Numerical Studies of Viscoelastic Flow Using the Software OpenFOAM

Viscoelastic fluids are a special class of non-Newtonian fluids. There are several types of viscoelastic fluid models, and all of them have a complex rheological response in comparison to Newtonian fluids. This response can be viewed as a combination of viscous and elastic effects and non-linear phenomena. This complex physics makes a numerical simulation a rather challenging task, even in simple test-cases. Studies presented in this paper are numerical studies of the viscoelastic fluid flow in several test cases. These studies have been done in OpenFOAM, an open-source CFD package. Implementation of viscoelastic models and a solver is only available in a community driven version of software (OpenFOAM-ext). One of the goals of research in this paper was to test the solver and models on some simple test cases. We considered start-up and pulsating flows of viscoelastic fluid in a channel and a circular pipe. The important thing is that an analytical solution can be found in these cases, making in possible to test all aspects of numerical simulation in OpenFOAM. Obtained results showed an excellent agreement with the analytical solution for both velocity and stress components. These results encouraged authors' motivation and a choice to use OpenFOAM for simulation of viscoelastic flows. We hope that our research will make a contribution to the OpenFOAM community. Our plan for the further research is a simulation of blood flow in arteries with the viscoelastic solver. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Simulation of wake effects of windfarms using an Actuator Disk implementation

Wind turbines extract energy from the approaching flow field resulting in reduced wind speeds, increased turbulence and a wake downstream of the wind turbine. Wakes extending up to 20 km downstream of a windfarm are reported [1]. In [2] a multi-scale numerical method is proposed that addresses length scales of the boundary layer, windfarm and meso-scale. As a step towards full realization of the multi scale approach the implementation of an Actuator Disk (AD) model into OpenFOAM including a proper atmospheric boundary layer (ABL) is presented. For a meso-scale area of open sea, the standard ABL conditions of OpenFOAM can not be used. The pre implemented ABL boundary condition for OpenFOAM is restricted to roughness lengths greater than 0.001 m. The boundary condition are modified in order to achieve adequate homogeneous flow properties throughout the considered domain enabling almost constant velocity profiles. A new AD class is implemented in OpenFOAM to establish an arbitrary number and location of windturbines. The class uses the standard k-ϵ turbulence model. The wake effect of windfarms composed of windturbines with different heights and different lateral spacing is investigated. Specifically the windfarm Trianel Borkum in the North Sea of Germany is simulated. Within this work wakes extending up to 20 km in length could be observed, suggesting to study the ABL-windfarm interaction in more detail. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Fluid-structure interaction of an elastic pipe immersed in a coaxial rigid pipe: a model for the Tullio Phenomenon

An axisymmetric, elastic pipe is filled with an incompressible fluid and is immersed in a second, coaxial rigid pipe which contains the same fluid. A pressure pulse in the outer fluid annulus deforms the elastic pipe which invokes a fluid motion in the fluid core. It is the aim of this study to investigate streaming phenomena in the core which may originate from such a fluid-structure interaction. This work presents a numerical solver for such a configuration. It was developed in the OpenFOAM software environment and is based on the Arbitrary Lagrangian Eulerian (ALE) approach for moving meshes. The solver features a monolithic integration of the one-dimensional, coupled system between the elastic structure and the outer fluid annulus into a dynamic boundary condition for the moving surface of the fluid core. Results indicate that our configuration may serve as a mechanical model of the Tullio Phenomenon (sound-induced vertigo). (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Direct numerical simulation of turbulent non-Newtonian flow using OpenFOAM

Understanding transition and turbulence in the flow of shear-thinning non-Newtonian fluids remains substantially unresolved and additional research is required to develop better computational methods for wall-bounded turbulent flows of these fluids. Previous DNS studies of shear-thinning fluids mainly use purpose-built codes and simple geometries such as pipes and channels. However in practical application, the geometry of mixing vessels, pumps and other process equipment is far more complex, and more flexible computational methods are required. In this paper a general-purpose DNS approach for shear-thinning fluids is undertaken using the OpenFOAM CFD library. DNS of turbulent Newtonian and non-Newtonian flow in a pipe flow are conducted and the accuracy and efficiency of OpenFOAM are assessed against a validated high-order spectral element-Fourier DNS code – Semtex. The results show that OpenFOAM predicts the flow of shear-thinning fluids to be a little more transitional than the predictions from Semtex, with lower radial and azimuthal turbulence intensities and higher axial intensity. Despite this, the first and second order turbulence statistics differ by at most 16%, and usually much less. An assessment of the parallel scaling of OpenFOAM indicates that OpenFOAM scales very well for the CPUs from 8 to 512, but the intranode scalability is poor for less than 8CPUs. The present work shows that OpenFOAM can be used for DNS of shear-thinning fluids in the simple case of pipe flow, and suggests that more complex flows, where flow separation is often important, are likely to be simulated with accuracies that are acceptably good for engineering application.     

Vertical impedance of a tapered pile in inhomogeneous saturated soil described by fractional viscoelastic model

Vertical impedance of a tapered pile embedded in the saturated viscoelastic half-space is theoretically investigated with the consideration of construction disturbances in radial direction. The constitutive behaviour of the soil is described by a fractional viscoelastic model. The tapered pile is divided to a series of stepping cylindrical segments to characterize its variable cross-section. An improved complex stiffness transfer model of the saturated soil is developed to determine the vertical reactions of the radially inhomogeneous soil on pile segments. The vertical impedance of the tapered pile is obtained by solving the differential equations for axial vibration of pile segments based on the Rayleigh-Love rod theory and recursive formulas. The validity and accuracy of the analytical solutions are demonstrated through the comparison examples for the cases of both soil compaction and soil softening. Parametric studies are performed to investigate the influences of tapered angle, fluid permeability and fractional order of soil constitutive model on vertical impedance of the tapered pile. The results indicate that the soil medium with high permeability, such as sandy and gravelly saturated foundation, has noticeable influence on the vertical impedance of tapered pile. In addition, it is suggested that the constitutive model of the soil should accurately describe the stress-strain experimental data to ensure the accuracy of the vertical impedance, especially for those tapered piles under excitations with high frequency.     

Two-dimensional viscous flow between circular cylinders: application to damping devices for seismic isolation

A detailed analysis of the fluid dynamics of the two-dimensional viscous flow between circular cylinders is dealt with in this paper. Analytic solutions are found on the basis of asymptotic expansions with respect to a small parameter defined by the ratio between the difference of the radii and the radius of the internal cylinder. The analysis is related to the study of recently developed devices for seismic isolation of buildings based on modified pile foundation, separated from the soil, in which a viscous fluid is inserted in the void space between the pile and the lining of the surrounding soil. The availability of this analytical solution contributes to obtaining accurate predictions of the force on the pile.     

Adjoint based topology optimization of conjugate heat transfer systems

This paper presents a topology optimization method for coupled thermal problems. Heat transfer linked with the forced convection flow inside cooling channels is investigated using a conjugate model. This model includes both the full Navier-Stokes equations for the fluid medium and the energy equations for both fluid and solid. In this present work, the adjoint method is extended to such conjugate heat transfer (CHT) systems to optimize their performance by the use of gradient based methods. This performance is usually a compromise between an increase in heat flux or temperature distribution at a surface and maintaining a low pressure loss within the system. To exemplify the method a uniform temperature distribution is chosen and evaluated numerically. For implementation the open source CFD Software OpenFOAM is used. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Numerical simulation of 1‐D incompressible laminar micro‐flow convection behaviour with temperature dependent fluid properties

This paper investigates the qualitative behaviour of single‐phase laminar convection for microchannels and conventionallysized channels formed between two parallel plates, captured by a numerical simulation on water flow. The convection parameters are obtained by separate numerical calculations on a series of parallel plates at constant temperatures. The pairs of parallel plates are maintained at progressively greater temperatures, to simulate the condition of increasing fluid temperature in a channel. The governing one‐dimensional (1‐D) momentum and energy equations are formulated to incorporate the dependence on temperature of both fluid viscosity (μ) and thermal conductivity (k). The qualitative behaviour of Nusselt number (Nu) decreasing with increasing Reynolds number (Re), exhibited by reported experimental data in literature, is simulated. Results show that it is practically dif_cult to observe this behaviour in the conventionally‐sized channels, but the effect easily surfaces in microchannels for practical lengths of flow and allowable high heat flux (q^″_W). (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Numerical simulation of cavitation around a two-dimensional hydrofoil using VOF method and LES turbulence model

In this paper simulation of cavitating flow over the Clark-Y hydrofoil is reported using the large eddy simulation (LES) turbulence model and volume of fluid (VOF) technique. We applied an incompressible LES modelling approach based on an implicit method for the subgrid terms. To apply the cavitation model, the flow has been considered as a single fluid, two-phase mixture. A transport equation model for the local volume fraction of vapour is solved and a finite rate mass transfer model is used for the vapourization and condensation processes. A compressive volume of fluid (VOF) method is applied to track the interface of liquid and vapour phases. This simulation is performed using a finite volume, two phase solver available in the framework of the OpenFOAM (Open Field Operation and Manipulation) software package. Simulation is performed for the cloud and super-cavitation regimes, i.e., σ = 0.8, 0.4, 0.28. We compared the results of two different mass transfer models, namely Kunz and Sauer models. The results of our simulation are compared for cavitation dynamics, starting point of cavitation, cavity’s diameter and force coefficients with the experimental data, where available. For both of steady state and transient conditions, suitable accuracy has been observed for cavitation dynamics and force coefficients.     

Direct numerical simulation of particles in a fluid interacting with a wall

We develop a code to be applied in the context of the cleaning of wafer surfaces by hydrodynamic forces. Our goal is to study the detachment of (submicron) particles, exposed to a shear flow, from a wall by means of direct numerical simulation. The particles are treated as rigid bodies fully interacting with the fluid. To simulate moving particles in the fluid we implement an immersed boundary method with direct forcing into OpenFOAM. The particle-wall interaction is treated with a soft contact model. As first simple examples we study the elastic normal impact of a cylinder onto a wall as well as the onset of sliding of a cylinder pressed to a horizontal wall by gravity under a time-depended drag force. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Numerical Modeling of Laser-Induced Cavitation Bubbles with a Finite Volume Method

We report on the numerical modeling of laser-induced cavitation bubbles with the finite volume method using the open source software package OpenFOAM. The numerical model is validated by comparison to experimental data for the two cases of a bubble collapsing under normal ambient conditions in an unbounded liquid as well as close to a solid wall. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Numerical modeling on inlet aperture effects on flow pattern in primary settling tanks

Inlets should be designed to dissipate the kinetic energy or velocity head of the mixed liquor and to prevent short-circuiting, mitigate the effects of density currents, and minimize blanket disturbances. Flow in primary settling tank is simulated by means of computational fluid dynamics. The fluid is assumed incompressible and non-buoyant. A two-dimensional computational and one phase fluid dynamics model was built to simulate the flow properties in the settling tank including the velocity profiles, the flow separation area and kinetic energy. In this study, the RNG turbulent model was solved with the Navier–Stokes equations. In order to evaluate hydraulic influences on the velocity profile, separation length and kinetic energy, three different of opening positions and two and three aperture in inlets were simulated. The flow model uses to apply a fixed-grid of cells that are all rectangular faces; the fluid moves through the grid and free surfaces are tracked with the volume-of-fluid (VOF) technique. Effects of numbers and locations of inlet apertures on the flow field are presented and the results show the positions of inlet apertures are affected on the flow pattern in the settling basin and increasing the numbers of slots can reduce kinetic energy in the inlet zone and produce uniform flow.     

Simulation of Premixed Turbulent Combustion in a Gas Engine using the Immersed Boundary Method and a Level Set Flame Model

An efficient simulation approach for turbulent flame brush propagation is a level set formulation closed by the turbulent flame speed. A formulation of the level set equation with the corresponding treatment of the turbulent mass burning rate that is compatible with standard Finite Volume discretization schemes available in computational fluid dynamics codes is employed. In order to simplify and to speed up the meshing process in complicated geometries (here in gas engines) the immersed boundary method in a continuous formulation, where the forces replacing the boundaries are introduced in the momentum conservation equations before discretization, is employed. In our contribution, aspects of the numerical implementation of the level set flame model combined with the immersed boundary formulation in OpenFOAM are presented. First representative simulation results of a homogeneous methane/air mixture combustion in a simplified engine geometry are shown. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Heat transfer in channel flow of a micropolar fluid

The study of heat transfer in channel flow has been done by previous authors for Newtonian and elastico-viscous fluids. It is the aim of the present paper to study the temperature profile for flow of a micropolar fluid in a channel induced by a constant axial pressure gradient, when the walls are maintained at constant temperatures. We have examined the effects of microrotation on the temperature profile and on the kinetic energy of the fluid. Three cases have been chosen by us for detailed study: (i) both the walls are maintained at different constant temperatures, (ii) both the walls are maintained at the same constant temperature, (iii) one wall is kept at a constant temperature and there is no heat flux at the other wall.     

Rheological and flow modelling of viscoelastic fluids between eccentric cylinders

Viscoelastic fluid flows within eccentric rotating cylinders are simulated using a finite element based commercial software POLYFLOW, and an approach based on the stream-tube method (STM) and domain decomposition.     

Influence of the pile shape on wind erosion CFD emission simulation

When designing an open storage system for bulk material like coal or iron ore, operational and investment parameters are to be considered. Those inputs are always managed by engineers and prolific literature can be found. But entering into environmental parameters like wind erosion, few methodologies are available, US EPA being one of the most extensive. This source is focused on certain conditions of wind direction, pile shape, etc. what sometimes are not matching the most interesting way of storing the material: area restrictions, stacking means, etc. Based on state of the art computational fluid dynamics (CFD) software, in this case we have used ANSYS CFX 5.7., modelling system was developed and compared to EPA results for conical and oval with flattop piles. After adjusting the calculation process and selecting the most effective variables, the semicircular shape was studied finding that for the same amount of material stored, lower emissions and wind erosions are to be expected; however depending on wind direction higher values of friction per surface unit are found but due to its higher volume of storage per square metre, the balance is positive to the semicircular pile.     

Temperature gradient in wood during grinding

Grinding is a commonly used method for producing pulps for papermaking, but its rather poor energy efficiency is a drawback. This paper focuses on developing a model dealing with temperature rise in wood during grinding. The model paves the way for the development of theoretical methods which can be used for reducing the energy consumption of the process. In grinding, wood is loaded by grits, which cause stress waves in the wood matrix. The stress waves fatigue the wood and ultimately separate fibres from the matrix, but because of wood’s viscoelasticity, part of the mechanical energy of waves is converted into heat. In order to understand the wood temperature increase in this process, a mechanistic model is developed here. The model is based on three hypotheses: a flux of mechanical energy occurs through the wood, the magnitude of the flux can be derived from the contact mechanics of the grits, and the rise in wood temperature can be determined from the dissipation of the flux. A temperature distribution in the actual grinding process was simulated with the model. The simulated temperatures were compared with a measured temperature profile obtained from the literature. The modelled and measured temperatures matched quite well. The simulations show that an increase in grit size results higher temperatures, whereas an increase in the distance between grits gives lower temperatures. The main result of the study is that the Hertz theory of contact mechanics can be considered an adequate method for analysing the effect of grits in the grinding process. The result shows that the Hertz theory is applicable when fatigue models are developed; these models can then be used to reduce the energy consumption of the process.     

相场方法模拟液滴的动态润湿行为

液滴的动态湿润现象广泛存在于自然界和工业生产中,该现象数值研究的建模需要解决接触线附近的奇异性并引入合理的接触角描述.基于相场方法,结合Yokoi动态接触角模型,建立了考虑动态润湿效应的两相流数值模型,并在OpenFOAM开源平台上实现相应程序.针对液滴撞击壁面的动态湿润过程,数值模拟和对比研究了不同的接触角模型.结果表明:接触角模型的选择对液滴动态润湿过程的模拟结果具有较大的影响,其中基于改进动态接触角模型的结果与文献中的实验结果具有很好的吻合度,反映了提出的数值模型在液滴的动态润湿行为模拟的有效性.     

Numerical simulation of dense fluid-particle flows using computational fluid dynamics (CFD) and discrete element method (DEM)

Discrete Element Method (DEM) has been successfully coupled with Computational Fluid Dynamics (CFD) in the framework of OpenFOAM an open source CFD simulation code. In the current study, at first the model is validated with the simple test case of spherical particle comparing the results with the analytical solution. Then the simulation of a gaseous fluidized bed is considered. The coupled mass and momentum balance equations are used to calculate the flow behavior, particle fluidization and bubble formation. The dimensions of the simulation domain are similar to Link et al. (2005) but with different stiffness of particles. The higher velocity of gaseous fluid relative to particles entering through a jet causes the particles to fluidize. The particles behavior, fluidization, bubble formation and the velocity vectors of particles show a good agreement with the literature. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Free vibration of piles embedded in soil having different modulus of subgrade reaction

The soil that the pile is embedded in is idealized by a Winkler model and is assumed to be two layered. The part of the pile extending above the ground is called the first region, and the parts embedded in the soil are called the second and the third regions, respectively. The dynamic displacement function of the pile subjected to an axial force is obtained as a fourth order partial differential equation by taking account of the effects of bending moment and shear force. It is assumed that the behavior of the material is linearly elastic and axial force along the pile length to be constant. Shear effects are included in the differential equations by the second derivative of the elastic curve function with respect to shear deformation. Normalized natural circular frequencies of the pile are calculated using a carry-over matrix and the secant method for non-trivial solution of the linear homogeneous system of equations obtained for a specific value of the axial force, and for two combinations of boundary conditions: