Low Reynolds number flow over a plane symmetric sudden expansion

Abstract

Flow visualization and laser-anemometry measurements are reported in the flow downstream of a plane 3: 1 symmetric expansion in a duct with an aspect ratio of 9·2: 1 downstream of the expansion. The flow was found to be markedly dependent on Reynolds number, and strongly three-dimensional even well away from the channel corners except at the lowest measurable velocities. The measurements at a Reynolds number of 56 indicated that the separation regions behind each step were of equal length. Symmetric velocity profiles existed from the expansion to a fully developed, parabolic profile far downstream, although there were substantial three-dimensional effects in the vicinity of the separation regions. The velocity profiles were in good agreement with those obtained by solving the two-dimensional momentum equation. At a Reynolds number of 114, the two separation regions were of different lengths, leading to asymmetric velocity profiles; three dimensional effects were much more pronounced. At a Reynolds number of 252, a third separation zone was found on one wall, downstream of the smaller of the two separation zones adjacent to the steps. As at the lower Reynolds numbers, the flow was very stable. At higher Reynolds numbers the flow became less stable and periodicity became increasingly important in the main stream; this was accompanied by a highly disturbed fluid motion in the separation zones, as the flow tended towards turbulence.

Data Assimilation with Gaussian Mixture Models Using the Dynamically Orthogonal Field Equations. Part II: Applications

“…Experimental results show that, for low Re, the flow is symmetric about the channel centerline, with circulation regions formed at the corners of the expansion (Durst et al 1973). This is the case depicted in figure 6, in which the flow is described by streamlines.…”

“…Specifically, we consider two-dimensional Sudden Expansion flows. In fluid dynamics, such flows have been of considerable interest (Durst et al 1973;Cherdron et al 1978;Fearn et al 1990) and continue to do so. Due to the breaking of symmetries with increasing Reynolds number and the consequent development of at least bimodal statistics, it provides a test case particularly well-suited to the evaluation of data assimilation schemes.…”

“…In section 2-b, we consider flows that are more realistic for coastal ocean or fluid dynamics. Specifically, we consider dynamic jets and eddies that occur in Sudden Expansion flows (Cherdron et al 1978;Fearn et al 1990;Durst et al 1973) of two dimensions in space. We illustrate and study the results of the GMM-DO filter, including the evolution of probability density functions (pdfs) and of their DO decomposition, the Bayesian impacts of observations, and the overall capabilities of the filter.…”

A Gaussian Mixture Model Smoother for Continuous Nonlinear Stochastic Dynamical Systems: Applications

“…For low Re, the flow remains steady and symmetric about the centerline, with recirculation zones appearing at the corners of the expansion (Durst et al 1974). At larger Re, the flow downstream of the expansion develops asymmetry and exhibits vortex shedding, which can either be steady or unsteady.…”

On the performance of a 2D unstructured computational rheology code on a GPU

“…Due to the very long downstream channel (300H), the gradient of flow variables at the outlet is null, except for the pressure that is linearly extrapolated from the domain. This benchmark problem has been extensively used to verify numerical solutions and schemes [33,34,35] used in incompressible laminar flow of Newtonian and non-Newtonian fluids. At low Reynolds numbers the flow is symmetric and at a critical Reynolds number, that depends on expansion ratio, the flow becomes asymmetric [34], but remains steady.…”