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Hydrodynamic Stability & Flow Control
Stability of Rotating Flows^
Swirling Jets^
FIGURE 1: Two examples of transient amplification in a turbulent swirling jet with a breakdown bubble, where the first column is the input structure for optimal perturbations, while the last column is the corresponding outcome.
We investigated the helical instabilities of a rapidly-swirling, high-speed jet that has transitioned into an axisymmetric bubble breakdown state, a common occurrence in modern aero engine combustion chambers. Instead of focusing on the normal-mode based instability, we considered whether short-time, local transient growths are important. Our calculations on top of an experimentally measured flow indicated strong transient amplifications inside the bubble and wake (FIGURE 1), but especially at the wake locations, where dynamically important instabilities were observed far outstripping the corresponding modal growths at shorter times. If these non-modal growths reach finite amplitudes, they are likely to yield non-trivial modifications of the underlying mean flow to fundamentally alter its primary instability character. More work is needed to fully delineate the mechanisms.
Selected Publication:
Muthiah, G. & Samanta, A. 2018 Transient energy growth of a swirling jet with vortex breakdown. J. Fluid Mech., 856, 288–322
Vortex Rings & Breakdown of Jets^
FIGURE 2: (TOP) Converged eigenspectrum of a Gaussian-core vortex ring; (BOTTOM) Reconnection of an isolated hairpin vortex showing vortex lines
FIGURE 3 Linear temporal evolution of a vortex ring
Near the end of the potential core, jets undergo a series of very rapid hydrodynamic evolutions which lead to their eventual breakdown. This is similar to events that happen for wall-bounded flows too. We have analyzed this in a series of steps.
The initial stages of this breakdown can be modeled via the evolution of a vortex ring subjected to azimuthal instabilities (FIGURE 2, TOP) which yields a streamwise component of vorticity. As a result, such rings get wrinkled (FIGURE 3), eventually forming hairpin vortices, finally leading to their breakdown. In our linear studies we found growth rates of rings to be very sensitive to the details of vorticity distribution, in a way not accounted for in previous asymptotic theories.
The post-linear stage is first studied via the evolution of an isolated hairpin vortex that appears to be ejected near the end of the linear evolution stages of FIGURE 4. Such a hairpin undergoes viscous vortex reconnection as it evolves within its background flow (FIGURE 2, BOTTOM).
The last stages before the jet fully breaks down is dominated via the dynamics of multiple such hairpins and their reconnections.
Selected Publications:
Balakrishna, N., Mathew, J. & Samanta, A. 2022 On late stages of transition in round jets. TSFP12, Osaka, Japan, Jul 2022
Balakrishna, N., Mathew, J. & Samanta, A. 2020 Inviscid and viscous global stability of vortex rings. J. Fluid Mech., 902, A9
Rotating Ducted Flows
FIGURE 4: Neutral curves show regions of convective stability, convective instability and absolute instability for a rotating pipe flow with constant mean density with the gray curves showing the incompressible case.
The application of this study is in stability of premixed flow inside air swirler ducts, upstream of fuel injection, a possible location for acoustic-hydrodynamic coupling in air-assisted atomizer designs. The potential for higher Mach numbers in such configurations led us to investigate the stability of a compressible rotating Hagen-Poiseuille flow with variable mean density as the flow model. A significant outcome of this work is the discovery that increased compressibility can actually promote instability at lower Reynolds numbers while appear stabilizing at the higher Re for certain types of density stratification (FIGURE 4).
Selected Publication:
Yadav, N. K. & Samanta, A. 2017 The stability of compressible swirling pipe flows with density stratification. J. Fluid Mech., 823, 689–715
Boundary Layer Control^
FIGURE 5: Schematic of a flat plate boundary layer control setup via volumetric / boundary forcings.
An input-output resolvent analysis of a flat plate boundary layer flow subjected to periodic blowing and suction is carried out to ascertain the optimal location and nature of forcings required from the control setup to delay the boundary layer transition. Ideally, this is a form of open-loop control done without any actual experiments or numerical simulations. This study is expected to establish a computationally low-cost, direct simulations/experiments-free, mathematically-optimal approach to control flat plate boundary layers via forcings applied directly at the plate.
Stability of Supersonic Jets
FIGURE 6: Comparing zeros and poles of dispersion relation for a supersonic jet showing how (shaded) instability spectrum widens for the latter.
Moderately high supersonic jets (with Mj > 2, relative to the ambient flow) are known to possess a new type of instability wave that is not purely hydrodynamic in nature, rather a coupling between the acoustic waves, repeatedly reflected off the flow interface at certain favourable angles, with the shear layer hydrodynamics results in their growth. The acoustically coupled modes are of supersonic phase speed, while we found that when such jets are also heated, a second kind of instability wave of subsonic phase speed can co-exist (FIGURE 6). These subsonic acoustically coupled modes, which first appear beyond a certain temperature ratio (between core and ambient) depending solely upon the corresponding ambient flow speed, are shown to have much greater potential to reach higher unstable growth rates (compared to supersonic modes). Further, at such conditions the traditional K–H mode is shown to completely disappear via turning into an acoustically coupled mode. This analysis explains why heated supersonic jets, in spite of being hydrodynamically more unstable in the near-field (due to the presence of subsonic acoustically coupled modes), do not necessarily yield in higher levels of radiated sound.
Selected Publication:
Samanta, A. 2016 On the axisymmetric stability of heated supersonic round jets. Proc. R. Soc. A, 472 (2188), 20150817
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