Numerical analysis of a natural and excited two-dimensional mixing layer

Abstract

Physical properties of a two-dimensional plane mixing layer are examined by numerical solution of the unsteady Navier-Stokes equations using a pressure velocity formulation. The natural (unforced) mixing layer due to the merging of two streams with a velocity ratio (r = 0.33) is studied at Reynolds numbers /?e = 200, 500, and 1000. Different transition zones are detected: stable, linear, and nonlinear. The roll-up process appears in the nonlinear zone. The main flow features are in agreement with the experimental evidence. The excited mixing layer at the first subharmonic and at the incommensurate frequency are investigated to analyze the coalescence mechanism and the nonlinear interaction. HE merging of two streams initially separated by a thin surface plays an important role in numerous applications such as aerodynamics and combustors. Experiments reported by a number of authors have shown that orderly structures are extant in the turbulent mixing layer. Visualization studies reported by Brown and Roshko1 confirm that large-scale coherent structures are indeed intrinsic features of the turbulent mixing layer at high Reynolds numbers. Furthermore, sequential mergings of the vortices constitute the primary mechanism for the spreading of the mixing layer in the downstream direction, as pointed out by the experiments of Winant and Browand.2 These observations have had a major impact on the understanding of turbulence in free shear flows. The large-scale vortices are observed not only in the early laminar stages of the flow, but also farther downstream in the turbulent region, where they coexist with a fine-scale motion. Hence, two issues need to be examined: the evolution of the large eddies identified in the viscous laminar flow and the link between these eddies and the coherent structures observed in the turbulent flow. The mechanisms of transition and coherent structures play an important role in the correct modeling of turbulent flows. Two main approaches are currently used in the experimental and theoretical analyses used to study these mechanisms: the classical linear hydrodynamic stability theory and the description of vorticity field in the physical space. In the classical hydrodynamic stability theory, the mixing layer is viewed as an overlapping of the instability waves that propagate and amplify in the downstream direction. The flow is naturally described in the Fourier space. Therefore, measured data in the frequency space cannot be easily related to the evolution of the orderly structures.3'4 The second approach, by taking into account the nonlinear character, explains the behavior of coherent structures by studying the evolution of the vorticity field in the physical space. The structures are considered to be vortices of a characteristic size that exhibit different types of interactions.5'6 In this case, the results can be compared with the flow visualization studies.