the drag force on a particle in a particulate mixture. This approach has been used in the non-Newtonian fluid mechanics to find the drag force on surfaces.     

An experimental study of diabatic spiral vortex flow

In spiral vortex flow, between concentric cylinders with the inner cylinder rotating and the outer stationary, the addition of a thermal gradient across the gap is a known complicating factor. The present diabatic study for narrow and wide gaps (radius ratios N=0.955 and N=0.8), with a heated outer and adiabatic inner cylinder, was undertaken to investigate this problem. The heat transfer characteristics and the modes of transition have been investigated together with the relationship between them. Using standard on-line digital computer techniques, the onset of vortex flow and its higher transitions have been shown to cause a sharp increase in Nusselt number. At higher Taylor numbers, of the order of 10⁶, a marked change in the Nusselt number occurs with the onset of the transition to periodic turbulent vortex flow. Outer wall heating is seen to affect the modes of transition. Diabatic critical Taylor numbers are much higher than those for adiabatic conditions and are found to depend on the close approach of the vortices to the outer wall     

Interaction of a heavy fluid flow in a channel with a transverse jet barrier

An experimental and numerical analysis of the interaction between a plane horizontal water flow in a rectangular channel (free water current) and a plane thin water jet (water jet curtain) is presented; the jet flows out vertically from either a slot nozzle in the bottom of the channel or the crest of a rigid spillway at a velocity appreciably (several times) greater than the water velocity in the channel. Numerical calculations were carried out using the STAR-CD software package preliminarily tested against the experimental data obtained. The dependence of the water level in the channel at a certain distance ahead of the jet barrier on the main jet parameters and the water flow rate in the horizontal channel is studied. It is found that in the region of the interface between the flows both steady and unsteady (self-oscillatory) flow patterns can be realized. Steady stream/jet interaction patterns of the “ejection” and “ejection-spillway” types are distinguished and a criterion separating these regimes is obtained. The notion of a rigid spillway equivalent to a jet curtain is introduced and an approximate dependence of its height on the relevant parameters of the problem is derived. The possibility of effectively controlling the water level ahead of a rigid spillway with a sharp edge by means of a plane water jet flowing from its crest is investigated. The boundary of transition to self-oscillation interaction patterns in the region of the flow interface is determined. The structure of these flows and a possible mechanism of their generation are described. Within the framework of the inviscid incompressible fluid model in the approximate formulation for a “thin” jet, an analytical dependence of the greatest possible depth of a reservoir filled with a heavy fluid at rest and screened by a vertical jet barrier on the jet parameters is obtained.     

Theoretical analysis of non-uniform extensional flows in relation to processing rheology and predictions of some constitutive equations

In this paper, a characteristic equation involving the stream function, already given by one of the authors in a previous work for classifying axisymmetric incompressible flows, is re-considered. Non-uniform nearly extensional flows are derived as particular solutions from this equation. Using experimental data in the literature for polymer solutions and melts, it is proved that particular solutions of the characteristic equation lead to kinematics very close to those encountered in the fiber-spinning process. The kinematic equations satisfactorily correlating the fiber-spinning data are used in order to determine the ability of constitutive equations to predict realistic stresses in the flow domain. The rheological parameters of the fluids, obtained from experiments, are used for computation of differential and integral constitutive equations in the spinning conditions. Comparisons with the stress response of adequate constitutive equations are given and discussed.Also affiliated to: Université Joseph Fourier Grenoble I and Institut National Polytechnique de Grenoble, Associé au CNRS (URA 1510)     

Coriolis Effect on the Linear Stability of Convection in a Porous Layer Placed Far Away from the Axis of Rotation

The linear stability theory is used to investigate analytically the Coriolis effect on centrifugally driven convection in a rotating porous layer. The problem corresponding to a layer placed far away from the axis of rotation was identified as a distinct case and therefore justifying special attention. The stability of the basic centrifugally driven convection is analysed. The marginal stability criterion is established as a characteristic centrifugal Rayleigh number in terms of the wavenumber and the Taylor number.