Numerical evaluation of turbulence models for dense to dilute gas–solid flows in vertical conveyor

A two-fluid model (TFM) of multiphase flows based on the kinetic theory and small frictional limit boundary condition of granular flow was used to study the behavior of dense to dilute gas–solid flows in vertical pneumatic conveyor. An axisymmetric 2-dimensional, vertical pipe with 5.6 m length and 0.01 m internal diameter was chosen as the computation domain, same to that used for experimentation in the literature. The chosen particles are spherical, of diameter 1.91 mm and density 2500 kg/m³. Turbulence interaction between the gas and particle phases was investigated by Simonin's and Ahmadi's models and their numerical results were validated for dilute to dense conveying of particles. Flow regimes transition and pressure drop were predicted. Voidage and velocity profiles of each phase were calculated in radial direction at different lengths of the conveying pipe. It was found that the voidage has a minimum, and gas and solid velocities have maximum values along the center line of the conveying pipe and pressure drop has a minimum value in transition from dense slugging to dilute stable flow regime. Slug length and pressure fluctuation reduction were predicted with increasing gas velocity, too. It is shown that solid phase turbulence plays a significant role in numerical prediction of hydrodynamics of conveyor and the capability of particles turbulence models depends on tuning parameters of slip-wall boundary condition.     

Effect of bubble size on void fraction fluctuations in dispersed bubble flows

It is known that bubble size affects seriously the average void fraction in bubbly flows where buoyant velocities vary considerably with bubble size. On the contrary, there is no systematic literature report about bubble size effects on the intensity and frequency of void fraction fluctuations around the average void fraction. This work aims to provide such information. An electrical impedance technique is employed along with non-intrusive ring electrodes to register void fraction fluctuations down to 10⁻⁵. Bubble size fluctuations are estimated from high resolution optical images. Experiments are conducted in co-current upward dispersed bubble flow inside a 21 mm tube with average bubble size between ∼50 and ∼700 μm. Water and blood simulant are used as test liquids with velocity from ∼3 to ∼30 cm s⁻¹. The above resemble conditions of Decompression Sickness (DCS) in the bloodstream of human vena cava. It is found that the intensity and frequency of void fraction fluctuations vary appreciably with bubble size at constant gas and liquid flow rates. Moreover, these variations are not random but scale with bubble size. As a first step to quantify this effect, an empirical expression is derived that relates average bubble size to the ratio standard deviation/average value of void fraction.     

An investigation into flow mode transition and pressure fluctuations for fluidized dense-phase pneumatic conveying of fine powders

This paper presents the results of an ongoing investigation into the fluctuations of pressure signals due to solids–gas flows for dense-phase pneumatic conveying of fine powders. Pressure signals were obtained from pressure transducers installed along different locations of a pipeline for the fluidized dense-phase pneumatic conveying of fly ash (median particle diameter 30 μm; particle density 2300 kg/m³; loose-poured bulk density 700 kg/m³) and white powder (median particle diameter 55 μm; particle density 1600 kg/m³; loose-poured bulk density 620 kg/m³) from dilute to fluidized dense-phase. Standard deviation and Shannon entropy were employed to investigate the pressure signal fluctuations. It was found that there is an increase in the values of Shannon entropy and standard deviation for both of the products along the flow direction through the straight pipe sections. However, both the Shannon entropy and standard deviation values tend to decrease after the flow through bend(s). This result could be attributed to the deceleration of particles while flowing through the bends, resulting in dampened particle fluctuation and turbulence. Lower values of Shannon entropy in the early parts of the pipeline could be due to the non-suspension nature of flow (dense-phase), i.e., there is a higher probability that the particles are concentrated toward the bottom of pipe, compared with dilute-phase or suspension flow (high velocity), where the particles could be expected to be distributed homogenously throughout the pipe bore (as the flow is in suspension). Changes in straight-pipe pneumatic conveying characteristics along the flow direction also indicate a change in the flow regime along the flow.     

Numerical investigation of particle deposition inside aero-shielded solar cyclone reactor: A promising solution for reactor clogging

Solar cracking of methane is considered to be an attractive option due to its CO₂ free hydrogen production process. Carbon particle deposition on the reactor window, walls and exit is a major obstacle to achieve continuous operation of methane cracking solar reactors. As a solution to this problem a novel “aero-shielded solar cyclone reactor” was created. In this present study the prediction of particle deposition at various locations for the aero-shielded reactor is numerically investigated by a Lagrangian particle dispersion model. A detailed three dimensional computational fluid dynamic (CFD) analysis for carbon deposition at the reactor window, walls and exit is presented using a Discrete Phase Model (DPM). The flow field is based on a RNG k–ε model and species transport with methane as the main flow and argon/ hydrogen as window and wall screening fluid. Flow behavior and particle deposition have been observed with the variation of main flow rates from 10–20 L/min and with carbon particle mass flow rate of 7 × 10⁻⁶ and 1.75 × 10⁻⁵ kg/s. In this study the window and wall screening flow rates have been considered to be 1 L/min and 10 L/min by employing either argon or hydrogen. Also, to study the effect of particle size simulations have also been carried out (i) with a variation of particle diameter with a size distribution of 0.5–234 μm and (ii) by taking 40 μm mono sized particles which is the mean value for the considered size distribution. Results show that by appropriately selecting the above parameters, the concept of the aero-shielded reactor can be an attractive option to resolve the problem of carbon deposition at the window, walls and exit of the reactor.     

Experimental investigation of a developing two-phase bubbly flow in horizontal pipe

Experimental results for various water and air superficial velocities in developing adiabatic horizontal two-phase pipe flow are presented. Flow pattern maps derived from videos exhibit a new boundary line in intermittent regime. This transition from water dominant to water–gas coordinated regimes corresponds to a new transition criterion C_T = 2, derived from a generalized representation with the dimensionless coordinates of Taitel and Dukler.Velocity, turbulent kinetic energy and dissipation rate, void fraction and bubble size radial profiles measured at 40 pipe diameters for J_L = 4.42 m/s by hot film velocimetry and optical probes confirm this transition: the gas influence is not continuous but strongly increases beyond J_G = 0.06 m/s. The maximum dissipation rate, derived from spectra, is increased in two-phase flow by a factor 5 with respect to the single phase case.The axial evolution of the bubble intercept length histograms also reveal the flow organization in horizontal layers, driven by buoyancy effects. Bubble coalescence is attested by a maximum bubble intercept evolving from 2.5 to 4.5 mm along the pipe. Turbulence generated by the bubbles is also manifest by the 4-fold increase of the maximum turbulent dissipation rate along the pipe.     

Reynolds number dependence of gas-phase turbulence in gas–particle flows

A downward flow of glass bead particles in a vertical pipe is investigated using a two-component LDV/PDPA for a range of Re (6400 < Re < 24,000) and a constant particle loading (m = 0.7). Two particle sizes of 70 and 200 μm are considered in the present work. For the 70 μm particles, the presence of the particles dampens the gas-phase turbulence intensity at the lowest value of Re investigated (8300) compared with the single-phase flow at the same Re. As Re increases, the gas turbulence increases, and for Re > 13,800 the gas turbulence is enhanced compared with the single-phase flow at the same Re. For the 200 μm particles, the intensity also increases with Re and is enhanced for all values of Re investigated, except at the lowest value of Re investigated (6400). At this value, the gas turbulence is equal to that of single-phase flow at the same Re. The observed trend in the gas-phase turbulence modulation with Re is proposed to be due to the change in the segregation patterns and in the average volume fractions of the particles with increasing Re. More importantly, the present experimental results suggest that, consideration of either the gas and particle characteristic length scales or the particle Reynolds number solely is insufficient to predict gas-phase turbulence modulation in gas–particle flows.     

Experimental investigation of turbulence modulation in particle-laden coaxial jets by Phase Doppler Anemometry

The effect of solid particles on the flow characteristics of axisymmetric turbulent coaxial jets for two flow conditions was studied. Simultaneous measurements of size and velocity distributions of continuous and dispersed phases in a two-phase flow are presented using a Phase Doppler Anemometry (PDA) technique. Spherical glass particles with a particle diameter range from 102 to 212 μm were used in this two-phase flow, the experimental results indicate a significant influence of the solid particles and the Re on the flow characteristics. The data show that the gas phase has lower mean velocity in the near-injector region and a higher mean velocity at the developed region. Near the injector at low Reynolds number (Re = 2839) the presence of the particles dampens the gas-phase turbulence, while at higher Reynolds number (Re = 11 893) the gas-phase turbulence and the velocity fluctuation of particle-laden jets are increased. The particle velocity at higher Reynolds number (Re = 11 893) and is lower at lower Reynolds number (Re = 2839). The slip velocity between particles and gas phase existed over the flow domain was examined. More importantly, the present experiment results suggest that, consideration of the gas characteristic length scales is insufficient to predict gas-phase turbulence modulation in gas-particle flows.     

Large Eddy Simulations of turbulent particle-laden channel flow

This paper scrutinises the Large Eddy Simulation (LES) approach to simulate the behaviour of inter-acting particles in a turbulent channel flow. A series of simulations that are fully (four-way), two-way and one-way coupled are performed in order to investigate the importance of the individual physical phenomena occurring in particle-laden flows. Moreover, the soft sphere and hard sphere models, which describe the interaction between colliding particles, are compared with each other and the drawbacks and advantages of each algorithm are discussed. Different models to describe the sub-grid scale stresses with LES are compared. Finally, simulations accounting for the rough walls of the channel are compared to simulations with smooth walls. The results of the simulations are discussed with the aid of the experimental data of Kussin J. and Sommerfeld M., 2002, Experimental studies on particle behaviour and turbulence modification in horizontal channel flow with different wall roughness, Exp. in Fluids, 33, pp. 143–159 of Reynolds number 42,000 based on the full channel height. The simulations are carried out in a three-dimensional domain of 0.175 m × 0.035 m  × 0.035 m where the direction of gravity is perpendicular to the flow. The simulation results demonstrate that rough walls and inter-particle collisions have an important effect in redistributing the particles across the channel, even for very dilute flows. A new roughness model is proposed which takes into account the fact that a collision in the soft sphere model is fully resolved and it is shown that the new model is in very good agreement with the available experimental data.     

Influence of sudden contractions on in situ volume fractions for oil–water flows in horizontal pipes

Oil–water two-phase flow experiments were conducted in horizontal ducts made of Plexiglas® to determine the in situ oil fraction (holdup) by means of the closing valves technique, using mineral oil (viscosity: 0.838 Pa s at 20 °C; density: 890 kg m⁻³) and tap water. The ducts present sudden contractions from 50 mm to 40 mm i.d. and from 50 mm to 30 mm i.d., with contraction ratios of 0.64 and 0.36, respectively. About 200–320 tests were performed by varying the flow rates of the phases. Flow patterns were investigated for both the up- and downstream pipe in order to assess whether relevant variations of the flow patterns across the sudden contraction take place. Data were then compared with predictions of a specific correlation for oil–water flow and some correlations for gas–water flow. A drift-flux model was also applied to determine the distribution parameter.     

Technique for quantitative mapping of three-dimensional liquid–gas phase boundaries in microchannel flows

A diagnostic technique capable of characterizing interfaces between transparent, immiscible fluids is developed and demonstrated by investigating the morphology of liquid–gas interfaces in an adiabatic two-phase flow through a microchannel of 500 μm × 500 μm square cross section. Water seeded with 0.5 μm-diameter fluorescent polystyrene particles is pumped through the channel, and the desired adiabatic two-phase flow regime is achieved through controlled air injection. The diagnostic technique relies on obtaining particle position data through epifluorescent imaging of the flow at excitation and emission wavelengths of 532 nm and 620 nm, respectively. The particle position data are then used to resolve interface locations to within ±1 μm in the focal plane. By mapping the interface within individual focal planes at various depths within the channel, it is possible to determine the complete liquid–gas interface geometry across the channel cross section in a dynamic flow environment. Utilizing this approach, the liquid–gas phase boundaries of annular flows within a microchannel have been successfully characterized.     

Experimental investigation into transient pressure pulses during pneumatic conveying of fine powders using Shannon entropy

This paper presents the results of an ongoing investigation into transient pressure pulses using Shannon entropy. Pressure fluctuations (produced by gas–solid two-phase flow during fluidized dense-phase conveying) are recorded by pressure transducers installed at strategic locations along a pipeline. This work validates previous work on identifying the flow mode from pressure signals (Mittal, Mallick, & Wypych, 2014). Two different powders, namely fly ash (median particle diameter 45 μm, particle density 1950 kg/m³, loosely poured bulk density 950 kg/m³) and cement (median particle diameter 15 μm, particle density 3060 kg/m³, loosely poured bulk density 1070 kg/m³), are conveyed through different pipelines (51 mm I.D. × 70 m length and 63 mm I.D. × 24 m length). The transient nature of pressure fluctuations (instead of steady-state behavior) is considered in investigating flow characteristics. Shannon entropy is found to increase along straight pipe sections for both solids and both pipelines. However, Shannon entropy decreases after a bend. A comparison of Shannon entropy among different ranges of superficial air velocity reveals that high Shannon entropy corresponds to very low velocities (i.e. 3–5 m/s) and very high velocities (i.e. 11–14 m/s) while low Shannon entropy corresponds to mid-range velocities (i.e. 6–8 m/s).     

Large-eddy simulations of chevron jet flows with noise predictions

Hybrid large-eddy type simulations for chevron nozzle jet flows are performed at Mach 0.9 and Re = 1.03 × 10⁶. Without using any subgrid scale model (SGS), the numerical approach applied in the present study is essentially implicit large-eddy simulation (ILES). However, a Reynolds-averaged Navier–Stokes (RANS) solution is patched into the near wall region. This makes the overall solution strategy hybrid RANS–ILES. The disparate turbulence length scales, implied by these different modeling approaches, are matched using a Hamilton–Jacobi equation. The complex geometry features of the chevron nozzles are fully meshed. With numerical fidelity in mind, high quality, hexahedral multi-block meshes of 12.5 × 10⁶ cells are used. Despite the modest meshes, the novel RANS–ILES approach shows encouraging performance. Computed mean and second-order fluctuating quantities of the turbulent near field compare favorably with measurements. The radiated far-field sound is predicted using the Ffowcs Williams and Hawkings (FW–H) surface integral method. Encouraging agreement of the predicted far-field sound directivity and spectra with measurements is obtained.     

LES of turbulent flow in a concentric annulus with rotating outer wall

Fully-developed turbulent flow in a concentric annulus, r₁/r₂ = 0.5, Re_h = 12,500, with the outer wall rotating at a range of rotation rates N = U_θ,wall/U_b from 0.5 up to 4 is studied by large-eddy simulations. The focus is on the effects of moderate to very high rotation rates on the mean flow, turbulence statistics and eddy structure. For N up to ∼2, an increase in the rotation rate dampens progressively the turbulence near the rotating outer wall, while affecting only mildly the inner-wall region. At higher rotation rates this trend is reversed: for N = 2.8 close to the inner wall turbulence is dramatically reduced while the outer wall region remains turbulent with discernible helical vortices as the dominant turbulent structure. The turbulence parameters and eddy structures differ significantly for N = 2 and 2.8. This switch is attributed to the centrifuged turbulence (generated near the inner wall) prevailing over the axial inertial force as well as over the counteracting laminarizing effects of the rotating outer wall. At still higher rotation, N = 4, the flow gets laminarized but with distinct spiralling vortices akin to the Taylor–Couette rolls found between the two counter-rotating cylinders without axial flow, which is the limiting case when N approaches to infinity. The ratio of the centrifugal to axial inertial forces, Ta/Re² ∝ N² (where Ta is the Taylor number) is considered as a possible criterion for defining the conditions for the above regime change.     

Numerical and experimental study of an axially induced swirling pipe flow

In-line flow segregators based on axial induction of swirling flow have important applications in chemical, process and petroleum production industries. In the later, the segregation of gas bubbles and/or water droplets dispersed into viscous oil by swirling pipe flow may be beneficial by either providing a pre-separation mechanism (bubble and/or drop coalescer) or, in the case of water-in-oil dispersions, by causing a water-lubricated flow pattern to establish in the pipe (friction reduction). Works addressing these applications are rare in the literature. In this paper, the features and capabilities of swirling pipe flow axially induced by a vane-type swirl generator were investigated both numerically and experimentally. The numerical analysis has been carried out using a commercial CFD package for axial Reynolds numbers less than 2000. Pressure drop, tangential and axial velocity components as well as swirl intensity along a 5 cm i.d. size and 3 m long pipe were computed. Single phase flow experiments have been performed using a water–glycerin solution of 54 mPa s viscosity and 1210 kg/m³ density as working fluid. The numerical predictions of the pressure drop were compared with the experimental data and agreement could be observed within the range of experimental conditions. The experiments confirmed that swirl flow leads to much higher friction factors compared with theoretical values for non-swirl (i.e. purely axial) flow. Furthermore, the addition of a conical trailing edge reduces vortex breakdown. Visualization of the two-phase swirling flow pattern was achieved by adding different amounts of air to the water–glycerin solution upstream the swirl generator.     

Lagrangian velocity and acceleration statistics of fluid and inertial particles measured in pipe flow with 3D particle tracking velocimetry

Three-dimensional particle tracking velocimetry (3D-PTV) has been applied to particle-laden pipe flow at Reynolds number 10,300, based on the bulk velocity and the pipe diameter. The volume fraction of the inertial particles was equal to 1.4 × 10⁻⁵. Lagrangian velocity and acceleration statistics were determined both for tracers and for inertial particles with Stokes number equal to 2.3, based on the particle relaxation time and the viscous time scale. The decay of Lagrangian velocity and acceleration correlation functions was measured both for the fluid and for the dispersed phase at various radial positions. The decay of Lagrangian velocity correlations is faster for inertial particles than for flow tracers, whereas the decay of Lagrangian acceleration correlations is about 25% slower for inertial particles than for flow tracers. Further differences between inertial and tracer particles are found in velocity fluctuations evaluated for both positive and negative time lags. The asymmetry in time of velocity cross-correlations is more pronounced for inertial particles. Quadrant analysis revealed another difference still near the wall: ejection and sweep events are less frequent for inertial particles than for tracers.     

Experiments with a Wire-Mesh Sensor for stratified and dispersed oil-brine pipe flow

Two-phase oil–water flow was studied in a 15 m long horizontal steel pipe, with 8.28 cm internal diameter, using mineral oil (having 830 kg/m³ density and 7.5 mPa s viscosity) and brine (1073 kg/m³ density and of 0.8 mPa s viscosity). Measurements of the holdup and of the cross-sectional phase fraction distribution were obtained for stratified flow and for highly dispersed oil–water flows, applying a capacitive Wire-Mesh Sensor specially designed for that purpose. The applicability of this measurement technique, which uses a circuit for capacitive measurements that is adapted to conductive measurements, where one of the fluids is water with high salinity (mimicking sea water), was assessed. Values for the phase fraction values were derived from the raw data obtained by the Wire-Mesh Sensor using several mixture permittivity models. Two gamma-ray densitometers allowed the accurate measurement of the holdups, which was used to validate the data acquired with the capacitive Wire-Mesh Sensor. The measured time-averaged distribution of the phase fraction over the cross-sectional area was used to investigate the details of the observed two-phase flow patterns, including the interface shape and water height. The experiments were conducted in the multiphase-flow test facility of Shell Global International B.V. in the Netherlands.     

Irreversible thermodynamics of triple junctions during the intergranular void motion under the electromigration forces

A rigorous reformulation of internal entropy production and the rate of entropy flow is developed for multi-component systems consisting of heterophases, interfaces and/or surfaces. The result is a well-posed moving boundary value problem describing the dynamics of curved interfaces and surfaces associated with voids and/or cracks that are intersected by grain boundaries. Extensive computer simulations are performed for void configuration evolution during intergranular motion. In particular we simulate evolution resulting from the action of capillary and electromigration forces in thin film metallic interconnects having a “bamboo” structure, characterized by grain boundaries aligned perpendicular to the free surface of the metallic film interconnects. Analysis of experimental data utilizing previously derived mean time to failure formulas gives consistent values for interface diffusion coefficients and enthalpies of voids. 3.0 × 10⁻⁶ exp(−0.62 eV/kT) m² s⁻¹ is the value obtained for voids that form in the interior of the aluminum interconnects without surface contamination. 6.5 × 10⁻⁶ exp(−0.84 eV/kT) m² s⁻¹ is obtained for those voids that nucleate either at triple junctions or at the grain boundary-technical surface intersections, where the chemical impurities may act as trap centers for hopping vacancies.     

Oil mist transport process in a long pipeline on turbulent flow transition region

Internal gas velocity fluctuations and their effects on the mist diffusion process were examined in a long horizontal pipe to understand oil mist transportation, particularly in the laminar-to-turbulent flow transition region. Three hot-wire anemometers and aerosol concentration monitors were used to deduce these effects as the two-phase mist flow gradually developed in the stream-wise direction. We found significant axial mist diffusion at Reynolds numbers (Re) < 1000 because of passive scalar transport by Poiseuille flow. However, this diffusion was restricted by the non-zero inertia of the mist at a Stokes number, O(10⁻⁵), relying on the Brownian motion of the mist. At Re > 2400, a sharp mist waveform was maintained by a turbulent flow with active radial mixing. New data were obtained within the range of 1000 < Re < 2400, which cannot be explained by interpolation between the above-mentioned two states. The mist concentration displays multiple temporal peaks at Re < 2000 owing to perturbations of localized turbulence as well as radial anisotropy as being conveyed more than 2000-diameters in distance. This behavior is caused by intermittent disturbances induced by the pipe wall roughness, which sharply distorts the wall-aligned laminar mist layer left by parabolic axial stretching of local laminar flow.     

An experimental study of circular sand–water wall jets

Laboratory experiments were carried out to study the effects of sand particles on circular sand–water wall jets. Mean and turbulence characteristics of sand particles in the sand–water wall jets were measured for different sand concentrations c_o ranging from 0.5% to 2.5%. Effects of sand particle size on the centerline sand velocity of the jets were evaluated for sand size ranging from 0.21 mm to 0.54 mm. Interesting results with the range of measurements are presented in this paper. It was found that the centerline sand velocity of the wall jets with larger particle size were 15% higher than the jets with smaller particle size. Concentration profiles in the vertical direction showed a peak value at x/d = 5 (where x is the longitudinal distance from the nozzle and d is the nozzle diameter) and the sand concentration decreased linearly for x/d > 5. Experimental results showed that the turbulence level enhanced from the nozzle to x/d = 10. For sand–water wall jets with a higher concentration (c_o = 1.5–2.5%), the turbulence intensity became smaller than the corresponding single-phase wall jets by 34% due to turbulent modulation. A modified logarithmic formulation was introduced to model the longitudinal turbulent intensity at the centerline and along the axis of the jet.