Showing papers on "Compressibility published in 2023"

A unified theory for bubble dynamics

Abstract: In this work, we established a novel theory for the dynamics of oscillating bubbles such as cavitation bubbles, underwater explosion bubbles, and air bubbles. For the first time, we proposed bubble dynamics equations that can simultaneously take into consideration the effects of boundaries, bubble interaction, ambient flow field, gravity, bubble migration, fluid compressibility, viscosity, and surface tension while maintaining a unified and elegant mathematical form. The present theory unifies different classical bubble equations such as the Rayleigh-Plesset equation, the Gilmore equation, and the Keller-Miksis equation. Furthermore, we validated the theory with experimental data of bubbles with a variety in scales, sources, boundaries, and ambient conditions and showed the advantages of our theory over the classical theoretical models, followed by a discussion on the applicability of the present theory based on a comparison to simulation results with different numerical methods. Finally, as a demonstration of the potential of our theory, we modeled the complex multi-cycle bubble interaction with wide ranges of energy and phase differences and gained new physical insights into inter-bubble energy transfer and coupling of bubble-induced pressure waves.

Mathematical Theory of Nonlinear Single-Phase Poroelasticity

Abstract: Abstract In this paper, we study the equations of nonlinear poroelasticity derived from mixture theory. They describe the quasi-static mechanical behavior of a fluid saturated porous medium. The nonlinearity arises from the compressibility of the fluid and from the dependence of porosity and permeability on the divergence of the displacement. We point some limitations of the model. In our approach, we discretize the quasi-static formulation in time and first consider the corresponding incremental problem. For this, we prove existence of a solution using Brézis’ theory of pseudo-monotone operators. Generalizing Biot’s free energy to the nonlinear setting, we construct a Lyapunov functional, yielding global stability. This allows us to construct bounds that are uniform with respect to the time step. In the case when dissipative interface effects between the fluid and the solid are taken into account, we consider the continuous time case in the limit when the time step tends to zero. This yields existence of a weak free energy solution.

Modeling acoustic emissions and shock formation of cavitation bubbles

Abstract: Despite significant progress in understanding and foretelling pressure-driven bubble dynamics, models that faithfully predict the emitted acoustic waves and the associated shock formation of oscillating or collapsing bubbles have received comparably little attention. We propose a numerical framework using a Lagrangian wave tracking approach to model the acoustic emissions of pressure-driven bubbles based on the Kirkwood–Bethe hypothesis and under the assumption of spherical symmetry. This modeling approach is agnostic to the equation of the state of the liquid and enables the accurate prediction of pressure and velocity in the vicinity of pressure-driven bubbles, including the formation and attenuation of shock fronts. We validate and test this new numerical framework by comparison with solutions of the full Navier–Stokes equations and by considering a laser-induced cavitation bubble as well as pressure-driven microbubbles in excitation regimes relevant to sonoluminescence and medical ultrasound, including different equations of state for the liquid. A detailed analysis of the bubble-induced flow field as a function of the radial coordinate r demonstrates that the flow velocity u is dominated by acoustic contributions during a strong bubble collapse and, hence, decays predominantly with [Formula: see text], contrary to the frequently postulated decay with [Formula: see text] in an incompressible fluid.

Error estimates for physics-informed neural networks approximating the Navier–Stokes equations

Abstract: Abstract We prove rigorous bounds on the errors resulting from the approximation of the incompressible Navier–Stokes equations with (extended) physics-informed neural networks. We show that the underlying partial differential equation residual can be made arbitrarily small for tanh neural networks with two hidden layers. Moreover, the total error can be estimated in terms of the training error, network size and number of quadrature points. The theory is illustrated with numerical experiments.

Behaviour of sand stabilised with xanthan gum under unconfined and confined conditions

Abstract: This study analyses the effectiveness of the biopolymer xanthan gum (XG) to improve the mechanical properties of silty sand. The study focuses on the effects of the curing time and the content of XG on the unconfined and confined behaviour of soil treated with this biopolymer. The study was carried out with specimens cured under high-humidity conditions, through the comparison of the unconfined compressive strength (UCS), stiffness, compressibility and vertical yield stress of non-stabilised and biostabilised specimens, obtained from UCS and oedometer tests. Additionally, the pH value and results of scanning electron microscopy (SEM)/ energy-dispersive X-ray analysis (EDX) tests are presented and discussed. The biostabilisation of this soil with XG induces a more ductile stress–strain behaviour, a moderate increase in UCS and stiffness, and in the increase of the one-dimensional compressibility, with a greater effect for higher XG contents. The SEM/EDX tests show that the biopolymer induces a random biopolymer network in the biostabilised specimens that is related to the strengthening obtained.

General Solutions for Some MHD Motions of Second-Grade Fluids between Parallel Plates Embedded in a Porous Medium

Abstract: General solutions are established for an initial boundary value problem by means of the integral transforms. They correspond to the isothermal MHD unidirectional motion of incompressible second-grade fluids between infinite horizontal parallel plates embedded in a porous medium. The fluid motion, which in some situations becomes symmetric with respect to the median plane, is generated by the two plates that apply time-dependent arbitrary shear stresses to the fluid. Closed-form expressions are established both for the fluid velocity and the corresponding non-trivial shear stress. Using an important remark regarding the governing equations of velocity and shear stress, exact general solutions are developed for similar motions of the same fluids when both plates move in their planes with arbitrary time-dependent velocities. The results that have been obtained here can generate exact solutions for any motion with the technical relevance of this type of incompressible second-grade fluids and their correctness being proved by comparing them with the numerical solution or with known results from the existing literature. Consequently, both motion problems of these fluids with shear stress or velocity on the boundary are completely solved.

SPHydro: Promoting smoothed particle hydrodynamics method toward extensive applications in ocean engineering

Abstract: This paper aims at presenting a general-purpose-oriented and fully parallelized meshless framework to simulate complex Fluid–Structure Interaction (FSI) problems in ocean engineering. In this framework, a Weakly Compressible Smoothed Particle Hydrodynamics (WCSPH) solver is combined with several advanced pre- and post-processing techniques. Based on the framework, we have been developing our in-house WCSPH-FSI package named SPHydro for solving hydrodynamic problems involving complex FSI processes in an accurate, efficient, and convenient manner. Three benchmarks are performed to qualitatively and quantitatively validate the accuracy and convergence of SPHydro. In addition, several practical applications are also provided to further highlight the generality and applicability of SPHydro in ocean engineering simulations. It is demonstrated that SPHydro holds satisfactory performance in solving complex FSI problems in ocean engineering and that the present framework can be further developed to tackle more complex FSI problems for general engineering applications due to its high flexibility and extensibility.

Post-processing subsonic flows using physics-informed neural networks

Abstract: The conservation equations describe the physics of flow and sound and one is possibly interested in what are vortical and compressible flow structures. For instance, the compressible flow velocity is analyzed to study acoustic waves. Another reason might be computing the compressible source structures of the aeroacoustic wave equation based on Pierce's operator. This work shows how neural networks can leverage physical knowledge to perform the inverse task of post-processing a compressible subsonic flow field into subparts by Helmholtz's decomposition. The Helmholtz decomposition of a velocity field into vortical and compressible structures is implemented using a finite element framework and physics-informed neural networks. These two implementations of Helmholtz's decomposition are compared. A verification example demonstrates the applicability of the methods by comparing the results to the analytical solution. The physics-informed neural network formulation results on the verification example outline promising directions for further applications to post-process compressible flow fields and the development of acoustic boundaries in fluid dynamics.

Consolidation and swelling behavior of kaolinite clay containing xanthan gum biopolymer

Abstract: Abstract Recently, microbial biopolymer-based soil treatment (BPST) has gained attention for its application in environmentally friendly soil stabilization, particularly for enhancing the strength and stability of fine-grained soils. However, the effects of BPST on clay’s compressibility (consolidation) and expansion (swelling) behaviors remain unclear. This study used xanthan gum, a microbially produced polysaccharide with anionic charges, to stabilize kaolinite clay. The effect of xanthan gum BPST on the consolidation and swelling behavior of cohesive kaolinite clays was assessed through a series of experimental tests, including one-dimensional consolidation tests with elastic wave measurements, swelling tests, environmental scanning electron microscopy, and unconsolidated-undrained triaxial tests. The formation of xanthan gum hydrogels induces pore-clogging, resulting in a delay in the consolidation process, increased energy dissipation, and compressibility. Furthermore, the interaction between kaolinite and xanthan gum improved the undrained shear strength of kaolinite soils, thereby reducing the consolidation time required for a specific bearing capacity. This study demonstrates the possible application of controlling hydraulic conductivity, seismic stabilization, and rapid surface stabilization. However, additional drainage is necessary for in situ applications.

Analysis of compressible bubbly flows. Part I: Construction of a microscopic model.

Abstract: In this note, we introduce a microscopic model for the motion of gas bubbles in a viscous fluid. By interpreting a bubble as a compressible fluid with infinite shear viscosity, we derive a pde/ode system coupling the density/velocity/pressure in the surrounding fluid with the linear/angular velocities and radii of the bubbles. We provide a 1D analogue of the system and construct an existence theory for this simplified system in a natural regularity framework. The second part of the paper is a preparatory work for the derivation of an averaged or macroscopic model.

Numerical research on the cavitation effect induced by underwater multi-point explosion near free surface

Abstract: In this study, the cavitation effect induced by two charges in underwater explosions near free surfaces is numerical researched by two dimensional compressible multiphase fluids based on a four-equation system with a phase transition model. The occurrence of the generation, development, and collapse of cavitation in two-charge underwater explosions near free surfaces can be captured directly. The detailed density, pressure, and vapor volume fraction contours during the interaction process are obtained and can better reveal the characteristic underlying the cavitation, free surface, and explosion bubbles. Numerical results reveal that the cavitation domain has expanded to an area much deeper than the explosion bubble location in two-charge underwater explosions, which should be paid enough attention due to its influence on the input load of underwater structures. The detailed density and pressure contours during the interaction process can also be captured and can better reveal the mechanism underlying the explosion bubble, cavitation, and surface wave dynamics. The present results can expand the currently limited database of multiphase fluid in underwater explosions and also provide new insights into the strong nonlinear interaction between underwater explosion and cavitation, which provides a deep understanding of multi-point explosions.

N-Side Cell-Based Smoothed Finite Element Method for Incompressible Flow with Heat Transfer Problems

Abstract: In this paper, an n-sided cell-based smoothed finite element method (nCS-FEM) is presented to solve the convective heat transfer in incompressible viscous fluid flow. The Characteristic-based-split (CBS) scheme is used to stabilize the spatial and pressure oscillations of CS-FEM that occur during the process of solving incompressible Navier-Stokes equations. Meanwhile, the characteristic-Galerkin method in CBS is adopted as the convective stabilization in the heat transfer equation. In order to verify the proposed method, typical numerical examples are used to test the computational accuracy of CS-FEM. Meanwhile, the investigation of the robustness of highly distorted element is conducted in a natural convection test case. The calculation results of numerical examples show that CS-FEM is qualified to solve the steady and unsteady convective heat transfer problems for incompressible laminar flow with high reliability. The flow across tube banks with complex geometry in the heat sinks is also simulated to prove the capabilities of the proposed method. Well agreed comparison with the results of CFD software, Fluent, proves that the present method can effectively simulate realistic and complex flow with heat transfer problems.

Liquid/liquid displacement in a vibrating capillary

Abstract: Mechanical vibrations can alter static and dynamic distributions of fluids in porous matrices. A popular theory that explains non-destructive changes in fluids percolation induced by vibrations involves elasticity of a solid matrix and compressibility of fluids. Owing to strong damping, elastic and acoustic deformations always remain bounded to narrow zones (a few centimetres) near the source of vibrations. However, field trials prove the existence of the effects that are induced by vibrations in geological reservoirs on a longer scale (100 m). In this study, we develop a non-elastic theory, assessing the time-averaged effects induced by small-amplitude high-frequency vibrations. We examine the immiscible liquid/liquid displacement flows in a capillary (which is a building element of a porous matrix) subjected to translational vibrations. We find that strong-enough vibrations alter the shapes of menisci and change the rates of displacement flows. We find that vibrations slow down or even stop the displacement flows (which is contrary to a common expectation that vibrations help to release fluids from a porous matrix). This article is part of the theme issue ‘New trends in pattern formation and nonlinear dynamics of extended systems’.

Implosion of a bubble pair near a solid surface

Abstract: A compressible two-phase flow solver is developed for the simulation of a collapsing bubble pair. With the adaptive mesh and high-resolution scheme, the discontinuities and shock waves due to bubble collapse are well captured. Numerical results show that the collapse of two bubbles horizontally arranged ($\ensuremath{\phi}={0}^{\ensuremath{\circ}}$) produces the highest wall pressure peak among the oblique angles (${0}^{\ensuremath{\circ}}\ensuremath{\le}\ensuremath{\phi}\ensuremath{\le}{90}^{\ensuremath{\circ}}$) while the perpendicular arrangement ( $\ensuremath{\phi}={90}^{\ensuremath{\circ}}$) leads to the lowest wall pressure peak, even weaker than that of the single bubble collapse.

Expressions of nonlocal quantities and application to Stoneley waves in weakly nonlocal orthotropic elastic half-spaces

Abstract: In this paper, we introduce a novel model of nonlocal elasticity, called the weakly nonlocal elasticity, and provide explicit expressions of nonlocal quantities for harmonic plane waves propagating in the weakly nonlocal elastic solids. Then, we apply these expressions to investigate the propagation of Stoneley waves along the interface between two weakly nonlocal orthotropic elastic half-spaces. The half-spaces may be compressible or incompressible, and they are in welded contact. Our main aim is to derive explicit dispersion equations of Stoneley waves. First, we derive the explicit dispersion equation for the compressible case (when two half-spaces are compressible) using the surface impedance matrices of half-spaces. Then, the explicit dispersion equations for the incompressible cases (at least one half-space is incompressible) are obtained using the incompressible limit method. The simple and immediate derivation of these equations proves the convenience of the incompressible limit method. Some numerical examples are carried out to examine the effect of nonlocality and incompressibility on the Stoneley wave velocity.