ABE, V.C. Determinação de parâmetros de operação de sistema de distribuição de ar frio pelo piso em ambientes de escritórios. 2007. 132 p. Dissertação (Mestrado) - Departamento de Engenharia de Construção Civil da Escola Politécnica da Universidade de São Paulo, São Paulo, 2007. Atualmente, um dos principais requisitos para que um ambiente de escritório atenda plenamente às necessidades de uso e ocupação é a flexibilidade, mas com conforto. O sistema de distribuição de ar frio pelo piso (Underfloor Air Distribution System - UFAD) está sendo utilizado nos edifícios de escritórios para garantir a flexibilização integrada do sistema com o mobiliário. Trata-se de um sistema que fornece ar frio proveniente de um plenum, através de difusores localizados nos painéis do piso elevado. Os difusores de ar podem ser ajustados, ou reposicionados pelos próprios usuários dos ambientes, possibilitando o controle das condições térmicas no entorno próximo, de acordo com suas preferências individuais. Embora o sistema de distribuição de ar pelo piso apresente diversas vantagens com relação ao sistema de distribuição de ar convencional, ainda há falta de informações objetivas e diretrizes de projeto padronizadas, havendo a necessidade de realização de mais pesquisas na área. A introdução da Dinâmica dos Fluidos Computacional (Computational Fluid Dynamics - CFD) apresentou uma alternativa para as pesquisas experimentais relacionadas ao estudo do escoamento do ar. Assim, para o desenvolvimento do presente estudo foram utilizados recursos de dinâmica dos fluidos computacional, com o uso do código FLUENT. O objetivo do presente trabalho é apresentar uma estratégia para a determinação dos parâmetros de operação de sistemas de distribuição de ar pelo piso aplicados a ambientes de escritórios. A estratégia baseiase no estabelecimento de inter-relações entre os principais parâmetros que definem o escoamento do ar em ambientes com o sistema de distribuição de ar pelo piso: a vazão de ar insuflado, a temperatura do ar insuflado e a diferença de pressão entre o plenum pressurizado e o interior do ambiente. O emprego da estratégia possibilita que o projetista identifique as diversas combinações entre os parâmetros de operação que resultem numa mesma condição desejada, permitindo assim a escolha da opção mais satisfatória. / ABE, V.C. Determination of operation parameters of rooms with underfloor air distribution system. 2007. 132 p. Dissertation (Master Course) - Departamento de Engenharia de Construção Civil da Escola Politécnica da Universidade de São Paulo, São Paulo, 2007. Nowadays, one of the main requirements of an office room to fully attend the use and occupation needs is the flexibility, but with comfort. The underfloor air distribution system is being used in the office buildings to guarantee the integrated flexibility of the system with the furniture layout. The system supplies cooled air to the room from a pressurized plenum, passing through air diffusers located in the raised floor panels. The air diffusers can be adjusted or relocated by the room users themselves, making possible the control of the thermal conditions in their surroundings, according to their individual preferences. Though the underfloor air distribution system presents a lot of advantages with regard to conventional overhead distribution systems, there is still a lack of objective information and standardized guidelines, and the necessity of accomplishment of more researches about the subject. The introduction of Computational Fluid Dynamics presented an alternative for the experimental tests related to the study of airflow in rooms. Thus, for the development of the present study a CFD tool was used, the code FLUENT. The purpose of the present work is to develop a strategy for the determination of the operation parameters of an underfloor air distribution system applied to office rooms. The strategy is based on the establishment of interrelations between the main parameters that define the airflow in rooms with the underfloor air distribution system: the input volume flux, the input air temperature and the pressure difference between underfloor plenum and the room. The use of this strategy enables the designer to identify several combinations of the operation parameters that result in one desired condition, allowing the choice of the most satisfactory option.

Inspired by the pectoral flippers of the humpback whale, the use of spanwise waviness in wings has been considered in the literature as a possible way of delaying the stall, and possibly also reducing the drag coefficient, allowing for improved aerodynamic characteristics. In order to provide a better understanding of this flow control mechanism, the present work investigates numerically the effect of the waviness on the flow around infinite wings with a NACA0012 profile. The study consists of direct numerical simulations employing the spectral/hp method, which is available through the nektar++ library. Considering the high computational cost of the simulations performed, several improvements were introduced to the method, making it more efficient and allowing higher Reynolds numbers to be analysed. These improvements to the method include a coordinate transformation technique to treat the waviness, changes to the parallelism strategy, and an adaptive polynomial order refinement procedure. Initially, simulations were performed for a very low value of the Reynolds number Re = 1, 000, allowing the three-dimensional flow structures to be observed in de- tail. In this case, the results show that the waviness leads to a decrease in the lift-to-drag ratio, accompanied by a strong reduction in the fluctuations of the lift force. The reduction in the lift-to-drag ratio is the combined effect of lower drag and lift forces, and is associated with a regime where the flow remains attached behind the peaks of the leading edge while there are distinct regions of flow separation behind the troughs. Then, simulations with Re = 10, 000 were considered. For high angles of attack, the results for this case are similar to the lower Re, with the waviness leading to separation behind the troughs and reducing both the lift and the drag. However, for a lower angle of attack the waviness leads to a large increase in the lift coefficient. This was observed to be related to the fact that flow around the straight wing is laminar in this case, with the waviness inducing transition to a turbulent state. Finally, the case Re = 50, 000 was considered, with the results showing a good agreement with experiments presented in the literature. / Inspirado na nadadeira peitoral da baleia jubarte, o uso de ondulações ao longo da envergadura de asas tem sido considerado na literatura como uma possível maneira de atrasar o estol, e possivelmente também reduzir o arrasto, levando a melhores características aerodinâmicas. Com o objetivo de obter um melhor entendimento desse mecanismo de controle do escoamento, o presente trabalho investiga numericamente o efeito de ondulações no escoamento ao redor de asas infinitas com o perfil NACA0012. O estudo consiste de simulações diretas do escoamento usando o método espectral/hp, que está disponível através da biblioteca nektar++. Considerando o alto custo computacional das simulações realizadas, diversas melhorias foram introduzidas no método, tornando-o mais eficiente e permitindo que números de Reynolds mais elevados fossem analisados. Essas melhorias ao método incluem uma técnica de mudança de coordenadas para tratar a ondulação, mudanças na estratégia de paralelismo e um procedimento de refinamento usando ordem polinomial variável. Inicialmente, simulações foram realizadas para um número de Reynolds muito baixo Re = 1, 000, o que permitiu observar as estruturas tridimensionais do escoamento em detalhe. Nesse caso, os resultados mostram que a ondulação leva a uma diminuição da razão sustentação-arrasto, combinada com uma forte redução das flutuações da força de sustentação. A redução da razão sustentação-arrasto é consequência de uma combinação de arrasto e sustentação mais baixos e está associada a um regime no qual o escoamento permanece colado atrás dos picos do bordo de ataque, enquanto que regiões distintas de escoamento separado estão presentes atrás dos vales. Em seguida, simulações com Re = 10, 000 foram consideradas. Para ângulos de ataque elevados, os resultados neste caso são similares àqueles com Re mais baixo, com a ondulação levando a separação atrás dos vales e provocando reduções na sustentação e no arrasto. No entanto, para um ângulo de ataque mais baixo a ondulação leva a um grande aumento na força de sustentação. Foi observado que isso está relacionado ao fato de que o escoamento ao redor da asa lisa é laminar neste caso, com a ondulação induzindo a transição para um estado turbulento. Finalmente, o caso Re = 50, 000 foi considerado, com os resultados apresentando uma boa concordância com experimentos apresentados na literatura.

Este trabalho tem como objetivo desenvolver ferramenta computacional para simulação e análise do fenômeno de penetração e cravação de estacas torpedos em solo marítimo. A abordagem será baseada no método Moving Particle Semi-Implicit (MPS). Por se tratar de um método de partícula, sem malha, o mesmo apresenta grande flexibilidade na modelagem de problemas de interação fluido-sólido com fragmentação ou junção de superfície livre e grandes deslocamentos ou deformações dos sólidos, fenômenos esses presentes no impacto e cravação da estaca no solo marítimo. Para isso, dois desafios foram elencados: a modelagem dos solos como fluidos não-newtonianos e a determinação da força de arrasto viscosa na superfície de sólidos. A modelagem do fluido não-newtoniano foi feita considerando os modelos de Power Law, Bingham e Herschel-Bulkley. O cálculo da força de arrasto viscosa foi avaliado determinando-se o gradiente da velocidade do fluido na direção normal à parede com base na regressão polinomial. Por simplicidade, foi considerada a hipótese de que a variação da velocidade na direção tangencial da parede é muito menor se comparada a variação da mesma na direção do vetor normal. O método implementado, assim como o escoamento de fluidos não-newtonianos, foi validado por meio de comparação entre o resultado obtido de simulações com geometrias pré-definidas e as respostas analíticas para tais casos. Como exemplo de aplicação da ferramenta computacional desenvolvida, um caso simplificado de cravação das estacas torpedos foi simulado avaliando-se o seu deslocamento dentro do solo e os esforços cisalhantes a ela submetidas. / This work aims to develop computational tools to simulate and analysis the torpedo anchor penetration in marine soil. The approach will be based on the Moving Particle Semi-Implicit (MPS) method. Because it is a meshless method, it is extremely flexible to model fluid-solid interaction with fragmentation or junction of free surface and large displacements or deformations of solids, phenomena presented at the torpedo anchor impact. Two challenges were listed: the modeling of soils as non-Newtonian fluids and the determination of the viscous drag on the solids surface. The modeling of non-Newtonian fluid was done based on the Power Law, Bingham and Herschel-Bulkley models. The calculation of the viscous drag was evaluated by determining the velocity gradient in the normal direction of the wall based on polynomial regression considering the fluid particles near the solid wall. In this work, for sake of simplicity, the hypothesis that the velocity variation in the tangential direction of the wall is much smaller compared to its variation in the normal direction is adopted. The proposed technique, as well as the flow of non-Newtonian fluids, were validated comparing the results obtained in flow simulations with predefined geometries with the expected analytical responses. As an example of the application of the computational tools developed, a simplified case of torpedo penetration was simulated by evaluating its displacement and the shear stresses submitted to it.

Este trabalho aborda o escoamento ao redor de cilindros flexíveis com grande razão de aspecto, representando os riser utilizados na indústria petrolífera. O escoamento foi dividido em seções bidimensionais ao longo do comprimento do riser. O método dos vórtices discretos foi utilizado para estimativa dos coeficientes hidrodinâmicos nas seções correspondentes e o acoplamento se dá através da dinâmica estrutural. Esta dinâmica é resolvida pelo método dos elementos finitos implementado no código Anflex (Mourelle et al. (2001)). Processamento paralelo é utilizado para acelerar o desempenho do método numérico. Um esquema master-slave (\"mestre-escravo\") utilizando MPI (Message Passing Interface1) é utilizado para que seja explorado o paralelismo da modelagem. As seções hidrodinâmicas são igualmente divididas ao longo dos nós de um cluster de computadores utilizado nos cálculos. Cada nó do cluster (núcleo de processamento) resolve o escoamento nas seções hidrodinâmicas necessárias. As forças hidrodinâmicas atuando nas seções correspondentes são enviadas ao processo mestre que também é responsável pela resolução da dinâmica estrutural. Uma das contribuições do presente trabalho é a possibilidade de análise de risers em regime pós-crítico, através da imposição do ponto de separação da camada-limite baseado em resultados experimentais, e da modelagem de casos com risers em tandem. O Método dos Vórtices Discretos (MVD) está detalhado de forma a facilitar a implementação computacional, levando em consideração a possibilidade de estudo de interferência entre esteiras de múltiplos corpos. Como primeira aproximação, foram simulados, casos de cilindros rígidos fixos e em base elástica para os quais foram examinadas as amplitudes máximas de oscilação e os coeficientes de arrasto e sustentação. Posteriormente, o MVD foi integrado ao Anflex dando origem ao AnflexCFD, com capacidade de processamento paralelo da parte correspondente ao CFD. Os resultados obtidos numericamente foram comparados a resultados experimentais realizados em laboratório. A metodologia de utilização do MVD para cálculo dos coeficientes hidrodinâmicos é baseada na comparação com resultados experimentais obtidos em laboratório para cilindros rígidos fixos e em base elástica para os quais se observa uma aderência satisfatória com relação aos resultados obtidos numericamente. O resultado do presente trabalho foi a criação de uma ferramenta alternativa no projeto de risers de grande razão de aspecto, como uma forma de avaliação do comportamento dinâmico da estrutura submetida a diferentes perfis de corrente e, consequentemente, a estimativa do tempo de sua vida útil. A característica puramente Lagrangiana do MVD possibilita a simulação de centenas de ciclos de oscilação da estrutura sendo que para os métodos Eulerianos tradicionais de CFD, como o método dos volumes finitos e o método dos elementos finitos, a simulação necessita de um tempo computacional inviável para projeto. A aderência do modelo adotado em relação aos resultados experimentais, aliada a eficiência do MVD, é um indicativo da vantagem da utilização de métodos Lagrangianos na modelagem do escoamento ao redor de cilindros flexíveis com grande razão de aspecto, em relação aos métodos Eulerianos tradicionais. A metodologia apresentada neste trabalho pode ser aplicada utilizando outros métodos de CFD, lembrando que isto pode implicar num aumento significativo do tempo computacional necessário para uma análise. / In this work the dynamic response of a high aspect ratio flexible cylinder due to vortex shedding is numerically investigated. The model is divided in two-dimensional sections along the riser length. The discrete vortex method (DVM) is employed for the assessment of the hydrodynamic forces acting on these two-dimensional sections. The hydrodynamic sections are solved independently, and the coupling among the sections is taken into account by the solution of the structure in the time domain by the finite element method implemented in Anflex code (Mourelle et al. (2001)). Parallel processing is employed to improve the performance of the method. A master-slave approach via MPI (Message Passing Interface) is used to exploit the parallelism of the present code. The riser sections are equally divided among the nodes of the cluster. Each node solves the hydrodynamic sections assigned to it. The forces acting on the sections are then passed to the master processor, which is responsible for the calculation of the displacement of the whole structure. One of the main contributions of the present work is the possibility of simulating the flow around flexible cylinders in the pos-critical regime and around bundle of risers.

Engine manufacturers are constantly seeking avenues to build cleaner and more ef cient engines to meet ever increasing stringent emission legislations. This requires a closer under- standing of the in-cylinder physical and chemical processes, which can be obtained either through experiments or simulations. The advent of computational hardware, methodologies and modelling approaches in recent times make computational uid dynamics (CFD) an important and cost-effective tool for gathering required insights on the in-cylinder ow, combustion and their interactions. Traditional Reynolds-Averaged Navier-Stokes (RANS) methods and emerging Large Eddy Simulation (LES) techniques are being used as a reli- able mathematical framework tools for the prediction of turbulent ow in such conditions. Nonetheless, the combustion submodels commonly used in combustion calculations are developed using insights and results obtained for atmospheric conditions. However, The combustion characteristics and its interaction with turbulence at Internal combustion (IC) engine conditions with, high pressure and temperatures can be quite different from those in conventional conditions and are yet to be investigated in detail. The objective here is to apply FlaRe (Flamelets revised for physical consistencies) model for IC engines conditions and assess its performance. This model was developed in earlier studies for continuous combustion systems. It is well accepted that the laminar burning velocity, SL, is an essential parameter to determine the fuel burn rate and consequently the power output and ef ciency of IC engines. Also, it is involved in almost all of the sophisticated turbulent combustion models for premixed and partially premixed charges. The burning velocities of these mixtures at temperatures of 850 ≤ T ≤ 950 decrease with pressure up to about 3 MPa as it is well known, but it starts to increase beyond this pressure. This contrasting behaviour observed for the rst time is explained and it is related to the role of pressure dependent reaction for iso-octane and involving OH and the in uence of this radical on the fuel consumption rate. The results iv seem to suggest that the overall order of the combustion reaction for iso-octane and gasoline mixture with air is larger than 2 at pressures higher than 3 MPa. The FlaRe combustion is used to simulate premixed combustion inside a spark-ignition engine. The predictive capabilities of the proposed approach and sensitivity of the model to various parameters have been studied. FlaRe approach includes a parameter βc representing the effects of ame curvature on the burning rate. Since the reactant temperature and pressure inside the cylinder are continually varying with time, the mutual in uence of ame curvature and thermo-chemical activities may be stronger in IC engines and thus this parameter is less likely to be constant. The sensitivity of engine simulation results to this parameter is investigated for a range of engine speed and load conditions. The results indicate some sensitivity and so a careful calibration of this parameter is required for URANS calculation which can be avoided using dynamic evaluations for LES. The predicted pressure variations show fair agreement with those obtained using the level-set approach. DNS data of a hydrogen air turbulent premixed ame in a rectangular constant volume vessel has been analysed to see the effect of higher pressure and temperature on the curvature parameter βc. Since the reactant temperature and pressure inside the cylinder are continually varying with time, the mutual in uence of ame curvature and thermo-chemical activities are expected to be stronger in IC engines and thus the parameter βc may not be constant. To shed more light on this, two time steps from the DNS data has been analysed using dynamic βc procedure. The results show that the effect of higher pressure and temperature need to be considered and taken into account while evaluating βc. When combustion takes place inside a closed vessel as in an IC engine the compression of the un-burnt gases by the propagating ame causes the pressure to rise. In the nal part of this thesis, the FlaRe combustion model is implemented in a commercial computational uid dynamics (CFD) code, STAR-CD, in the LES framework to study swirling combustion inside a closed vessel. Different values of βc has been tested and the need for dynamic evaluation is observed.

No description available.

Results from direct numerical simulations (DNS) of multiphase bubbly flows in vertical and horizontal channels were compared to averaged models of multiphase flows (two-fluid model etc.). The data from the direct numerical simulation were also used to calibrate and improve the averaged models. Steady state laminar flow in a vertical channel was analyzed first. Results from direct numerical simulations are compared with prediction of the steady-state two-fluid model of Antal, Lahey, and Flaherty (1991). The simulations are done assuming a two-dimensional system and the model coefficients are adjusted slightly to match the data for upflow. The model is then tested by comparisons with different values of flow rate and gravity, as well as down flow. Results agree reasonably in the middle of the channel. However, for upflow, model performs poorly near the no-slip wall. To better understand the flow with rising bubbles hugging the no-slip wall, detailed direct numerical simulations of the problem were performed in three dimensions. Deformability of the bubbles was found to play a significant role in the flow structure and averaged flow rate. Finally, the transient buoyancy driven motion of two-dimensional bubbles across a domain bounded by two horizontal walls is studied by. The bubbles are initially released next to the lower wall and as they rise, they disperse. Eventually all the bubbles collect at the top wall. The goal of the study is to examine how a simple one-dimensional model for the averaged void fraction captures the unsteady bubble motion. By using void fraction dependent velocities, where the exact dependency is obtained from simulations of homogeneous bubbly flows, the overall dispersion of the bubbles is predicted. Significant differences remain, however. Results suggest that bubble dispersion by the bubble induced liquid velocity must be included, and by using a simple model for the bubble dispersion improved agreement is found.

A fire growth calculation method has been developed that couples a computational fluid dynamics (CFD) model with bench scale cone calorimeter test data for predicting the rate of flame spread on compartment contents such as furniture. The commercial CFD code TASCflow has been applied to solve time averaged conservation equations using an algebraic multigrid solver with mass weighted skewed upstream differencing for advection. Closure models include k-epsilon for turbulence, eddy breakup for combustion following a single step irreversible reaction with Arrhenius rate constant, finite difference radiation transfer, and conjugate heat transfer. Radiation properties are determined from concentrations of soot, CO2 and H2O using the narrow band model of Grosshandler and exponential wide band curve fit model of Modak. The growth in pyrolyzing area is predicted by treating flame spread as a series of piloted ignitions based on coupled gas-fluid boundary conditions. The mass loss rate from a given surface element follows the bench scale test data for input to the combustion prediction. The fire growth model has been tested against foam-fabric mattresses and chairs burned in the furniture calorimeter. In general, agreement between model and experiment for peak heat release rate (HRR), time to peak HRR, and total energy lost is within pm 20%. Used as a proxy for the flame spread velocity, the slope of the HRR curve predicted by model agreed with experiment within pm 20% for all but one case.

Este trabalho tem como objetivo desenvolver ferramenta computacional para simulação e análise do fenômeno de penetração e cravação de estacas torpedos em solo marítimo. A abordagem será baseada no método Moving Particle Semi-Implicit (MPS). Por se tratar de um método de partícula, sem malha, o mesmo apresenta grande flexibilidade na modelagem de problemas de interação fluido-sólido com fragmentação ou junção de superfície livre e grandes deslocamentos ou deformações dos sólidos, fenômenos esses presentes no impacto e cravação da estaca no solo marítimo. Para isso, dois desafios foram elencados: a modelagem dos solos como fluidos não-newtonianos e a determinação da força de arrasto viscosa na superfície de sólidos. A modelagem do fluido não-newtoniano foi feita considerando os modelos de Power Law, Bingham e Herschel-Bulkley. O cálculo da força de arrasto viscosa foi avaliado determinando-se o gradiente da velocidade do fluido na direção normal à parede com base na regressão polinomial. Por simplicidade, foi considerada a hipótese de que a variação da velocidade na direção tangencial da parede é muito menor se comparada a variação da mesma na direção do vetor normal. O método implementado, assim como o escoamento de fluidos não-newtonianos, foi validado por meio de comparação entre o resultado obtido de simulações com geometrias pré-definidas e as respostas analíticas para tais casos. Como exemplo de aplicação da ferramenta computacional desenvolvida, um caso simplificado de cravação das estacas torpedos foi simulado avaliando-se o seu deslocamento dentro do solo e os esforços cisalhantes a ela submetidas. / This work aims to develop computational tools to simulate and analysis the torpedo anchor penetration in marine soil. The approach will be based on the Moving Particle Semi-Implicit (MPS) method. Because it is a meshless method, it is extremely flexible to model fluid-solid interaction with fragmentation or junction of free surface and large displacements or deformations of solids, phenomena presented at the torpedo anchor impact. Two challenges were listed: the modeling of soils as non-Newtonian fluids and the determination of the viscous drag on the solids surface. The modeling of non-Newtonian fluid was done based on the Power Law, Bingham and Herschel-Bulkley models. The calculation of the viscous drag was evaluated by determining the velocity gradient in the normal direction of the wall based on polynomial regression considering the fluid particles near the solid wall. In this work, for sake of simplicity, the hypothesis that the velocity variation in the tangential direction of the wall is much smaller compared to its variation in the normal direction is adopted. The proposed technique, as well as the flow of non-Newtonian fluids, were validated comparing the results obtained in flow simulations with predefined geometries with the expected analytical responses. As an example of the application of the computational tools developed, a simplified case of torpedo penetration was simulated by evaluating its displacement and the shear stresses submitted to it.

In this thesis, a numerical method is developed for simulating non-isothermal multiphase flows, which are important in many technical applications such as crystal growth and welding. The method is based on the arbitrary Lagrangian Eulerian method of Li (2013). The interface is represented explicitly by mesh lines, and is tracked by an adaptive moving unstructured mesh. The $P2-P1d$ finite element method (FEM) is used for discretisation and the incompressible Navier-Stokes equations are solved by the uzawa method. Firstly, a thorough study is presented on the method's capability in numerically representing the force balance condition on the interface. An inaccurate representation of this condition induces the non-physical spurious currents, which degrade the simulation accuracy especially when the viscous damping is weak (small Ohnesorge number, $Oh$). For the example of a circular/spherical droplet, the interfacial tension and the associated pressure jump are exactly balanced numerically and thus the static Laplace solution exists in our method. The stability of this solution is examined numerically. The amplitude of the dimensionless spurious currents is found to be around $10^{−15}$ for $Oh \geq 10^{−3} $. Another benchmark test is the axisymmetric oscillation of a freesurface droplet/bubble. The simulation results are in good agreement with the analytical solution for $Oh = 10^{−3}$. This is by far the first successful simulation of droplet/bubble oscillation with such weak viscous damping and it demonstrates the ability of our method in simulating flows with strong capillary forces. Secondly, a numerical treatment of interface topology changes is incorporated into our method for studying problems with interface breakup. Thanks to the adaptive mesh generator, the thin region between the interface boundary and another boundary consists of one layer of elements. The interface topology change is performed once the minimum distance between the two boundaries falls below a pre-set scale $l_{breakup}$ . The numerical implementation is verified through two different examples: dripping faucet and droplet coalescence. Remarkably good agreement has been obtained with the experimental results. The simulation of the low Oh dripping problem shows both the accuracy and robustness of our method. The simulation of droplet coalescence demonstrates the great advantage of our method in solving problems with a large disparity in length scales. Finally, an FEM solver for temperature is developed and the non-isothermal effects are included in our method for the purpose of simulating non-isothermal multiphase flows. The modified method is validated to be accurate through three benchmark examples: natural convection in a cavity, thermocapillary convection of two layers, and droplet migration subject to a temperature gradient. Our method is then applied to investigate the liquid bridge breakup with thermocapillary effect. The non-isothermal liquid bridge breakup in the viscous and inertial regimes are studied. It has been found that the inertial regime breakup exhibits different pinchoff shapes as the Capillary number increases, and that the viscous regime breakup is accelerated by the thermocapillary motion.