FINITE ELEMENT SOLUTIONS OF FLUID FLOW WITH HEAT TRANSFER PAST OBSTRUCTIONS

Abstract

The thesis deals with the numerical study of flow past obstructions and the convectlve heat transfer in the separation region downstream of the same. The analysis is carried out using the finite element method using eight noded isoparametric elements alongwith the Galcrkin's weighted residua] method. Tho Navier stokes/Reynolds equations and the corresponding energy equations have been solved for laminar and turbulent flows with appropriate boundary conditions. A coupled solution of these equations has been obtained. The two-equation k-e model has been used for turbulence modelling and a similar two equation model has been adopted for determining the eddy diffusivity of heat. Flow past obstructions has been studied exclusively using the same. Starting from the case of flow past a fence (T/h • 0, where T is the thickness and h the height of the obstruction), the analysis has been extended for values of T/h = 1, 4, 7 and 10 and finally for a backward facing step (T/h = «). For all these cases the heat transfer characteristics in the region immediately downstream of the obstruction have also been studied. The results have been compared with available experimental/analytical results wherever possible. It is found that while the results are qualitatively in good agreement with experimental values, quantitatively there is an underprediction of the length of the separation zone - a characteristic of the k-e model which has been reported by other investigators also. (i) The length of the downstream separation bubble expressed in terms of the height of the obstructions (Ld/h) is found to decrease with increase in T/h value and attains a constant value for T/h £ 4. The convective heat transfer rate as expressed in terms of the local Nusselt number reaches a maximum near the reattachment point and drops down on either side. (