Eddy correlations for water flow in a single fracture with abruptly changing aperture

Abstract Fluid flow in single fractures with non‐uniform apertures is an important research subject in many disciplines. The abruptly changing aperture is a special case of such non‐uniformity. This paper simulates water flow in a single fracture with abruptly changing aperture (SF‐ACA) using the Lattice Boltzmann Method (LBM) and the Finite Volume Method (FVM). The flow occurs with the Reynolds number ( Re ) ranging from 5 to 900 and a ratio of aperture change ( E ) of 3 ( E = D/d , where D and d are the larger and smaller apertures, respectively). For Re values between 5 and 100, both LBM and FVM can successfully simulate the eddy development in the expansion regime of an SF‐ACA. Flow with high Re values (up to 900) is simulated by FVM, which appears to be numerically more stable than LBM for high‐ Re flow problems studied here. The flow symmetry in the expansion regime breaks at the Re value between 400 and 500. Our simulation result shows a linear relationship between l 1 / d and Re at low Re (5–100) or higher Re (110–900) values, where defined as the length from the location of abrupt expansion to the right edge of the first eddy along the flow direction. If considering the simulation results for the entire simulated range of Re (5–900), the l 1 / d–Re relationship is better described by a non‐linear logarithmical function. The l 1 / d approaches an asymptotic constant at large Re . Copyright © 2011 John Wiley & Sons, Ltd.