Two‐dimensional non‐Newtonian injection molding with a new control volume FEM/volume of fluid method

A new method based on volume of fluid for interface tracking in the simulation of injection molding is presented. The proposed method is comprised of two main stages: accumulation and distribution of the volume fraction. In the first stage the equation for the volume fraction with a noninterfacial flux condition is solved. In the second stage the accumulated volume of fluid that arises as a consequence of the application of the first one is dispersed. This procedure guarantees that the fluid fills the available space without dispersion of the interface. The mathematical model is based on two‐phase transport equations that are numerically integrated through the control volume finite element method. The numerical results for the interface position are successfully verified with analytical results and numerical data available in the literature for one‐dimensional and two‐dimensional domains. The transient position of the advance fronts showed an effective and consistent simulation of an injection molding process. The nondispersive volume of fluid method here proposed is implemented for the simulation of nonisothermal injection molding in two‐dimensional cavities. The obtained results are represented as transient interface positions, isotherms and pressure distributions during the injection molding of low density polyethylene. Copyright © 2012 John Wiley & Sons, Ltd.     

Vision-based measurement of spatio-temporal deformation of excavated soil for the estimation of bucket resistive force

This paper reports a vision-based technique of measuring the spatio-temporal deformation of excavated soil for estimating the bucket resistive force. The proposed measurement technique uses two depth cameras to determine three-dimensional soil-surface displacement. The technique consists of the following two processes: the first is related to image correlation between the two cameras, and the second involves data filtering and smoothing for generating soil deformation as a continuously curved surface. The proposed technique delivers measurement accuracy to the nearest centimeter. Typical experimental results of the three-dimensional measurement of soil deformation using the proposed technique are presented in the paper. Further, this study updates an interaction model for the resistive-force estimation while a bucket excavates soil. The model introduces a correction variable that changes with the bucket wrist angle by exploiting the experimental measurement of soil deformation. The model estimates the resistive force with an error of less than one quarter of the maximum force. These updates also exhibit the effectiveness of the proposed technique.     

Upwind sail aerodynamics: A RANS numerical investigation validated with wind tunnel pressure measurements

The aerodynamics of a sailing yacht with different sail trims are presented, derived from simulations performed using computational fluid dynamics. A Reynolds-averaged Navier–Stokes approach was used to model sixteen sail trims first tested in a wind tunnel, where the pressure distributions on the sails were measured. An original approach was employed by using two successive simulations: the first one on a large domain to model the blockage due to the wind tunnel walls and the sails model, and a second one on a smaller domain to model the flow around the sails model. A verification and validation of the computed aerodynamic forces and pressure distributions was performed. The computed pressure distribution is shown to agree well with the measured pressures. The sail surface pressure was correlated with the increase of turbulent viscosity in the laminar separation bubble, the flow reattachment and the trailing edge separation. The drive force distribution on both sails showed that the fore part of the genoa (fore sail) provides the majority of the drive force and that the effect of the aft sail is mostly to produce an upwash effect on the genoa. An aerodynamic model based on potential flow theory and a viscous correction is proposed. This model, with one free parameter to be determined, is shown to fit the results better than the usual form drag and induced drag only, even if no friction drag is explicitly considered.     

Exact solution of free vibration of adjacent buildings interconnected by visco-elastic dampers

With consideration of a high-rise coupled building system, a flexible beams-based analytical model is setup to characterize the dynamic behavior of the system. The general motion equation for the two beams interconnected by multiple viscous/visco-elastic dampers is rewritten into a non-dimensional form to identify the minimal set of parameters governing the dynamic characteristics. The corresponding exact solution suitable for arbitrary boundary conditions is presented. Furthermore, the methodology for computing the coefficients of the modal shape function is proposed. As an example, the explicit expression of the modal shape function is derived, provided only one damper is adopted to connect the adjacent buildings. Finally, to validate the proposed methodologies, three case studies are performed, in which the existence of the overdamping and the optimal damping coefficient are revealed. In the case of using one damper in connecting two similar buildings, the estimating equations for the first modal damping ratio are formulated.     

A turbulence model for inclined, bubbly flows

A new turbulence model for the flow of a two phase (liquid-liquid) flow in an inclined pipe is presented. An eddy viscosity is used to model the effects of shear induced turbulence and bubble induced turbulence. The cross-pipe momentum transport arising from the buoyant rise of bubbles across the axial flow is also modelled. Numerical simulations have been carried out in both one and two dimensions. One and two dimensional numerical simulations are presented.On leave from the University of Leeds, Leeds LS2 9JT, U.K.     

Order reduction of structural dynamic systems with static piecewise linear nonlinearities

A technique for order reduction of dynamic systems in structural form with static piecewise linear nonlinearities is presented. By utilizing two methods which approximate the nonlinear normal mode (NNM) frequencies and mode shapes, reduced-order models are constructed which more accurately represent the dynamics of the full model than do reduced models obtained via standard linear transformations. One method builds a reduced-order model which is dependent on the amplitude (initial conditions) while the other method results in an amplitude-independent reduced model. The two techniques are first applied to reduce two-degree-of-freedom undamped systems with clearance, deadzone, bang-bang, and saturation stiffness nonlinearities to single-mode reduced models which are compared by direct numerical simulation with the full models. It is then shown via a damped four-degree-of-freedom system with two deadzone nonlinearities that one of the proposed techniques allows for reduction to multi-mode reduced models and can accommodate multiple nonsmooth static nonlinearities with several surfaces of discontinuity. The advantages of the proposed methods include obtaining a reduced-order model which is signal-independent (doesn’t require direct integration of the full model), uses a subset of the original physical coordinates, retains the form of the nonsmooth nonlinearities, and closely tracks the actual NNMs of the full model.     

A method for analysing nesting techniques for the linearized shallow water equations

A method for analysing different nesting techniques for the linearized shallow water equations is presented. The problem is formulated as an eigenvector–eigenvalue problem. A necessary condition for stability is that the spectral radius of the propagation matrix is less than or equal to one. Two test cases are presented. The first test case is analysed, and effects of enforcing volume conservation and nudging in time are studied. A nesting technique is found that causes no growth of any eigenvectors for reasonable time steps. This nesting technique is then used on both test cases, and results are compared to an everywhere refined model and a coarse grid model. Copyright © 2002 John Wiley & Sons, Ltd.     

Passivity-based control for a flexible spacecraft in the presence of disturbances

The attitude regulation control problem for flexible spacecraft is investigated in this paper. Two extended PD+variable structure controllers are proposed using passivity-based control technique instead of sliding mode control approach. The first controller is a basic one, while the second one is an extension of the first one which relaxes the bound requirement for the external disturbances. In the presence of model uncertainties and external disturbances, both controllers presented in this research can make the flexible spacecraft UGAS (uniformly globally asymptotically stable). By virtue of related analysis tools, stability of the proposed controllers is proven theoretically. Numerical simulations are also included to demonstrate the performance of the developed controllers.     

High-order methods for differential equations with large first-derivative terms

A method is developed to solve elliptic singular perturbation problems. Examples are presented in one and two dimensions for both linear and non-linear problems. In particular, examples are presented for fluid flow problems with boundary layers. In the one-dimensional case an approximating equation is developed using just three points. The method first presented is a fourth-order approximation but is extended to become a higher-order method. Results are included for the fourth-, sixth-, eighth- and tenth-order methods. The results are first compared with results found by Segal in an article about elliptic singular perturbation problems. The elliptic singular perturbation problems are compared with a method by Il'in and also with central and backward difference schemes from Segal's article. There was only one case where the results in Segal's paper were as accurate as the results presented in this paper. However, in this case the method used by Segal did not give accurate values for a second problem presented. The results are also compared with results given by Spalding and by Christie. The method of this paper was also tested on the solution of some non-linear diffusion equations with concentration-dependent diffusion coefficients. The results were superior to results presented by Lee and by Schultz. Finally, the method is extended to several two-dimensional problems. The method developed in this paper is accurate, easy to use and can be generalized to other problems.     

Numerical simulations of compressible flows using multi-fluid models

Numerical simulations of two-fluid flow models based on the full Navier–Stokes equations are presented. The models include six and seven partial differential equations, namely, six- and seven-equation models. The seven-equation model consists of a non-conservative equation for volume fraction evolution of one of the fluids and two sets of balance equations. Each set describes the motion of the corresponding fluid, which has its own pressure, velocity, and temperature. The closure is achieved by two stiffened gas equations of state. Instantaneous relaxation towards equilibrium is achieved by velocity and pressure relaxation terms. The six-equation model is deduced from the seven-equation model by assuming an infinite rate of velocity relaxation. In this model, a single velocity is used for both fluids. The numerical solutions are obtained by applying the Strang splitting technique. The numerical solutions are examined in a set of one, two, and three dimensions for both the six- and seven-equation models. The results indicate very good agreement with the experimental results. There is an insignificant difference between the results of the two models, but the six-equation model is much more economical compared to the seven-equation model.     

Transient response of a ship to an abrupt flooding accounting for the momentum flux

Numerical non-linear time domain simulation method for damaged ship motions is presented. Floodwater motion modelling is based on the lumped mass method with a moving free surface. The ship and floodwater motions are fully coupled. The variation of the floodwater mass is accounted for. A model to account for the flooding ingress transporting the momentum is presented. The experiments of abrupt flooding have shown that the ship may experience the first large roll towards the undamaged side, especially when a large undivided compartment is flooded. The presented time domain model is validated against the experimental data on the roll damping of the flooded ship and transient flooding. Two different initial stability conditions and two different compartment layouts are studied. Viscous dissipation of the floodwater motions is modelled with an equivalent friction coefficient. The impact of the viscous damping is studied. Transient flooding tests show that the inflow momentum has to be accounted for when the undivided compartment is flooded. The simulation model is capable of capturing the impact of the inflooding jet and the first roll on the opposite side of the damage is reproduced.     

Modelling Turbulent Premixed Combustion Using the Level Set Approach for Reynolds Averaged Models

A model for premixed turbulent combustion is investigated using a RANS-approach. The evolution of the flame front is described in terms of the G-equation. The numerical instabilities of the G-field are resolved using a reinitialisation procedure. For the G-points near the flame surface an algorithm proposed by Russo and Smereka [1] and modificated by Düsing [2] is presented. For all other points the standard Sussman algorithm is employed. Fluid properties are conditioned on the flame front position using a burnt-unburnt probability function across the flame front. Computations are performed using the code FASTEST-3D [3] which is a flow solver for a non-orthogonal, block-structured grid. The computational examples include two test cases, the first containing the propagation of two circular merging flames and the second one containing the simulation of the ORACLES-burner [4].     

An arbitrary Lagrangian–Eulerian finite element approach to non‐steady state turbulent fluid flow with application to mould filling in casting

This paper presents a two‐dimensional Lagrangian–Eulerian finite element approach of non‐steady state turbulent fluid flows with free surfaces. The proposed model is based on a velocity–pressure finite element Navier–Stokes solver, including an augmented Lagrangian technique and an iterative resolution of Uzawa type. Turbulent effects are taken into account with the k–ε two‐equation statistical model. Mesh updating is carried out through an arbitrary Lagrangian–Eulerian (ALE) method in order to describe properly the free surface evolution. Three comparisons between experimental and numerical results illustrate the efficiency of the method. The first one is turbulent flow in an academic geometry, the second one is a mould filling in effective casting conditions and the third one is a precise confrontation to a water model. Copyright © 2000 John Wiley & Sons, Ltd.     

On non-linear dynamics of a coupled electro-mechanical system

Electro-mechanical devices are an example of coupled multi-disciplinary weakly non-linear systems. Dynamics of such systems is described in this paper by means of two mutually coupled differential equations. The first one, describing an electrical system, is of the first order and the second one, for mechanical system, is of the second order. The governing equations are coupled via linear and weakly non-linear terms. A classical perturbation method, a method of multiple scales, is used to find a steady-state response of the electro-mechanical system exposed to a harmonic close-resonance mechanical excitation. The results are verified using a numerical model created in MATLAB Simulink environment. Effect of non-linear terms on dynamical response of the coupled system is investigated; the backbone and envelope curves are analyzed. The two phenomena, which exist in the electro-mechanical system: (a)?detuning (i.e. a natural frequency variation) and (b)?damping (i.e. a decay in the amplitude of vibration), are analyzed further. An applicability range of the mathematical model is assessed.     

有阻尼体系的时域边界元法

针对时域边界元方法的特点，提出了一种新的阻尼模型（称为比例时耗阻尼），并成功地应用于时域边界元方法中．这是在时域边界元方法中首次考虑阻尼这一影响结构动力响应的重要因素，为时域边界元在实际工程中的应用解决了一个难题．通过对简单问题的分析和计算，验证了本文模型的正确性．     

Improved droplet breakup models for spray applications

The current study examines the performance of two zero-dimensional (0D) aerodynamically-induced breakup models, utilized for the prediction of droplet deformation during the breakup process in the bag, multi-mode and sheet-thinning regimes. The first model investigated is an improved version of the widely used Taylor analogy breakup (TAB) model, which compared to other models has the advantage of having an analytic solution. Following, a model based on the modified Navier–Stokes (M-NS) is examined. The parameters of both models are estimated based upon published experimental data for the bag breakup regime and CFD simulations with Diesel droplets performed as part of this work for the multi-mode and sheet-thinning regimes, for which there is a scarcity of experimental data. Both models show good accuracy in the prediction of the temporal evolution of droplet deformation in the three breakup regimes, compared to the experimental data and the CFD simulations. It is found that the best performance of the two is achieved with the M-NS model. Finally, a unified secondary breakup model is presented, which incorporates various models found in the literature, i.e. TAB, non-linear TAB (NLTAB), droplet deformation and breakup (DDB) and M-NS, into one equation using adjustable coefficients, allowing to switch among the different models.     

A multi-scale enriched model for the analysis of masonry panels

A multi-scale model for the structural analysis of the in-plane response of masonry panels, characterized by periodic arrangement of bricks and mortar, is presented. The model is based on the use of two scales: at the macroscopic level the Cosserat micropolar continuum is adopted, while at the microscopic scale the classical Cauchy medium is employed. A nonlinear constitutive law is introduced at the microscopic level, which includes damage, friction, crushing and unilateral contact effects for the mortar joints. The nonlinear homogenization is performed employing the Transformation Field Analysis (TFA) technique, properly extended to the macroscopic Cosserat continuum. A numerical procedure is developed and implemented in a Finite Element (FE) code in order to analyze some interesting structural problems. In particular, four numerical applications are presented: the first one analyzes the response of the masonry Representative Volume Element (RVE) subjected to a cyclic loading history; in the other three applications, a comparison between the numerically evaluated response and the micromechanical or experimental one is performed for some masonry panels.     

On Vortex Tube Stretching and Instabilities in an Inviscid Fluid

We study instabilities that are present in two models that retain some of the dynamics of vortex tube stretching in the motion of a fluid in 3 dimensions. Both models are governed by a 2-dimensional PDE and are hence more tractable than the full 3-dimensional Euler equations. The first model is the so called surface quasi-geostrophic equation. The second model is a class of 3-dimensional flows that are invariant with respect to one spatial coordinate. Both models appear in the context of a rapidly rotating fluid. Instabilities due to an effect analogous to vortex tube stretching are detected: these instabilities are in the linearised equations in the first model and in the nonlinear equations in the second model. Such instabilities are absent, or weaker, in strictly 2-dimensional fluid motion.     

Analytical and numerical analysis of frictional damage in quasi brittle materials

Frictional sliding and crack growth are two main dissipation processes in quasi brittle materials. The frictional sliding along closed cracks is the origin of macroscopic plastic deformation while the crack growth induces a material damage. The main difficulty of modeling is to consider the inherent coupling between these two processes. Various models and associated numerical algorithms have been proposed. But there are so far no analytical solutions even for simple loading paths for the validation of such algorithms. In this paper, we first present a micro-mechanical model taking into account the damage-friction coupling for a large class of quasi brittle materials. The model is formulated by combining a linear homogenization procedure with the Mori–Tanaka scheme and the irreversible thermodynamics framework. As an original contribution, a series of analytical solutions of stress–strain relations are developed for various loading paths. Based on the micro-mechanical model, two numerical integration algorithms are exploited. The first one involves a coupled friction/damage correction scheme, which is consistent with the coupling nature of the constitutive model. The second one contains a friction/damage decoupling scheme with two consecutive steps: the friction correction followed by the damage correction. With the analytical solutions as reference results, the two algorithms are assessed through a series of numerical tests. It is found that the decoupling correction scheme is efficient to guarantee a systematic numerical convergence.