Turbulence characteristics of a gas-stirred steel bath outside the bubble plume

In order to understand the turbulence characteristic in melts stirred with injected gas, the relations for effective diffusion coefficient, turbulent kinetic energy and mean size of energy containing eddies were derived from the energy equation with an extended flow field for the steel bath, where strong bubble plume and surface currents are present. 67 or 23% of the energy is dissipated in the bubble plume or surface flow zone. An increasing entrainment coefficient leads to higher values of energy dissipation factor, effective diffusion coefficient and mean size of energy containing eddies, but to low degrees of turbulence. With increasing bath aspect ratio the energy dissipation factor increases, but the degree of turbulence decreases. With increasing gas flow rate and bath height the effective diffusion coefficient enlarges. Increasing bath size leads to large mean size of energy containing eddies, which reaches 17% of the bath diameter at high gas flow rates.     

Measurement and modeling of turbulence in the gas/liquid two-phase zone during gas injection

Averaged and turbulent fluctuating liquid velocities in the gas/liquid plume zone of a gas-stirred water model ladle were measured with a combined laser Doppler anemometer (LDA) and elec-trical probe technique. The measured turbulence fields, void fraction distribution, and gas and liquid velocities in the plume zone were used for evaluation of various turbulence models. It was found that, among all of the turbulence models tested, only a modified k-ε model, with extra source terms to take into account the generation and dissipation resulting from the inter-action of the bubbles with the liquid, yielded good agreement with both the mean liquid flow field and the turbulent kinetic energy distribution. However, the values of the coefficients orig-inally proposed by their authors were found inapplicable to the bubbly plume situation; more appropriate values of the coefficients were determined based on comparison with experimental measurement.     

Numerical Solution of Fully Developed Flow with Vegetative Resistance

This paper presents a numerical solution of the Reynolds averaged Navier-Stokes and the near-wall k- (turbulent kinetic energy) and ω- (specific dissipation or dissipation per unit kinetic energy) transport equations, which are modified to include vegetative drag terms. For similar treatment of the model coefficients, the use of the near-wall k-ω model produces similar results to previous models that employed the standard k-ε models with wall functions. The study shows that reasonable predictions of streamwise velocity and Reynolds stress profiles can be achieved by adopting universal values for all model coefficients, but the calculated energy gradient can have significant error. The study also indicates that predictions of streamwise turbulence intensity are significantly improved by adopting the universal values of Cfk = 0.05 and Cfω = 0.16 rather than the theoretically based values, Cfk = 1.0 and Cfω = β/αβ?Cfk.     

Measurement of physical characteristics of bubbles in gas-liquid plumes: Part II. Local properties of turbulent air-water plumes in vertically injected jets

The structural development of air-water bubble plumes during upward injection into a ladle-shaped vessel has been measured under different conditions of air flow rate, orifice diameter, and bath depth. The measured radial profiles of gas fraction at different axial positions in the plume were found to exhibit good similarity, and the distribution of the phases in the plume was correlated to the modified Froude number. Different regions of flow behavior in the plume were identified by changes in bubble frequency, bubble velocity, and bubble pierced length which occur as bubbles rise in the plume. Measurement of bubble velocity indicates that close to the nozzle the motion of the gas phase is strongly affected by the injection velocity; at injection velocities below 41 m/s, the velocity of the bubbles along the centerline exhibits an increase with height, while above, the tendency reverses. High-speed film observations suggest that this effect is related to the nature of gas discharge,i.e., whether the gas discharge produces single bubbles or short jets. In this region of developing flow, measurement of bubble frequency and pierced length indicates that break-up of the discharging bubbles occurs until a nearly constant bubble-size distribution is established in a region of fully developed flow. In this largest zone of the plume the bubbles influence the flow only through buoyancy, and the spectra of bubble pierced length and diameter can be fitted to a log-normal distribution. Close to the bath surface, a third zone of bubble motion behavior is characterized by a faster decrease in bubble velocity as liquid flows radially outward from the plume.     

Gas Transfer During Bubbler Destratification of Reservoirs

In this paper, dimensional analysis has been carried out to derive general equations that predict: the total gas transferred to the ambient reservoir water from an air bubbler, total volume entrained, and total energy consumed for a known or equivalent linear stratification. The equations are tested by comparison with a one-dimensional bubbler model developed by the authors. It is shown that the oxygen transfer to the water column can be significant if small bubbles are used. The mechanical destratification efficiency ηmech (%), destratification time per unit surface area Γ?(s/m2), oxygen dissolution efficiency Ω (%), and oxygen transferred per unit input energy are examined as functions of bubble size. It is concluded that an average bubble radius of 1?mm should be considered for design purposes. However, if oxygen transfer from the bubbler is not considered important, then a bubble size of up to 4?mm is acceptable for destratification purposes.     

Measurements on the local properties of the vertical heterogeneous buoyant plume

An electroresistivity sensor probe is developed and used to measure gas fraction and bubble frequency in turbulent air/water plume formed during upward injection of gas. The measured gas fraction and bubble frequency profiles at different axial positions in the plume are found to exhibit good similarity. It is found that the axial gas fraction decreases and plume radius increases with increase in axial distance. From the values of axial gas fraction and plume half radius, turbulent viscosity of liquid in bubble plume is determined and is found to be several times higher than the molecular viscosity.     

Plume characteristics and liquid circulation in gas injection through a porous plug

Various forms of plumes have been identified following the injection of air at different rates through a porous plug into water contained in a ladle-shaped vessel. Discrete bubbles form at the plug and rise uniformly through the column of liquid at gas flow rates up to 14 cm³/s cm² of plug surface; at higher flow rates, groups of bubbles increasingly coalesce into larger gas pockets, and beyond about 40 cm³/s cm², the gas globes are large enough to cover the entire plug surface before detachment and gradual disintegration as they rise through the body of liquid. The gas fraction, as well as bubble frequency, bubble velocity, and bubble size, have been measured in the various dispersion regimes by means of an electroresistivity probe. The radial distributions of gas fraction and bubble frequency are approximately bell-shaped about the axis of flow, and the reduced values are close to Gaussian functions of the reduced radial distance from the axis. The gas fraction along the axis has been correlated to the reduced height of the plume; it increases with decreasing distance above the plug and with increasing gas flow rate. The axial bubble frequency shows a decrease in the vicinity of the plug with the onset of bubble coalescence, but the values of the frequencies at all gas injection rates converge to about 12 s⁻¹ toward the surface of the bath. The mean bubble velocity increases with increasing flow rate but drops once coalescence is fully established. Conversely, there is a sudden increase in the mean bubble diameter with the onset of coalescence. The axial and radial components of the velocity of the liquid surrounding the plume have been measured by means of a Laser-Doppler Velocimeter (LDV), and the results show that the circulation patterns are identical, irrespective of the dispersion regime. The axial flow which is upward in the vicinity of the plume decreases in magnitude with increasing radial distance, ultimately reversing to an in-creasing downward flow beyond a certain distance from the plug axis. Similarly, the radial flow which is outward from the plume near the liquid surface decreases steadily with depth and eventually reverses to an inward flow at a depth independent of the gas injection rate. The profiles of the axial velocities are almost sigmoidal, except in the coalescence regime, where the effect of turbulence is profound at the upper liquid layers. The radial liquid velocities are generally small relative to the axial components, only about one-fifth as large, considering the maximum average values.     

Fluid flow and mass transfer in an inductively stirred four-ton melt of molten steel: A comparison of measurements and predictions

Experimental measurements are reported on melt velocities and on the rate at which immersed carbon rods dissolve in a 4-ton induction furnace, holding a low carbon steel melt. These measurements are compared with theoretical predictions, based on the numerical solution of Maxwell’s equations and the turbulent Navier-Stokes equations. In general, good agreement has been obtained, both regarding the absolute values of the velocities and the mass transfer coefficients and the trends predicted by the theoretical analysis. In addition to providing further proof regarding the applicability of the mathematical modeling technique, the principal contribution of the work is that it provides an improved insight into the behavior of inductively stirred melts. In particular it was found that for an inductively stirred melt both the velocities and the rate of turbulence energy dissipation are relatively uniform spatially, in contrast to bubble stirred systems, where most of the agitation is confined to the jet plume and to the near surface region. It was found, furthermore, that the mass transfer coefficient characterizing the rate of dissolution of immersed carbon rods depends both on the absolute values of the melt velocity and on the local values of the turbulence intensity; thus significant mass transfer will occur in the region of the eye of the circulation, where the absolute value of the mean velocity is small. On leave at Massachusetts Institute of Technology     

Volume of Fluid Model for Turbulence Numerical Simulation of Stepped Spillway Overflow

The stepped spillway has increasingly become an effective energy dissipator. When the hydraulic performance of the overflow is clearly known, the energy dissipation could be increased. However, the study of stepped spillway overflow has been based only on model tests until now. In this paper, the k–? turbulence model is used to simulate the complex turbulence overflow. The unstructured grid is used to fit the irregular boundaries and the volume of fluid method is introduced to solve the complex free-surface problem. The free surface, velocities, and pressures on the stepped spillway are obtained by the turbulence numerical simulation. Furthermore, the simulation results compare well with measured data. The study indicates that the turbulence numerical simulation is an efficient and useful method for the complex stepped spillway overflow.     

Mean Flow and Turbulence Structure in Vertical Slot Fishways

This paper presents the results of an experimental study on the mean and turbulence structures of flow in a vertical slot fishway with slopes of 5.06 and 10.52%. Two flow patterns existed in the fishway and for each one, two flow regions were formed in the pools: a jet flow region and a recirculating flow region. The mean kinetic energy decays rapidly in the jet region and the dissipation rate in most of the areas in the pool is less than 200?W/m3. For the jet flow, the nondimensional mean velocity profile across the jet agrees very well with that of a plane turbulent jet in the central part of the jet with some scatter near its boundaries. Its maximum velocity decays faster compared to a plane turbulent jet in a large stagnant ambient. The jet presents different turbulence structure for the two flow patterns and for each pattern, the turbulence characteristics appear different between the left and right halves of the jet. However, the turbulence characteristics show some similarity for each case. The normalized energy dissipation rate shows some similarity and has a maximum value on the center of the jet. The results are believed to provide useful insight on the turbulence characteristics of flow in vertical slot fishways and can be used to verify numerical models and also for guidance in the design of fishways in the future.     

Modeling Energy Dissipation in Slag-Covered Steel Baths in Steelmaking Ladles

Physical and mathematical modeling of energy dissipation phenomena in a gas-stirred ladle with, and without, an overlying second-phase liquid have been carried out at relatively low gas flow rate and specific energy input rate. Data from the literature are applied to infer the extent of energy dissipation caused by various mechanisms. An analysis reveals that bubble slippage and friction at the vessel walls dominate energy dissipation in such systems, each contributing roughly one third of the input energy. The remainder is dissipated because of turbulence in the bulk of the liquid, the formation of a spout, and interactions between the upper phase and the bulk liquid when an overlying liquid is present. Remarkably, the overlying liquid despite its small volume (~3 pct to 13 pct of the bulk), is found to dissipate about 10 pct of input energy. To understand the way the total input energy is dissipated via the overlying liquid, flow and mixing studies were carried out with different types of upper phase liquids. Tracer dispersion studies conducted with Petroleum ether as the overlying liquid show reasonably intense flow within the upper phase with no noticeable entrainment around the spout. In contrast, a thick layer of highly viscous upper phase liquid such as mustard oil shows extensive deformation of the upper phase around the spout, but no discernable motion within. However, remarkably, the thickness of the upper phase rather than its physical properties was found to influence bath hydrodynamics and mixing most significantly. A mechanism based on the rerouting of the surfacing plume and the attendant reversal of flow in the vicinity of the spout is advocated to explain energy dissipation caused by the overlying liquid. This finding is rationalized with our experimental results on composition adjustment with sealed argon bubbling (CAS) alloy addition procedures reported more than two decades ago, wherein flow reversal caused by the baffle in the immediate vicinity of the surfacing plume was shown to cause significant energy dissipation, leading to much sluggish flow and slower mixing in the bulk of the liquid, in comparison with an equivalent unbaffled situation.     

Modeling of a Rough-Wall Oscillatory Boundary Layer Using Two-Equation Turbulence Models

The standard k?ω turbulence model and two versions of blended k?ω/k?ε models have been used to study the characteristics of a one-dimensional oscillatory boundary layer on a rough surface. The wall boundary condition for the specific dissipation rate of turbulent kinetic energy at the wall is specified in terms of a function based on wall roughness. A detailed comparison has been made for mean velocity, turbulent kinetic energy, Reynolds stress, and wall shear stress with the available experimental data. The three models predict the above properties reasonably well. In particular, the prediction of turbulent kinetic energy for the rough case by the blended models is much better than that for smooth oscillatory boundary layers as reported in previous studies. As a result of the present study, the use of one of the blended models in calculating the sediment transport in coastal environments may be recommended.     

Marine Wastewater Discharges from Multiport Diffusers. I: Unstratified Stationary Water

Laboratory experiments on the near-field mixing of buoyant plumes discharged from multiport diffusers into unstratified stationary water are reported. Dilution was measured by a newly developed three-dimensional laser-induced fluorescence system and a microconductivity probe. Significant additional mixing (and dilution) occurs beyond the point where the plume impacts the water surface. This mixing ceases when the turbulence generated by the plumes collapses in the surface spreading layer. The port spacing, s, was varied through a range encompassing line to point source conditions. In all cases, the concentration distribution in the surface layer eventually becomes laterally uniform. Measurements of the near-field dilution, length, and layer thickness, and semiempirical equations to predict them are presented. The discharge behaves as a line plume when s/H ? 0.3, and as a point plume when s/H ≥ 1.0. The additional near-field mixing for a point plume is much greater than for a line plume. Basing diffuser design on near-field dilution rather than impact-point dilution allows the use of far fewer ports, or risers, with considerable potential cost savings, particularly for tunneled outfalls.     

Evaluation of Mixing Energy in Laboratory Flasks Used for Dispersant Effectiveness Testing

The evaluation of dispersant effectiveness used for oil spills is commonly done using tests conducted in laboratory flasks. The success of a test relies on replication of the conditions at sea. We used a hot wire anemometer to characterize the turbulence characteristics in the swirling flask (SF) and the baffled flask (BF), the latter is being considered by the Environmental Protection Agency to replace the prior. We used the measurements to compute the velocity gradient, G and the energy dissipation rate per unit mass, ε. The study shows that the mixing in the BF is more uniformly distributed than that in the SF. Flask average energy dissipation rates in the SF were about 2 orders of magnitude smaller than those in the BF. The sizes of the microscales in the BF were found to be much smaller than that in the SF. Also, in the BF, the sizes of the microscales approached the size of oil droplets observed at sea (50–400?μm), which means that the turbulence in the BF closely resembles the turbulence occurring at sea during breaking waves. Hence, the BF is preferable for dispersant testing in the laboratory.     

Particle Image Velocimetry Measurements of the Mean Flow Characteristics in a Bubble Plume

A direct measurement method for the velocity field in multiphase flows using the particle image velocimetry (PIV) and particle tracking velocimetry (PTV) methods is developed to study the flow characteristics of an unbounded bubble plume in quiescent, unstratified ambient conditions. A single camera is used to obtain images containing both bubbles and fluid tracer particles. Using gray-scale thresholding, phase-separated images of the bubbles are produced, and bubble velocities are obtained from these images using the standard PTV method. Regular PIV is applied to the mixed fluid images, and bubble vectors are removed using a velocity threshold and vector median filter that is calibrated to the PTV result. From the separate velocity fields, the time-averaged flow characteristics of a bubble plume are studied. Gaussian velocity profiles match the entrained fluid velocity, and top-hat velocity profiles match the bubble velocity. Time-averaged values are also presented of velocity, plume width, entrained fluid volume flux, and void fraction as a function of height. From these data, the entrainment coefficient for the entrained ambient fluid is calculated and lies between 0.08 near the plume source and 0.05 in the upper reaches. The results for the entrainment coefficient, together with those from the literature, are correlated to a nondimensional velocity, given by the ratio of the bubble slip velocity us to a characteristic velocity in the plume (B/z)1/3, where B = kinematic buoyancy flux and z is the height above the source.     

Numerical and Experimental Study on Fluid Dynamic Features of Combined Gas and Electromagnetic Stirring in Ladle Furnace

Basic fluid dynamic features of combined electromagnetic stirring, EMS, and gas stirring (EMGAS) have been studied in the present work. A transient and turbulent multiphase numerical flow model was built. Simulations of a real size ladle furnace were conducted for 7 cases, operating with and without combined stirring and varying the argon gas inlet plug position. The results of these simulations are compared considering melt velocity, melt turbulence, melt/slag‐interface turbulence and dispersion of gas bubbles. An experimental water model was also built to simulate the effects of combined stirring. The water model was numerically simulated and visual comparison of the gas plume shape and flow pattern in the numerical and in the experimental model was also done for 3 flow situations. The results show that EMGAS has a strong flexibility regarding the flow velocity, gas plume, stirring energy, mixing time, slag layer, etc.     

Experimental studies on the flow velocity of molten metals in a ladle model at centric gas blowing

Experimental measurements of the flow velocity were carried out with liquid Wood's metal in a ladle-shaped vessel with an inner diameter of 40 cm at centric gas blowing. By means of permanent magnet probes the liquid flow field was measured under various blowing conditions. The results show that a circulating flow field is established in the vessel. In the bubble plume zone an upwardly directed liquid flow is formed. The radial distribution of the flow velocity in this zone follows a Gaussian function. The axial flow velocity increases with growing gas flow rate and is nearly constant in vertical direction. The width of the upward flow becomes larger with increasing distance from the nozzle and its dependence from the gas flow rate is not considerable. At centric gas blowing the liquid in the upper part of the bath streams quickly, whereas in the lower part so-called “dead zones” with very low flow velocity are present. Besides the time-averaged value of the flow velocity, the turbulent behaviours of the liquid flow such as fluctuation velocity, the turbulent kinetic energy and its dissipation rate were investigated on the basis of measured data. It was found that the liquid flow is turbulent particularly in the region of bubble plume and of bath surface. The radial profiles of these parameters can also be described by a Gaussian function. Only a small part of the gas stirring energy is changed into the kinetic energy of the directed liquid flow. Most of the stirring energy is already dissipated in the bubble plume zone.     

Effect of interphase lift force on fluid flow in air stirred cylindrical vessel

Abstract

In the present paper, based on the two-phase model (Eulerian model), the two-dimensional fluid flow in air stirred water systems is simulated, and the effect of interphase lift force on the fluid flow is specially discussed. In the Eulerian two-phase model, the gas and liquid phases are considered to be two different continuous fluids interacting with each other through the finite interphase areas. The exchange between the phases is represented by source terms in conservation equations. Turbulence is assumed to be a property of the liquid phase. The k–? model is used to describe the behaviour of the liquid phase. The dispersion of phases due to turbulence is represented by introducing a diffusion term into the mass conservation equation. The contribution of bubble movement to the turbulent energy and its dissipation rate are taken into account by adding extra volumetric source terms to the equations of turbulent energy and its dissipation rate. Comparison between the mathematical simulation and experimental data indicates that the interphase lift force has a strong effect on flow behaviour, and considering both drag force and lift force as interphase forces is important to accurately simulate the gas–water two-phase fluid flow in air stirred systems. The interphase lift force makes bubbles move away from the centreline; the gas concentration decreases near the centreline, and increases near the wall. The lift force is smaller than the drag force at the same place, especially far away from the centreline.     

Application of Several Depth-Averaged Turbulence Models to Simulate Flow in Vertical Slot Fishways

Vertical slot fishways are hydraulic structures which allow the upstream migration of fish through obstructions in rivers. The velocity, water depth, and turbulence fields are of great importance in order to allow the fish swimming through the fishway, and therefore must be considered for design purposes. The aim of this paper is to assess the possibility of using a two-dimensional shallow water model coupled with a suitable turbulence model to compute the flow pattern and turbulence field in vertical slot fishways. Three depth-averaged turbulence models of different complexity are used in the numerical simulations: a mixing length model, a k?ε model, and an algebraic stress model. The numerical results for the velocity, water depth, turbulent kinetic energy, and Reynolds stresses are compared with comprehensive experimental data for three different discharges covering the usual working conditions of vertical slot fishways. The agreement between experimental and numerical data is very satisfactory. The results show the importance of the turbulence model in the numerical simulations, and can be considered as a useful complementary tool for practical design purposes.