Single-phase Flow Model Research Articles

Direct Numerical Simulation of Pore-scale Unidirectional Plow in Porous Media

The paper presents the results of mathematical and numerical modeling of single-phase fluid flow in porous media with periodic microstructure. Object of study is the area in which the cylinders are arranged in a periodic manner. At the boundaries of the area for the flow parameters is set periodic boundary condition. Also in the paper presents comparison with Darcy’s law and the calculation of the permeability coefficient for different values of the radius of the cylinders.

Large-scale model of flow in heterogeneous and hierarchical porous media

Heterogeneous porous structures are very often encountered in natural environments, bioremediation processes among many others. Reliable models for momentum transport are crucial whenever mass transport or convective heat occurs in these systems. In this work, we derive a large-scale average model for incompressible single-phase flow in heterogeneous and hierarchical soil porous media composed of two distinct porous regions embedding a solid impermeable structure. The model, based on the local mechanical equilibrium assumption between the porous regions, results in a unique momentum transport equation where the global effective permeability naturally depends on the permeabilities at the intermediate mesoscopic scales and therefore includes the complex hierarchical structure of the soil. The associated closure problem is numerically solved for various configurations and properties of the heterogeneous medium. The results clearly show that the effective permeability increases with the volume fraction of the most permeable porous region. It is also shown that the effective permeability is sensitive to the dimensionality spatial arrangement of the porous regions and in particular depends on the contact between the impermeable solid and the two porous regions.

Metal vapor micro-jet controls material redistribution in laser powder bed fusion additive manufacturing

The results of detailed experiments and finite element modeling of metal micro-droplet motion associated with metal additive manufacturing (AM) processes are presented. Ultra high speed imaging of melt pool dynamics reveals that the dominant mechanism leading to micro-droplet ejection in a laser powder bed fusion AM is not from laser induced recoil pressure as is widely believed and found in laser welding processes, but rather from vapor driven entrainment of micro-particles by an ambient gas flow. The physics of droplet ejection under strong evaporative flow is described using simulations of the laser powder bed interactions to elucidate the experimental results. Hydrodynamic drag analysis is used to augment the single phase flow model and explain the entrainment phenomenon for 316 L stainless steel and Ti-6Al-4V powder layers. The relevance of vapor driven entrainment of metal micro-particles to similar fluid dynamic studies in other fields of science will be discussed.

Numerical modeling of pseudo-homogeneous fluid flow in a pipe with leaks

This work deals with the numerical modeling of single-phase flow in a pipe with one leak. The mathematical model governing mass, momentum and energy transport was established containing three coupled partial differential equations. These governing equations were numerically solved by discretizing time and space with backward finite differences, leading to one implicit scheme at every time step. The numerical solution was validated with available lab data obtaining good agreement. We present relevant results as the time behavior of upstream and downstream flow and pressure, while varying the leak location. Besides, we also show the temperature, pressure and flow profiles along the pipe when the leak is located near the inlet and outlet of the pipe. The predictive capabilities of the numerical model are remarkable to simulate the transient state of volumetric flow rate and pressure when a single leak is provoked at the pipe. A future application of our numerical scheme is for rapid automatic detection of loss of containment in pipes transporting valuable fluids as, for instance: oil, refined hydrocarbons, fuel, liquid catalysts, etc.

Experimental and Numerical Investigation on Non-Newtonian Nanofluids Flowing in Shell Side of Helical Baffled Heat Exchanger Combined with Elliptic Tubes

In this paper, an aqueous solution of xanthan gum (XG) at a weight fraction as high as 0.2% was elected as the non-Newtonian base liquid, the multi-walled carbon nanotubes (MWCNTs) dispersed into non-Newtonian XG aqueous at different weight factions of MWCNTs was prepared. Convection heat transfer of non-Newtonian nanofluids in the shell side of helical baffled heat exchanger combined with elliptic tubes has been investigated experimentally and numerically using single-phase flow model. Results showed that the enhancement of the convective heat transfer coefficient increases with an increase in the Reynolds number and the nanoparticle concentration. For nanofluids with 0.2 wt %, 0.5 wt % and 1.0 wt % MWCNTs, the Nusselt number, respectively, increases by 11%, 21% and 35% on average at the same Reynolds number, while the comprehensive thermal performance factors are 3%–5%, 15%–17% and 24%–26% higher than that of base fluid at the same volume rate. A remarkable heat transfer enhancement can be obtained by adding MWCNTs into XG aqueous solution based on thermal resistance analysis. Correlations have been suggested for the shell-side Nusselt number and friction factor of non-Newtonian nanofluids in the helical baffled heat exchanger with elliptic tubes. Good agreements existed between corrections and experimental data.

Trefftz method in solving Fourier-Kirchhoff equation for two-phase flow boiling in a vertical rectangular minichannel

This paper presents the results of investigations into flow boiling heat transfer in an asymmetrically heated vertical minichannel of 1.7 mm depth. The heated element for FC-72 flowing in the minichannel was an alloy plate 0.45 mm thick, microstructured on one side, in direct contact with the flowing fluid. The computational part of the study contains approximate steady state solutions of the heat transfer problems described by Poisson.s equation and the energy equation for the heated plate and the fluid, respectively. For both equations, the boundary conditions were specified on the basis of experimental data. Temperature of the outer plate surface, measured by infrared thermography, and heat losses to ambient air were included in the calculations. For the energy equation we assumed parabolic profile of fluid velocity and the equality of temperatures and heat fluxes at the interface between the heated surface and the fluid. The void fraction was taken from a single-phase flow model. Two-dimensional temperature distributions were obtained by the Trefftz method and, due to the Robin condition at the interface between them, it was possible to calculate the heat transfer coefficient. Its values were compared to those obtained by other correlations known from literature.

A Computational Dynamic Fluid Analysis of Compressible Flow in PorousMedia

The study is a computational dynamic analysis which investigated the dynamics of fluid flow patterns in a homogeneous oil reservoir using the Radial Diffusivity Equation (RDE). The model was solved analytically for pressure using the Constant Terminal Rate Solution (CTRS) and numerically using the fully implicit Finite Difference Method (FDM). Results from the study indicated that the initial reservoir pressure would be able to do the extraction of oil for an extended period of time before any other recovery method would be used to aid in further extraction process depending on the rate at which oil is produced. The study further confirmed that reservoir simulation describing a radial flow of a compressible fluid in porous media may be adequately performed using ordinary laptop computers. It could be seen from the analysis of the plots of pressure vs. time, and space that the Pressure Transient Analysis (PTA) was duly followed. The approximate solutions of the analytical and numerical solutions to the model were in excellent agreement, thus the reservoir simulation model developed could be used to describe typical pressure-time relationships. The analytical solution was used to verify the numerical solution as an application. Overall, this study provides an improved platform for modeling single phase flow in oil and gas reservoirs.

Turbulence Modelling of a Single-Phase Flow Cyclone Gasifier

The current work aims to make a foundation for an engineering design of a cyclone gasifier to be able not only to predict its flow field with a suitable accuracy but also to investigate a large number of design alternatives with limited computer resources. A good single-phase flow model that can form the basis in an Euler-Lagrange model for multi-phase flow is also necessary for modelling the reacting flow inside a cyclone gasifier. The present paper provides an objective comparison between several popular turbulence modelling options including standard k-e and SST with curvature corrections, SSG-RSM and LES Smagorinsky models, for the single-phase flow inside cyclone separators/gasifiers that can serve as a guide for further work on the reacting multi-phase flow inside cyclone gasifiers and similar devices. A detailed comparison between the models and experimental data for the mean velocity and fluctuating parts of the velocity profiles are presented. Furthermore, the capabilities of the turbulence models to capture the physical phenomena present in a cyclone gasifier that affects the design process are investigated.

Effects of Airflow Induced by Rainfall on Shallow Groundwater Table Fluctuations.

An investigation of groundwater table fluctuations induced by rainfall should consider interactions between the liquid and gas phases in soils. In this study, a water-air two-phase flow model was initially verified by simulating an infiltration experiment. It was then employed to model the interactions between liquid and gas phases regarding actions of airflow on the groundwater table and the fluctuations of the phreatic level and water level in the well induced by rainfall. The effects of airflo7w caused by rainfall on phreatic level fluctuations were also studied quantitatively by comparing the results obtained using the proposed model with those obtained from a water single-phase flow model. The simulation results show that in addition to actual recharge, compressed airflow in unsaturated zones causes the phreatic level to increase, but the rise in the phreatic level is lower than that in the pore-air pressure head in unsaturated zones due to the mitigation of capillary fringe. The existence of airflow enhances the phreatic level rise during and after rainfall. In addition, the water level in the well, pushed by the phreatic level fluctuations, varies similarly to the phreatic level, but it experiences somewhat delayed and slightly attenuated. The Lisse effect precisely reflects the phreatic level fluctuations before actual recharge. Furthermore, the fluctuations in the phreatic level and water level in the well and the contributions of airflow to phreatic level fluctuations are affected by many factors: rain intensity, initial moisture, overlying aquitard, groundwater table depths, and screen depths of the well.

Geomechanical response of overburden caused by CO2 injection into a depleted oil reservoir

This study investigates the hydro-mechanical aspects of carbon dioxide (CO2) injection into a depleted oil reservoir through the use of coupled multiphase fluid flow and geomechanical modeling. Both single-phase and multiphase fluid flow analyses coupled with geomechanics were carried out at the West Pearl Queen depleted oil reservoir site, and modeling results were compared with available measured data. The site geology and the material properties determined on the basis of available geophysical data were used in the analyses. Modeling results from the coupled multiphase fluid flow and geomechanical analyses show that computed fluid pressures match well with available measured data. The hydro-mechanical properties of the reservoir have a significant influence on computed fluid pressures and surface deformations. Hence, an accurate geologic characterization of the sequestration site and determination of engineering properties are important issues for the reliability of model predictions. The computed fluid pressure response is also significantly influenced by the relative permeability curves used in multiphase fluid flow models. While the multiphase fluid flow models provide more accurate fluid pressure response, single-phase fluid flow models can be used to obtain approximate solutions. The ground surface deformations obtained from single-phase fluid flow models coupled with geomechanics are slightly lower than those predicted by multiphase fluid flow models coupled with geomechanics. However, the advantage of a single-phase model is the simplicity. Limited field monitoring of subsurface fluid pressure and ground surface deformations during fluid injection can be used in calibrating coupled fluid flow and geomechanical models. The calibrated models can be used for investigating the performance of large-scale CO2 storage in depleted oil reservoirs.

Flow models and numerical schemes for single/two-phase transient flow in one dimension

In the two-phase flow field, a traditional mathematical model for simulating the transition of severe slugging flow presents a challenge when liquid slugs completely block pipelines. Accordingly, an advanced and practical slug model that is derived from a mixture model associated with a slip closure is essential to solving the problem in cooperation with the two-fluid model. The model can offset numerical instability that arises from the discontinuous function of the friction factor across the transition from one flow pattern to the other. Two numerical schemes, the non-iterative and the iterative, are developed, and the proposed schemes can stably predict the transient problems under the Courant–Friedrichs–Lewy (CFL) condition for semi-implicit/implicit schemes. In the present work, pressure transients produced by a complex phenomenon, named water hammer effect, are captured using the single-phase flow model in one-dimension to verify the applicability of the numerical schemes and the friction factor model. At last, the analysis of the two-phase transient flow in a pipeline-riser system indicates that the significant advantage of the present schemes is the robustness that the numerical prediction of the severe slugging behaviour is accurate and stable.

Analysis on vibration response of U-tube bundles caused by two-phase cross-flow turbulence

In steam generators and other heat exchangers, there are a lot of tube bundles subjected to two-phase cross-flow. The fluctuating pressure on tube bundle structure caused by turbulence can induce structural vibration. The power spectral density (PSD) of buffeting force is usually required as the input of random vibration analysis. Since there is no generally accepted method to compute the normalized buffeting forces, the acknowledged upper bound of buffeting forces due to two-phase flow is absent. This paper presents a new set of upper bound of buffeting forces in two-phase flow by modifying the mixture velocity proposed by de Langre. The new upper bound is compared with the one based on single-phase flow, and de Langre’s upper bound when two-phase flow is considered. Through a sample of steam generator tube subjected to non-uniform two-phase cross-flow, the random vibration responses based upon three types of upper bounds are computed. The proposed upper bound lies between the one derived from single-phase flow modeling and the one proposed by de Langre. It turns out that the newly proposed upper bound could cover sufficient experimental data sets of the buffeting force and is below the de Langre’s bound over a wide frequency range.

Low-Dimensional Modeling of Transient Two-Phase Flow in Pipelines

Presented are reduced-order models of one-dimensional transient two-phase gas–liquid flow in pipelines. The proposed model is comprised of a steady-state multiphase flow mechanistic model in series with a transient single-phase flow model in transmission lines. The steady-state model used in our formulation is a multiphase flow mechanistic model. This model captures the steady-state pressure drop and liquid holdup estimation for all pipe inclinations. Our implementation of this model will be validated against the Stanford University multiphase flow database. The transient portion of our model is based on a transmission line modal model. The model parameters are realized by developing equivalent fluid properties that are a function of the steady-state pressure gradient and liquid holdup identified through the mechanistic model. The model ability to reproduce the dynamics of multiphase flow in pipes is evaluated upon comparison to olga, a commercial multiphase flow dynamic code, using different gas volume fractions (GVF). The two models show a good agreement of the steady-state response and the frequency of oscillation indicating a similar estimation of the transmission line natural frequency. However, they present a discrepancy in the overshoot values and the settling time due to a difference in the calculated damping ratio. The utility of the developed low-dimensional model is the reduced computational burden of estimating transient multiphase flow in transmission lines, thereby enabling real-time estimation of pressure and flow rate.

Pressure transient analysis of low permeability reservoir with pseudo threshold pressure gradient

Threshold pressure gradient (TPG) is an important mechanism for fluid flow through low-permeability reservoirs, which would explain the phenomena that pressure derivative curves exhibit a straight line of slope that is larger than zero after radial flow regime. A mathematical single-phase flow model incorporating pseudo TPG is proposed to describe the flow behavior in low permeability reservoirs. Fully implicit numerical simulation based on PEBI grid is developed to study the transient pressure response. Two field data are used to calibrate and validate the proposed model and the code. Based on one of field data, parametric studies are conducted to investigate the effect of minimum TPG, pseudo TPG and nonlinear exponent on the pressure transient response for a vertical well. We find that pseudo TPG can explain the unique and consistent characteristic of the pressure transient response in low permeability reservoirs. The finding is useful for petroleum engineers to interpret the field data to obtain some basic parameters for low permeability reservoirs.

The Corrected Simulation Method of Critical Heat Flux Prediction for Water-Cooled Divertor Based on Euler Homogeneous Model**supported by the National Magnetic Confinement Fusion Science Program of China (No. 2010GB104005) and National Natural Science Foundation of China (No. 51406085)

An accurate critical heat flux (CHF) prediction method is the key factor for realizing the steady-state operation of a water-cooled divertor that works under one-sided high heating flux conditions. An improved CHF prediction method based on Euler's homogeneous model for flow boiling combined with realizable k-ϵ model for single-phase flow is adopted in this paper in which time relaxation coefficients are corrected by the Hertz-Knudsen formula in order to improve the calculation accuracy of vapor-liquid conversion efficiency under high heating flux conditions. Moreover, local large differences of liquid physical properties due to the extreme nonuniform heating flux on cooling wall along the circumference direction are revised by formula IAPWS-IF97. Therefore, this method can improve the calculation accuracy of heat and mass transfer between liquid phase and vapor phase in a CHF prediction simulation of water-cooled divertors under the one-sided high heating condition. An experimental example is simulated based on the improved and the uncorrected methods. The simulation results, such as temperature, void fraction and heat transfer coefficient, are analyzed to achieve the CHF prediction. The results show that the maximum error of CHF based on the improved method is 23.7%, while that of CHF based on uncorrected method is up to 188%, as compared with the experiment results of Ref. [12]. Finally, this method is verified by comparison with the experimental data obtained by International Thermonuclear Experimental Reactor (ITER), with a maximum error of 6% only. This method provides an efficient tool for the CHF prediction of water-cooled divertors.

Reliable Bridge Scour Simulation Using Eulerian Two-Phase Flow Theory

AbstractA CFD-based simulation methodology for bridge scour using an Eulerian two-phase flow model is proposed in the present study. The basic conservation equations and four unique simulation issues are firstly addressed during the model establishment process. The solutions are given to each of the four simulation challenges, and the discrepancies between the two-phase and single-phase modeling methods are clarified. Secondly, based on the Eulerian two-phase flow theory, a three dimensional (3D) bridge scour model is numerically established by redeveloping a commercial computational fluid dynamics (CFD) program. A comparison between the numerical results and measurements in a classic experiment from the literature validate the proposed simulation methodology that can comprehensively predict the flow field and scour (riverbed) profile. The accuracy advantages over the single-phase flow model are demonstrated from three aspects including the scour-hole profile, flow field, and scour depth. Finally, a param...

Adaptive Hierarchical Fracture Model for Enhanced Geothermal Systems

In enhanced geothermal systems, cold working fluid (usually water) is injected into a fractured reservoir to enhance the efficiency of the power plant by increasing the conductivity of existing fractures and by creating new ones. For the modeling of single phase flow and transport in such dynamically changing fractured reservoirs, a new approach is presented. It is based on a hierarchical fracture representation that results in a network of multiple dominant fractures through which most of the mass flow occurs. These large fractures have a discrete representation, i.e., each fracture is represented by a lower dimensional continuum. A single continuum representation is also employed for the damaged matrix, which consists of many small and medium sized fractures accounted for by appropriate effective properties. The main advantage of the new approach is that no expensive remeshing of the domain is required whenever new fractures are added. Here, discretization and coupling between the different continua (damaged matrix with discrete dominant fractures) are explained. In order to remove singularities, kernel functions have been introduced in the governing equations to capture discontinuities like fractures and intersections thereof. This way transfer coefficients are well defined. Numerical verification studies involving flow and heat transport are presented and discussed. It has to be emphasized that geomechanics, rock chemistry, and upscaling are not topics of this paper.

МАТЕМАТИЧЕСКАЯ МОДЕЛЬ НЕСТАЦИОНАРНОГО ТЕПЛОМАССОПЕРЕНОСА В КАНАЛЕ С ЖИДКОМЕТАЛЛИЧЕСКИМ ТЕПЛОНОСИТЕЛЕМ С УЧЕТОМ ПРОЦЕССА КРИСТАЛЛИЗАЦИИ-ПЛАВЛЕНИЯ

The mathematical model has been developed describing heat and mass transfer in a channel with liquid metal coolant when there is a crystallization-melting process. The model is based on a one-dimensional description of heat and mass transfer, taking into account the qualitative differences of the process depending on the condition of the contact surfaces. The thermodynamic equilibrium of the phases at the boundary of phase transfer is postulated. It is shown that a two-speed heterogeneous flow model describing the formation of solid layer on the surface of heat exchange is reduced to the solution of two more simple interrelated initial-boundary value problems: the Stefan problem of phase transfer and the single-phase flow model with a source and a variable cross-sectional area. The process of crystallization with the formation of micro fine liquid-metal suspension can be described in terms of the homogeneous model of heat and mass transfer. Represented mathematical model can be used for developing numerical algorithms and programs for calculating of heat-hydro-dynamics in steam generators and circuits of nuclear power plants with heavy liquid metal coolants. Keywords: homogeneous model, quasi-homogeneous model, heterogeneous model, the liquidmetal coolant, Stefan problem, interfacial exchange, steam generator, wet ability of surface, phase transfer. &nbsp

On the Analysis and Numerical Formulation of Miscible Fluid Flow in Porous Media Using Chebyshev Wavelets Collocation Method

In this paper, the Chebyshev wavelet method, constructed from the Chebyshev polynomial of the first kind is proposed to numerically simulate the single-phase flow of fluid in a reservoir. The method was used together with the operational matrices of integration which resulted in an algebraic system of equations. The system of equation was solved for the wavelet coefficient and used to construct the solutions. The efficiency and accuracy of the method were demonstrated through error measurements. Both the root mean square and the maximum absolute error analysis used in the study were within significantly close range. The Chebyshev wavelet collocation method subsequently was observed to closely approximate the analytic solution to the single phase flow model quite well.

A numerical study of the gas-liquid, two-phase flow maldistribution in the anode of a high pressure PEM water electrolysis cell

Abstract In this work, the use of a circular-planar, interdigitated flow field for the anode of a high pressure proton exchange membrane (PEM) water electrolysis cell is investigated in a numerical study. While PEM fuel cells have separated flow fields for reactant transport and coolant, it is possible to operate a PEM electrolysis cell with the anode flow field serving as both. This allows for a simpler system and a thinner design, however sets new and more strict requirements for the flow field to distribute uniformly. For the present study, two computational fluid dynamics models are developed; a single-phase flow model for establishing the effect of geometry and a two-phase flow model for studying the effect of dispersed gas bubbles. Both models account for turbulence and heat transport as well as associated dispersion phenomena. By means of the developed models, it is elucidated that the circular-planar shape of the interdigitated flow field causes maldistribution, if land areas of equal width are applied. Moreover, below a water stoichiometry of 350, and at a current density of 1 A/cm 2 , flow and temperature maldistribution is adversely affected by the presence of the gas phase; particularly gas hold-up near outlet channels can cause excessive formation of hotspots. As the water stoichiometry increases, the flow maldistribution increases as well. Nonetheless, its impact on the temperature distribution is counterbalanced by the overall increase in heat capacity of the flow. Hence, a relative uniform temperature distribution is achieved at and above nominal flow conditions. In a parametric investigation, it is further underlined that the predicted formation of hotspots is sensitive to the employed particle diameter of the two-phase channel flow model. The larger the particle size, the more severe the maldistribution of temperature becomes. It is therefore concluded that further experimental validation and research into particle size modeling is necessary.