Abstract In this paper, we have applied a recently-developed numerical technique to study the three-dimensional dynamics of a confined air bubble rising in shear thinning and shear-thickening power-law fluids. The method is a blend of Volume of Fluid and Level Set methods and incorporates a Sharp Surface Force Method (SSF) for surface tension forces by solving a second Pressure Poisson Equation (PPE). The gas-liquid interface is captured by an equation for the liquid volume fraction and advected using the geometry reconstruction method. The interface normal and curvature are computed using level-set and height function methods. The accurate representation of the interface and interfacial forces significantly suppressed the spurious velocities commonly observed with conventional volume of fluid method and the Continuum Surface Force (CSF). The algorithm is implemented in a in-house code called CUFLOW and runs on multiple GPUs platform. We explored the effects of fluid rheology, Bond number, and wall confinement on bubble’s transient shape, rise velocity, rise path, and generated vortex structures. The power-law index is varied from 0.25 to 1.50 covering shear-thinning and shear-thickening regimes. Three Bond numbers (Bo = 2, 10 and 50) and three confinement ratios (C r = 4, 6 and 8) are considered, and their impacts on bubble’s dynamics are analyzed. For the range of parameters examined here, bubble motion in a shear-thinning fluid is seen to be unsteady with significant shape oscillations. The bubble rises with a secondary motion in the cross-sectional plane along with its primary vertical rise. However, in the Newtonian and shear-thickening fluids, the bubble’s shape is seen to reach a steady-state in a relatively short time and rise with only minor deviations from the vertical path.

Abstract The accuracy of the continuous random walk (CRW) stochastic model for prediction of dispersion and deposition of suspended particles in inhomogeneous turbulent channel flows was explored. The Reynolds-averaged Navier-Stokes (RANS) equations in conjunction with the Reynolds Stress Transport model was used to evaluate the mean flow and RMS velocity fluctuation characteristics of a fully developed turbulent channel flow at shear Reynolds number of 219. Then, spherical particles with diameters ranging from 10 nm to 30 μm and dimensionless relaxation times of 10 −4 to 50 (in wall units) were uniformly introduced into the channel and their trajectories were evaluated by using the equation of particle motion including the Stokes drag and Brownian excitation. The particle laden flow was assumed to be sufficiently dilute so that the particle-particle collisions and the effects of particles on the flow could be ignored. To incorporate the effects of turbulence velocity fluctuations on particle motions, first, the Conventional-CRW stochastic model, which was originally proposed for homogenous turbulent flows, was used. The particles were tracked for the duration of 10,000 wall units of time and the deposition of particles on the walls was evaluated. By conducting ensemble averaging, the steady-state concentration profiles and deposition velocity of the particles were calculated. Comparison of the predicted results with the direct numerical simulation (DNS) and experimental data suggests that the deposition velocity was overestimated. In addition, unrealistic accumulation of fluid-point particles in the near-wall regions, and overestimation of the turbophoresis effects on finite-size particles were also observed. The poor agreement of the concentration profiles and deposition velocities resulting from the conventional (homogenous flow) CRW model with the experimental and the DNS data pointed to the lack of accuracy of the Conventional-CRW model in generating instantaneous fluid velocity fluctuations seen by ultrafine and finite-size particles in inhomogeneous turbulent flows. Then, the normalized Langevin equation with a drift correction term that was suggested by Bocksell and Loth [1] was used as an improved CRW model for applications to inhomogeneous flows. The simulations for the same range of particle sizes were repeated and the corresponding concentration profiles and the deposition velocity were evaluated. It was shown that the improved CRW model led to a reasonable uniform concentration profile for the ultrafine particles and the predicted concentration profiles of finite-size particles quantitatively matched with the DNS data. In addition, the evaluated deposition velocities from the improved CRW model were also in a good agreement with the experimental data and empirical model predictions.

Abstract This study theoretically investigates plane progressive quasi-monochromatic waves in an initially quiescent compressible liquid containing many spherical gas bubbles, on the basis of the derivation of a nonlinear wave equation that represents waves propagating at a high phase velocity induced by taking the effect of liquid compressibility in consideration. The governing equations for bubbly flows are composed of the conservation equations of mass and momentum, the equation of bubble dynamics as radial oscillations, and so on. By using the method of multiple scales with an appropriate choice of set of scaling relations of nondimensional parameters, the nonlinear Schrödinger (NLS) equation with an attenuation term and some correction terms can be derived from the governing equations. The decrease in the group velocity in a far field is then clarified. The dependence of waveform on wavenumber is implied.

Abstract The effects of particle size on erosion magnitude and erosion profiles are investigated experimentally in a submerged slurry jet impingement facility. The slurries were diluted to avoid concentration effects on the flow field and the resulting erosion. The experiments are performed with particle sizes of 25, 75, 150, 300, and 600 μm. Experimental results demonstrate different erosion severity and pattern for the various particle sizes. It is critical to have a reliable and accurate tool to predict erosion for different particle sizes. Previously, a comprehensive CFD-based procedure to predict erosion for various particle sizes was proposed by investigators at the Erosion/Corrosion Research Center (E/CRC). A feature of this procedure is that it can account for particle size in more detail than previous methods. In this study, the computational procedure is applied to conditions of the present experimental data. Particle impact parameters are extracted to explain the effect of particle size on the resulting erosion. The predicted results are compared with data which demonstrate possible shortcomings of the available CFD based techniques for predicting solid particle erosion. The results indicate that with proper use of grid spacing near the wall, the CFD-based erosion calculation method with existing erosion models can predict the trend of the experimental data, though improvements are still needed to the models to accurately account for particle size effects.

Abstract During production of oil and gas from wells, solid particles such as removed scales or sand may accompany petroleum fluids. These particles present in this multiphase flow can impact inner walls of transportation infrastructure (straight pipelines, elbows, T-junctions, flow meters, and reducers) multiple times. These repeated impacts degrades the inner walls of piping and as a result, reduce wall thickness occur. This is known as solid particle erosion, which is a complex phenomenon involving multiple contributing factors. Prediction of erosion rates and location of maximum erosion are crucial from both operations and safety perspective. Various mechanistic and empirical solid particle erosion models are available in literature for this purpose. The majority of these models require particle impact speed and impact angle to model erosion. Furthermore, due to complex geometric shapes of process equipment, these solid particles can impact and rebound from walls in a random manner with varying speeds and angles. Hence, this rebound characteristic is an important factor in solid particle erosion modeling which cannot be done in a deterministic sense. This challenge has not been addressed in literature satisfactorily. This study uses experimental data to model particle rebound characteristics stochastically. Experimental setup consists of a nozzle and specimen, which are aligned at different angles so particles impact the specimen at various angles. Information regarding particle impact velocities before and after the impacts are obtained through Particle Tracking Velocimetry (PTV) technique. Distributions of normal and tangential components of particle velocities were determined experimentally. Furthermore, spread or dispersion in these velocity components due to randomness is quantified. Finally, based on these experimental observations, a stochastic rebound model based on normal and tangential coefficients of restitutions is developed and Computational Fluid Dynamics (CFD) studies were conducted to validate this model. The model predictions are compared with experimental data for elbows in series. It is found that the rebound model has a great influence on erosion prediction of both first and second elbows especially where subsequent particle impacts are expected.

Abstract Phenomenological equations derived for the convective heat and mass transfer to Taylor bubbles (TB) rising in vertical cylindrical pipes. Three models presented; first for the bubble thin liquid layer region, second for the rounded nose region, and third for the wake region. The solution is confined to flat-ended Taylor bubbles under laminar flow and constant heat flux conditions. The results compared reasonably well with the experimental data of other investigators.

Abstract In this study, the hybrid immersed boundary-thermal lattice Boltzmann method was developed and applied to assess the inclusion of heat transfer in flows containing non-circular particles. The direct forcing/heating immersed boundary method was used for determining the hydrodynamic forces and energy exchange. A complementary method was also implemented to treat non-circularity. The accuracy of the computational model and the employed complementary method were properly validated. Two cases for the falling ellipse were considered. A set of comprehensive simulations were performed and the effects of geometry, Grashof number, repulsive force, and heat transfer were analyzed. The findings of this study would be useful for a better understanding of settling non-circular particles in a thermal field.

Abstract The cavitating flows created in a small Venturi tube with throat cross section 4 × 15.34 mm 2 are investigated based on ultra-fast x-ray imaging. The instantaneous velocities of the liquid and vapor are measured simultaneously by tracking seeding particles and vapor structures respectively while the vapor volume fraction is derived from the different x-ray attenuation. Wavelet decomposition with appropriate thresholds is used to separate seeding particles from vapor structures, so that image cross-correlations could be applied on the two phases separately. This study presents data on mean velocity and void ratio field, statistical turbulent quantities in three different cavitation levels with the same reference velocity. A type of cavitation associated with a weak but persistent re-entrant jet is described. The comparison between the cavitation and the noncavitating flow shows that the averaged flow field is significantly altered by the presence of cavitation and the vapor formation near the throat area is observed to suppress velocity fluctuations.

Abstract The present study theoretically carries out a derivation of the Korteweg–de Vries–Burgers (KdVB) equation and the nonlinear Schrödinger (NLS) equation for weakly nonlinear propagation of plane (i.e., one-dimensional) progressive waves in water flows containing many spherical gas bubbles that oscillate due to the pressure wave approaching the bubble. Main assumptions are as follows: (i) bubbly liquids are not at rest initially; (ii) the bubble does not coalesce, break up, extinct, and appear; (iii) the viscosity of the liquid phase is taken into account only at the bubble–liquid interface, although that of the gas phase is omitted; (iv) the thermal conductivities of the gas and liquid phases are dismissed. The basic equations for bubbly flows are composed of conservation equations for mass and momentum for the gas and liquid phases in a two-fluid model, the Keller-Miksis equation (i.e., the equation for radial oscillations as the expansion and contraction), and so on. By using the method of multiple scales and the determination of size of three nondimensional ratios that are wavelength, propagation speed and incident wave frequency, we can derive two types of nonlinear wave equations describing long range propagation of plane waves. One is the KdVB equation for a low frequency long wave, and the other is the NLS equation for an envelope wave for a moderately high frequency short carrier wave.

Abstract Gas hydrates can be an efficient replacement for the conventional fossil fuels, as the large amount of methane gas is trapped in the gas hydrate reservoirs that can be used as a potential source of energy. In this study, we investigate the impact of a combination of horizontal and vertical wells on the gas production from oceanic Class-2, unconfined gas hydrate reservoirs. An In-house multicomponent, multiphase, thermal, 3-D finite volume simulator is used. Different locations of horizontal and vertical wells as warm water injectors and methane gas producers are investigated. For unconfined reservoirs, depressurization is found to be ineffective with horizontal and vertical wells. Horizontal warm water injectors are more effective for gas production. The gas production increases from 22% of original gas in place (OIGP) when vertical injector is used to 48% of OGIP when horizontal injector is used.

Abstract Condensation phenomenon has been studied actively for decades because of its extensive and significant applications in various fields of technology and engineering. The condensation phenomenon of condensable component in supersonic flows is still not understood very well as a result of the complex nucleation and droplet growth process, especially the condensation characteristic of gas mixture. In this paper, the Laval nozzle was designed based on the bi-cubic curve, state equation of real gas, arc plus straight line and viscous correction of boundary layer. The physical and mathematical models were developed to predict the condensation process in the supersonic air flows based on the nucleation and droplet growth theories, surface tension model and gas-liquid governing equations. The condensation processes of gaseous water/air binary (single condensable) gas and water/ethanol/air ternary (double condensable) gas mixture in the designed nozzle were simulated, and the reliability of the established models was verified by the experimental data. By comparing the condensation process of water/air binary gas with water/ethanol ternary gas, the influence of the second condensable component on the condensation process was analyzed. The results show that in the condensation process of gaseous water, as the pressure and temperature of water vapor decrease in the nozzle, spontaneous condensation occurs further downstream the nozzle throat. The nucleation rate grows rapidly from 0 to peak in a very short distance. With the consumption of water vapor, due to the decrease of the degree of supercooling, the nucleation environment is destroyed, and the nucleation rate quickly decreases to 0. The nucleation process is rapid in time and space, while the droplet growth process could maintain longer. The droplet number and mass fraction increase continuously till the nozzle outlet. There is a weak condensation in the nozzle due to the release of latent heat, but it is not obvious because the air acts as a heat container and absorbs the latent heat released by condensation. In the water/ethanol/air ternary system, the ethanol nucleates prior to water vapor. With the increase of supercooling, water vapor also begins to nucleate. In essence, there are two kinds of condensation nuclei (water nuclei and ethanol nuclei), and both the water and ethanol vapor can aggregate on these two kinds of condensation nuclei. Compared with the condensation process of water, the Wilson point of condensation is closer to the throat and the outlet mass fraction of liquid phase is greater in the condensation process of water/ethanol mixture, which shows that the water and ethanol can affect and promote each other. The maximum nucleation rate, droplet growth rate, droplet radius and outlet mass fraction of liquid phase of water/air binary and water/ethanol/air ternary mixture are about 9.46 × 10 26 m −3 s −1 and 2.57 × 10 27 m −3 s −1 , 1.65 × 10 −5 m/s and 1.02 × 10 −5 m/s, 1.32 × 10 −7 m and 1.63 × 10 −7 m, 0.19% and 1.34%, respectively.

Abstract As a typical fluid mechanics problem, pump blockage has always been a hot research topic. The obtaining of the distribution of coarse particles in the solid-liquid two-phase flow pump is the basis of improving its non-blocking performance. High-speed photography technique is applied to do visualizing test and research on the distribution of coarse particles in a double blade pump. The effects of particle concentration, particle density and particle diameter on the distribution of coarse particles in the solid-liquid two-phase flow pump at different phases are studied. Besides, the variation of hydraulic performance of the double blade pump under different parameters is also analyzed. The results show that the particles in the impeller mainly located in the vicinity of the blade pressure surface, and the distribution of the particles in each section of the volute is quite different. The great difference in particle density can result in obviously uneven distribution of particles. With the increase of particle diameter, particle density and particle concentration, the pump head and efficiency both decrease while the shaft power increase on the contrary. This research results can also provide a basis for the optimization design of solid-liquid two-phase flow pumps.

Abstract Impinging-jet injectors are commonly used in liquid propellant rocket engines. Two cylindrical liquid jets impinge at a certain angle and form a liquid sheet in the plane normal to the jets. When the Reynolds and Weber numbers are large, the liquid sheet becomes unstable and disintegrates into liquid ligaments and droplets. In the present study, we focus on cases with moderate injection velocities so that the liquid sheet remains unbroken. Detailed numerical simulations are performed using the adaptive multiphase flow solver, Basilisk. The volume-of-fluid method is used to resolve the gas-liquid interface. Grid-refinement studies are conducted to verify the formation of the liquid sheet is accurately captured in simulation. The numerical results are compared to the recent experimental measurement of the sheet thickness distribution by partial coherent interferometry and a good agreement is achieved.

Abstract The present paper theoretically treats weakly nonlinear propagation of plane progressive waves in an initially quiescent compressible liquid containing a tremendously large number of spherical gas bubbles, focusing on the derivation of an amplitude evolution equation (i.e., nonlinear wave equation). We emphasize the following points: (i) the compressibility of the liquid phase, which has long been neglected, is considered; (ii) the wave propagates with a large phase velocity exceeding the speed of sound in pure water; (iii) bubbles are not created or annihilated. From the method of multiple scales with an appropriate scaling of three nondimensional parameters, we can derive an attenuated nonlinear Schrödinger (NLS) equation, where the phase velocity is larger than the speed of sound in a pure liquid.

Abstract We performed numerical simulation to understand deposition phenomena on high-pressure turbine vane. Several deposition models were compared and the OSU model showed good adaptation to any flow field and material, so it was implemented on UPACS. After the implementation, the simulations of deposition phenomenon in several cases of the flow field were conducted. From the results, particles adhere on the leading edge and the trailing edge side of the pressure surface. Also, the calculation of the total pressure loss coefficient was conducted after computing the flow field after deposition. The total pressure loss coefficient increased after deposition and it was revealed that the deposition deteriorates aerodynamic performance.

Abstract Gas Carry-Under (GCU) is one of the two undesirable phenomena that occur in the GLCC ©,1 (Gas-Liquid Cylindrical Cyclone) separators when it operates even within the Operational Envelope (OPEN). Earlier studies have shown that maintaining a liquid level below the inlet of the GLCC under control configuration affects the GCU in GLCC. It has been identified that the tangential wall jet is the cause of gas entrainment within the GLCC and has been understood to change with liquid level maintained at the inlet. Also, it has been theorized that effective formation of the vortex formed in the lower part of the GLCC, or a stable gas core enhances the separation of gas entrained in the liquid. At present, there is no mechanistic model which captures these complex physical phenomena in the GLCC. This paper presents a newly developed mechanistic model which can predict the GCU for different flow conditions, fluid properties, and various liquid levels. The proposed model captures the various physical phenomena namely: saturated flow at the inlet, tangential wall jet phenomena, gas entrainment and vortex flow that results in separation of gas. The developed model has been compared with the extensive experimental data and is said to be in good agreement.

Abstract Fluidized beds are used in a wide range of applications in gasification, combustion, and process engineering. Multiphase flow in such applications involves numerous uncertain parameters. Uncertainty quantification provides uncertainty in syngas yield and efficiency of coal/biomass gasification in a power plant. Techniques such as sensitivity analysis are useful in identifying parameters that have the most influence on the quantities of interest. Also, it helps to decrease the computational cost of the uncertainty quantification and optimize the reactor. We carried out a nondeterministic analysis of flow in a biomass reactor. The flow in the reactor is simulated with National Energy Technology Laboratory’s open source multiphase fluid dynamics suite MFiX. It does not possess tools for uncertainty quantification. Therefore, we developed a C++ wrapper to integrate an uncertainty quantification toolkit developed at Sandia National Laboratory with MFiX. The wrapper exchanges uncertain input parameters and critical output parameters among Dakota and MFiX. We quantify uncertainty in key output parameters via a sampling method. In addition, sensitivity analysis is carried out for all eight uncertain input parameters namely particle-particle restitution coefficient, angle of internal friction, coefficient of friction between two-phases, velocity of the fluidizing agent at the inlet, velocity of the biomass particles at the inlet, diameter of the biomass particles, viscosity of the fluidizing agent, and the percentage of nitrogen/oxygen in the fluidizing agent.

Abstract A series of numerical simulations using “interThermalPhaseChangeFOAM” solver with improved VOF multiphase flow model in OpenFOAM were conducted to investigate the heat transfer and phase change characteristics for liquid-vapor boiling flow in quenching process. The computational domain is a cuboid with the heating wall at the bottom for both the variable and fixed wall temperature cases. The results for the variable wall temperature case with the heating wall temperature T wall = 150K show that the boiling phenomenon can be divided into the vapor film stage, the boiling stage and the convection stage. Then the fixed wall temperature cases with T wall = 110K, 120K and 140K are analyzed. It is found that 140K case is the most stable one, in which bubble formation is regular such as the bubble at the corner, resulting in the steady variation of heat flux. 120K case is the most unstable one, since the liquid phase and gas phase form the cross-interface shape and maintain this for a long time, leading to the fluctuations in heat flux. Finally, the influence of computational sizes on predicting the properties of boiling phenomenon is investigated. Although the variations of heat flux are not exactly same, the whole tendency is similar.

Abstract With the increasing demand of higher performance and efficiencies for marine propulsion and hydropower system, structures became more flexible and were subjected to high flow rates. Cavitation-structure interaction has become one of the major issues for most engineering applications. In order to analyze the characteristics of unsteady cavitating flow induced vibration, the cloud cavitation flow over three dimensional NACA66 hydrofoil is studied by numerical simulation in this paper. The cavitating flow is modeled by large eddy simulation method and Zwart cavitation model, and the structural vibration model of three dimensional hydrofoil is established. The numerical calculation of fluid-solid coupling is realized based on ANSYS Workbench. The main dimensionless parameters of three-dimensional hydrofoil cavitation flow-induced vibration are obtained by means of dimensional analysis, including density ratio, cavitation number, Reynolds number, and the frequency ratio of flow to structure. The changes of cavity morphology during the cloud cavitation development of flexible hydrofoil and the flow-induced vibration characteristics under cloud cavitation flow of flexible hydrofoil are analyzed. The results showed that the periodic development of cavitation can be divided into three stages: the growth of attached cavity, the development of re-entrant jet and the shedding of cavity in cloud cavitaion stage. The centroid displacement of the free end of the flexible hydrofoil varies periodically with time at the stage of cloud cavitation. The hydrofoil vibration is affected by the development of cloud cavitation, and the vibration frequency corresponds to the shedding frequency of cloud cavitation.

Abstract Three-dimensional numerical simulations of turbulent mixing at a perturbed interface of a dense shell compressed by a spherically imploding shock wave are presented. This case is a simplified version of inertial confinement fusion implosion (ICF) where a small capsule containing nuclear material is compressed to extremely high pressure and temperature to achieve fusion burn. The current simulations were performed using a high-order spherical method and a semi-Lagrangian moving mesh algorithm implemented in our in-house code Flamenco. Results of narrowband and broadband initial perturbations are presented at different grid resolutions along with mix layer limits, molecular mixing, turbulent kinetic energy and bubble/spike heights. The initial multimode perturbations applied at the interface consist of a superposition of cosine waves and are determined according to a specified power spectrum and standard deviation. These are employed in a spherical segment, enabling the efficient computation of a wide range of low to relatively high mode-number perturbations. The overall grid convergence of the solution is analysed and the different findings from the integral quantities and bubble/spike amplitudes are indicated.