Records with Subject: Numerical Methods and Statistics
Showing records 1 to 25 of 39. [First] Page: 1 2 Last
Approximate Moment Methods for Population Balance Equations in Particulate and Bioengineering Processes
Robert Dürr, Andreas Bück
June 10, 2020 (v1)
Keywords: approximate moment methods, cell-to-cell variability, heterogeneity, moment methods, particle formation, population balance equations
Population balance modeling is an established framework to describe the dynamics of particle populations in disperse phase systems found in a broad field of industrial, civil, and medical applications. The resulting population balance equations account for the dynamics of the number density distribution functions and represent (systems of) partial differential equations which require sophisticated numerical solution techniques due to the general lack of analytical solutions. A specific class of solution algorithms, so-called moment methods, is based on the reduction of complex models to a set of ordinary differential equations characterizing dynamics of integral quantities of the number density distribution function. However, in general, a closed set of moment equations is not found and one has to rely on approximate closure methods. In this contribution, a concise overview of the most prominent approximate moment methods is given.
Keller-Box Simulation for the Buongiorno Mathematical Model of Micropolar Nanofluid Flow over a Nonlinear Inclined Surface
Khuram Rafique, Muhammad Imran Anwar, Masnita Misiran, Ilyas Khan, Asiful H. Seikh, El-Sayed M. Sherif, Kottakkaran Sooppy Nisar
January 7, 2020 (v1)
Keywords: inclined surface, Keller-Box method, MHD, micropolar nanofluid, power law fluid
Brownian motion and thermophoresis diffusions are the fundamental ideas of abnormal upgrading in thermal conductivity via binary fluids (base fluid along with nanoparticles). The influence of Brownian motion and thermophoresis are focused on in the Buongiorno model. In this problem, we considered the Buongiorno model with Brownian motion and thermophoretic effects. The nonlinear ordinary differential equations are recovered from the partial differential equations of the boundary flow via compatible similarity transformations and then employed to the Keller-box scheme for numerical results. The physical quantities of our concern including skin friction, Nusselt number, and Sherwood number along with velocity, temperature and concentration profile against involved effects are demonstrated. The impacts of the involved flow parameters are drawn in graphs and tabulated forms. The inclination effect shows an inverse relation with the velocity field. Moreover, the velocity profile increases w... [more]
The Fast Potential Evaluation Method of Enhanced Oil Recovery Based on Statistical Analysis
Zhengbo Wang, Qiang Wang, Desheng Ma, Wanchun Zhao, Xiaohan Feng, Zhaoxia Liu
December 16, 2019 (v1)
Keywords: grey correlation, potential evaluation, rapid analogy, screening method, tertiary oil recovery
Based on a large number of empirical statistics of tertiary oil recovery technology in China, including polymer flooding, chemical flooding, gas flooding, in situ combustion, steam flooding, ect., 22 key reservoir parameters were filterized. Five levels of quantitative screening criteria were developed for different tertiary oil recovery methods. The mean algorithm for the downward approximation and the grey correlation theory were used in this paper to quickly select the appropriate tertiary oil recovery method for the target blocks, which provides a preferred development method for subsequent potential evaluation. In the rapid analogy evaluation method of tertiary oil recovery potential, the total similarity ratio between the target block and the example block is determined. The target block is matched with the appropriate instance block according to the total similarity ratio value, using 80% as the boundary. The ratio of the geological reserves is used to predict the oil recovery i... [more]
DynamFluid: Development and Validation of a New GUI-Based CFD Tool for the Analysis of Incompressible Non-Isothermal Flows
Héctor Redal, Jaime Carpio, Pablo A. García-Salaberri, Marcos Vera
December 11, 2019 (v1)
Keywords: benchmark problems, Boussinesq approximation, characteristic-based-split algorithm, finite element method, flow past a circular cylinder, lid-driven cavity flow, non-isothermal vertical channel
A computational fluid dynamics software (DynamFluid) based on the application of the finite element method with the characteristic-based-split algorithm is presented and validated. The software is used to numerically integrate the steady and unsteady Navier−Stokes equations for both constant-density and Boussinesq non-isothermal flows. Benchmark two-dimensional computations carried out with DynamFluid show good agreement with previous results reported in the literature. Test cases used for validation include (i) the lid-driven cavity flow, (ii) mixed convection flow in a vertical channel with asymmetric wall temperatures, (iii) unsteady incompressible flow past a circular cylinder, and (iv) steady non-isothermal flow past a circular cylinder with negligible buoyancy effects. The new software is equipped with a graphical user interface that facilitates the definition of the fluid properties, the discretization of the physical domain, the definition of the boundary conditions, and the po... [more]
An Active Power Filter Based on a Three-Level Inverter and 3D-SVPWM for Selective Harmonic and Reactive Compensation
José Luis Monroy-Morales, David Campos-Gaona, Máximo Hernández-Ángeles, Rafael Peña-Alzola, José Leonardo Guardado-Zavala
December 10, 2019 (v1)
Keywords: active power filters, neutral point clamped, selective harmonic compensation, synchronous rotatory frames
Active Power Filters (APFs) have been used for reducing waveform distortion and improving power quality. However, this function can be improved by means of a selective harmonic compensation. Since an APF has rating restrictions, it is convenient to have the option of selecting an individual or a set of particular harmonics in order to compensate and apply the total APF capabilities to eliminate these harmonics, in particular those with a greater impact on the Total Harmonic Distortion (THD). This paper presents the development of a new APF prototype based on a three-phase three-level Neutral Point Clamped (NPC) inverter with selective harmonic compensation capabilities and reactive power compensation. The selective harmonic compensation approach uses several Synchronous Rotating Frames (SRF), to detect and control individual or a set of harmonics using d and q variables. The APF includes a Three-Dimensional Space Vector Modulator (3D-SVPWM) in order to generate the compensation current... [more]
Analysis of Pressure Rise in a Closed Container Due to Internal Arcing
Peng Li, Jiangjun Ruan, Daochun Huang, Ziqing OuYang, Li Zhang, Mingyang Long, Mengting Wei
December 10, 2019 (v1)
Keywords: arc fault, arc voltage, closed container, computational fluid dynamics (CFD), pressure rise, pressure wave, switchgear
When an arc fault occurs in a medium-voltage (MV) metal enclosed switchgear, the arc heats the filling gas, resulting in a pressure rise, which may seriously damage the switchgear, the building it is contained in, or even endanger maintenance personnel. A pressure rise calculation method based on computational fluid dynamics (CFD) has been put forward in this paper. The pressure rise was calculated and the arc tests between the copper electrodes were performed in the container under different gap lengths by the current source. The results show that the calculated pressure rise agrees well with the measurement, and the relative error of the average pressure rise is about 2%. Arc volume has less effect on the pressure distribution in the container. Arc voltage Root-Mean-Square (RMS) has significant randomness with the change of arc current, and increases with the increase of gap length. The average arc voltage gradients measure at about 26, 20 and 16 V/cm when the gap lengths are 5, 10 a... [more]
An Efficient Phase-Locked Loop for Distorted Three-Phase Systems
Yijia Cao, Jiaqi Yu, Yong Xu, Yong Li, Jingrong Yu
December 10, 2019 (v1)
Keywords: distorted grid conditions, frequency adaption, Lagrange-interpolation method, SC, SGDFT
This paper proposed an efficient phase-locked loop (PLL) that features zero steady-state error of phase and frequency under voltage sag, phase jump, harmonics, DC offsets and step-and ramp-changed frequency. The PLL includes the sliding Goertzel discrete Fourier transform (SGDFT) filter-based fundamental positive sequence component separator (FPSCS), the synchronousreference-frame PLL (SRF-PLL) and the secondary control path (SCP). In order to obtain an accurate fundamental positive sequence component, SGDFT filter is introduced as it features better filtering ability at the frequencies that are integer times of fundamental frequency. Meanwhile, the second order Lagrange-interpolation method is employed to approximate the actual sampling number including both integer and fractional parts as grid frequency may deviate from the rated value. Moreover, an improved SCP with single-step comparison filtering algorithm is employed as it updates reference angular frequency according to the FPSC... [more]
Numerical Solutions of Heat Transfer for Magnetohydrodynamic Jeffery-Hamel Flow Using Spectral Homotopy Analysis Method
Asad Mahmood, Md Faisal Md Basir, Umair Ali, Mohd Shareduwan Mohd Kasihmuddin, Mohd. Asyraf Mansor
November 24, 2019 (v1)
Keywords: boundary value problems, fluid, heat transfer, Jeffery-Hamel, ordinary differential equations, partial differential equations, semi-analytical technique, spectral homotopy
This paper studies heat transfer in a two-dimensional magnetohydrodynamic viscous incompressible flow in convergent/divergent channels. The temperature profile was obtained numerically for both cases of convergent/divergent channels. It was found that the temperature profile increases with an increase in Reynold number, Prandtl number, Nusselt number and angle of the wall but decreases with an increase in Hartmann number. A relatively new numerical method called the spectral homotopy analysis method (SHAM) was used to solve the governing non-linear differential equations. The SHAM 3rd order results matched with the DTM and shooting, showing that SHAM is feasible as a technique to be used.
Application of Transformation Matrices to the Solution of Population Balance Equations
Vasyl Skorych, Nilima Das, Maksym Dosta, Jitendra Kumar, Stefan Heinrich
November 5, 2019 (v1)
Keywords: agglomeration, dynamic flowsheet simulation, milling, multidimensional distributed parameters, population balance equation, process modelling, solids, transformation matrix
The development of algorithms and methods for modelling flowsheets in the field of granular materials has a number of challenges. The difficulties are mainly related to the inhomogeneity of solid materials, requiring a description of granular materials using distributed parameters. To overcome some of these problems, an approach with transformation matrices can be used. This allows one to quantitatively describe the material transitions between different classes in a multidimensional distributed set of parameters, making it possible to properly handle dependent distributions. This contribution proposes a new method for formulating transformation matrices using population balance equations (PBE) for agglomeration and milling processes. The finite volume method for spatial discretization and the second-order Runge−Kutta method were used to obtain the complete discretized form of the PBE and to calculate the transformation matrices. The proposed method was implemented in the flowsheet mod... [more]
A Numerical Approach to Solve Volume-Based Batch Crystallization Model with Fines Dissolution Unit
Safyan Mukhtar, Muhammad Sohaib, Ishfaq Ahmad
September 23, 2019 (v1)
Keywords: orthogonal polynomials, quadrature method of moments, volume-based population balance model with fines dissolution
In this article, a numerical study of a one-dimensional, volume-based batch crystallization model (PBM) is presented that is used in numerous industries and chemical engineering sciences. A numerical approximation of the underlying model is discussed by using an alternative Quadrature Method of Moments (QMOM). Fines dissolution term is also incorporated in the governing equation for improvement of product quality and removal of undesirable particles. The moment-generating function is introduced in order to apply the QMOM. To find the quadrature abscissas, an orthogonal polynomial of degree three is derived. To verify the efficiency and accuracy of the proposed technique, two test problems are discussed. The numerical results obtained by the proposed scheme are plotted versus the analytical solutions. Thus, these findings line up well with the analytical findings.
Simulating Stochastic Populations. Direct Averaging Methods
Vu Tran, Doraiswami Ramkrishna
July 11, 2019 (v1)
Keywords: direct averaging, drug resistance, stochastic simulation, transfer
A method of directly computing the average behavior of stochastic populations is established, which obviates the time-consuming process of generating detailed sample paths. The method relies on suitably discretized time intervals in which nonlinearities are quasi-linearized to produce random variables with known expectations and variances. The pair of equations is directly solved to obtain the average behavior of the system at the end of a time interval based on its knowledge at the beginning of the interval. The sample path requirement for this process is considerably lower than that for the process over the entire simulation period. The efficiency of the method is demonstrated on the transfer of antibiotics resistance between two bacterial species which is a problem of mounting concern in fighting disease.
Discrete Element Method Model Optimization of Cylindrical Pellet Size
Jiri Rozbroj, Jiri Zegzulka, Jan Necas, Lucie Jezerska
June 10, 2019 (v1)
Keywords: DEM, friction coefficient, hopper discharge, particle image velocimetry, pellets
The DEM (Discrete Element Method) is one option for studying the kinematic behaviour of cylindrical pellets. The DEM experiments attempted to optimize the numerical model parameters that affected time and velocity as a cylindrical vessel emptied. This vessel was filled with cylindrical pellets. Optimization was accomplished by changing the coefficient of friction between particles and selecting the length accuracy grade of the sample cylindrical pellets. The initial state was a series of ten vessel-discharge experiments evaluated using PIV (Particle Image Velocimetry). The cylindrical pellet test samples were described according to their length in three accuracy grades. These cylindrical pellet length accuracy grades were subsequently used in the DEM simulations. The article discusses a comparison of the influence of the length accuracy grade of cylindrical pellets on optimal calibration of time and velocity when the cylindrical vessel is emptied. The accuracy grade of cylindrical pell... [more]
On the Boundary Conditions in a Non-Linear Dissipative Observer for Tubular Reactors
Irandi Gutierrez-Carmona, Jaime A. Moreno, H.F. Abundis-Fong
April 9, 2019 (v1)
Keywords: distributed observers, PDE, perturbation estimation, sensor position
The modal injection mechanism ensures the exponential convergence of an observer in a continuous tubular reactor in dependence with the system parameters, the sensor location, and the observer gains. In this paper, it is shown that by simple considerations in the boundary conditions, the observer convergence is improved regardless of the presence of perturbations, the sensor locations acquire a meaningful physical meaning, and by simple numerical manipulations, the perturbations in the inflow can be numerically estimated.
Numerical Models for Viscoelastic Liquid Atomization Spray
Lijuan Qian, Jianzhong Lin, Fubing Bao
February 27, 2019 (v1)
Keywords: atomization spray, numerical modeling, viscoelastic fluid
Atomization spray of non-Newtonian liquid plays a pivotal role in various engineering applications, especially for the energy utilization. To operate spray systems efficiently and well understand the effects of liquid rheological properties on the whole spray process, a comprehensive model using Euler-Lagrangian approaches was established to simulate the evolution of the atomization spray for viscoelastic liquid. Based on the Oldroyd model, the viscoelastic linear dispersion relation was introduced into the primary atomization; an extended viscoelastic version of Taylor analogy breakup (TAB) model was proposed; and the coalescence criteria was modified by rheological parameters, such as the relaxation time, the retardation time and the zero shear viscosity. The predicted results are validated with experimental data varying air-liquid mass flow ratio (ALR). Then, numerical calculations are conducted to investigate the characteristics of viscoelastic liquid atomization process. Results s... [more]
Assessing Steady-State, Multivariate Experimental Data Using Gaussian Processes: The GPExp Open-Source Library
Sylvain Quoilin, Jessica Schrouff
November 28, 2018 (v1)
Keywords: experimental data, feature selection, Gaussian processes, kriging, outlier, regression, surface response
Experimental data are subject to different sources of disturbance and errors, whose importance should be assessed. The level of noise, the presence of outliers or a measure of the “explainability” of the key variables with respect to the externally-imposed operating condition are important indicators, but are not straightforward to obtain, especially if the data are sparse and multivariate. This paper proposes a methodology and a suite of tools implementing Gaussian processes for quality assessment of steady-state experimental data. The aim of the proposed tool is to: (1) provide a smooth (de-noised) multivariate operating map of the measured variable with respect to the inputs; (2) determine which inputs are relevant to predict a selected output; (3) provide a sensitivity analysis of the measured variables with respect to the inputs; (4) provide a measure of the accuracy (confidence intervals) for the prediction of the data; (5) detect the observations that are likely to be outliers.... [more]
Comparison of Moving Boundary and Finite-Volume Heat Exchanger Models in the Modelica Language
Adriano Desideri, Bertrand Dechesne, Jorrit Wronski, Martijn van den Broek, Sergei Gusev, Vincent Lemort, Sylvain Quoilin
November 27, 2018 (v1)
Keywords: Dynamic Modelling, dynamic validation, Modelica, organic Rankine cycle (ORC)
When modeling low capacity energy systems, such as a small size (5⁻150 kWel) organic Rankine cycle unit, the governing dynamics are mainly concentrated in the heat exchangers. As a consequence, the accuracy and simulation speed of the higher level system model mainly depend on the heat exchanger model formulation. In particular, the modeling of thermo-flow systems characterized by evaporation or condensation requires heat exchanger models capable of handling phase transitions. To this aim, the finite volume (FV) and the moving boundary (MB) approaches are the most widely used. The two models are developed and included in the open-source ThermoCycle Modelica library. In this contribution, a comparison between the two approaches is presented. An integrity and accuracy test is designed to evaluate the performance of the FV and MB models during transient conditions. In order to analyze how the two modeling approaches perform when integrated at a system level, two organic Rankine cycle (ORC... [more]
Constant Jacobian Matrix-Based Stochastic Galerkin Method for Probabilistic Load Flow
Yingyun Sun, Rui Mao, Zuyi Li, Wei Tian
November 27, 2018 (v1)
Keywords: generalized polynomial chaos, Nataf transformation, probabilistic load flow, stochastic Galerkin method, uncertainty quantification
An intrusive spectral method of probabilistic load flow (PLF) is proposed in the paper, which can handle the uncertainties arising from renewable energy integration. Generalized polynomial chaos (gPC) expansions of dependent random variables are utilized to build a spectral stochastic representation of PLF model. Instead of solving the coupled PLF model with a traditional, cumbersome method, a modified stochastic Galerkin (SG) method is proposed based on the P-Q decoupling properties of load flow in power system. By introducing two pre-calculated constant sparse Jacobian matrices, the computational burden of the SG method is significantly reduced. Two cases, IEEE 14-bus and IEEE 118-bus systems, are used to verify the computation speed and efficiency of the proposed method.
Implementing a Novel Hybrid Maximum Power Point Tracking Technique in DSP via Simulink/MATLAB under Partially Shaded Conditions
Shahrooz Hajighorbani, Mohd Amran Mohd Radzi, Mohd Zainal Abidin Ab Kadir, Suhaidi Shafie, Muhammad Ammirrul Atiqi Mohd Zainuri
November 16, 2018 (v1)
Keywords: digital signal processing (DSP), global maximum power point (GMPP), O), partial shadow (PS), perturb and observation (P&, photovoltaic (PV), Simulink/MATLAB
This paper presents a hybrid maximum power point tracking (MPPT) method to detect the global maximum power point (GMPP) under partially shaded conditions (PSCs), which have more complex characteristics with multiple peak power points. The hybrid method can track the GMPP when a partial shadow occurs either before or after acquiring the MPP under uniform conditions. When PS occurs after obtaining the MPP during uniform conditions, the new operating point should be specified by the modified linear function, which reduces the searching zone of the GMPP and has a significant effect on reducing the reaching time of the GMPP. Simultaneously, the possible MPPs are scanned and stored when shifting the operating point to a new reference voltage. Finally, after determining the possible location of the GMPP, the GMPP is obtained using the modified P&O. Conversely, when PS occurs before obtaining the MPP, the referenced MPP should be specified. Thus, after recognizing the possible location of... [more]
A Novel Computational Approach for Harmonic Mitigation in PV Systems with Single-Phase Five-Level CHBMI
Rosario Miceli, Giuseppe Schettino, Fabio Viola
September 21, 2018 (v1)
Keywords: multilevel power converter, phase shifted, photovoltaic systems, selective harmonic mitigation, soft switching, voltage cancellation
In this paper, a novel approach to low order harmonic mitigation in fundamental switching frequency modulation is proposed for high power photovoltaic (PV) applications, without trying to solve the cumbersome non-linear transcendental equations. The proposed method allows for mitigation of the first-five harmonics (third, fifth, seventh, ninth, and eleventh harmonics), to reduce the complexity of the required procedure and to allocate few computational resource in the Field Programmable Gate Array (FPGA) based control board. Therefore, the voltage waveform taken into account is different respect traditional voltage waveform. The same concept, known as “voltage cancelation„, used for single-phase cascaded H-bridge inverters, has been applied at a single-phase five-level cascaded H-bridge multilevel inverter (CHBMI). Through a very basic methodology, the polynomial equations that drive the control angles were detected for a single-phase five-level CHBMI. The acquired polynomial equations... [more]
Periodic Steady State Assessment of Microgrids with Photovoltaic Generation Using Limit Cycle Extrapolation and Cubic Splines
Marcolino Díaz-Araujo, Aurelio Medina, Rafael Cisneros-Magaña, Amner Ramírez
September 21, 2018 (v1)
Keywords: cubic splines, limit cycle, numerical differentiation method, periodic steady state, photovoltaic energy sources, time domain
This paper proposes a fast and accurate time domain (TD) methodology for the assessment of the dynamic and periodic steady state operation of microgrids with photovoltaic (PV) energy sources. The proposed methodology uses the trapezoidal rule (TR) technique to integrate the set of first-order differential algebraic equations (DAE), generated by the entire electrical system. The Numerical Differentiation (ND) method is used to significantly speed-up the process of convergence of the state variables to the limit cycle with the fewest number of possible time steps per cycle. After that, the cubic spline interpolation (CSI) algorithm is used to reconstruct the steady state waveform obtained from the ND method and to increase the efficiency of the conventional TR method. This curve-fitting algorithm is used only once at the end part of the algorithm. The ND-CSI can be used to assess stability, power quality, dynamic and periodic steady state operation, fault and transient conditions, among... [more]
BiPAD: Binomial Point Process Based Energy-Aware Data Dissemination in Opportunistic D2D Networks
Seho Han, Kisong Lee, Hyun-Ho Choi, Howon Lee
September 21, 2018 (v1)
Keywords: binomial point process (BPP), data dissemination, device-to-device (D2D) communication, k-th furthest distance, relay selection
In opportunistic device-to-device (D2D) networks, the epidemic routing protocol can be used to optimize the message delivery ratio. However, it has the disadvantage that it causes excessive coverage overlaps and wastes energy in message transmissions because devices are more likely to receive duplicates from neighbors. We therefore propose an efficient data dissemination algorithm that can reduce undesired transmission overlap with little performance degradation in the message delivery ratio. The proposed algorithm allows devices further away than the k-th furthest distance from the source device to forward a message to their neighbors. These relay devices are determined by analysis based on a binomial point process (BPP). Using a set of intensive simulations, we present the resulting network performances with respect to the total number of received messages, the forwarding efficiency and the actual number of relays. In particular, we find the optimal number of relays to achieve almost... [more]
Identification of the Heat Equation Parameters for Estimation of a Bare Overhead Conductor’s Temperature by the Differential Evolution Algorithm
Mirza Sarajlić, Jože Pihler, Nermin Sarajlić, Gorazd Štumberger
September 21, 2018 (v1)
Keywords: conductor temperature, measurement, Optimization, overhead transmission line, parameter identification, Simulation
This paper deals with the Differential Evolution (DE) based method for identification of the heat equation parameters applied for the estimation of a bare overhead conductor`s temperature. The parameters are determined in the optimization process using a dynamic model of the conductor; the measured environmental temperature, solar radiation and wind velocity; the current and temperature measured on the tested overhead conductor; and the DE, which is applied as the optimization tool. The main task of the DE is to minimise the difference between the measured and model-calculated conductor temperatures. The conductor model is relevant and suitable for the prediction of the conductor temperature, as the agreement between measured and model-calculated conductor temperatures is exceptional, where the deviation between mean and maximum measured and model-calculated conductor temperatures is less than 0.03 °C.
Parameter Estimation of Electromechanical Oscillation Based on a Constrained EKF with C&I-PSO
Yonghui Sun, Yi Wang, Linquan Bai, Yinlong Hu, Denis Sidorov, Daniil Panasetsky
September 21, 2018 (v1)
Keywords: C&, constrained parameter estimation, extended Kalman filter, I particle swarm optimization, power systems, ringdown detection
By combining together the extended Kalman filter with a newly developed C&I particle swarm optimization algorithm (C&I-PSO), a novel estimation method is proposed for parameter estimation of electromechanical oscillation, in which critical physical constraints on the parameters are taken into account. Based on the extended Kalman filtering algorithm, the constrained parameter estimation problem is formulated via the projection method. Then, by utilizing the penalty function method, the obtained constrained optimization problem could be converted into an equivalent unconstrained optimization problem; finally, the C&I-PSO algorithm is developed to address the unconstrained optimization problem. Therefore, the parameters of electromechanical oscillation with physical constraints can be successfully estimated and better performed. Finally, the effectiveness of the obtained results has been illustrated by several test systems.
Choosing the Optimal Multi-Point Iterative Method for the Colebrook Flow Friction Equation
Pavel Praks, Dejan Brkić
August 28, 2018 (v1)
Keywords: Colebrook equation, Colebrook–White, explicit approximations, hydraulic resistances, iterative methods, pipes, three-point methods, turbulent flow
The Colebrook equation is implicitly given in respect to the unknown flow friction factor λ; λ = ζ ( R e , ε * , λ ) which cannot be expressed explicitly in exact way without simplifications and use of approximate calculus. A common approach to solve it is through the Newton⁻Raphson iterative procedure or through the fixed-point iterative procedure. Both require in some cases, up to seven iterations. On the other hand, numerous more powerful iterative methods such as three- or two-point methods, etc. are available. The purpose is to choose optimal iterative method in order to solve the implicit Colebrook equation for flow friction accurately using the least possible number of iterations. The methods are thoroughly tested and those which require the least possible number of iterations to reach the accurate solution are identified. The most powerful three-point methods require, in the worst case, only two iterations to reach the final solution. The recommended representativ... [more]
A Coupled Thermal-Hydraulic-Mechanical Nonlinear Model for Fault Water Inrush
Weitao Liu, Jiyuan Zhao, Ruiai Nie, Yuben Liu, Yanhui Du
August 28, 2018 (v1)
Keywords: coupled THM model, fault water inrush, nonlinear flow in fractured porous media, numerical model, warning levels of fault water inrush
A coupled thermal-nonlinear hydraulic-mechanical (THM) model for fault water inrush was carried out in this paper to study the water-rock-temperature interactions and predict the fault water inrush. First, the governing equations of the coupled THM model were established by coupling the particle transport equation, nonlinear flow equation, mechanical equation, and the heat transfer equation. Second, by setting different boundary conditions, the mechanical model, nonlinear hydraulic-mechanical (HM) coupling model, and the thermal-nonlinear hydraulic-mechanical (THM) coupling model were established, respectively. Finally, a numerical simulation of these models was established by using COMSOL Multiphysics. Results indicate that the nonlinear water flow equation could describe the nonlinear water flow process in the fractured zone of the fault. The mining stress and the water velocity had a great influence on the temperature of the fault zone. The temperature change of the fault zone can r... [more]
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