Air–water flow properties in step cavity down a stepped chute

For the last three decades, the research into skimming flows down stepped chutes was driven by needs for better design guidelines. The skimming flow is characterised by some momentum transfer from the main stream to the recirculation zones in the shear layer developing downstream of each step edge. In the present study some physical modelling was conducted in a relatively large facility and detailed air–water flow measurements were conducted at several locations along a triangular cavity. The data implied some self-similarity of the main flow properties in the upper flow region, at step edges as well as at all locations along the step cavity. In the developing shear layer and cavity region (i.e. y/h < 0.3), the air–water flow properties presented some specific features highlighting the development of the mixing layer downstream of the step edge and the strong interactions between cavity recirculation and mainstream skimming flows. Both void fraction and bubble count rate data showed a local maximum in the developing shear layer, although the local maximum void fraction was always located below the local maximum bubble count rate. The velocity profiles had the same shape as the classical mono-phase flow data. The air–water flow properties highlighted some intense turbulence in the mixing layer that would be associated with large shear stresses and bubble–turbulence interactions.     

Local properties of vertical mercury-argon two-phase flow in a circular tube under transverse magnetic field

Experimental data are presented in this paper on the profiles of local void fraction, bubble impaction rate, bubble velocity and its spectrum, and also bubble length and its spectrum, of mercury-argon two-phase slug flow flowing upwards in a vertical circular tube in the presence of a transverse magnetic field. Decrease in void fraction and increase in bubble velocity are significant when the magnetic flux density is larger than $\text{0.3～0.4}$$\text{T}\text{(Ha ? 100)}$. This effect is discussed by analyzing the bubble size distribution. Recovery of local void fraction profile in the downstream of an obstacle and diffusion of void injected from only one nozzle in the presence of magnetic field are also discussed.     

Wall shear stress characterization of a 3D bluff-body separated flow

Efficient flow control strategies aimed at reducing the aerodynamic drag of road vehicles require a detailed knowledge of the reference flow. In this work, the flow around the rear slanted window of a generic car model was experimentally studied through wall shear stress measurements using an electrochemical method. The mean and fluctuating wall shear stress within the wall impact regions of the recirculation bubble and the main longitudinal vortex structures which develop above the rear window are presented. Correlations allow a more detailed characterization of the recirculation phenomenon within the separation bubble. In the model symmetry plane the recirculation structure compares well with simpler 2D configurations; specific lengths, flapping motion and shedding of large-scale vortices are observed, these similarities diminish when leaving the middle plane due to the strong three-dimensionality of the flow. A specific attention is paid to the convection processes occurring within the recirculation: a downstream convection velocity is observed, in accordance with 2D recirculations from the literature, and an upstream convection is highlighted along the entire bubble length which has not been underlined in some previous canonical configurations.     

Characterization of Turbulent Structures in a Transonic Backward-Facing Step Flow

A transonic backward-facing step flow, at a free stream Mach number of 0.8 and a Reynolds number of 1.86 × 10⁵ with respect to the step height, was investigated experimentally by means of planar and stereo Particle Image Velocimetry (PIV) measurements for multiple fields of view. The primary aim of this analysis is to examine whether the large temporal variations of the reattachment location is associated with the presence of large scale coherent flow structures. The mean flow reattaches ≈6.1±0.2 times the step height downstream of the step. This value fluctuates temporally as much as ±3 step heights. Measurements of the wake flow in horizontal planes show that the strong variations of the reattachment length are associated with spanwise variations of the streamwise velocity. Two-point correlations revealed large–scale coherent regions with a length of up to 7 step heights and a dominant spanwise wave-length of 1.5…2.5 step heights. Furthermore, close to the step large structures are found, which span more than 5 step heights in spanwise direction. The Reynolds stress distribution of the separated region strongly suggests that the initial streamwise momentum is transferred to the vertical component as well as to the spanwise component in comparable portions by the deformation of the initial Kelvin-Helmholtz vortices and the generation of secondary ones. As a result, the separated shear layer is characterized by eddies of various sizes and orientations. The mean flow field only shows the primary separation bubble and a secondary recirculation region. No stationary streamwise vortices could be found for the tested Reynolds number.     

Interfacial structure in an air–water planar bubble jet

The objective of the current study is to better understand the interfacial structure and its development in an air–water planar bubble jet, as well as to provide a unique benchmark data set for a 3D thermal-hydraulic analysis code. Both flow visualization and local measurements were performed in three characteristic flow conditions at four elevations along a test section with a cross section of 200 mm in width and 10 mm in gap. A high-speed digital video camera was applied in the flow visualization study to capture the flow structures and bubble interaction phenomena, while a miniaturized four-sensor conductivity probe was used to acquire the time-averaged local void fraction, interfacial velocity, and bubble number frequency. Also, the interfacial area concentration and the averaged bubble Sauter mean diameter were obtained from the local measurements. The lateral bubble transport and bubble interaction mechanisms were clearly demonstrated in the acquired data.     

Numerical simulation of the turbulent wake behind a normal flat plate

The three-dimensional wake flow behind a flat plate placed normal to the free stream has been investigated by means of direct numerical simulations. The Reynolds number Re based on the homogeneous inflow velocity and the uniform width d of the plate was 750. Coherent vortices were alternately shed from the sides of the plate with a frequency corresponding to a Strouhal number 0.168. The wake was distinctly turbulent downstream of the plate whereas the mean recirculation bubble extended 1.96d downstream. A steady 2D mean flow and the accompanying Reynolds stresses were obtained by averaging in time and along the span of the plate. These Reynolds-averaged statistics exhibited the same qualitative features as corresponding data from cylinder wakes.     

Characterization of particle-laden, confined swirling flows by phase-doppler anemometry and numerical calculation

The particle dispersion characteristics in a confined swirling flow with a swirl number of approx. 0.5 were studied in detail by performing measurements using phase-Doppler anemometry (PDA) and numerical predictions. A mixture of gas and particles was injected without swirl into the test section, while the swirling airstream was provided through a co-flowing annular inlet. Two cases with different primary jet exit velocities were considered. For these flow conditions, a closed central recirculation bubble was established just downstream of the inlet.

The PDA measurements allowed the correlation between particle size and velocity to be obtained and also the spatial change in the particle size distribution throughout the flow field. For these results, the behaviour of different size classes in the entire particle size spectrum, ranging from about 15 to 80 μm, could be studied, and the response of the particles to the mean flow and the gas turbulence could be characterized. Due to the response characteristics of particles with different diameters to the mean flow and the flow turbulence, a considerable separation of the particles was observed which resulted in a streamwise increase in the particle mean number diameter in the core region of the central recirculation bubble. For the lower particle inlet velocity (i.e. low primary jet exit velocity), this effect is more pronounced, since here the particles have more time to respond to the flow reversal and the swirl velocity component. This also gave a higher mass of recirculating particle material.

The numerical predictions of the gas flow were performed by solving the time-averaged Navier-Stokes equations in connection with the well known kε turbulence model. Although this turbulence model is based on the assumption of isotropic turbulence, the agreement of the calculated mean velocity profiles compared to the measured gas velocities is very good. The gas-phase turbulent kinetic energy, however, is considerably underpredicted in the initial mixing region. The particle dispersion characteristics were calculated by using the Lagrangian approach, where the influence of the particulate phase on the gas flow could be neglected, since only very low mass loadings were considered. The calculated results for the particle mean velocity and the mass flux are also in good agreement with the experiments. Furthermore, the change in the particle mean diameter throughout the flow field was predicted approximately, which shows that the applied simple stochastic dispersion model also gives good results for such very complex flows. The variation of the gas and particle velocity in the primary inlet had a considerable impact on the particle dispersion behaviour in the swirling flow and the particle residence time in the central recirculation bubble, which could be determined from the numerical calculations. For the lower particle inlet velocity, the maximum particle size-dependence residence time within the recirculation region was considerably shifted towards larger particles.     

Interfacial aeration and bubble count rate distributions in a supercritical flow past a backward-facing step

An example of high-velocity open channel flows is a supercritical flow past an abrupt drop. In such a geometry, the basic air–water flow properties were measured, including distributions of void fraction and bubble count rate, and local air and water chord size distributions, at and downstream of the backward-facing step. The bubble count rate distributions were compared with a conceptual model of streamwise distribution of air and water chords which yields a quasi-parabolic relationship between bubble count rate and void fraction. The proposed model was an attempt to explain the experimental relationship between bubble count rate and void fraction, rather a meticulous breakdown of the complex air–water structure.     

Turbulence Characteristics in Flows Over Solid and Porous Square Ribs Mounted on Porous Walls

PIV measurements have been performed for turbulent flows in a rib-mounted channel whose bottom wall is made of a porous layer. The ratio of the rib and channel heights is fixed at 0.5. The effects of the wall and rib permeability are investigated focusing on the separating and reattaching flows at the bulk Reynolds number of 10³???10⁴. Three kinds of foamed ceramics are employed as the porous media. They have the same porosity of 0.8 but each permeability is different from the others. Its normalized values by the rib height are 0.89 × 10^???4, 1.47 × 10^???4 and 3.87 × 10^???4. Two kinds of square cylinder ribs: an impermeable smooth solid rib or a permeable porous rib which is made of the same porous medium as that for the bottom wall are used. The obtained turbulent velocity fields of the solid rib flows indicate that the turbulent intensity behind the rib becomes weak and the recirculation bubble in the clear channel tends to vanish as the the wall permeability increases. In the porous rib flow, the recirculation and the reattachment point shift downstream and turbulence becomes weaker due to the bleeding flow through the rib. In the higher permeability cases, the recirculation bubble hardly exists due to the flows through not only the bottom wall but also the porous rib. From the measurements, it is suggested that in the solid rib flows, a reverse flow region exists inside the porous wall whereas in porous rib flows, such reverse flow does not exist at higher permeability.     

Local and non-local Gurson-based ductile damage and failure modelling at large deformation

The purpose of this work is the formulation, numerical implementation and initial application of a non-local extension of existing Gurson-based modelling for isotropic ductile damage and attendant crack growth. It is being carried out under the premise that void coalescence results not only in accelerated damage development (e.g., Needleman and Tvergaard, 1984), but also in damage delocalisation (i.e., via interaction between neighbouring Gurson RVE's). To this end, we proceed by analogy with the approach of Needleman and Tvergaard (1984) who replaced the Gurson void volume fraction f with a (local) effective damage parameter f^* in the Gurson yield condition to account for the effect of void coalescence on the material behaviour. In the current case, the role of f^* is taken over and generalised by an effective continuum damage field ν. A field relation for ν is formulated here in the framework of continuum thermodynamics. In the simplest case, the resulting relation is formally analogous to the inhomogeneous temperature equation in which void nucleation and growth represent (local) sources for ν and in which void coalescence takes place in a process zone whose dimension is determined by a characteristic material lengthscale. Analogous to temperature, then, ν represents an additional continuum degree-of-freedom here, resulting in a coupled deformation-damage field model. In the last part of the work, the complete model for coupled damage-deformation is implemented numerically using the finite-element method on the basis of backward-Euler integration and consistent linearisation. Using this implementation, the behaviour of the current extended Gurson-based damage model is investigated for the case of simple tension of an inhomogeneous steel block. In particular, the corresponding simulation results document quantitatively the dependence of the delocalisation of the model damage process and minimisation of mesh-dependence on the characteristic dimension of the damage process zone.     

Numerical modeling of vortex/shock wave interaction and its transformation by localized energy deposition

Three-dimensional unsteady Euler simulations are presented for the interaction of a streamwise vortex with an oblique shock of angle β = 23.3° at Mach 3 and 5. The flowfield features are analyzed for weak, moderate and strong interaction regimes. The details of the free recirculation zone at conditions of subsonic and supersonic flow on the vortex axis are considered. The vortex breakdown under conditions of a subsonic vortex core is characterized by a continuous growth and gradual degeneration of the region, unlike the supersonic core condition wherein a steady recirculation zone is achieved. The possibility of using a localized steady and pulsed periodic energy deposition on the vortex axis for stimulating the breakdown is demonstrated for various interaction regimes. It is shown that the formation of a subsonic wake downstream of an energy source lying on the vortex axis contributes to a more significant growth of the dimensions of the recirculation zone compared to the case when the vortex core remains supersonic. The possibility of achieving the effects similar to the steady case is demonstrated by the effect of a pulsed periodic energy source on the flow under consideration for corresponding equivalence parameters.      

Turbulent characteristics of shear-thinning fluids in recirculating flows

 A miniaturised fibre optic Laser-Doppler anemometer was used to carry out a detailed hydrodynamic investigation of the flow downstream of a sudden expansion with 0.1–0.2% by weight shear-thinning aqueous solutions of xanthan gum. Upstream of the sudden expansion the pipe flow was fully-developed and the xanthan gum solutions exhibited drag reduction with corresponding lower radial and tangential normal Reynolds stresses, but higher axial Reynolds stress near the wall and a flatter axial mean velocity profile in comparison with Newtonian flow. The recirculation bubble length was reduced by more than 20% relative to the high Reynolds number Newtonian flow, and this was attributed to the occurrence further upstream of high turbulence for the non-Newtonian solutions, because of advection of turbulence and earlier high turbulence production in the shear layer. Comparisons with the measurements of Escudier and Smith (1999) with similar fluids emphasized the dominating role of inlet turbulence. The present downstream turbulence field was less anisotropic, and had lower maximum axial Reynolds stresses (by 16%) but higher radial turbulence (20%) than theirs. They reported considerably longer recirculating bubble lengths than we do for similar non-Newtonian fluids and Reynolds numbers. Received: 23 February 1999/Accepted: 28 April 1999     

Eulerian and Lagrangian description of a pulsatile,partially turbulent flow

A detailed flow field analysis is carried out downstream of a Björk-Shiley prosthetic aortic valve, placed in a Great Circulation simulator. Mean periodic velocity and turbulence are obtained by means of selective sampling through enabling windows. Flow mapping includes three different heights and three meridional planes (i.e. nine diameters). Some effort is devoted to study cycle-to-cycle variations, and to remove them for determining true turbulence values. A lagrangian interpretation, based upon the convection of vorticity produced at the aortic prosthesis, is needed to understand the flow pattern behaviour.A version of this paper was presented at the 11 th Symposium on Turbulence, University of Missouri-Rolla, Oct. 17–19, 1988     

Numerical studies of fluid flow through tubes with double constrictions

The flow fields in the neighbourhood of double constrictions in a circular cylindrical tube were studied numerically. The effects on the streamline, velocity and vorticity distributions as the flow passes through the constrictions in the tube were studied in the Reynolds number range 5–200. Double constrictions with dimensionless spacing ratios of 1, 2, 3 and ∞ were studied for a 50% constriction. It is noted that when the Reynolds number is below 10, no recirculation region is formed in the above constricted flow. For Reynolds numbers greater than 10, a recirculation region forms downstream of each of the constrictions. For constriction spacing ratios of 1, 2, and 3, when the Reynolds number is high, a recirculation region spreads between the valley of the constrictions. The recirculation region formed between the two constrictions has a diminishing effect on the generation of wall vorticity near the second constriction area. In general, the peak value of wall vorticity is found slightly upstream of each of the constrictions. When the Reynolds number is increased, the peak wall vorticity value increases and its location is moved upstream. Maximum wall vorticity generated by the first constriction is found to be always greater than the maximum wall vorticity generated by the second constriction. The extent of this spreading of the recirculation region from the first constriction and its effects on the second constriction depend on the constriction spacing ratio and the flow Reynolds number.     

Fiber-optic probe measurements of void fraction and bubble size distributions beneath breaking waves

Experiments were performed to determine the accuracy of single-tip fiber-optic probes for making simultaneous measurements of the void fraction and bubble size distributions under breaking waves. Tests in a vertical bubble column showed that the normalized RMS error in the void fraction measurements was ∼10%. The relationship between bubble rise time and bubble velocity was investigated in a unidirectional flow cell. Similar to previous studies the rise time and bubble velocity were found to be related by a power law equation. The probes can provide mean bubble velocities accurate to ±10% when a minimum of ∼15 individual bubble velocities are averaged. The fiber-optic probes were deployed beneath a plunging breaking wave in a laboratory wave channel. The slope and shape of the bubble cord length size distribution measured with the probes was found to agree closely with the size distribution measured from digital video recordings. The probes were then positioned in the splash-up zone of a plunging breaker and the resulting cord length distribution had a shape and slope that was in agreement with previous measurements. These results demonstrate that single-tip fiber optic probes can provide accurate simultaneous measurements of the void fraction and bubble sizes inside the dense bubble clouds entrained by breaking waves.     

Experimental Investigation of Separated Shear Flow under Subharmonic Perturbations over a Backward-Facing Step

Subharmonic-perturbed shear flow downstream of a two-dimensional backward-facing step was experimentally investigated. The Reynolds number was Re_h = 2.0 ×10⁴, based on free-stream velocity and step height. Planar 2D-2C particle image velocimetry was employed to measure the separating and reattaching flow in the horizontal-vertical plane in the center position. The subharmonic perturbations were generated by an oscillating flap which was implemented over the step edge and driven by periodic Ampere force. The subharmonic frequency was 55 Hz as the half of the fundamental frequency of the turbulent shear layer. As a result of the subharmonic perturbations, the size of recirculation region behind the backward-facing step is reduced and the time-averaged reattachment length is 31.0% shorter than that of the natural flow. The evolution of vortices, including vortex roll-up, growth and breakdown process, is analyzed by using phase-averaging, cross-correlation function and proper orthogonal decomposition. It is found that Reynolds shear stress is considerably increased in which the vortices roll up and then break down further downstream. In particular, rapid growth of vortices based on the “step mode” occurs at approximate half of the recirculation region, caused by in interaction between the shear layer and the recirculation region. Furthermore, the coherent structures, which are represented by a phase-correlated POD mode pair, are reconstructed in phases in order to show regular patterns of the subharmonic-perturbed coherent structures.     

Void fraction,bubble velocity and bubble size in two-phase flow

Experiments were performed in atmosphereic vertical air-water flows, for void fractions between 0.25 and 0.75 (cross-sectional averages) and superficial liquid velocities of 1.3, 1.7 and 2.1 m/s. Local values of void fraction and bubble velocity as well as the bubble diameter were measured by means of a resistivity probe technique. Reliable values were obtained for the local void fraction over the entire range $\text{0 ≤ α ≤ 1}$. The void fraction profiles appeared to have a local maximum at the pipe center, local maxima close to the wall were obviously absent. The resistivity probes are shown to measure the velocity of the interface between the conducting and nonconducting phases, which equals the gas velocity only for low void fractions. The measured data for void fraction and bubble velocity were correlated by means of power law distribution functions, with exponents given by a function of the cross-sectionally averaged void fraction. The Sauter mean diameters for the bubble size spectra found, agree reasonably well with diameters predicted by a theoretical model based on the energy dissipation in the flow.     

Turbulent flow past a bubble and an ellipsoid using shadow-image and PIV techniques

An experimental investigation on flow around an oscillating bubble and solid ellipsoid with a flat bottom was conducted. A single air bubble (equivalent diameter D_e=9.12 mm) was attached to a small disk (1 mm) at the end of a needle and suspended across a vertical square channel (100 mm) by wire wherein water flowed downward at a constant flowrate. The solid ellipsoid (D_e9.1 mm) was suspended across the square channel in the same manner. The equivalent diameter-based Reynolds and Eotvos number range, 1950<Re<2250 and 11<Eo<11.5, placed the bubble in the ‘wobbly’ regime while the flow in its wake was turbulent. A constant flowrate and one bubble size was used such that flow in the wake was turbulent. Velocity measurements of the flow field around the bubble or solid were made using a one CCD camera Digital Particle Image Velocimetry (DPIV) system enhanced by Laser Induced Fluorescence (LIF). The shape of the bubble or solid was simultaneously recorded along with the velocity using a second CCD camera and an Infrared Shadow Technique (IST). In this way both the flow-field and the boundary of the bubble (solid) were measured. The velocity vector plots of flow around and in the wake of a bubble/solid, supplemented by profiles and contours of the average and root-mean-square velocities, vorticity, Reynolds stress and turbulent kinetic energy, revealed differences in the wake flow structure behind a bubble and solid. One of the significant differences was in the inherent, oscillatory motion of the bubble which not only produced vorticity in the near-wake, but as a result of apparent vorticity stretching distributed the turbulent kinetic energy associated with this flow more uniformly on its wake, in contrast to the solid.     

Bubble generation and transport in a microfluidic device with high aspect ratio

Bubble generation and transport in a micro-device composed of a micro-T-junction and a following serpentine micro-channel was experimentally investigated. It has a rectangular cross-sectional with an aspect ratio of 7.425. Air and water were used as gas and liquid, respectively. Mixtures of water–glycerol and water–Tween-20 were used to study the effects of liquid viscosity and surface tension. Compared with previous T-junction bubble generation, the liquid and gas inlets orientation was switched in this work. The continuous flow was driven from the perpendicular channel and the dispersion flow was from the main channel. It shows that the break-up process has three periodic steps under certain operating conditions. The dimensionless bubble length L/w in the micro-channel with high aspect ratio is much larger than that in square microchannels. A correlation is proposed to correlate L/w with liquid flow rate J_L, gas flow rate J_G, and liquid viscosity μ_L. Surface tension σ can change the bubble shape but almost does not affect the bubble length in this fast break-up process. Additionally, a long bubble may be broken up at the corners at the same time because the locations of gas and liquid are exchanged relative to the concave and convex portions of an elbow after a turn which may result in the change of fluid velocities and gas–liquid pressure drop.     

A hybrid method for bubble geometry reconstruction in two-phase microchannels

Understanding bubble dynamics is critical to the design and optimization of two-phase microchannel heat sinks. This paper presents a hybrid experimental and computational methodology that reconstructs the three-dimensional bubble geometry, as well as provides other critical information associated with nucleating bubbles in microchannels. Rectangular cross-section silicon microchannels with hydraulic diameters less than 200 μm were fabricated with integrated heaters for the flow experiments, and the working liquid used was water. Bubbles formed via heterogeneous nucleation and were observed to grow from the silicon side walls of the channels. Two-dimensional images and two-component liquid velocity field measurements during bubble growth were obtained using micron-resolution particle image velocimetry (μPIV). These measurements were combined with iterative three-dimensional numerical simulations using finite element software, FEMLAB. The three-dimensional shape and location of the bubble were quantified by identifying the geometry that provided the best match between the computed flow field and the μPIV data. The reconstructed flow field through this process reproduced the experimental data within an error of 10–20%. Other important information such as contact angles and bubble growth rates can also be estimated from this methodology. This work is an important step toward understanding the physical mechanisms behind bubble growth and departure.