Development of coherent structures in the separated shear layer and wake of an airfoil in low-Reynolds-number flows was studied experimentally for a range of airfoil chord Reynolds numbers, 55 × 10 3 ≤ Re c ≤ 210 × 10 3 , and three angles of attack, α = 0°, 5° and 10°. To illustrate the effect of separated shear layer development on the characteristics of coherent structures, experiments were conducted for two flow regimes common to airfoil operation at low Reynolds numbers: (i) boundary layer separation without reattachment and (ii) separation bubble formation. The results demonstrate that roll-up vortices form in the separated shear layer due to the amplification of natural disturbances, and these structures play a key role in flow transition to turbulence. The final stage of transition in the separated shear layer, associated with the growth of a sub-harmonic component of fundamental disturbances, is linked to the merging of the roll-up vortices. Turbulent wake vortex shedding is shown to occur for both flow regimes investigated. Each of the two flow regimes produces distinctly different characteristics of the roll-up and wake vortices. The study focuses on frequency scaling of the investigated coherent structures and the effect of flow regime on the frequency scaling. Analysis of the results and available data from previous experiments shows that the fundamental frequency of the shear layer vortices exhibits a power law dependency on the Reynolds number for both flow regimes. In contrast, the wake vortex shedding frequency is shown to vary linearly with the Reynolds number. An alternative frequency scaling is proposed, which results in a good collapse of experimental data across the investigated range of Reynolds numbers.

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On vortex shedding from an airfoil in low-Reynolds-number flows

[1] The turbulent flows and tangled magnetic fields of the Earth's plasma sheet are explored theoretically and by means of ISEE-2 plasma and magnetic-field measurements. The goal is to obtain a basic understanding of (1) the dynamics, (2) the driving, and (3) the dissipation of the turbulence. Dynamically, the turbulence of the plasma sheet appears to be a turbulence of eddies, rather than a turbulence of Alfven waves or other MHD modes. In this respect, it is similar to the two-dimensional turbulence of the solar wind. Previously published statistical arguments that the correlation length (= integral scale = eddy size) of the turbulence fluctuations in the plasma sheet is leddy ∼ 1.6 RE are confirmed by analyzing plasma sheet magnetic-field measurements during two special “sweeping” intervals that follow the passage of interplanetary shocks. For dissipation of the turbulence, two mechanisms appear to be important. The first is a cascade of energy in the turbulence to small spatial scales, where internal dissipation at non-MHD spatial scales should occur. The second mechanism is electrical coupling of the turbulent flows to the resistive ionosphere, which introduces a “quasi-viscosity” to the plasma sheet. This quasi-viscosity is complicated owing (1) to a time delay associated with Alfven-transit-time coupling (introducing a viscoelasticity to the turbulence), (2) to a scalesize dependence of the coupling (introducing a hypoviscosity), and (3) to a dependence of the coupling on the sign of the flow shear (introducing a sign-vorticity effect). For the coupling of the plasma sheet turbulence to the ionosphere, retarded-time Reynolds numbers R* are derived to describe the importance of the resulting dissipation (quasi-viscosity) and a Deborah number D is derived to describe the importance of the time lag (elasticity). The difference of the plasma sheet turbulence from homogeneous turbulence is discussed; this dissimilarity is owed to (a) dissipation at all wave numbers in the plasma sheet, (b) the presence of boundaries, and (c) the limited range of spatial scales that will allow scale-invariant dynamics. A better description of the plasma sheet turbulence would be “turbulence in a box” or a turbulent wake.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/2002JA009625

MHD turbulence in the Earth's plasma sheet: Dynamics, dissipation, and driving

Self-sustained aeroelastic oscillations of a NACA0012 airfoil at low-to-moderate Reynolds numbers

Boundary layer and turbulent wake development for a NACA 0025 airfoil at low Reynolds numbers was studied experimentally. Wind tunnel experiments were carried out for a range of Reynolds numbers and three angles of attack. Laminar boundary layer separation occurs on the upper surface of the airfoil for all Reynolds numbers and angles of attack examined. Two flow regimes are investigated (i) boundary layer separation without reattachment and (ii) separation bubble formation. The results suggest that coherent structures form in the separated flow region and the wake of the airfoil for both flow regimes. The formation of the roll-up vortices in the separated shear layer is linked to inviscid spatial growth of disturbances and is attributed to the Kelvin-Helmholtz instability. Linear stability theory can be employed to adequately describe the salient characteristics of such vortices and the initial stage of the separated shear layer transition. The development of the roll-up vortices leads to boundary layer transition, and the vortices break down during the transition process. Vortex shedding also occurs in the airfoil wake and vortices form in the near-wake region. It is shown that the boundary layer behavior has a profound effect on the identified coherent structures, and each of the two flow regimes is associated with distinctly different vortex shedding characteristics.

Coherent structures in an airfoil boundary layer and wake at low Reynolds numbers

Lift force and the near wake of an NACA 0012 airfoil were measured over the angle (α) of attack of 0°–90° and the chord Reynolds number (Re
 c
 ), 5.3 × 103–5.1 × 104, with a view to understand thoroughly the near wake of the airfoil at low- to ultra-low Re
 c
 . While the lift force is measured using a load cell, the detailed flow structure is captured using laser-Doppler anemometry, particle image velocimetry, and laser-induced fluorescence flow visualization. It has been found that the stall of an airfoil, characterized by a drop in the lift force, occurs at Re
 c
  ≥ 1.05 × 104 but is absent at Re
 c
  = 5.3 × 103. The observation is connected to the presence of the separation bubble at high Re
 c
 but absence of the bubble at ultra-low Re
 c
 , as evidenced in our wake measurements. The near-wake characteristics are examined and discussed in detail, including the vortex formation length, wake width, spanwise vorticity, wake bubble size, wavelength of K–H vortices, Strouhal numbers, and their dependence on α and Re
 c
 .

The ultra-low Reynolds number airfoil wake

Flow patterns and characteristics of vortex shedding and shear-layer instability of a NACA 0012 cantilever wing are experimentally studied. Smoke-wire and surface oil-flow techniques are employed to visualize the flow patterns and evolution of vortex shedding. Hot-wire anemometers are used to characterize the frequency domain of the unsteady flow structures. Several characteristic flow modes are classified in the domain of chord Reynolds number and root angle of attack. Effects of the juncture and wing tip are discussed. Vortex shedding can be classified into four characteristic modes. Vortex shedding at low and high angles of attack are found to have different dominant mechanisms. Effects of the juncture and wing tip on the vortex shedding are discussed. Shear-layer instabilities are found to be closely related to the behaviors of the vortex shedding. Behaviors of the shear-layer instabilities can be traced back to the characteristics of the boundary layer on the suction surface of the airfoil.

Vortex shedding and shear-layer instability of wing at low-Reynolds numbers

Velocity field of a bluff-body wake

The flow structures in the near wake region of the unducted double concentric jets at low Reynolds numbers are studied by smoke-wire flow visualization technique. Four typical characteristic flow regimes—weak flow, pre-penetration, transition, and penetration—are identified for different jet velocities in the near disk region. Flow patterns and behavior in each characteristic flow regime are investigated. The contours of the separation surfaces and the lengths of the recirculation zone in various flow regimes are correlated with nondimensional parameters. The recirculation length reaches a maximum in the transition region. The toroidal recirculation region exhibits both expelling and shear-layer vortex shedding. The shedding processes are presented, and the frequencies are correlated with Strouhal number and central-to-annular jet velocity ratio. Nomenclature D - diameter of circular disk, 20 mm Da = outer diameter of annular jet, 30 mm Dc = exit diameter of central jet, 3.4 mm / = frequency of vortex shedding, Hz Ja = momentum flux of annular jet, pau2a Jc = momentum flux of central jet, pcwj Lr = axial length of recirculation zone R - radius of circular disk, 10 mm Rea = Reynolds number of annular jet based on the disk diameter Rec - Reynolds number of central jet based on the central jet diameter r = radial coordinate, originated from center of circular disk St = Strouhal number, fD/ua ua = average exit velocity of annular jet uc = average exit velocity of central jet ud = displacement velocity, 03uc- ua wmax = maximum half-width of the recirculation zone Z = axial coordinate, originated from center of circular disk pa = mass density of annular flow pc = mass density of central jet

Chih L. Lin

Papers

Vortex shedding and shear-layer instability of wing at low-Reynolds numbers

Velocity field of a bluff-body wake

Visualized Flow Patterns of Double Concentric Jets at Low Annulus Velocities