Session H08: Flow Instability: Global Modes (5:45pm - 6:30pm CST)

A Mathematical Framework for Linear Analysis of Large-Scale $n$-Periodic Systems: Applications to Spanwise Arrays of Wall Irregularities or Jets

Boundary-layer stability and transition to turbulence is a major field of research for aerospace vehicle design. While unperturbed flow poses complexities in itself, in a variety of applications the boundary layer encounters a spanwise $n$-periodic array of surface irregularities, such as roughness or jet injections. In most cases, numerical simulations treat these configurations as periodic over each unit, thus neglecting cross-unit dynamics. In this work, we expand an earlier mathematical framework for the analysis of n-periodic arrays of fluid systems and apply it to large-scale simulations of flows using an operator-free approach for the linear analysis. Using a domain that spans only a triplet of units it is possible to extract the linear dynamics for arbitrary numbers of units with minimal additional cost. This formulation allows to study the stability, wake synchronization, and cross-unit dynamics of $n$-periodic systems from reduced-cost simulations without the assumption of fully periodic flow. We test this mathematical framework to canonical flat-plate boundary layer with roughness or jet injections; it is possible to extend the methodology to complex configurations and implement it in existing codes in a minimally intrusive way. Preliminary results will be presented.   

Global Analysis of Oblique Convective Instabilities in Laminar Shock-Wave/Boundary-Layer Interactions

The stability of the interaction between a laminar boundary layer and an incident shock wave is investigated. In particular, we aim to represent convective instabilities with BiGlobal stability analysis. The convective nature of these instabilities causes BiGlobal stability analyses in a stationary frame of reference to be artificially affected by the finite size of the computational domain, because eigenmodes are non-localized in the streamwise direction in this case. Recent work on the incompressible boundary layer (Groot and Niessen, arXiv:2001.04124) and on shock-wave/boundary-layer interactions (Niessen et al., APS DFD G33.007, 2019) shows that two-dimensional convective instabilities can now be resolved with the stability equations formulated in a moving frame of reference. In the present work, we deploy this methodology to obtain localized wave packets for oblique convective modes, that are independent of domain size and truncation boundary conditions. The long-time behavior is subsequently determined by time integration, which results in the propagation of the localized wave packets in the flow. Finally, we highlight the physical mechanisms constituting the convective instabilities through a Reynolds-Orr energy budget analysis.   

Identification of optimal linear perturbations in a premixed laminar flame by global resolvent analysis

The global response to forcing of a 2D laminar premixed slot flame is investigated with a linearized approach, where multi-physics coupling in a non-parallel reacting flow is accounted for. The classical flame transfer functions obtained this way are in good agreement with nonlinear reference calculations, performed with the AVBP code from CERFACS. Optimal forcing input, leading to maximal heat release fluctuations, are identified via resolvent analysis. Compared to similar recent investigations, we use a finite-element discretization on an unstructured mesh, and we employ a reduced two-step scheme for methane-air reaction. Strong sensitivity to flame parameters and chemical modeling is observed. The present linear analysis opens new ways for the physical discussion of instability dynamics in flames.   

Linear Modal Instabilities on Swept Finite-Aspect Ratio Wings at Low Reynolds Numbers and High Angles of Attack

Low Reynolds number separated laminar flow over finite swept wings is investigated numerically for a range of sweep angles ($\Lambda$) and aspect ratios ($AR$) at high angles of attack ($\alpha$). Modal TriGlobal stability analysis, POD and SPOD analyses of the 3-D flows are performed. Global stability analysis is performed on selected cases in order to identify the mechanisms leading to the formation of linear global mode. POD and SPOD are carried out in the nonlinear regime to classify the dominant structures and corresponding individual frequencies of the separated flow and assess the effects of geometrical parameters. Several distinct modes are identified in the separated flow. First, the Kelvin-Helmholtz mode dominates the low-$\alpha$ flow similar to previous studies. As $\alpha$ increases, the flow exhibits more complex 3-D behaviour associated with the Interaction Mode (IM), which is affected by the sweep angle. At high-$\Lambda$, the dominant mode takes the form of streamwise vortices for the larger $AR=4$ wing, while on the $AR=2$ wing the tip effect leads to the dominant mode being a tip instability. TriGlobal analysis reveals that the unstable wake is caused by an amplified global mode close to the symmetry plane similar to previous work on the elliptic wing.   

Are Low Viscosity Jets Globally Unstable

Many studies on stability in variable low-density jets exhibit the existence of instabilities that may lead to self-sustained oscillations. However, most studies neglect viscous effects, which are also found to dramatically alter the flow stability. Hence, experiments are performed with a low viscosity, density-matched jet introduced into a more viscous ambient. A study of instability and the subsequent breakdown of an axisymmetric jet with a jet-to-ambient viscosity ratio, $M$, ranging from 1 to 40 has been carried out for jet Reynolds number ranging from 400 to 2500. Flow visualization results indicate that viscosity stratification influences the growth rate and favors the growth of helical modes. A sharp peak in the hotwire spectra indicates the existence of a single-mode present in the near field of the jet, which is a weak function of the Reynolds number. The self-excited frequency of the jet appears to increase with increasing $M$. The response of the jet to external forcing using an acoustic driver is studied and it is observed that the self-excited nature of the jet can be modified by a forcing frequency allowing for controlled mixing.   

The effects of confinement on absolute and convective instabilities for momentum-driven countercurrent shear layers

h $-abstract-$\backslash $pardConfinement related flows are ubiquitous in both nature and engineering, but the study about the confinement on the absolute and convective instabilities is relatively rare, even for the confined planer shear layers. Recently, we have studied the absolute and convective instabilities for confined planar shears for both inviscid and viscous disturbances. For inviscid shear flow, we find the effect of confinement on the high-speed side is totally different from that on the low-speed side. For both cases, there exists more than one mode, one of which is similar to the free shear layer mode, the others are new findings that become more unstable as the location of the inflection point is reduced and will be the dominant mode when the confinement is strong enough. Also, the effect of boundary layer development on the unstable frequencies has been examined. At last, we compare the predictions of linear stability theory with experimental observations of confined countercurrent shear layers.$\backslash $pard-/abstract-\tex