Steep Front Research Articles

A meshless Radial Basis Method (RBM) for solving the detailed population balance equation

The Radial Basis Method (RBM) is introduced for solving the Population Balance Equation (PBE). In this method, the continuous number density function is approximated by a series of symmetric multiquadric basis functions at selected global collocation points along the internal coordinates. Therefore, the RBM is considered as a meshless method. The RBM is convenient and suitable for complex problems involving nucleation, growth, breakage and aggregation phenomena. The method provides naturally a continuously differentiable, or “smooth”, solution and avoids solving ill-conditioned problems. The numerical solutions are validated analytically and numerically using different case-studies for uniform stirred-tank. For these examples, 20 collocation points were found to be enough to achieve accurate predictions. The RBM ability to predict multimodal distribution functions and moving steep fronts is moreover highlighted. The proposed method proves to be very efficient for solving the detailed PBE in terms of accuracy, stability and CPU time requirements.

Evaluating escarpment evolution and bedrock erosion rates in the western Guadalupe Mountains, West Texas and New Mexico

The Guadalupe Mountains tower above surrounding plains and basins in western Texas and southeast New Mexico. Although this mountain range is extensively studied for the Permian stratigraphy related to the petroleum reservoirs in the adjacent Delaware Basin, little is known about the geomorphic history. The western escarpment, in particular, rises abruptly from the Salt Basin to the west of the range, and Guadalupe Peak rises ~1600 m above the surrounding landscape. This study investigates how geologic processes create and maintain the steep profile of the escarpment on the western boundary of the Guadalupe Mountain Range. In-situ produced cosmogenic nuclides were used to quantify erosion rates across the steep western front of the range to assess how tectonic, climatic, and lithologic forces influence the escarpment profile. Erosion rates range from 1 to 73 m/Myr. Faster erosion rates in the southern area of the escarpment coincide with more frequently mapped faults, higher elevations at the top of the Rim, and locations with colder temperatures and higher precipitation. Topographic profiles across the western escarpment surfaces indicate greater retreat from the original positions of fault surfaces at the north end of the mountain range. Faster erosion rates in the mountain range are linked to greater uplift and more recent activity in the southern end of the Guadalupe Mountains.

Evaluation and Application of Newly Designed Finite Volume Coastal Model FESOM-C, Effect of Variable Resolution in the Southeastern North Sea

A newly developed coastal model, FESOM-C, based on three-dimensional unstructured meshes and finite volume, is applied to simulate the dynamics of the southeastern North Sea. Variable horizontal resolution enables coarse meshes in the open sea with refined meshes in shallow areas including the Wadden Sea and estuaries to resolve important small-scale processes such as wetting and drying, sub-mesoscale eddies, and the dynamics of steep coastal fronts. Model results for a simulation of the period from January 2010 to December 2014 agree reasonably well with data from numerous regional autonomous observation stations with high temporal and spatial resolutions, as well as with data from FerryBoxes and glider expeditions. Analyzing numerical solution convergence on meshes of different horizontal resolutions allows us to identify areas where high mesh resolution (wetting and drying zones and shallow areas) and low mesh resolution (open boundary, open sea, and deep regions) are optimal for numerical simulations.

Locally bound-preserving enriched Galerkin methods for the linear advection equation

In this work, we introduce algebraic flux correction schemes for enriched (P1⊕P0 and Q1⊕P0) Galerkin discretizations of the linear advection equation. The piecewise-constant component stabilizes the continuous Galerkin approximation without introducing free parameters. However, violations of discrete maximum principles are possible in the neighborhood of discontinuities and steep fronts. To keep the cell averages and the degrees of freedom of the continuous P1/Q1 component in the admissible range, we limit the fluxes and element contributions, the complete removal of which would correspond to first-order upwinding. The first limiting procedure that we consider in this paper is based on the flux-corrected transport (FCT) paradigm. It belongs to the family of predictor-corrector algorithms and requires the use of small time steps. The second limiting strategy is monolithic and produces nonlinear problems with well-defined residuals. This kind of limiting is well suited for stationary and time-dependent problems alike. The need for inverting consistent mass matrices in explicit strong stability preserving Runge–Kutta time integrators is avoided by reconstructing nodal time derivatives from cell averages. Numerical studies are performed for standard 2D test problems.

Snubber and Metal Oxide Varistor Optimization Design of Modular IGCT Switch for Overvoltage Suppression in Hybrid DC Circuit Breaker

The power electronic switches have great influences on the performance of the hybrid dc circuit breaker (DCCB). Recently, the integrated gate commutated thyristor (IGCT) is considered to be a suitable alternative full-control power device due to its high surge capability, high gate driver reliability, and low cost. Remarkably, high economic efficiency overvoltage suppression is important to the practical use of the IGCT switch. In this article, snubber and metal oxide varistor (MOV) optimization design for the purpose of reducing the passive components' cost is studied. Theoretical and mathematical analysis shows that the highest overvoltage precedes MOV's peak current. Then, the dynamic MOV model considering the response delay and steep front effect is built up. Next, an improved simulation circuit for calculating the highest overvoltage is established. The comparisons with experiment indicate the feasibility and accuracy of the simulation circuit. Based on the simulation results, the optimization design for overvoltage suppression is demonstrated and a cost performance promotion of 8.5% is obtained. Furthermore, the guidance of stray inductance for the structural design is also determined. In the end, a prototype for 10-kV DCCB is constructed and the tests of the IGCT switches verify the feasibility and validity of the overvoltage suppression design.

Seismic modeling and expression of common fold-thrust structures

We have conducted seismic modeling of common fold-thrust structures to understand the common geologic parameters influencing seismic data and to understand the common pitfalls associated with interpreting prestack time migration (PSTM) and prestack depth migration (PSDM) data. Mode 1 fault-bend folds are generally well-imaged in PSTM data, provided the correct migration velocities are used for the dipping back and front limbs. Seismic pull-ups of the footwall related to lateral velocity variations can result in problems in interpreting the fault geometry and the subthrust area underlying the crest. Fault-tip fault-propagation folds also show significant footwall pull-ups and show poor to no imaging of the steep front limbs. The geometry of trishear fault-propagation folds is dependent on the maximum slip on the fault (S) and the fault propagation to slip ratio (P/S ratio). We found that the slip has a strong influence on the dip of the front limb and therefore the quality of imaging whereas the P/S ratio, which controls the degree of folding versus thrust faulting, has only a secondary effect. For the front limb, only the area near the synclinal axial plan is well-imaged, so that the fault geometry and extent of propagation are typically difficult to interpret. The front limb dips are also sensitive to the accuracy of the rms velocity model used for migration. Lower velocities result in steeper dipping reflectors, whereas higher velocities result in shallower dips. In general, PSDM provides better imaging of the structures; however, the accuracy and quality of the image are dependent on the velocity models and interpretation derived from the PSTM data.

Non‐hydrostatic, Non‐linear Processes in the Surf Zone

AbstractIn the surf zone, non‐hydrostatic processes are either neglected or estimated using linear wave theory. The recent development of technologies capable of directly measuring the free surface elevation, such as 2‐D lidar scanners, allow for a thorough assessment of the validity of such hypotheses. In this study, we use subsurface pressure and lidar data to study the non‐linear and non‐hydrostatic character of surf zone waves. Non‐hydrostatic effects are found important everywhere in the surf zone (from the outer to the inner surf zones). Surface elevation variance, skewness, and asymmetry estimated from the hydrostatic reconstruction are found to significantly underestimate the values obtained from the lidar data. At the wave‐by‐wave scale, this is explained by the underestimation of the wave crest maximal elevations, even in the inner surf zone, where the wave profile around the broken wave face is smoothed. The classic transfer function based on linear wave theory brings only marginal improvements in this regard, compared to the hydrostatic reconstruction. A recently developed non‐linear weakly dispersive reconstruction is found to consistently outperform the hydrostatic or classic transfer function reconstructions over the entire surf zone, with relative errors on the surface elevation variance and skewness around 5% on average. In both the outer and inner surf zones, this method correctly reproduces the steep front of breaking and broken waves and their individual wave height to within 10%. The performance of this irrotational method supports the hypothesis that the flow under broken waves is dominated by irrotational motions.

Monolithic convex limiting for continuous finite element discretizations of hyperbolic conservation laws

Using the theoretical framework of algebraic flux correction and invariant domain preserving schemes, we introduce a monolithic approach to convex limiting in continuous finite element schemes for linear advection equations, nonlinear scalar conservation laws, and hyperbolic systems. In contrast to flux-corrected transport (FCT) algorithms that apply limited antidiffusive corrections to bound-preserving low-order solutions, our new limiting strategy exploits the fact that these solutions can be expressed as convex combinations of bar states belonging to a convex invariant set of physically admissible solutions. Each antidiffusive flux is limited in a way which guarantees that the associated bar state remains in the invariant set and preserves appropriate local bounds. There is no free parameter and no need for limit fluxes associated with the consistent mass matrix of time derivative term separately. Moreover, the steady-state limit of the nonlinear discrete problem is well defined and independent of the pseudo-time step. In the case study for the Euler equations, the components of the bar states are constrained sequentially to satisfy local maximum principles for the density, velocity, and specific total energy in addition to positivity preservation for the density and pressure. The results of numerical experiments for standard test problems illustrate the ability of built-in convex limiters to resolve steep fronts in a sharp and nonoscillatory manner.

Observations of Shoaling Nonlinear Internal Bores across the Central California Inner Shelf

AbstractWe present observations of shoaling nonlinear internal bores off the coast of central California. The dataset includes 15 moorings deployed during September–October 2017 and cross-shore shipboard surveys. We describe the cross-shore structure and evolution of large-amplitude internal bores as they transit from 9 km (100-m depth) to 1 km offshore (10 m). We observe that two bores arrive each semidiurnal period, both propagating from the southwest; of the total, 72% are tracked to the 10-m isobath. The bore speeds are subtidally modulated, but there is additional bore-to-bore speed variability that is unexplained by the upstream stratification. We quantify temporal and cross-shore variability of the waveguide (the background conditions through which bores propagate) by calculating the linear longwave nonrotating phase speed co and using the nonlinearity coefficient of the Korteweg–de Vries equation α as a metric for stratification. Bore fronts are generally steeper when α is positive and are more rarefied when α is negative, and we observe the bore’s leading edge to rarefy from a steep front when α is positive offshore and negative inshore. High-frequency α fluctuations, such as those nearshore driven by wind relaxations, contribute to bore-to-bore variability of the cross-shore evolution during similar subtidal waveguide conditions. We compare observed bore speeds with co and the rotating group velocities cg, concluding that observed speeds are always faster than cg and are slower than co at depths greater than 32 m and faster than co at depths of less than 32 m. The bores maintain a steady speed while transiting into shallower water, contrary to linear estimates that predict bores to slow.

Catastrophic landscape modification from a massive landslide tsunami in Taan Fiord, Alaska

The October 17th, 2015 Taan Fiord landslide and tsunami generated a runup of 193 m, nearly an order of magnitude greater than most previously surveyed tsunamis. To date, most post-tsunami surveys are from earthquake-generated tsunamis and the geomorphic signatures of landslide tsunamis or their potential for preservation are largely uncharacterized. Additionally, clear modifications described during previous post-tsunami surveys are often ephemeral and unlikely to be preserved. Documented geomorphic modifications of several low gradient fan deltas within Taan Fiord make it an excellent laboratory for characterizing signatures of a landslide tsunami event. Geomorphic changes to fan deltas in Taan Fiord caused by the landslide-generated tsunami included complete vegetation loss over more than 0.6 km2 of fan surfaces, formation of steep fan front scarps up to 10 m high, extensive local alterations of fan topography, and formation of new tsunami return-flow channels. Two relatively stable fan deltas in Taan Fiord were heavily vegetated prior to the Taan event and may preserve features of tsunami modification for decades to centuries. If this is the case, fan deltas may be a previously unrecognized location for preservation of tsunami signatures in the recent past. Fans in poorly monitored regions, such as Greenland, could thus hold evidence of previously unidentified recent landslide tsunami events.

Development of the Concept of High-Power Microwave Oscillators with Phase Locking by an External Signal

By simulations and experiments we develop a method for generation phase locking of a Ka-band subgigawatt nonstationary relativistic backward-wave oscillator (BWO) with an external radio pulse, the duration of which is considerably greater than the pulse duration of a driven BWO. The level of input power (about 20 kW), which provided phase locking with a total spread of about 1.2 rad, is determined both for the case of competition with an electromagnetic disturbance from a steep front of the beam current and the case of a slow current rise without phase locking in the self-excitation mode. The phase locking effect is achieved with a significant difference in the frequencies of the external radio pulse and driven BWO (about 1 GHz) and hence differs from the amplification mode.

Polynomial Chaos Level Points Method for One-Dimensional Uncertain Steep Problems

We propose an alternative approach to the direct polynomial chaos expansion in order to approximate one-dimensional uncertain field exhibiting steep fronts. The principle of our non-intrusive approach is to decompose the level points of the quantity of interest in order to avoid the spurious oscillations encountered in the direct approach. This method is more accurate and less expensive than the direct approach since the regularity of the level points with respect to the input parameters allows achieving the convergence with low-order polynomial series. The additional computational cost induced in the post-processing phase is largely offset by the use of low-level sparse grids that require a weak number of direct model evaluations in comparison with high-level sparse grids. We apply the method to subsurface flows problem with uncertain hydraulic conductivity. Infiltration test cases having different levels of complexity are presented.

An exact source-term balancing scheme on the finite element solution of shallow water equations

In this paper, a numerical model is presented based on a semi-discrete Streamline Upwind Petrov–Galerkin scheme for solving the two-dimensional shallow water equations with arbitrary bed topography and wetting–drying fronts. The present finite element method is implemented for moving-boundary problems on fixed numerical meshes. In order to satisfy the C-property for both still water and dry regions, a new exact source-term balancing method is presented within the finite element framework. The formulation is stabilized using two different stabilization terms, and a discontinuity-capturing scheme is used to simulate steep wave fronts. The second-order scheme is applied for both temporal and spatial discretization. The proposed mathematical balancing method is verified through well-known test cases including the traditional dam break problem, evolution of a dam break wave over an obstacle, and oscillation of a bead of water in a parabolically-shaped basin.

Active distant binocular filter with complementary nematic liquid crystal structures for observation of millisecond stereoscopic images

The fast active distant binocular filter (DBF) with two complementary nematic liquid crystal (NLC) π-structures for observing the frame-sequential stereoscopic images is described. The DBF is characterized by steep front and rear edges of the pulse optical response defined by the fast (about 50 to 200 μs) rise time of the π-structures. Their relatively long decay time (about 2 ms) during relaxation processes does not affect the transition times of the DBF optical response. The corresponding long phase shifts in two π-structures are mutually compensated with use of the developed algorithms of electronic control. The DBF optical characteristics are studied theoretically and experimentally for selection of white light fluxes with duration in several milliseconds typical for the common stereoscopic system. The minimum duration of the selected view images can be a fraction of a millisecond. When compared stereo glasses with conventional NLC shutters, the described active DBF allows to provide the increased optical efficiency and absence of mechanical stress on the face (head) of the observer to improve the comfort of stereo image observation.

Modular Design Methodology of DC Breaker Based on Discrete Metal Oxide Varistors With Series Power Electronic Devices for HVdc Application

Different from the continuous-switching behavior of series power electronic devices in converters, the single-switching attribute of dc circuit breakers (DCBs) provides opportunities to integrate metal oxide varistors (MOVs), balancing circuits, and series power devices. This paper proposes a modular design methodology based on discrete MOVs of a DCB with series power electronic devices. The modular dc circuit breaker (MDCB) topology and voltage balance issues, the steep front effect and solution, and the design method are proposed and analyzed in this paper. Compared with the traditional DCB, the MDCB has a self-balancing ability, thereby removing the voltage-balancing circuit and reducing the number of series modules. The standard designed cell can be operated as an independent DCB or compose a high-voltage DCB in series flexibly, which decreases the difficulty of design and commission. Finally, a series experimental platform based on an insulated-gate commutated thyristor, an insulated-gate bipolar transistor, and an injection-enhanced gate transistor is built to verify the correctness and effectiveness of the proposed design methodology.

A Lagrangian Particle Algorithm (SPH) for an Autocatalytic Reaction Model with Multicomponent Reactants

For the numerical simulation of convection-dominated reacting flow problems governed by convection-reaction equations, grids-based Eulerian methods may cause different degrees of either numerical dissipation or unphysical oscillations. In this paper, a Lagrangian particle algorithm based on the smoothed particle hydrodynamics (SPH) method is proposed for convection-reaction equations and is applied to an autocatalytic reaction model with multicomponent reactants. Four typical Eulerian methods are also presented for comparison, including the high-resolution technique with the Superbee flux limiter, which has been considered to be the most appropriate technique for solving convection-reaction equations. Numerical results demonstrated that when comparing with traditional first- and second-order schemes and the high-resolution technique, the present Lagrangian particle algorithm has better numerical accuracy. It can correctly track the moving steep fronts without suffering from numerical diffusion and spurious oscillations.

Piecewise loading bed for reversible adsorption of VOCs on silica gels

Abstract The vacuum swing adsorption (VSA) with silica gel (SG) is proved to be a promising method for the recovery of volatile organic compounds (VOCs). The adsorption mechanisms of o-xylene on silica gels with different pore size have been revealed through the mathematic modeling of adsorption isotherms. The analysis of adsorption kinetics indicates that SG with micropore shows a steep concentration front and a long breakthrough time due to the strong adsorption force field, negligible transfer resistance and compressive effect of favorable isotherm. However, the reversible capillary condensation and mass transfer resistance cause a dispersed front and a short breakthrough time for mesoporous SG. The fast desorption rate makes mesoporous SG more energy-efficient compared with SG with micropore. Accordingly, to further improve the front slope and utilization of mesoporous SG in the adsorption process, a small amount of SG with micropore was loaded in the end of the fixed bed. The breakthrough time of the piecewise loading bed increased by 55.8% at the same loading volume with single mesoporous SG. The energy consumption was observed to exhibit an obviously decrease from 1.819 kWh/m3 to 1.295 kWh/m3, which proved that the piecewise loading method could recover VOCs in a more energy-saving way.

Viscoplastic surges down an incline

Asymptotic analyses and numerical computations are reported for surges of viscoplastic fluid down an incline with low inertia. The asymptotic theory applies for relatively shallow gravity currents. The computations use the volume-of-fluid method for tracking the interface; the constitutive law is dealt with by the augmented-Lagrangian method. The anatomy of the surge consists of an upstream region that converges to a uniform sheet flow, and over which a truly rigid plug sheaths the surge. The plug breaks further downstream due to the build up of the extensional stress acting upon it, leaving instead a weakly yielded superficial layer, or pseudo-plug. Finally, the surge ends in a steep flow front that lies beyond the validity of shallow asymptotics.

RS-20MR High-Current Relativistic Electron Beam Generator Based on a Plasma Opening Switch and Its Applications

A modified scheme of the RS-20MR generator is presented that can be used not only as a source of high-power pulsed hard X-ray emission (the dose power per 1-L volume in atmospheric air exceeds 1010 rad/s) but also as a tool to study various processes occurring under the interaction of high-current electron beams with materials: excitation and propagation of shock waves, destruction of solids, etc. Due to specific properties of the sharpening system, the diode voltage pulse has a relatively steep front, which ensures the dominance electrons with energies of about 1 MeV in the beam. For electron beams with currents of I = 20–100 kA and particle energies of E ≥ 0.5 MeV, isochoric energy release can be achieved in the volume of the irradiated sample. This can lead to substantial changes in the formation mechanism of a shock wave and the character of damage it causes. The results of the first experiments of this kind are reported.

Simulation and analysis of a gas insulated switchgear explosion accident caused by a failure of high‐voltage circuit breaker in a thermal power plant

This study analyses a gas insulated switchgear explosion accident caused by a failure of the circuit breaker (CB) in a thermal power plant, which resulted in the explosion of the CB and the burning of the potential transformer (PT). Through X-ray detection and disassemble examination of the damaged CB, it is found that the A-phase moveable contact was not opened completely. After analysing the voltage waveform obtained from the phasor measurement unit recorder system, it is speculated that this failure is caused by the process of repeated arc strike. For verification and further analysis, the fault process is simulated in the EMTP; the arc is properly modelled by an extended KEMA's equation-based model which is proposed in this study. The simulation results match well with the actual situation; the contact gap would be repeated breakdown because its breakdown voltage is reduced, and the very fast transient overvoltage (VFTO) would be generated in these repeated strike processes. Due to the steep front and high amplitude of VFTO, the insulation of the PT would be damaged and led to the occurrence of PT short-circuit fault. The current would increase rapidly and causes the CB to explode subsequently.