Mixture Flow Model Research Articles

Numerical modeling of turbulent air-water mixture flows in spilling breaking waves

This paper presents a numerical study of turbulent air-water mixture flows under spilling breaking waves by using a mixture-flow model. The model is extended from the earlier 2D numerical framework NEWFLUME, which solves the Reynolds-averaged Navier-Stokes (RANS) equations for mean flow motions. The turbulence closure is accomplished by a modified k−ε two-equations model, in which the effect of entrained bubbles on turbulence production and dissipation is considered by incorporating additional buoyancy terms. A transient equation based on two-fluid formulation is solved for air bubble transport. The present model is validated by comparing the simulated free surface displacement, void fraction, mean velocity and turbulence kinetic energy against existing experimental data and the previous numerical results. The effects of the additional convective term in transient equation of void fraction and the bubble-induced turbulence term in turbulence transport equation are further explored. The results reveal that the additional convective term in the transient equation of void fraction plays an essential role of suppressing unphysical turbulence growth and bringing correct amount of air entrainment into water during wave breaking processes. The additional bubble-induced turbulence production and dissipation terms become effective after wave breaks when the void fraction has been appropriately modeled, and they can further reduce the simulated turbulence intensities in spilling breaking wave, rendering a better agreement with the experimental measurements.

Numerical Evaluation of Harmful Consequences after Accidental Explosion at a Hydrogen Filling Station

Abstract This study aims to present computational technology that can be used to evaluate numerically the harmful environmental consequences caused by an accidental hydrogen release from failed high-pressure dispensing cylinders and its explosion at a vehicle hydrogen filling station. A coupled problem of a hydrogen explosion products expansion in the atmospheric ground layer and a harmful explosion pressure wave shock impact on service personnel and infrastructure buildings at an accident site is solved by means of computer experiment simulation series. A spatial time-dependent model of compressible hydrogen-air mixture flow is used to obtain pressure history in calculation area in order to assess maximum overpressure in control points of human possible locations and on building surfaces exposed to hydrogen blast wave impact. A deterministic impact consequences model is based on comparing maximum overpressure values extracted from the mathematical model with threshold ranges corresponding to certain degrees of human damage and infrastructure destruction. The presented computer technology allows safety experts to identify potentially dangerous zones by means of mathematical modelling and recommend effective protection measures to mitigate negative consequences of explosions.

Water–rock two-phase flow model for water inrush and instability of fault rocks during mine tunnelling

Water inrush hazard is one of the major threats in mining tunnel construction. Rock particle migration in the seepage process is the main cause of water inrush pathway and rock instability. In this paper, a radial water–rock mixture flow model is established to study the evolution laws of water inrush and rock instability. The reliability of the proposed model is verified by the experimental data from a previous study. Through the mixture flow model, temporal-spatial evolution laws of different hydraulic and mechanical properties are analysed. And the proposed model’s applicability and limitations are discussed by comparing it with the existing water inrush model. The result shows that this model has high accuracy both in temporal evolution and spatial distribution. The accuracy of the model is related to the fluctuation caused by particle migration and the deviation of the set value. During the seepage, the porosity, permeability, volume discharge rate and volume concentration of the fluidized particle increase rapidly due to the particle migration, and this phenomenon is significant near the fluid outlet. As the seepage progresses, the volume concentration at the outlet decreases rapidly after reaching the peak, which leads to a decrease in the growth rate of permeability and porosity, and finally a stable seepage state can be maintained. In addition, the pore pressure is not fixed during radial particle migration and decreases with particle migration. Under the effect of particle migration, the downward radial displacement and decrease in effective radial stress are observed. In addition, both cohesion and shear stress of the rock material decreased, and the rock instability eventually occurred at the outlet.

Numerical simulations of cavitating water jet by an improved cavitation model of compressible mixture flow with an emphasis on phase change effects

Focusing on cavitation phenomena caused by high-speed submerged water jets, this paper presents an improved cavitation model for a compressible fluid mixture based on a concise estimation of fluid compressibility that considers phase change effects. The homogeneous two-phase flow assumption is adopted, and the gas phase is assumed to consist of vapor and non-condensable components. Equations of state for a pure liquid and an ideal gas are employed to evaluate the compressibility of the liquid and non-condensable components, and the compressibility of the vapor is treated semi-empirically as a constant. The model is embedded in an unsteady Reynolds-averaged Navier–Stokes solver, with the realizable k-ε model employed to evaluate the eddy viscosity. The turbulent cavitating flow caused by an impulsively started submerged water jet is treated. The pattern of periodic cavitation cloud shedding is acceptably captured, and the mass flow rate coefficient and its fluctuation frequency evaluated by simulations agree with the experimental results well. The validity of the proposed method is confirmed. The results reveal that cavitation occurs when pin/Pin reaches 0.65 and fluid flow begins to pulsate. In the well-developed stage, the leading cavitation cloud and a subsequent cloud are successively shed downstream, and this process is repeated. The subsequent cloud catches the leading cloud, and they coalesce in the range x/d≈ 2–3. The pressure fluctuations concentrate in the range of x/d≈2–5 corresponding to the periodic shedding of cavitation clouds. The mass flow rate coefficient pulsates from 0.59–0.66 under the effect of cavitation.

Experimental and Computational Fluid Dynamics‐Based Simulation of Oil‐in‐Water Emulsion Flow through a Pipeline

AbstractDue to its high viscosity, heavy crude oil (HCO) is often transported through pipelines as concentrated oil‐in‐water emulsion. Here, emulsions were prepared with different concentrations of polyoxyethylene (5) sorbitan monooleate to study their flow characteristics through a horizontal pipeline. Laminar flow of HCO and an emulsion with 75 % (v/v) HCO and 25 % (v/v) water was simulated by using Ansys Fluent 2019 R3 to study the effect of temperature, volumetric flow rate, and surfactant concentration on pressure drop, dynamic viscosity, hydrodynamic entrance length, flow behavior index, consistency index, and pumping power requirement. Laminar flow of the emulsion was simulated by using a two‐phase mixture flow model considering the emulsion as a pseudo‐homogeneous mixture, while the flow of HCO was simulated as viscous laminar flow. Flow behavior index and consistency index were predicted from experimental viscosity data and used to predict pressure drop and, hence, the pumping power requirement.

Mathematical model of the process of mixing and separation in a microfluid channel with five outlets

The article presents the results of mathematical modeling in a two-dimensional formulation of the mixing process by mutual diffusion and separation of flows of Newtonian fluids in a microfluidic mixing channel with five outlets. Branches are used to separate flows into fractions with a given concentration of one of the components in the mixture. The diffusion process occurs in a laminar flow regime, without chemical and thermal interaction. The mixture flow model was set up in a two-dimensional formulation. One component of the mixture flows through the main channel 1 mm wide, then at a distance of 5 mm from the entry point to the channel perpendicular to it, there are two more entrances also 1 mm wide, through which the second component is fed. At the outlet, there are five taps with dimensions of 0.2 mm to take the mixture of the desired concentration. Four outlets for the intake of the mixture are located opposite each other in pairs. Liquids with the physical characteristics of water and ethyl alcohol were taken as miscible components. The problem was solved using the ANSYS-Fluent software package.

Compressible gas-droplet flow and heat transfer behind a condensation shock in an expanding channel

A two-fluid mathematical model of a supersonic gas-droplet mixture flow with account of droplet growth due to vapor condensation behind a condensation shock in a plane expanding channel is constructed. The flow structure in both the inviscid core and the two-phase boundary layer assumed to be laminar is studied numerically. The range of flow parameters is considered in which the spontaneous condensation zone (“condensation shock”) is fairly narrow, and just behind this shock thermal parameters of the phases almost reach thermodynamic equilibrium. Downstream, the droplet radius continues to grow due to the flow expansion and further vapor condensation. Of primary concern is the flow region where the droplets become sufficiently inertial to travel with a velocity slip, and hence to model adequately the velocity and temperature fields in both phases a two-fluid model is required. In addition to the Stokes drag, the Saffman lifting force exerted on the droplets in the boundary layer is taken into account. The Saffman force results in droplet deposition and the formation of a thin liquid film on the channel walls. A parametric numerical analysis of the two-phase flow structure in the inviscid flow region and in the near-wall boundary layer is performed, and the effects of phase transitions (droplet condensation and evaporation, as well as the film formation) on the reduction of the adiabatic channel wall temperature are analyzed.

Calculation of depressurization coordinate in underground and offshore gas pipelines

The paper introduces a method for calculating the depressurization coordinate of an extended ultra-high pressure gas pipeline from the data measurements of pressure and flow rate at the outlet. The method is based on a mathematical model of a non-isothermal steady single-phase gas mixture flow through a pipeline of constant section on the quasi-linearization method. It allows to calculate the depressurization coordinate for extended underground and offshore ultra-high pressure gas pipelines with high accuracy, while considering varying leakage size and location. Examples of solving problems of practical interest are given. The influence of the flow rate and pressure settings error on the coordinate of depressurization calculating error has been demonstrated.

Two-Pressure Model of Particle-Fluid Mixture Flow with Pressure-Dependent Viscosity in a Porous Medium

Equations governing the flow of a fluid-particle mixture with variable viscosity through a porous structure are developed. Method of intrinsic volume averaging is used to average Saffman’s dusty gas equations. A modelling flexibility is offered in this work by introducing a dust-phase partial pressure in the governing equations, interpreted as the pressure necessary to maintain a uniform particle distribution in the flow field. Viscosity of the fluid-particle mixture is assumed to be variable, with variations in viscosity being due to fluid pressure. Particles are assumed spherical and Stokes’ coefficient of resistance is expressed in terms of the pressure-dependent fluid viscosity. Both Darcy resistance and the Forchheimer micro-inertial effects are accounted for in the developed model

Cooling effects on the heat transfer characteristics of a rectangular thermosyphon with PCM suspension fluid

A numerical and experimental study is presented to explore the effects of cooling (the section on subcooling and phase-change material (PCM) supercooling) on the thermal performance of a rectangular thermosyphon containing PCM suspensions. In the numerical simulation, a continuum mixture flow model is used for the buoyancy-driven circulation flow of the PCM suspensions together with an approximate enthalpy model to detail the solid-liquid phase change process of the PCM particles in the loop. Parametric simulations are conducted in the following ranges: heat input at the heating section = 12 W, average temperature of the outer wall of the cooling section = 10–25 °C, and PCM mass concentration = 0–15%. The results show that in the configuration of this study, the downward flow of the high-density fluid in the cooling section became the main driving force of the circulation loop. Therefore, the cooling effects affected the overall thermal performance. To allow the proper melting/freezing of PCM particles, it is critical to control the wall temperature at the cooling section to achieve an appropriate subcooling effect.

An ultrasonic-assisted soft abrasive flow processing method for mold structured surfaces

As a fluid-based precise processing method, soft abrasive flow processing has been widely used in advanced electromechanical systems, complex mold manufacturing, and other engineering fields. Because of the low volume fraction of abrasive particles and micro-force/cutting removal characteristics, there exists a potential improvement in terms of processing efficiency and uniformity. In view of the above problems, this article presents an ultrasonic-assisted soft abrasive flow processing method. Based on the realizable k–ε turbulence model and the mixture flow model, an ultrasonic coupling enhancement dynamic model for soft abrasive flow is set up, and the kinetic energy transport equation of realizable k–ε turbulence model can be revised. Using particle image velocimetry technology, an on-line observation experimental platform for ultrasonic-assisted soft abrasive flow is developed to conduct the real-time acquisition of abrasive flow state and particle distribution in a constrained flow passage. An ultrasonic-assisted soft abrasive flow processing experimental platform is established to complete the processing experiment. The experimental results show that the ultrasonic excitation vibration can effectively enhance the turbulence intensity and distribution uniformity of the abrasive flow, the average processing time can be shortened by more than 6 h, and a better surface quality can be obtained.

An assessment of the effectiveness of the analytical methods to fracture propagation control using accurate mathematical modelling

Simple analytical methods are usually used to fracture propagation control in pipeline systems transmitting the natural gas and carbon dioxide mixtures. The minimum of fracture arrest toughness is determined employing analytical approaches such as the Battelle Two-Curve Method (BTCM), for example. The decompression wave speed in the gases and the crack propagation velocity in the pipe wall material are calculated independently from each other and compared thereafter. The crack is arrested if those two curves plotted at the same figure are not intersected. The accuracy and universality such kind of approaches is in great doubt because the effect of gas decompression on the crack velocity is not considered. An assessment of the accuracy and effectiveness of engineering analytical approaches to fracture propagation control is considered in the paper using accurate mathematical modelling. A coupled transient mathematical model of dynamic crack propagation in the shock tube is developed to determine the minimum of fracture arrest toughness/wall thickness. Here in the study, the model of crack propagation in the pipe wall is integrated into one-dimensional model of compressible thermal multi-component natural gas mixture flow in a shock tube. The dynamic pressure at the crack tip is determined numerically from gas decompression model. Both models work together consistently at each time step one after another. The set of mass, momentum and enthalpy conservation equations is solved for the natural gas. Thermo-physical properties of multi-component natural gas mixture are calculated by solving the Equation of State in the form of the Soave-Redlich-Kwong (SRK-EOS) model. Gas decompression model is validated against the experiments. The proposed accurate numerical tool simulates a continuous development of crack propagation together with rapid decompression of the natural gas mixture, and its arrest (or not) after some time successfully. The proposed coupled model shows that the crack is not arrested in the case where the analytical approach (BTCM) points to the crack arrest because two curves are not intersected in the figure. This makes it possible to base on the conclusion that the engineering analytical method (i.e. Two-Curve Method) does not work in some cases and cannot give 100% of confidence in assessing. The error in the assessment using the analytical method can reach up to 10%.

On the effects of landslide deformability and initial submergence on landslide-generated waves

This paper represents a numerical study on the effects of landslide initial submergence and its geotechnical and rheological properties on the characteristics of landslide-generated waves (LGWs) and landslide deformation. A number of 117 numerical experiments are performed using a two-layer Coulomb Mixture Flow (2LCMFlow) model on a real-sized numerical flume as a simplified cross section of the Maku dam reservoir, located in the Northwest of Iran. Three different initial locations are considered for landslide representing a subaerial (SAL), a semi-submerged (SSL), and a submarine (SML) landslide. Based on the numerical results, the majority of SMLs and in some cases SSLs generate tsunami waves with a larger wave trough than the wave crest. The maximum negative wave amplitudes of LGWs caused by SMLs (SMLGWs) can be up to 55% larger than that for SALs. LGWs caused by SALs (SALGWs) commonly have a higher wave crest than the wave trough. In 70% of cases, the maximum wave crests of SALGWs are larger than that for LGWs caused by SSLs (SSLGWs) and SMLGWs. While, in the rest 30% of simulations, the maximum SSLGW crests are up to 60% larger than SALGWs. Due to the landslide inter-phase interactions in combination with its basal and internal friction resistances, only 10–40% of the SAL initial mass contributes in LGW generation process. Energy transfer from landslide into water is about 0.5–7.5% for SMLs, 6–17.2% for SSLs, and 5–15% for SALs. The final deposit of SMLs generally has a short and thick profile while SALs and SSLs elongate more and travel longer distances. Finally, a Coulomb mixture product parameter, PCM, is defined to relate the maximum LGW heights to the considered landslide properties.

Numerical simulation of bubble collapse between two parallel walls and saturated film boiling on a sphere

The present study aims at validating a computer simulation code for compressible interface flows with and without mass transfers. The numerical method was based on a dual-time fully compressible multiphase homogeneous mixture flow model. The interfaces with a large jump in density, pressure, velocity, and temperature were captured using a compressive high-resolution interface-capturing scheme. Lee’s boiling model was adopted for implementing the mass and energy transfers via interfaces. The bubble collapse between two parallel walls was first examined. The bubble profile during the collapse process was predicted and compared with experimental images. The numerical results showed good agreement. To evaluate the present model for multiphase flows, including the effects of heat and mass transfers, computations were performed for saturated film boiling on a sphere at atmospheric pressure. The evolution of the wavy liquid–vapor interface around the sphere during the film boiling process was observed. The time-averaged heat fluxes obtained from the numerical simulation were compared with those predicted from numerical data and analytical correlations. The effects of the superheated wall on heat fluxes were also investigated.

Axisymmetric simulation of bubble condensation of pure steam and steam–air mixture

Abstract A coupled compressive interface capturing scheme and dual-time preconditioned approach was developed for the two-dimensional axisymmetric computation of compressible interface flows with mass transfers. The fully-compressible three-phase homogeneous mixture flow model was implicitly solved using the dual-time preconditioned technique on generalized curvilinear grids. The interfaces between the three phases were captured by the solution of two interface advection equations using a compressive high resolution interface capturing method. The predictive capabilities of the numerical scheme were examined for a series of bubble condensations of pure steam and steam–air mixtures in different thermal and hydrodynamic subcooled boiling flows. Reasonably good agreement with the experimental data was obtained. Subsequently, several test cases on the condensation of single steam–air mixture bubbles were performed to investigate the effects of non-condensable gases on the characteristics of a condensing bubble. The numerical results revealed a nearly linear decrease of the condensation rate with an increase of the non-condensable gas void fraction in the mixture bubble.

Two-phase explicit CBS procedure for compressible viscous flow transport in porous materials

PurposeIn this work, a new two-phase version of the finite element-based Artificial Compressibility (AC) Characteristic-Based Split (CBS) algorithm is developed and applied for the first time to heat and mass transfer phenomena in porous media with associated phase change. The purpose of this study is to provide an alternative for the theoretical analysis and numerical simulation of multiphase transport phenomena in porous media. Traditionally, the more complex Separate Flow Model was used in which the vapour and liquid phases were considered as distinct fluids and mathematically described by the conservation laws for each phase separately, resulting in a large number of governing equations.Design/methodology/approachEven though the adopted mathematical model presents analogies with the conventional multicomponent mixture flow model, it is characterized by a considerable reduction in the number of the differential equations for the primary variables. The fixed-grid numerical formulation can be applied to the resolution of general problems that may simultaneously include a superheated vapour region, a two-phase zone and a sub-cooled liquid region in a single physical domain with irregular and moving phase interfaces in between. The local thermal non-equilibrium model is introduced to consider the heat exchange between fluid and solid within the porous matrix.FindingsThe numerical model is verified considering the transport phenomena in a homogenous and isotropic porous medium in which water is injected from one side and heated from the other side, where it leaves the computational domain in a superheated vapour state. Dominant forces are represented by capillary interactions and two-phase heat conduction. The obtained results have been compared with the numerical data available in the scientific literature.Social implicationsThe present algorithm provides a powerful routine tool for the numerical modelling of complex two-phase transport processes in porous media.Originality/valueFor the first time, the stabilized AC-CBS scheme is applied to the resolution of compressible viscous flow transport in porous materials with associated phase change. A properly stabilized matrix inversion-free procedure employs an adaptive local time step that allows acceleration of the solution process even in the presence of large source terms and low diffusion coefficients values (near the phase change point).

Математическая модель течения многокомпонентной смеси газов с учетом возможности возникновения жидкой фазы

Математическая модель течения многокомпонентной смеси газов с учетом возможности возникновения жидкой фазы

Sensitivity Analysis of Depth-Integrated Numerical Models for Estimating Landslide Movement

Landslides are natural phenomena that occur in slopes with thick layers of weathered soil or weak geological formations. High intensity of precipitation, earthquake, and human interference can cause a huge landslide disaster. To mitigate landslide risk, an appropriate investigation to determine the stability and movement mechanisms is important to predict its potential scale. This paper proposes a sensitivity analysis of depth-integrated numerical model of landslide movement by implementing solid friction and fluid friction as the shear resistance in the constitutive systems. The hyperconcentrated solid-liquid mixture flow model and Voellmy-fluid friction model are employed in the solid friction and fluid friction mechanism, whereas the Mohr-Coulomb model is used in the solid friction mechanism. In order to analyze model characteristics and sensitivity to the inputted parameters, the parametric studies on an imaginary slope were examined. The results show that the internal friction angle among input data strongly affects the runout distance and moving velocity. The Voellmy-fluid friction model produces more lateral tendency and wider deposit in transversal directions of landslide compared to other models. The numerical model along with three constitutive equations of shear resistance was applied to the Bishamon Landslide. The hyperconcentrated solid-liquid mixture flow model and Mohr-Coulomb model yield a good agreement with the actual deposition area, whereas the Voellmy-fluid friction model produces more lateral tendency in transversal directions. The calculated runout distance reaches more than 350 m and 10.3 to 13.9 m/s of maximum velocity.

Development of the analysis tool for the water cooling type passive residual heat removal system of Chinese pressurized reactor

An innovative design for Chinese pressurized reactor is the steam generator (SG) secondary side water cooling passive residual heat removal system (PRHRS). The new design is expected to improve reliability and safety of the Chinese pressurized reactor during the event of feed line break or station blackout (SBO) accident. The new system is comprised of a SG, a cooling water pool, a heat exchanger (HX), an emergency makeup tank (EMT) and corresponding valves and pipes. In order to evaluate the reliability of the water cooling PRHRS, an analysis tool was developed based on the drift flux mixture flow model. The preliminary validation of the analysis tool was made by comparing to the experimental data of ESPRIT facility. Calculation results under both high pressure condition and low pressure condition fitted the experimental data remarkably well. A hypothetical SBO accident was studied by taking the residual power table under SBO accident as the input condition of the analysis tool. The calculation results showed that the EMT could supply the water to the SG shell side successfully during SBO accident. The residual power could be taken away successfully by the two-phase natural circulation established in the water cooling PRHRS loop. Results indicate the analysis tool can be used to study the steady and transient operating characteristics of the water cooling PRHRS during some accidents of the Chinese pressurized reactor. The present work has very important realistic significance to the engineering design and assessment of the water cooling PRHRS for Chinese NPPs.

Development and preliminary validation of a steam generator 3D thermohydraulics analysis code STAF

Porous media model in Fluent code, coupled with two-phase mixture flow model, resistance model of tubes and heat transfer model through tubes, is employed to develop a steam generator thermohydraulics analysis code STAF (Steam generator Thermohydraulics Analysis code based on Fluent). In this code, the heat transfer from primary to secondary side is calculated three-dimensionally during iteration. The localized velocity, temperature, enthalpy, quality and void fraction in steam generator can be obtained by this code. STAF is validated in two ways. First, STAF is used to calculate the thermal-hydraulic parameters in steam generator of AP 1000. The calculated results are compared with designed values to prove that the coupled heat transfer calculation in STAF is accurate. Second, STAF is employed to simulate the FRIGG test to validate the localized parameter calculation performance by comparing the calculated localized void fraction with test values.