Estudo numérico da convecção natural em um banco de tubos elípticos verticais

Abstract

Natural convection from elliptical tubes is present in many engineering applications. Electric power transformers are examples of equipment that use a bundle of elliptical tubes setting radiators to dissipate the heat generated in this electric machine. Due to the high cost and great importance of transformers for the electrical power networks, it is essential to analyse the thermal performance of these machines. However, experimental tests may require huge efforts in terms of setup and time resources. Given this situation, CFD techniques become a great ally for the investigation of heat transfer in transformer radiators. Current scientific literature does not provide specific numerical studies on a bank of vertical elliptical tubes similar to that used in transformer radiators. In order to fill this gap, this work proposes carrying out a numerical study on a representative computational model of the elliptical tubes radiator, aiming to obtain numerical correlations of the average Nusselt number as a function of the Rayleigh number and the spacing between tubes. The numerical study of the above physical problem is achieved by the finite volume method. To this end, the tools from the Ansys® R2021 commercial package are used both in the pre-processing and to solve the governing equations in order to obtain the heat transfer rate from the elliptical tubes to the ambient air. The CFD model consists of a bundle of vertical elliptical tubes immersed in a volume of quiescent air. The surfaces of elliptical tubes are defined as walls assigned to constant temperature. The flow was assumed to be three-dimensional, in steady-state condition and laminar. Air was modeled as according to the incompressible ideal gas law. The values of the average Nusselt number of elliptical tubes are computed for different ambient temperature values and in different distance configurations between the tubes. From the results of the various simulations, numerical correlations are proposed for the Nusselt number, which may serve as a guide for numerical studies of transformers as well as for optimizing the design of elliptical tubes radiators.