Session J32: Flow Instability: General

Bifurcations and instabilities of stratified anabatic flows in idealized valleys

Due to evening cooling of the atmospheric boundary layer, areas of complex terrain experience downslope, or katabatic, winds during the night time. In valleys, this process leads to the formation of a stably stratified cold pool at the base of the valley. Subsequently, morning heating will cause upslope, or anabatic flows, leading to the destruction of the stratified layer. However, the specific dynamics of these stratified anabatic flows in valleys are not well understood. This study investigates stably stratified anabatic flows in an idealized valley geometry using local and bi-global linear stability analysis (LSA) as well as direct numerical simulations (DNS) for extensive validation of the results. Through LSA, we observe a unique series of bifurcations, which includes a pair of pitchfork bifurcations, followed by a Hopf bifurcation that initiates a three-dimensional unsteady flow in the idealized valley. We also observe a unique three-dimensional instability which returns to a two-dimensional state in DNS, when control parameters are sufficiently low. Finally, we classify each flow regime by a unique set of novel dimensionless parameters.   

The stability of two-dimensional cylinder wakes in the presence of a wavy ground

A local and global linear stability analysis was conducted for flow past a circular cylinder in the presence of wavy ground. The relative position of the cylinder with respect to the wavy ground was varied for four different cases. The global stability computations were performed using Nektar++, which utilized spectral/hp element methods. The baseflow for each case was obtained by increasing the Reynolds number (Re) until the lift coefficient varied through time by less than 10^-6. Stability analysis was then performed on the baseflow. The results of the simulations indicated an increase in the critical Re when compared to the basic flow past cylinder (Critical Re = 45). A critical value of approximately Re = 65 was found for cases 1-3, and a value of approximately Re = 200 was found for case 4. The various cases were also simulated at Re = 200, which showed boundary layer effects from the wavy ground and vorticity generation from the peaks of the wavy ground that convected into the cylinder wake. Skewed trajectories of vortices shed from the cylinder were also observed for cases 1-3 at Re = 200. The eigenmodes for cases 1-3 skewed upward as they traveled downstream, and the vortex shedding mode, which is most dominant for basic flow past a cylinder, got suppressed for cases 1-4.    

Resolvent-based reconstruction of trailing-edge noise of the transitional flow over a NACA0012 airfoil

This numerical work investigates the relation between trailing-edge noise generated by a NACA0012 profile at 3° angle of attack and spanwise-coherent structures developing in the naturally transitional boundary layer over the airfoil. The aim of this work is to propose a low-order model of the radiated sound, based on surface pressure fluctuations obtained from resolvent analysis combined with acoustic analogies. The analysis is based on a numerical dataset obtained from a compressible large eddy simulation (LES) at a chord Reynolds number of 5e4 and a Mach number of 0.3.

Coherent structures are obtained from a spectral proper orthogonal decomposition (SPOD) of the LES snapshots, and from incompressible global resolvent modes of the mean fields. Preliminary results show a very good agreement between the most energetic structures captured by the SPOD and the leading resolvent mode, both in terms of the most frequency and mode shape. The mode shapes reveal that disturbances start to grow in the detached boundary layer on the suction side due to the Kelvin-Helmholtz mechanism and extend into the wake. Furthermore, surface pressure fluctuations obtained from the resolvent modes compare well with Fourier modes of the LES snapshots. These fluctuations are then used to rebuild the noise radiated based on acoustic analogy.   

Linear stability analysis of compressible flows using a conservative-variable formulation

High-speed compressible flows are often characterized by the presence of strong gradients that take the form of compression and expansion waves. For these configurations, a well-established practice in CFD consists in solving the governing equations in conservation form. This enables the numerical discretization to act on the conservative variables and the associated flux vectors, thus introducing advantageous wave-capturing capabilities in the solution.

Up to present, the stability analysis of high-speed flows has been almost exclusively performed using primitive-variable formulations, even though the base-flow solutions on which they are deployed usually come from conservative solvers.

By employing a linearization of the Navier-Stokes equations expressed in conservative variables, linear stability analyses of supersonic jet flows and high-speed boundary layers are performed. The resulting spectra and the amplitude functions of different relevant stability mechanisms are described in terms of conservative variables, and are compared against identical analyses based on primitive variables. In addition, non-modal analyses are carried out using both primitive and conservative formulations, and relevant differences between them are discussed.   

A multi-wavelet frequency sift analysis method for analyzing intermittency in transitional flow

Transition to turbulence is marked by intermittent flow structures, commonly referred to as "turbulent puffs", and causes fluctuations in flow parameters. Quantifying this fluctuating, intermittent flow behavior is important as it can accelerate material failure and cause performance reductions in flow-systems. 'Intermittency' inherently suggests that the flow structures maintain a characteristic time-scale, such that time-frequency-based methods can be effective for such analysis. However, existing time-frequency-based analysis tools, such as the empirical mode decomposition (EMD), have been noted to fail for intermittent signals, as observed in transitional flows. In this work, we propose a novel method that utilizes the dual-tree continuous wavelet transform (DT-CWT) and a frequency isolation sifting process in order to evaluate the instantaneous frequencies of a flow field. We demonstrate our method using particle image velocimetry (PIV) data of transitional pulsatile pipe flow. Furthermore, we compare this flow frequency information to traditional analysis such as coherent structure identification to demonstrate its utility in analyzing transitional flows.   

A Model to Study Microscale Bone Flows in Microgravity

As the Artemis program is aimed at sustained human presence in space, astronauts will spend increasing time in microgravity, known to cause bone loss, or osteoporosis. Extending low gravity stays demands understanding fluid behavior at microscales in relation to biological systems such as fluid flow channels to represent shear stresses that affect cellular growth. Studying these microscale mechanisms in low gravity yields insight required for biological systems to thrive, which is critical for success in space exploration. 

Microfluidic devices were designed to represent fluid channels in bones. The effort used computational fluid dynamics (CFD) simulations and ground experiments using oleic acid, glass beads, and pulsatile flow to simulate bone marrow. In Summer 2022, microgravity testing is anticipated on Blue Origin’s New Shepard to provide experimental data and validate the CFD models. The experiment uses imec’s lens free imaging system; a compact and wide field-of-view microscope suitable for recording fluids and biology processes. This work provides insight into microscale biological flow systems, evaluates a new microscope in microgravity, and validates related CFD predictions. This work is funded by NASA under award #80NSSC21K0338 and the Florida High Tech Corridor.   

Influence of compressibility on gas-driven viscous fingering in a Hele-Shaw cell

One of the most well-studied problems in interfacial fluid dynamics is the gas-driven displacement of a viscous liquid from a Hele-Shaw cell. This problem has received significant attention because of the distinct interfacial patterns that form due to the Saffman-Taylor instability. Generally, mathematical models of Hele-Shaw flow assume that both phases are incompressible and identify the Capillary number as the key parameter for determining the intensity of the instability. Recently, effort has been targeted at controlling the instability by modifying the geometry of the Hele-Shaw cell and/or the properties of the fluids. However, the practicality of such modifications can be limited. By contrast, compression of the invading gas occurs ‘naturally in experiments and is essentially unavoidable (unless the injection pressure is held constant). Here, we use state-of-the-art numerical simulations and laboratory experiments to study the influence of has compression on viscous fingering. We identify a second key control parameter, the ‘compressibility number’, that is comparable in importance to the capillary number. As such, we argue that compressibility offers a novel and powerful new means of controlling viscous fingering.

    

Not Participating

Understanding the primary instabilities of a pressure-driven flow in a grooved channel has been critical due to the broad range of industrial applications. This study is investigating the instability behavior of a pure Newtonian fluid passing over and through the periodic two-dimensional groove geometries perpendicular to the flow direction. We performed a combination of flow visualization and particle-image velocimetry and particle tracking velocimetry (PIV/PTV) measurements for a wide range of Reynolds numbers, along stream and span-wise directions to observe the flow patterns.  The experimental data of the primary instability for the Newtonian fluid quantitatively validate the supercritical character predicted by direct numerical simulations (DNS) and also characterizes the convective nature of the instability as well as the determination of critical Reynolds numbers, using well-established methods of applying controlled disturbances. The geometry-induced shear layer destabilization which results in a low-Reynolds number supercritical primary instability has been analyzed in detail.

    

Flow instabilities due to Marangoni stresses in ternary systems

We study the flow patterns resulting from a flow instability of a ternary system in a co-flow configuration inside a channel, where the jet consists of a binary mixture (oil and solvent), and the surrounding sheath flow of the third component (water). Due to a solvent-exchange process at the jet boundary, small oil droplets nucleate close to the inlet, while further downstream large oil-rich droplets on the scale of the jet diameter form. Using high-speed imaging, we demonstrate that the resulting droplets grow over time, and are able to migrate upstream, either engulfed axisymmetrically by the jet, or in an oscillatory motion around the jet center axis. We rationalize these observations by demonstrating a similar instability in a binary system of an ethanol jet in water, where a gas bubble is introduced at the jet center axis, and show that the driving force of the droplet or bubble motion is due to solutal Marangoni stresses acting at the fluid interface. Our results emphasize the complex interaction between fluid flow, species transport and interfacial properties, and allow for a better understanding of channel flows of ternary systems.

    

Correlating the Den Hartog instability criterion to the dynamic response of an oscillating system

The Den Hartog criterion has been used for decades to evaluate the susceptibility of a cross-section to galloping instability. We will present results from our experimental campaign that aims to correlate the Den Hartog stability assessment of altered circular cross-sections and the dynamic response of a 1D oscillator with an identical cross-section.  Dynamic tests for the Reynolds number range of 5000 – 35600 with a circular cylinder attached with strips of thickness varying from 0.8% to 8.2% of the cylinder diameter were performed. The results were compared to the static tests with thickness varying from 0 to 12.8% at Reynolds number values of 10000, 20000, and 30000. The maximum angles of attack of the vibrating configuration were projected onto the Den Hartog instability map generated from fixed cylinder lift-drag measurements, and it was found that the maximum angle of attack experienced by the galloping cylinder fell within the Den Hartog instability zones. Increasing the thickness ratio postpones the angle where the lift reaches its maximum and increases the maximum lift and drag values.

    

Linear path instability of permeable buoyancy-driven disks

The prediction of trajectories of falling or rising objects in a viscous fluid is a relevant problem in fluid dynamics. Falling disks have been widely investigated since they exhibit diverse trajectories, ranging from zig-zag to tumbling and chaotic motions. Yet, similar studies are lacking when the object is permeable. We perform a linear stability analysis of the steady vertical path of a thin microstructured, permeable, disk modeled via a stress-jump model which stems from homogenization theory. The flow associated with the steady vertical path presents a recirculation region detached from the disk, which shrinks and disappears as the disk becomes more permeable. In analogy with the impervious disk, one non-oscillatory and several oscillatory unstable modes are identified. Permeability profoundly modifies the destabilization picture. For sufficiently large permeabilities, the primary bifurcation at low disk inertia is nonoscillatory and leads to a steady tilting of the disk. A further increase of permeability reduces the unstable regions in the parameters space until all linear instabilities are damped.