Wake Size Research Articles

Near-wake structure of a single gas bubble in a two-dimensional liquid-solid fluidized bed: Vortex shedding and wake size variation

The fluid mechanic behavior of a single gas bubble and its wake in a two-dimensional liquid-solid fluidized bed was examined visually via a video camera moving at the same s peed as the bubble. The bubble wake was observed to consist of two regions: primary wake (near wake) and secondary wake. Wake formation-shedding mechanisms were illustrated for both symmetric and asymmetric shedding modes. The shedding frequency, expressed in terms of the Strouhal number, was shown to be a function of the bubble Reynolds number but independent of particle properties. The boundaries between the primary and secondary wakes were qualitatively identified for several wake structures. The primary-wake size periodically varies in the form of a saw-tooth wave function, while the liquid wake exhibits no appreciable cyclic variation in size.

Experimental studies of wakes behind circularly capped bubbles

The wake behind a circularly capped bubble rising in fluids of different viscosity has been experimentally investigated using aspirin powder for flow visualization and high-speed photography synchronized with pressure-time measurements to measure the pressure field. The bubble plus its primary wake with a cusped tail is observed to contain symmetric pressure minima within the primary wake. Adjacent to the boundary wake is a free shear layer which contains large-scale vortices generated near the bubble rim that remain essentially stationary to an observer in the laboratory reference frame. The change in wake geometry and the transition to an ellipsoidal bubble shape as fluid viscosity increases is documented.The airfoil shape of the boundary of the circularly capped bubble and its closed primary wake is modelled using a Joukowski transformation in which the Joukowski constant is adjusted to match the experimental and potential-flow pressures along the bubble cap. The model successfully predicts the frontal pressure field, and the wake size and shape. The Davies & Taylor bubble-cap boundary condition is also verified.

Analysis of the central blockage wake in an LMFBR-subassembly

A simple model is presented to estimate the wake size and the average velocity of the circulating flow downstream of a central blockage in a subassembly. A computer code, newly developed for the purpose was used to examine the model results. It is shown that both the model results and the code closely fit experimental results. It is seen that the size of a turbulent wake is nearly independent of inlet coolant velocity, whereas the velocity of the circulating glow in the wake is nearly proportional to the inlet velocity. Both the length of the wake and the velocity in it increase as the blockage increases. The maximum temperature is reached with a blockage of more than 0.6 of the subassembly cross section, and varies inversely with inlet velocity.

Performance and Flow Regime of Annular Diffusers With Axial Turbomachine Discharge Inlet Conditions

An experimental investigation of the flow regime and the performance of straight-core annular diffusers operating immediately downstream of an axial compressor was carried out. Features of the compressor’s discharge including the size of the blade wakes, the streamwise relative turbulence intensity and the periodic streamwise component of velocity induced by the rotor blades were studied. The periodic streamwise velocity component was found to be quite small and it decayed as the flow proceeded through the diffusers. The relative turbulence intensities were comparatively large and increased along the diffusers. The statistical distribution of the stall periods for the diffuser with transitory stall had characteristics similar to those found for two-dimensional diffusers.

Wake Growth and Collapse in Stratified Flow

The objective of this research was to obtain data that could be used to predict the effect of stratification on the development of a momentumless wake. Experiments were performed in which a grid was oscillated in a stablystratified flow to produce the steady-state counterpart of the momentumless wake of a self-propelled vehicle. A pH-sensitive indicator was used to produce a neutrally-buoyant tracer to visualize wake development and subsequent vertical collapse. Measured velocity profiles in the simulated wake indicated that it was nearly momentumless, and vertical temperature surveys revealed the degree of mixing in the wake. The wake growth before and after collapse and the distance to collapse were correlated by using power laws and a theoretical analysis of wake collapse. The scaling relations established for predicting stratified flow wake dimensions revealed that the important parameters were the Froude number, defined as the product of the flow velocity and the Brunt-Vaisala period divided by the initial wake size, and the ratio of the time after wake generation to the Brunt-Vaisala period. Through the use of these parameters, two unique curves were obtained for estimating the horizontal width and vertical height of a wake in a stratified flow.

Characteristics of large two-dimensional air bubbles in liquids and in three-phase fluidised beds

The rising velocity, included angle and wake size of large single air bubbles have been measured in a two-dimensional column, 39.5 cm wide and 112 cm high, which contained a liquid or three-phase fluidised bed. The liquids used were water, 82% w/w aqueous glycerol, 90% w/w aqueous glycerol and methanol The fluidised beds consisted of glass beads with diameters 0.2 mm, 1 mm and 3 mm, fluidised by water. Bed porosities varied between 0.5 and 0.75. In all the liquids and fluidised beds, except 3 mm fluidised particles, bubble velocities werefound to be proportional to the square root of the radius of curvature of the circular cap. The included angle of the cap increased as the viscosity of the liquid increased. Bubble shapes were used to estimate an apparent viscosity for the fluidised beds which varied from 0.12 to 3.1O P.

Wake phenomena in a liquid‐liquid fluidized bed

AbstractMeasurements of the size and rate of shedding of wakes of drops, average drop holdup and velocity of the continuous phase as functions of drop size for kerosene, hexane, and benzene dispersed in water in a liquid‐liquid fluidized bed are reported. The average drop size ranged between 3.3 and 4.8 mm. The water velocity was 5.0 to 12.05 cm/s. The average drop hold up was 0.065 to 0.560.The ratio of wake to drop volume was 0.2 to 2.4, and the rate of wake shedding, reported as time of wake transfer units, was 0.7 to 2.4. At low drop holdups, the effect of single drops and groups of drops is dominant. At high drop holdups, the effect of neighboring drops and wakes is dominant. The wake size is correlated with slip velocity and can be calculated from empirical holdup measurements.

Viking Pitch Damping Derivatives as Influenced by Support Interference and Test Techniques

Sting support interference effects on the pitch damping derivatives and a comparison of damping characteristics using forced and free oscillation test methods were investigated on 140° spherically blunted cone configurations at M = 1.76-3.0. Sting influences are minimal with sting/model diameter ratios =0.183 and effective sting lengths =3.55 dm. Increasing ds/dm to 0.53 provides a considerable influence to the damping parameter at a = 0°-3° at all Reynolds numbers but shows little or no effect at higher alphas. A good correlation of freeflight and small diameter sting captive model wake geometries (wake neck position and size) was obtained which adds confidence in obtaining damping derivatives through captive model testing. The damping characteristics obtained on 11.23% and 4.35% scale Viking configurations using forced and free oscillation test methods respectively in two different test facilities are compared. The agreement is quite good at almost all test conditions.

Solids motion caused by a bubble in a fluidized bed

Theoretical analyses of the motion of a sphere or a cylinder through an inviscid fluid have been applied by previous authors to consideration of particle motion caused by a single bubble in a fluidized bed. The theories, however, take no account of the wake attached to a bubble; examination of the effect of the wake on the interpretation of displacement profiles has shown that the wake size can readily be calculated from experimental profiles using a thin layer of tracer particles. Profiles obtained in a two-dimensional bed of glass ballotini indicate that the wake area is 13–28% of the bubble area. The passage of a bubble across any horizontal plane causes a downward displacement of the dense phase to replace the wake material. Superimposed on this net downward displacement is a drift movement, similar to that of the inviscid fluid theories. Only a small area at the top of the peak of the drift profile crosses the horizontal level under consideration; this constitutes an additional quantity of material displaced upwards by the bubble with area about 5% of the bubble area. Consideration in the same terms of the results of other authors indicates that these conclusions are roughly applicable also to three-dimensional beds.

Fluid mixing in particulate fluidized beds

A hydrodynamic mathematical model is developed for particulate batch fluidization. Longitudinal dispersion in such systems is predicted analytically. It is governed by the particle wake: its size and shedding rate. The wake size is evaluated from photographs and the shedding rate is calculated from boundary layer flow. The predicted Peclet numbers compare very well with experimental data in the flow range of 40 < Re < 2300.

The Mechanism of heat transfer in a spray column heat exchanger: II. Dense packing of drops

AbstractTemperature profiles of water in a spray column heat exchanger, 15 cm. in diameter and 150 cm. long, operating with a dense packing of kerosene drops, were measured. The range of superficial velocities was 0 to 0.8 cm./sec. of water and 0.5 to 1.7 cm./sec. of kerosene. The bottom of the dense packing was either slightly above or 15 cm. below the bottom of the column proper.The physical picture of heat transfer is similar to that for dispersed packings of drops and emphasizes the dominant role of wakes in the heat transfer mechanism. The mathematical equations for dispersed packings of drops were modified to take into account the reduction of wake size at the interface of the two packings and the difference in the mixing patterns at the top of the column. An empirical allowance for the effect of bypassing is suggested. The volume of the wakes and the rate of wake shedding were estimated from the temperature profiles. General agreement was found between the theory and the experimental data of this and three other studies.

Drag of Spheres in Dilute High Polymer Solutions

WHITE1 showed that the drag on spheres in water, at Reynolds numbers exceeding the critical value (vd/ν > about 2 × 105), could be increased by dissolving a very small quantity of polyethylene oxide (Union Carbide ‘Polyox WSR301’) in the water, and suggested that this effect resulted from suppression of turbulence in the boundary layer by the additive, which caused earlier separation and a corresponding increase in the wake size.

Effect of Polymer Additives on Boundary Layer Separation and Drag of Submerged Bodies

THIS communication describes a simple experiment which demonstrates that in some circumstances the use of polymer additives can increase drag owing to a change in the position of boundary layer separation which results in a change of wake size and thus form drag.

Turbulent Wakes in Pressure Gradients

The application of moderate pressure gradients can exercise a large influence on the decay of wakes produced by obstructions in a flow field. In fact, a positive pressure gradient may arrest completely the decay process and cause the relative wake size to grow rapidly. This phenomenon could exist in any diffusing passage whose entrance flow has a wake-type distortion. Such a nonuniformity, due to a blade or a strut or other cause of stagnation-pressure variation in the stream, could lead to diffuser stall, as has been demonstrated experimentally. An analytical study of the problem has been made on the basis of measurements made in the M.I.T. Gas Turbine Laboratory. Theoretical considerations have led to a very convenient calculation formula which shows quite acceptable agreement with experimental data. The methods employ momentum integral equations and an “eddy viscosity” which is uniform across the wake and proportional to the product of the local free-stream velocity and the momentum thickness.