RESUMO Este artigo apresenta um estudo teórico-experimental com o objetivo de determinar o coeficiente de transferência de calor interfacial, as variáveis térmicas de solidificação, os espaçamentos dendríticos primários e secundários bem como a microdureza Vickers da liga Al-11%Si solidificada direcionalmente, sob condições transientes de fluxo de calor, em um dispositivo de configuração horizontal refrigerado a água. Para o monitoramento dos perfis de temperatura utilizou-se um conjunto de termopares tipo K localizados em diferentes posições a partir da interface metal-molde, considerando a linha central correspondente ao eixo longitudinal do lingote. Uma técnica numérica, que compara perfis térmicos teóricos e experimentais, foi utilizada no cálculo do coeficiente de transferência de calor na interface metal/molde durante a solidificação cuja condição transiente é representada por uma equação analítica na forma de potência. Foram aplicadas técnicas experimentais para o cálculo das variáveis térmicas de solidificação, ou seja, deslocamento da frente de solidificação, velocidade da isoterma liquidus e taxa de resfriamento. Os resultados experimentais e simulados apresentaram uma concordância muito boa e possibilitaram estabelecer correlações analíticas entre tais variáveis térmicas e os espaçamentos dendríticos primários e secundários obtidos, por meio de equações na forma de potência representadas por expoentes característicos. Finalmente, são também apresentadas expressões experimentais capazes de correlacionar os valores dos espaçamentos dendríticos estudados com o comportamento da microdureza Vickers da referida liga.

ABSTRACT This paper presents a theoretical-experimental study aiming to determine the interfacial heat transfer coefficient and solidification thermal parameters from experimentally obtained data correlating these with the primary and secondary dendritic spacings as well as microhardness during the horizontal solidification of the Al-11wt.%Si alloy under transient heat flow conditions. For the experimental procedure, a water-cooled solidification device was used which allows the horizontal directional solidification and the monitoring of the temperature profiles in different positions from the metal-mold interface considering the center line corresponding to the longitudinal axis of the ingot. A numerical technique which compares theoretical and experimental thermal profiles has permitted the evaluation of the variation of metal-mold heat transfer coefficient along the solidification. The interfacial heat transfer coefficient of studied alloy is represented by a equation which show the time dependence during the process. The experimental and calculated values have shown a very good agreement. Experimental techniques were applied to calculate the following solidification thermal variables: solidification front displacement, growth rate and cooling rate. The experimental results allowed establishing a quantitative correlation between such thermal variables and the studied structural parameters by means of power type equations represented by characteristic exponents. Finally, correlation between the values of both primary and secondary dendritic spacings found with Vickers microhardness behavior for the studied alloy is also presented.

Abstract This work presents an analytical method for the study of the solid state diffusion process in binary systems of two phases with cylindrical radial atomic flux. The method is developed from the differential equation that describes Fick's second law that is modified by geometric function and suitable changes of variables. The modified differential equation is solved by using a well-known closed form solution based on the error function, and then analytical equations are obtained to analyze the diffusion interface position as a function of time, and the concentration profiles as a function of time and position. The predictions provided by the analytical method are compared with numerical results.

In order to analyze the effect of the growth direction on dendrite arm spacing (λ1) and microhardness (HV) during horizontal directional solidification (HDS), experiments were carried out with the Al-3wt.%Cu-5.5wt.%Si alloy and the results compared with others from the literature elaborated for upward directional solidification (UDS). For this purpose, a water-cooled directional solidification experimental device was developed, and the alloy investigated was solidified under unsteady-state heat flow conditions. Thermal parameters such as growth rate (VL) and cooling rate (TR) were determined experimentally and correlations among VL, TR, λ1 and HV has been performed. It is observed that experimental power laws characterize λ1 with a function of VL and TRgiven by: λ1=constant(VL)-1.1 and λ1=constant(TR)-0.55. The horizontal solidification direction has not affected the power growth law of λ1 found for the upward solidification. However, higher values of λ1 have been observed when the solidification is developed in the horizontal direction. The interrelation of HV as function of VL, TR and λ1 has been represented by power and Hall-Petch laws. A comparison with the Al-3wt.%Cu alloy from literature was also performed and the results show the Si element affecting significativaly the HV values.

RESUMONa Amazônia, a navegação é muito importante devido a extensão de rios navegáveis e a falta de redes rodoviárias alternativas. As embarcações geralmente trabalham em condições desfavoráveis, uma vez que não há relação entre a hidrodinâmica dos hélices, geometria e as dimensões do casco da embarcação. Atualmente, não há metodologia para otimização hidrodinâmica com baixo custo computacional e fácil implementação na região. O objetivo deste trabalho foi o desenvolvimento de uma abordagem matemática voltada para o projeto de propulsores marítimos aplicados as embarcações tipicamente encontradas nos rios da Amazônia. Nós desenvolvemos uma formulação otimizada para o cálculo das distribuições de corda e ângulo de torção, considerando o modelo clássico de Glauert. Uma análise teórica para as relações de empuxo e torque em um volume de controle anular foi realizado. O modelo matemático utilizado foi baseado na teoria do momento do elemento de pá (BEMT). Concluímos que a nova metodologia, proposta neste trabalho, demonstra bom comportamento físico quando comparado com a teoria de Glauert e os dados experimentais do propulsor Wageningen B3-50.

ABSTRACTIn the Amazon, river navigation is very important due to the length of navigable rivers and the lack of alternative road networks. Boats usually operate in unfavorable conditions, since there is no hydrodynamic relation among propellers, geometry, and the dimensions of the boat hull. Currently, there is no methodology for propeller hydrodynamic optimization with low computational cost and easy implementation in the region. The aim of this work was to develop a mathematical approach for marine propeller design applied to boats typically found on Amazon rivers. We developed an optimized formulation for the chord and pitch angle distributions, taking into account the classical model of Glauert. A theoretical analysis for the thrust and torque relationships on an annular control volume was performed. The mathematical model used was based on the Blade Element Momentum Theory (BEMT). We concluded that the new methodology proposed in this work demonstrates a good physical behavior when compared with the theory of Glauert and the experimental data of the Wageningen B3-50 propeller.

In order to investigate the effect of natural convection in columnar to equiaxed transition (CET), Al-3.0wt.%Cu and Al-3.0wt.%Cu-5.5wt.%Si alloys ingots were obtained during the transient horizontal directional solidification (THDS). Aiming to analyze the effect of superheat in the formation of the macrostructure in ternary Al-Cu-Si alloy, the experiments were conducted with three superheat temperatures above the liquidus temperature of the ternary alloy. A water-cooled solidification experimental device was used. Continuous temperature measurements were made during solidification at different positions in the casting and the data were automatically acquired. Thermal analysis has been applied to determine the thermal parameters such as growth rate (VL), cooling rate (TR) and temperature gradient (GL), whose values have been interrelated with the CET. The observation of the macrostructures has indicated that the resulting thermosolutal convection combined with superheat seem to favor the transition, which did not occur in a single plane, for all ingots obtained, i.e., it has been seen in a range of positions in ingots. The addition of Si element in binary Al-Cu alloy anticipates the CET. A comparison with experimental results for CET occurrence in different growth directions has been carried out.

A liga Al-6%Cu foi solidificada direcionalmente sob condições transitórias de extração de calor e microestruturas dendríticas, variáveis térmicas de solidificação, ou seja, velocidade de deslocamento da isoterma líquidus (VL), taxa de resfriamento (TR) e gradiente de temperatura à frente da isoterma liquidus (GL) foram caracterizadas, determinadas experimentalmente e correlacionadas com os espaçamentos dentríticos terciários (λ3). Para tanto, foi projetado, construído e aferido um dispositivo de solidificação direcional horizontal. Os resultados encontrados mostram que leis de potência -1,1 e -0,55 caracterizam a variação dos espaçamentos terciários com a velocidade de deslocamento da isoterma liquidus (VL) e a taxa de resfriamento (TR), respectivamente. Finalmente, é realizado um estudo comparativo entre os resultados obtidos neste trabalho e aqueles publicados na literatura para ligas Al-Cu solidificadas direcionalmente sob condições transientes de fluxo de calor nos sistemas verticais ascendente e descendente.

The Al-6wt%Cu alloy was directionally solidified and dendritic microstructure, solidification thermal variables, i.e., tip growth rate (VL), cooling rate (TR) and temperature gradient ahead of liquidus isotherm (GL) were characterized and correlated with tertiary dendritic spacings ((λ3) determined experimentally. For this purpose, a horizontal solidification experimental apparatus was developed and specimens were solidified under unsteady state heat flow conditions. It was observed that power laws -1.1 and -0.55 characterize the tertiary spacing variations with tip growth rate (VL) and cooling rate (TR), respectively. Comparisons with other studies published in the literature for Al-Cu alloys solidified in upward and downward vertical directional conditions were performed.

O principal objetivo desse trabalho é investigar a influência dos parâmetros térmicos velocidade de solidificação (V L) e taxa de resfriamento (T R), nos espaçamentos dendríticos primários (λ1) da liga hipoeutética Al-7%Si, durante a solidificação direcional horizontal, em regime transiente. Os valores de λ1 foram medidos ao longo do comprimento do lingote e correlacionados com esses parâmetros. A variação dos espaçamentos dendríticos estudados é expressa por meio de funções na forma de potência de V Le T Rdadas, respectivamente, por λ1= 55(V L)-1.1e λ1= 212 (T R)-0.55. Um estudo comparativo é realizado entre os resultados encontrados nesse trabalho e aqueles obtidos para a mesma liga quando solidificada direcionalmente nos sistemas verticais ascendente e descendente, sob as mesmas condições assumidas. Finalmente, os resultados experimentais obtidos são comparados com valores fornecidos por alguns modelos teóricos propostos na literatura para analisar espaçamentos dendríticos primários.

The main purpose of this work is to investigate the influence of thermal parameters such as growth rate (V L) and cooling rate (T R) on the primary dendrite arm spacings (λ1) during the horizontal transient directional solidification of Al-7wt.%Si hypoeutectic alloy. The primary dendrite spacings were measured along the length of the samples and correlated with these thermal parameters. The variation of dendrite spacings is expressed as a power law function of V L and T R given by the formulas λ1 = 55(V L)-1.1 and λ1 = 212 (T R)-0.55, respectively. A comparative study between the results of this work and those from the literature proposed to investigate these dendrite spacings during the upward and downward vertical directional solidification of Al-7wt.%Si alloy is also conducted. Finally, the experimental data are compared with some predictive dendritic models from the literature.

As ligas Al-Sn são amplamente utilizados em aplicações tribológicas. Nesse estudo, análises térmica, microestrutural e dureza (HV) foram realizadas ao longo de um lingote da liga Al-5,5%Sn, obtido por solidificação direcional horizontal transitória. Os principais parâmetros analisados incluem a velocidade de deslocamento da isoterma liquidus (V L) e a taxa de resfriamento (T R). Esses parâmetros térmicos desempenham um papel fundamental na formação da microestrutura. A microestrutura dendrítica foi caracterizada através dos espaçamentos dentríticos primários (λ1), os quais foram determinados, experimentalmente, e correlacionados com V L, e T R. O comportamento apresentado pela liga Al- 5,5% Sn, durante a solidificação,é semelhante ao de outras ligas de alumínio, isto é, observa-se rede dendrítica mais grosseira com a diminuição da taxa de resfriamento, indicando que a imiscibilidade entre o alumínio e estanho não tem um efeito significativo sobre o relação entre o espaçamento dendrítico primário e taxa de resfriamento. A dependência da microdureza em V L, T R e no λ1 foi também analisada. Verificaram-se menores valores de HV para maiores T R. Por outro lado, os valores HV aumentam com valores crescentes de λ1.

Al-Sn alloys are widely used in tribological applications. In this study, thermal, microstructural and microhardness (HV) analysis were carried out with an Al-5.5wt.%Sn alloy ingot produced by horizontal directional transient solidification. The main parameters analyzed include the growth rate (V L) and cooling rate (T R).These thermal parameters play a key role in the microstructural formation. The dendritic microstructure has been characterized by primary dendritic arm spacing (λ1) which was experimentally determined and correlated with V L, and T R. The behavior presented by the Al-5.5wt.%Sn alloy during solidification was similar to that of other aluminum alloys, i.e., the dendritic network became coarser with decreasing cooling rates, indicating that the immiscibility between aluminum and tin does not have a significant effect on the relationship between primary dendritic arm spacing and the cooling rate. The dependence of the microhardness on V L, T R and λ1 was also analyzed. It was found that for increasing values of T R, the values of HV decrease. On the other hand, the values of HV increase with increasing values of λ1.

The main purpose of this paper is to investigate both the columnar to equiaxed transition and primary dendritic arm spacings of Al-3wt.%Si alloy during the horizontal directional solidification. The transient heat transfer coefficient at the metal-mold interface is calculated based on comparisons between the experimental thermal profiles in castings and the simulations provided by a finite difference heat flow program. Simulated curve of the interfacial heat transfer coefficient was used in another numerical solidification model to determine theoretical values of tip growth rates, cooling rates and thermal gradients that are associated with both columnar to equiaxed transition and primary dendritic arm spacings. A good agreement was observed between the experimental values of these thermal variables and those numerically simulated for the alloy examined. A comparative analysis is carried out between the experimental data of this work and theoretical models from the literature that have been proposed to predict the primary dendritic spacings. In this context, this study may contribute to the understanding of how to manage solidification operational parameters aiming at designing the microstructure of Al-Si alloys.