A comparative study of inflow conditions for two‐ and three‐dimensional spatially developing mixing layers using large eddy simulation

Abstract

SUMMARYA series of spatially developing mixing layers are simulated using the large eddy simulation (LES) technique. A hyperbolic tangent function and data derived from boundary layer simulations are used to generate the inflow condition, and their effects on the flow are compared. The simulations are performed in both two and three dimensions. In two-dimensional simulations, both types of inflow conditions produce a layer that grows through successive pairings of Kelvin-Helmholtz (K-H) vortices, but the composition ratio is lower for the hyperbolic tangent inflow simulations. The two-dimensional simulations do not undergo a transition to turbulence. The three-dimensional simulations produce a transition to turbulence, and coherent structures are found in the post-transition region of the flow. The composition ratio of the three-dimensional layers is reduced in comparison to the counterpart two-dimensional runs. The mechanisms of growth are investigated in each type of simulation, and amalgamative pairing interactions are found in the pre-transition region of the three-dimensional simulations, and throughout the entire computational domain of those carried out in two-dimensions. The structures beyond the post-transition region of the three-dimensional simulations appear to behave in a much different manner to their pre-transition cousins, with no pairingtype interactions observed in the turbulent flow. In order to accurately simulate spatially developing mixing layers, it is postulated that the inflow conditions must closely correspond to the conditions present in the reference experiment.

Organised large structure in the post-transition mixing layer. Part 2. Large-eddy simulation

“…Because the transition is itself dependent on the development of three-dimensional large-scale motions, this has necessarily required spatially evolving simulations in three dimensions. Comparative two-and three-dimensional simulations performed previously by the present authors (McMullan, Gao & Coats 2007 have confirmed that, without the three-dimensional large-scale motions, the flow does not undergo the type of transition seen in real mixing layers. It has also required realistic evolution of the inflected velocity profile through the progressive merging of the laminar boundary layers formed on the two sides of the splitter plate.…”

“…If numerical simulations are performed in two dimensions no transition of the type that was seen in the experiments occurs and subharmonics of the fundamental Kelvin-Helmholtz mode continue to be excited naturally throughout the available flow length (McMullan et al 2007(McMullan et al , 2010. If the simulations are performed in three dimensions, on the other hand, the secondary streamwise vortices are able to develop and interact with the primary spanwise vortices to produce the transition at which point, as was shown in §4.3, there is a switch to the regime in which the large structures all undergo continuous linear growth.…”

“…It has also required realistic evolution of the inflected velocity profile through the progressive merging of the laminar boundary layers formed on the two sides of the splitter plate. As has been demonstrated elsewhere (McMullan et al 2007(McMullan et al , 2009, if a symmetrical inflected velocity profile (e.g. one of hyperbolic-tangent form) is taken instead as the inlet condition, not only is the pre-transition development of the flow altered but an unrealistically symmetrical balance of entrainment from the two free streams persists into the post-transition flow.…”

Streamwise vortices in plane mixing layers originating from laminar or turbulent initial conditions

“…The method applied here is very similar to that employed in previous studies of the idealised mixing layer by the author. 28,29 In those studies, it was found that the transition to turbulence, and the coherent structures in the turbulent flow were readily captured.…”

Resolved Scalar Mixing in Large Eddy Simulations of a Low Reynolds Number Plane Mixing Layer

“…21,22 Whilst these simulations are attractive on grounds of computational cost, it has been shown that mixing layers confined to two-dimensional domains do not undergo the mixing transition, as the formation of the secondary instability is inhibited. 23,24 This has a knock-on effect on the growth of the mixing layer, and entrainment of fluid into it. 23 Furthermore, the specification of idealised inflow conditions with white noise disturbances, common in mixing layer simulations, 20,25 can lead to different types of streamwise vorticity being formed in the mixing layer when compared to highly two-dimensional white noise fluctuations, 26 or physically-correlated inflow disturbances.…”