Self-Induced Large-Scale Motions in a Three-Dimensional Diffuser

A direct numerical simulation of a three-dimensional diffuser at Reynolds number Re = 10,000 (based on inlet bulk velocity) has been performed using a low-dissipation finite element code. The geometry chosen for this work is the Stanford diffuser, introduced by Cherry et al. (Int. J. Heat Fluid Flow 29:803–811, 2008). Results have been exhaustively compared with the published data with a quite good agreement. Additionally, further turbulent statistics have been provided such as the Reynolds stresses or the turbulent kinetic energy. A proper orthogonal decomposition and a dynamic mode decomposition analyses of the main flow variables have been performed to identify the main characteristics of the large-scale motions. A combined, self-induced movement of the large-scales has been found to originate in the top-right expansion corner with two clear features. A low-frequency diagonal cross-stream travelling wave first reported by Malm et al. (J. Fluid Mech. 699:320–351, 2012), has been clearly identified in the spatial modes of the stream-wise velocity components and the pressure, associated with the narrow band frequency of \(St \in [0.083,0.01]\). This movement is caused by the geometrical expansion of the diffuser in the cross-stream direction. A second low-frequency trait has been identified associated with the persisting secondary flows and acting as a back and forth global accelerating-decelerating motion located on the straight area of the diffuser, with associated frequencies of \(St < 0.005\). The smallest frequency observed in this work has been \(St = 0.0013\). This low-frequency observed in the Stanford diffuser points out the need for longer simulations in order to obtain further turbulent statistics.