The Equilibrium Flux Method for the calculation of flows with non-equilbrium chemical reactions

The Equilibrium Flux Method [1] is a kinetic theory based finite volume method for calculating the flow of a compressible ideal gas. It is shown here that, in effect, the method solves the Euler equations with added pseudo-dissipative terms and that it is a natural upwinding scheme. The method can be easily modified so that the flow of a chemically reacting gas mixture can be calculated. Results from the method for a one-dimensional non-equilibrium reacting flow are shown to agree well with a conventional continuum solution. Results are also presented for the calculation of a plane two-dimensional flow, at hypersonic speed, of a dissociating gas around a blunt-nosed body.

Theory manual to OctVCE – a cartesian cell CFD code with special application to blast wave problems, Department of Mechanical Engineering Report 2007/12

OctVCE is a cartesian cell CFD code produced especially for numerical simulations of shock and blast wave interactions with complex geometries, in particular, from explosions. Virtual Cell Embedding (VCE) was chosen as its cartesian cell kernel for its simplicity and sufficiency for practical engineering design problems. The code uses a finite-volume formulation of the unsteady Euler equations with a second order explicit Runge-Kutta Godonov (MUSCL) scheme. Gradients are calculated using a least-squares method with a minmod limiter. Flux solvers used are AUSM, AUSMDV and EFM. No fluid-structure coupling or chemical reactions are allowed, but gas models can be perfect gas and JWL or JWLB for the explosive products. This report also describes the code’s ‘octree’ mesh adaptive capability and point-inclusion query procedures for the VCE geometry engine. Finally, some space will also be devoted to describing code parallelization using the shared-memory OpenMP paradigm. The user manual to the code is to be found in the companion report 2007/13.

User guide for shock and blast simulation with the OctVCE code (version 3.5+), Department of Mechanical Engineering Report 2007/13

OctVCE is a cartesian cell CFD code produced especially for numerical simulations of shock and blast wave interactions with complex geometries. Virtual Cell Embedding (VCE) was chosen as its cartesian cell kernel as it is simple to code and sufficient for practical engineering design problems. This also makes the code much more ‘user-friendly’ than structured grid approaches as the gridding process is done automatically. The CFD methodology relies on a finite-volume formulation of the unsteady Euler equations and is solved using a standard explicit Godonov (MUSCL) scheme. Both octree-based adaptive mesh refinement and shared-memory parallel processing capability have also been incorporated. For further details on the theory behind the code, see the companion report 2007/12.

A computational study of shock speeds in high-performance shock tubes

This paper describes U2DE, a finite-volume code that numerically solves the Euler equations. The code was used to perform multi-dimensional simulations of the gradual opening of a primary diaphragm in a shock tube. From the simulations, the speed of the developing shock wave was recorded and compared with other estimates. The ability of U2DE to compute shock speed was confirmed by comparing numerical results with the analytic solution for an ideal shock tube. For high initial pressure ratios across the diaphragm, previous experiments have shown that the measured shock speed can exceed the shock speed predicted by one-dimensional models. The shock speeds computed with the present multi-dimensional simulation were higher than those estimated by previous one-dimensional models and, thus, were closer to the experimental measurements. This indicates that multi-dimensional flow effects were partly responsible for the relatively high shock speeds measured in the experiments.

Hybrid modelling of coupled pore fluid-solid deformation problems

A hybrid formulation for coupled pore fluid-solid deformation problems is proposed. The scheme is a hybrid in the sense that we use a vertex centered finite volume formulation for the analysis of the pore fluid and a particle method for the solid in our model. The pore fluid formally occupies the same space as the solid particles. The size of the particles is not necessarily equal to the physical size of materials. A finite volume mesh for the pore fluid flow is generated by Delaunay triangulation. Each triangle possesses an initial porosity. Changes of the porosity are specified by the translations of the mass centers of particles. Net pore pressure gradients are applied to the particle centers and are considered in the particle momentum balance. The potential of our model is illustrated by means of a simulation of coupled fracture and fluid flow developed in porous rock under biaxial compression condition.

Mathematical models in percutaneous absorption

A number of mathematical models have been used to describe percutaneous absorption kinetics. In general, most of these models have used either diffusion-based or compartmental equations. The object of any mathematical model is to a) be able to represent the processes associated with absorption accurately, b) be able to describe/summarize experimental data with parametric equations or moments, and c) predict kinetics under varying conditions. However, in describing the processes involved, some developed models often suffer from being of too complex a form to be practically useful. In this chapter, we attempt to approach the issue of mathematical modeling in percutaneous absorption from four perspectives. These are to a) describe simple practical models, b) provide an overview of the more complex models, c) summarize some of the more important/useful models used to date, and d) examine sonic practical applications of the models. The range of processes involved in percutaneous absorption and considered in developing the mathematical models in this chapter is shown in Fig. 1. We initially address in vitro skin diffusion models and consider a) constant donor concentration and receptor conditions, b) the corresponding flux, donor, skin, and receptor amount-time profiles for solutions, and c) amount- and flux-time profiles when the donor phase is removed. More complex issues, such as finite-volume donor phase, finite-volume receptor phase, the presence of an efflux. rate constant at the membrane-receptor interphase, and two-layer diffusion, are then considered. We then look at specific models and issues concerned with a) release from topical products, b) use of compartmental models as alternatives to diffusion models, c) concentration-dependent absorption, d) modeling of skin metabolism, e) role of solute-skin-vehicle interactions, f) effects of vehicle loss, a) shunt transport, and h) in vivo diffusion, compartmental, physiological, and deconvolution models. We conclude by examining topics such as a) deep tissue penetration, b) pharmacodynamics, c) iontophoresis, d) sonophoresis, and e) pitfalls in modeling.

Modeling of columnar-to-equiaxed transition in solidified Al-Si alloys

A Cellular-Automaton Finite-Volume-Method (CAFVM) algorithm has been developed, coupling with macroscopic model for heat transfer calculation and microscopic models for nucleation and growth. The solution equations have been solved to determine the time-dependent constitutional undercooling and interface retardation during solidification. The constitutional undercooling is then coupled into the CAFVM algorithm to investigate both the effects of thermal and constitutional undercooling on columnar growth and crystal selection in the columnar zone, and formation of equiaxed crystals in the bulk liquid. The model cannot only simulate microstructures of alloys but also investigates nucleation mechanisms and growth kinetics of alloys solidified with various solute concentrations and solidification morphologies.

Numerical and experimental study of a homogenizer impinging jet

High-pressure homogenization is a key unit operation used to disrupt cells containing intracellular bioproducts. Modeling and optimization of this unit are restrained by a lack of information on the flow conditions within a homogenizer value. A numerical investigation of the impinging radial jet within a homogenizer value is presented. Results for a laminar and turbulent (k-epsilon turbulent model) jet are obtained using the PHOENICS finite-volume code. Experimental measurement of the stagnation region width and correlation of the cell disruption efficiency with jet stagnation pressure both indicate that the impinging jet in the homogenizer system examined is likely to be laminar under normal operating conditions. Correlation of disruption data with laminar stagnation pressure provides a better description of experimental variability than existing correlations using total pressure drop or the grouping 1/Y(2)h(2).

Brain structure and symptom dimension relationships in obsessive-compulsive disorder: A voxel-based morphometry study

Background: Obsessive-compulsive disorder (OCD) is a clinically heterogenous disorder characterized by temporally stable symptom dimensions. Past inconsistent results from structural neuroimaging studies of OCD may have resulted from the effects of these specific symptom dimensions as well as other socio-demographic and clinical variables upon gray matter (GM) volume. Methods: GM volume was measured in 25 adult OCD patients and 20 adult healthy controls using voxel-based morphometry (VBM), controlling for age and total brain GM volume. Univariate and multivariate regression analyses were carried out between regions of GM difference and age, age of onset, medication load, OCD severity, depression severity, and separate symptom dimension scores. Results: Significant GM volumetric differences in OCD patients relative to controls were found in dorsal cortical regions, including bilateral BA6, BA46, BA9 and right BA8 (controls > patients), and bilateral midbrain (patients > controls). Stepwise regression analyses revealed highly significant relationships between greater total OCD symptom severity and smaller GM volumes in dorsal cortical regions and larger GM volumes in bilateral midbrain. Greater age was independently associated with smaller GM volumes in right BA6, left BA9, left BA46 and larger GM volumes in right midbrain. Greater washing symptom severity was independently associated with smaller GM volume in right BA6, while there was a trend association between greater hoarding symptom severity and lower GM volume in left BA6. Limitations: The sample was relatively small to examine the relationship between symptom scores and GM volumes. Multiple patients were taking medication and had comorbid disorders. Conclusions: These analyses suggest dorsal prefrontal cortical and bilateral midbrain GM abnormalities in OCD that appear to be primarily driven by the effects of total OCD symptom severity. The results regarding the relationship between GM volumes and symptom dimension scores require examination in larger samples. (C) 2008 Elsevier B.V. All rights reserved.

Effects of changing blood viscosity and heart rate on vena contracta width as evaluated by color Doppler flow mapping. An in vitro study with a pulsatile flow model

Background: There is only limited knowledge on how the quantification of valvular regurgitation by color Doppler is affected by changing blood viscosity. This study was designed to evaluate the effect of changing blood viscosity on the vena contracta width using an in vitro model of valvular insufficiency capable of providing ample variation in the rate and stroke volume. Methods: We constructed a pulsatile flow model filled with human blood at varying hematocrit (15%, 35%, and 55%) and corresponding blood viscosity (blood/water viscosity: 2.6, 4.8, 9.1) levels in which jets were driven through a known orifice (7 mm(2)) into a 110 mL compliant receiving chamber (compliance: 2.2 mL/mmHg) by a pulsatile pump. In addition, we used variable pump stroke volumes (5, 7.5, and 10 mL) and rates (40, 60, and 80 ppm). Vena contracta region was imaged using a 3.5 MHz transducer. Pressure and volume in the flow model were kept constant during each experimental condition, as well as ultrasound settings. Results: Blood viscosity variation in the experimental range did not induce significant changes in vena contracta dimensions. Also, vena contracta width did not change from normal to low hematocrit and viscosity levels. A very modest increase only in vena contracta dimension was observed at very high level of blood viscosity when hematocrit was set to 55% . Pump rate, in the evaluated range, did not influence vena contracta width. These results in controlled experimental settings suggest that the vena contracta is an accurate quantitative method for quantifying valvular regurgitation even when this condition is associated with anemia, a frequent finding in patients with valvular heart disease.

Avaliação dosimétrica em tumores de mama: comparação de três técnicas

Objetivo – Comparar a técnica convencional, a técnica de energias mistas e a técnica field-in-field com energias mistas, verificando a dose recebida nos órgãos de risco e no volume alvo. Metodologia – Quinze doentes com carcinoma da mama esquerda classificadas de T1-T3N0M0 foram tratadas com cirurgia conservadora da mama, seguida de radioterapia pós-operatória. Para cada doente realizaram-se 3 planeamentos dosimétricos, sendo que cada um deles diz respeito a uma das diferentes técnicas em estudo. Através dos HDV gerados avaliaram-se a Dmáx, Dmed, Dmín, D95%, D3% e a homogeneidade da dose no volume alvo, bem como a dose nos órgãos de risco. Utilizou-se o teste de Friedman para verificar a significância do estudo, com um intervalo de confiança de 95%. Resultados – Relativamente ao pulmão esquerdo e ao coração obtiveram-se, com a técnica field-in-field com energias mistas, doses inferiores em comparação com as outras duas técnicas. Para a Dmáx e a homogeneidade de dose no PTV, a técnica field-in-field com energias mistas revelou-se mais eficaz, comparativamente às outras técnicas. No entanto, verificou-se uma melhor cobertura de dose no PTV com a técnica convencional. Considerações finais – A técnica field-in-field com energias mistas permite uma redução da dose nos órgãos de risco, uma redução significativa da Dmáx no PTV e melhora a homogeneidade da dose, comparativamente com as outras técnicas. Os resultados obtidos com a técnica field-in-field com energias mistas apontam para a redução dos efeitos secundários provocados pelo tratamento. ABSTRACT - Purpose – To compare the conventional technique, the technique of mixed energies and the technique field-in-field with mixed energies, checking the received dose in organs at risk and target volume. Methods – Fifteen patients with carcinoma of the left breast classified as T1-T3N0M0 were treated with breast-conserving surgery, followed by postoperative radiotherapy. For each patient were carried out three dosimetric plannings, each one of them concerns the different techniques under study. Through the DVH generated to evaluate Dmax, Dmed, Dmin, D95%, D3% and the homogeneity of the target volume dose, well as the dose in organs at risk. We used the Friedman test to assess the significance of the study, with a confidence interval of 95%. Results – For the left lung and heart were obtained with the technique field-in-field with mixed energies, lower doses compared with the other two techniques. For the Dmax and the homogeneity of the PTV dose, the technique field-in-field with mixed energies was more effective compared to other techniques. However, there was a better coverage of the PTV dose with conventional technique. Conclusions – The technique field-in-field with mixed energy allows a reduction in dose for organs at risk, a significant reduction Dmax in PTV and improves the homogeneity of the dose compared with other techniques. The results obtained with the technique field-in-field with mixed energy indicate to reduce the side effects caused by the treatment.

Colloidal interactions in two-dimensional nematics

The interaction between two disks immersed in a 2D nernatic is investigated i) analytically using the tenser order parameter formalism for the nematic configuration around isolated disks and ii) numerically using finite-element methods with adaptive meshing to minimize the corresponding Landau-de Gennes free energy. For strong homeotropic anchoring, each disk generates a pair of defects with one-half topological charge responsible for the 2D quadrupolar interaction between the disks at large distances. At short distance, the position of the defects may change, leading to unexpected complex interactions with the quadrupolar repulsive interactions becoming attractive. This short-range attraction in all directions is still anisotropic. As the distance between the disks decreases, their preferred relative orientation with respect to the far-field nernatic director changes from oblique to perpendicular.

Determinação da tenacidade à fratura em corte (GIIc) de adesivos estruturais pelo ensaio End-Notched Flexure (ENF)

Os adesivos têm sido alvo de estudo ao longo dos últimos anos para ligação de componentes a nível industrial. Devido à crescente utilização das juntas adesivas, torna-se necessária a existência de modelos de previsão de resistência que sejam fiáveis e robustos. Neste âmbito, a determinação das propriedades dos adesivos é fundamental para o projeto de ligações coladas. Uma abordagem recente consiste no uso de modelos de dano coesivo (MDC), que permitem simular o comportamento à fratura das juntas de forma bastante fiável. Esta técnica requer a definição das leis coesivas em tração e corte. Estas leis coesivas dependem essencialmente de 2 parâmetros: a tensão limite e a tenacidade no modo de solicitação respetivo. O ensaio End-Notched Flexure (ENF) é o mais utilizado para determinar a tenacidade em corte, porque é conhecido por ser o mais expedito e fiável para caraterizar este parâmetro. Neste ensaio, os provetes são sujeitos a flexão em 3 pontos, sendo apoiados nas extremidades e solicitados no ponto médio para promover a flexão entre substratos, o que se reflete numa solicitação de corte no adesivo. A partir deste ensaio, e após de definida a tenacidade em corte (GIIc), existem alguns métodos para estimativa da lei coesiva respetiva. Nesta dissertação são definidas as leis coesivas em corte de três adesivos estruturais através do ensaio ENF e um método inverso de ajuste dos dados experimentais. Para o efeito, foram realizados ensaios experimentais considerado um adesivo frágil, o Araldite® AV138, um adesivo moderadamente dúctil, o Araldite® 2015 e outro dúctil, o SikaForce® 7752. O trabalho experimental consistiu na realização dos ensaios ENF e respetivo tratamento dos dados para obtenção das curvas de resistência (curvas-R) através dos seguintes métodos: Compliance Calibration Method (CCM), Direct Beam Theory (DBT), Corrected Beam Theory (CBT) e Compliance-Based Beam Method (CBBM). Os ensaios foram simulados numericamente pelo código comercial ABAQUS®, recorrendo ao Métodos de Elementos Finitos (MEF) e um MDC triangular, com o intuito de estimar a lei coesiva de cada um dos adesivos em solicitação de corte. Após este estudo, foi feita uma análise de sensibilidade ao valor de GIIc e resistência coesiva ao corte (tS 0), para uma melhor compreensão do efeito destes parâmetros na curva P- do ensaio ENF. Com o objetivo de testar adequação dos 4 métodos de obtenção de GIIc usados neste trabalho, estes foram aplicados a curvas P- numéricas de cada um dos 3 adesivos, e os valores de GIIc previstos por estes métodos comparados com os respetivos valores introduzidos nos modelos numéricos. Como resultado do trabalho realizado, conseguiu-se obter uma lei coesiva única em corte para cada um dos 3 adesivos testados, que é capaz de reproduzir com precisão os resultados experimentais.

Slip flows of Newtonian and viscoelastic fluids in a 4:1 contraction

This work presents a numerical study of the 4:1 planar contraction flow of a viscoelastic fluid described by the simplified Phan-Thien–Tanner model under the influence of slip boundary conditions at the channel walls. The linear Navier slip law was considered with the dimensionless slip coefficient varying in the range ½0; 4500. The simulations were carried out for a small constant Reynolds number of 0.04 and Deborah numbers (De) varying between 0 and 5. Convergence could not be achieved for higher values of the Deborah number, especially for large values of the slip coefficient, due to the large stress gradients near the singularity of the reentrant corner. Increasing the slip coefficient leads to the formation of two vortices, a corner and a lip vortex. The lip vortex grows with increasing slip until it absorbs the corner vortex, creating a single large vortex that continues to increase in size and intensity. In the range De = 3–5 no lip vortex was formed. The flow is characterized in detail for De ¼ 1 as function of the slip coefficient, while for the remaining De only the main features are shown for specific values of the slip coefficient.

Improvign mixing processes with the help of numerical tools

In several industrial applications, highly complex behaviour materials are used together with intricate mixing processes, which difficult the achievement of the desired properties for the produced materials. This is the case of the well-known dispersion of nano-sized fillers in a melt polymer matrix, used to improve the nanocomposite mechanical and/or electrical properties. This mixing is usually performed in twin-screw extruders, that promote complex flow patterns, and, since an in loco analysis of the material evolution and mixing is difficult to perform, numerical tools can be very useful to predict the evolution and behaviour of the material. This work presents a numerical based study to improve the understanding of mixing processes. Initial numerical studies were performed with generalized Newtonian fluids, but, due to the null relaxation time that characterize this type of fluids, the assumption of viscoelastic behavior was required. Therefore, the polymer melt was rheologically characterized, and, a six mode Phan-Thien-Tanner and Giesekus models were used to fit the rheological data. These viscoelastic rheological models were used to model the process. The conclusions obtained in this work provide additional and useful data to correlate the type and intensity of the deformation history promoted to the polymer nanocomposite and the quality of the mixing obtained.