Vortical Boundary Layer Research Articles

An experimental study of the aerodynamics of micro corrugated wings at low Reynolds number

In this paper, an experimental study was performed to examine the flow characteristics of fabricated micro corrugated wings by fully mimicking the real 3D Odonata wing. For this purpose, a true scale hind wing from the Orthetrum caledonicum species with a semi span length of 60 mm was reconstructed by non-destructive close-range photogrammetry and fabricated with an advanced 3D printer. The accuracy of the proposed reconstruction technique was evaluated and compared with a 3D model of the same wing created using a Micro-Computed Tomography (CT) scanning technique to show that the close-range photogrammetry method was able to predict the pattern of micro corrugation of the wings with satisfactory fidelity. To do that, the corrugation patterns of both reconstructed wings were compared at different sections of the wings. Then, high-resolution Particle Image Velocimetry was used to investigate the flow field of the wing during gliding flight at three low Reynolds numbers Re = 5 × 103, Re = 8 × 103 and Re = 12 × 103, and angle of attack 10°. The results include free stream velocity, vorticity distribution, boundary layer, and flow visualization. The velocity contour and vorticity boundary layer of both wings were compared experimentally. The flow behavior around the corrugated patterns reconstructed from both methods were compared with satisfactory agreement. The results support that the corrugations of the wing act as turbulators to generate unsteady vorticity to transition the boundary layer from laminar to turbulent quickly, leading to delayed stall and improved aerodynamic performance. Moreover, this study shows the application of the presented photogrammetry method for corrugated wing reconstruction, which is fast, low-cost, non-destructive, with high replication accuracy for the next generation of micro air vehicles.

Hydrodynamics of two-dimensional compressible fluid with broken parity: Variational principle and free surface dynamics in the absence of dissipation

We consider an isotropic compressible non-dissipative fluid with broken parity subject to free surface boundary conditions in two spatial dimensions. The hydrodynamic equations describing the bulk dynamics of the fluid as well as the free surface boundary conditions depend explicitly on the parity breaking non-dissipative odd viscosity term. We construct a variational principle in the form of an effective action which gives both bulk hydrodynamic equations and free surface boundary conditions. The free surface boundary conditions require an additional boundary term in the action which resembles a $1+1D$ chiral boson field coupled to the background geometry. We solve the linearized hydrodynamic equations for the deep water case and derive the dispersion of chiral surface waves. We show that in the long wavelength limit the flow profile exhibits an oscillating vortical boundary layer near the free surface. The thickness of the layer is controlled by the length scale given by the ratio of odd viscosity to the sound velocity $\delta \sim \nu_o/c_s$. In the incompressible limit, $c_s\to \infty$ the vortical boundary layer becomes singular with the vorticity within the layer diverging as $\omega \sim c_s$. The boundary layer is formed by odd viscosity coupling the divergence of velocity $\boldsymbol\nabla \cdot \boldsymbol{v}$ to vorticity $\boldsymbol\nabla \times \boldsymbol{v}$. It results in non-trivial chiral free surface dynamics even in the absence of external forces. The structure of the odd viscosity induced boundary layer is very different from the conventional free surface boundary layer associated with dissipative shear viscosity.

Reconciling different formulations of viscous water waves and their mass conservation

The viscosity of water induces a vorticity near the free surface boundary. The resulting rotational component of the fluid velocity vector greatly complicates the water wave system. Several approaches to close this system have been proposed. Our analysis compares three common sets of model equations. The first set has a rotational kinematic boundary condition at the surface. In the second set, a gauge choice for the velocity vector is made that cancels the rotational contribution in the kinematic boundary condition, at the cost of rotational velocity in the bulk and a rotational pressure. The third set circumvents the problem by introducing two domains: the irrotational bulk and the vortical boundary layer. This comparison puts forward the link between rotational pressure on the surface and vorticity in the boundary layer, addresses the existence of nonlinear vorticity terms, and shows where approximations have been used in the models. Furthermore, we examine the conservation of mass for the three systems, and how this can be compared to the irrotational case.

Start-up vortex flow past an accelerated flat plate

Viscous flow past a finite flat plate accelerating in the direction normal to itself is studied numerically. The plate moves with nondimensional speed tp, where p = 0, 1/2, 1, 2. The work focuses on resolving the flow at early to moderately large times and determining the dependence on the acceleration parameter p. Three stages in the vortex evolution are identified and quantified. The first stage, referred to as the Rayleigh stage [Luchini and Tognaccini, “The start-up vortex issuing from a semi-infinite flat plate,” J. Fluid Mech. 455, 175–193 (2002)], consists of a vortical boundary layer of roughly uniform thickness surrounding the plate and its tip, without any separating streamlines. This stage is present only for p > 0, for a time-interval that scales like p3, as p → 0. The second stage is one of self-similar growth. The vortex trajectory and circulation satisfy inviscid scaling laws, the boundary layer thickness satisfies viscous laws. The self-similar trajectory starts immediately after the Rayleigh stage ends and lasts until the plate has moved a distance d = 0.5 to 1 times its length. Finally, in the third stage, the image vorticity due to the finite plate length becomes relevant and the flow departs from self-similar growth. The onset of an instability in the outer spiral vortex turns is also observed, however, at least for the zero-thickness plate considered here, it is shown to be easily triggered numerically by underresolution. The present numerical results are compared with experimental results of Pullin and Perry [“Some flow visualization experiments on the starting vortex,” J. Fluid Mech. 97, 239–255 (1980)], and numerical results of Koumoutsakos and Shiels [“Simulations of the viscous flow normal to an impulsively started and uniformly accelerated flat plate,” J. Fluid Mech. 328, 177–227 (1996)].

Particles turbulence interactions in boundary layers

AbstractTurbulent dispersed flows in boundary layers are crucial in a number of industrial and environmental applications. In most applications, the key information is space distribution of particles which is known to be strongly non‐homogeneous. Specifically, inertial particles distribute preferentially avoiding strong vortical regions and segregating into straining regions. The vortical boundary layer structures control momentum, mass, heat, and particle transfer. Coherent structures bring particles toward the wall and away from the wall and favour particle segregation in the viscous region giving rise to nonuniform particle distribution profiles which peak close to the wall. The reason for this behavior is particle inertia, which filters the high frequency turbulence fluctuations. The object of this work is to review the current understanding of turbulent boundary layer dynamics and to examine the mechanisms for particle transfer, segregation, and preferential distribution. The physical mechanisms discussed and proposed are based on Direct Numerical Simulations of turbulence and Lagrangian tracking of inertial particles.

A new matched asymptotic expansion for the intermediate and far flow behind a finite body

An approximated Navier–Stokes steady solution is here presented for the two dimensional bluff body wake region that is intermediate between the field on the body scale LD, which includes the two symmetric counter-rotating eddies, and the ultimate far wake. The nonparallelism of the streamlines in the intermediate wake cannot yet be considered negligible. The R is of the order of the critical value for the onset of the first instability and the limiting behavior for large R is not considered. The solution is obtained by matching an inner solution—a Navier–Stokes expansion in powers of the inverse of the longitudinal coordinate—and an outer solution, which is a Navier–Stokes asymptotic expansion in powers of the inverse of the distance from the body. The matching is built on the criteria that, where the two solutions meet, the longitunal pressure gradients and the vorticities must be equal and the flow toward the inner layer must be equal to the outflow from the external stream. At high orders in the inner expansion solution, the lateral decay turns out to be algebraic. This approximate solution is here examined in relation to the class of asymptotic solutions that, in the past, were obtained by adopting the rapid decay principle, which implies an irrotational outer flow. The theme running through this paper is the necessity of the addition of this criterion to the equations of motion to build a solution that describes the intermediate wake. The present solution has been obtained by relaxing the imposition of the rapid decay principle. It can be concluded that, at Reynolds numbers as low as the first critical value and where the nonparallelism of the streamlines is not yet negligible, the division of the field into two basic parts—an inner vortical boundary layer flow and an outer potential flow—is spontaneously shown up to the second order of accuracy: at higher orders in the expansion solution the vorticity is first convected and then diffused in the outer field. If exploited to represent the basic flow of bluff body wakes, the analytical simplicity of this asymptotic expansion could be useful for the nonparallel analysis of the instability of two-dimensional wakes.

Theory of weakly damped Stokes waves: a new formulation and its physical interpretation

A tractable theory for weakly damped, nonlinear Stokes waves on deep water was recently formulated by Ruvinsky & Friedman (1985a, b; 1987). In this paper we show how the theory can be simplified, and that it is equivalent to a boundary-layer model for surface waves proposed by Longuet-Higgins (1969), when the latter is generalized to include surface tension and nonlinearity. The potential part of the flow is determined by boundary conditions applied at the base of the vortical boundary layer. The theory may be of use in discussing the generation of waves by wind.

On the Dynamics of Equatorial Subsurface Countercurrents

The equatorial subsurface countercurrents (SSCC are strong, steady, geostrophically balanced eastward flows situated below the high speed core of the Equatorial Undercurrent (EUC) at ∼3–5°N and S. The dynamics of these currents are explored using a continuously stratified, vertically diffusive, linear, steady state ocean model forced by zonal winds with effectively no wind stress curl. Model results agree favorably with observations in that both EUC- and SSCC-like structures are generated. A diagnosis of the model momentum, vorticity and continuity balances at various depths and latitudes reveals that the SSCC lie outside a vertically diffusive equatorial momentum boundary layer so that both components of velocity are geostrophically balanced. They are, however, located at the poleward of a broader diffusive equatorial vorticity boundary layer. Within this boundary layer, cyclonic vorticity associated with the EUC diffuses to the level of the SSCC where it is balanced by poleward advection of planetary vorticity. Outside this boundary layer, the induced planetary vorticity advection is balanced by vortex stretching that weakens the temperature stratification to generate a thermostad-like structure. The SSCC are in turn geostrophically balanced by the meridional pressure gradients associated with this structure.

Boundary-layer Acceleration and Particle Mirroring in Pulsar Magnetospheres

Where the number density of a species becomes very small, inertial development of vorticity occurs; so a magnetospheric zone in which a species is contained must be enclosed by a vortical boundary layer. Where zones of corotating electrons and ions abut, there exists a large local non-corotational electric field, directed so as to force a merging of the electron and ion boundary layers. The poloidalaccelerations and azimuthal drift velocities generated in these layers are estimated here. Ions are accelerated to nonrelativistic or mildly relativistic poloidal speeds, then penetrate into the electron corotation zones where they are centrifugally decelerated as they travel approximately along magnetic field lines. They mirror between points above the stellar surface and the boundary layer, resumably moving to lower magnetic field lines until they reach the star. Electrons are accelerated to poloidal speeds that are relativistic for istances from the axis of rotation exceeding about 1/30 of the radius of the light cylinder. They enter the ion corotation zone where they are further accelerated as they travel approximately along outgoing portions of the closed magnetic field lines, and are then decelerated on ingoing portions. They mirror between the northern and southern boundary layers, presumably moving to lower magnetic field lines until they reach the star. The electrons in the outer parts of the ion.zone are very highly relativistic and emit gamma radiation which, in the case of the Crab pulsar, might create electron-positron pairs.