Linear instability analysis of low- incompressible flow over a long rectangular finite-span open cavity

Abstract

TriGlobal linear instability analysis and direct numerical simulations have been performed to unravel the mechanisms ultimately responsible for transition of steady laminar flow over a long rectangular finite-span open cavity with dimensions $L$ : $D$ : $W$$=$ 6 : 1 : 2 to unsteadiness. The steady laminar three-dimensional flow loses stability at $\mathit{Re}_{D,cr}\approx 1080$ as a consequence of linear amplification of a travelling eigenmode that is qualitatively analogous to the shear-layer mode known from analyses of flow in spanwise-periodic cavities, but has a three-dimensional structure which is strongly influenced by the cavity lateral walls. Differences in the eigenspectrum of the present and the spanwise homogeneous flow configuration are documented. Topological changes exerted on the steady laminar flow by linear amplification of the unstable shear-layer mode are reminiscent of observations in experiments at an order of magnitude higher Reynolds number.

Resolvent-analysis-based design of airfoil separation control

“…a solution to the Navier-Stokes equations. Such an approach forms an eigenvalue problem for the global instability modes and emphasizes on the spectrum of the linearized Navier-Stokes operator (Barkley & Henderson 1996;Sipp & Lebedev 2007;Liu et al 2016;Sun et al 2017;Taira et al 2017). Inherently, it characterizes the asymptotic long-time behavior of the perturbations in the flow.…”

Effects of Sidewalls and Leading-Edge Blowing on Flows over Long Rectangular Cavities

“…A joint work of experiments and simulations was reported by Arunajatesan et al 6 to investigate effects of finite width on transonic cavity flows. Triglobal stability analysis 23 has also been carried out by Liu et al 19 for finite-span cavity flows. As additional findings on sidewalls effects are revealed, it becomes necessary and valuable to assess the appropriateness of spanwise periodic cavity flow as a suitable model for practical cavity flows.…”

Control of flow instabilities in an open aircraft bay model cavity

“…All these physical features have been subject of an extensive research since the 1950's 1-4 and a large number of experimental and numerical studies of cavity flow have been carried out since then. A representative list of works describing studies of rectangular open cavity flows, using linear and nonlinear instability analysis, simulations and experiments are described in the recent work by Liu et al 5,6 In the incompressible regime, different flow features have been reported in the literature. Rossiter 7 was the first to describe the physical mechanism driving the self-sustained oscillations in cavity flows.…”

“…17 Many studies [18][19][20][21][22][23] emphasize the existence of more complex cavity flow structures in a realistic open cavity configuration, i.e., bounded by lateral walls, and at high Reynolds number. In this context, Liu et al 6 were the first to unravel the mechanisms ultimately responsible for laminar-turbulent transition of the long rectangular parallelepipedic open cavity using TriGlobal linear instability analysis. The results revealed that the three-dimensional shear layer mode, which is strongly influenced by the cavity lateral walls, triggers the first bifurcation from steady to unsteady flow.…”

“…The cavity configuration, flow parameters and numerical methodology are documented in §II. At the light of the results described by, 6 TriGlobal direct and adjoint instability analysis is employed to take into account the influence of the lateral walls. The flow control results based on small modifications of the base flow at the obtained structural sensitivity region are then reported in §III.…”