SPH method for long-time simulations of sloshing flows in LNG tanks

Simulation of wave overtopping by an incompressible SPH model

Study of beach permeability's influence on solitary wave runup with ISPH method

The load assessment in water impacts problems involving complex geometries is generally a quite challenging task for numerical solvers. Indeed, the occurrence of large free-surface deformation, air cushioning and possible compressibility effects strain the standard Computational Fluid Dynamics (CFD) codes to their limits. In the present work, an enhanced Smoothed Particle Hydrodynamics (SPH) model is adopted to evaluate the pressures acting on the surface of smooth and corrugated panels impacting water and the numerical outcomes are compared to experimental data and analytical solutions. Specifically, the water entry of a flat panel at 4° is firstly studied in order to highlight the main critical aspects underlying the numerical solution of water impacts with small deadrise angles. Then, the water impact of a Mark III type panel (a corrugated insulation panel) adopted in LNG tanks is considered. Experimental data involving wet drop tests of both flat and corrugated panels have been performed and the pressures during the impact have been measured at several points along the panel surface. Complex features of the flow, such as 3D effects and air-cushioning, have been addressed by a developing the numerical study in steps of increasing complexity.

To simulate free surface flows, various numerical methods can be used. One of these numerical schemes is Smoothed particle hydrodynamics which, as a Lagrangian method, has been considered by many of researchers to model violent free surface deformation. In the present article, an effort has been made to find how solitary wave generation can be simulated using SPH method, more accurately. WCSPH formulation was utilized, different time stepping algorithms were considered and the effects of density filter and smoothing length on simulated solitary wave, and wave breaking were studied. The obtained results were compared with other solutions existing in the literature. Based on the numerical findings, it is concluded that predictor-corrector scheme in conjunction with moving least square (MLS) density filter can give more accurate results. It was also indicated that number of time steps in which density filter must be performed, plays an important role in achieving favorable results.

A novel CFD approach based on adaptive mesh refinement (AMR) technique is being developed for numerical simulation of violent free surface flows. CIP method is applied to the flow solver and tangent of hyperbola for interface capturing with slope weighting (THINC/SW) scheme is implemented as the free surface capturing scheme. The PETSc library is adopted to solve the linear system. The linear solver is redesigned and modified to satisfy the requirement of the AMR mesh topology. In this paper, our CFD method is outlined and newly obtained results on numerical simulation of violent free surface flows are presented.

In this study, a new model of Laplacian operator is formulated as a hybrid of an incompressible SPH (I-SPH) method with Taylor expansion and moving least-squares method. Accuracy of the proposed Laplacian model in solving 2-D elliptic partial differential equations for a unit square computational domain is compared with the conventional I-SPH Laplacian operator. The results show significant improvement in accuracy for the proposed model on regular, highly irregular and multi-resolution irregular node distributions employed for computational domain discretization. The proposed Laplacian model because of notable accuracy can be applied for more efficient simulation of free surface flows.

A diffuse interface method for complex three-dimensional free surface flows

The smoothed particle hydrodynamics method has been applied in modeling violent flows with the free surface. Much effort has been made in reducing the computational costs in simulating the three-dimensional two-phase flows with the violently deformed free surface and breaking waves. Although the adaptive particle refinement approach has been developed to concentrate fine resolution only in the region of interest, its efficiency still hardly meets the demand of large-scale numerical simulation. In order to improve its efficiency further, a multi-cell linked list algorithm coupling with the adaptive particle refinement for the smoothed particle hydrodynamics model is implemented in the graphic processing unit-based code. Particles are identified not only by its position but also by its resolution and trait. The accuracy of the numerical model for solving two-phase flows with the free surface is validated through computing a two-dimensional dam-break flow and the hydrodynamic flows of spheres vertically entering the water from the air. The numerical results agree well with the experimental data available. For the cases of water entry of a sphere of different densities, the development of open cavity and cavity sealing is discussed in terms of the pinch-off depth and the corresponding sphere depth. Simulations show that the smoothed particle hydrodynamics method with the adaptive particle refinement possesses the characteristics of good accuracy, time-saving, and high efficiency in simulating three-dimensional two-phase flows.

Purpose – The purpose of this paper is to present an efficient smoothed particle hydrodynamics (SPH) method particularly adapted for the geometrically nonlinear analysis of structures. Design/methodology/approach – In order to resolve the inconsistency phenomenon which systematically occurs in the standard SPH method at the domain’s boundaries of the studied structure, the classical kernel function and its spatial derivatives were modified by the use of Taylor series expansion. The well-known tensile instabilities inherent to the Eulerian SPH formulation were attenuated by the use of the Total Lagrangian Formulation (TLF). Findings – In order to demonstrate the effectiveness of the present improved SPH method, several numerical applications involving geometrically nonlinear behaviors were carried out using the explicit dynamics scheme for the time integration of the PDEs. Comparisons of the obtained results using the present SPH model with analytical reference solutions and with those obtained using ABAQUS finite element (FE) commercial software, show its good accuracy and robustness. Practical implications – An additional application including a multilayered composite structure and involving buckling and delamination was investigated using the present improved SPH model and the results are compared to the FE results, they confirmed both the efficiency and the accuracy of the proposed method. Originality/value – An efficient 2D-continuum SPH model for the geometrically nonlinear analysis of thin and thick structures is proposed. Contrarily to the classical SPH approaches, here the constitutive material relations are used to link naturally the stresses and strains. The Total Lagrangian approach is investigated to alleviate the tensile instabilities problem, allowing at the same time to avoid the updating procedure of the neighboring particles search and therefore reducing CPU usage. The proposed approach is valid for isotropic and multilayered composites structures undergoing large transformations. CPU time savings and better results with the new 2D-continuum SPH formulation compared to the classical continuum SPH. The explicit dynamic scheme was used for time integration allowing a fast resolution algorithm even for highly nonlinear problems.

Multi-symplectic quasi-interpolation method for Hamiltonian partial differential equations

For violent sloshing, the flow field becomes complicated and 3-D effect is non-negligible. In addition to the excitation direction, the wave can also propagate perpendicular to the excitation direction. Due to the superposition of waves from different directions, the impact pressure imposed on the wall of the tank may increase. In this paper, our in-house solver MPSGPU-SJTU based on moving particle semi-implicit (MPS) method coupled with GPU techniques is employed for the liquid sloshing simulation, to study the factors leading to the 3-D effect. Firstly, a series of sloshing simulations are carried out to validate the reliability of present solver. Then, the sensitivity of 3-D effect against some parameters, such as excitation frequency, dimensions of the tank and filling ratio, is checked through numerical simulations. Time histories of pressure obtained by 2-D and 3-D simulations are compared to judge the occurrence of 3-D effect. It concludes that effects of those parameters are all significant.

Hydrodynamic flow transition dynamics in a spacer filled filtration channel using direct numerical simulation

It is known that the Euler and Navier-Stokes equations, which describe flows of ideal and viscid gases, are the set of equations that are modelling the conservation laws for energy, linear momentum and mass. As it will be shown, the integrability and properties of the solutions to the Euler and Navier-Stokes equations depend, firstly, on the consistency of equations in the set of Euler and Navier-Stokes equations and, secondly, on the properties of conservation laws.It was found that the Euler and Navier-Stokes equations have solutions of two types, namely, the solutions that are not functions (depend not only on coordinates) and generalized solutions that are functions but realized discretely, and hence, functions or their derivatives have discontinuities. A transition from the solutions of first type to generalized solutions describes the process of transition of gas-dynamic system from non-equilibrium state to the locally-equilibrium one. Such a process is accompanied by the emergence of any observable formations (such as waves, vortices, turbulent pulsations and so on), which are described by generalized solutions.This discloses the mechanism of such processes as emergence vorticity and turbulence.These results were obtained using the relation that is deduced from the Euler and Navier-Stokes equations and contains the entropy, which specifies the state of gas-dynamic system.

The present study performed numerical simulations of a solitary wave propagation problem using a modified surface capturing method, and examined numerical accuracy for applications to free surface flow. The moving free surface was accurately tracked by the modified surface capturing method. Maximum run-up heights in the present study are in good agreement with the previous theoretical, numerical and experimental results. The phase shift qualitatively agrees with theoretical result, while there is a discrepancy between numerical and experimental ones. As compared with the previous method, the modified surface capturing method suppressed the numerical smearing of the free surface which is generated by the numerical diffusions. Furthermore, it was confirmed that the volume error is small and that the conservation property in the present study is greatly improved when the wave is propagating.

Reciprocating compressors represent the most renowned and extensively utilized compressors within the positive displacement category. A compressor that takes input gas at pressures above atmospheric and delivers it very high pressures (> 100 bar) is specifically called a booster pump. These pumps commonly consist of two or more piston-cylinder units in series, connected through check valves that determine the final delivery pressure, and they are instrumental in a range of applications centered around the storage and delivery of gases and fuels. Despite the availability of various booster pumps in the global market, literature offers limited insights into their design specifics. The design intricacies of a booster pump, tailored to operate at specified output pressure and mass flow rate, are contingent upon the interplay of coupled flow dynamics and heat transfer phenomena within the system. These phenomena include fluid flow dynamics through check valves, heat transfer across cylinder walls, and mechanical properties of pump materials, alongside cyclic operational parameters. To address this gap, we have embarked on an experimental-computational investigation aimed at elucidating the transport processes occurring in a single-cylinder booster pump. This work focuses on computational investigations concerning gas compression and the actuation of check valves in a single-cylinder reciprocating booster. Momentum and energy conservation equations were solved on a dynamic mesh platform through Ansys Fluent. Adiabatic conditions were employed, and the numerical solver was partially validated by comparison with thermodynamic theory for simulations conducted in a closed adiabatic cylinder. Calculations were then extended for an open cylinder with inlet and outlet check valves. Simulations indicate that forced cooling plays an important role for the longevity of sealing parts.