An Account of the Development of High-Level Numerical Methods for Engineering Simulations [Historical

Rubber gaskets are commonly adopted as the waterproof component in shield tunnels for their outstanding sealing performance. The contact pressure between surfaces generated by the assembly stress ensures that the gaskets resist certain water pressure without leaking. However, with the continuous occurrence of leakage accidents, attention has been drawn to the topic of the waterproof performance of gasketed joint shield tunnels. In this article, prominent contributions to the waterproof performance of sealing gasket in shield tunnels are listed and sorted into four sections: (1) structural behavior of lining and joint; (2) material constitutive model and durability; (3) numerical simulation methods; (4) thermal-mechanical coupling analysis. First, examples of leakage are discussed and tests on gaskets are elucidated, which is followed by a summary of the progress on material mechanical properties and durability. Then, the development of the simulation methods is presented. Finally, the existing research on the thermal-mechanical coupling analysis is summarized. It is found that the contributions to gaskets’ waterproof performance are fruitful, however, with stringent construction conditions, such as the material constitutive model and aging mechanism under special conditions, such as high temperature, numerical simulation, and laboratory test methods, which need to be further explored.

Centrifugal pumps are required to sustain a stable operation of the system they support under all operating conditions. Minor modifications of the surfaces defining the pump's water passage can influence the tendency to unstable system operation significantly. The action of such modifications on the flow are yet not fully understood, leading to costly trial and error approaches in the solution of instability problems. The part-load flow in centrifugal pumps is inherently time-dependent due to the interaction of the rotating impeller with the stationary diffuser (Rotor-Stator Interaction, RSI). Furthermore, adverse pressure gradients in the pump diffuser may cause flow separation, potentially inducing symmetry-breaking non-uniformities, either spatially stationary or rotating and either steady or intermittent. Rotating stall, characterized by the presence of distinct cells of flow separation on the circumference, rotating at a fraction of the impeller revolution rate, has been observed in thermal and hydraulic turbomachines. Due to its complexity, the part-load flow in radial centrifugal pumps is a major challenge for numerical flow simulation methods. The present study investigates the part-load flow in radial centrifugal pumps and pump-turbines by experimental and numerical methods, the latter using a finite volume discretization of the Reynolds-averaged Navier-Stokes (RANS) equation. Physical phenomena of part load flow are evidenced based on three case studies, and the ability of numerical simulation methods to reproduce part-load flow in radial centrifugal pumps qualitatively and quantitatively is assessed. A numerical study of the flow in a high specific speed radial pump-turbine using steady approaches and the hypothesis of angular periodicity between neighboring blade channels evidences the relation of sudden flow topology changes with an increase of viscous losses, impacting on the energy-discharge characteristic, and thus increasing the risk of unstable operation. When the flow rate drops below a critical threshold, the straight through-flow with flow separation zones attached to the guide vanes changes to an asymmetrical flow. Energy is drawn off the mean flow and dissipated in a large vortex-like structure. Besides flow separation in some diffuser channels, time-dependent numerical simulations of the flow in a double suction pump evidence a flow rate imbalance between both impeller sides interacting with asymmetric flow separation in the diffuser. Viscous losses increase substantially as this imbalance occurs, the resulting segment of positive slope in the energy-discharge characteristic is found for a flow rate sensibly different from measurements. Different modes of rotating stall are identified by transient pressure measurements in a low-specific-speed pump-turbine, showing 3 to 5 zones of separated flow, rotating at 0.016 to 0.028 times impeller rotation rate, depending on discharge. For operating conditions where stall with 4 cells is most pronounced, velocity is measured by Laser-Doppler methods at locations of interest. The velocity field is reconstructed with respect to the passage of stall cells by definition of a stall phase obtained from simultaneous transient pressure measurements. Time-dependent numerical simulation predicting rotating stall with 4 cells shows velocity fields that are in reasonable agreement with the measured velocity fields, but occurring at a sensibly higher flow rate than found from experiments. In consideration of the quantitative shortcomings of the numerical simulation, a novel modelling approach is proposed: Replacing the costly 3-dimensional simulation of the major part of the impeller channels by a 1-dimensional model allows a significant economy in computational resources, allowing an improved modeling for the remainder of the domain at constant computational cost. The model is validated with the challenging cases of rotating stall and impeller side flow rate imbalance. The satisfying coherence of the results with the simulation including the entire impeller channels qualifies this approach for numerous turbomachinery applications. It could also provide improved, time-dependent boundary conditions for draft tube vortex rope simulations at reasonable computational cost. Parameter studies modifying deliberately some quantities of mean flow and turbulence at the modeled boundary surfaces can be implemented in the framework of the method.

The works in which designs of the dust collectors, which are often used in the industry, are analyzed. It is shown that the efficiency of dust collectors largely depends on the structure of the gas flow in the apparatus. Based on the analysis of the current cyclone devices, a picture of the separation process is obtained, and the factors that negatively affect the operation of dust collectors are identified. It is established that forecasting the work of dust collecting devices in certain conditions is most effective to perform methods of numerical modeling and simulation of the separation process, which are widely used for the research of devices of this type. Using the methods of numerical simulation, the study of the cyclone with intermediate dust removal was carried out. In this cyclone, the change in the radius of the apparatus of the tangential, radial, and axial velocity components is investigated. In the course of the research, it is established that in the separation space the tangential component of velocity increases from 18–20 m/s in the upper part of the device to 22–25 m/s in the area of the lower end of the exhaust pipe, the radial component of velocity takes values from 0 to 2 m/s, and the axial component of the speed has a maximum value of 10–15 m/s. In the conical part of the apparatus the tangential component of velocity decreases from 27 m/s in the upper planes of the conical part of the apparatus to 10 m / s near the dust unloading pipe, the radial component of speed has centripetal character, the axial component of speed decreases as the gas flow to the dust unloading pipe decreases. It has been established that in the cylindrical part of the apparatus about 60 % of the gas flow volume is transferred from the downstream to the upstream by a secondary vortex, and in the conical part, about 40 % of the gas volume is transferred from the downstream to the upstream. It is shown that large values of the tangential component of velocity in the separation zone contribute to the ingress of dust particles into the annular space behind the dust unloading holes, and small values of the tangential component of velocity, axial and radial in the annular space behind the dust unloading holes has a positive effect on the operation of the dust collector.

In the field of engineering, field testing and laboratory simulations are important in understanding the nonlinear behaviour of structures during strong earthquakes. Numerical simulation can be used to predict the effects of changes in systems under extreme conditions, for example serves to answer the question what would happen if …? Hence the importance of engineering students know the methods of numerical simulation, following schemes modelling, implementation, software verification and validation of methods. In this article an Interactive Simulation Laboratory (LIS) for the numerical display and validation of nonlinear oscillations and its implementation as a teaching tool in teaching Physical Fundamentals in Mechanical Engineering degree from the University of Cordoba, it is presented. The development of this tool aims to which the student of first courses were introduced in the methods of numerical simulation and how it is used, verification and validation using a simple but very complex nonlinear oscillations is the simple pendulum example and help them design environments and unpredictable contour conditions under unfavourable circumstances. For this, the LIS allows simultaneous use different numerical methods to solve the experiments studied and compare the results, initiating the students in the techniques of solving engineering problems using numerical methods and understand the influence of the chosen in the final result method. Key Words: dynamic tests, pendulum, numerical methods, oscillations, structures

Model-based autotuning of discretization methods in numerical simulations of partial differential equations

In this paper, a new type of bottom trawl was designed for target fishing vessels to use in deep-water fishing grounds. The trawl’s hydrodynamic performance was investigated using numerical simulation and physical modeling methods, and a numerical model based on the finite element method was proposed for estimating hydrodynamic forces and predicting performances. A series of physical model tests based on Tauti’s law were carried out in a towing tank to explore the hydrodynamic performance of the trawl and to assess the applicability of the numerical simulation method. The results showed that the working towing speed of the trawl was 3.5 kn. The drag force and the height of net opening were 50 kN and 5.62 m, respectively, and the swept area was 128 m2 at that speed. The simulated result was close to the experimental result, with a maximum relative error less than 20%, and an average relative error of 10%. The net shape and tension distribution of the trawl were analyzed using the numerical simulation method, and the hanging ratio in T-direction of the mesh of the codend was 0.25 at the working towing speed. The newly designed deep bottom trawl had a superior hydrodynamic performance for high catch efficiency and selectivity and may be applied to commercial fishing operations.

Layer system recombination is the combination of main layers and non-main layers into a new injection-production well pattern respectively, in order to reduce interlayer contradictions. The main factors restricting layer system recombination are reservoir physical properties, residual material basis, and economic benefits. In this study, according to the actual reservoir characteristics, a conceptual model is established to study the technical policy limits of layer system recombination. Through numerical simulation and mathematical statistics methods, the variation rules of permeability rank difference, recovery degree rank difference, pressure rank difference, viscosity rank difference, and effective thickness upper limit are studied. And the inflection point of the curve is identified as the technical policy limit of layer system recombination. At the same time, the lower limit of reserve abundance under different oil prices is calculated as the economic limit of layer system recombination. Through remaining oil research and well pattern adaptability evaluation, the well pattern reconstruction study is carried out to effectively expand the water drive sweep range and reconstruct efficient displacement flow field. On the basis of layer system recombination and well pattern reconstruction optimization study, the numerical simulation method is used to carry out the research of injection-production technology policy such as reasonable pressure maintenance level, reasonable injection-production ratio, and reasonable oil production rate, which effectively guides the reservoir injection and production control and consolidates the effect of layer system well pattern reconstruction.

Polymer grouting materials are increasingly used in the filling of mine fissures. Unlike conventional inorganic grouting materials, the self-expansion of polymers adds complexity to their diffusion process within the crack. The objective of this research was to examine how polymer grouting material spreads in cracks at ambient temperatures and pressure. The investigation involved conducting grouting tests and performing numerical fluid simulation calculations using the finite-volume method in the computational fluid dynamics software, ANSYS FLUENT 2022 R1. The fluid volume approach was employed to determine the boundary between fluid and air and to ascertain the variation patterns of density in the slurry and the fracture system. This study applied the principles of fluid mechanics to investigate the patterns of variation in the physical characteristics of polymer grouting materials, including their density, pressure, flow velocity, and movement distance, during the diffusion process. The results indicated that the density of the polymer grouting material decreased exponentially over time throughout the diffusion process. With the increase in the grouting's volume, the grout's pressure and the permeable distance of the grout increased. The slurry's pressure near the grouting hole exceeded the other points' pressure. The physical parameters of the slurry were numerically simulated by ANSYS FLUENT 2022 R1 software, and the results were compared with the experimental data. After comparing the numerical simulation results with the test data, it was clear that the numerical simulation method was superior in accurately predicting the distribution pattern of each parameter of the polymer slurry during diffusion. The grouting volume, pressure distribution, and real-time change in the position of the flow of slurry could be efficiently determined through numerical calculation and simulated grouting tests. This work can offer valuable information for designing polymer grouting materials used in underground mine fissures.

The lithology of the roof of the mining roadway is compound and the thickness of each layer varies considerably, and it is disturbed by dynamic load all the year round. The above factors has caused a huge difference in the stability of the roadway surrounding rock. Taking the 11,020 lower tunnel of a mine in Henan Province as the engineering geological background, using on-site investigation, formula derivation, numerical simulation and other methods, the composite roof roadway model group was established to study the deflection evolution characteristics of the surrounding rock under dynamic load disturbance, and summarize the plastic zone of the surrounding rock of the roadway Deformation and evolution of roof surrounding rock to evaluate the stability of surrounding rock with different roof structures. The research results show that the change of the roof surrounding rock structure will also lead to the change of the center deflection of the roadway roof. Therefore, the center deflection of the surrounding rock of various roof composite structures is different, and the deflection is the most direct indicator of the stability of the surrounding rock. The center deflection (\(\omega_{0}\)) of the soft rock type is the largest, the center deflection (\(\omega_{0}\))of the upper soft and the lower hard type, and the soft and hard type is larger, and the soft and hard progressive type, thin, hard and thick soft type (\(\omega_{0}\)) is the smallest, and the dynamic load The relationship between the magnitude of deflection before and after the disturbance is consistent. By constructing a composite roof roadway numerical model group, using the plastic failure zone of the roadway as the evaluation standard, the surrounding rock stability is evaluated and divided, and then the cross-point field measurement method is used to verify the stability of the surrounding rock on the roof of different composite structures. And the development of composite roof roadway surrounding rock deformation and failure mechanism and numerical simulation method has important theoretical significance and practical value for the analysis and control of composite roof roadway surrounding rock stability.

The co-extrusion process is widely used to produce composite tire treads with better performance. This study investigated the rubber co-extrusion flow process and quality influencing factors of tri-composite tire tread through numerical simulation and experimental methods. Here, RPA 2000 rubber processing analyzer was used to carry out rheological tests on the three rubber materials, the PTT viscoelastic constitutive model was fitted, and the fitting curves were in good agreement with the test data. Then, a three-dimensional viscoelastic numerical simulation model of the tri-composite tread co-extrusion process was established using Ansys Polyflow software. The parameter evolution technique is adopted in the model establishment to improve the calculation convergence. In addition, a global remeshing function is used to avoid excessive mesh deformation. A co-extrusion experiment is conducted to verify the model's accuracy using a tri-screw extruder. The extruded tread size error rate between the experiment and simulation is less than 6%. The variation of the velocity field, pressure field and shear rate field during extrusion is analyzed, and the formation mechanism of die swell is explained simultaneously. Finally, the influence of process parameters (inflow rate and traction speed) and die structure (convergence angle and thickness) on the extruded tire tread shape and quality was investigated, which can provide theoretical guidance for improving tread quality and production efficiency. Furthermore, the numerical simulation method can assist the design of the die plate in enhancing the efficiency of the die plate design.

Over the past two decades or so, computational fluid dynamics (CFD) has been employed to predict overall mixing times inside jet mixing tanks instead of non-universal mixing time correlations obtained by experiments. However, the numerical methods for jet mixing tank simulations were not clearly tested and the discretization errors of the previous CFD models were not assessed. So, in this paper, the suitable turbulence model and numerical methods for pump-around jet mixing tank simulations were investigated. Further, the discretization errors of the present CFD models were estimated with the help of grid convergence index (GCI). The results revealed that the realizable k-epsilon model, SIMPLE, second order upwind, and first order implicit were proper turbulence model and numerical methods for pump-around jet mixing tank simulations. From GCI analyses, the maximum discretization uncertainty in overall mixing time of the present CFD models was about ±0.08 s.

In this paper, we firstly study numerical methods for gas flow simulation in dual-continuum porous media. Typical methods for oil flow simulation in dual-continuum porous media cannot be used straightforward to this kind of simulation due to the artificial mass loss caused by the compressibility and the non-robustness caused by the non-linear source term. To avoid these two problems, corrected numerical methods are proposed using mass balance equations and local linearization of the non-linear source term. The improved numerical methods are successful for the computation of gas flow in the double-porosity double-permeability porous media. After this improvement, temporal advancement for each time step includes three fractional steps: (i) advance matrix pressure and fracture pressure using the typical computation; (ii) solve the mass balance equation system for mean pressures; (iii) correct pressures in (i) by mean pressures in (ii). Numerical results show that mass conservation of gas for the whole domain is guaranteed while the numerical computation is robust.

Magnetic fluid was a novel functional material with many unique properties, especially in the case that the magnetic field was applied. It was found that the special properties of magnetic fluid were determined by its unique microstructure. Then, the special properties could be understood fundamentally by researching the extraordinary nature of the microstructure of the magnetic fluid. At the same time, it was a good theoretic guidance for the experimental research on the properties of magnetic fluid to make clear about the microstructure model theoretically. Therefore, it was particularly important to study the simulation methods to obtain the microstructure of magnetic fluid. The development of the microstructure simulation methods of magnetic fluid were introduced in this article, and the basic principles of various simulation methods were expounded in detail. The features of each microstructure simulation methods of magnetic fluid were summarized and compared with each other. Finally, the key problems and research direction of the numerical simulation method in the future were described.

Recent researches have revealed that, for a tracked uplink Gaussian beam, the scintillation index predicted by the weak fluctuation theory is significantly different from that of the numerical wave optics simulation method when the size of the transmitter aperture is large. In this paper, turbulence-induced scintillation index and the probability distribution of fluctuating irradiance for a tracked uplink Gaussian beam are studied using numerical wave optics simulation method. The simulated data show that in the discrepancy region between the weak fluctuation theory and the numerical simulation method, the simulated fluctuating irradiance is not governed by the generally accepted lognormal distribution even when the weak fluctuation condition is still satisfied.

For the problem with a fuzzy failure state which commonly exists in degradation structures and systems, the fuzzy failure probability based importance measure indices can be used to measure the effect of the input variables on the fuzzy failure probability effectively. However, the computational cost is unaffordable for estimating the indices directly. For efficiently evaluating the fuzzy failure probability based importance measure indices, this paper proposed two numerical simulation methods, i.e., the direct Monte Carlo simulation method based on the Bayesian formula (B-DMCS) and the adaptive radial-based importance sampling method based on the Bayesian formula (B-ARBIS). The two proposed methods employ the Bayesian formula to eliminate the dependence of the computational cost on the dimensionality of the input variables. Compared with the B-DMCS method, the B-ARBIS method can enhance the computational efficiency significantly due to repeatedly utilizing the same group of samples of the input variables and the strategy to adaptively search the optimal hypersphere in the safety domain. After giving the principles and implementations of the two methods, three examples are employed to validate the effectiveness of the two proposed numerical simulation methods. The results of the examples demonstrate that the effectiveness of the two proposed methods is higher than the direct Monte Carlo method, and the B-ARBIS method can improve the efficiency obviously in contrast with the B-DMCS method.