L’urbanisation croissante fait émerger des enjeux sociétaux et environnementaux relatifs à la pollution atmosphérique et au microclimat urbain. La compréhension des phénomènes physiques de transport de quantité de mouvement, de chaleur et de masse entre la canopée urbaine et la couche limite atmosphérique est primordiale pour évaluer et anticiper les impacts négatifs de l’urbanisation. Les processus turbulents spécifiques à la couche limite urbaine sont étudiés par une approche de simulation des grandes échelles, dans une configuration urbaine représentée par un arrangement de cubes en quinconce. Le modèle de sous-maille de type Smagorinsky dynamique est implémenté pour mieux prendre en compte l’hétérogénéité de l’écoulement et les retours d’énergie des petites vers les grandes structures. Le nombre de Reynolds basé sur la hauteur du domaine et la vitesse de l’écoulement libre est de 50000. L’écoulement est résolu dans les sous-couches visqueuses et le maillage est raffiné dans la canopée. Le domaine est composé de 28 millions de cellules. Les résultats sont comparés à la littérature et aux données récentes obtenues dans la soufflerie du LHEEA. Chaque contribution au bilan d’énergie cinétique turbulente est calculée directement en tout point. Cette information, rare dans la littérature, permet d’étudier les processus dans la sous couche rugueuse. Grâce à ces résultats 3D, l’organisation complexe de l’écoulement moyen (recirculations, vorticité, points singuliers) est analysée en relation avec la production de turbulence. Enfin, une simulation où les obstacles sont remplacés par une force de traînée équivalente est réalisée à des fins d’évaluation de cette approche. / The rapid development of urbanization raises social and environmental challenges related to air pollution and urban climate. Understanding the physical processes of momentum, heat, and mass exchanges between the urban canopy and the atmospheric boundary-layer is a key to assess,predict and prevent negative impacts of urbanization. The turbulent processes occurring in the urban boundary-layer are investigated using computational fluid dynamics (CFD). The unsteady flow over an urban-like canopy modelled by a staggered arrangement of cubes is simulated using large eddy simulation (LES). Considering the highspatial and temporal in homogeneity of the flow, a dynamic Smagorinsky subgrid-scale model is implemented in the code to allow energyback scatter from small to large scales. The Reynolds number based on the domain height and free-stream velocity is 50000. The near-wall viscous sub-layers are resolved and the grid is refined in the canopy resulting in about 28 million grid cells. LES results are assessed by comparison with literature and data recently acquired in the wind tunnel of the LHEEA. The turbulent kinetic energy budget in which all contributions are independently computed is investigated. These rarely available data are used to analyse the turbulent processes in the urban canopy. By taking advantage of the three-dimensionality of the simulated flow, the complex 3D time-averaged organization of the flow (recirculation, vorticesor singular points) is analyzed in relation with production of turbulence. Finally a drag approach where obstacles are replaced by an equivalent drag force is implemented in the same domain and results are compared to obstacle-resolved data.

[pt] A correta operação de equipamentos na indústria de Óleo e Gás é fundamental para a reduzir perdas ambientais, humanas e financeiras. Neste cenário, foram estudados selos secos a gás (em inglês,DGS) de compressores cetrífugos, por serem identificados como os mais críticos devido à extensão dos danos potenciais causados em caso de falha. Neste estudo, foram desenvolvidos 31 modelos regressivos disponíveis no Scikit-Learn através de técnicas de aprendizado de máquina (em inglês, ML). Estes foram treinados com um conjunto de dados escassos, criado a partir de uma técnica de planejamento de experimentos, para substituir simulações numéricas na previsão de confiabilidade operacional de DGSs. Primeiramente, foi validado um modelo baseado na simulação da Dinâmica dos Fluidos Computacionais (em inglês, CFD) para representar o escoamento do gás entre as faces de selagem, a fim de possibilitar o cálculo da confiabilidade operacional do equipamento. Neste, foi utilizado o software de CFD de código aberto OpenFOAM em conjunto com o banco de dados de substâncias do software REFPROP, a fim de possibilitar ao usuário definir a mistura gasosa e as condições operacionais avaliadas. Em seguida, foram realizados dois estudos de caso seguindo um fluxograma genérico de projeto proposto. O primeiro consistiu na determinação de um modelo regressivo para estimar a confiabilidade de um DGS cuja composição gasosa (composta por metano, etano e octano) é fixa porém suas condições operacionais podem ser alteradas. Já o segundo consistiu na determinação de um modelo regressivo mais robusto, onde tanto a composição gasosa como as condições operacionais podem ser alteradas. Por fim, foi avaliada a viabilidade de implementação de ambos os modelos em condições reais de operação, baseado na norma infinita obtida para a predição do conjunto de teste. As performances atingidar foram de 1.872 graus Celsius e 6.951 grau Celsius para o primeiro e segundo estudos de caso, respectivamente. / [en] The correct equipment operation in the Oil and Gas industry is essential to reduce environmental, human, and financial losses. In this scenario, dry gas seals (DGS) of centrifugal compressors were studied, as they are identified as the most critical device due to the extent of the potential damage caused by their failure. In this study, 31 regression models available at Scikit-Learn were developed using machine learning (ML) techniques. They were trained with a scarce dataset, created based on a design of experiment technique, to replace numerical simulations in predicting the operational reliability of DGSs. First, a model based on Computational Fluid Dynamics (CFD) simulation was validated to represent the gas flowing between the sealing faces, to enable the calculation of the equipment’s operational reliability. Thus, the open-source CFD software OpenFOAM was used together with the substance database of the software REFPROP, to allow the user to define the gas mixture and the evaluated operational conditions. Then, two case studies were carried out following a proposed generic workflow. The first comprised determining a regression model to estimate the reliability of a DGS whose mixture composition (composed of methane, ethane, and octane) is fixed but its operating conditions can vary. The second consisted of determining a more robust regressive model, where both the mixture composition and the operational conditions can vary. Finally, the feasibility of implementing both models under realistic operating conditions was evaluated, based on the infinity norm obtained for the prediction of the test set. The performances achieved were 1.872 degrees Celsius and 6.951 degrees Celsius for the first and second case studies, respectively.

In recent years, the Helicon Plasma Thruster (HPT) has become one of the most promising technologies of in-space electric propulsion. T4i Technology for Propulsion and Innovation S.P.A. is one of the leading companies working with this new type of systems, and their thruster, REGULUS, is the first HPT ever to be operated in orbit. To better assess the performance of the motor, the company has developed, in conjunction with the University of Padova and the University of Bologna, a numerical tool called 3DVIRTUS (3Dimensional adVanced fluId dRifT diffUsion plaSma solver), which simulates the plasma dynamics in the production stage of the thruster. The model describes the species present in the plasma (electrons, ions, excited and neutrals) by means of a fluid approach, as the plasma density in this part of the motor is in the order of 1017-1018 m−3. Particularly, the tool considers the Drift-Diffusion (DD) approximation instead of the full set of fluid momentum equations. Unfortunately, for typical discharges applied to HPTs, this assumption is accurate only for the electrons species, but not for the heavy species in the plasma, i.e. ions, excited and neutrals. The thesis project presented in this report, executed in collaboration with T4i S.P.A, proposes an updated numerical tool which solves the fully coupled continuity and momentum equations for the neutrals species in the plasma. The new solver is implemented with OpenFOAM®, a finite volume library written in C++, and the Semi-Implicit Method for Pressure Linked Equations (SIMPLE) is utilised to resolve the pressure-velocity coupling in the continuity and momentum equations. Four different test cases are considered: a one-dimensional typical discharge, a cylindrical discharge, the Schwabedissen GECICP reactor experiment and the Piglet helicon reactor of Lafleur. The obtained results have been compared against the original drift-diffusion solver, and when available, with experimental data. The new tool produced similar results to the older one, even though the neutrals density computed with the former generally presented stronger gradients. Additionally, in the case of the GECICP and Piglet reactors, the agreement in terms of electrons density computed with the new solver was satisfactory compared to the empirical data. Nevertheless, all the analysis performed during the thesis project revealed that the keys to obtain physically realistic results are the boundary conditions for the neutrals’ pressure and velocity, which greatly affects the outcome of the simulations. Overall, the new solver has shown to provide accurate results with reasonable computational time. / Under de senaste åren har Helicon Plasma Thruster (HPT) blivit en av de mest lovande teknikerna för elektrisk framdrift i rymden. T4i Technology for Propulsion and Innovation S.P.A. är ett av de ledande företagen som arbetar med denna nya typ av system, och deras motor, REGULUS, är den första HPT som har demonstrerats fungera i omloppsbana. För att bättre kunna bedöma motorns prestanda har företaget tillsammans med universitetet i Padova och universitetet i Bologna utvecklat ett numeriskt verktyg som kallas 3DVIRTUS (3Dimensional adVanced fluId dRifT diffUsion plaSma solver), som simulerar plasmadynamiken i thrusterns produktionsstadium. Modellen beskriver de typer av partikler som finns i plasma (elektroner, joner, exciterade och neutrala) med hjälp av en vätskeapproximation, eftersom plasmatätheten i denna del av motorn är i storleksordningen 10171018 m−3. Särskilt överväger verktyget approximationen Drift-Diffusion (DD) istället för hela uppsättningen vätska ekvationer. Dessvärre, för typiska urladdningar som appliceras på HPT, är detta antagande korrekt endast för elektroner, men inte för de tunga partiklarna i plasma, dvs joner, exciterade och neutrala partiklar. Avhandlingsprojektet som presenteras i denna rapport, utfört i samarbete med T4i S.P.A, föreslår ett uppdaterat numeriskt verktyg som löser de fullständigt kopplade kontinuitets och rörelseekvationerna för neutrala partiklar i plasma. Den nya lösaren implementeras med OpenFOAM®, ett begränsat volymbibliotek skrivet i C++, och Semi-Implicit Method for Pressure Linked Equations (SIMPLE) används för att lösa tryck hastighetskopplingen i kontinuitets och rörelseekvationer. Fyra olika testfall övervägs: en endimensionell typisk urladdning, en cylindrisk urladdning, Schwabedissen GECICP reaktorförsöket och Piglet helicon reaktorn i Lafleur. De erhållna resultaten har jämförts med det ursprungliga driftdiffusions antagandet, och när möjligt, med experimentella data. Det nya verktyget gav liknande resultat som det äldre, även om densiteten av neutrala partiklar beräknad med den tidigare generellt visade starkare gradienter. Dessutom, när det gäller GECICP och Piglet reaktorerna, var överenskommelsen i termer av elektrontäthet beräknad med den nya lösaren tillfredsställande jämfört med empiriska data. Ändå avslöjade all analys som gjordes under avhandlingsprojektet att nycklarna för att få fysiskt realistiska resultat är randvillkoren för de neutrala partiklarnas tryck och hastighet, vilket i hög grad påverkar resultatet av simuleringarna. Sammantaget har den nya lösaren visat sig ge noggranna resultat med rimlig beräkningstid.

In the context of an aviation industry whose top priority is to face the sustainability challenge, the growing civil UAV branch is not an exception. Hydrogen-powered UAVs equipped with PEM (Polymer Electrolyte Membrane) fuel cells are more and more frequently identified as the most convincing and promising technology, particularly for long-endurance mission requirements. However, the onboard carriage of a hydrogen fuel cell leads to unexplored internal flow characteristics, including the introduction of water vapour. The purpose of this master thesis is to develop a valid CFD model and methodology for the internal flow simulation of hydrogen-powered UAVs. Given the strict environmental operational requirements of PEM fuel cells, the intended application of the model is to effectively assess the evolution of the internal bay flow temperature and humidity fields. An explicit-time fourth-order Runge-Kutta projection method is tested successfully on a sample 2D case setup. The case geometry and flow conditions are inspired by the Green Raven UAV project conceived by the Department of Aeronautical and Vehicle Engineering at KTH. / I samband med en flygindustri vars högsta prioritet är att bemöta hållbarhetsutma- ningen är den växande civila UAV-sektorn inget undantag. Vätgasdrivna UAV:er utrustade med PEM (Polymer Electrolyte Membrane) bränsleceller betecknas allt oftare som den mest övertygande och lovande teknologin, särskilt för att de ska kunna utföra långvariga uppdrag. Den ombordgående transporten av en vätebränslecell leder emellertid till outforskade inre flödesfenomen, inklusive alstrad vattenånga. Syftet med detta examensarbete är att utveckla en lämplig CFD-modell och metodik för intern flödesimulering av vätgasdrivna UAV. Med tanke på de strikta miljökraven för PEM-bränsleceller är modellens avsedda tillämpning att eektivt utvärdera utvecklingen av de inre flödestemperaturerna och luftfuktighetsfälten. En tidsexplicit Runge-Kutta-projektionsmetod av fjärde ordningen testas framgångsrikt på ett 2D-exempel. Fallets geometri och flödesförhållanden är inspirerade av Green Raven UAV-projektet som utförts på Farkost och Flyg avdelningen på KTH.

Solid oxide fuel cells represent a potentially important application for ceramic materials. There are, however, some significant issues which can affect the reliability and durability of the cell. Mechanical failure owing to stress is one of the critical factors which can affect the stability and working life of the fuel cell stacks. These stresses generate in Solid Oxide Fuel Cells (SOFCs) owing to mechanical forces and change in temperature during fabrication, assembly and operating conditions. There can be chances of cell delamination and micro-cracks in cell electrodes if these stresses are too high. The elastic properties and thermal expansion coefficient play a vital role to improve cell stability and performance. These properties depend on the types of materials and geometries of the composites. In this research, a numerical framework to predict the effective elastic properties and the effective thermal expansion coefficient for porous Yttria-Stabilized Zirconia (YSZ) electrode microstructures in a Solid Oxide Fuel Cell is presented. The electrodes of Solid Oxide Fuel Cells are discretized as porous microstructures that are formed by randomly distributed and overlapping spheres with particle size distributions that match those of actual ceramic powder. Three-dimensional (3D) microstructures of YSZ-pore are formed with a porosity ranging from 25% to 40%. The technique involves the construction of the YSZ-pores microstructures based on measurable starting parameters and subsequent numerical prediction of effective elastic properties and effective thermal expansion coefficient. Three domain sizes are considered for the generation of YSZ-pore microstructures. The method of prediction of effective Young’s modulus (Eeff), effective Poisson’s ratio , effective bulk modulus effective shear modulus , and effective thermal expansion coefficients for various porosities (P) of Yttria-Stabilized Zirconia (YSZ) electrode material in Solid Oxide Fuel Cells is based on the Finite Volume analysis which in turn is based on the solution of the linear elastic stress analysis problem. The predicted results are compared with some theoretical correlations of two-phase composites for effective elastic properties and effective thermal expansion coefficient. It has been found that predicted results are falling inside of the upper and lower bounds. / Thesis (Master, Mechanical and Materials Engineering) -- Queen's University, 2013-10-01 17:01:05.068

Super Duplex Stainless Steels have superior corrosion resistance properties and strength compared to conventional steels. However, these properties are influenced by the different phases that precipitate during the heat treatment process. The conventional way of studying the time and temperature effects on the properties and micro-structure of SDSS is to prepare many samples at different temperatures and holding times. The welding research group at Production Technology Center, Trollhättan, Sweden, has recently developed a unique heat treatment method to produce a wide range of temperature by using a stationary TIG arc heat source. It results in a graded micro-structure in a single sample at a specific time period. The accuracy of the results ob-ained from this process is highly related to the accuracy of the temperature field model next to weld pool. In this work, a model was developed by using OpenFOAM CDF code, to predict the temperature field of the super duplex stainless steel samples that have been subjected to this novel TIG arc heat treatment process. The developed model was able to capture the trend in the overall temperature field in the heat affected zone. However, there was some mismatch between the modelled and experimental temperature profiles in certain locations in the heat affected zone. Further improvements have to be done to the developed model in order to take the phase transformation effect into account. A preliminary investigation has been carried out on how to implement this in the current model and reported in the thesis.

In the rapidly growing field of CFD-calculations (Computational Fluid Dynamics), companies and organizations are bringing forth new tools, tools that display an image of a given fire scenario. These tools are developed because they provide time efficiency as well as a sustainable economic approach. Another useful tool is analytical solutions, these analytical solutions serve the same purpose as CFD-modeling, providing results of a given scenario. The purpose of this thesis was to simulate a fire plume with two different CFDprograms and compare the gas temperature from each simulation with a full-scale test. Also, analytical solutions were used to perform the same comparisons. Four different calculation models were utilized to obtain results. The CFD-programs were FDS (Fire Dynamics Simulator) and FireFOAM. The analytical solutions were performed using McCaffrey´s plume equation and Eurocode solutions for localized fire temperatures. FDS is a very well documented program, due to this, problems that arose were easily fixed. The structure of FDS enables the user to maneuver the program easily. SmokeView was used to visualize the simulation. FireFOAM is written in C++ and is operated through the command prompt. The structure of the program was time-consuming to understand mainly because of two reasons, primarily because the authors lack of knowledge in coding in C++, and second because of the LINUX environment. Moreover, the process of working in FireFOAM was mostly through trial and error. On some occasions, issues arose that could be solved by communication with other CFD users at CFD-Online. When major problems occurred, regarding the code or other CFD issues, Johan Anderson at RISE Research Institutes of Sweden guided us through most of these problems and enabled us to move forward with the work. ParaView was used to visualize the simulation, and Excel was used to evaluate the temperature data from the FDS- and FireFOAM simulations. For the calculations in FDS and FireFOAM, a sensitivity analysis was performed to see which grid size presented best results in each program. A grid size of 5 cm, 10 cm, and 20 cm were applied in FDS, and in FireFOAM the grid dimensions were set to 5 cm and 10 cm. The results showed that 5 cm was the most appropriate grid size for both programs. It would have been more favorably to simulate with several different grid sizes, to further strengthen the grid analysis. Though, due to the time frame of the thesis, further simulations were not performed. Calculations were repeated for the same scenario only with a lower HRR (Heat release rate). An extensive sensitivity analysis was conducted for FDS in the form of two different simulations. One simulation where HRR was the same as the full-scale test but with twice the area of the burner. In the second simulation, the same area was used on the burner as the fullscale test, but with half the HRR. Results from the analytical solutions were easy to achieve; however, the model has some limitations regarding calculations within the flame region. The estimated gas temperature, using FDS, aligns well with the full-scale test. The temperatures analyzed from FireFOAM deviated in general through the flame region and reached unreasonable high temperatures close to the ceiling. Since the analytical solutions were based on different conditions compared to those applied in the full-scale test, it was expected that the results should deviate. However, McCaffrey plume equations can still be used to give an approximate picture of scenarios similar to that of the full-scale test, and the same applies to Eurocode solutions for localized fire temperatures. Analysis of the results shows that FDS can be used to simulate similar scenarios. FireFOAM simulates a gas temperature that is overestimated within the flame region. One of the reasons for this was due to the grid size since the sensitivity analysis III showed that a refined grid size resulted in more correct temperature value, the reason for not simulating with a more refined grid size was due to the restricted time frame of this thesis. FireFOAM is, at present, recommended for researchers who wish to use the code for specific purposes. Therefore, given the same premises, FireFOAM is not recommended for the standard fire safety analysis.

In this study, Computational Fluid Dynamics (CFD) simulations have been carried out in order to investigate and improve the performance of the Standard Cirrus glider, using different Navier-Stokes methods and solving the equations for the steady flow. The work has been divided in two parts: First, a study is performed to test the quality of the transition model (Gamma-ReTheta). The two dimensional results of the glider´s airfoil are compared against the results from panel’s methods and the open-source CFD codes: SU2 and OpenFoam. In addition, three dimensional glider´s models are simulated using the transition model with the purpose of creating a validated reference model of the glider’s performance in steady level flight. The simulations are carried out in two dimensions for the outer wing airfoil for a 1.5 e+06 Reynolds number and in three dimensions for the Wing & Fuselage model and Tail & Fuselage model under a range of velocities. Both simulations are validated against experimental data. In the second part of the study, the validated model is used to developed possible improvements in the glider´s external geometry that could produce possible benefits in the performance and handling qualities of the glider.

The objective for this master thesis project was to perform simulations for high and low Reynolds number for a porousmedia modelled as quadratic packed cylinders. The simulations were to be performed by using the open source codeOpenFOAM and the turbulence should be modelled by the LES turbulence model in order to resolve details about theturbulence. In Hellström et al. (2009) simulations were performed for a similar setup but for the k-Omega SST turbulencemodel. In this project simulations were performed not only for LES but also with the k-Omega SST model and for the laminar description in order to validate the LES problem setup. For the simulations Reynolds number was calculatedbased on the porosity and the cylinder diameter and was denoted Re’. The simulations were performed for a set of Re’and for each Re’ the permeability was calculated based on Darcy’s law. The calculations of the permeability showed,in line with the results from Hellström, that at Re’ around 20 there is a drop in the permeability both for the LESand SST simulations. From the permeability simulations it was also seen that for low Re’ flows the LES and laminardescriptions agreed with each other, but that the SST simulations yielded lower values of the permeability. Accordingto Hellström the permeability drop was due to onset of inertia effects. When looking at the resulting flow field plots itgave the idea that the amount of turbulence could also have influence on the resulting permeability.

Uma das mais recentes abordagens propostas na literatura para tratar o problema do alto número de Weissenberg (We) é a Formulação Log-Conformação (FLC). Nesta formulação, a equação constitutiva viscoelástica utilizada é reescrita em termos de uma variável Ψ, que é o logaritmo do tensor conformação. Apesar do potencial de aplicação da FLC, pouca atenção tem sido dirigida para análise da acurácia da solução obtida para o campo de tensões quando se utiliza esta formulação. Assim, o objetivo do presente trabalho foi estudar a acurácia da solução obtida pela FLC na análise de escoamentos de fluidos viscoelásticos usando duas geometrias padrão de estudo: placas paralelas e cavidade quadrada com tampa móvel. Primeiramente, a FLC foi implementada no pacote de CFD OpenFOAM. Em seguida foram verificados os limites do número de Weissenberg na formulação numérica padrão (Welim,P), onde para a geometria de placas paralelas foi encontrado Welim,P = 0,3 e para a geometria da cavidade quadrada com tampa móvel foi encontrado Welim,P = 0,8. Depois o código implementado foi aplicado em ambas as geometrias, comparando-se a solução obtida pela FLC com aquela da formulação padrão na faixa de We < Welim,P. Os resultados obtidos na geometria de placas paralelas apresentaram boa concordância com a solução padrão e solução analítica. Para a geometria da cavidade quadrada com tampa móvel, que não possui solução analítica, boa concordância dos resultados também foi observada em comparação com a solução padrão. Posteriormente foram comparados os resultados obtidos pela FLC na faixa de We > Welim,P. Na geometria de placas paralelas, além da boa concordância com a solução analítica, obteve-se convergência em todos os casos estudados neste trabalho, com o maior número de Weissenberg utilizado sendo igual a 8 Os resultados da geometria da cavidade quadrada com tampa móvel também apresentaram boa concordância em comparação com dados da literatura, porém a convergência foi obtida até para We = 2. Com respeito à comparação das formulações numéricas com a solução analítica, feita apenas na geometria de placas paralelas, foi observado um erro máximo de 7,57% na solução padrão e de 12,33% na FLC. Em relação à análise da qualidade das tensões usando os resíduos da equação constitutiva viscoelástica como critério de acurácia, foi verificado nas duas geometrias que os valores de tensão obtidos usando a FLC são menos acurados que aqueles obtidos pela formulação explícita no tensor das tensões nos casos em que esta última converge. Também foi observado que a acurácia diminui com o aumento do We. Esse efeito pôde ser melhor notado na geometria de placas paralelas. Uma razão para a perda de acurácia da tensão provavelmente ocorre devido à natureza matemática da transformação algébrica inversa de Ψxx para τxx. O novo solver implementado neste trabalho apresentou convergência e soluções corretas para as duas geometrias, logo foi implementado corretamente. Ele também potencializa o solver de partida viscoelastiFluidFoam ao estender simulações para uma faixa maior do número de Weissenberg. / A recent approach proposed in the literature to deal with the High Weissenberg Number Problem is the Log-Conformation formulation (LCF). In this formulation the viscoelastic constitutive equation is rewritten in terms of the logarithm of the conformation tensor Ψ. Despite the great potential application of the LCF, little attention has been given in the literature to the accuracy of the obtained stress fields. The purpose of this work was to study the solution obtained by LCF in the analysis of viscoelastic flows using two benchmark geometries: parallel plates and lid driven cavity. Firstly, the LCF was implemented in the OpenFOAM CFD package. Then, the limits of Weissenberg number for the standard numerical formulation (Welim,P) were verified, obtaining Welim,P = 0.3 for the parallel plates and Welim,P = 0.8 for the lid driven cavity. When comparing the solution obtained by the LCF with that of the standard formulation in a range of We < Welim,P, the results obtained for the parallel plates geometry showed good agreement with the standard solution and the analytical solution. For the lid driven cavity geometry, for which there is not analytical solution, good agreement with the standard solution was also observed. For We > Welim,P in the parallel plates geometry, in addition to the good agreement with the analytical solution, it was possible to obtain convergence in all the cases studied in this work, with the largest number of Weissenberg used being equal to 8 The results of the lid driven cavity geometry also presented good agreement in comparison with literature data, but convergence was obtained up to We = 2. With respect to the comparison of the numerical formulations with the analytical solution for the parallel plates geometry, a maximum error of 7.57% was observed in the standard solution and of 12.33% in the LCF. When using the residues of the viscoelastic constitutive equation as a criterion of accuracy, it was verified that for the two geometries the stress values obtained using the LCF were less accurate than those obtained by the explicit formulation in the stress tensor. It has also been observed that accuracy decreases with increasing of We. One reason for the loss of stress accuracy probably occurs because of the mathematical nature of the inverse algebraic transformation from Ψxx to τxx. The new solver implemented in this work presented convergence and correct solutions for the two geometries, so it was implemented correctly. It also potentiates the viscoelastiFluidFoam starting solver by extending simulations to a larger range of Weissenberg number.