Bulletin of the American Physical Society
75th Annual Meeting of the Division of Fluid Dynamics
Volume 67, Number 19
Sunday–Tuesday, November 20–22, 2022; Indiana Convention Center, Indianapolis, Indiana.
Session L18: Flow Instability: Theory & Global Modes |
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Chair: Michael Karp, Technion - Israel Institute of Technology Room: 145 |
Monday, November 21, 2022 8:00AM - 8:13AM |
L18.00001: A General Framework for Destabilizing Neutrally-Stable Flows Applied to Aircraft Wake Vortices Philip S Marcus, Jinge Wang, Sangjoon Lee Moore & Saffman (1975), Tsai & Widnall (1976), and others considered forced, resonant instabilities of a neutrally-stable aircraft wake vortex. Generally, the wake vortex was modeled as a q-vortex. In the previous studies, the q-vortex was forced by a finite-amplitude perturbation of the form of a linear strain field or as a boundary layer mode. Using resonance theory, the previous authors showed that the finite forcing could perturb the eigenvalues of a degenerate pair of neutrally-stable eigenmodes of the q-vortex such that one had a positive growth rate. Here we introduce a general framework based, in part, on the degenerate perturbation theory used in quantum mechanics, to show how to perturb a q-vortex, or any other neutrally stable flow, such as Couette-Taylor flow, to produce unstable eigenmodes. Using a perturbed eigenmode, along with the perturbed q-vortex as an initial condition in a code that solves Euler’s equation, we show that the amplitudes of the perturbed eigenmode initially grow linearly with the rates predicted by our degenerate perturbation theory. Our initial-value code is then used to determine which perturbed modes saturate with weak amplitudes (i.e., have large Landau coefficients) and which grow large enough to potentially de-stabilize a vortex wake. |
Monday, November 21, 2022 8:13AM - 8:26AM |
L18.00002: A statistical perspective on transient growth Peter K Frame, Aaron S Towne The theory of transient growth investigates how linear mechanisms can cause temporary amplification of disturbances even when the linearized system is asymptotically stable as defined by its eigenvalues. This growth is traditionally quantified by finding the initial disturbance that generates the maximum response, in terms of energy gain, at the peak time of its evolution. In this presentation, we introduce a novel statistical perspective on transient growth which seeks statistics of the energy gain in terms of those of the initial disturbance. We derive a formula for the expected energy and two-point spatial correlation of the growing disturbance as a function of the two-point spatial correlation of the initial disturbance. We apply our analysis to Poisseuille and Couette flow and show that the characteristic length scale of the initial disturbances, encapsulated by the spatial decay within the correlation function, has a significant impact on the expected growth. Specifically, large-scale initial disturbances produce orders-of-magnitude-larger expected growth than smaller scales, indicating that the length scale of incoming disturbances may be key in determining whether transient growth leads to transition for a particular flow. Additionally, we consider the probability of observing various levels of growth given a distribution of initial conditions. |
Monday, November 21, 2022 8:26AM - 8:39AM |
L18.00003: Stabilisation of cylindrical liquid bridges using radial, oscillatory body force: theoretical and computational analysis. Ratul Dasgupta, Sagar Patankar, Lohit Kayal Dynamic stabilisation of Rayleigh-Plateau modes on a liquid cylinder employing a radial oscillatory body force has been recently shown in (Patankar, Basak & Dasgupta, J. Fluid Mech. 2022, In Press). In this study, we show that this mechanism can be employed to stabilise cylindrical liquid bridges of finite length with pinned contact line at the end substrate. We derive a matrix Mathieu equation via linear stability analysis, extending the scalar Mathieu equation derived earlier in (Patankar, Farsoiya & Dasgupta, J. Fluid Mech. 2018, vol. 857) to the pinned case. Solutions to this equation predict that hitherto unstable modes can be stabilised via forcing. Analytical predictions show excellent agreement with numerical simulations of the incompressible, Euler's equations with surface tension. The stability diagram of the matrix Mathieu equation and the combination resonance regions will be discussed in the presentation. |
Monday, November 21, 2022 8:39AM - 8:52AM |
L18.00004: Axisymmetric and flapping global instabilities of a Ma = 1 jet Michael Karp, Philipp Hack The global instabilities of a perfectly expanded jet at Ma = 1 are investigated. Two configurations are compared. A reference setup represents the full geometry including the walls of the convergent nozzle within the computational domain. A second case indirectly models the effect of the nozzle on the flow. Both configurations are found to be globally unstable, indicative of the presence of an absolute instability mechanism. The results ascribe the generation of the absolute instability to the instantaneous transformation of the boundary layer within the nozzle into a rapidly expanding free shear layer past the nozzle exit. The constraining effect of the nozzle walls in the reference configuration leads to a lower instability growth rate than in the modeled case. The eigenfunctions are split into upstream- and downstream-traveling parts, and decomposed into vortical, acoustic and thermal components using momentum potential theory (Doak 1989). The most highly amplified axisymmetric and flapping modes are found to have a common structure. In the reference case, the eigenfunctions consist of upstream-traveling acoustic waves and downstream-traveling Kelvin-Helmholtz modes. The eigenfunctions in the modeled case are concentrated at the location of the rapidly expanding shear layer. |
Monday, November 21, 2022 8:52AM - 9:05AM Not Participating |
L18.00005: Shape optimization to suppress the helical vortex breakdown based on linear stability and adjoint theory Jens S Müller, Sophie Knechtel, Thomas L Kaiser, Kilian Oberleithner Global instabilities that lead to large-scale periodic fluctuations play a key role in many engineering applications. They arise due to a distinct self-excitation mechanism that is often spatially localized in a narrow region. It is, therefore, often minor changes of the flow-immersed geometry that can have a large impact on the instability. In this work, a shape optimization framework is developed to exploit this property in order to suppress an instability by delaying its bifurcation. |
Monday, November 21, 2022 9:05AM - 9:18AM |
L18.00006: On new unstable three-dimensional oblique modes examplified by plane Couette flow Martin Oberlack, Alparslan Yalcin Squire proved that temporally unstable 2D modes are the most unstable ones. In the present work, we expand the Squire theorem by extending it to spatial instabilities allowing for growth in both the streamwise and in the spanwise direction, i.e. we imply complex wave numbers $\alpha$ and $\beta$, i.e. growth rates are then tightly coupled in both directions. The key result is that we can thus generate critical Reynolds numbers that are significantly lower than those of 2D modes, and, if no unstable modes exist at a finite Reynolds number as for plane Couette flow, unstable modes can be calculated at a finite Reynolds number. The complex $\alpha$ and $\beta$ represent an oblique mode structure, which brakes spanwise reflection symmetry. The new modes are generic, but we apply them to the plane Couette flow. For this flow, oblique-type modes at finite amplitude are documented in the literature in experiments and simulations. The present theory shows that no explicit limit can be given for the critical Reynolds number, because it depends on the fact which modes can be realised in streamwise and spanwise directions and these in turn depend on the size of the domain under consideration. By means of highly accurate simulations, we can verify the oblique modes for the Couette flow. |
Monday, November 21, 2022 9:18AM - 9:31AM |
L18.00007: Global forced response analysis of reacting swirling flows Parth Patki, Benjamin L Emerson, Timothy C Lieuwen Swirling jets are canonical flow fields in reacting flow systems. This study considers hydrodynamic global flow response to an imposed forcing function. A bi-global stability analysis is done on DNS and LES base flow data by the means of linearized, incompressible Navier Stokes and continuity equations. The disturbance equations are obtained around the unforced mean flow, which serves as the base state for this study. The unforced bi-global analysis is used to test the linear stability of the base flow before a forced bi-global analysis framework is set up to examine the flow's dominant coherent structures in a paired forcing/response fashion. Locations of coherent structures in the domain are probed to evaluate a point-to-point transfer function in terms of a flow variable and the results are studied as a function of Strouhal number. The numerical methods in this study involve discretization of the linearized disturbance equations, application of cylindrical boundary conditions for the swirling jet domain, and the solutions obtained using Taylor-hood finite elements in COMSOL. Lastly, the implications for extension of this study to a strict, fully-global analysis along with experimental validation are considered. |
Monday, November 21, 2022 9:31AM - 9:44AM |
L18.00008: Time-stepping global stability analysis using open-source DNS and DSMC codes Kamil Dylewicz, Nicolas Cerulus, Angelos Klothakis, Vassilis Theofilis, Deborah A Levin On occasion TriGlobal linear stability analysis is prohibitively expensive within a matrix-forming paradigm due to its very high memory requirement. Moreover, a matrix-based approach is inapplicable to rarefied flows encountered at high altitudes, where one resorts to particle-based numerical simulations. In such situations, global stability analysis can be performed using matrix-free, time-stepping approaches recovering flow eigenmodes directly from nonlinear solvers, while preserving all underlying assumptions with additional advantage of drastic reduction in memory requirements. |
Monday, November 21, 2022 9:44AM - 9:57AM |
L18.00009: Modal analysis of a shear layer in high-supersonic cavity flows using data-driven and operator-based resolvent analysis Aravinth Sadagopan, Daning Huang, Maryam Safari, Chi-An Yeh Shear layer oscillations (SLO) are common phenomena in aerospace applications inducing unfavorable acoustic radiation and structural fatigue. SLO driving mechanism over open cavity flows at subsonic and supersonic speeds has been well studied. However, for SLO over a cavity in high supersonic flows, the stability properties are relatively unexplored, i.e., for flow regimes beyond Mach 3. The classical Rossiter model fails to predict the SLO characteristics. Therefore, in this work resolvent analysis has been employed to identify the dominant dynamic mechanisms and modal characteristics of self-sustained SLO at high Mach numbers. In particular, the resolvent analyses are performed using data-driven and operator-based frameworks. The comparisons between both implementations will be highlighted for the resolvent modes and spectra. We will also discuss the influence of the baseflows due to the differences in the solver fidelity. With a series of implicit large-eddy simulations at Mach numbers 2 to 5, we observe a weak coupling between standing waves within the cavity and SLO. The strong compression/expansion waves on the shear layer and cavity wall reflected Mach waves significantly contribute to the SLO characteristics. |
Monday, November 21, 2022 9:57AM - 10:10AM |
L18.00010: The Role of Global Hydrodynamic Mode Receptivity in Vortex-Acoustic Lock-On Joel V Vasanth, Satyanarayanan R Chakravarthy In unstable reacting flows, 'lock-on' is defined as the transition of the frequency of dominant thermoacoustic oscillations fd from the natural acoustic frequency fa to that of the vortex shedding fv as a parameter is varied, and the persistence of fd at fv with further change in parameter. We perform a linear global direct and adjoint stability analysis of reacting flow past a backward-facing step to quantify the role of its hydrodynamics and justify why lock-on occurs. Base flow profiles are acquired from an experiment where lock-on is observed as the inlet flow velocity is increased. Two flow rates are selected for the stability analysis - 1000lpm (F1) and 2500lpm (F2), corresponding to states before and after lock-on. We show that both flows are globally unstable, with F2 having a larger growth rate. These agree with spectral peaks from the experimental data. The receptivity of the modes to forcing depends on the adjoint mode shapes and detuning fv-fa. Both flows have a finite detuning, but the adjoint mode has a more distributed high amplitude region for F2 compared to F1, implying F2 is more receptive to acoustic forcing. Both these points imply that, despite a finite detuning, a highly receptive globally unstable hydrodynamic mode can act as the driver for lock-on. |
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