Solution properties and approximate Riemann solvers for two-layer shallow flow models

The 4 × 4 system of governing equations for two-layer shallow flow models is known to exhibit particular behaviours such as loss of hyperbolicity under certain flow configurations. An eigenvalue analysis of the conservation part of the equations shows that the loss of hyperbolicity is due only to the reaction exerted by each fluid onto the other at the interface between the fluids. Three Riemann solvers derived from the HLL formalism are presented. In the first solver, the pressure-induced terms are accounted for by the source term; in the second solver, they are incorporated into the fluxes; the third solver uses the same formulation as the first, except that the mass and momentum balance for the bottom layer are replaced with the balance equations for the system formed by the two layers as a whole. Numerical results using the three solvers are presented for (1) static conditions such as two fluids of identical densities at rest above each other, (2) dam-break flows involving the collapse of a body of light fluid over a uniform layer of a denser fluid, and (3) Liska and Wendroff’s ill-posed test cases [24] involving two-layer flows over a topographic bump. The three solvers produce quasi-undistinguishable results for the dam-break flows, and produce sharp solutions over the full range of density ratio, from 0 to 1. However, only the third solver allows a strict preservation of static configurations. Moreover, a method is proposed to assess the convergence of the numerical solutions in the configurations for which no analytical solution can be obtained.     

A generalized continuous surface tension force formulation for phase-field models for multi-component immiscible fluid flows

We present a new phase-field method for modeling surface tension effects on multi-component immiscible fluid flows. Interfaces between fluids having different properties are represented as transition regions of finite thickness across which the phase-field varies continuously. At each point in the transition region, we define a force density which is proportional to the curvature of the interface times a smoothed Dirac delta function. We consider a vector valued phase-field, the velocity, and pressure fields which are governed by multi-component advective Cahn–Hilliard and modified Navier–Stokes equations. The new formulation makes it possible to model any combination of interfaces without any additional decision criteria. It is general, therefore it can be applied to any number of fluid components. We give computational results for the four component fluid flows to illustrate the properties of the method. The capabilities of the method are computationally demonstrated with phase separations via a spinodal decomposition in a four-component mixture, pressure field distribution for three stationary drops, and the dynamics of two droplets inside another drop embedded in the ambient liquid.     

Topology optimization of electrode coverage of piezoelectric thin-walled structures with CGVF control for minimizing sound radiation

It is impractical to implement arbitrary-shaped piezoelectric patches from the view point of manufacturability of fragile piezoelectric ceramics, thus using designable electrode layers to deliver desired actuation forces provides a more realistic option in engineering applications. This study develops a topological design method of surface electrode distribution over piezoelectric sensors/actuators attached to a thin-walled shell structure for reducing the sound radiation in an unbounded acoustic domain. In the optimization model, the sound pressure norm at specific reference points under excitations at a certain excitation frequency or in a given frequency range is taken as the objective function. The pseudo densities for indicating absence and presence of surface electrodes at each element are taken as the design variables, and a penalized relationship between the densities and the active damping effect is employed. The vibrating structure is discretized with finite element model for the frequency response analysis and the sound radiation analysis in the unbounded acoustic domain is treated by boundary element method. The applied voltage on each actuator is determined by the constant gain velocity feedback (CGVF) control law. The technique of the complex mode superposition in the state space, in conjunction with a model reduction transformation, is adopted in the response analysis of the system characterized by a non-proportional active damping property. In this context, the adjoint-variable sensitivity analysis scheme is derived. The effectiveness and efficiency of the proposed method are demonstrated by numerical examples, and several key factors on the optimal designs are also discussed.     

Output pressure and efficiency of electrokinetic pumping of non-Newtonian fluids

Theoretical expressions of the flow rate, output pressure and thermodynamic efficiency of electrokinetic pumping of non-Newtonian fluids through cylindrical and slit microchannels are reported. Calculations are carried out in the framework of continuum fluid mechanics. The constitutive model of Ostwald-de Waele (power law) is used to express the fluid shear stress in terms of the velocity gradient. The resulting equations of flow rate and electric current are nonlinear functions of the electric potential and pressure gradients. The fact that the microstructure of non-Newtonian fluids is altered at solid–liquid interfaces is taken into account. In the case of fluids with wall depletion, both the output pressure and efficiency are found to be several times higher than that obtained with simple electrolytes under the same experimental conditions. Apart from potential applications in electrokinetic pumps, these predictions are of interest for the design of microfluidic devices that manipulate non-Newtonian fluids such as polymer solutions and colloidal suspensions. From a more fundamental point of view, the paper discusses a relevant example of nonlinear electrokinetics.     

A semi-analytical coupled finite element formulation for shells conveying fluids

A new formulation, based on the semi-analytical finite element method, is proposed for elastic shells conveying fluids. The structural equations are based on the shell element proposed by Ramasamy and Ganesan [Comput Struct 70 (1998) 363] while the fluid model is based on velocity potential. Dynamic pressure acting on the walls is derived from Bernoulli's equation. Imposing the requirement that the normal components of velocity of the solid and fluid be equal, introduces fluid–structure coupling. The proposed technique has been validated using results available in the literature. This study shows that instability occurs at a critical fluid velocity corresponding to the shell circumferential mode with the lowest natural frequency and this phenomenon is also independent of the type of structural boundary conditions imposed.     

Euler–Lagrange coupling with damping effects: Application to slamming problems

During a high velocity impact of a structure on a nearly incompressible fluid, impulse loads with high-pressure peaks occur. This physical phenomenon called ‘slamming’ is a concern in shipbuilding industry because of the possibility of hull damage. Shipbuilding companies have carried out several studies on slamming modeling using FEM software with added mass techniques to represent fluid effects. In the added mass method inertia effects of the fluid are not taken into account and are only valid when the deadrise angle is small. This paper presents the prediction of the local high pressure load on a rigid wedge impacting a free surface, where the fluid is represented by solving Navier–Stokes equations with an Eulerian or ALE formulation. The fluid–structure interaction is simulated using a coupling algorithm; the fluid is treated on a fixed or moving mesh using an ALE formulation and the structure on a deformable mesh using a Lagrangian formulation.A new coupling algorithm is developed in the paper. The coupling algorithm computes the coupling forces at the fluid–structure interface. These forces are added to the fluid and structure nodal forces, where fluid and structure are solved using an explicit finite element formulation. Predicting the local pressure peak on the structure requires an accurate fluid–structure interaction algorithm. The Euler–Lagrange coupling algorithm presented in this paper uses a penalty based formulation similar to penalty contact in Lagrangian analyses. Both penalty coupling and penalty contact can generate high frequency oscillations due to the nearly incompressible nature of the fluid. In this paper, a damping force based on the relative velocity of the fluid and the structure is introduced to smooth out non-physical high frequency oscillations induced by the penalty springs in the coupling algorithm.     

Visual Simulation of Multiple Unmixable Fluids

We present a novel grid-based method for simulating multiple unmixable fluids moving and interacting. Unlike previous methods that can only represent the interface between two fluids （usually between liquid and gas）, this method can handle an arbitrary number of fluids through multiple independent level sets coupled with a constrain condition. To capture the fluid surface more accurately, we extend the particle level set method to a multi-fluid version. It shares the advantages of the particle level set method, and has the ability to track the interfaces of multiple fluids. To handle the dynamic behavior of different fluids existing together, we use a multiphase fluid formulation based on a smooth weight function.     

Topology optimization of sound absorbing layer for the mid-frequency vibration of vibro-acoustic systems

Due to the significant difference of dynamic properties between the fluid medium and the structure, when a vibro-acoustic system is subjected to a higher frequency excitation, it may typically exhibit mid-frequency behavior which involves different wavelength deformations and is very sensitive to the uncertainties of the system. This paper deals with optimized distribution of a sound absorbing layer for the mid-frequency vibration of vibro-acoustic systems by using hybrid boundary element analysis and statistical energy analysis. Based on the solid isotropic material with penalization approach, an artificial sound absorbing material model is suggested and the relative densities of the sound absorbing material are taken as design variables. The sound pressure level at a specified point in the acoustic cavity is to be minimized by distributing a given amount of sound absorbing material. An efficient direct differentiation scheme for the response sensitivity analysis is proposed. Then, the optimization problem is solved by using the method of moving asymptotes. A numerical example illustrates the validity and effectiveness of the present optimization model. Impact of the excitation frequency on optimized topology is also discussed.

     

A fully discrete scheme for the pressure–stress formulation of the time-domain fluid–structure interaction problem

We propose an implicit Newmark method for the time integration of the pressure–stress formulation of a fluid–structure interaction problem. The space Galerkin discretization is based on the Arnold–Falk–Winther mixed finite element method with weak symmetry in the solid and the usual Lagrange finite element method in the acoustic medium. We prove that the resulting fully discrete scheme is well-posed and uniformly stable with respect to the discretization parameters and Poisson ratio, and we provide asymptotic error estimates. Finally, we present numerical tests to confirm the asymptotic error estimates predicted by the theory.     

A mixed finite element for shell model with free edge boundary conditions Part 2. The numerical scheme

From the mixed variational formulation which was suggested in Part 1, we construct a finite element scheme. Then, a mathematical justification concerning the error estimate is developed. The most important point is to justify two compatibility conditions between the approximation of the kinematics and the stresses. Because of the structure of the shell operator they are not obvious at all and several restrictions on the mesh are necessary. Therefore, the classical result known in fluid mechanics for Stokes equations cannot be applied directly.     

Towards a continuous microfluidic rheometer

In a previous paper we presented a way to measure the rheological properties of complex fluids on a microfluidic chip (Guillot et al., Langmuir 22:6438, 2006). The principle of our method is to use parallel flows between two immiscible fluids as a pressure sensor. In fact, in a such flow, both fluids flow side by side and the size occupied by each fluid stream depends only on both flow rates and on both viscosities. We use this property to measure the viscosity of one fluid knowing the viscosity of the other one, both flow rates and the relative size of both streams in a cross-section. We showed that using a less viscous fluid as a reference fluid allows to define a mean shear rate with a low standard deviation in the other fluid. This method allows us to measure the flow curve of a fluid with less than 250 μL of fluid. In this paper we implement this principle in a fully automated set up which controls the flow rate, analyzes the picture and calculates the mean shear rate and the viscosity of the studied fluid. We present results obtained for Newtonian fluids and complex fluids using this set up and we compare our data with cone and plate rheometer measurements. By adding a mixing stage in the fluidic network we show how this set up can be used to characterize in a continuous way the evolution of the rheological properties as a function of the formulation composition. We illustrate this by measuring the rheological curve of four formulations of polyethylene oxide solution with only 1.3 mL of concentrated polyethylene oxide solution. This method could be very useful in screening processes where the viscosity range and the behavior of the fluid to an applied stress must be evaluated.     

A priori and a posteriori error analyses of a velocity-pseudostress formulation for a class of quasi-Newtonian Stokes flows

In this paper we introduce and analyze new mixed finite element schemes for a class of nonlinear Stokes models arising in quasi-Newtonian fluids. The methods are based on a non-standard mixed approach in which the velocity, the pressure, and the pseudostress are the original unknowns. However, we use the incompressibility condition to eliminate the pressure, and set the velocity gradient as an auxiliary unknown, which yields a twofold saddle point operator equation as the resulting dual-mixed variational formulation. In addition, a suitable augmented version of the latter showing a single saddle point structure is also considered. We apply known results from nonlinear functional analysis to prove that the corresponding continuous and discrete schemes are well-posed. In particular, we show that Raviart–Thomas elements of order k ? 0 for the pseudostress, and piecewise polynomials of degree k for the velocity and its gradient, ensure the well-posedness of the associated Galerkin schemes. Moreover, we prove that any finite element subspace of the square integrable tensors can be employed to approximate the velocity gradient in the case of the augmented formulation. Then, we derive a reliable and efficient residual-based a posteriori error estimator for each scheme. Finally, we provide several numerical results illustrating the good performance of the resulting mixed finite element methods, confirming the theoretical properties of the estimator, and showing the behaviour of the associated adaptive algorithms.     

Doubly asymptotic approximations as non-reflecting boundaries in fluid-structure interaction problems

Acoustic approximations are differential relations between induced fluid pressure and velocity in an acoustic medium. The plane wave approximation (PWA) is valid for high frequency response while doubly asymptotic approximations (DAA) are valid at very high and very low frequencies and, in advanced versions, at selected intermediate frequencies.These relations have been applied extensively on the wet surface of submerged structures to completely uncouple the equations of motion of the structure from those of the surrounding fluid. If DAA are used, a different virtual mass matrix and, in the advanced versions, fitting matrices must be evaluated for each structural geometry.In this paper, the approximations are used on a fluid surface which encloses the structure and has a geometry for which virtual mass and fitting matrices are known. The response is obtained by solving numerically the coupled fluid-structure equations within this approximation to a non-reflecting boundary.A numerical example of the dynamic response of a spheroidal shell is solved using a sphere as the absorbing boundary and the response obtained is compared to exact results.     

基于声表面波技术数字微流体基片间输运研究

复杂的生化分析系统往往很难集成于一个微流基片中,而按功能分别集成于两个或多个基片,为此,需要实现质荷在两基片间输运.提出了采用声表面波技术实现数字微流体在压电基片和玻璃基片间输运的新方法,它在128°YX-LiNbO3基片上光刻一个叉指换能器和一个反射栅,经功率放大器放大后频率为27.5 MHz的RF信号加到叉指换能器上,它激发的声表面波驱动其声路径上的数字微流体,使其按声传播方向快速运动,并到达与其相连接且经疏水处理的弧形聚合物表面,数字微流体由于自身重力克服表面张力作用沿弧形聚合物表面滑落到玻璃基片,实现两基片间输运.实验结果表明弧形聚合物曲率半径和微流体体积的大小影响其在两基片间输运.同时,提出了较小体积的微流体采用不相溶的油作为辅助微流体实现目标数字微流体在两基片间输运.     

蒸汽发生器干燥器声疲劳行波管模型仿真分析

随着核电企业采用提升功率的方式提高发电效益,其内部的干燥器容易受到较高的脉动压力载荷而导致声疲劳.介绍蒸汽发生器干燥器声疲劳试验方案——行波管混响腔模型.利用计算声学软件Actran进行仿真分析,研究试验装置内部声载荷分布特征.研究结果为后续试验研究提供技术支撑.     

A Rigging‐Skinning Scheme to Control Fluid Simulation

Inspired by skeletal animation, a novel rigging‐skinning flow control scheme is proposed to animate fluids intuitively and efficiently. The new animation pipeline creates fluid animation via two steps: fluid rigging and fluid skinning. The fluid rig is defined by a point cloud with rigid‐body movement and incompressible deformation, whose time series can be intuitively specified by a rigid body motion and a constrained free‐form deformation, respectively. The fluid skin generates plausible fluid flows by virtually fluidizing the point‐cloud fluid rig with adjustable zero‐ and first‐order flow features and at fixed computational cost. Fluid rigging allows the animator to conveniently specify the desired low‐frequency flow motion through intuitive manipulations of a point cloud, while fluid skinning truthfully and efficiently converts the motion specified on the fluid rig into plausible flows of the animation fluid, with adjustable fine‐scale effects. Besides being intuitive, the rigging‐skinning scheme for fluid animation is robust and highly efficient, avoiding completely iterative trials or time‐consuming nonlinear optimization. It is also versatile, supporting both particle‐ and grid‐ based fluid solvers. A series of examples including liquid, gas and mixed scenes are presented to demonstrate the performance of the new animation pipeline.     

Topology optimization of continuum structures with local and global stress constraints

Topology structural optimization problems have been usually stated in terms of a maximum stiffness (minimum compliance) approach. The objective of this type of approach is to distribute a given amount of material in a certain domain, so that the stiffness of the resulting structure is maximized (that is, the compliance, or energy of deformation, is minimized) for a given load case. Thus, the material mass is restricted to a predefined percentage of the maximum possible mass, while no stress or displacement constraints are taken into account. This paper presents a different strategy to deal with topology optimization: a minimum weight with stress constraints Finite Element formulation for the topology optimization of continuum structures. We propose two different approaches in order to take into account stress constraints in the optimization formulation. The local approach of the stress constraints imposes stress constraints at predefined points of the domain (i.e. at the central point of each element). On the contrary, the global approach only imposes one global constraint that gathers the effect of all the local constraints by means of a certain so-called aggregation function. Finally, some application examples are solved with both formulations in order to compare the obtained solutions.     

Hybrid Simulation of Miscible Mixing with Viscous Fingering

By modeling mass transfer phenomena, we simulate solids and liquids dissolving or changing to other substances. We also deal with the very small‐scale phenomena that occur when a fluid spreads out at the interface of another fluid. We model the pressure at the interfaces between fluids with Darcy's Law and represent the viscous fingering phenomenon in which a fluid interface spreads out with a fractal‐like shape. We use hybrid grid‐based simulation and smoothed particle hydrodynamics (SPH) to simulate intermolecular diffusion and attraction using particles at a computable scale. We have produced animations showing fluids mixing and objects dissolving.     

Stability of annular sectors and plates subjected to follower loads based on a mixed finite element formulation

A compatible mixed finite element is developed utilizing a weak variational formulation and applied to vibration and stability analysis of annular sectors and plates subjected to follower loads. The relaxed continuity requirement of the normal rotation is taken into account in this formulation. The transverse displacement and moments are interpolated by bilinear polynomials. The nodal unknowns are the field variable values at each vertex of the trapezoidal curved element. Examples are presented and their results are discussed.