Non-isothermal Two-phase Flow Research Articles

LES of turbulent non-isothermal two-phase flows within a multifield approach

Safety issues in nuclear power plant involve complex turbulent bubbly flows. To predict the behavior of these flows, the two-fluid approach is often used. Nevertheless, this model has been developed for the simulation of small spherical bubbles, considered as a dispersed field. To deal with bubbles with a large range of sizes, a multifield approach based on this two-fluid model has been proposed. A special treatment, called the Large Bubble Model (LBMo), has been implemented and coupled to the dispersed model. However, only laminar and isothermal flows were considered in previous papers. Thus, here, Large Eddy Simulations (LES) are investigated to model turbulence effects. For this purpose, the two-fluid model equations are filtered to highlight the specific subgrid terms. Then, an a priori LES study using filtered Direct Numerical Simulation (DNS) results is detailed. This analysis allows classifying these terms according to their relative weight and then concentrating the modelling efforts on the predominant ones. Five different turbulence models are compared. These results are finally used to perform true LES on a turbulent two-phase flow. Moreover, in order to tackle non-isothermal flows occurring in industrial studies, a new heat transfer model is implemented and validated to deal with phase change at large interfaces using the Large Bubble Model.

Numerical simulation of non-isothermal two-phase flow in pipelines using a two-fluid model

The analysis of two-phase flows through numerical simulations is a very useful tool to design and operate long pipelines. It is also important for monitoring the flow during adverse situations, such as the formation of hydrates and wax deposition that may occur due to temperature variations in the fluids along the pipe. The present work aims to validate a model along with a numerical technique for analyzing non-isothermal stratified-pattern two-phase flows that occur in typical gas-gathering offshore pipelines. The mathematical model is one-dimensional and based on a two-fluid model that comprises two mass and two momentum conservation equations, one for each phase, along with one energy conservation equation for the mixture. The system of equations is discretized in a conservative form within a finite-difference framework and is solved by the flux-corrected transport (FCT) numerical method. Because an ill-posed mathematical problem is obtained if the system of equations is not hyperbolic, a hyperbolicity analysis is performed for all cases simulated in this work, which also indicates how to impose the boundary conditions adequately and avoids the production of non-physical output. The results obtained for the distribution of pressure, fluid velocities, holdup and temperature along the pipeline demonstrated that even relatively small temperature differences between the fluids and the external environment at the pipe inlet cause significant thermal effects on the entire flow. The simulations also predicted results in good agreement with those of a commercial software used for comparison, for steady-state regime, and significantly different results from those produced by an isothermal-flow model, which emphasizes the importance of considering the heat transfer in the problem. In summary, the results showed that the mathematical model and the numerical method form together a reliable tool of second-order accuracy in space that perform accurate numerical simulations of two-phase flows in long pipelines that are subject to non-isothermal conditions.

Development of a transient non-isothermal two-phase flow model for gas kick simulation in HTHP deep well drilling

The simulation of gas/liquid two-phase flow, considering the heat transfer between the annulus fluid and the surrounding environment, is of significance in predicting temperature and pressure distributions after a gas kick in HTHP deep well drilling. This paper presents the development of a transient non-isothermal two-phase flow model for the dynamic simulation of multiphase flow in the wellbore after a gas kick. The drift-flux model is used to describe gas/liquid two-phase flow, and multiple transient energy conservation equations are used for predicting temperature profiles of fluids in the drillpipe, drillpipe, the fluid in the annulus, casing string, and formation. As for numerical scheme of this strongly coupled model, the advection upstream splitting model (AUSMV) hybrid scheme is adapted for solving flow equations, while the finite difference approach is adapted for simultaneously solving energy conservation equations of the wellbore-formation system. Physical properties of gas and liquid phases are updated at each timestep. Predicted temperature and pressure distributions are validated against the field data. Flow behaviors predicted by the models with and without the heat transfer effect are compared. The effects of some major parameters (reservoir pressure, choke pressure, geothermal gradient, liquid mass flow rate) on temperature, pressure, and gas fraction distributions along the wellbore are investigated.

Homogenization of nonisothermal immiscible incompressible two-phase flow in porous media

In this paper, we consider nonisothermal two-phase flows through heterogeneous porous media with periodic microstructure. Examples of such models appear in gas migration through engineered and geological barriers for a deep repository for radioactive waste, thermally enhanced oil recovery and geothermal systems. The mathematical model is given by a coupled system of two-phase flow equations, and an energy balance equation. The model consists of the usual equations derived from the mass conservation of both fluids along with the Darcy–Muskat and the capillary pressure laws. The problem is written in terms of the phase formulation, i.e. the saturation of one phase, the pressure of the second phase and the temperature are primary unknowns. The major difficulties related to this model are in the nonlinear degenerate structure of the equations, as well as in the coupling in the system. As fluid properties are defined as a function of temperature and pressure, there is a strong coupling between the mass balance and energy balance equations. Under some realistic assumptions on the data, we obtain a nonlinear homogenized coupled system of three coupled partial differential equations with effective coefficients (porosity, permeability, thermal conductivity, heat capacity) which are computed via solving cell problems. We give a rigorous mathematical derivation of the upscaled model by means of the two-scale convergence.

Thermodynamics and Optimal Control of Porous Media Flows in Oil Field Development

The nonisothermal two-phase porous media flow of oil and hot water in a horizontal oil reservoir is considered. An asymptotic method for calculating the flow and solving related optimal control problems is proposed. Namely, the problem of choosing optimal control actions to maximize the oil production for a given level of financial costs and to minimize the costs for a given level of oil production is considered.

하이브리드 자동차용 모터 내부의 오일 냉각 시스템에 대한 수치해석

This paper presents the numerical study on the flow and heat transfer in an oil cooling system for the motor employed in a hybrid vehicle. The heat sources in the motor are identified by conducting numerical simulations for the electromagnetic field. Then, they are used as input parameters in the thermal analysis. The multiple reference frame(MRF) scheme in a commercial software, ANSYS CFX, is used to treat the rotating rotor. A separated flow model is employed to solve the non-isothermal two-phase flow of the oil-air mixture. We mainly focus on the influence of the oil injection and the fluid flow caused by rotating parts on the performance of the oil cooling system. At two typical operating points of the motor, it is found that the temperature distribution in the motor is highly affected by the injection rate of the oil. In addition, the convective heat transfer caused by the secondary flows occurring in the gap between the stator and rotor also contribute to cooling.

Probabilistic modeling and global sensitivity analysis for CO2 storage in geological formations: a spectral approach

• Comprehensive analysis of impact of parametric uncertainties on simulation of CO 2 storage in porous media is performed. • A non-isothermal two-phase two-component flow system is considered. • Rigorous numerical study of the accuracy of the polynomial chaos surrogate model is performed. • A comprehensive global sensitivity analysis is conducted. This work focuses on the simulation of CO 2 storage in deep underground formations under uncertainty and seeks to understand the impact of uncertainties in reservoir properties on CO 2 leakage. To simulate the process, a non-isothermal two-phase two-component flow system with equilibrium phase exchange is used. Since model evaluations are computationally intensive, instead of traditional Monte Carlo methods, we rely on polynomial chaos (PC) expansions for representation of the stochastic model response. A non-intrusive approach is used to determine the PC coefficients. We establish the accuracy of the PC representations within a reasonable error threshold through systematic convergence studies. In addition to characterizing the distributions of model observables, we compute probabilities of excess CO 2 leakage. Moreover, we consider the injection rate as a design parameter and compute an optimum injection rate that ensures that the risk of excess pressure buildup at the leaky well remains below acceptable levels. We also provide a comprehensive analysis of sensitivities of CO 2 leakage, where we compute the contributions of the random parameters, and their interactions, to the variance by computing first, second, and total order Sobol’ indices.

Well-posed Euler model of shock-induced two-phase flow in bubbly liquid

A well-posed mathematical model of non-isothermal two-phase two-velocity flow of bubbly liquid is proposed. The model is based on the two-phase Euler equations with the introduction of an additional pressure at the gas bubble surface, which ensures the well-posedness of the Cauchy problem for a system of governing equations with homogeneous initial conditions, and the Rayleigh–Plesset equation for radial pulsations of gas bubbles. The applicability conditions of the model are formulated. The model is validated by comparing one-dimensional calculations of shock wave propagation in liquids with gas bubbles with a gas volume fraction of 0.005–0.3 with experimental data. The model is shown to provide satisfactory results for the shock propagation velocity, pressure profiles, and the shock-induced motion of the bubbly liquid column.

Dynamic reduced-order models of integrated physics-specific systems for carbon sequestration

$$\text {CO}_2$$ leakage from a deep storage reservoir into a shallow groundwater aquifer through a wellbore is simulated using physics-specific models conceptualized as nonisothermal two-phase flow in a deep storage reservoir and through the wellbore, and reactive transport in the aquifer. Supercritical $$\text {CO}_2$$ is injected into the reservoir subsystem with uncertain permeabilities of reservoir and injection strategies (rate and duration as decision variables). The simulated pressure and $$\text {CO}_2$$ saturation at an uncertain location are connected to the wellbore model as a boundary condition to output $$\text {CO}_2$$ flux to the reactive transport model in the shallow aquifer. Uncertainties are propagated from the deep reservoir model, to the wellbore leakage model, and eventually to the reactive transport model, thus contributing to system performance. To minimize the risk associated with the $$\text {CO}_2$$ leakage, we develop dynamic reduced order models for quantifying and managing the uncertainty propagation.

New approach to develop a 3D non-isothermal computational framework for injection molding process based on level set method

The simulation of three-dimensional (3D) non-isothermal, non-Newtonian fluid filling process is an extremely difficult task and remains a challenging problem, which includes polymer melt flow with free surface coupled with transient heat transfer. This paper presents a full 3D non-isothermal two-phase flow model to predict the complex flow in melt filling process, where the Cross-WLF model is applied to characterize the rheological behavior of polymer melt. The governing equations are solved using finite volume method with SIMPLEC algorithm on collocated grids and the melt front is accurately captured by a high resolution level set method. A domain extension technique is adopted to deal with the complex cavities, which greatly reduces the computational burden. To verify the validity of the developed 3D approach, the melts filling processes in two thin rectangular cavities (one of them with a cylindrical insert) are simulated. The predicted melt front interfaces are in good agreement with the experiment and commercial software prediction. For a case with a rather complex cavity, the dynamic filling process in a hemispherical shell is successfully simulated. All of the numerical results show that the developed numerical procedure can provide a reasonable prediction for injection molding process.

(Invited) Advanced Control of Two-Phase Flow in Gdl for PEM Fuel Cells

Water management is a central issue in the development of polymer electrolyte fuel cells (PEFCs): liquid water could considerably increase the oxygen transport resistance and hence the transport polarization whereas dryness dehydrates the electrolyte membrane, raising the Ohmic voltage loss. PEFCs produce water during operation and the electro osmosis enlarges the water imbalance between the anode and cathode sides, making water management a complex operation that requires a careful treatment. Issues such as diffusion media dewetting, anode rehydration, and internal humidification have received much attention in recent years. Modeling, numerical simulation, and advanced imaging techniques are capable of revealing details of transport phenomena, and are a powerful tool for elucidating water management. In this talk, I will cover the below subjects which are the major contributions of UC Irvine to water management: 1.) nonisothermal two-phase flow modeling; 2.) transient dewetting of gas diffusion layer (GDL); 3.) theoretical approach of defining control parameters to characterize two-phase flows; and 4.) experimental evaluation of two-phase flow in PEFCs using neutron radiography. In 1.), a nonisothermal two-phase model, accounting for vapor-phase diffusion and heat pipe effect, was developed and implemented to investigate liquid water distribution. The model was validated in detail against liquid water distribution across GDLs. In 2.), a transient model was developed to capture the phase change and interface movement in PEFCs. A case study will be presented to show the timescale of material dewetting at different regions of GDLs. In 3.), A dimensionless parameter Da0 will defined to characterize the in-plane two-phase region. When Da0 is over 1, part of the GDL region is free of water due to waste heat production and evaporation. A liquid-free GDL region is defined and related to Da0. Impacts of operating temperatures, GDL thermal conductivities, and current densities on the region will be discussed. In 4.), I will present an in-situ study to examine the water content in PEFCs using neutron radiography. Various conditions such as different PTFE loadings in the GDL including the micro-porous layer (MPL), different flow fields (single-channel and quad-serpentine channels), and co-/counter-flow configurations are investigated.

Numerical simulation of flow-induced stresses in mold filling process using a three-dimensional two-phase flow model

The flow-induced stresses which arise during the filling stage have significant influences on the mechanical and optical properties of injection-molded products. The prediction of flow-induced stresses in mold-filling process is a challenging problem, which includes viscoelastic polymer melt free surface flow. Thus, this paper presents a three-dimensional (3D) non-isothermal two-phase flow model to quantitative predict the flow-induced stresses in polymer mold-filling process based on the XPP model. In this model, the governing equations for gas and viscoelastic melt are united into a system namely the generalized Navier–Stokes equations. In order to improve the stability of the numerical method in 3D, an enhanced treatment of stress solid boundaries is proposed. The stresses on solid boundaries are calculated using an effective second-order Runge–Kutta method. The model is successfully solved by using the finite volume method, and the melt front is accurately captured by level set method. The validity of the method is verified by two benchmark problems. Then the mold-filling process of a rectangular plate is studied numerically, obtaining the evolutions of flow-induced stresses at different levels along the gap-wise direction, which can not be simulated by 2.5D model. The predicted flow-induced birefringence is in agreement with the experimental result reported in the literature. Furthermore, the effects of injection velocity and some model parameters of XPP model on flow-induced stresses are numerically predicted. The numerical results show that the 3D simulation technology can effectively predict the flow-induced stresses and birefringence in non-isothermal viscoelastic polymer mold-filling process. The results can provide the theory foundation for improving the properties of products in actual production processes.

Extending the persistent primary variable algorithm to simulate non-isothermal two-phase two-component flow with phase change phenomena

Abstract In high-enthalpy geothermal reservoirs and many other geo-technical applications, coupled non-isothermal multiphase flow is considered to be the underlying governing process that controls the system behavior. Under the high temperature and high pressure environment, the phase change phenomena such as evaporation and condensation have a great impact on the heat distribution, as well as the pattern of fluid flow. In this work, we have extended the persistent primary variable algorithm proposed by (Marchand et al. Comput Geosci 17(2):431–442) to the non-isothermal conditions. The extended method has been implemented into the OpenGeoSys code, which allows the numerical simulation of multiphase flow processes with phase change phenomena. This new feature has been verified by two benchmark cases. The first one simulates the isothermal migration of H 2 through the bentonite formation in a waste repository. The second one models the non-isothermal multiphase flow of heat-pipe problem. The OpenGeoSys simulation results have been successfully verified by closely fitting results from other codes and also against analytical solution.

Existence of solutions to a two-dimensional model for nonisothermal two-phase flows of incompressible fluids

We consider a thermodynamically consistent diffuse interface model describing two-phase flows of incompressible fluids in a non-isothermal setting. The model was recently introduced in [11] where existence of weak solutions was proved in three space dimensions. Here, we aim to study the properties of solutions in the two-dimensional case. In particular, we can show existence of global in time solutions satisfying a stronger formulation of the model with respect to the one considered in [11].

Nonisothermal two-phase flow in a vertical well

This paper presents a mathematical model for bubble flow in a vertical borehole under non-isothermal conditions and the results of calculations of the volume fraction and temperature of the phases. The influence of the bubble size on the formation phase of the temperature fields of the phases.

Исследование неизотермического двухфазного течения в вертикальной скважине

Исследование неизотермического двухфазного течения в вертикальной скважине

Computational Modeling and Simulation of Nonisothermal Free-surface Flow of a Liquid Jet Impinging on a Heated Surface

The study is aimed at formulating and validating the computational model for the nonisothermal two-phase flow with free-surfaces. The testing flow configuration consists of the liquid jet impacting on a heated wall generating simultaneous heat transfer from the wall surface. The interface capturing methodology implemented in the open-source software OpenFOAM® based on the volume-of-fluid (VOF) model in the framework of Computational Fluid Dynamics (CFD) is extended to incorporate heat transfer. The potential of the model is evaluated by contrasting the results of numerical simulations to the existing experimental and numerical results. The computational procedure based on the numerical model demonstrates good qualitative and quantitative predictive capabilities by reproducing correctly the studied flow and heat transfer characteristics.

Non-isothermal hydrophobicity-dependent two-phase flow in the porous cathode gas diffusion layer of a polymer electrolyte fuel cell

In this paper, we extend a recent one-dimensional isothermal steady-state generalized Darcy model for two-phase flow in the porous cathode gas diffusion layer of a polymer electrolyte fuel cell, so as to include the effect of heat transfer. As for the isothermal case, we arrive at either a fixed- or free-boundary problem, depending on the main problem parameters: inlet temperature ( $$T^\mathrm{in}$$ ), inlet water saturation ( $$s^\mathrm{in}$$ ), inlet relative humidity (RH), porous medium hydrophobicity and cathode overpotential ( $$\eta $$ ). The inclusion of heat transfer is found to limit the range of values of $$\eta ,T^\mathrm{in}$$ and RH over which two-phase flow can occur, as compared to that predicted by the isothermal model. The ensuing non-isothermal two-phase flow model equations are then computed numerically, with particular care being required for the treatment of an integrably singular inter-phase mass transfer term.

Multi-physics modeling of non-isothermal compositional flow on adaptive grids

Abstract A multi-physics framework for compositional and non-isothermal two-phase flow in a porous medium is presented which adapts locally the model complexity depending on the physical state. It is based on a sequential (IMPET) solution scheme. As a second adaptive strategy, the simulation grid can be refined locally. This may lead to a mesh with hanging nodes, which is treated by a multi-point flux approximation (MPFA) for improved flux representation. The two adaptivity concepts are employed to simulate a combined subsurface CO 2 injection and geothermal application in an existing reservoir, the Tensleep formation.

Three-dimensional streamline-based simulation of non-isothermal two-phase flow in heterogeneous porous media

Streamline-based simulation is extended to simulate non-isothermal two-phase flow of hot water injection in three-dimensional (3D) realistic field-scale reservoirs containing heavy oil. First the pressure equation is solved on the 3D Eulerian grid for a global time-step and the total velocity is calculated at cell faces. Then the streamlines are traced from injector wells to producers, implementing a semi-analytical method and the time-of-flight (TOF) is computed over the streamlines. The mass and energy transport equations are mapped onto streamlines using the TOF as the distance variable. The advective part of the transport equations are solved along the streamlines. The saturation and temperature are calculated in the TOF domain until the end of the global time-step and then mapped back to the 3D grid. The effects of gravity and heat conduction are included by an operator splitting technique, at the end of each global time-step.A 2D petroleum reservoir model without gravity is tested to show the feasibility of the method. To further test the approach, a 3D heterogeneous model with a fine grid and multiple wells is simulated, and the results are compared with those of a commercial grid-based thermal simulator. The predicted saturation distribution, temperature and oil production at the wells are in good agreement with the commercial code; furthermore the streamline technique is significantly faster while generating results similar to those obtained using a conventional method that has a finer grid. We conclude that the streamline method can simulate non-isothermal two-phase flow of water–oil in heterogeneous porous media accurately with lower cost and better performance than grid-based approaches.