Numerical prediction of three-dimensional time-dependent viscoelastic extrudate swell using differential and algebraic models

This study investigates the numerical simulation of three-dimensional time-dependent viscoelastic free surface flows using the Upper-Convected Maxwell (UCM) constitutive equation and an algebraic explicit model. This investigation was carried out to develop a simplified approach that can be applied to the extrudate swell problem. The relevant physics of this flow phenomenon is discussed in the paper and an algebraic model to predict the extrudate swell problem is presented. It is based on an explicit algebraic representation of the non-Newtonian extra-stress through a kinematic tensor formed with the scaled dyadic product of the velocity field. The elasticity of the fluid is governed by a single transport equation for a scalar quantity which has dimension of strain rate. Mass and momentum conservations, and the constitutive equation (UCM and algebraic model) were solved by a three-dimensional time-dependent finite difference method. The free surface of the fluid was modeled using a marker-and-cell approach. The algebraic model was validated by comparing the numerical predictions with analytic solutions for pipe flow. In comparison with the classical UCM model, one advantage of this approach is that computational workload is substantially reduced: the UCM model employs six differential equations while the algebraic model uses only one. The results showed stable flows with very large extrudate growths beyond those usually obtained with standard differential viscoelastic models. (C) 2010 Elsevier Ltd. All rights reserved.

Numerical study of the atmospheric flow over a coastal cliff

This work presents a numerical method suitable for the study of the development of internal boundary layers (IBL) and their characteristics for flows over various types of coastal cliffs. The IBL is an important meteorological occurrence for flows with surface roughness and topographical step changes. A two-dimensional flow program was used for this study. The governing equations were written using the vorticity-velocity formulation. The spatial derivatives were discretized by high-order compact finite differences schemes. The time integration was performed with a low storage fourth-order Runge-Kutta scheme. The coastal cliff (step) was specified through an immersed boundary method. The validation of the code was done by comparison of the results with experimental and observational data. The numerical simulations were carried out for different coastal cliff heights and inclinations. The results show that the predominant factors for the height of the IBL and its characteristics are the upstream velocity, and the height and form (inclination) of the coastal cliff. Copyright (C) 2010 John Wiley & Sons, Ltd.

A computational study of some rheological influences on the ""splashing experiment""

In various attempts to relate the behaviour of highly-elastic liquids in complex flows to their rheometrical behaviour, obvious candidates for study have been the variation of shear viscosity with shear rate, the two normal stress differences N(1) and N(2), especially N(1), the extensional viscosity, and the dynamic moduli G` and G ``. In this paper, we shall confine attention to `constant-viscosity` Boger fluids, and, accordingly, we shall limit attention to N(1), eta(E), G` and G ``. We shall concentrate on the ""splashing"" problem (particularly that which arises when a liquid drop falls onto the free surface of the same liquid). Modern numerical techniques are employed to provide the theoretical predictions. We show that high eta(E) can certainly reduce the height of the so-called Worthington jet, thus confirming earlier suggestions, but other rheometrical influences (steady and transient) can also have a role to play and the overall picture may not be as clear as it was once envisaged. We argue that this is due in the main to the fact that splashing is a manifestly unsteady flow. To confirm this proposition, we obtain numerical simulations for the linear Jeffreys model. (C) 2010 Elsevier B.V. All rights reserved.

A numerical method for solving the dynamic three-dimensional Ericksen-Leslie equations for nematic liquid crystals subject to a strong magnetic field

A finite difference technique, based on a projection method, is developed for solving the dynamic three-dimensional Ericksen-Leslie equations for nematic liquid crystals subject to a strong magnetic field. The governing equations in this situation are derived using primitive variables and are solved using the ideas behind the GENSMAC methodology (Tome and McKee [32]; Tome et al. [34]). The resulting numerical technique is then validated by comparing the numerical solution against an analytic solution for steady three-dimensional flow between two-parallel plates subject to a strong magnetic field. The validated code is then employed to solve channel flow for which there is no analytic solution. (C) 2009 Elsevier B.V. All rights reserved.

The competing roles of extensional viscosity and normal stress differences in complex flows of elastic liquids

In various attempts to relate the behaviour of highly-elastic liquids in complex flows to their rheometrical behaviour, obvious candidates for study have been the variation of shear viscosity with shear rate, the two normal stress differences N(1) and N(2) especially N(1), and the extensional viscosity eta(E). In this paper, we shall be mainly interested in `constant-viscosity` Boger fluids, and, accordingly, we shall limit attention to N(1) and eta(E). We shall concentrate on two important flows - axisymmetric contraction flow and ""splashing"" (particularly that which arises when a liquid drop falls onto the free Surface of the same liquid). Modem numerical techniques are employed to provide the theoretical predictions. It is shown that the two obvious manifestations of viscoelastic rheometrical behaviour can sometimes be opposing influences in determining flow characteristics. Specifically, in an axisymmetric contraction flow, high eta(E) , can retard the flow, whereas high N(1) can have the opposite effect. In the splashing experiment, high eta(E) can certainly reduce the height of the so-called Worthington jet, thus confirming some early suggestions, but, again, other rheometrical influences can also have a role to play and the overall picture may not be as clear as it was once envisaged.

Evaluation of a bounded high order upwind scheme for 3D incompressible free surface flow computations

fit the context of normalized variable formulation (NVF) of Leonard and total variation diminishing (TVD) constraints of Harten. this paper presents an extension of it previous work by the authors for solving unsteady incompressible flow problems. The main contributions of the paper are threefold. First, it presents the results of the development and implementation of a bounded high order upwind adaptative QUICKEST scheme in the 3D robust code (Freeflow), for the numerical solution of the full incompressible Navier-Stokes equations. Second, it reports numerical simulation results for 1D hock tube problem, 2D impinging jet and 2D/3D broken clam flows. Furthermore, these results are compared with existing analytical and experimental data. And third, it presents the application of the numerical method for solving 3D free surface flow problems. (C) 2007 IMACS. Published by Elsevier B.V. All rights reserved,

Stability of numerical schemes on staggered grids

This paper considers the stability of explicit, implicit and Crank-Nicolson schemes for the one-dimensional heat equation on a staggered grid. Furthemore, we consider the cases when both explicit and implicit approximations of the boundary conditions arc employed. Why we choose to do this is clearly motivated and arises front solving fluid flow equations with free surfaces when the Reynolds number can be very small. in at least parts of the spatial domain. A comprehensive stability analysis is supplied: a novel result is the precise stability restriction on the Crank-Nicolson method when the boundary conditions are approximated explicitly, that is, at t =n delta t rather than t = (n + 1)delta t. The two-dimensional Navier-Stokes equations were then solved by a marker and cell approach for two simple problems that had analytic solutions. It was found that the stability results provided in this paper were qualitatively very similar. thereby providing insight as to why a Crank-Nicolson approximation of the momentum equations is only conditionally, stable. Copyright (C) 2008 John Wiley & Sons, Ltd.

An implicit technique for solving 3D low Reynolds number moving free surface flows

This paper describes the development of an implicit finite difference method for solving transient three-dimensional incompressible free surface flows. To reduce the CPU time of explicit low-Reynolds number calculations, we have combined a projection method with an implicit technique for treating the pressure on the free surface. The projection method is employed to uncouple the velocity and the pressure fields, allowing each variable to be solved separately. We employ the normal stress condition on the free surface to derive an implicit technique for calculating the pressure at the free surface. Numerical results demonstrate that this modification is essential for the construction of methods that are more stable than those provided by discretizing the free surface explicitly. In addition, we show that the proposed method can be applied to viscoelastic fluids. Numerical results include the simulation of jet buckling and extrudate swell for Reynolds numbers in the range [0.01, 0.5]. (C) 2008 Elsevier Inc. All rights reserved.

Semiconductor nanoparticle modeling via density functional theory

In this work, a 2.0 nm nanoparticle (low limit synthesized system) is compared to possible simplified models: passivated clusters, small (1.3 nm) nanoparticles and sets of plane surfaces. Our density functional theory results suggest that even when geometric aspects are properly described by the simplifications considered, electronic properties might be very different, especially when edge atoms are not properly taken into account in the nanoparticle`s modeling. In addition, we propose a protocol that might help future theoretical descriptions of nanoparticles.

A Robust, Fully Adaptive Hybrid Level-Set/Front-Tracking Method for Two-Phase Flows with an Accurate Surface Tension Computation

We present a variable time step, fully adaptive in space, hybrid method for the accurate simulation of incompressible two-phase flows in the presence of surface tension in two dimensions. The method is based on the hybrid level set/front-tracking approach proposed in [H. D. Ceniceros and A. M. Roma, J. Comput. Phys., 205, 391400, 2005]. Geometric, interfacial quantities are computed from front-tracking via the immersed-boundary setting while the signed distance (level set) function, which is evaluated fast and to machine precision, is used as a fluid indicator. The surface tension force is obtained by employing the mixed Eulerian/Lagrangian representation introduced in [S. Shin, S. I. Abdel-Khalik, V. Daru and D. Juric, J. Comput. Phys., 203, 493-516, 2005] whose success for greatly reducing parasitic currents has been demonstrated. The use of our accurate fluid indicator together with effective Lagrangian marker control enhance this parasitic current reduction by several orders of magnitude. To resolve accurately and efficiently sharp gradients and salient flow features we employ dynamic, adaptive mesh refinements. This spatial adaption is used in concert with a dynamic control of the distribution of the Lagrangian nodes along the fluid interface and a variable time step, linearly implicit time integration scheme. We present numerical examples designed to test the capabilities and performance of the proposed approach as well as three applications: the long-time evolution of a fluid interface undergoing Rayleigh-Taylor instability, an example of bubble ascending dynamics, and a drop impacting on a free interface whose dynamics we compare with both existing numerical and experimental data.

Modeling and simulation of the anode in direct ethanol fuels cells

Mathematical modeling has been extensively applied to the study and development of fuel cells. In this work, the objective is to characterize a mechanistic model for the anode of a direct ethanol fuel cell and perform appropriate simulations. The software Comsol Multiphysics (R) (and the Chemical Engineering Module) was used in this work. The software Comsol Multiphysics (R) is an interactive environment for modeling scientific and engineering applications using partial differential equations (PDEs). Based on the finite element method, it provides speed and accuracy for several applications. The mechanistic model developed here can supply details of the physical system, such as the concentration profiles of the components within the anode and the coverage of the adsorbed species on the electrode surface. Also, the anode overpotential-current relationship can be obtained. To validate the anode model presented in this paper, experimental data obtained with a single fuel cell operating with an ethanol solution at the anode were used. (C) 2008 Elsevier B.V. All rights reserved.

Accelerated aging of thick glass second surface silvered reflectors under sandstorm conditions

Concentrated solar power systems are expected to be sited in desert locations where the direct normal irradiation is above 1800 kWh/m2.year. These systems include large solar collector assemblies, which account for a significant share of the investment cost. Solarreflectors are the main components of these solar collector assemblies and dust/sand storms may affect their reflectance properties, either by soiling or by surface abrasion. While soiling can be reverted by cleaning, surface abrasion is a non reversible degradation.The aim of this project was to study the accelerated aging of second surface silvered thickglass solar reflectors under simulated sandstorm conditions and develop a multi-parametric model which relates the specular reflectance loss to dust/sand storm parameters: wind velocity, dust concentration and time of exposure. This project focused on the degradation caused by surface abrasion.Sandstorm conditions were simulated in a prototype environmental test chamber. Material samples (6cm x 6cm) were exposed to Arizona coarse test dust. The dust stream impactedthese material samples at a perpendicular angle. Both wind velocity and dust concentrationwere maintained at a stable level for each accelerated aging test. The total exposure time in the test chamber was limited to 1 hour. Each accelerated aging test was interrupted every 4 minutes to measure the specular reflectance of the material sample after cleaning.The accelerated aging test campaign had to be aborted prematurely due to a contamination of the dust concentration sensor. A robust multi-parametric degradation model could thus not be derived. The experimental data showed that the specular reflectance loss decreasedeither linearly or exponentially with exposure time, so that a degradation rate could be defined as a single modeling parameter. A correlation should be derived to relate this degradation rate to control parameters such as wind velocity and dust/sand concentration.The sandstorm chamber design would have to be updated before performing further accelerated aging test campaigns. The design upgrade should improve both the reliability of the test equipment and the repeatability of accelerated aging tests. An outdoor exposure test campaign should be launched in deserts to learn more about the intensity, frequencyand duration of dust/sand storms. This campaign would also serve to correlate the results of outdoor exposure tests with accelerated exposure tests in order to develop a robust service lifetime prediction model for different types of solar reflector materials.

Radiation properties of coil-coated steel in building envelope surfaces and the influence on building thermal performance

Recent studies have shown that the optical properties of building exterior surfaces are important in terms of energy use and thermal comfort. While the majority of the studies are related to exterior surfaces, the radiation properties of interior surfaces are less thoroughly investigated. Development in the coil-coating industries has now made it possible to allocate different optical properties for both exterior and interior surfaces of steel-clad buildings. The aim of this thesis is to investigate the influence of surface radiation properties with the focus on the thermal emittance of the interior surfaces, the modeling approaches and their consequences in the context of the building energy performance and indoor thermal environment. The study consists of both numerical and experimental investigations. The experimental investigations include parallel field measurements on three similar test cabins with different interior and exterior surface radiation properties in Borlänge, Sweden, and two ice rink arenas with normal and low emissive ceiling in Luleå, Sweden. The numerical methods include comparative simulations by the use of dynamic heat flux models, Building Energy Simulation (BES), Computational Fluid Dynamics (CFD) and a coupled model for BES and CFD. Several parametric studies and thermal performance analyses were carried out in combination with the different numerical methods. The parallel field measurements on the test cabins include the air, surface and radiation temperatures and energy use during passive and active (heating and cooling) measurements. Both measurement and comparative simulation results indicate an improvement in the indoor thermal environment when the interior surfaces have low emittance. In the ice rink arenas, surface and radiation temperature measurements indicate a considerable reduction in the ceiling-to-ice radiation by the use of low emittance surfaces, in agreement with a ceiling-toice radiation model using schematic dynamic heat flux calculations. The measurements in the test cabins indicate that the use of low emittance surfaces can increase the vertical indoor air temperature gradients depending on the time of day and outdoor conditions. This is in agreement with the transient CFD simulations having the boundary condition assigned on the exterior surfaces. The sensitivity analyses have been performed under different outdoor conditions and surface thermal radiation properties. The spatially resolved simulations indicate an increase in the air and surface temperature gradients by the use of low emittance coatings. This can allow for lower air temperature at the occupied zone during the summer. The combined effect of interior and exterior reflective coatings in terms of energy use has been investigated by the use of building energy simulation for different climates and internal heat loads. The results indicate possible energy savings by the smart choice of optical properties on interior and exterior surfaces of the building. Overall, it is concluded that the interior reflective coatings can contribute to building energy savings and improvement of the indoor thermal environment. This can be numerically investigated by the choice of appropriate models with respect to the level of detail and computational load. This thesis includes comparative simulations at different levels of detail.

Numerical Simulation Of Sediment Transport And Bedmorphology Around A Hydraulic Structure On A River

Scour around hydraulic structures is a critical problem in hydraulic engineering. Under prediction of scour depth may lead to costly failures of the structure, while over prediction might result in unnecessary costs. Unfortunately, up-to-date empirical scour prediction formulas are based on laboratory experiments that are not always able to reproduce field conditions due to complicated geometry of rivers and temporal and spatial scales of a physical model. However, computational fluid dynamics (CFD) tools can perform using real field dimensions and operating conditions to predict sediment scour around hydraulic structures. In Korea, after completing the Four Major Rivers Restoration Project, several new weirs have been built across Han, Nakdong, Geum and Yeongsan Rivers. Consequently, sediment deposition and bed erosion around such structures have became a major issue in these four rivers. In this study, an application of an open source CFD software package, the TELEMAC-MASCARET, to simulate sediment transport and bed morphology around Gangjeong weir, which is the largest multipurpose weir built on Nakdong River. A real bathymetry of the river and a geometry of the weir have been implemented into the numerical model. The numerical simulation is carried out with a real hydrograph at the upstream boundary. The bedmorphology obtained from the numerical results has been validated against field observation data, and a maximum of simulated scour depth is compared with the results obtained by empirical formulas of Hoffmans. Agreement between numerical computations, observed data and empirical formulas is judged to be satisfactory on all major comparisons. The outcome of this study does not only point out the locations where deposition and erosion might take place depending on the weir gate operation, but also analyzes the mechanism of formation and evolution of scour holes after the weir gates.

Extension And Testing Of A 2D Hydrodynamic Model For Direct Rainfall Runoff Simulation

While the simulation of flood risks originating from the overtopping of river banks is well covered within continuously evaluated programs to improve flood protection measures, flash flooding is not. Flash floods are triggered by short, local thunderstorm cells with high precipitation intensities. Small catchments have short response times and flow paths and convective thunder cells may result in potential flooding of endangered settlements. Assessing local flooding and pathways of flood requires a detailed hydraulic simulation of the surface runoff. Hydrological models usually do not incorporate surface runoff at this detailedness but rather empirical equations are applied for runoff detention. In return 2D hydrodynamic models usually do not allow distributed rainfall as input nor are any types of soil/surface interaction implemented as in hydrological models. Considering several cases of local flash flooding during the last years the issue emerged for practical reasons but as well as research topics to closing the model gap between distributed rainfall and distributed runoff formation. Therefore, a 2D hydrodynamic model, depth-averaged flow equations using the finite volume discretization, was extended to accept direct rainfall enabling to simulate the associated runoff formation. The model itself is used as numerical engine, rainfall is introduced via the modification of waterlevels at fixed time intervals. The paper not only deals with the general application of the software, but intends to test the numerical stability and reliability of simulation results. The performed tests are made using different artificial as well as measured rainfall series as input. Key parameters of the simulation such as losses, roughness or time intervals for water level manipulations are tested regarding their impact on the stability.