On the Instability of the Three Dimensional Rectangular Duct Flow using the Energy Gradient Method

In this study, the unsteady flow of three dimensional rectangular ducts is investigated using the energy gradient method. The instability maximum ratio of the energy gradient in the two orthogonal directions is predicted for different aspect ratios. For specific Reynolds numbers, the ratio of the energy gradient in the two orthogonal directions is obtained for different aspect ratios and validated with the previous available data. The comparison of the present results shows excellent agreement with the previous available data. From the results of present work we conclude that as the aspect ratio increases the time required for the flow to reach the steady state is lesser, in other words the larger the aspect ratios are the sooner the steady state flow conditions are achieved. Resultsof this paper show that the maximum ratio of the energy gradient in the two orthogonal directions, K-max, for three dimensional rectangular duct flows is in the range of 402-403. Also, the variations of K/Re versus y/b at different dimensionless times and different aspect ratios are investigated. The onset of the instability in R=infinity is so similar to the plane poiseulle'sresult of Dou(2006).