scholarly journals Coupled THM and Matrix Stability Modeling of Hydroshearing Stimulation in a Coupled Fracture-Matrix Hot Volcanic System

2018 ◽  
Vol 2018 ◽  
pp. 1-15 ◽  
Author(s):  
Yong Xiao ◽  
Jianchun Guo ◽  
Hehua Wang ◽  
Lize Lu ◽  
John McLennan ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Thermal Conduction ◽  
Dominant Role ◽  
Injection Well ◽  
Time Step ◽  
Volcanic System ◽  
Induced Stress ◽  
The Matrix ◽  
Matrix Stability ◽  
The Stability

A coupled thermal-hydraulic-mechanical (THM) model is developed to simulate the combined effect of fracture fluid flow, heat transfer from the matrix to injected fluid, and shearing dilation behaviors in a coupled fracture-matrix hot volcanic reservoir system. Fluid flows in the fracture are calculated based on the cubic law. Heat transfer within the fracture involved is thermal conduction, thermal advection, and thermal dispersion; within the reservoir matrix, thermal conduction is the only mode of heat transfer. In view of the expansion of the fracture network, deformation and thermal-induced stress model are added to the matrix node’s in situ stress environment in each time step to analyze the stability of the matrix. A series of results from the coupled THM model, induced stress, and matrix stability indicate that thermal-induced aperture plays a dominant role near the injection well to enhance the conductivity of the fracture. Away from the injection well, the conductivity of the fracture is contributed by shear dilation. The induced stress has the maximum value at the injection point; the deformation-induced stress has large value with smaller affected range; on the contrary, thermal-induced stress has small value with larger affected range. Matrix stability simulation results indicate that the stability of the matrix nodes may be destroyed; this mechanism is helpful to create complex fracture networks.

scholarly journals New Thermal-Conductivity Constitutive Matrix in Fourier’s Law for Heat Transfer Using the Cell Method

2019 ◽  
Vol 9 (21) ◽  
pp. 4521
Author(s):  
González-Domínguez ◽  
Monzón-Verona ◽  
García-Alonso
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Finite Element Method ◽  
Thermal Conduction ◽  
Computational Method ◽  
The Finite Element Method ◽  
Cell Method ◽  
Tetrahedral Meshes ◽  
The Matrix ◽  
Constitutive Matrix

In this paper, a new constitutive matrix Mτ for thermal conduction, for tetrahedral meshes, in a steady state thermal regime is developed through a new algebraic methodology, using the Cell Method as a computational method, which is included in the finite formulation. The constitutive matrix defines the behavior of solids when they are under a thermal potential. The results are compared with those obtained for the same problem by means of the constitutive matrix Mλ developed previously, taking in both cases with a 2D axisymmetric model as reference, calculated with the finite element method. The errors obtained with the new matrix Mτ are of the order of 0.0025%, much lower than those obtained with the matrix Mλ.

Stability Analysis of Smoothed Finite Element Methods with Explicit Method for Transient Heat Transfer Problems

2019 ◽  
Vol 17 (02) ◽  
pp. 1845005 ◽  
Author(s):  
Xin Rong ◽  
Ruiping Niu ◽  
Guirong Liu
Keyword(s):  
Heat Transfer ◽  
Finite Element ◽  
Critical Time ◽  
Transient Heat Transfer ◽  
Explicit Method ◽  
Time Step ◽  
Smoothed Finite Element Method ◽  
The Stability ◽  
Transfer Problems ◽  
Critical Time Step

In this paper, transient heat transfer problems are analyzed using the smoothed finite element methods (S-FEMs) with explicit time integration. For a numerical method with spatial discretization, the computational cost per time step in the explicit method is less than that in the implicit method, but the time step is much smaller in the explicit analysis than that in the implicit analysis when the same mesh is used. This is because the stability is of essential importance. This work thus studies the stability of S-FEMs, when applied to transient heat transfer problems. Relationships are established between the critical time steps used in S-FEMs with the maximum eigenvalues of the thermal stiffness (conduction) matrix and mass matrix. It is found that the critical time step relates to the “softness” of the model. For example, node-based smoothed finite element method (NS-FEM) is softer than edge-based smoothed finite element method (ES-FEM), which leads to that the critical time step of NS-FEM is larger than that of ES-FEM. Because computing the eigenvalues and condition numbers of the stiffness matrices is very expensive but valuable for stability analysis, we proposed a concise and effective algorithm to estimate the maximum eigenvalue and condition number. Intensive numerical examples show that our scheme for computing the critical time step can work accurately and stably for the explicit method in FEM and S-FEMs.

Optimization of immobilization of strontium and uranium by the solid matrix

1999 ◽  
Vol 556 ◽  
Author(s):  
S. Raicevic ◽  
I. Plecas ◽  
D. I. Lalovic ◽  
V. Veljkovic
Keyword(s):  
Interaction Potential ◽  
Solid Phase ◽  
Solid Matrix ◽  
Physical Parameters ◽  
Phosphate Rocks ◽  
Pseudopotential Theory ◽  
The Matrix ◽  
Impurity System ◽  
Matrix Stability ◽  
The Stability

AbstractOne of the basic physical parameters which defines: (1) the capacity of the solid matrix for the incorporation (sorption) of the impurity and (2) the stability of the solid matrix -impurity system, is the ion-ion interaction potential, representing the main term of the cohesive energy. Using this parameter determined in the frame of the pseudopotential theory and pseudoatomic approximation we have investigated the systems HAP-Sr and HAP-UO2. In analysis, the hydroxyapatite (HAP, Ca10(PO4)6(OH)2) was selected as a model solid matrix since insoluble phosphates, phosphate ceramic and apatite-like materials are candidates for the immobilization of radionuclides. The substitution of calcium atoms by different impurities in HAP can be presented by the formula: Ca10-xMx(PO4)6(OH)2, where 0 ≤ x ≤ 10 and M = Sr2+, UO22+. It has been shown that (1) Sr can be safely immobilized by HAP, natural apatites and phosphate rocks in the whole range of its concentrations, and (2) that HAP is not an appropriate solid-matrix for immobilization of UO22+ because its incorporation in the low concentration results in a decrease of the matrix stability, stimulating formation of the inhomogeneous structure containing isolated clusters of the UO2- apatite solid phase.

scholarly journals Krylov SSP Integrating Factor Runge–Kutta WENO Methods

Mathematics ◽  
2021 ◽  
Vol 9 (13) ◽  
pp. 1483
Author(s):  
Shanqin Chen
Keyword(s):  
Large Time ◽  
Hyperbolic Equations ◽  
Strong Stability ◽  
Matrix Exponential ◽  
Linear Component ◽  
Nonlinear Hyperbolic Equations ◽  
Time Step ◽  
Integrating Factor ◽  
The Matrix ◽  
Runge Kutta

Weighted essentially non-oscillatory (WENO) methods are especially efficient for numerically solving nonlinear hyperbolic equations. In order to achieve strong stability and large time-steps, strong stability preserving (SSP) integrating factor (IF) methods were designed in the literature, but the methods there were only for one-dimensional (1D) problems that have a stiff linear component and a non-stiff nonlinear component. In this paper, we extend WENO methods with large time-stepping SSP integrating factor Runge–Kutta time discretization to solve general nonlinear two-dimensional (2D) problems by a splitting method. How to evaluate the matrix exponential operator efficiently is a tremendous challenge when we apply IF temporal discretization for PDEs on high spatial dimensions. In this work, the matrix exponential computation is approximated through the Krylov subspace projection method. Numerical examples are shown to demonstrate the accuracy and large time-step size of the present method.

scholarly journals On the Numerical Simulation of HPDEs Using θ-Weighted Scheme and the Galerkin Method

Mathematics ◽  
2020 ◽  
Vol 9 (1) ◽  
pp. 78
Author(s):  
Haifa Bin Jebreen ◽  
Fairouz Tchier
Keyword(s):  
Differential Equation ◽  
Galerkin Method ◽  
Linear Ordinary Differential Equation ◽  
Time Interval ◽  
Hyperbolic Partial Differential Equation ◽  
Time Step ◽  
Numerical Examples ◽  
One Dimensional ◽  
The Stability ◽  
The Galerkin Method

Herein, an efficient algorithm is proposed to solve a one-dimensional hyperbolic partial differential equation. To reach an approximate solution, we employ the θ-weighted scheme to discretize the time interval into a finite number of time steps. In each step, we have a linear ordinary differential equation. Applying the Galerkin method based on interpolating scaling functions, we can solve this ODE. Therefore, in each time step, the solution can be found as a continuous function. Stability, consistency, and convergence of the proposed method are investigated. Several numerical examples are devoted to show the accuracy and efficiency of the method and guarantee the validity of the stability, consistency, and convergence analysis.

scholarly journals Combined Heat Transfer Mechanisms in the Porous Char Layer Formed from the Intumescent Coatings under Fire

Coatings ◽  
2021 ◽  
Vol 11 (2) ◽  
pp. 200
Author(s):  
Lingyun Zhang ◽  
Yupeng Hu ◽  
Minghai Li
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Thermal Conduction ◽  
Total Heat ◽  
Surface Radiation ◽  
Total Heat Transfer ◽  
Char Layer ◽  
Competition Result ◽  
Transfer Mechanisms ◽  
Combined Heat Transfer

This study examines the combined heat transfer by thermal conduction, natural convection and surface radiation in the porous char layer that is formed from the intumescent coating under fire. The results show that some factors, such as the Rayleigh number, conductivity ratio, emissivity, radiation–conduction number, void fraction and heating mode have a certain effect on the total heat transfer. In addition, the natural convection of the air in the cavity always inhibits surface radiation among the solid walls and thermal conduction, and the character of the total heat transfer is the competition result of the three heat transfer mechanisms.

Fast Conjugate Heat Transfer Simulation of Long Transient Flexible Operations Using Adaptive Time Stepping

2018 ◽  
Vol 140 (9) ◽  
Author(s):  
R. Maffulli ◽  
L. He ◽  
P. Stein ◽  
G. Marinescu
Keyword(s):  
Heat Transfer ◽  
Conjugate Heat Transfer ◽  
Time Derivative ◽  
Computational Cost ◽  
Strong Impact ◽  
Time Step ◽  
Time Stepping ◽  
Adaptive Time ◽  
Fully Coupled ◽  
Adaptive Time Stepping

The emerging renewable energy market calls for more advanced prediction tools for turbine transient operations in fast startup/shutdown cycles. Reliable numerical analysis of such transient cycles is complicated by the disparity in time scales of the thermal responses in fluid and solid domains. Obtaining fully coupled time-accurate unsteady conjugate heat transfer (CHT) results under these conditions would require to march in both domains using the time-step dictated by the fluid domain: typically, several orders of magnitude smaller than the one required by the solid. This requirement has strong impact on the computational cost of the simulation as well as being potentially detrimental to the accuracy of the solution due to accumulation of round-off errors in the solid. A novel loosely coupled CHT methodology has been recently proposed, and successfully applied to both natural and forced convection cases that remove these requirements through a source-term based modeling (STM) approach of the physical time derivative terms in the relevant equations. The method has been shown to be numerically stable for very large time steps with adequate accuracy. The present effort is aimed at further exploiting the potential of the methodology through a new adaptive time stepping approach. The proposed method allows for automatic time-step adjustment based on estimating the magnitude of the truncation error of the time discretization. The developed automatic time stepping strategy is applied to natural convection cases under long (2000 s) transients: relevant to the prediction of turbine thermal loads during fast startups/shutdowns. The results of the method are compared with fully coupled unsteady simulations showing comparable accuracy with a significant reduction of the computational costs.

THE STABILITY ANALYSIS OF HEAT TRANSFER IN SATURATED LIQUID FILM OF THE SPECIAL MATERIALS

2005 ◽  
Vol 19 (28n29) ◽  
pp. 1547-1550
Author(s):  
YOULIANG CHENG ◽  
XIN LI ◽  
ZHONGYAO FAN ◽  
BOFEN YING
Keyword(s):  
Heat Transfer ◽  
Differential Equation ◽  
Surface Tension ◽  
Stability Analysis ◽  
Liquid Film ◽  
Nonlinear Relationship ◽  
Saturated Liquid ◽  
Nonlinear Surface ◽  
Isothermal Wall ◽  
The Stability

Representing surface tension by nonlinear relationship on temperature, the boundary value problem of linear stability differential equation on small perturbation is derived. Under the condition of the isothermal wall the effects of nonlinear surface tension on stability of heat transfer in saturated liquid film of different liquid low boiling point gases are investigated as wall temperature is varied.

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