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In this paper, we discuss the well‐posedness of impinging flow through a semi‐infinitely long nozzle and impacting on a plane. More precisely, given the semi‐infinitely long nozzle with finite inlet, the plane, and the positive incoming horizontal velocity, then there exists a unique smooth solution to the impinging flow. Moreover, there exists a smooth free interface that separates the fluid such that it flows out of different outlets in the downstream. [ABSTRACT FROM AUTHOR]

In this work, the deformation of free interface during water entry and exit of a circular cylinder is investigated numerically by using the two-dimensional (2D) immersed boundary-multiphase lattice Boltzmann flux solver (IB-MLBFS). The fluid domain is discretized by finite volume discretization, and the flux on the grid interface is evaluated by lattice Boltzmann equations. Both the implicit velocity correction and the surface flux correction are implemented by using the immersed boundary-method to consider the fluid-structure interaction and the contact interface between the multiphase fluids and the structure. First, the water entry of a circular cylinder is simulated and the results are compared with the experiment, which considered the length-diameter ratio of the circular cylinder. The reliability of 2D simulation is verified and the deformation of the free interface is well investigated. Afterward, the water exit of a circular cylinder with constant velocity is simulated, which is less researched. In addition, the results show the advantage of present IB-MLBFS to some extent. Finally, the water exit and re-entry of a circular cylinder are presented, and the results present the complex deformation of the free interface and the dynamic response of the moving structure. Based on the numerical results, the free interface of the multiphase fluids is well captured, and the contact interface on the boundary of the moving structure is accurately presented by the IB-MLBFS. [ABSTRACT FROM AUTHOR]

Microorganisms often swim within heterogeneous fluid media composed of multiple materials with very different properties. The swimming speed is greatly affected by the composition and rheology of the fluidic environment. In addition, biological locomotions are also strongly influenced by the presence of phase boundaries and free interfaces, across which physical properties of the fluid media may vary significantly. Using a two-fluid immersed boundary method, we investigate the classical Taylor's swimming sheet problem near interfaces within multi-fluid media. The accuracy of the methodology is illustrated through comparisons with analytical solutions. Our simulation results indicate that the interface dynamics and phase separation in the multi-fluid mixture are closely coupled with the movement of the swimmer. Depending on the interface location, the frictional coefficient, and the multi-fluid composition, the swimmer can move faster or slower than that in a single phase fluid. [ABSTRACT FROM AUTHOR]

In this paper, we study the global existence of steady subsonic flows with collision, where the collision is caused by a confluence of two semi‐infinitely incoming flows that are nonmiscible steady subsonic irrotational Euler flows come from two different infinitely nozzles. First, we prove that when the total flux of two incoming flows is less that the critical mass flux, there exists a unique global smooth subsonic flow with collision. Meanwhile, the interface between two flows is a smooth free interface, which is determined uniquely by the mass fluxes of incoming flows. Second, by using the blowup argument, we establish the asymptotic behaviors for the stream function. Finally, we prove that the position of free interface can be determined uniquely by the mass fluxes of incoming flows. Moreover, we establish the monotonicity of the relation between the position of free interface and the mass fluxes of incoming flows. [ABSTRACT FROM AUTHOR]

A well-posedness analysis of steady state of inviscid compressible subsonic impinging flows with non-zero vorticity is developed. A nonlinear nonhomogeneous second-order partial differential equation for the solution of the flow stream function is derived in terms of the inlet flow specifying the horizontal velocity. We first construct a subsonic solution to the impinging flow problem with special horizontal velocity and specific effluent fluxes in the outlets. Moreover, we showed that such a subsonic impinging flow with the same asymptotic behavior in the upstream and downstreams is unique. Furthermore, the existence, uniqueness and regularity of the interface separating the two fluids with different outlets are obtained. This result extends the recent result on the compressible subsonic irrotational impinging flows in [5]. Finally, as a byproduct, we obtain the existence of subsonic-sonic impinging flows. [ABSTRACT FROM AUTHOR]

Microorganisms often swim within heterogeneous fluid media composed of multiple materials with very different properties. The swimming speed is greatly affected by the composition and rheology of the fluidic environment. In addition, biological locomotions are also strongly influenced by the presence of phase boundaries and free interfaces, across which physical properties of the fluid media may vary significantly. Using a two-fluid immersed boundary method, we investigate the classical Taylor’s swimming sheet problem near interfaces within multi-fluid media. The accuracy of the methodology is illustrated through comparisons with analytical solutions. Our simulation results indicate that the interface dynamics and phase separation in the multi-fluid mixture are closely coupled with the movement of the swimmer. Depending on the interface location, the frictional coefficient, and the multi-fluid composition, the swimmer can move faster or slower than that in a single phase fluid.

• A free-interface based dynamic condensation method is newly developed. • In the formulation, substructural FE models are fully decoupled. • Non-matching mesh and complicated substructural interfaces can be modeled. • Accuracy, computational efficiency and modeling ability are demonstrated. In this paper, a novel dynamic condensation method is proposed with free interface substructuring, in which the substructures are completely decoupled. The substructures are independently defined and the substructural finite element (FE) models are individually reduced by adopting the improved reduced system (IRS) method. The reduced mass and stiffness matrices of substructures are assembled using a Lagrange multiplier vector, leading to the final reduced model. Using the proposed method, each of the substructural FE models can be reduced in parallel without coupling among the neighboring substructures. Thus, the method can be applied with ease to substructures connected through non-matching meshes. Moreover, complicated substructural interfaces can be accommodated when employing this method. The formulation of the proposed method is presented in detail, and its accuracy, computational efficiency, and modeling ability are investigated using several demonstrative engineering problems. [ABSTRACT FROM AUTHOR]

This paper is devoted to the mathematical theory for the steady state collision of two compressible subsonic irrotational flows issuing from two infinitely long nozzles. We established the existence, uniqueness and asymptotic behavior of the subsonic collision flow with a smooth interface for the steady Euler system in an important physical regime. More precisely, there exists a critical value, if the summation of the incoming mass fluxes in the inlets of the nozzles is less than the critical value, then there exists a unique smooth subsonic compressible collision flow. And furthermore, there exists a smooth interface which separates the two non-miscible compressible subsonic flows. In particular, a key observation is that the location of the interface can be determined uniquely by the incoming mass fluxes in the inlets of the nozzles. Finally, we showed some monotonic relationship between the location of the interface and the incoming mass fluxes. [ABSTRACT FROM AUTHOR]

In order to improve the computational efficiency of the large-scale structures with uncertainty parameters, this paper present a methodological approach for interval uncertainty treatment based on an improved free interface Component Mode Synthesis (CMS) method. Firstly, the structure is divided into substructures and the perturbation method is employed for the eigenvalue analysis of substructures with the interval non-deterministic characteristics. To reduce the mode truncation error, the residual flexibility matrix is considered by constructing a set of weighted orthogonal modal vectors with low-order system modal vectors and system matrices. Different from the previous studies, this method proposed in this paper avoids calculating directly inverse of the stiffness matrix, which makes it easier to get the residual flexibility matrix. Then the synthesis equations including parameters perturbation can be deduced in terms of the interface compatibility conditions. Finally, two examples including with a numerical example as well as an experiment example are given to demonstrate the effectiveness and the efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

In this review article, we exemplify the use of stability analysis tools to rationalize pattern formation in complex media. Specifically, we focus on fluid flows, and show how the destabilization of their interface sets the blueprint of the patterns they eventually form. We review the potential use and limitations of the theoretical methods at the end, in terms of their applications to practical settings, e.g. as guidelines to design and fabricate structures while harnessing instabilities. This article is part of the themed issue 'Patterning through instabilities in complex media: theory and applications'. [ABSTRACT FROM AUTHOR]

We consider a model of gas-solid combustion with free interface proposed by L. Kagan and G. I. Sivashinsky. Our approach is twofold: (I) We eliminate the front and get to a fully nonlinear system with boundary conditions; (II) We use a fourth-order pseudo-differential equation for the front to achieve asymptotic regimes in rescaled variables. In both cases, we implement a numerical algorithm based on spectral method and represent numerically the evolution of the char. Fingering pattern formation occurs when the planar front is unstable. A series of simulations is presented to demonstrate the evolution of sparse fingers (I) and chaotic fingering (II). [ABSTRACT FROM AUTHOR]

Abstract: This study presents an analytical model of the dynamics of an axisymmetric liquid bridge confined between two circular pads and subjected to small vertical periodic perturbations. Such system finds important applications in microassembly and microjoint design, where force and damping need to be precisely controlled. The liquid bridge is modelled by an equivalent spring/dashpot/mass system characterised by the spring constant , the damping coefficient and the equivalent mass , respectively. An abacus for as well as analytical approximations for , and based on simplifications of the Navier–Stokes equation are provided. The study is validated by experiments and numerical simulations of the system. We describe the experimental setup we designed to investigate vertical forces arising on the bottom pad from small periodic perturbations of the top pad confining the liquid meniscus. The setup allowed the accurate control of all physical and geometrical parameters relevant for the experiments. The parameters we investigated are both physical (viscosity and surface tension of the fluid) and geometrical (the edge angle between the meniscus and the pad, the height of the meniscus). The good agreement between model predictions and results let us conclude that , and involve only one physical property of the liquid, namely the surface tension, the viscosity and the density, respectively. [Copyright &y& Elsevier]

The authors consider a free interface problem which stems from a gas-solid model in combustion with pattern formation. A third-order, fully nonlinear, self-consistent equation for the flame front is derived. Asymptotic methods reveal that the interface approaches a solution to the Kuramoto-Sivashinsky equation. Numerical results which illustrate the dynamics are presented. [ABSTRACT FROM AUTHOR]

Abstract: According to the definition of link substructure in component mode synthesis (CMS) method, link substructure is essentially a kind of super element whose master degree of freedoms (DOF) is the interface DOF. Based on this, a new method of free-interface CMS, compatible for both displacement and force on interfaces, was proposed, by transforming link substructure into super element with Guyan static condensation or dynamic condensation. The new method not only retains free-interface CMS''s advantages of reducing the system DOF efficiently and high accuracy, but also can deal with lumped damping reasonably, thus, it has a widespread application prospect in dynamic analysis of the structures with local non-linearity. Then, the application of the proposed technique was shown by modal and seismic response analysis of a truss bridge in which the girder and brace are lead rubber bearings (LRB) linked, in the automated container terminal. Regarding LRB as super element link substructure, the calculation accuracy and efficiency of Guyan and dynamic condensation methods are compared with finite element method (FEM) or direct integration method. Furthermore, inherent characteristic results of the truss bridge under different LRB disposition forms were obtained. [Copyright &y& Elsevier]

Abstract: This short note presents an improved multi-dimensional algebraic VOF method to capture moving interfaces. The interface jump in the THINC (tangent of hyperbola for INterface capturing) scheme is adaptively scaled to a proper thickness according to the interface orientation. The numerical accuracy in computing multi-dimensional moving interfaces is significantly improved. Without any geometrical reconstruction, the proposed method is extremely simple and easy to use, and its numerical accuracy is superior to other existing methods of its kind and comparable to the conventional PLIC (piecewise linear interface calculation) type VOF schemes. [Copyright &y& Elsevier]

Abstract: A novel computational fluid dynamics (CFD) based approach is suggested, which incorporates interfacial mass transfer at moving interfaces. This approach is general and able to govern multicomponent systems as well as interfacial boundary conditions in an arbitrary form. This is important in order to properly handle the typical concentration jump at the phase interface and to avoid an assumption of a constant distribution coefficient, which is seldom met in real processes. A test case study is carried out for a gas bubble rising in a stagnant liquid phase, whereas two different liquids, namely water and water–carboxymethylcellulose solution, are used. The gas bubble contains 99% of oxygen diffusing into continuous phase. The movement of the bubble is simulated using the level set method. Both velocity vectors and concentration contours are demonstrated and analysed. [Copyright &y& Elsevier]

solution was put forward to predicate the flow pattern of gas penetration in gas-assisted injection molding. The differential equations that governed the flow field and gas/melt free-interface evolution were analyzed and discretized by Galerkin finite element method, and the free interface was located by the volume of fluid method. The gas was assumed as a fluid phase of constant density and viscosity instead of being simply treated as boundary conditions. The non-Newtonian property of polymer melt was characterized by Carreau model with four parameters. As a case study, different kinds of gas channel were modeled. The gas/melt free interface was captured. The gas front velocity and the pressure of gas/melt front were also computed. The edge shape of gas channel was discussed, which are helpful for the design of gas-assisted injection molding. [ABSTRACT FROM AUTHOR]

Abstract: The electro-slag remelting (ESR) process has been used effectively to produce large ingots of high quality based on the controlled solidification that can be achieved. Despite numerous simulations, it is still challenging to predict important operating details of the process, such as the effect of the electrode immersion and, more importantly, the results of instabilities in the melting system (electrode, slag, pool). In order to have a better understanding of the process, the present work aims to verify the validity of two assumptions which were widely used in previous simulations. First is the flatness of the slag/steel interface, and second concerns the verticality and the stationarity of the density of the electric current over the entire domain. In the present paper, a mathematical model of the magneto-hydrodynamic (MHD) phenomena occurring during ESR, modelling more rigorously the closure of the electric current at the mould is presented. At the present stage, the model does not include any buoyancy or solidification effects. The multiphase aspect of the problem is solved by using a VOF model, the domain is divided in two sub-domains (steel and slag) separated by a free interface. The effect of the imposed dc current and the mould diameter on the initial interface was investigated. We show that except if the mould is insulating, the interface is never flat. In some cases the interface even becomes unstable leading to an electric shortcut. [Copyright &y& Elsevier]

In this paper mathematical expressions have been developed to describe the hydrodynamic resistance force on a colloidal particle as it slides along a slip surface of a gas bubble held stationary in a quiescent liquid. The particle size was considered to be sufficiently small relative to the bubble size so that the bubble surface could be locally approximated to a planar interface. The modeling incorporated a bispherical coordinate transformation to solve the equations governing the liquid creeping flow disturbed by the particle. Exact numerical solutions for the resistance coefficients of the particle-shearing motion parallel to the slip bubble surface were obtained as a function of the separation distance from the bubble surface. Finally, simplified analytical rational approximations for the whole range of the separation distance were presented, which were in good agreement with the exact numerical result. Importantly, the approximations for the modeling and simulation of the bubble–particle interactions are mathematically tractable. [Copyright &y& Elsevier]

This paper concerns laminar countercurrent gas–liquid flow over a wavy wall column, in the case of a falling liquid film. The modelling concerns the coupling of hydrodynamic and heat and mass transfer for an absorption as an example of application. The falling liquid film interacts, through the free interface, with the gas phase. The wavy surface generates particular hydrodynamic conditions with the presence of a vortex in both phases. The consequence of these vortices is an increase of transfers compared to the smooth wall. [Copyright &y& Elsevier]

We report on the numerical simulation of a two-fluid magnetohydrodynamics problem arising in the industrial production of aluminium. The motion of the two non-miscible fluids is modeled through the incompressible Navier–Stokes equations coupled with the Maxwell equations. Stabilized finite elements techniques and an arbitrary Lagrangian–Eulerian formulation (for the motion of the interface separating the two fluids) are used in the numerical simulation. With a view to justifying our strategy, details on the numerical analysis of the problem, with a special emphasis on conservation and stability properties and on the surface tension discretization, as well as results on tests cases are provided. Examples of numerical simulations of the industrial case are eventually presented. [Copyright &y& Elsevier]

When a concentrated suspension of small inertia-less particles in a viscous fluid is sheared between two parallel-belts a free surface exists with a direction orthogonal to the plane of the simple shear flow. We observed a development of corrugation on this surface. The corrugation appears as an ensemble of disturbances driven by shear-induced diffusion and restrained by surface forces. The roughness of the surface disturbances depends on the particle size, on particle concentration and on the fluid surface tension. The corrugation has many lengthscales above and below particle size and it appears in the form of waves traveling with the local surface fluid speed.In this communication, we present a report on the phenomenon and its dependence on the physical parameters. A qualitative description is presented and the dimensionless groups governing the extent of the shear-induced corrugation are defined. We introduce the notion of a macroscopic effective surface tension, which depends on the surface particle concentration, with possible influence on the stability of the surface flow. [Copyright &y& Elsevier]