Free Surface Model Research Articles

An overset-grid finite-difference algorithm for seismic wavefield propagations modelling in the polar coordinate system with a complex free-surface topography

Summary Nowadays, finite-difference method has been widely applied to simulate seismic wavefield propagation in a local seismic model with a complex topography by utilizing curvilinear grids and traction image method in Cartesian coordinates system. For a global seismic model in polar coordinate system, it is still a challenge for the conventional finite-difference method to deal with the grid singularity at the center and the topographic free surface at the top. In this study, we develop a finite-difference method in polar coordinates for seismic wavefield propagation in the 2D global model. In the proposed finite-difference method, the overset-grid algorithm is used to handle the grid singularity at the center, and the curvilinear grid technique as well as the traction image method are applied to implement free-surface boundary condition on the complex topography. The proposed finite-difference method is validated in flat and topographic free-surface models by comparing synthetic waveforms with reference solutions. The seismic wavefield propagation in a realistic Mars profile is computed by the proposed finite-difference method. The proposed finite-difference method is an efficient and accurate method for seismic wave modeling in the polar coordinate system with a complex free-surface topography.

Influence of gate cutoff effect on flow mode conversion and energy dissipation during power-off of prototype tubular pump system

Understanding the cutoff effect of gates is essential for enhancing the overall quality of the pump system's power-off process, minimizing energy losses, and reducing potential risks associated with hydraulic transients. In this study, both numerical simulations and experimental investigations were conducted on the power-off process of a tubular pump system, considering scenarios with and without gate functionality. The simulations utilized a dynamic mesh method to model gate movement, incorporated the torque balance equation to determine the real-time impeller speed, and applied the 3D-VOF method for free surface modeling in reservoirs. Power-off experiments were performed on a model pump system and a prototype pump system to validate the numerical simulation results. To elucidate the mechanism of the gate's cutoff effect, flow modes during the power-off process were categorized based on the four-quadrant static test results of the pump, revealing the deviations between transient and static characteristics. By comparing the transient flow structures of the pump system under different gate operating states, specific energy dissipation behaviors during gate cutoff were analyzed. The research findings enhance the understanding of hydraulic transients, which is essential for developing more sustainable and resilient energy systems.

A natural vertical distribution calculation scheme for salinity simulation in free-surface model with quasi-stationary coordinates

A natural vertical distribution calculation scheme for salinity simulation in free-surface model with quasi-stationary coordinates

Advances of the in-house developed SWLBM framework in simulating large-scale three-dimensional violent free surface flow with intense splashing

The accurate and efficient simulation for violent free surface flow with intense splashing is import in engineering. The purpose of this paper was to extend and validate the capabilities of Sunway Lattice Boltzmann Method code (SWLBM, our in-house developed CFD framework) in simulating large-scale three-dimensional violent free surface flow. The lattice Boltzmann method was employed to solve the fluid dynamics. The interface was captured by the single-phase free surface model. For parallel computing, the computational domain was divided into parallel blocks and overlap layers were designed for inter-block communications. Several typical dam-break problems were selected for validating the ability of reproducing splashing details, where finest spatial resolution was up to about 0.6 billion cells. The numerical results were in good agreement with experimental results. The present results revealed more plentiful splashing details than various published results with relatively coarser spatial resolution. The efficiency of SWLBM was over 100 times higher than that of OpenFOAM in the testing example. It was demonstrated that SWLBM is capable of simulating large-scale violent free surface flow and reproducing splashing details with sufficient accuracy and efficiency. SWLBM has the potential to be applied in real engineering problems including simulating wave impact on decks.

DOT-type schemes for hybrid hyperbolic problems arising from free-surface, mobile-bed, shallow-flow models

Free-surface, mobile-bed, shallow-flow models may present Hybrid hyperbolic systems of partial differential equations characterised by conservative and non-conservative fluxes that can only be expressed in primitive variables. This paper presents the effort we made to derive DOT-type schemes (Osher-type schemes derived by Dumbser and Toro, 2011 [1]) for these kinds of systems formulated for the one-dimensional case. Firstly, for a Hybrid system, we managed to write a quasi-linear form characterised by the presence of a matrix, expressed as a function of the primitive variables, that multiplies the spatial derivative of the conserved variables. Next, we derived the first numerical flux by adapting the approach of Leibinger et al., 2016 [2] to this quasi-linear form. We called this result DOTHCP flux. To achieve a faster algorithm, instead of using an integration path in the space of conserved variables, as in the previous case, we employed a path in the space of primitive variables. We called this second formulation DOTHPP flux. Subsequently, we managed to account for certain physical constraints arising from the generalised Rankine-Hugoniot relations in the expression of one term of the previous flux formulation, thus obtaining the DOTHZR flux. Finally, we showed that these methods can also be applied to Combined systems characterised by conservative and non-conservative fluxes expressed in conserved variables. Several tests show the characteristics and good performances of the proposed methods when applied to Riemann problems of Hybrid and Combined systems deriving from free-surface models. Finally, thanks to the general formulation of the proposed DOT-type fluxes, these can also be applied to Hybrid and Combined hyperbolic systems deriving from different physical problems.

Constraining subducting slab viscosity with topography and gravity fields in free-surface mantle convection models

Subducted slabs provide the primary driving force for mantle convection and plate tectonics. The strength of the slab directly controls the transfer of forces between it and the lithospheric plates at the surface. However, slab viscosity constrained by surface topography and gravity data is significantly lower than that suggested by mineral physics laboratory experiments. It is unclear whether the free-slip top boundary condition used by many studies affects the inverted slab viscosity with gravity or geoid data. In this study, we constrain the subducting slab viscosity structure by comparing the computed topography and gravity in slab subduction models with a free surface with observations. The free-surface model results support relatively weak slabs (20–120 times more viscous than the upper mantle) at the bending region, consistent with previous studies with a free-slip top boundary. The viscosity of the slab below the bending region barely affects the surface topography and gravity field, and both strong and weak slabs fit the observed topography and gravity field, suggesting that extra independent observations are needed to constrain the deep slab viscosity. We investigate the comprehensive relations between subduction interface viscosity, surface topography and gravity anomaly, and trench motion. Models with trench advance have significantly low topography and gravity above the volcanic arc, contradicting subduction zone observations. Together with present trench motion observations and previous studies, we support the idea that the trench retreats under normal single-slab subduction conditions.

Numerical Investigation of Flow and Scour around Complex Bridge Piers in Wind–Wave–Current Conditions

A sea-crossing bridge is typically constructed in a marine environment with complex piers, and is susceptible to severe scour at the foundation. This study presents a numerical investigation on flow and scour around a complex pier, specifically focusing on a real-world sea-crossing bridge in China. A comprehensive CFD model incorporating hydrodynamic, free surface, sediment transport, and morphological models is employed for numerical modeling. Additionally, a wind shear stress model is considered to accurately simulate wind generation. The validation of the CFD model is achieved through comparison with experimental data of scour around a cylinder, demonstrating its capability to accurately replicate scour morphology and the temporal evolution of scour depth. Subsequently, the validated model is utilized for full-scale simulation of scour around the complex bridge pier under different wind, wave, and current conditions. The results indicate that compared to single piers with uniform cross-sectional shapes, flow patterns around complex piers are much more complicated. Scour predominantly occurs around the first row of group piles, while downstream piles experience less scour due to the sheltering effect from upstream piles. Furthermore, it becomes evident that the current exerts greater influence on pier scour than waves and wind, while the latter two factors primarily influence the superstructure of the bridge.

Computational Modeling of Gold Nanoparticle Interacting with Molecules of Pharmaceutical Interest in Water.

We derived a theory of biomolecule binding to the surface of Aun clusters and of the Au plane based on the hard soft acid base (HSAB) principle and the free electron metallic surface model. With the use of quantum mechanical calculations, the chemical potential (μ) and the chemical hardness (η) of the biomolecules are estimated. The effect of the gold is introduced via the empirical value of the gold chemical potential (-5.77 eV) as well as by using the expression (modified here) for the chemical hardness (η). The effect of an aqueous environment is introduced by means of the ligand molecular geometry influenced by the PCM field. This theory allows for a fast and low-cost estimation of binding biomolecules to the AuNPs surface. The predicted binding of thiolated genistein and abiraterone to the gold surface is about 20 kcal/mol. The model of the exchange reaction between these biomolecules and citrates on the Au surface corresponds well with the experimental observations for thiolated abiraterone. Moreover, using a model of the place exchange of linear mercaptohydrocarbons on 12-mercaptododecane acid methyl ester bound to the Au surface, the present results reflect the known relation between exchange energy and the size of the reagents.

The formation of bioaerosols in the reopening of an occluded airway

The reopening of an occluded airway can lead to the formation of droplets and aerosols, which can be released during exhalation, providing a possible mechanism of disease transmission. In this study, the flow behavior of airway occlusions (“plugs”) close to their point of rupture is examined using a free-surface model (volume of fluid), such that factors influencing the formation of droplets during their reopening can be identified. The propagation of airway occlusions is highly influenced by recirculating flow at the edge of the front interface, where significant fluctuations of wall shear stresses occur. The resulting drag force causes the rear interface to advance at a greater rate, destabilizing the plug. As the plug thickness decreases, a thin film with uniform thickness forms, resulting in a disk-like structure around the centerline. Rupture occurs around the disk formation largely due to surface tension instability. At lower pressures, smaller disks form causing the rupture to occur through a puncture point (forming no droplets); at higher pressures, a larger disk forms, with rupture occurring along the disk edge and at the center (forming multiple droplets). Upon reopening, a jet of air is produced, causing a temporary increase in shear stress along the wall. However, the magnitude and duration of this increase do not scale directly to the applied pressure, as the formation of droplets and irregularities in airway lining were found to disrupt the flow field and the shear stresses at the wall.

Highly nonlinear internal solitary waves with a free surface

A new mathematical model is derived for internal wave propagation in a two-layer fluid domain with a free surface in which the lower layer is of finite depth. The mathematical model consists of three coupled nonlinear equations for displacement of the interface and velocity potentials of the two layers, each of which is expressed as the convex combination of their values at two arbitrary depths. Model equations are correct up to O(μ4) terms, where μ is the ratio of harmonic mean of the depths of the two layers to double of a typical wavelength. Finite amplitude internal solitary wave profiles as well as free surface wave profiles are obtained numerically for different wave speeds, density ratios and depth ratios. Interfacial solitary wave profiles obtained here are in very good agreement with recent experimental observations of Zhao et al. (2020). The figures presented here demonstrate how the interfacial wave profile predicted by the free surface model differs from predictions of rigid-lid two-layer fluid models.

An improved three-dimensional lattice Boltzmann-volume of fluid (LB-VOF) method for simulation of laminar liquid jet breakup with high density ratio

Lattice Boltzmann method (LBM) has been widely developed in the past decade, while most of the previously presented LBMs are confined to two-phase problems with a low-density ratio. In the present study, we developed the free surface model based on the volume of fluid (VOF) method to a three-dimensional two-phase LBM (LBM-VOF) and utilized this new model to simulate the breakup of a water jet in the air. This problem is characterized by high density and viscosity ratios with the values of about 830 and 58, respectively. Numerical codes are implemented in the open-source library of parallel Lattice Boltzmann solver (PALABOS), and the results are compared and validated against experimental and published numerical outcomes. It is shown this new model could properly confine spurious currents. Afterward, the LBM-VOF model is used to simulate different water jet regimes, including periodic dripping, dripping faucet, and jetting regimes. Furthermore, the dynamics of fluid jet formation and droplet breakup are comprehensively discussed in different ranges of the Weber number (0.063 < We < 6) and three nozzles with different sizes. Results show that the proposed LBM-VOF model is capable of simulating all the three mentioned regimes and their specific characteristics. The proposed model accurately predicts the ranges of critical Weber number (2.4 < We < 2.84) at which the regime transition from periodic dripping to jetting occurs; which is in agreement with the theoretical relation. Moreover, when the dripping to jetting transition occurs, the length of breakup and the frequency of droplet production increased sharply by approximately 3.6 and 3, respectively, while the volume of produced droplets decreased by about 2.4.

Numerical simulation of flow-induced vibration of a circular cylinder close to a free surface at low Reynolds number

The flow-induced vibration of a two-degree-of-freedom cylinder near a free surface at low Reynolds number (Re = 200) is numerically investigated using the lattice Boltzmann method and a free-surface model. The effects of the Froude number and submergence depth on the characteristics of the flow field and cylinder vibration are discussed. With the approach of the free surface, the wake behind the cylinder interacts with the free surface, resulting in a switch in the vortex shedding mode and the fluctuation of the free surface, which in turn affects the vibration of the cylinder. Additionally, a decrease in the normalized submergence depth h ∗ results in a decrease in the transverse amplitude of vibration and an increase in the streamwise amplitude. The topology of the cylinder vibration trajectory changes from a curve of eight to a teardrop, half-moon, or ellipse shape and gradually loses symmetry. Seven characteristic parameters are extracted from the trajectory of the cylinder, among which the amplitude of the vibration frequency and the phase difference of the vibration in different directions mainly affect the symmetry and topological structure of the trajectory.

Investigation on the Performance of CO2 Absorption in Ceramic Hollow-Fiber Gas/Liquid Membrane Contactors.

The absorption efficiencies of CO2 in ceramic hollow-fiber membrane contactors using monoethanolamine (MEA) absorbent under both cocurrent- and countercurrent-flow operations were investigated theoretically and experimentally; various MEA absorbent flow rates, CO2 feed flow rates, and inlet CO2 concentrations were used as parameters. Theoretical predictions of the CO2 absorption flux were analyzed by developing the mathematical formulations based on Happel's free surface model in terms of mass transfer resistances in series. The experiments of the CO2 absorption were conducted by using alumina (Al2O3) hollow-fiber membranes to confirm the accuracy of the theoretical predictions. The simplified expression of the Sherwood number was formulated to calculate the mass transfer coefficient of the CO2 absorption incorporating experimental data. The data were obtained numerically using the fourth-order Runge-Kutta method to predict the concentration distribution and absorption rate enhancement under various fiber packing configurations accomplished by the CO2/N2 stream passing through the fiber cells. The operations of the hollow-fiber membrane contactor encapsulating N = 7 fiber cells and N = 19 fiber cells of different packing densities were fabricated in this work to examine the device performance. The accuracy derivation between experimental results and theoretical predictions for cocurrent- and countercurrent-flow operations were 1.31×10-2≤E≤4.35×10-2 and 3.90×10-3≤E≤2.43×10-2, respectively. A maximum of 965.5% CO2 absorption rate enhancement was found in the module with embedding multiple fiber cells compared with that in the device with inserting single-fiber cell. Implementing more fiber cells offers an inexpensive method of improving the absorption efficiency, and thus the operations of the ceramic hollow-fiber membrane contactor with implementing more fiber cells propose a low-priced design to improve the absorption rate enhancement. The higher overall CO2 absorption rate was achieved in countercurrent-flow operations than that in cocurrent-flow operations.

Efficient lattice Boltzmann simulation of free-surface granular flows with μ(I)-rheology

This paper presents a lattice Boltzmann framework for accurate and efficient simulation of free-surface granular flows. The granular assembly is treated as a viscoplastic fluid, whose apparent viscosity varies locally with the shear rate and pressure according to a regularized μ(I)-rheology. A single-phase free-surface model is employed to track the evolution of the particle-air interface. The lattice Boltzmann implementation is first validated by simulating a steady-state granular flow on a rough inclined plane and a good agreement with the analytical solution is achieved. The validated model is then applied to simulate a transient granular column collapse problem. Compared to a companion discrete element simulation, the lattice Boltzmann model with the μ(I)-rheology is able to capture the overall dynamic behaviors of granular column collapse. However, a different behavior is observed when a similar Bingham viscoplastic model with a fixed yield stress is applied, highlighting the pressure dependent nature of granular flows. The proposed lattice Boltzmann formulation is highly efficient compared to the conventional computational fluid dynamics, and has the potential to conduct three-dimensional continuum simulation of large-scale geophysical flows with microscopic granular physics.

A Numerical Study on the Influence of Caterpillars to the Resistance Performance of an Amphibious Vehicle

A computational fluid dynamic (CFD) simulation is performed to evaluate the resistance performance of a self-propelled amphibious vessel with caterpillars to be operated as a marine debris collection vessel at hard-to-reach areas. This study focuses on the influence of the addition of caterpillars on the vessel to the resistance performance. To capture the free surface model, the volume of fluid (VOF) method was adopted, and to express the sinkage and trim acting on the ship the Dynamic Fluid-body Interaction (DFBI) model was applied. A series of numerical simulations for resistance performance were carried out in the range of Froude number (Fn) of 0.12–0.32 for the vessels with and without caterpillars. A model test was carried out independently to verify the numerical simulation of resistance, and it indicated that the present simulation is valid with relative errors of less than 2% over the entire speed range. In subsequence, the resistance performance of the ship due to the addition of the caterpillars was evaluated, and an increase of nearly 40% at the design speed of Fn = 0.27 could be observed. In addition, in the present amphibious vessel, it was found that the ratio of the pressure resistance occupied in the total resistance was dominant, reaching around 81~92% for both cases.

Numerical simulation of the bubbling phenomenon ahead of the dam using a two-phase seepage free surface model

The bubbling phenomenon that occurred in the Huangbizhuang reservoir has caused panic and concern, as it could potentially threaten the dam safety owing to the uncertainty of causes. In contrast to the general seepage problem, the challenges of studying the bubbling process include the description of the unsteady seepage free surface and consideration of gas compressibility. To investigate the seepage behaviours of the water–air two-phase and analyse the bubbling causes, an improved conservation level set-based two-phase seepage method is established. In this new method, the generalised Darcy's law is employed to obtain the seepage pressure and velocity fields of the water–gas phases. Furthermore, the physical properties near the interface zone are determined using a Heaviside function rather than the soil–water retention curve. Before modelling the bubbling phenomenon, the performance of the proposed method is validated using two benchmark examples. Simulation results of the bubbling process show that the generation, development, and release of pore gas pressure are the root causes of the bubbling phenomenon. Moreover, the water-storage process is a key factor that affects the occurrence and development of this phenomenon. In addition, the simulation results agree well with the actual observations, verifying the effectiveness of the proposed method.

Development and implementation of a Direct Surface Description method for free surface flows in OpenFOAM

The solution procedure for two phases in OpenFOAM suffers from unphysical velocity oscillations at the free surface between the two phases. It is likely that this problem also exists in other two-phase Computational Fluid Dynamics (CFD) codes. We aim to solve this by imposing boundary conditions directly on the free surface. We have taken the first step towards a new two-phase solution method by first addressing the water phase alone. It is a free surface modelling method based on merging concepts from two existing methods: (1) A single-phase free surface method and (2) the solution method used in OpenFOAM. The underlying motivation is to enable more accurate estimation of wave induced load distributions from wave crest impacts on offshore structures. This first and foremost requires an accurate prediction of the kinematics near the free surface. We present a solution method with boundary conditions directly on the free surface, thereby the name: Direct Surface Description (DSD). Additionally it is the first time that the isoAdvector algorithm is combined with a single phase free surface method. The implementation is made in OpenFOAM, but may also relevant to other codes as well. First a still water level simulation is presented to illustrate the unphysical behavior of the existing solvers and validate the behaviour of the DSD method. The second test case is a moderately steep stream function wave in intermediate water depth. The DSD method is validated and compared to the existing solution methods of OpenFOAM: interFoam and interIsoFoam . We present a detailed comparison of surface elevations and velocity profiles. This is followed by a convergence study including wave height, velocity and phase shift. Additionally the influence of the Courant–Friedrichs–Lewy (CFL) number is studied. The stream function wave case demonstrates that the DSD method accurately predicts the free surface elevation and velocity fields without free surface undulations or oscillatory velocity fields. The convergence study underlines an increased accuracy of the DSD method. Finally, a 2D and a 3D showcase with breaking waves are presented to show that the DSD method is capable of simulating more complex and realistic cases. • The oscillatory velocities at free surface in OpenFOAM is removed by DSD-method. • Presents a rarely seen comparison of velocity profiles below wave crest and trough. • New DSD-method eliminates the air region leading to decreased CPU time. • Implementation in OpenFOAM makes the method ready for unstructured meshes. • Presents convergence study of velocity and wave heights w.r.t. mesh and CFL number.

Oxygen bubble transport in a porous transport layer of polymer electrolyte water electrolyzer

Considerable efforts have been taken to develop an effective porous transport layer (PTL) that can mitigate the mass transport resistance of proton exchange water electrolysis (PEWE). Several experiments have been conducted to understand the underlying mechanisms in the PTL that are responsible for bubble removal and performance improvement. Here, we investigate the dynamic behavior of oxygen bubble in a PTL using a free surface model in a lattice Boltzmann framework. Various PTL properties are examined to gain a fundamental understanding of the bubble transport phenomena and perform effective bubble removal from the PTL at a high current density operation. We report on the bubble volume fraction and bubble distribution inside the PTL to elucidate the impact of the PTL properties on the bubble transport behavior. Oxygen bubble transport characteristics that determine the bubble removal time have been extensively studied. The findings will enable more reliable bubble management and the development of related high-power PEWE technologies.

Two-Dimensional Conjugated Mass Transfer of Carbon Dioxide Absorption in a Hollow-Fiber Gas-Liquid Membrane Contactor.

The absorption efficiencies of CO2 in hollow-fiber membrane contactors using an ethanolamine (MEA) solvent under both concurrent- and countercurrent-flow operations were investigated theoretically and experimentally. Two-dimensional mathematical modeling was developed by Happel’s free surface model, and the resultant partial differential equations were solved analytically using the separated variables method with the use of an orthogonal expansion technique. A simplified expression of Sherwood number variations was reported by employing the relevant operations conditions and expressed in terms of the computed eigenvalues for predicting concentration distribution and absorption efficiency. It is emphasized that, in comparing various fiber packing configurations, both theoretical predictions and experimental results should be compared to find the absorption flux increment accomplished by the CO2/N2 stream passing through the fiber cells under the same mass flow rate. The value of the present mathematical treatment is evident to propose a simplified expression of the averaged Sherwood number variations, and provides the predictions of the absorption flux, absorption efficiency, average Sherwood number with the absorbent Graetz number, inlet CO2 concentration, and absorbent flow rates as parameters. The availability of such concise expressions, as developed directly from the analytical formulations, is the value of the present study. The experiments of the CO2 absorption using MEA with alumina (Al2O3) hollow fiber membranes are also set up to confirm the accuracy of the theoretical predictions. The accuracy derivations between the experimental results and theoretical predictions for concurrent- and countercurrent-flow operations are and , respectively. The operations of the hollow-fiber membrane contactor implementing N = 7 fiber cells and N = 19 fiber cells offer an inexpensive method of improving absorption efficiency by increasing fiber numbers with consideration of device performance.

Experimental and numerical investigation of a counter-flow hollow fiber membrane-based evaporative cooler

A counter-flow hollow fiber membrane-based evaporative cooler (HFMEC) was proposed. An experimental setup was developed to investigate the air handling performance of the HFMEC under various operating conditions. A numerical model was established and validated. The outlet air temperature predicted by the numerical model using free surface model showed a maximum deviation of 5% comparing with the experimental data. The model was further used to conduct a parametric analysis of the HFMEC. Six key parameters, including geometric specifications and operating conditions, were selected as factors for the sensitivity analysis. The cooling capacity and coefficient of performance (COP) were chosen as performance evaluation indicators. The simulation was performed with 27 cases for the orthogonal test. The range analysis revealed that the inlet air relative humidity and velocity, as well as packing fraction had significant impact on its cooling capacity and COP. Ranking the influence degree of key design parameters on performance evaluation indicators, this paper provides a convenient method to design and optimize the counter-flow HFMEC.