Transient Problems Research Articles

Inspecting the role of vapour loss and other model strategies in the mod-elling of a bentonite thermo-hydraulic cell

Inspecting the role of vapour loss and other model strategies in the mod-elling of a bentonite thermo-hydraulic cell

A finite volume method based multi-group neutron diffusion model for space-time nuclear reactor kinetics problems in RZ geometry

The transient analysis of Fast Breeder Reactor (FBR) requires the development of high fidelity space-time nuclear reactor kinetics codes for the realistic prediction of spatial and temporal behavior of neutron flux and fission power along with the feedback effects. So, a space-time nuclear reactor kinetics model has been developed for solving the coupled time dependent multi-group neutron diffusion equations and the delayed neutron precursor equations in axi-symmetric cylindrical (r-z) geometry. The numerical model employs an orthogonal mesh finite volume method for spatial discretization and implicit method for time discretization. A computer code named MANDIR-KRZ (Multi-group Analysis of Neutron DIffusion in Reactor for Kinetics problems in RZ geometry) has been developed and employed to reconstruct the keff, transient neutron flux and power results of different benchmark problems. Mathematical formulation of the numerical model and results of the code for Dodds and FBR transient benchmark problems are discussed in this paper.

Sequential Regularization Method for the Identification of Mold Heat Flux during Continuous Casting Using Inverse Problem Solutions Techniques

A two-dimensional transient inverse heat-conduction problem (2DIHCP) was established to determine the mold heat flux using observed temperatures. The sequential regularization method (SRM) was used with zeroth-, first-, and second-order spatial regularization to solve the 2DIHCP. The accuracy of the 2DIHCP was investigated under two strict test conditions (Case 1: heat flux with time-spatial periodically varying, and Case 2: that with sharp variations). The effects of the number of future time steps, regularization parameters, order of regularization, discrete grids, and time step size on the accuracy of the 2DIHCP were analyzed. The results showed that the minimum relative error (epred) of the predicted Case 1 heat flux is 5.05%, 5.39%, and 5.88% for zeroth-, first-, and second-order spatial regularization, respectively. The corresponding values for the predicted Case 2 heat flux are 6.31%, 6.30%, and 6.36%. Notably, zeroth- and first-order spatial regularization had higher accuracy than second-order spatial regularization, while zeroth-order spatial regularization was comparable to first-order. Additionally, first-order spatial regularization was more accurate in reconstructing heat flux containing sharp spatial variations. The CPU time of the predicted Case 2 heat flux is 1.71, 1.71, and 1.70 s for zeroth-, first-, and second-order spatial regularization, respectively. The corresponding values for the predicted Case 1 heat flux are 6.18, 6.15, and 6.17 s. It is noteworthy that the choice of spatial regularization order does not significantly impact the required computing time. Lastly, the minimum epred of Case 2 heat flux with zeroth-order spatial regularization is 7.96%, 6.42%, and 7.87% for time step sizes of 1/fs, 1/2fs, and 1/5fs, respectively. The accuracy of the inverse analysis displays an initial improvement followed by degradation as the time step size decreases. A recommended time step size is 1/2fs, where fs denotes the temperature-sampling rate.

Numerical Simulation of the Conjugate Heat Transfer of a “Fluid–Solid Body” System on an Unmatched Grid Interface

Recently, when modeling transient problems of conjugate heat transfer, the independent construction of grid models for fluid and solid subdomains is increasingly being used. Such grid models, as a rule, are unmatched and require the development of special grid interfaces that match the heat fluxes at the interface. Currently, the most common sequential approach to modeling problems of conjugate heat transfer requires the iterative matching of boundary conditions, which can significantly slow down the process of the convergence of the solution in the case of modeling transient problems with fast processes. The present study is devoted to the development of a direct method for solving conjugate heat transfer problems on grid models consisting of inconsistent grid fragments on adjacent boundaries in which, in the general case, the number and location of nodes do not coincide. A conservative method for the discretization of the heat transfer equation by the direct method in the region of inconsistent interface boundaries between liquid and solid bodies is proposed. The proposed method for matching heat fluxes at mismatched boundaries is based on the principle of forming matched virtual boundaries, proposed in the GGI (General Grid Interface) method. A description of a numerical scheme is presented, which takes into account the different scales of cells and the sharply different thermophysical properties at the interface between liquid and solid media. An algorithm for constructing a conjugate matrix, the form of matrix coefficients responsible for conjugate heat transfer, and methods for calculating them are described. The operability of the presented method is demonstrated by the example of calculating conjugate heat transfer problems, the grid models of which consist of inconsistent grid fragments. The use of the direct conjugation method makes it possible to effectively solve both stationary and non-stationary problems using inconsistent meshes, without the need to modify them in the conjugation region within a single CFD solver.

Geometric inverse estimation for the inner wall of a furnace under transient heat conduction based on dual reciprocity boundary element method

A boundary shape estimation problem for the furnace’s inner surface is solved using the dual reciprocity boundary element method (DRBEM) and the conjugate gradient method (CGM) under transient heat conduction. The DRBEM is utilized to eliminate the drawbacks of traditional numerical methods and classical boundary element method of discretizing the entire computational domain, with only boundary discretization. The inversion results are obtained by applying the CGM to minimize the objective function, in which the sensitivity coefficients are calculated with the complex variable derivation method (CVDM), making the calculation precise and independent of step size. To verify the accuracy of the DRBEM in solving the transient heat conduction problem, the influencing factors including radial-basis function, the number of internal collocation points, and time step size are investigated. The influences of measurement time interval, future time step, initial guess, measurement error, and the number and position of measurement points on the inversion results are analyzed. Meanwhile, the effectiveness of the proposed approach is tested by numerical examples, and the inversion results show that it is stable, accurate, and efficient for identifying different and complicated unknown boundary shapes of the furnace.

Pattern-based action engine: Generating process management actions using temporal patterns of process-centric problems

As business environments become more competitive, organizations strive to improve their business processes to reduce costs and increase quality and productivity. As process improvement traditionally embraces manual creative tasks that are time-consuming and labor-intensive, the need for automating it arises. Action-Oriented Process Mining (AOPM) aims to support automated process improvement by leveraging various process mining techniques. To that end, AOPM first monitors the presence of operational constraints, i.e., operational problems, in business processes, e.g., a high waiting time for patients to register. Next, it produces interim management actions designed to address these transient problems by analyzing the monitoring results. For instance, if an excessive waiting time persists for more than a week, the system might recommend dispatching additional resources for the upcoming week. Contrary to the mature process mining support for monitoring operational constraints, the action part is typically missing in today’s process mining tools. In this work, we propose an action engine to support the automatic generation of actions. It analyzes temporal patterns of monitoring results and produces action plans that describe the execution of management actions. We have demonstrated a use case using the data of a Dutch financial institute to evaluate the feasibility of the proposed action engine and conducted experiments to evaluate its effectiveness.

A hybrid numerical method for non-linear transient heat conduction problems with temperature-dependent thermal conductivity

This paper introduces a hybrid numerical technique aimed at effectively addressing two-dimensional (2D) non-linear transient heat conduction problems, featuring temperature-dependent thermal conductivity. This scheme involves integrating the Krylov deferred correction (KDC) method in the temporal discretization and the generalized finite difference method (GFDM) in the spatial discretization. The core of the KDC method introduces a new unknown variable in the form of the first-order time derivative of temperature, leading to a non-linear equation after temporal discretization. Subsequently, the corresponding non-linear equation is solved in the spatial domain using the GFDM, supported by the Jacobian-free Newton–Krylov (JFNK) solver and fourth-order Taylor series expansion. The accuracy and stability of the hybrid approach are verified through two numerical experiments, demonstrating the strong performance of the present algorithm known as the KDC-GFDM for the simulations of the interested problems in long-time intervals.

Heterogeneous parallel computing method for 3D transient nonlinear thermomechanical problems on CPU-GPU platforms

A heterogeneous parallel computing method for 3D transient nonlinear thermomechanical problems is proposed based on CPU-GPU platforms. The method is developed based on the stable node-based smoothed finite element method (SNS-FEM) and element-by-element (EBE) strategy. The SNS-FEM method ensures the accuracy of temperature and displacement solution. To obtain higher computational efficiency, a series of parallel computing strategies are proposed in this paper. A one-to-one mapping relationship is established between smoothing domains calculation and threads in GPU. To improve the efficiency of constructing the smoothing domain, a semi-parallel construction method is developed. And a preindexing method is proposed to improve the computational efficiency of solving linear equations by the parallel preconditioned conjugate gradient (PCG) method. The developed heterogeneous parallel computing method is quite accurate and efficient in computing the model composed of tetrahedral elements, obtaining a speedup ratio of 52.31 when the model contains 67,204 degrees of freedom.

MLS-based numerical manifold method based on IPIM for 3D transient heat conduction of FGMs

In this study, the moving least squares based numerical manifold method (MLS-NMM) is presented to solve three-dimensional (3D) transient heat conduction problems of functionally graded materials (FGMs), where the increment dimensional precise integration method (IPIM) is applied to integrate the ordinary differential equations derived from the semi-discrete form. In the 3D MLS-NMM, the influence domains of the MLS-nodes are taken as the mathematical patches which are used to construct the mathematical cover (MC), and the shape functions of the MLS-nodes are employed as the weight functions subordinate to the MC. MLS-NMM is utilized for spatial discretization of the weak form of the problem. The IPIM overcomes the shortcomings of traditional backward difference scheme dependent on the time step and greatly improves the computing efficiency. Meanwhile, a mass lumping technique is proposed for the 3D MLS-NMM. Furthermore, a number of numerical experiments on transient thermal conduction are conducted, suggesting that the 3D MLS-NMM based on IPIM and the proposed mass lumping has excellent accuracy, absolutely stable and high computing efficiency.

Approximate semi-analytical technique based on eigenfunction expansion for phase change heat transfer in a cylindrical body contained within a thick multilayered annular wall

Phase change heat transfer occurs commonly in thermal management and energy storage problems. Most literature in this direction assumes direct contact between the phase change material (PCM) and the heat source/sink. However, in practical problems, the PCM is often enclosed within a non-melting wall. This work presents an approximate eigenfunction expansion-based analysis of inwards phase change propagation in a cylindrical PCM encapsulated in a multilayer annular wall. The model accounts for imperfect thermal contact between layers. The transient temperature distribution is determined by solving a transient multilayer thermal conduction problem. Evolution of the phase change front is determined by inserting the temperature distribution into the interfacial energy conservation equation. Results are shown to agree with past work for special cases of the general problem considered here. Good agreement with both experimental and numerical data from past work, and with finite-element numerical simulations is demonstrated. The role of key non-dimensional parameters on phase change characteristics, including total time to melt/freeze is quantified. Ranges of non-dimensional numbers in which the approximate method offers good accuracy are determined. This work extends the state-of-the-art of phase change modeling, with potential applications in energy storage, nuclear engineering, oil/gas transport, and in mass transport problems.

The impact of thermal insulation on the vulnerability of hollow masonry walls under elevated temperatures

There is little doubt that masonry walls have, throughout the history of mankind, been a critical part of building construction. From this standpoint, the present study aims to unfold the thermal behaviour of masonry walls when subjected to the standard cellulosic curve prescribed in ISO 834. Particular attention has been paid on temperature variations that are intimately connected to insulation fire resistance. The investigation initially focuses on the vulnerability of clay hollow-brick masonry wall arrangements with a varying thickness and position of insulation. These parameters are shown to significantly affect the penetration of heat through walls. In addition, temperature-dependent relationships among thermophysical properties of a combustible and a non-combustible insulation material, are examined. Alongside this, the effect of volumetric mass density on thermal conductivity for two sets of masonry units has been also taken into account. At last, this work is extended to identify the heat storage capacity of masonry walls depending on the construction arrangement of materials which can affect compartment fire dynamics. Within this framework, a numerical technique has been implemented to realise a finite element analysis (FEA) with respect to this transient thermal problem. Computational simulations have been carried out by adopting a well-known FEA modelling program.

A novel method for simultaneous determination of thermophysical properties and boundary conditions of phase change problems based on element differential method

Thermophysical properties and boundary conditions for phase change thermal management systems are challenging to be accurately determined, due to the phase change heat transfer phenomenon and complex working conditions. In this work, the element differential method (EDM) and a gradient-based method are combined to simultaneously predict thermal conductivity, mass specific heat, and boundary heat flux in two-dimensional (2D) and three-dimensional (3D) inverse phase change problems, for the first time. The multi-parameter identification for the 3D physical model with phase change is more general than the previous attempts. Moreover, the effective heat capacity method is employed to deal with phase change problems, to improve efficiency. The sensitivity coefficient is accurately determined by the complex-variable-differentiation method (CVDM) in the multi-parameter prediction. Finally, the effect of measurement points, measurement errors, and initial guessed values on the multi-parameter identification are investigated. This study demonstrates that the present method has good accuracy, efficiency, stability, and robustness in dealing with transient nonlinear inverse problems during phase change process.

A coupled MPM and CBFEM framework for large deformation simulation of porous media interacting with pore and free fluid

The hydromechanical interaction of porous media with pore and free fluid widely exists in geotechnical engineering. In some situations, the solid phase would exhibit large deformation, and the boundaries between the solid and fluid phases might change substantially, making it challenging for computational simulation. A framework coupling the material point method (MPM) with the characteristic-based finite element method (CBFEM) was proposed for simulating the behavior of porous media and fluid systems with large deformation. It employs the MPM to discretize the solid domain and solve corresponding momentum equations in the Lagrangian framework in favor of its advantage for large deformation simulation, and the CBFEM to discretize the fluid domain and solve the Navier-Stokes and free-surface equations of the fluid phase in the Eulerian framework in favor of its maturity and high efficiency. The fractional-step approach was adopted to solve velocity and pressure separately in a time step to make the MPM-CBFEM coupling more flexible. In addition, an implicit drag-force term was proposed to grow the time step in undrained conditions. A series of quasi-static and transient problems were simulated to show the performance and prospects of the proposed framework for the large deformation of the porous media and fluid systems.

Simulation and FPGA Implementation of Transient Power Quality Disturbance Detection

With the access to new energy in the smart grids and the massive use of nonlinear and unbalanced large loads, the problem of power quality becomes more and more serious. At present, the transient power quality disturbance problem has been paid more attention to. The research on transient power quality is relatively late, and various detection methods and technologies are not mature. It is necessary to use more efficient methods to detect and identify transient power quality to improve the safety of electricity use. This paper proposes to detect transient power quality disturbance by wavelet transform. In this paper, the original signal modelling of five kinds of power quality problems such as voltage sag and voltage swell. The 9/7 wavelet lifting coefficient is optimized in this paper and is carried out on the MATLAB software platform to improve the processing speed of the algorithm and realize parallel processing. The simulation results show that the improved lifting wavelet processing can effectively detect the transient power quality disturbance.

Synchronization Stability of the MMC-Connected Wind Farm Under Severe Asymmetrical Faults

This paper analyzes the phase-locked loop (PLL) synchronization stability of an offshore wind farm connected via the modular multilevel converter (MMC)-based high-voltage direct-current (HVDC) transmission system. The investigated wind farm is composed of full-scale type-4 wind turbines, and severe asymmetrical faults between these turbines and the MMC are considered. The MMC has dual-sequence control requirements under such faults, which interacts with the control systems of the wind turbines and further complicates the transient stability problem for the system. Thus, we thoroughly investigate how the interaction caused by the MMC affects the synchronization stability of wind turbines. Under severe faults, the MMC would be switched into a current limitation mode and act as a current source. Therefore, the influences of the MMC’s positive- and negative-sequence currents as well as their assignments between dq axes, on transient synchronization stability of wind turbines, are studied according to the phase portrait method. Furthermore, the optimal assignment region (OAR) is proposed for the stability-oriented assignment of MMC’s positive- and negative-sequence currents. This theoretical analysis is validated through extensive simulation results obtained from MATLAB/Simulink.

ANALYSIS OF RWANDA’S GRID POINT OF STABILITY LOSS

E Electricity stability is the key component in ensuring reliable power supply which is a major hurdle in most developing countries. Power angle being part of grid stability pillars, this work sought to theoretically and numerically investigate the maximum power angle variation that the power system in Rwanda could experience while maintaining transient stability at an acceptable range beyond which generators lose synchronism affecting overall system stability. A steady state and dynamic stability assessment of the lightly loaded Rwandan grid is conducted using PSS/E while MATLAB is used to obtain input values for calculating the system stability power angle. This involved collecting actual network parameters, creating an accurate model of the entire Rwandan grid and validating the model simulation results using regularly metered values at various critical busbars of the network. Results from the study show that a sudden drop in load of 11 MW and 6 MVAr leads to a variation of power angle of the largest power plant by 23o triggering transient stability problems leading to loss of synchronism. Both calculated and simulation results show that, a sudden power angle variation of between 23o to 23.5o at the swing bus power plant, causes the monitored generating units to trip triggering a long-term instability. This was done while also interrogating possible mitigation measures based on the developed and validated model. Based on the system status, the study revealed that the grid point of stability can be determined through simulation using software and to further obtain optimum stability, installation of active devices such as shunt reactors helps the grid to counter sudden variation of power angle due to line and load tripping. B

A Dimension-Reduced Line Element Method for 3D Transient Free Surface Flow in Porous Media

In order to reduce the numerical difficulty of the 3D transient free surface flow problems in porous media, a line element method is proposed by dimension reduction. Different from the classical continuum-based methods, homogeneous permeable pores in the control volume are conceptualized by a 3D orthogonal network of tubes. To obtain the same hydraulic solution with the continuum model, the equivalent formulas of flow velocity, continuity equation and transient free surface boundary are derivable from the principle of flow balance. In the solution space of transient free surface flow, the 3D problem is transformed into 1D condition, and then a finite element algorithm is simply deduced. The greatest advantage of the line element method is line integration instead of volume/surface integration, which has dramatically decreased the integration difficulty across the jump free surface. Through the analysis of transient free surface flow in the unconfined aquifer, trapezoidal dam, sand flume and wells, the transient free surface locations predicted from the proposed line element method generally agree well with the analytical, experimental and other numerical data in the available literatures, the numerical efficiency can also be well guaranteed. Furthermore, the hydraulic anisotropy has significant effect on the evolution of free surface locations and the shape of depression cones in spatial. The line element method can be expanded to model the 3D unsaturated seepage flow, two-phase flow and thermos problems in porous media because of the similarity between the similarity of Darcy’s law, Buckingham Law and Fourier’s law.

Transient Thermoelastic Analysis of Rectangular Plates with Time-Dependent Convection and Radiation Boundaries

Approximate analytical solutions are presented for the transient thermoelastic problem of rectangular plates with time-dependent convection and radiation boundaries. To include the nonlinear radiation boundary, the whole heating process is divided into several time steps, and a linearized approximation is used to simplify the radiation term for each step. The one-dimensional transient temperature along the thickness direction is solved using the technique of the separation of variables. The displacement and stress solutions are obtained by applying the state-space method to the three-dimensional thermoelasticity equations. The accuracy of the present solutions is demonstrated by comparison with the reported results in the open literature and the finite element solutions. In the numerical examples, two kinds of thermal boundaries, namely, time-independent convection boundaries and time-dependent convection and radiation boundaries, are considered to show the availability of the present solutions.

Response spatiotemporal correlation and transient temperature field direct reconstruction for heat conduction system

In this paper, according to a spatiotemporal correlation characteristic of the temperature response of a transient heat conduction system, a response spatiotemporal correlation (RSTC) model of the temperatures between measurement space and estimation space of the system is proposed. Furthermore, a RSTC based direct reconstruction (RSTC-DR) method is developed for a transient temperature field reconstruction problem of a heat conduction system with unknown heat sources. In the offline stage, firstly, mapping eigenvectors of a heat conduction system are determined by the transfer equations without specific heat source information. Then, according to the correlation degree between the mapping eigenvectors, a finite number of representative spatial points (RPs) are extracted. Meanwhile, a fuzzy membership relationship between the mapping characteristics of the RPs and that of the temperature field is determined. Namely, effective mapping characteristic coverage of the RPs to the whole temperature field is realized. Moreover, a RSTC model between the measurement spatial points (MPs) and the RPs is obtained by the step response model of the temperature field. In the online stage, based on the RSTC model, the temperature responses of the RPs are estimated by employing the time series vector of the temperature measurements of the MPs. Next, according to the fuzzy membership relationship, the temperature field can be reconstructed in real time by synthesizing the temperature estimations of the RPs. The RSTC-DR method is employed to achieve the non-destructive reconstruction of the transient temperature field of a two-dimensional heat conduction system. The temperature field is reconstructed by the numerical experiment to verify the effectiveness of the proposed method and to discuss its adaptability. Furthermore, the practical effectiveness of the method is demonstrated by applying the existing experimental data.

A numerical investigation of 2D transient heat conduction problems in anisotropic FGMs with time-dependent conductivity

A class of two-dimensional (2D) transient heat conduction problems for anisotropic Functionally Graded Materials (FGMs) of space–time dependent conductivity and coefficient of variable separable forms is considered. The problems are reduced to a boundary-only integral equation which can be solved numerically using a standard Boundary Element Method (BEM). Some examples are considered to show the validity of the analysis and to examine the accuracy of the numerical method.