Unsteady Two-phase Flow Research Articles

Experimental Investigation on Rapid Filling of a Large-Scale Pipeline

This study presents the results from detailed experiments of the two-phase pressurized flow behavior during the rapid filling of a large-scale pipeline. The physical scale of this experiment is close to the practical situation in many industrial plants. Pressure transducers, water-level meters, thermometers, void fraction meters, and flow meters were used to measure the two-phase unsteady flow dynamics. The main focus is on the water-air interface evolution during filling and the overall behavior of the lengthening water column. It is observed that the leading liquid front does not entirely fill the pipe cross section; flow stratification and mixing occurs. Although flow regime transition is a rather complex phenomenon, certain features of the observed transition pattern are explained qualitatively and quantitatively. The water flow during the entire filling behaves as a rigid column as the open empty pipe in front of the water column provides sufficient room for the water column to occupy without invoking air compressibility effects. As a preliminary evaluation of how these large-scale experiments can feed into improving mathematical modeling of rapid pipe filling, a comparison with a typical one-dimensional rigid-column model is made.

Effect of Virtual Mass Force on the Mixed Transport Process in a Multiphase Rotodynamic Pump

To explore the effect of virtual mass force, the unsteady two-phase flow in a multiphase rotodynamic pump impeller was numerically simulated, where the inlet gas void fraction was 4.9%, 14.9%, and 25.2%, respectively. The drag force and the virtual mass force were accounted for and the cases with and without the latter one were both analyzed for comparison. The results show that the trajectories of the gas bubbles are influenced by the virtual mass force evidently in the inlet extended region. Due to the effect of virtual mass force, some gas will firstly move to the shroud before accumulating in the hub region of the impeller. The characteristic of the pump head was discussed and the results demonstrate that the virtual mass force can decrease the pump head and lead to its fluctuation. In addition, the comparison between the steady and unsteady simulation shows that the virtual mass effect can be found only by unsteady simulation.

Semi-empirical Method for Estimation of Energy Losses in a Large- scale Pipeline

The high frequency (0.1kHz) pressure and velocity measurements of two-phase unsteady flow are used to determine the hydraulic-grade-line (HGL) along the pipeline with a complex layout. The semi-empirical method is applied to estimate the pressure drop for the outflow, and thus determine the pipe downstream-end conditions for the modeling purposes. A Control- Volume (CV) model coefficient β, representing residual motion due to the pressurized water-column stratification is specified. Pressurized two-phase unsteady flow phases in a 250mm diameter and 275 meters long PVC pipeline with steel inlet and outlet counterparts are considered for the evaluation of this method.

Study on solid-liquid two-phase unsteady flow characteristics with different flow rates in screw centrifugal pump

The screw centrifugal pump is used as an object, and the unsteady numerical simulation of solid-liquid two-phase flow is carried out under different flow rate conditions in one circle by choosing the two-phase flow of sand and water as medium, using the software FLUENT based on the URANS equations, combining with sliding mesh method, and choosing the Mixture multiphase flow model and the SIMPLE algorithm. The results show that, with the flow rate increasing, the change trends for the pressure on volute outlet are almost constant, the fluctuation trends of the impeller axial force have a little change, the pressure and the axial force turn to decrease on the whole, the radial force gradually increases when the impeller maximum radius passes by half a cycle near the volute outlet, and the radial force gradually decreases when the maximum radius passes by the other half a cycle in a rotation cycle. The distributions of the solid particles are very uneven under a small flow rate condition on the face. The solid particles under a big flow rate condition are distributed more evenly than the ones under a small flow rate condition on the back. The theoretical basis and reference are provided for improving its working performance.

Application of two-fluid model in the unsteady flow simulation for a multiphase rotodynamic pump

Based on the assumption of tiny bubbly flow, the gas-liquid two-phase unsteady flow in a multiphase rotodynamic pump was numerically simulated with two-fluid model. The two-phase transport process and the evolution characteristic of the pump head were analyzed. In the working conditions, the liquid flow rate was constant, and the IGVF (inlet gas volume fraction) was 0.05, 0.15 and 0.25, respectively. The k ω− based SST model was used for turbulence; the drag force and the added mass force were accounted for in the interfacial momentum transfer terms. Because the wrap angle of the blade was large, the hybrid mesh was adopted to guarantee high mesh quality. The simulation results demonstrate that two-fluid model can more reasonably capture the transport process than the homogeneous model; and the drag law should be corrected based on the mixture viscosity in high gas volume fraction conditions. If the liquid flow rate is constant, the increase of IGVF can raise the pressure in the inlet extended region, while the pressure in the outlet extended region will not be affected much, thus the pump head will go down. In addition, due to the fluctuation of gas volume fraction field, the pump head will also fluctuate around a stable value in the transport process.

Implementation of the Ideal Algorithm on Unsteady Two-Phase Flows and Application Examples

For unsteady two-phase flows, the most widely used numerical approaches for coupled solution of continuity and momentum equations are fractional-step methods and SIMPLE-family algorithms. Fractional-step methods have advantages in their fast convergence rates, while their disadvantages lie in conditional stability for initial-value problems. SIMPLE-family algorithms are absolutely stable; however, their convergence rates are slow. To overcome the shortcoming of traditional SIMPLE-family algorithms the, IDEAL algorithm is proposed by the present authors. It is concluded that the IDEAL algorithm overcomes the shortcoming of traditional SIMPLE-family algorithms, thus possessing two advantages of fast convergence rate and absolute stability simultaneously.

NUMERICAL INVESTIGATION OF THE SPREADING AND HEAT TRANSFER CHARACTERISTICS OF EX-VESSEL CORE MELT

The flow and heat transfer characteristics of the ex-vessel core melt (corium) were investigated using a commercial CFD code along with the experimental data on the spreading of corium available in the literature (VULCANO VE-U7 test). In the numerical simulation of the unsteady two-phase flow, the volume-of-fluid model was applied for the spreading and interfacial surface formation of corium with the surrounding air. The effects of the key parameters were evaluated for the corium spreading, including the radiation, decay heat, temperature-dependent viscosity and initial temperature of corium. The results showed a reasonable trend of corium progression influenced by the changes in the radiation, decay heat, temperature-dependent viscosity and initial temperature of corium. The modeling of the viscosity appropriate for corium and the radiative heat transfer was critical, since the front progression and temperature profiles were strongly dependent on the models. Further development is required for the code to consider the formation of crust on the surfaces of corium and the interaction with the substrate.

Investigation of the hydrodynamic characteristics of abrasive water jet cutting head

Cutting heads are core components of abrasive water jet cutting plants which dramatically affect the achievable cutting performance. Therefore, investigating their characteristics to achieve an efficient design is fundamental to improve the AWJ technology. In this study, computational fluid dynamics models for ultrahigh velocity waterjets and abrasive waterjets are established using ANSYS FLUENT® software. Jet flow dynamic characteristics inside a cutting head are simulated under unsteady state, turbulent, two-phase and three-phase flow conditions. Water and particles velocities are obtained under different operating conditions to provide an insight into the jet characteristics and study the effect of cutting head geometry. The comparison with experimental data shows the accuracy of the numerical simulations in predicting cutting head performance, as well as revealing the effect of operating conditions. Moreover, the fact that results obtained with two different geometrical models (2D-axisymmetric and 3D) are similar reveals that the flow pattern does not depend much on the position of the abrasive and air suction zone. This investigation aids the understanding of the flow inside the AWJ cutting head and provides information for designing this component to suit optimum performances.

Numerical simulation of the effect of solid-volume fraction on induction force of screw centrifugal pump

The solid-liquid two-phase unsteady flow in a screw centrifugal pump was simulated with unsteady Reynolds averaged Navier-Stokes equations and sliding mesh technology. The distribution of the pressure at volute outlet, radial force, axial force and total moment are presented in this paper. The effects of solid-phase volume fractions on the value and direction of the induction thrust are analyzed. Seven monitor points are arranged on the inner surface of volute along the impeller rotation. The characters of the induced force on the monitor points with different solid-phase volume fractions are investigated. The results indicated that different solid-volume fractions have litter effects on the trend and direction of pressure at volute, radial force, axial force and total moment during one period, but the value of induction forces increase with the increasing of solid-volume fraction; The pressure fluctuation on the monitor points has with different trends during one period, which depends on the direction of the monitor points and the rotor-stator interaction strength of impeller and volute. With the rotation of impeller, the values of pressure in the whole passage are further increased along the rotation direction with the role of impeller vane. Solid-phase volume fraction has few effects on change trend of induced thrust as radial force and axial force on the monitor points, but the values of pressure on the monitor points increase with the increasing of solid-volume fraction.

Eulerian multi-fluid models for the simulation of dynamics and coalescence of particles in solid propellant combustion

The accurate simulation of polydisperse sprays undergoing coalescence in unsteady gaseous flows is a crucial issue. In solid rocket motors, the internal flow depends strongly on the alumina droplet size distribution, which spreads up with coalescence. Yet solving for unsteady two-phase flows with high accuracy on the droplet sizes is a challenge for both modeling and scientific computing. As an alternative to Lagrangian approaches, a wide range of Eulerian models have been recently developed to describe the disperse liquid phase at a lower cost, with an easier coupling to the gaseous phase and with massively parallel codes. Among these models, the multi-fluid model allows the detailed description of polydispersity and size/velocity correlations by separately solving fluids of size-sorted droplets, the so-called sections. The existing one size moment method, which describes the size distribution with one size moment per section, provides simple and fast resolution for coalescence. On the other hand, a two size moment method has been suggested to reduce the number of sections but it lacks an efficient coalescence resolution method. After introducing a new strategy for two size moment coalescence, the two methods are compared on various configurations in a research code and an industrial-oriented code, in order to conclude on computational accuracy and cost. Then the paper aims at describing the most efficient approach for multi-dimensional unsteady and eventually coalescing rocket chamber simulations. Its objective is threefold: first, to validate the two size moment method by comparing simulations to reference solutions and dedicated experimental measurements conducted at ONERA, second to study the efficiency and robustness of both methods, third, to draw some firm conclusions about the necessity to use the one size moment or two size moment method to simulate solid propellant alumina sprays. We finally perform the first simulations of coalescence in realistic 2D boosters with the two size moment method, implemented in the industrial-oriented code CEDRE.

Temperature Field Analysis on the Hydrodynamic Retarder of Heavy Vehicle

According to the working characteristics of the hydrodynamic retarder, the hydrodynamic retarder D300 is chosen in this research. Based on three-dimensional flow theory, the internal temperature fields of hydrodynamic retarder with different liquid-filled ratios of 100%, 75%, 50%, 25% are numerically simulated. The standard k-ε model is chosen as turbulent model for calculation. The SIMPLEC algorithm is chosen as velocity-pressure coupling algorithm and the second order upwind scheme is used as discrete method. The mixture multiphase model is used to calculate the unsteady gas-liquid two-phase flow in the condition of partial charging. Through simulating and analyzing, it provides an important theoretical basis for the heat exchange of the hydrodynamic retarder at different gears.

The Numerical Analysis of Radial Thrust and Axial Thrust in the Screw Centrifugal Pump

The solid-liquid two-phase unsteady flow in the screw centrifugal pump is simulated during one revolution by using CFD software. The pressure fluctuations at the volute outlet, the distribution of radial thrust and axial thrust in the screw centrifugal pump during one revolution are given in the paper. The results show that the minimum pressure value at the volute outlet occurs when the maximum impeller radius just turned the tongue of volute, and maximum value occurs when the maximum impeller radius just turned between the section VI and VII the radial thrust on the impeller is assumed the circumference distribution approximately during one revolution. As the solid volume fraction increases, the radial thrust increases gradually. The direction of radial thrust is inverse against the maximum value of pressure in the pump outlet; the maximum radius position has much influence on the changes of axial thrust, the axial thrust maximum value occurs when the maximum impeller radius just turned the tongue of volute, and minimum value occurs when the maximum impeller radius is away from the tongue of volute.

Numerical Simulation of Cavitation and Aeration in Discharge Gated Tunnel of a Dam Based on the VOF Method

Cavitation, usually known as a destructive phenomenon, involves turbulent unsteady two-phase flow. Having such features, cavitating flows have been turned to a challenging topic in numerical studies and many researches are being done for better understanding of bubbly flows and proposing solutions to reduce its consequent destructive effects. Aeration may be regarded as an effective protection against cavitation erosion in many hydraulic structures, like gated tunnels. The paper concerns numerical simulation of flow in discharge gated tunnel of a dam using RNG model coupled with the volume of fluid (VOF) method and the zone which is susceptible of cavitation inception in the tunnel is predicted. Then a vent is considered in the mentioned zone for aeration and the numerical simulation is done again to study the effects of aeration. The results show that aeration is an impressively useful method to exclude cavitation in mentioned tunnels.

Numerical Simulation of Cavitation and Aeration in Discharge Gated Tunnel of a Dam Based on the VOF Method

Cavitation, usually known as a destructive phenomenon, involves turbulent unsteady two-phase flow. Having such features, cavitating flows have been turned to a challenging topic in numerical studies and many researches are being done for better understanding of bubbly flows and proposing solutions to reduce its consequent destructive effects. Aeration may be regarded as an effective protection against cavitation erosion in many hydraulic structures, like gated tunnels. The paper concerns numerical simulation of flow in discharge gated tunnel of a dam using RNG model coupled with the volume of fluid (VOF) method and the zone which is susceptible of cavitation inception in the tunnel is predicted. Then a vent is considered in the mentioned zone for aeration and the numerical simulation is done again to study the effects of aeration. The results show that aeration is an impressively useful method to exclude cavitation in mentioned tunnels.

1D numerical evaluation of dike erosion due to overtopping

Dike overtopping is an important issue in both scientific and practical aspects of sediment embankment erosion. This research is concerned with the validation of a one-dimensional numerical code applied to an unsteady two-phase flow over an initially trapezoidal-shaped sediment dike, including the transition from sub- to supercritical flows and the flow propagation over a steep slope. The approach is based on the shallow-water equations coupled with a sediment erosion code. The numerical results are compared with recent laboratory experiments, resulting in a reasonable prediction of the temporal free surface and bed evolution. The remaining model inaccuracies mainly originate from overflow initiation with extremely small flow depths, streamline curvature effects with the related underestimation of flow velocities close to the sediment surface, and the changing saturation in the dike body not accounted for in the model. Despite these deficiencies, the computational model will be helpful, particularly in flood risk assessment and management.

Simulation of unsteady two-phase flows using a parallel Eulerian–Lagrangian approach

The present study details the implementation of a time accurate method for the tracking of particles being acted upon by a continuous gas phase and gravity. The Lagrangian particle tracking approach was implemented within the framework of a parallel, incompressible, unstructured, node-centered finite-volume flow solver. The paper gives a method for selecting time steps for individual particles such that interactions with the continuum phase are updated at particle locations nearest the continuum-phase nodes while constraining the particle from passing beyond boundaries of the relevant adjacent cell. An implementation of this technique for three-dimensional nonuniform multi-element unstructured grids is given in the context of domain decomposition for implementation on distributed-memory parallel computers. Results of simulations with and without particle–particle collisions compare favorably with experimental validation results.

Numerical modeling of two-phase transonic flow

Our work is aimed at the development of numerical method for the modeling of transonic flow of wet steam including condensation/evaporation phase change. We solve a system of PDE’s consisting of Euler or Navier-Stokes equations for the mixture of vapor and liquid droplets and transport equations for the integral parameters describing the droplet size spectra. Numerical method is based on a fractional step technique due to the stiff character of source terms, i.e. we solve separately the set of homogenous PDE’s by the finite volume method and the remaining set of ODE’s either by explicit Runge-Kutta or implicit Euler method. The finite volume method is based on the Lax-Wendroff scheme with conservative artificial dissipation terms for structured grid. We also note result achieved by recently developed finite volume method with VFFC scheme. We discuss numerical results of steady and unsteady two-phase transonic flow in 2D nozzle, 2D and 3D turbine cascade and 2D turbine stage with moving rotor cascade.

Un modèle hyperbolique diphasique bi-fluide en milieu poreux

We introduce an hyperbolic two-fluid two-pressure model to compute unsteady two-phase flows in porous media. The closure laws comply with the entropy inequality, and a unique set of jump conditions holds within each field. To cite this article: J.-M. Hérard, C. R. Mecanique 336 (2008).

Numerical investigation of three-dimensional cloud cavitation with special emphasis on collapse induced shock dynamics

The aim of the present investigation is to model and analyze compressible three-dimensional (3D) cavitating liquid flows with special emphasis on the detection of shock formation and propagation. We recently developed the conservative finite volume method CATUM (Cavitation Technische Universität München), which enables us to simulate unsteady 3D liquid flows with phase transition at all Mach numbers. The compressible formulation of the governing equations together with the thermodynamic closure relations are solved by a modified Riemann approach by using time steps down to nanoseconds. This high temporal resolution is necessary to resolve the wave dynamics that leads to acoustic cavitation as well as to detect regions of instantaneous high pressure loads. The proposed two-phase model based on the integral average properties of thermodynamic quantities is first validated against the solution of the Rayleigh–Plesset equation for the collapse of a single bubble. The computational fluid dynamics tool CATUM is then applied to the numerical simulation of the highly unsteady two-phase flow around a 3D twisted hydrofoil. This specific hydrofoil allows a detailed study of sheet and cloud cavitation structures related to 3D shock dynamics emerging from collapsing vapor regions. The time dependent development of vapor clouds, their shedding mechanism, and the resulting unsteady variation of lift and drag are discussed in detail. We identify instantaneous local pressure peaks of the order of 100bar, which are thought to be responsible for the erosive damage of the surface of the hydrofoil.

A Grid-Free Lagrangian Approach of Vortex Method and Particle Trajectory Tracking Method Applied to Internal Fluid-Solid Two-Phase Flows

Abstract We have developed a numerical simulation scheme combining a vortex method and a particle trajectory tracking method, which is applicable to internal unsteady two-phase flows. It is a completely grid-free Lagrangian–Lagrangian simulation, which is able to simulate the primary effect of vortical flow on the unsteady particle motion and dispersion. It can handle unsteady high Reynolds number flows. So far, no one has applied this kind of method internal multiphase flows, though many industrial multiphase flows are internal. In this study, internal liquid-solid two-phase flows in a vertical channel and a mixing tee have been calculated by the new method, in which use of the vortex introduction model enables the simulation of the dynamic behavior of separation or reattachment. In the mixing tee, solid particle phenomena such as depositions or particle-wall collisions have been simulated and measured. Numerical results based on simple two-dimensional flow and one-way model show good agreement with the experimental data. The results show that turbulent vortices dominate particle motion. It has been shown that the present method can be useful in the design of industrial multiphase flows with particle mixing, dispersion, deposition, and particle-wall collision because it is possible to simulate the effect of turbulent vortices on the particle motion.