Session L32: Flow Instability: Vortex-Dominated Flows & Wakes

Instabilities in the flow generated by a finite-size rotating disk

A rotating disk is the canonical experiment for measuring surface reaction rates in geochemical and electrochemical systems. Using the similarity solution for laminar flow around an infinite disk, the mass transfer coefficient can be simply related to the intrinsic reaction rate at the surface. However, measurements of mass transfer rates use a finite-size disk within a larger container of solution. Numerical simulations suggest that the flow around a finite-size disk becomes time dependent at Reynolds number below 1000, which is much smaller than the typical values in mass-transfer measurements (Re ~ 10⁴). We observe the formation of coherent structures in the flow, which suggest the possibility of a non-uniform mass transfer at the disk surface. In the specific geometry studied, a rotating-disk flow follows a similar sequence of instabilities to the Taylor-Couette flow: a centrifugal instability leading an axisymmetric, time-invariant flow, followed by a Hopf bifurcation to a time-periodic flow.. Increasingly chaotic flows at higher Reynolds number eventually lead to turbulence at Reynolds numbers between 3000 and 5000.   

Author not Attending

We present experimental results complemented with numerical simulation of a recently discovered instability observed in a free-surface flow driven by an azimuthal electromagnetic force in a thin layer of an electrolyte contained in an open annulus. The force is created by a radial current flowing between two concentric electrodes and a uniform magnetic field produced by a permanent magnet. The flow instability leads to the formation of travelling anticyclonic vortices close to the external electrode that exist for long times once they appear. Experimental characterization includes dye visualization, thermography and PIV. A small layer thickness and the circumferential direction of the driving force suggest that the flow should be essentially uni-directional and could be described by approximate Q2D equations. Surprisingly, we found that not only the flow is fully 3D, but also multiple axisymmetric flow solutions can exist for the same set of governing parameters. However, a linear stability analysis indicates that only one of such solutions can potentially lead to azimuthally periodic vortex patterns observed in our experiments. Finally, it is shown that it is possible to reproduce the emergence of the instability using a fully 3D hybrid finite volume-spectral numerical method.

    

On the origin of mode B instability of the wake of a square cylinder

Three-dimensional numerical simulations of flow passing a square cylinder are performed using a spectral element method. Reynolds numbers of 200 and 300, corresponding to mode A and B respectively, are used to study the two- to three-dimensional transition of the wake flow. It is shown that the wake transition occurs in the early-time prior to the onset of the vortex shedding event. For mode A, the spanwise instability grows exponentially downstream of the cylinder with a constant wavelength in the early-time dynamics and continue after the vortex separation. However, in the case of mode B, the exponential amplification reaches a saturation state before the vortex separation occurs. A splitting of the initially obtained wavelength of the spanwise instability occurs and is related to the splitting of spanwise vortical structures which develops at the cores of the separation bubbles prior to the vortex shedding.   

Three dimensionalization of stratified shear instability in the cabbeling regime

In this talk I will discuss direct numerical simulations of shear instability in the cold water regime, or in other words the regime in which the range of temperatures includes the temperature of the density maximum (around 4 degrees Centigrade). In this regime, the mixing of two fluid parcels can lead to a child fluid parcel with a larger density than either parent parcel. This phenomenon is called cabbeling. I will demonstrate that cabbeling fundamentally alters the three dimensionalization of shear instability. I will subsequently show various properties of the fully three-dimensionalized state, which has many hallmarks of turbulence, but does not have a well developed inertial subrange. I will discuss how entrainment can drive continuing instabilities in the three-dimensionalized region, as well as how the vertical transport of both scalars and momentum is modified from the classical picture of natural waters. Time permitting I will present some new ideas of how parametrizations for this regime may be constructed for basin scale lake models.   

Withdrawn

For uniform steady flow past two cylinders aligned parallel to the flow, an extended bluff body regime (for small cylinder spacing) and a co-shedding regime (for large spacing) can be seen. The "critical spacing" at which the flow structure shifts between these regimes depends on the Reynolds number. For a specific Re, the critical spacing depends on if the cylinder separation is being (quasi-statically) increased or decreased; this hysteresis is also found when fixing the spacing and varying Re. Analyzing the critical spacing is important owing to the quick jump in Strouhal number and surface forces seen during the shift. Accurately quantifying these responses can, for example, guide the development of energy harvesting methods or the prevention of body clashing. Extensive past studies agree on the general trends in critical spacing, but there remains a discrepancy in the details, especially between experiments and computations. Using a flowing soap film "tunnel", Yang & Stremler (2019, JFS 89) found experimental critical spacing values consistent with published computational results for Re=100. We expand on this study by considering multiple cases for 50   

Author not Attending

The flow around a geometrically simple cylindrical roughness element submerged in a laminar boundary layer is a seemingly simple problem in fluid mechanics. However, a more in-depth analysis reveals intricate phenomena in specific parameter ranges, illustrating that more research is required. A smoke-flow visualization study in a large parameter space was performed. The experimental setup features a cylindrical roughness element connected to a linear traverse, enabling almost continuous variation of the roughness height. Three synchronized high-speed cameras were used to record the smoke streaks, illuminated by a continuous laser sheet. Results reveal that the instability in the roughness wake switches from convective to global instability at a critical Reynolds number. While the convective instability always exhibits a varicose shape, the shape of the global instability depends on the geometrical properties of the roughness element. Depending on the ratio of roughness diameter and height, the shape can be varicose or sinuous. Furthermore, frequency information is extracted from the smoke-flow visualization images and indicate that, in the sinuous instability regime, the dominating frequency in the wake can be well predicted using a Strouhal number.   

The impact of harmonic inflow variations on the size and dynamics of the separated flow over a bump

Laminar flow separation has detrimental effects on the aerodynamics and performance of low pressure turbines (LPT). Flow separation is caused by the presence of adverse pressure gradient on the upper side of the blade past the suction peak, and is followed by laminar-to-turbulent transition and the subsequent turbulent mean reattachment due to the enhanced mixing. These phenomena characterise the size and dynamics of the separated flow, which are primarily dominated by the laminar-turbulent transition process. This study examines the influence of periodic variations of the inflow on the separated flow over a bump geometry at low Reynolds numbers. The geometry and flow conditions represent the upper surface of small LPT during high-altitude flight. Direct numerical simulations are performed, in which a harmonic variation of the inlet total pressure is imposed as an approximation of the passage of the upstream blade's wake. Three frequencies and two amplitudes of the total pressure are simulated. The dynamics of the separated shear layer and the transition process are studied by separating the flow components correlated and un-correlated to the inflow frequency. Even moderate frequencies are found to have a strong effect in reducing the averaged size of the separated flow region.   

Generation of streamwise helical vortex loops via successive reconnections in early pipe transition

We extend the vortex-surface field (VSF), a Lagrangian-based structure identification method, to investigate the vortex reconnection in temporally evolving transitional pipe flows. In the direct numerical simulation, a radial wave-like velocity disturbance is imposed on the inlet region to trigger the pipe transition. The VSF isosurfaces are vortex surfaces composed of vortex lines, and they are concentric tubes with different wall distances at the initial time. The VSF evolution is effective to identify the vortex reconnection. In the early stage of transition, the vortex surfaces are first corrugated with streamwise elongated bulges, along with the surge of the wall-friction. The resultant highly coiled and stretched vortex loops then reconnect with each other. Then, successive vortex reconnections occur via a "greedy snake" mechanism. The streamwise vortex loops consecutively capture the secondary vortex rings pinched off with self-reconnection, forming long helical vortex loops spanning over ten pipe radii in the streamwise direction. Finally, the Kelvin-Helmholtz instability of the shear layer at the trailing edge breaks down the streamwise helical vortex loops into turbulent spots.   

Author not Attending

Increasing the efficiency of modern aircraft is an important topic in reducing the environmental effect of air travel. Aircraft efficiency is largely dependent on the overall drag effect during flight. Skin friction drag increases over time as a result of the harsh conditions of atmospheric flight and inclement weather. As the smooth surface of an aircraft deteriorates, the surface roughness increases. These conditions cause early boundary layer separation and a corresponding increase in skin friction drag. This paper will seek to demonstrate the effect of surface roughness on the wake of a cylindrical body, thereby providing an estimation of the drag increase by comparing the wake of a smooth cylinder to a rough cylinder. The experiment will be conducted in the University of Texas at San Antonio’s low speed, 1.5’x1.5’ wind tunnel. A traverse mechanism will be employed over the cross-sectional area of the test section at increasing axial distances behind the bodies. In this way, the complete profile of the wake can be observed as it develops.

Using this method, the author will evaluate the wake profile and the effect of surface roughness on the skin friction drag of a fundamental aerodynamic shape under the greater context of aircraft efficiency.

    

Thermal-fluctuation-induced vortex shedding behind a circular cylinder

We examine the role played by thermal molecular fluctuations near the critical Reynolds number Re_c for the onset of vortex shedding behind a circular cylinder. Using the direct simulation Monte Carlo (DSMC) method, we show that molecular fluctuations exhibit nontrivial spatiotemporal correlations even far below Re_c. As Re_c is approached from below, the fluctuation amplitude increases dramatically until macroscopic vortex shedding is established. These results are consistent with previous observations of the onset of convection rolls in Rayleigh-Bénard convection and show that thermal fluctuations can also play a significant role in the onset of instabilities in open shear flows.

This paper describes objective technical results and analysis. Any subjective views or opinions that might be expressed in the paper do not necessarily represent the views of the U.S. Department of Energy or the United States Government. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology and Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525.