Two-dimensional Test Research Articles

Physical Modeling of Horizontal and Vertical Tsunami Forces on the Elevated Overland Structure

Park, H.; Cox, D.T., and Shin, S., 2019. Physical modeling of horizontal and vertical tsunami forces on the elevated overland structure. In: Lee, J.L.; Yoon, J.-S.; Cho, W.C.; Muin, M., and Lee, J. (eds.), The 3rd International Water Safety Symposium. Journal of Coastal Research, Special Issue No. 91, pp. 51-55. Coconut Creek (Florida), ISSN 0749-0208.In this study, two-dimensional hydraulic model tests were conducted to investigate the characteristics of the force of tsunami waves on the simplified box-type elevated structure. The vertical elevation of the structure was changed to investigate the relation between the wave force and the air gap. The tsunami waves were generated by using the error function with the full-stroke of the wave paddle to maximize inundation. The horizontal and vertical wave forces and pressures on the structure by the tsunami waves were measured, and the relation between the maximum wave force, air gap and the incident wave condition was derived. Using the measured maximum horizontal wave force from the different wave conditions, the empirical formula of the non-dimensionalized horizontal wave force as a function of the surf similarity parameter was obtained. It was found that the horizontal wave force is inversely proportional to the surf similarity parameter in the case of the unelevated structure. The experimental results also showed that the ratio of the horizontal force to the vertical force is larger in the case of broken and breaking wave conditions in the case of the elevated structures.

Optimization of deep well gate-controlled dual direction SCR device for ESD protection in 0.5 μm CMOS process

Both traditional dual direction SCR (TDDSCR) and deep well gate-controlled dual direction SCR (DGC-DDSCR) are designed and fabricated in a 0.5 μm CMOS process. The ESD performance of the DDSCR device is predicted and verified by two-dimensional device simulation and transmission line pulse test results. The results show that when the TDDSCR changes the distance between the electrode N+ and the trigger surface P+(D4), the holding voltage increased from 10.1 V to 13.53 V, and the failure current remains stable (13.9A). The RS485 bus requires that the trigger voltage and the holding voltage of the ESD device be greater than 14.4 V, while TDDSCR is still unable to meet the on-chip ESD protection requirements for RS485 bus. However, when DGC-DDSCR increases the gate length (D4) of the anode and cathode, the holding voltage increases from 10.21 V to 15.18 V, and the failure current remains 14.63A. The test data has met the on-chip ESD protection requirements of the RS485 bus, and the size optimization problem of the DGC-DDSCR is discussed. The device has a strong current handling capability (91.25 mA/μm).

A conservation-moment-based implicit finite volume lattice Boltzmann method for steady nearly incompressible flows

This paper presents an efficient, low memory cost, implicit finite volume lattice Boltzmann method (FVLBM) based on conservation moments acceleration for steady nearly incompressible flows. In the proposed scheme, not as the conventional implicit schemes, both the micro lattice Boltzmann equations (LBE) and the associated conservation moment equations are solved by the matrix-free, lower-upper symmetric Gauss-Seidel scheme (LUSGS) and the conservation moment equations are used to predict equilibrium distribution functions at the new time, which eliminates the storage of the Jacobian matrix of the collision term in the implicit LBE system and provides a driving force for the fast convergence of the LBE. Moreover, by utilizing the projection matrix and the collision invariant, we can construct the fluxes of the moment equations efficiently from the fluxes of the LBE and avoid the time-consuming reconstruction procedure for obtaining the fluxes of the moment equations. To demonstrate the accuracy and high efficiency of the proposed scheme, comparison studies of simulation results of several two-dimensional testing cases by the present scheme and an explicit FVLBM are conducted and numerical results show that the proposed implicit scheme can be as accurate as its explicit counterpart with 1 or 2 orders times speedup.

A point-mass particle method for the simulation of immiscible multiphase flows on an Eulerian grid

We present an Eulerian-Lagrangian approach for the modeling and simulation of immiscible multiphase flow systems. The Naiver-Stokes equations are solved on a traditional Eulerian grid while the fluid mass and phase information is discretized by Lagrangian particles. The method is novel because the particles move with a velocity that enforces consistency between the particle field density and the fluid density. The approach is advantageous in that (i) an arbitrary number of phases are easily represented, (ii) the particles remain well-distributed in space, even near merging and diverging characteristics, (iii) mass conservation is easily controlled, and (iv) the methodology is applicable to a wide range of Courant numbers. The governing equations are derived and a numerical method is presented that is applicable to incompressible flows. Performance is assessed via standard two-dimensional and three-dimensional phase transport tests as a function of both Eulerian grid resolution and Lagrangian particle resolution. Results show that the shape error converges with first-order with respect to increasing either Eulerian grid resolution or particle resolution, while mass conservation errors converge with the square root. The method is shown to successfully simulate expanding elliptical regions, stationary and oscillating droplets, a droplet in shear flow, a Rayleigh-Taylor instability, and the air blast atomization of a droplet.

Airgap Search Coil-Based Detection of Damper Bar Failures in Salient Pole Synchronous Motors

Damper bars are often used in high output salient pole synchronous motor (SM) rotors for motor starting and stabilization of performance. Several cases of broken damper bars in the rotor of SMs that lead to motor starting failure and/or forced outage have recently been reported. However, detection of damper bar failures is difficult, since the damper bars are active only under the starting or load transients. Damper bar testing in the field currently relies on off-line visual inspection, and there is no means available for detecting failures on line. In this paper, a new method for detecting damper bar failures based on the analysis of airgap search coil measurements under the starting transient is proposed. Since airgap search coils are being increasingly installed in large SMs for detecting field winding short circuits, the proposed method can be implemented without additional hardware. The effectiveness of the proposed method is verified with two-dimensional finite element analysis and experimental testing on a custom-built 30 kW salient pole SM under controlled fault conditions. It is shown that the proposed method can provide reliable and sensitive detection of broken damper bars whenever the motor is started at low additional cost. The off-line single phase rotation test is also shown to provide reliable monitoring of damper bar condition.

Development of high resolution methods for analyzing multi-fluid problems

High resolution multi-fluid solvers are developed, using a fifth order weighted essentially non-oscillatory approach for spatial reconstruction and a third order Runge-Kutta scheme for temporal integration. Several flux evaluation schemes, comprising of exact and approximate Riemann solvers available in the literature are incorporated. Multi-fluid simulation capability is achieved using the ghost fluid method. Two-dimensional geometry is considered, and the Euler equations of gas dynamics are used as the basic flow model in view of the fact that the viscosity effects are negligible for most of the time of interest. Relative performance of these solvers is evaluated for several one- and two-dimensional test cases, before simulating the shock-bubble interaction. Three Mach numbers and air-Helium gas combination is studied and the results are presented in this study. Numerical schlieren images are rendered for qualitative study while time evolution of several integral features such as the axial and lateral deformations, the translational velocity of the bubble, the circulation in the flow-field, and the stretching rates of the bubbles are analyzed for quantitative studies. The results are consistent with the strength of baroclinic source term.

High-order implicit palindromic discontinuous Galerkin method for kinetic-relaxation approximation

We construct a high order discontinuous Galerkin method for solving general hyperbolic systems of conservation laws. The method is CFL-less, matrix-free, has the complexity of an explicit scheme and can be of arbitrary order in space and time. The construction is based on: (a) the representation of the system of conservation laws by a kinetic vectorial representation with a stiff relaxation term; (b) a matrix-free, CFL-less implicit discontinuous Galerkin transport solver; and (c) a stiffly accurate composition method for time integration. The method is validated on several one-dimensional test cases. It is then applied on two-dimensional and three-dimensional test cases: flow past a cylinder, magnetohydrodynamics and multifluid sedimentation.

Comparative Study of Metamodeling and Sampling Design for Expensive and Semi-Expensive Simulation Models Under Uncertainty

In spite of the wide improvements in computer simulation packages, many complex simulation models, particularly under uncertainty, may be inefficient to run in terms of time, computation, and resources. To address such a challenge, integrating metamodels and robust design optimization has been applied. In the current paper, a systematic comparative study is implemented to evaluate the performance of three common metamodels, namely polynomial regression, kriging, and radial basis function. The required experiments are designed by different space-filling methods including the orthogonal array design and three forms of Latin hypercube sampling such as randomized, maximin, and correlation approaches. Although, the impact of sample size on the performance of metamodels in robust optimization results are investigated. All methods are analyzed using five two-dimensional test problems and one engineering problem while all of them are considered in two forms that are expensive (with a small sample size) and semi-expensive (with a large sample size). Uncertainty is assumed in all problems as a source of variability, so all test problems are conducted in the format of robust optimization in the class of dual response surface in order to estimate robust Pareto frontier. The performances of methods are studied in two terms of accuracy and robustness. Finally, the results of comparison, an applicable guideline is provided to aid the practitioners in selecting the appropriate combination of metamodels and sampling design methods for investigating set of robust optimal points (estimated Pareto frontier) in simulation–optimization problems under uncertainty.

A preconditioned solver for sharp resolution of multiphase flows at all Mach numbers

A preconditioned five-equation two-phase model coupled with an interface sharpening technique is introduced for simulation of a wide range of multiphase flows with both high and low Mach regimes. Harten-Lax-van Leer-Contact (HLLC) Riemann solver is implemented for solving the discretized equations while tangent of hyperbola for interface capturing (THINC) interface sharpening method is applied to reduce the excessive diffusion of the method at the interface. In this work, preconditioning technique is used in a system of equations including viscous and capillary effects. Several one- and two-dimensional test cases are used to evaluate the performance and accuracy of this method. Numerical results demonstrate the efficiency of preconditioning in low Mach number flows. Comparisons between results of preconditioned and conventional system highlight the necessity of using preconditioning technique to reproduce main characteristics of low-speed flow regimes. Additionally, preconditioned systems transform to the conventional systems at high Mach number flows thus exhibiting the same level of accuracy as the standard flow solver. Therefore, the preconditioned compressible two-phase method can be used as an all-speed two-phase flow solver accounting for capillary and viscous stresses.

Comparative study of metamodeling and sampling design for expensive and semi-expensive simulation models under uncertainty

In spite of the wide improvements in computer simulation packages, many complex simulation models, particularly under uncertainty, may be inefficient to run in terms of time, computation, and resources. To address such a challenge, integrating metamodels and robust design optimization has been applied. In the current paper, a systematic comparative study is implemented to evaluate the performance of three common metamodels, namely polynomial regression, kriging, and radial basis function. The required experiments are designed by different space-filling methods including the orthogonal array design and three forms of Latin hypercube sampling such as randomized, maximin, and correlation approaches. Although, the impact of sample size on the performance of metamodels in robust optimization results are investigated. All methods are analyzed using five two-dimensional test problems and one engineering problem while all of them are considered in two forms that are expensive (with a small sample size) and semi-expensive (with a large sample size). Uncertainty is assumed in all problems as a source of variability, so all test problems are conducted in the format of robust optimization in the class of dual response surface in order to estimate robust Pareto frontier. The performances of methods are studied in two terms of accuracy and robustness. Finally, the results of comparison, an applicable guideline is provided to aid the practitioners in selecting the appropriate combination of metamodels and sampling design methods for investigating set of robust optimal points (estimated Pareto frontier) in simulation–optimization problems under uncertainty.

Analysis and Numerical Approximation of a Contact Problem Involving Nonlinear Hencky-Type Materials with Nonlocal Coulomb’s Friction Law

A static frictional contact problem between an elasto-plastic body and a rigid foundation is considered. The material’s behavior is described by the nonlinear elastic constitutive Hencky’s law. The contact is modeled with the Signorini condition and a version of Coulomb’s law in which the coefficient of friction depends on the slip. The existence of a weak solution is proved by using Schauder’s fixed-point theorem combined with arguments of abstract variational inequalities. Afterward, a successive iteration technique, based on the Kačanov method, to solve the problem numerically is proposed, and its convergence is established. Then, to improve the conditioning of the iterative problem, an appropriate Augmented Lagrangian formulation is used and that will lead us to Uzawa block relaxation method in every iteration. Finally, numerical experiments of two-dimensional test problems are carried out to illustrate the performance of the proposed algorithm.

Comparison between the diffuse interface and volume of fluid methods for simulating two-phase flows

A wide variety of interface capturing methods have been introduced for simulating two-phase flows throughout the years. However, there is a noticeable dearth of literature focusing on objective comparisons between these methods, especially when they are coupled to the momentum equation and applied in physically relevant regimes. In this article, we compare two techniques for simulating two-phase flows that possess attractive qualities, but belong to the two distinct classes of diffuse interface (DI) and volume of fluid (VOF) methods. Both of these methods allow for mass-conserving schemes that can naturally capture large interfacial topology changes omnipresent in realistic two phase flows. The DI solver used in this work is based on a conservative and bounded phase field method, developed recently. Similar to level set methods, this diffuse interface method takes advantage of the smoothness of the phase field in computing curvature and surface tension forces. Geometric VOF methods track the fractional tagged volume in a cell. The specific geometric VOF scheme used here is a discretely conservative and bounded implementation that uses geometric algorithms for unsplit advection and interface reconstruction, while employing height functions for normal and curvature calculation. We present a quantitative comparison of these methods on Cartesian meshes in terms of their accuracy, convergence rate, and computational cost using canonical two-dimensional (2D) two-phase test cases: an equilibrium static drop, an oscillating drop, damped surface wave and the Rayleigh–Taylor instability. We further compare these methods in their ability to resolve thin films by simulating the impact of a water drop on a deep water pool. Using results of these studies, we suggest qualitative guidelines for selection of schemes for two-phase flow calculations.

Efficient Aeroelastic Solution Based on Time-Spectral Fluid–Structure Interaction Method

Although the traditional transonic aeroelastic numerical analysis in the time domain is accurate, the high computational cost limits its application. Therefore, in this Paper, an efficient aeroelastic numerical solution based on the time-spectral method, called the time-spectral fluid–structure interaction method, is developed. The periodic aerodynamic forces and structure equations are calculated by using the time-spectral method and the double-iteration method, respectively. The novelty of this method is that in the inner iteration the variable with a strong coupling effect is solved by using the gradient method and the remaining variables are then solved by using the least-square method. Moreover, the computational fluid dynamics solver is not required in the inner iteration. By using the double-iteration method, not only does the computational cost decrease, but the stagnation of the convergence, which occurs frequently when using the one-shot method to search for the critical point, can be avoided. The two-dimensional aeroelastic standard test cases are then used to validate this method. Results show that the flutter boundary and the critical characteristics of the limit cycle oscillation can be captured with a few iterations by the time-spectral fluid–structure interaction method, and the results of this method agree well with those of the traditional time-domain method. This method can improved by one to two orders of magnitude in computational efficiency with a good robustness to initial conditions.

A new formulation for two-wave Riemann solver accurate at contact interfaces

This study proposes a new formulation for the Harten, Lax, and van Leer (HLL) type Riemann solver which is capable of solving contact discontinuities accurately but with robustness for strong shock. It is well known that the original HLL, which has incomplete wave structures, is too dissipative to capture contact discontinuities accurately. On the other side, contact-capturing approximate Riemann solvers such as HLL with Contact (HLLC) usually suffer from spurious solutions, also called carbuncle phenomenon, for strong shock. In this work, a new accurate and robust HLL-type formulation, the so-called HLL-BVD (HLL Riemann solver with boundary variation diminishing) is proposed by modifying the original HLL with the BVD algorithm. Instead of explicitly recovering the complete wave structures like the way of HLLC, the proposed method restores the missing contact with a jump-like function. The capability of solving contact discontinuities is further improved by minimizing the inherent dissipation term in HLL. Without modifying the original incomplete wave structures of HLL, the robustness for strong shock has been reserved. Thus, the proposed method is free from the shock instability problem. The accuracy and robustness of the new method are demonstrated through solving several one- and two-dimensional tests. Results indicate that the new formulation based on the two-wave HLL-type Riemann solver is not only capable of capturing contact waves more accurately than the original HLL or HLLC but, most importantly, is free form carbuncle instability for strong shock.

An Electron-Balance Based Approach to Predict the Decreasing Denitrification Potential of an Aquifer.

Numerical models for reactive transport can be used to estimate the breakthrough of a contaminant in a pumping well or at other receptors. However, as natural aquifers are highly heterogeneous with unknown spatial details, reactive transport predictions on the aquifer scale require a stochastic framework for uncertainty analysis. The high computational demand of spatially explicit reactive-transport models hampers such analysis, thus motivating the search for simplified estimation tools. We suggest performing an electron balance between the reactants in the infiltrating solution and in the aquifer matrix to obtain the hypothetical time of dissolved-reactant breakthrough at a receptor if the reaction with the matrix was instantaneous. This time we denote as the advective breakthrough time for instantaneous reaction (τinst ). It depends on the amount of the reaction partner present in the matrix, the mass flux of the dissolved reactant, and the stoichiometry. While the shape of the reactive-species breakthrough curve depends on various kinetic parameters, the overall timing scales with τinst . We calculate the latter by particle tracking. The effort of computing τinst is so low that stochastic calculations become feasible. We apply the concept to a two-dimensional test case of aerobic respiration and denitrification. A detailed spatially explicit reactive-transport model includes microbial dynamics. Scaling the time of local breakthrough curves observed at individual points by τinst decreased the variability of electron-donor breakthrough curves significantly. We conclude that the advective breakthrough time for instantaneous reaction is efficient in estimating the time over which an aquifer retains its degradation potential.

Three-Dimensional Physical and Numerical Modelling of Fracturing and Deformation Behaviour of Mining-Induced Rock Slopes

Fracturing behaviour of jointed rock mass subjected to mining can significantly affect the stability of the rock structures and rock slopes. Ore mining within an open-pit final slope would lead to large-scale strata and surface movement of the rock slope. Rock mass structure, or more specifically, the strength, spacing and distribution of rock joints, are the controlling factors that govern the failure and deformation mechanisms of the final slope. Two-dimensional (2-D) physical modelling tests have been conducted in the literature, but in general, most of them have simplified the geological conditions and neglected some key features of rock mass structure in the field. In this study, new three-dimensional (3-D) physical modelling methods are introduced, with realistic modelling of mechanical behaviour of rock mass as well as identified properties of predominant rock joint sets. A case study of Yanqianshan iron mine is considered and the corresponding 1:200 model rock slope was created for studying the rock joint effects on the strata movement and the subsidence mechanism of the slope. The physical model test results are subsequently verified with 3-D discrete element numerical modelling. Due to the presence of the predominant joints, the observed well-shaped strata subsidence in Yanqianshan iron mine was successfully reproduced in the 3-D physical model. The failure mechanism of rock slopes differs from the trumpet-shaped subsidence observed in unconsolidated soil. Due to the formation of an arching mechanism within the rock mass, the strata deformation transferred gradually from the roof of the goaf to the slope surface.

Position and flux estimation of the unexpected seepage of CO2 purposefully stored in a subseabed geological formation

To mitigate global warming, the large volume of CO2 released into the atmosphere must be reduced. CO2 capture and storage (CCS) are promising means for this. In addition, CCS operators who inject and store CO2 into subseabed geological formations may be legally required to monitor CO2 leakage into seawater, even though such events are very unlikely; after detecting unusually high CO2 concentrations, their social responsibility implies specifying the position and flux of the associated CO2 seepage in the sea site. In this study, we adopted the adjoint marginal sensitivity method to predict such parameters based on the information recorded by a limited number of CO2 sensors located on the seafloor. In particular, we newly derived the adjoint marginal sensitivity from the relationship between a source term and the measured concentrations. We successfully conducted two-dimensional tests and three-dimensional simulations with a realistic topography; tidal and ocean currents with CO2 dispersion were time-forwardly simulated and the seepage information was efficiently evaluated via time-backward numerical tests. However, the limitation of this method also emerged. We accumulated knowledge on its practical utility and proposed some ways to reduce the estimation errors. It is also inferred that this method can be applied for the source detection of various marine pollutants and resources.

An isotropic unstructured mesh generation method based on a fluid relaxation analogy

In this paper, we propose an unstructured mesh generation method based on Lagrangian-particle fluid relaxation, imposing a global optimization strategy. With the presumption that the geometry can be described as a zero level set, an adaptive isotropic mesh is generated by three steps. First, three characteristic fields based on three modeling equations are computed to define the target mesh-vertex distribution, i.e. target feature-size function and density function. The modeling solutions are computed on a multi-resolution Cartesian background mesh. Second, with a target particle density and a local smoothing-length interpolated from the target field on the background mesh, a set of physically-motivated model equations is developed and solved by an adaptive-smoothing-length Smoothed Particle Hydrodynamics (SPH) method. The relaxed particle distribution conforms well with the target functions while maintaining isotropy and smoothness inherently. Third, a parallel fast Delaunay triangulation method is developed based on the observation that a set of neighboring particles generates a locally valid Voronoi diagram at the interior of the domain. The incompleteness of near domain boundaries is handled by enforcing a symmetry boundary condition. A set of two-dimensional test cases shows the feasibility of the method. Numerical results demonstrate that the proposed method produces high-quality globally optimized adaptive isotropic meshes even for high geometric complexity.

Peridynamic simulation of two-dimensional axisymmetric pull-out tests

In this study, a systematic pull-out simulation scheme in the formwork of two dimensional (2D) axisymmetric domain using peridynamics (PD) is presented. An axisymmetric ordinary state-based peridynamic model is used to model the pull-out deformation just like the axisymmetric stress element in the finite element method (FEM). A failure criterion based on the bond energy density is adopted to predict the interfacial debonding, while a new PD contact model in the 2D axisymmetric domain is proposed to simulate the friction sliding during the pull-out process. The PD pull-out simulation scheme based on the respective 2D axisymmetric model, interfacial failure criterion and contact model is quantitatively validated in comparisons with either the FEM or analytical solutions. The whole process of the pull-out test is simulated using the proposed PD scheme, and the influences of both the interfacial fracture toughness and friction coefficient on the bond-slip behavior are investigated. The developed PD pull-out modeling scheme is capable of effectively simulating the pull-out tests and predicting the bond-slip behavior.

Improvement of ultrasonic heat transfer enhancement using acoustical focusing and resonance properties

This paper is aiming to improve the ultrasonic heat transfer enhancement by controlling the sound intensity distribution and constructing an acoustic focusing field, which can reduce energy dissipation and dramatically enhance the local sound intensity of heat transfer surface. Two design criteria are proposed to construct the acoustic focusing field by utilizing acoustic interference and acoustic resonance. Correspondingly, an elliptical acoustic focusing tank is designed and fabricated. Two-dimensional simulation and experimental tests of sound intensity distribution in the elliptical acoustic focusing tank are performed to verify the theoretical conception and design. In addition, the heat transfer coefficients are measured at different locations in the elliptical tank under natural convection, using a square tank as a control. The experimental results show that the elliptical acoustic focusing tank can promote the intensity of the whole sound field, especially the focus region compared with the square tank. The heat transfer coefficient and heat transfer enhancement rate anywhere in the elliptical tank is higher than that in the square tank. The maximum heat transfer enhancement rate of the elliptical tank is 55.3% in natural convection, which is 47.1% higher than that of the square tank under the same condition.