Bulletin of the American Physical Society
74th Annual Meeting of the APS Division of Fluid Dynamics
Volume 66, Number 17
Sunday–Tuesday, November 21–23, 2021; Phoenix Convention Center, Phoenix, Arizona
Session M06: Flow Instability: General I |
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Chair: Clarence Rowley, Princeton Room: North 122 AB |
Monday, November 22, 2021 1:10PM - 1:23PM |
M06.00001: 2D and 3D Modes in Supersonic Mach number Open Cavity Flows Parshwanath S Doshi, Datta V Gaitonde The coupled resonant oscillations in shallow open cavity flows at supersonic Mach numbers (1.4-3) are investigated for a fixed L/D ratio (6), depth-based Reynolds number (10,000), and incoming boundary layer thickness. By combining local spatial stability and global resolvents, it is demonstrated that increasing the freestream Mach number in this parameter range could lead to a destabilization of higher order 2D modes due to a shift in the convective Mach number of the underlying instabilities from subsonic to supersonic within the cavity. The mode shapes reveal that when the convective Mach number is supersonic, these instabilities are not only associated with growth rates that are comparable to those at subsonic convective Mach numbers, they also support waves that reflect back and forth between the shear layer and the cavity floor, thus providing a mechanism for instability that is not typically found at subsonic freestream Mach numbers. Furthermore, by varying the spanwise wavenumber, it is observed that an increase in Mach number in this range renders the cavity more three-dimensional due to reduced differences between the gain of the 2D and 3D modes. The results of this study are especially pertinent to the design of flameholders that operate in the supersonic regime. |
Monday, November 22, 2021 1:23PM - 1:36PM |
M06.00002: Linear stability analysis of particle-laden flows in channels with porous walls Saman Hooshyar, HARUNORI N YOSHIKAWA, Parisa Mirbod Suspension flows with small particle inertia are encountered in environmental, industrial, pharmaceutical, and geological applications. However, the stability of this type of flow in the presence of porous media is poorly understood. We investigate the effects of porous surfaces on flow stability by performing linear stability analysis of dilute particle-laden flows in channels bounded by rigid, homogenous, and isotropic porous walls. The particles field is two-way coupled with the fluid field through Stokes drag only. Particles are assumed to be uniform, solid, and spherical with a significantly smaller size than the characteristic scale of the flow. Brinkman equation is adopted to characterize the fluid behavior inside the porous layers. It is found that porous walls exert destabilizing effects on the system. Increasing the porous layer permeability or thickness triggers instabilities at smaller Reynolds numbers. The presence of porous walls therefore may work as a strategy to enhance efficiency in mixing processes. Our results also reveal that increasing the particles size results in a monotonic rise in the critical Reynolds number, which is in contrast with the particle-laden flow in a channel with impermeable walls where stability alternates with particles size. |
Monday, November 22, 2021 1:36PM - 1:49PM |
M06.00003: Bifurcation of polygonal spiral patterns in wide-gap spherical Couette flow Fumitoshi Goto, Tomoaki Itano, Masako Sugihara-Seki In spherical Couette flow between rotating inner and fixed outer concentric spheres, the radius ratio η = rin / rout determines the laminar-turbulent transition scenario. For narrow gaps (small η), the transition starts with Taylor vortices formed near the equatorial zone. On the other hand, for wide gaps (large η), the transition triggered by cross-flow instability around mid-latitude generates secondary wave with spiral vortices. We searched for the Reynolds numbers that spiral states exist in a wide gap case η = 0.5. We developed Newton method code for Navier-Stokes equation of spherical Couette flow and specified the spiral states. In the present study, we found that 3-fold spiral state and 4-fold spiral state coexist over the critical Reynolds number. It was confirmed that the 4-fold spiral state exists at a smaller Re than 3-fold spiral state. We also found that the periodic-like state is composed of the 3- and 4-fold spiral states, as if it is a beat of two different frequencies. |
Monday, November 22, 2021 1:49PM - 2:02PM |
M06.00004: Flake alignment in the secondary wave in a wide spherical Couette flow Tomoaki Itano, Fumitoshi Goto, Masako Sugihara-Seki In spherical Couette flow between rotating inner and fixed outer concentric spheres, the radius ratio determines the laminar-turbulent transition scenario. For small radius ratio, the transition triggereed by cross-flow instability around mid-latitude generates secondary wave with spiral vortices. |
Monday, November 22, 2021 2:02PM - 2:15PM |
M06.00005: Analysis of the sensitivity of periodic flows to subharmonic perturbations using the harmonic transfer function Alberto Padovan, Clancy Rowley Many flows in nature and in engineering applications exhibit complicated dynamics arising from the nonlinear interaction between different time scales. For instance, it is well-known that the vortex pairing observed in high-shear flows such as mixing layers and jets is due to the high underlying sensitivity of the flow to subharmonic disturbances. |
Monday, November 22, 2021 2:15PM - 2:28PM |
M06.00006: Transition between intermediate states in Taylor vortex flows in the presence of riblet-covered rotors Shabnam Raayai In flows ranging from boundary layers to internal flows and Taylor-Couette flows, riblet surfaces can alter the frictional drag force on the wall. Mimicking natural patterns such as ribs on denticles of sharks or the ridges on rice leaves, and butterfly wings, 2D textures have been effectively used as a means of passively reducing the drag force. In this talk, the effect of 2D streamwise textures on the onset of instability and transition between different flow states in a Taylor-Couette flow is experimentally examined. Using a wide-gap Taylor-Couette cell, I will present torque measurements as well as velocity profiles in the vicinity of the transitional flow as a function of the geometry of the textures as well as the Reynolds number. Focusing on the Taylor-vortex regime, I will show that unlike the case of smooth rotors, where after the onset of the Taylor vortices the flow settles into a 6-cell Taylor-vortex, periodic and symmetric textures in the circumference of the inner rotors can sustain an intermediate 4-cell Taylor-vortex flow over a range of Reynolds numbers before ultimately transitioning to the 6-cell state. Lastly, I will discuss how the geometric features of the textures affect the critical Reynolds number and the extent of this intermediate state. |
Monday, November 22, 2021 2:28PM - 2:41PM |
M06.00007: Adjoint-based analysis of jet-in-crossflow linear instability David D.W. Ren, Ann R Karagozian, Davi B Souza, Rômulo B Freitas, Leonardo Alves Experiments and direct numerical simulations have demonstrated that the jet-in-crossflow (JICF) features coherent upstream shear layer oscillations in a manner consistent with linear stability analyses, where the shear layer is convectively unstable at relatively large jet-to-crossflow velocity ratios R and absolutely unstable at low R. Small perturbations applied near the jet exit, through either passive or active means, are known to affect these shear layer instabilities, in addition to affecting jet structure and mixing. This work investigates the effect of base flow deviations, such as those created by such perturbations, on JICF linear stability characteristics. The continuous 1D linear stability analysis of Alves, et al., JFM 2008 is extended to an adjoint-leveraged 2D stability analysis to (i) determine the dominant spatial growth rates for the convectively unstable JICF more accurately, (ii) establish the onset of absolute instability for different flow conditions and downstream locations, and (iii) determine the sensitivity of spatial growth rates and onset of absolute instability to base flow modifications. |
Monday, November 22, 2021 2:41PM - 2:54PM |
M06.00008: How a leak can stop itself Caroline D Tally, Heather E Kurtz, Rose B Tchuenkam, Katharine E Jensen Small fluid leaks are a common - and often troublesome - occurrence in everyday life. We often consider what action is required to stop a leak, or to prevent one from starting in the first place, but here we consider somewhat different questions: how might a leak stop itself? What governing physics determines the moment and mechanism of this spontaneous arrest? We report experiments that quantify the initiation and spontaneous self-arrest of leaking fluid flows emerging from a small hole in a vertical tube as a function of hole size and surface hydrophobicity. We use high-speed imaging to capture the mechanism of flow-stop, and observe that the leaking fluid undergoes a Rayleigh-Plateau-like rivulet instability leading to the creation of a final, static "capping droplet" whose surface curvature prevents further leakage. We compute the potential energy landscape of such capping droplets as a function of volume, hole size, and material properties, and combine this with existing rivulet stability theory to predict when a flow-stop transition will occur. |
Monday, November 22, 2021 2:54PM - 3:07PM |
M06.00009: Recursive one-way Navier-Stokes equations: accurate, low-cost spatial marching Min Zhu, Aaron S Towne We introduce a new recursive formulation of the one-way Navier-Stokes (OWNS) equations that reduces cost to a level similar to the parabolized stability equations (PSE) while retaining superior accuracy. Many free-shear and wall-bounded flows contain a slowly varying direction that can be leveraged to efficiently study their linear and nonlinear stability, transition, and turbulent dynamics using spatial marching methods. The widely used parabolized stability equations (PSE) have severe limitations, due to regularization required to overcome the ill-posedness of the spatial march, for flows involving multiply instability mechanisms, transient growth, and acoustics. One-way Navier-Stokes (OWNS) equations overcome these limitations by formally removing the upstream-traveling waves responsible for ill-posedness, but doing so increases CPU and memory cost by one to two orders-of-magnitude relative to PSE. Our new formulation avoids this increased cost by modifying the OWNS equations to avoid large systems of equations in favor of a recursive series of smaller ones, reducing computational complexity. The new formulation is also easier to implement and comes with a priori error estimates. The efficiency of the method is demonstrated using a hypersonic boundary layer and a turbulent jet. |
Monday, November 22, 2021 3:07PM - 3:20PM |
M06.00010: Linear stability analysis of the flow in an oblique lid-driven cavity Pierre-Emmanuel des Boscs, Hendrik C Kuhlmann In this presentation, we analyse the linear stability of the flow in a in cavity, driven by the motion of a lid tangential to itself but not aligned with the cross section. The angle between the direction of the lid and the cross section α is varied from 0° to 90°. At α= 0° and a cavity of square cross section, the classical Taylor-Goertler modes with high wavenumbers are recovered at a critical Reynolds number about Rec=800, while at α = 90°, the laterally bounded Couette flow is linearly stable. Upon increasing α from 0°, the flow becomes more unstable and Rec decreases down to Rec = 620 at α = 22.5°. As α is further increased towards 75°, the critical modes become more elongated in the spanwise direction. Similar transitions are obtained for shallow and deep cavities. For all angles, the lift-up effect is the main instability mechanism, extracting kinetic energy from streamwise vortices feeding streaky structures. As long as the lid velocity drives the in-plane velocity components a feedback mechanism promoting the streamwise vortices is present. However, this feedback mechanism progressively vanishes as α tend towards 90°, and the flow strongly stabilizes. |
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