Session EP: Basic Separated Flows

Unsteady Aspects of Turbulent Boundary Layer Separation

This experimental study is focused on the physics of unsteady turbulent boundary layer separation under conditions relevant to the dynamic stall process that occurs in helicopter rotors. A flat boundary layer development plate allows for the growth of a nominally zero pressure gradient turbulent boundary layer of thickness sufficient for high spatial resolution measurements. Downstream of the flat plate, a convex ramp section imposes a streamwise adverse pressure gradient that gives rise to boundary layer separation. In order to impose an unsteady pressure gradient, an airfoil equipped with leading edge plasma flow control is located above the ramp section. With the airfoil placed at a post-stall angle of attack, the boundary layer on the ramp remains attached but near a state of incipient separation. Plasma flow control is used to alternately attach and separate the airfoil flow which gives rise to unsteady turbulent boundary layer separation on the convex ramp. The resulting unsteady turbulent boundary layer separation is investigated via phase-locked two-component PIV, unsteady surface pressure measurements and high speed digital imaging.   

An Experimental Study of Near Wake Structure Behind Two Circular Cylinders with Heat Addition

In this study, we present flow visualization data on the effect of heat addition on the near wake structure behind two identical circular cylinders separated in the span-wise direction perpendicular to the flow at Re = 350. Flow visualization is done using the hydrogen bubble technique. The spacing between the two cylinders is T/D = 1.7, where T = center-to-center spacing and D = cylinder diameter. The gap flow is known to be intermittently bi-stable at this spacing, which is clearly demonstrated in the study. The present study focuses on the response of the gap flow to the heat release in one cylinder. The study shows clearly that the gap flow deflects towards the heated cylinder resulting in a narrower wake behind the heated cylinder as compared to the wake behind the unheated cylinder. The response of the gap-flow is further demonstrated by turning the heat off on one cylinder and switching the heat on the other cylinder resulting in the gap flow deflection as well. The cylinders in the present experiments are heated by joule heating with an estimated wall temperature difference of 30$^{\circ}$C in water at the given Reynolds number resulting in Richardson number of about 0.2 in the present experiments.   

Three-dimensional Dynamics of the Gravity Current Flow past a Submerged Cylinder

The three-dimensional dynamics of the gravity current flow past a submerged cylinder are investigated by means of large eddy simulations. The geometries considered are a bottom-mounted rectangular cylinder and a circular cylinder mounted above a bottom wall. The Reynolds number is of O(100). The agreement with previous experimental measurements of the drag and lift coefficients is excellent. The simulation for the rectangular cylinder case shows that the gravity current front's lobe-and cleft structure sets the characteristic length of the spanwise variation of the drag during impact, while an unsteady cellular flow structure upstream of the cylinder sets this characteristic length during the later quasi-steady stage. The simulation for the circular cylinder case shows during the quasi-steady stage the shedding of primary Karman vortices, the presence in the near wake of, apparently, secondary mode-B streamwise vortices, and an interaction further downstream between the Karman vortices and the boundary layer at the bottom wall and the shear layer between the two fluids.   

Nonlinear spacing and frequency effects of an oscillating cylinder in the wake of a stationary cylinder

Nonlinear responses to a transversely oscillating cylinder in the wake of a stationary upstream cylinder are studied theoretically by using an immersed-boundary method. It is found that flow around the two cylinders varies with different spacing between the two cylinders and the oscillation frequency of the downstream cylinder. As known in a stationary tandem-cylinder system, there exist the ``vortex suppression regime'' (VS) and the ``vortex formation regime'' (VF). These two regimes are divided by a critical spacing. When the downstream cylinder is forced to oscillate at a fixed amplitude but different frequency, different flow patterns appear in each of the regime. On the other hand, at the same oscillating frequency but different spacing, the response state (lock-in, transient or non-lock-in) changes. While each state has periodic or quasi-periodic behaviors, nonlinear responses appear. All of the analyses are based on vorticity contours, time histories of the velocities in the near wake regions, spectral analyses, and related phase portraits.   

The effect of Reynolds number on the dynamics of freely rising and falling spheres

In this study, we investigate the effect of Reynolds number on the dynamics and vorticity patterns of spheres rising or falling freely through a fluid. Initially, our experiments focused on two Reynolds numbers, \textit{Re} = 450 and 10,000. At both \textit{Re}, all falling spheres, with a mass ratio (or density relative to the fluid), $m* >$ 1, are found to descend rectilinearly. For rising spheres, we observe that contrary to previous studies, rectilinear trajectories persist until some critical mass ratio, $m*_{crit}$, below which the spheres suddenly begin to vibrate vigorously in a vertical plane. At \textit{Re} $\approx $ 10,000, we find $m*_{crit}$ = 0.61, while at \textit{Re} = 450, the critical mass is distinctly lower, $m*_{crit}$ = 0.36. To explore the dynamics of spheres over a wide range of \textit{Re}, we controlled the fluid viscosity using glycerin-water mixtures, and considered over 130 cases of $m*$ = 0.08-1.5 and \textit{Re} = 100-15,000. For all \textit{Re} studied, we find a wide range of spheres that rise rectilinearly, yielding $m*_{crit}$ significantly below 1. The only regimes observed in our study are rectilinear motion and periodic zigzag vibration. The vortex wakes for the rectilinear regime resemble those of a fixed sphere at similar \textit{Re}, either a single-sided chain (\textit{Re} = 450), or a double-sided chain (\textit{Re} $\approx $ 10,000) of vortex rings. However, for the whole range of \textit{Re} studied, we discover that the periodic zigzag regime is associated with a new vortex formation mode comprising \textit{four vortex rings} per cycle of oscillation.   

Hydrodynamic Forces On A Cylinder Vibrating Transversely And In-Line To A Steady Stream

We present computational results on the flow structure and forces in flow past a circular cylinder oscillating transversely and in-line to a uniform stream at Reynolds number 400. Three values of the transverse vibration frequency are implemented, corresponding to 1.0, 0.9 and 1.1 times the natural frequency of the Karman vortex street. The in-line vibration occurs at twice the frequency of the transverse oscillation. The cylinder thus follows an ``eight''-like trajectory, emulating the trajectory of a free vortex-induced vibration. We find that the results of the simulation are greatly influenced by the direction in which the ``eight'' figure is traversed. We distinguish between a ``counterclockwise'' mode (if the upper part of the trajectory is traversed counterclockwise), and a ``clockwise'' mode (if the upper part of the trajectory is traversed clockwise). We find that the counterclockwise mode results in larger fluid forces than the clockwise mode for the same amplitude of oscillation. The power transfer from the fluid to the cylinder remains positive for the counterclockwise mode at higher values of the amplitude-over-diameter-ratio than it does either for the clockwise mode or for a transversely only vibrating cylinder.   

LES of flows around a circular cylinder at critical and supercritical Reynolds numbers

It is well known that the flow around a circular cylinder in the critical Reynolds number region represents an intricate combination of laminar separation, turbulence transition, reattachment and turbulent separation of a boundary layer on the cylinder. According to previous experimental studies, separation bubbles are formed in association with the process of a separation-to-reattachment flow on the cylinder. Also, the structure of a separation bubble and its behavior is sensitively changed, dependent on the Reynolds number from the critical to the supercritical region. In this research, LES method is applied to the flow around a circular cylinder in the supercritical as well as the critical Reynolds number region. Detailed structures of the separation bubble are investigated by using time-sequential computed results as the Reynolds number changes. We have found a divergent type of flow with 3D structures near the reattachment area and its physical meaning is discussed.   

Flow Pattern past Two Spheres in Proximity

As a follow-up study of flow-induced forces on two nearby spheres [Phys. Fluids 19, 098103 (2007)], this paper establishes a systematic characterization of flow patterns past two identical spheres in proximity at Re=300. We consider all possible arrangements of two spheres in terms of the distance between the spheres and the angle inclined with respect to the main flow direction. It turns out that significant changes in shedding characteristics are noticed depending on how the two spheres are positioned. Ten distinct flow patterns are identified in total, and a detailed description is given to each pattern. Collecting all the numerical results obtained, we propose two comprehensive tables; one for flow pattern for each arrangement of the spheres and the other for Strouhal number of the corresponding vortex shedding. The perfect geometrical symmetry implied in the flow configuration allows one to use those tables for any two identical spheres arbitrarily positioned in physical space with respect to the main flow direction.   

Flow past an Inclined Square Cylinder

Numerical investigation has been carried out for laminar flow (\textit{Re}$\le $150) past an inclined square cylinder in cross freestream. The motivation stems from characterization of flow-induced forces on a sharp-edged cylindrical object immersed in cross flow with an angle of attack. From the viewpoint of wind hazards, this study would be the first step towards understanding flow-induced forces on cylindrical structures under a strong gust of wind. In this flow configuration, there exist two kinds of critical Reynolds numbers in laminar regime; flow separation occurs at a lower critical Reynolds number (\textit{Re}$_{c1})$ and flow becomes unsteady at an upper critical Reynolds number (\textit{Re}$_{c2})$. It is seen that the values of \textit{Re}$_{c1}$ and \textit{Re}$_{c2}$ change depending on the inclination angle (\textit{$\theta $}) of the cylinder. In particular, \textit{Re}$_{c2}$ decreases as \textit{$\theta $} increases, being consistent with the instability theory based on Stuart-Landau equation in literature. Furthermore, the cylinder vertices at which flow separation takes place are determined by \textit{$\theta $}. Consequently, key flow characteristics such as drag/lift forces on the cylinder and vortex-shedding frequency could drastically alter depending on \textit{$\theta $}. We propose contour diagrams of mean drag/lift coefficients, Strouhal number (\textit{St}) of vortex shedding, and rms of lift coefficient fluctuation$_{ }$on \textit{Re}--\textit{$\theta $} plane.