Labyrinth seals are often utilized in locations where contact seals cannot be utilized due to the large displacements of the rotating shaft. The performance evaluation of a labyrinth seal is very important to make sure that optimum performance of turbomachinery is attained. Performance parameters such as carryover coefficient, discharge coefficient were evaluated for a see through triangular tooth on stator labyrinth seal. This computational study investigates how flow conditions and seal parameter variations for see through tooth on stator triangular cavity labyrinth seals affect the value of the carryover coefficient and discharge coefficient. A Finite volume CFD commercial code was used to accomplish the above study. The influence of Reynolds number, rotational speed, seal radial clearance, pitch, tooth angle, tooth width are considered using the finite volume method of computational fluid dynamics. It was found that Reynolds number, high shaft speed and clearance have a significant effect on the carryover coefficient and the discharge coefficient. Clearance is the major influential parameter to be considered among all seal geometric parameters to optimize an ideal seal.

O presente estudo teve por objetivo avaliar as características anatômicas das bifurcações radiculares, e compará-las às dimensões das pontas ativas das curetas de Gracey e Pádua-Lima. Foram utilizados 198 dentes, distribuídos entre primeiros e segundos molares superiores e inferiores, provenientes do Banco de Dentes da Universidade de Taubaté. Depois de codificados, os dentes foram fotografados por meio de uma câmera acoplada a um aparelho estereoscópio. As imagens foram digitalizadas por meio de um programa de captação de imagens (Pixel View) e avaliadas por meio de um programa de leitura (Image Tool). Nos dentes foram avaliados: a altura dos troncos radiculares, o ângulo de divergência e a distância interradiculares. Nos instrumentais foram avaliados o comprimento, a largura e a espessura das lâminas. Após análise estatística dos dados, os resultados obtidos mostraram que as bifurcações vestibulares de 2MS foram as que menos permitiram o acesso dos instrumentais avaliados, sendo as curetas Gracey acessíveis à maioria das bifurcações. As bifurcações mesiais e distais de molares superiores, por apresentarem maior distância interradicular e ângulos mais divergentes, são as que mais permitem acesso aos instrumentais avaliados. Baseados nestes resultados podemos concluir que as características anatômicas radiculares podem ser um fator de restrição à instrumentação periodontal. / The present study aimed to evaluate the anatomic characteristics of the root bifurcations and compare them with the active tips of the curettes of Gracey and Pádua-Lima. One hundred ninety eight teeth were used, distributed among first and second upper and lower molars, from the Teeth Bank of the University of Taubaté. After received a numerical code, the teeth were photographed by a camera attached to a stereomicroscope. The images were scanned through a capture image program (Pixel View) and evaluated through a software program (Image Tool for Windows 2.0). The length of the root trunk, the divergence angle between the roots and the inter-root dimensions in the bifurcation region were evaluated. In the instruments, characteristics as width, thickness and length of the curettes blade were analyzed. After the statistics analysis, the results obtained showed that the 2MS buccal bifurcations are those least allow access by the instruments evaluated, and the Gracey curettes had access of the majority of the bifurcations. The mesiais and distal bifurcations of upper molars, to have greater inter-root dimensions distance and divergent angles, are those that allow access to more instrumental evaluated. Based in those results, we can conclude that the roots anatomic characteristics can be a factor to restriction the periodontal instrumentation.

The labyrinth seal is a non-contact annular type sealing device used to reduce the internal leakage of the working fluid which is caused by the pressure difference between each stage in a turbomachine. Reducing the leakage mass flow rate of the working fluid through the labyrinth seal is desirable because it improves the efficiency of the turbomachine. The carry-over coefficient, based on the divergence angle of the jet, changed with flow parameters with fixed seal geometry while earlier models expressed the carry-over coefficient solely as a function of seal geometry. For both compressible and incompressible flows, the Reynolds number based on clearance was the only flow parameter which could influence the carry-over coefficient. In the case of incompressible flow based on the simulations for various seal geometries and operating conditions, for a given Reynolds number, the carry-over coefficient strongly depended on radial clearance to tooth width ratio. Moreover, in general, the lower the Reynolds number, the larger is the divergence angle of the jet and this results in a smaller carry-over coefficient at lower Reynolds numbers. However, during transition from laminar to turbulent, the carry-over coefficient reduced initially and once the Reynolds number attained a critical value, the carry-over coefficient increased again. In the case of compressible flow, the carry-over coefficient had been slightly increased if radial clearance to tooth width ratio and radial clearance to tooth pitch ratio were increased. Further, the carry-over coefficient did not considerably change if only radial clearance to tooth width ratio was decreased. The discharge coefficient for compressible and incompressible flows depended only on the Reynolds number based on clearance. The discharge coefficient of the tooth in a single cavity labyrinth seal was equivalent to that in a multiple tooth labyrinth seal indicating that flow downstream had negligible effect on the discharge coefficient. In particular, for compressible fluid under certain flow and seal geometric conditions, the discharge coefficient did not increase with an increase in the Reynolds number. It was correlated to the pressure ratio, Pr. Moreover, it was also related to the fact that the flow of the fluid through the constriction became compressible and the flow eventually became choked. At low pressure ratios (less than 0.7), Saikishan’s incompressible model deviated from CFD simulation results. Hence, the effects of compressibility became significant and both the carry-over coefficient compressibility factor and the discharge coefficient compressibility factor needed to be considered and included into the leakage model. The carry-over coefficient compressibility factor, phi, had two linear relationships with positive and negative slopes regarding the pressure ratios. This result was not associated with the seal geometry because the seal geometry ratios for each instance were located within the nearly same ranges. Further, the phi-Pr relationship was independent of the number of teeth regardless of single and multiple cavity labyrinth seals. The discharge coefficient compressibility factor, psi, was a linear relationship with pressure ratios across the tooth as Saikishan predicted. However, in certain flow and seal geometric conditions, Saikishan’s model needed to be modified for the deviation appearing when the pressure ratios were decreased. Hence, a modified psi-Pr relationship including Saikishan’s model was presented in order to compensate for the deviation between the simulations and his model.