Numerical study of instabilities in separated–reattached flows

On secondary instability of a transitional separation bubble

“…The LES code used has been very well validated in many transitional studies (Yang andVoke, 2000a, 2001; Yang, 2004, 2005;Yang and Abdalla, 2009) and a comprehensive validation of the predicted mean velocity and Reynolds stresses for the current study can be found in Yang (2004, 2005). The focus here will be on the transition process and especially on the analysis of secondary instability.…”

“…When the finite volume method is employed the governing equations are integrated over control volumes, equivalent to convolution with a top-hat filter, hence there is no need to apply a filter to the instantaneous equations explicitly and in this case it is called implicit filtering. A dynamic sub-grid-scale model based on Germano et al (1991) and Lilly (1992) is implemented where the model coefficient C is obtained as described in Yang andVoke (2000b, 2001). The mesh is refined in important flow regions where the mesh resolution are quite fine which is not far away from what would be recognized as DNS, with the averaged sub-grid eddy viscosity is below 4 times of the molecular viscosity and the maximum sub-grid eddy viscosity is about 8 times of the molecular viscosity.…”

“…The explicit second order Adams-Bashforth scheme is used for temporal discretisation with a time step of 2x10 -6 second to ensure that the Courant number is below 0.3 for numerical stability. Further details of the mathematical formulation and numerical methods can be found in several papers (Yang andVoke, 2000b, 2001;Yang, 2004, 2005). The simulation ran for 5 flow-through times to allow the flow to become well established and reach a statistically stationary state.…”

“…Transition process in separation bubbles are more complex and depends on many factors such as freestream turbulence intensity (Simoni et al 2017;Istvan and Yarusevych 2018) and passing wakes in turbomachinery flows (Sarkar 2008). Our understanding of the transition process in separation bubbles is limited apart from the primary instability stage which is due to the Kelvin-Helmholtz (KH) mechanism in the absence of any large magnitude environmental disturbances as demonstrated vigorously by the LES study of Yang andVoke (2000a, 2001) for a transitional separation bubble on a flat plate with a semi-circular leading edge and by the LES study of Abdalla and Yang (2004) on a flat plate with a blunt leading edge, and by many other experimental and numerical studies (Burgmann et al, 2008;Yaras, 2009, 2010;Satta et al, 2010;Dahnert et al, 2012). What is happening after the primary instability stage and how the three-dimensional motion develops from the initial quasi two-dimensional KH rolls via a secondary instability is not well understood.…”

“…Several studies have been carried out to investigate secondary instability of transitional separation bubbles formed on a flat plate where a laminar boundary layer develops over certain distance and separates due to an adverse pressure gradient (Rist et al, 1996;Maucher et al, 1990, 2000, Marxen et al, 2003, 2013Rodriguez and Gennaro, 2015). It was found that a mechanism of secondary, temporal amplification exists in transitional separation bubbles for large boundary layer Reynolds numbers at separation (Maucher et al, 1999(Maucher et al, , 2000 and this 4 Sensitivity: Confidential new mechanism of secondary instability is likely to have great impact on the onset of transition.…”