Iterative Coupling Method Research Articles

Temperature Rise Calculation of Magnetic Core Considering the Temperature Effect of Magnetic Properties in an Electrical Steel Sheet

The magnetic properties of electrical steel sheets are affected by magnetization patterns, working temperature, and external pressure. In order to study the temperature effect of electrical steel sheets on the temperature rise of a transformer core, in this paper, based on the magnetic property test system of an electrical steel sheet, the permeability and loss of a 50AW600 grain non-oriented electrical steel sheet and a 30ZH120 grain oriented electrical steel sheet under different temperatures and excited frequencies were measured, and the influence of temperature on the properties of the material was analyzed. A magneto-thermal iterative coupling method considering the temperature effects of magnetic properties in the electrical steel sheet was investigated. Based on the above measurement data and iterative coupling method, the temperature distribution of the core of a 500-kV power transformer was simulated and analyzed, and compared with the simulation results of the traditional coupling method without considering the temperature effect of the electrical steel sheet. Magneto-thermal coupling simulation under no-load operation is a symmetrical problem. It was found that the temperature of the hottest spot of the transformer core calculated by the magneto-thermal iteration method proposed in this paper was significantly reduced, the temperature of the hottest spot on the core column was about 45 °C, and the temperature of the hottest spot on the upper and lower yoke was about 39 °C, which provides an effective simulation method for accurately calculating the temperature rise distribution of electrical products such as transformers.

Iteratively Coupled Flow and Geomechanics in Fractured Poroelastic Reservoirs: A Phase Field Fracture Model

Fluid-solid coupling in fractured reservoirs plays a critical role for optimizing and managing in energy and geophysical engineering. Computational difficulties associated with sharp fracture models motivate phase field fracture modeling. However, for geomechanical problems, the fully coupled hydromechanical modeling with the phase field framework is still under development. In this work, we propose a fluid-solid fully coupled model, in which discrete fractures are regularized by the phase field. Specifically, this model takes into account the complex coupled interaction of Darcy-Biot-type fluid flow in poroelastic media, Reynolds lubrication governing flow inside fractures, mass exchange between fractures and matrix, and the subsequent geomechanical response of the solid. An iterative coupling method is developed to solve this multifield problem efficiently. We present numerical studies that demonstrate the performance of our model.

Numerical and experimental verification of an iterative coupling method for analyzing the Lorentz-force-driven sheet metal stamping process

The Lorentz-force-driven stamping process is a newly developed forming process, which combines the advantages of the quasi-static stamping and electromagnetic forming to a certain extent. It involves complex physical problems such as strong electro-magneto-mechanical interactions and considerable deformation. Therefore, it is still a challenge to accurately predict the electromagnetic parameters (coil current and Lorentz force, etc.) and workpiece deformation (forming height and material flow) during the stamping process for different forming conditions. To solve this problem, taking the cylindrical cup forming of 5052-O aluminum alloy sheet metal as an example, a numerical method based on the iterative calculation of a circuit-electromagnetic model and an electromagnetic-mechanical model is developed and systematically validated. Numerical tests show that, compared with the non-iterative model, the proposed iterative mode can significantly improve the simulation accuracy for different forming conditions (such as varied discharge voltages and initial gaps between the coil and the punch). It has been confirmed that the iterative procedure can well consider the effect of the increased distance between the coil and the punch on the calculations of electromagnetic and mechanical parameters. Furthermore, numerical and experimental investigations for a Lorentz-force-driven stamping system using a discharge circuit with an additional crowbar branch are carried out, showing the simulation data of discharge current and workpiece deformation agree well with that of experiment measurement. This confirms the applicability of the proposed method to different discharge circuits.

Fluid-cloth coupling algorithm based on PBD and CCD

In order to simulate the interaction between cloth and fluid, we use Smooth Particle Hydrodynamics (SPH) as a method in fluid simulation, we propose a Continuous collision detection (CCD) and position-based dynamics (PBD) collision constrained iterative flow coupling method. By analyzing the parallelism of the algorithm, we implement a low storage and load balanced fluid and cloth coupling algorithm parallel computing is used to accelerate the simulation. The experimental results show that our method realizes the bidirectional coupling of fluid and cloth, and improves the simulation performance.

Non-conforming interface coupling and symmetric iterative solution in isogeometric FE–BE​ analysis

In this paper, a three-dimensional (3D) isogeometric finite element (FE) and boundary element (BE) coupling approach based on non-uniform rational B-splines (NURBS) is developed to simulate the deformed body. Based on the geometric exactness and higher smoothness of isogeometric analysis (IGA), NURBS discretization is applied to the approximation of geometric representation, displacement field and traction field simultaneously. An improved power series expansion method (M-PSEM) is used to evaluate the singular integral and is suitable for high order (≥3) NURBS basis functions, which is the limitation of the traditional method. Adaptive integration scheme based on quadtree subdivision technique is adopted to enable the non-singular integration computation more flexible and efficient at optimal computational cost. The relationship between the tractions and nodal external forces on the interface is established by using the virtual work principle. On the other hand, displacement coupling constraints among the non-conforming (or incomplete coincident) surface meshes are constructed by a virtual knot insertion technique. The main advantages of this method are simplicity and robustness, as it is problem-independent and only depends on the NURBS meshes on both sides of the interface. Introducing an enhanced symmetric matrix related to the BE subdomain, the symmetric iterative coupling method (SICM) is extended to solve the final system coupling equation. The final coupling matrix obtained by this iterative method is symmetric, and its dimension is the same as that of the stiffness matrix of IGA finite element method (IGAFEM). Numerical examples are investigated to assess the accuracy and efficiency of the presented method.

Quasi‐Newton waveform iteration for partitioned surface‐coupled multiphysics applications

SummaryWe present novel coupling schemes for partitioned multiphysics simulation that combine four important aspects for strongly coupled problems: implicit coupling per time step, fast and robust acceleration of the corresponding iterative coupling, support for multirate time stepping, and higher‐order convergence in time. To achieve this, we combine waveform relaxation—a known method to achieve higher‐order in applications with split time stepping based on continuous representations of coupling variables in time— with interface quasi‐Newton coupling, which has been developed throughout the last decade and is generally accepted as a very robust iterative coupling method even for gluing together black‐box simulation codes. We show convergence results (in terms of convergence of the iterative solver and in terms of approximation order in time) for two academic testcases—a heat transfer scenario and a fluid‐structure interaction simulation. We show that we achieve the expected approximation order and that our iterative method is competitive in terms of iteration counts with those designed for simpler first‐order‐in‐time coupling.

Study on Viscous Fluid Flow in Disordered-Deformable Porous Media Using Hydro-mechanically Coupled Pore-Network Modeling

We investigate viscous fluid flows and concurrent fluid-driven deformations in porous media. The hydro-mechanically (H-M) coupled pore-network model (PNM) is developed, which combines the two-dimensional square-lattice PNM and block-spring model. The single-/two-phase flows into saturated deformable porous media are simulated through iterative two-way coupling method in H-M coupled PNM. A comparison between simulations and laboratory observations on flow patterns, solid deformation behaviors, and pressure responses ensures the validity of our H-M coupled PNM in both single-/two-phase flows. Parametric studies using the validated model examine the effects of mechanical coupling, stiffness of solid particles, the viscosity of invading fluids, injection flow rate, and degree of disorder during immiscible viscous fluid injection. The viscous fluid-driven deformation increases the pore throat size and hence reduces the injection pressure. In particular, the viscosity of invading fluid significantly alters the patterns of fluid propagation and solid deformation, along with a transition from the viscous fingering to the stable displacement with increasing viscosity. Moreover, the structural disorder in porous networks magnifies the irregular flow pattern, the pressure fluctuation associated with Haines jumps, and the poromechanical deformation. The particle-level force analysis delineates two distinct regimes: fluid invasion with no deformation and drag-driven deformation, which depends on the balance between the seepage drag force and the skeletal force. The presented results contribute to a better understanding of the H-M coupled fluid flows during the injection of viscous fluids into disordered-deformable porous media.

An Assessment of Stress States in Passive Margin Sediments: Iterative Hydro-Mechanical Simulations on Basin Models and Implications for Rock Failure Predictions

Capturing the past and present hydro-mechanical behavior of passive margin sediments raises noticeable interest, notably in geo-hazard risk assessment and hydrocarbon exploration. In this work, we aim at assessing the stress states undergone by these sedimentary deposits through geological time. To do so, we use an iterative coupling between a basin simulator and a finite element mechanical solver. This method conciliates a computation of the full stress tensors with a dynamic and geologically detailed modelling of the sedimentation. It is carried out on a dedicated set of 2D synthetic basin models, designed to be representative of siliciclastic deposition in passive margins and integrating variations in their geological history. Contrary to common assumptions in operational basin modelling studies, our results imply that passive margin sedimentary wedges are multidimensional mechanical systems, which endure significant non-vertical stress without external tectonic input. Our results also highlight the variability of the stress states through space and time, with a strong control from the geometry and lithological heterogeneities of the deposits. Lastly, we used the simulation results to predict a location and timing for the development of weakness zones in the sedimentary stacks, as privileged areas for rock failure. The outcome underlines the influence of the basal tilt angle, with a slight tilt impacting the wedges stability to a similar extent as a substantial increase in sedimentation rate. Altogether, this study emphasizes the need for careful consideration of non-vertical stresses in basin simulations, including in passive tectonic contexts. It also suggests that the iterative coupling method employed is a promising way to match industrial needs in this regard.

Effective elastic properties of doubly periodic array of functionally graded inclusions by an iterative FE-BE coupling method

This paper is devoted to the study of the effective elastic properties of doubly periodic array of functionally graded inclusion problems by an iterative FE-BE coupling method. This method has some advantages compared with boundary element method (BEM), e.g. (1) inclusions can be isotropic, orthotropic, anisotropic or functionally graded materials; (2) various shaped inclusions can be easily solved; (3) the fundamental solutions for functionally graded inclusion materials are not needed. Some numerical examples are used to validate the applicability and reliability of the adopted scheme.

Development and validation of an explicitly coupled geomechanics module for a compositional reservoir simulator

Pore pressure-stress analyses in stress-sensitive reservoirs investigate interactions between the in-situ stress and fluid flow; these interactions help or resist production, or conclude surface subsidence during production. Among the tools for these analyses, an explicitly coupled geomechanics and fluid flow model provides an essential, reliable, and fast production estimate for field planning and development. In this work, we implemented this model in an in-house, three dimensional, compositional reservoir simulator, UTCOMP, using Chin's iterative coupling method. This development integrated a stand-alone geomechanics module based on finite element method with the reservoir simulator, an advantage of our coupling algorithm, and improved our understanding of the production through various enhanced oil recovery processes such as water and CO2 flooding processes previously coded in UTCOMP. Benefiting from the higher time scales of solution variations due to the geomechanics module, we lowered the frequency of calling this computationally expensive module. Also, we reduced the order of the finite element shape functions for displacement from quadratic to linear, which majorly mitigated the high computational cost of our geomechanics studies while we almost maintained the solution accuracy. To validate our implementation, we investigated a primary oil production case and compared the results from UTCOMP with those from two other simulators: (1) CMG software program using different coupling methods; and (2) another pre-validated in-house reservoir simulator, GPAS. In order to evaluate our improvements in this work, we compared our results with those from a pre-validated in-house reservoir simulator, GPAS. We observed a minor discrepancy between the solutions at very early times which originates from the different structures in these two reservoir simulators, IMPEC in UTCOMP and fully implicit in GPAS.

Wellbore Failure During Water-Alternating-Gas Injection by Use of Flow-Stress Coupling Method

Summary Accurate evaluation of failure pressure is crucial in the design of injection wells. Besides, in-situ stresses play an important role in obtaining the results. Pressure and rock stresses are related together as the role of effective-stress theorem. In fact, pressure changes with stress alteration caused by change in porosity and permeability. Therefore, it should be obtained with the coupling method. Moreover, to calculate pressure, temperature, and stress in the fully coupling method, a huge matrix should be solved, and it takes long processing time to implement it. Therefore, this study developed a wellbore geomechanical model for stability during injection by use of the iterative coupling method. The processing speed was enhanced in this study because the parameters were calculated separately. The parameters of pressure, temperature, saturation, and stress were obtained for the multiphase-flow condition with numerical modeling. Furthermore, in this study, the finite-difference method (FDM) had been used to solve pressure, temperature, and saturation, whereas the finite-volume method (FVM) was applied to solve the wellbore stress. On top of that, the iterative coupling method was used to improve the accuracy of the stress results. As a result, a correction of approximately 20 psi (0.14 MPa) was noted for pressure in relation to stress, which is 1 psi (6.89 kPa). Moreover, the Drucker-Prager failure criterion was used to model the fracturing on the basis of the stress results. Other than that, sensitivity analysis on horizontal maximum (σH) and minimum (σh) stresses showed that by increasing σH, the maximum injection pressures to avoid fracturing had been reduced, whereas in the case for σh, an increment was observed.

Transient Coupled Borehole/Formation Fluid-Flow Model for Interpretation of Oil/Water Production Logs

Summary Interpretation of two-phase production logs (PLs) traditionally constructs borehole fluid-flow models decoupled from the physics of reservoir rocks. However, quantifying formation dynamic petrophysical properties from PLs requires simultaneous modeling of both borehole and formation fluid-flow phenomena. This paper develops a novel transient borehole/formation fluid-flow model that allows quantification of the effect of formation petrophysical properties on measurements acquired with production-logging tools (PLTs). We invoke a 1D, isothermal, two-fluid formulation to simulate borehole fluid-phase velocity, pressure, volume fraction, and density in oil/water-flow systems. The developed borehole fluid-flow model implements oil-dominant and water-dominant bubbly flow regimes with the inversion point taking place approximately when the oil volume fraction is equal to 0.5. Droplet diameter is dynamically modified to simulate interfacial drag effects, and to effectively account for variations of slip velocity in the borehole. Subsequently, a new successive iterative method interfaces the borehole and formation fluid-flow models by introducing appropriate source terms into the borehole fluid-phase mass-conservation equations. The novel iterative coupling method integrated with the developed borehole fluid-flow model allows dynamic modification of reservoir boundary conditions to accurately simulate transient behavior of borehole crossflow taking place across differentially depleted rock formations. In the case of rapid variations of near-borehole properties, frequent borehole/formation communication inevitably increases the computational time required for fluid-flow simulation. Despite this limitation, in a two-layer reservoir model penetrated by a vertical borehole, the coupling method accurately quantifies a 14% increase of volume-averaged oil-phase relative permeability of the low-pressure layer caused by through-the-borehole cross-communication of differentially depleted layers. Sensitivity analyses indicate that the alteration of near-borehole petrophysical properties primarily depends on formation average pressure, fluid-phase density contrast, and borehole-deviation angle. A practical application of the new coupled fluid-flow model is numerical simulation of borehole production measurements to estimate formation average pressure from two-phase selective-inflow-performance (SIP) analysis. This study suggests that incorporating static (shut-in) PL passes into the SIP analysis could result in misleading estimation of formation average pressure.

Development of Stress Model near the Wellbore Using an Iterative Coupling Method

AbstractWater-alternating-gas (WAG) injection is increasingly applied globally as the effective enhanced oil recovery (EOR) method in oil wells. High injection pressure or low injection temperature could lead to wellbore failure. The rock stress around the wellbore is a function of the wellbore pressure and temperature, and it should be precisely determined to avoid wellbore failure. This study aimed to develop a wellbore geomechanical model for WAG injection using an iterative coupling method. The parameters of pressure, temperature, saturation, and stress were obtained for the multiphase flow condition using mathematical modeling. The finite-difference method was used to solve pressure, temperature, and saturation, and the finite-volume method was used to solve the rock stresses. Because the values for flow and rock stresses are related by the role of effective stress, the pressure is the key parameter to determine the stress. However, pressure changes with stress because of the change in porosity and p...

Wellbore stability model based on iterative coupling method in water alternating gas injection

Ensuring wellbore integrity is the most important factor in injection well design. The water alternating gas (WAG) injection is increasingly applied globally as the effective enhanced oil recovery (EOR) method in oil wells. High injection pressure or low injection temperature could lead to compressive wellbore failure. The rock stress around the wellbore is a function of the wellbore fluid flow and it should be precisely determined to avoid the wellbore failure. The purpose of this study is to propose a method to ensure the stability of the wellbore for the WAG process using iterative coupling method. The parameters of pressures, temperature, saturations and stresses are obtained for the multiphase flow condition using mathematical modeling. In this study, finite difference method is used to solve pressure, temperature and saturations; and finite volume method is acquired to solve the rock stresses. Iterative coupling method is employed to improve the accuracy of the results. This study introduces improved iterative coupling method between flow and stress models to reduce the processing time of obtaining corrected stress and failure results. Wellbore stability model is developed to determine the maximum pressure values, which lead to wellbore failure in WAG injection process for some different boundary conditions.

065 分離反復連成解法による受動的フェザリングを考慮した羽ばたき運動の解析と評価

本研究では、羽ばたき型MAVの設計支援のため、翼の弾性変形が飛行性能に与える影響を調べる。このため、分離反復連成解法による流体構造連成解析システムを用いて受動的featheringが発現するモデルについて解析を行った。解析結果から翼の弾性変形と揚力発生の関係を評価し、羽ばたき型MAVの翼の設計に必要な知見を得た。

Analysis of Ocean-atmosphere Coupling Algorithms: Consistency and Stability

This paper is focused on the numerical and computational issues associated to ocean-atmosphere coupling. It is shown that usual coupling methods do not provide the solution to the correct problem, but to an approaching one since they are equivalent to performing one single iteration of an iterative coupling method. The stability analysis of these ad-hoc methods is presented, and we motivate and propose the adaptation of a Schwarz domain decomposition method to ocean-atmosphere coupling to obtain a stable and consistent coupling method.

Thermal fluid-solid interaction model and experimental validation for hydrostatic mechanical face seals

Hydrostatic mechanical face seals for reactor coolant pumps are very important for the safety and reliability of pressurized-water reactor power plants. More accurate models on the operating mechanism of the seals are needed to help improve their performance. The thermal fluid-solid interaction (TFSI) mechanism of the hydrostatic seal is investigated in this study. Numerical models of the flow field and seal assembly are developed. Based on the mechanism for the continuity condition of the physical quantities at the fluid-solid interface, an on-line numerical TFSI model for the hydrostatic mechanical seal is proposed using an iterative coupling method. Dynamic mesh technology is adopted to adapt to the changing boundary shape. Experiments were performed on a test rig using a full-size test seal to obtain the leakage rate as a function of the differential pressure. The effectiveness and accuracy of the TFSI model were verified by comparing the simulation results and experimental data. Using the TFSI model, the behavior of the seal is presented, including mechanical and thermal deformation, and the temperature field. The influences of the rotating speed and differential pressure of the sealing device on the temperature field, which occur widely in the actual use of the seal, are studied. This research proposes an on-line and assembly-based TFSI model for hydrostatic mechanical face seals, and the model is validated by full-sized experiments.

Design and analysis of a Schwarz coupling method for a dimensionally heterogeneous problem

SUMMARYIn the present work, we propose and analyse an efficient iterative coupling method for a dimensionally heterogeneous problem. We consider the case of a 2D Laplace equation with non‐symmetric boundary conditions coupled with a corresponding 1D Laplace equation. We first show how to obtain the 1D model from the 2D one by integration along one direction, by analogy with the link between shallow water equations and the Navier–Stokes system. Then we focus on the design of a Schwarz‐like iterative coupling method. We discuss the choice of boundary conditions at coupling interfaces. We prove the convergence of such algorithms and give some theoretical results related to the choice of the location of the coupling interface, and to the control of the difference between a global 2D reference solution and the 2D coupled solution. These theoretical results are illustrated numerically. Copyright © 2014 John Wiley & Sons, Ltd.

Utilizing CFD‐Simulations to Assess Flow‐Induced Vibrations of Slender Beams in Cross‐Flow

AbstractFlow‐induced vibrations of a slender U‐beam in cross‐flow are assessed, using the proprietary CFD‐solver ANSYS‐CFX. The U‐beam has two degrees of freedom: heaving motion and rotation. The flow‐ and motion‐governing equations are solved together, using an iterative coupling method. We find, that using this iterative coupling does not ensure a valid long‐time behaviour of the solution. The results of free vibration simulations would allow investigation of the excitation mechanisms. But for determining possibility of large amplitude vibrations, methods relying on forced motion are deemed more promising. (© 2013 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

2309 分離反復連成解法の弾塑性き裂問題への適用

2309 分離反復連成解法の弾塑性き裂問題への適用