Search Results (16)

This research addresses and resolves current challenges in meshless Lagrangian methods for simulating viscoelastic materials. A split-step scheme, or pressure Poisson reformulation of the Navier–Stokes equations, is introduced for incompressible viscoelastic flows in a Lagrangian context. The Lagrangian differencing dynamics (LDD) method, which is a thoroughly validated Lagrangian method for Newtonian and non-Newtonian incompressible flows, is extended to solve the introduced split-step scheme to simulate viscoelastic flows based on the Oldroyd-B constitutive model. To validate and evaluate the new method’s capabilities, the following benchmarks were used: lid-driven cavity flow, droplet impact response, 4:1 planar sudden contraction, and die swelling. These findings highlight the LDD method’s effectiveness in accurately simulating viscoelastic flows and capturing large deformations and memory effects. Even though the extra stress was directly modeled without any regularization approach, the method produced stable simulations for high Weissenberg numbers. The stability and performance of the the Lagrangian numerics for complex temporal evolution of material properties and stress responses encourage its use for industrial problems dealing with polymers. Full article

In this paper, we study the properties of trajectories of systems of ordinary differential equations generated by the velocity field of a moving incompressible viscoelastic fluid with memory along the trajectories in a domain with multiple boundary components. The case of a velocity field from a Sobolev space with inhomogeneous boundary conditions is considered. The properties of the maximal intervals of existence of solutions to the Cauchy problem corresponding to a given velocity field are investigated. The study assumes the approximation of a velocity field by a sequence of smooth fields followed by a passage to the limit. The theory of regular Lagrangian flows is used. Full article

We propose a methodology for the rheological characterization of a semisolid metal slurry using experimental squeeze-flow data. The slurry is modeled as a structural thixotropic viscoplastic material, obeying the regularized Herschel–Bulkley constitutive equation. All rheological parameters are assumed to vary with the structure parameter that is governed by first-order kinetics accounting for the material structure breakdown and build-up. The squeeze flow is simulated using finite elements in a Lagrangian framework. The evolution of the sample height has been studied for wide ranges of the Bingham and Reynolds numbers, the power-law exponent as well as the kinetics parameters of the structure parameter. Systematic comparisons have been carried out with available experimental data on a semisolid aluminum alloy (A356), where the sample is compressed from its top side under a specified strain of 80% at a temperature of 582 °C, while the bottom side remains fixed. Excellent agreement with the experimental data could be achieved provided that at the initial instances (up to 0.01 s) of the experiment, the applied load is much higher than the nominal experimental load and that the yield stress and the power-law exponent vary linearly with the structure parameter. The first assumption implies that a different model, such as an elastoviscoplastic one, needs to be employed during the initial stages of the experiment. As for the second one, the evolution of the sample height can be reproduced allowing the yield stress to vary from 0 (no structure) to a maximum nominal value (full structure) and the power-law exponent from 0.2 to 1.4, i.e., from the shear-thinning to the shear-thickening regime. These variations are consistent with the internal microstructure variation pattern known to be exhibited by semisolid slurries. Full article

This article is devoted to the study of the existence of trajectory and global attractors in the Kelvin–Voigt fluid model, taking into account memory along the trajectories of fluid motion. For the model under study, the concept of a weak solution on a finite segment and semi-axis is introduced and the existence of their solutions is proved. The necessary exponential estimates for the solutions are established. Then, based on these estimates, the existence of trajectory and global attractors in the problem under study is proved. Full article

This article is devoted to the investigation of the weak solvability to the initial boundary value problem, which describes the viscoelastic fluid motion with memory. The memory of the fluid is considered not at a constant position of the fluid particle (as in most papers on this topic), but along the trajectory of the fluid particle (which is more physical). This leads to the appearance of an unknown function z, which is the trajectory of fluid particles and is determined by the velocity v of a fluid particle. However, in this case, the velocity v belongs to $L_2(0,T;V^1)$, which does not allow the use of the classical Cauchy Problem solution. Therefore, we use the theory of regular Lagrangian flows to correctly determine the trajectory of the particle. This paper establishes the existence of weak solutions to the considered problem. For this purpose, the topological approximation approach to the study of mathematical hydrodynamics problems, constructed by Prof. V. G. Zvyagin, is used. Full article

In this paper, we numerically investigate the turbulence modulation produced by long flexible fibres in channel flow. The simulations are based on an Euler–Lagrangian approach, where fibres are modelled as chains of constrained, sub-Kolmogorov rods. A novel algorithm is deployed to make the resolution of dispersed systems of constraint equations, which represent the fibres, compatible with a state-of-the-art, Graphics Processing Units-accelerated flow-solver for direct numerical simulations in the two-way coupling regime on High Performance Computing architectures. Two-way coupling is accounted for using the Exact Regularized Point Particle method, which allows to calculate the disturbance generated by the fibers on the flow considering progressively refined grids, down to a quasi-viscous length-scale. The bending stiffness of the fibers is also modelled, while collisions are neglected. Results of fluid velocity statistics for friction Reynolds number of the flow $R{e}_{\tau }=150$ and fibers with Stokes number $St$ = 0.01 (nearly tracers) and 10 (inertial) are presented, with special regard to turbulence modulation and its dependence on fiber inertia and volume fraction (equal to $\varphi =2.12$·${10}^{-5}$ and $2.12$·${10}^{-4}$). The non-Newtonian stresses determined by the carried phase are also displayed, determined by long and slender fibers with fixed aspect ratio ${\lambda }_{tot}=200$, which extend up to the inertial range of the turbulent flow. Full article

Polymer extrudate swelling is a rheological phenomenon that occurs after polymer melt flow emerges at the die exit of extrusion equipment due to molecular stress relaxations and flow redistributions. Specifically, with the growing demand for large scale and high productivity, polymer pipes have recently been produced by extrusion. This study reports the development of a new incompressible non-isothermal finite volume method, based on the Arbitrary Lagrangian–Eulerian (ALE) formulation, to compute the viscous flow of polymer melts obeying the Herschel–Bulkley constitutive equation. The Papanastasiou-regularized version of the constitutive equation is employed. The influence of the temperature on the rheological behavior of the material is controlled by the Williams–Landel–Ferry (WLF) function. The new method is validated by comparing the extrudate swell ratio obtained for Bingham and Herschel–Bulkley flows (shear-thinning and shear-thickening) with reference data found in the scientific literature. Additionally, the essential flow characteristics including yield-stress, inertia and non-isothermal effects were investigated. Full article

This paper presents the Eulerian–Lagrangian approach for numerical modeling of high-speed gas-droplet flows and aeroacoustics. The proposed hybrid approach is implemented using the OpenFOAM library and two different methods. The first method is based on a hybrid convective terms approximation method employing a Kurganov–Tadmor and PIMPLE scheme. The second method employs the regularized or quasi-gas dynamic equations. The Lagrangian part of the flow description uses the OpenFOAM cloud model. Within this model, the injected droplets are simulated as packages (parcels) of particles with constant mass and diameter within each parcel. According to this model, parcels moving in the gas flow could undergo deceleration, heating, evaporation, and breakup due to hydrodynamic instabilities. The far-field acoustic noise is predicted using Ffowcs Williams and Hawking’s analogy. The Lagrangian model is verified using the cases with droplet evaporation and motion. Numerical investigation of water microjet injection into the hot ideally expanded jet allowed studying acoustic properties and flow structures, which emerged due to the interaction of gas and liquid. Simulation results showed that water injection with a mass flow rate equal to 13% of the gas jet mass flow rate reduced the noise by approximately 2 dB. This result was in good coincidence with the experimental observations, where maximum noise reduction was about 1.6 dB. Full article

A new coupling method, immersed moving boundary–discrete element method–lattice Boltzmann method (IMB-DEM-LBM), is proposed to simulate particle flow for application in soil mechanics or coastal engineering. In this study, LBM fluid is simulated on the regular Eulerian grid and Lagrangian particle motion is governed by DEM while IMB couples the two algorithms. The new method is promising and robust as it resolves numerical instability near the particle boundary caused by mesh distortion in the conventional grid method. In IMB, the interface lattice solid fraction determines the distribution function ratio of non-equilibrium bounce back and Bhatnagar-Gross-Krook (BGK) collision. The non-equilibrium bounce back at moving boundary results in the fluid momentum change and contributes to the hydrodynamic force on particle. For numerical stability, this paper introduces the hydrodynamic force calculation concept from IB (immersed boundary method) to IMB, and at the same time, proposes a new solid fraction calculation method for sphere that divides the intersection into simple sector and triangle, as well as calculates the intersection area by vector. With this method, approximate inaccuracy is overcome while complicated integration is avoided. Full article

In this paper, we consider some two phase problems of compressible and incompressible viscous fluids’ flow without surface tension under the assumption that the initial domain is a uniform $W_q^{2-1/q}$ domain in ${\mathbb{R}}^N$ ($N\ge 2$). We prove the local in the time unique existence theorem for our problem in the $L_p$ in time and $L_q$ in space framework with $2<p<\infty$ and $N<q<\infty$ under our assumption. In our proof, we first transform an unknown time-dependent domain into the initial domain by using the Lagrangian transformation. Secondly, we solve the problem by the contraction mapping theorem with the maximal $L_p$-$L_q$ regularity of the generalized Stokes operator for the compressible and incompressible viscous fluids’ flow with the free boundary condition. The key step of our proof is to prove the existence of an $\mathcal{R}$-bounded solution operator to resolve the corresponding linearized problem. The Weis operator-valued Fourier multiplier theorem with $\mathcal{R}$-boundedness implies the generation of a continuous analytic semigroup and the maximal $L_p$-$L_q$ regularity theorem. Full article

In this paper, we investigated how the added mass, the hydrodynamic damping and the drag coefficient of a Wave Energy Converter (WEC) can be calculated using DualSPHysics. DualSPHysics is a software application that applies the Smoothed Particle Hydrodynamics (SPH) method, a Lagrangian meshless method used in a growing range of applications within the field of Computational Fluid Dynamics (CFD). Furthermore, the effect of the drag force on the WEC’s motion and average absorbed power is analyzed. Particularly under controlled conditions and in the resonance region, the drag force becomes significant and can greatly reduce the average absorbed power of a heaving point absorber. Once the drag coefficient has been determined, it is used in a modified equation of motion in the frequency domain, taking into account the effect of the drag force. Three different methods were compared for the calculation of the average absorbed power: linear potential flow theory, linear potential flow theory modified to take the drag force into account and DualSPHysics. This comparison showed the considerable effect of the drag force in the resonance region. Calculations of the drag coefficient were carried out for three point absorber WECs: one spherical WEC and two cylindrical WECs. Simulations in regular waves were performed for one cylindrical WEC with two different power take-off (PTO) systems: a linear damping and a Coulomb damping PTO system. The Coulomb damping PTO system was added in the numerical coupling between DualSPHysics and Project Chrono. Furthermore, we considered the optimal PTO system damping coefficient taking the effect of the drag force into account. Full article

The study of the existence of an optimal feedback control problem for the initial-boundary value problem that describes the motion of the fractional Voigt- $\alpha$ model of a viscoelastic medium is investigated in this paper. In this model, the Voigt rheological relation is considered with the left-side fractional Riemann-Liouville derivative, which allows to take into account the memory of the medium. Also in this model, the memory is considered along the trajectory of the motion of fluid particles, determined by the velocity field. Due to the insufficient smoothness of the velocity field and, as a consequence, the impossibility of uniquely determining the trajectory for the velocity field for any initial value, a weak solution to the problem under study is introduced using regular Lagrangian flows. Based on the approximation-topological approach to the study of fluid dynamic problems, the existence of an optimal solution that gives a minimum to a given cost functional is proved. Full article

A two-dimensional boundary element method (BEM) based on the potential flow theory is adopted to study the combined wave radiation and diffraction by a single barge. The wave-body interaction problems are simulated using a mixed Euler-Lagrangian scheme, with fully nonlinear boundary conditions. The numerical schemes are verified through comparing with existing results, which show that both the wave runups on the barge and hydrodynamic forces can be calculated with sufficient accuracy. Cases of a single barge subjected to sway motion and regular waves are studied. The real contribution of this study is the outcomes of the spectral analysis conducted for test cases when wave radiation effects are considered in addition to pure wave diffraction. The cases of sway motion with the same frequency as incident wave are simulated first. It is found that sway motion will reduce the overall horizontal force when the frequency is lower than a critical frequency. After that, the higher the frequency, the bigger the horizontal force increasing effect. When the frequency of sway motion is lower than that of incident wave, in terms of the magnitude of the horizontal force, sway motion of the body will always make the resultant force larger than that of pure diffraction case. Full article

The smoothed particle hydrodynamics (SPH) method has been playing a more and more important role in violent flow simulations since it is easy to deal with the large deformation and breaking flows from its Lagrangian particle characteristics. In this paper, the incompressible SPH (ISPH) method was used to simulate the liquid sloshing in a 2D tank with water jet flows. The study compares the liquid sloshing under different water jet conditions to analyze the effects of the excitation frequency and the water jet on impact pressure. The results demonstrate that the water jet flows can significantly affect the impact pressures on the wall caused by violent sloshing. The main purpose of the paper is to test the ISPH ability for this study and some useful regulars that are obtained from different numerical cases and study the effect of their practical importance. Full article

A prediction–correction solver is presented here for rapid simulation of free-surface flows in dendritic and looped river networks. Rather than solving a large global algebraic system over the entire domain of river networks, the model solves subsystems for subdomains of branches in two steps: prediction and correction. With the help of the prediction–correction method (PCM), the partial linearization technique, the semi-implicit method, and the Eulerian–Lagrangian method (ELM), the model only needs to solve tridiagonal linear systems for branches and is free of any iteration. The new model was tested using a hypothetical looped river network with regular cross sections, the Three Gorges Reservoir (TGR) dendritic river network, and the Jing-south looped river system (with seasonally flooding branches). In the first test, a time-step sensitivity study was conducted and the model was revealed to produce accurate simulations at large time steps when the condition for application of the PCM to river networks was satisfied. In the TGR test, the PCM model provided almost the same histories of water levels and discharges as those simulated by the HEC-RAS model. In the Jing-south test, the mean absolute error in simulated water levels was 0.07–0.24 m, and the relative error in simulated cross-section water flux was 0.5–4.9% compared with field data; the conservation error was generally 2 × 10⁻⁴ to 3 × 10⁻⁴. The PCM model was revealed to be 2–4 times as fast as a reported model, which solves local nonlinear subsystems using two-layer iterations, and 1.2–1.4 times as fast as the HEC-RAS. Using a time step of 1200 s, it took the sequential code 26.8 and 23.1 s to complete a simulation of a one-year unsteady flow process, respectively, in the TGR river networks (with 588 cells) and the Jing-south river system (with 662 cells). Full article