Two-Phase Flow in Single-Screw Extruders

This work concerns numerical simulation of free-surface flows of highly viscous liquids in single-screw extruders.The numerical treatment of a partially filled extruder is a challenging task due to the complex geometry and the large differences in density and viscosity between the two phases, e.g. polymer melt and air. Furthermore, the rotation of the screw leads to a continuous renewing of the free-surface. For this purpose the Volume of Fluid (VOF) method is used. First a simplified two-dimensional model of a single-screw extruder is considered. Good agreement is obtained between the numerical results and experimental data. Finally, the three dimensional free-surface flow in a partially filled single-screw extruder with dynamic mesh motion is presented. In addition, the power characteristics of a conveying screw element with varying degree of filling is discussed. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

An exact Riemann solver and a Godunov scheme for simulating highly transient mixed flows

The current research aims at deriving a one-dimensional numerical model for describing highly transient mixed flows. In particular, this paper focuses on the development and assessment of a unified numerical scheme adapted to describe free-surface flow, pressurized flow and mixed flow (characterized by the simultaneous occurrence of free-surface and pressurized flows). The methodology includes three steps. First, the authors derived a unified mathematical model based on the Preissmann slot model. Second, a first-order explicit finite volume Godunov-type scheme is used to solve the set of equations. Third, the numerical model is assessed by comparison with analytical, experimental and numerical results. The key results of the paper are the development of an original negative Preissmann slot for simulating sub-atmospheric pressurized flow and the derivation of an exact Riemann solver for the Saint-Venant equations coupled with the Preissmann slot.     

Numerical modeling of 3-D flow on porous broad crested weirs

Gabion weirs with optional design as a broad crested weirs are suitable structures to reduce flash flood with a minimal negative impact on the water environment. In the present study, the 3-D flow was simulated around gabion weirs with respect to free-surface water. The Reynolds-averaged Navier–Stokes equations are solved to predict water surface over the gabion weir. The VOF method with the geometric reconstruction scheme was applied to treat the complex free-surface flow. Simulations were performed using three variants of the k–ε and the RSM models to find the water level and velocity distribution profile and results are compared with several experimental data available in the literature. The structured mesh was used for all domains with high dense mesh near the solid region. A comparison between experimental data and simulations indicates that the k–ε model can be used to predict the complex flow and water level with high accuracy.     

Efficient non-hydrostatic modelling of surface waves interacting with structures

An efficient three-dimensional non-hydrostatic model is applied to simulate free-surface waves interacting with structures. The model employs an implicit Crank–Nicholson scheme to discretize the Navier–Stokes equations under a Cartesian staggered grid framework. An integration method is introduced to account for the full effects of non-hydrostatic pressure at the free-surface layer. A domain decomposition method is proposed to effectively solve the resulting matrix system. The model is first validated by simulating three-dimensional sloshing waves in a container. The model is then applied to simulate waves propagating over two-dimensional and three-dimensional submerged structures, in which the effects of non-linearity and dispersion are important. The model results show that the model using only two vertical layers are in all favorable agreements with experimental data, demonstrating the efficiency and accuracy of the model on simulating surface waves interacting with structures.     

A model describing pressure buildup in rough surfaces with partially filled gaps

Because of an ecological and economical need to reduce the application of lubricants, the tribological regime of starved lubrication in the field of mechanical engineering has gained importance during the last decades. In order to describe the respective processes properly, models should consider that the gap between the bodies is not fully but only partially filled with a fluid. Recently, the authors introduced a model which explicitly describes the fluid flow and its interaction with the buildup of pressures under these conditions [1]. This paper points out that the correlation between the filling ratio and a time- and space-averaged pressure value is highly nonlinear. This is due to the fact that the system's load bearing character changes from being a local effect to a global effect, in particular near the fully filled regime. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Numerical Investigation of the Free-Surface Flow within an Annulus

This study describes the free-surface flow of a highly viscous liquid between two concentric cylinders. In the process the morphology of the phase boundary is determined using a straight volume of fluid approach. Due to large differences in viscosity the gaseous phase is considered as vacuum. The numerical results of free-surface flow measures are compared to previous calculations and experimental values. The investigation shows that the used two-phase method is well-suited to predict the location and shape of the interface. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Approximate analytical solution for supercritical flow in rectangular curved channels

In this study, we present an asymptotical mathematical model and an analytical solution for a supercritical flow in curved rectangular open channels. An original approach is proposed for solving the free-surface configuration and features of the flow in the presence of cross shock waves. The two-dimensional steady depth-averaged shallow water equations are transformed into an equivalent one-dimensional (1D) unsteady flow problem and a first order approximation is then obtained using small perturbation theory. Furthermore, the 1D asymptotic model is solved analytically by Laplace integral transformation and the two-dimensional flow field solution is reconstructed according to the translating planes. The free-surface profile along the outer chute wall and downstream channel was compared with the available experimental data, and the results indicated the satisfactory agreement of the maximum flow depth, peak positions, and wavelength. The proposed approach provides accurate predictions of the flow features and it facilitates the safe design of curved channel transitions.     

Free-surface,purely azimuthal equatorial flows in spherical coordinates with stratification

In this paper we derive an exact solution to the governing equations for geophysical fluid dynamics in spherical coordinates which incorporates fluid stratification. This solution represents a steady, purely–azimuthal equatorial flow with an associated free-surface. Following the derivation of the solution we demonstrate that there is a well-defined relationship between the imposed pressure at the free-surface and the resulting distortion of the surface's shape. Finally, the solution for stratified fluid flow is subjected to a short-wavelength stability analysis.     

Computational simulation of fluid and dilute particulate flows on spiral concentrators

Spiral separators are used globally in the fine coal and heavy mineral processing industries as gravity-concentration devices. Consisting of an open trough that spirals vertically downwards in helix configuration about a central axis, a slurry mix of particles and water is fed to the top of the concentrator. Particles are then separated radially on the basis of density and size as they gravitate downwards. To enhance performance, the geometric design has evolved historically by experimental trial-and-error investigations to develop a prototype suited to the given industrial application. This approach has proved somewhat prohibitive for design purposes however, and researchers have accordingly turned to numerical techniques in an attempt to develop a fully predictive and reliable model for use in the design process. Towards this end, the present paper uses Computational Fluid Dynamics (CFD) analysis to simulate fluid and dilute particulate flows on one operational spiral unit. The free-surface Volume-of-Fluid (VOF) algorithm, isotropic RNG k–ε turbulence model and Lagrangian method have been used for this purpose. Satisfactory predictions have been obtained with respect to a collaborative experimental program, and the model forms the basis for future examination of the two-way fluid-particle coupling processes and inter-particle effects.     

Synchronization effects in rotors partly filled with fluid

In fluid-filled rotors self-excited vibrations occur induced by a surface wave of the fluid. A characteristic property is the instability over the full range of angular velocity above the Eigenfrequency of the system. A possible explanation is the occurrence of synchronization effects between fluid and rotor. The behaviour of rotors partly filled with fluid was mostly studied under the aspect of stability in steady-state conditions. For non-steady-state investigations, discrete models with reduced number of degrees of freedom and reasonable ability to model the system behaviour are desirable due to the complexity of fluid modelling. This paper analyses a simple minimal model and shows synchronization effects between fluid and rotor model. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A model for fluid flow in non-fully filled tribological interfaces – Part 1: Basics and Numerics

In literature, most contributions on starved lubrication focus on the occurring pressures in macroscopic devices. Hereby, usually the Reynolds equation is modified in different ways. In contrast to this proceeding, this paper's intention is the general investigation of this tribological regime to get a fundamental comprehension on the transition from boundary lubrication to mixed lubrication. The respective model describes the flow of the fluid through two rough surfaces moving relative to each other. The lack of fluid is regarded by the fact that elements may not be fully filled with the fluid. Only elements where the fluid fully fills the gap, generate a pressure. This effect is considered by a type of unilateral constraint in combination with a penalty function. The fluid flow is computed according to the Navier-Stokes equation. In combination with the continuity equation, a set of implicit nonlinear equations has to be solved. Its potential and basic application fields are finally discussed. A further paper will show applications of the algorithm towards different scenarios. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Synchronization effects in rotors partially filled with fluid-influence on propulsion

In fluid-filled Rotors occur self-excited vibrations induced by surface waves of the fluid. A characteristic property is the instability over an interval of angular velocity above the natural frequency of the system. One explanation is the occurrence of synchronization effects between fluid waves and the critical rotor speed. The behaviour of rotors partly filled with fluid was mostly studied under the aspect of stability in steady-state conditions. For non-steady-state investigations, discrete models with reduced number of degrees of freedom and reasonable ability to model the system behaviour are desirable for observer-based real-time control. This paper analyses a model based on a laval rotor and shows synchronization effects between fluid waves and rotor model and its influence on the rotor propulsion. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A Lagrangian-based SPH-DEM model for fluid–solid interaction with free surface flow in two dimensions

A Lagrangian-based SPH-DEM coupling model is proposed to study fluid–solid interaction (FSI) problems with free-surface flow. In this model, SPH uses an incompressible divergence-free scheme for simulating complex flow problems. Based on the Mohr–Coulomb criterion with tension cut, the DEM describes the characteristics of solid deformation and failure by means of contact models between particles. The coupling mechanism between SPH and DEM is realised by the decoupling of the force field during the process of fluid–solid interaction. That is, the motions of fluid and solid particles are reflected by the Navier–Stokes equations and interactions among solid particles are determined by Newton's second law in the DEM. To demonstrate the applicability of the SPH-DEM model, three case studies are used to verify the different fluid interaction situations with rigid bodies, deformable objects, and granular assemblies, respectively. The results of the proposed model shows good agreement with experimental data and indicates that it is capable of capturing the features of solid movement, deformation and failure under complex flow conditions with convincing accuracy and high efficiency.     

A new discrete filled function method for solving large scale max-cut problems

The global optimization method based on discrete filled function is a new method that solves large scale max-cut problems. We first define a new discrete filled function based on the structure of the max-cut problem and analyze its properties. Unlike the continuous filled function methods, by the characteristic of the max-cut problem, the parameters in the proposed filled function does not need to be adjusted. By combining a procedure that randomly generates initial points for minimization of the proposed filled function, the proposed algorithm can greatly reduce the computational time and be applied to large scale max-cut problems. Numerical results and comparisons with several heuristic methods indicate that the proposed algorithm is efficient and stable to obtain high quality solution of large scale max-cut problems.     

混合微通道中不稳定的广义Couette流

在一个平行板通道中,部分充满了均匀的多孔介质,部分为纯流体的流动区,对其微通道中完全发展的不稳定层流进行了数值分析,流动由其中一块板的运动和压力梯度所引起.多孔介质区域的流动,采用扩展的Brinkman模型,即Darcy模型,纯净流动区域的流动,采用Stokes方程.还对稳定的完全发展流进行了理论分析,给出了分界面速度、边界板处的速度和表面摩擦的闭式解.通过数值计算发现,稳定完全发展流的闭式解,和不稳定流动的数值解,在所有时间点上得到很好地吻合.     

Well-posedness of the free-surface incompressible Euler equations with or without surface tension

We provide a new method for treating free boundary problems in perfect fluids, and prove local-in-time well-posedness in Sobolev spaces for the free-surface incompressible 3D Euler equations with or without surface tension for arbitrary initial data, and without any irrotationality assumption on the fluid. This is a free boundary problem for the motion of an incompressible perfect liquid in vacuum, wherein the motion of the fluid interacts with the motion of the free-surface at highest-order.

     

非牛顿流体内流传热研究

在本文中,研究了注入轴对称模腔非牛顿流体非定常流动.本文的第二部份研究了上随体Maxwell流体管内热流动.对于注入模腔流动.其本构方程采用幂律流体模型方程.为了避免在表现粘度中温度关系引起的非线性.引进了一特征粘度的概念.描述本力学过程的基本方程是,本构方程、定常状态的运动方程、非定常能量方程及连续方程.该方程组在空间是二维问题,在数学上是三维问题.采用分裂差分格式求得本方程组的数值解答.分裂法曾成功应用于求解牛顿流体问题.在本文中,首次将分裂法成功地应用解决非牛顿流体流动问题.对于圆管内热流,给出了差分格式,使基本方程组化为一个三对角方程组.其结果,给出了不同时刻的模腔内二维温度分布.     

RANS-simulation of premixed turbulent combustion using the level set approach

A model for premixed turbulent combustion is investigated using a RANS-approach. The evolution of the flame front is described with the help of the level set approach [1] which is used for tracking of propagating interfaces in free-surface flows, geodesics, grid generation and combustion. The fluid properties are conditioned on the flame front position using a burntunburnt probability function across the flame front. Computations are performed using the code FASTEST-3D which is a flow solver for a non-orthogonal, block-structured grid. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A Formulation for Water Waves over Topography

Many interesting free-surface flow problems involve a varying bottom. Examples of such flows include ocean waves propagating over topography, the breaking of waves on a beach, and the free surface of a uniform flow over a localized bump. We present here a formulation for such flows that is general and, from the outset, demonstrates the wave character of the free-surface evolution. The evolution of the free surface is governed by a system of equations consisting of a nonlinear wave-like partial differential equation coupled to a time-independent linear integral equation. We assume that the free-surface deformation is weakly nonlinear, but make no a priori assumption about the scale or amplitude of the topography. We also extend the formulation to include the effect of mean flows and surface tension. We show how this formulation gives some of the well-known limits for such problems once assumptions about the amplitude and scale of the topography are made.