The axisymmetric boundary layer beneath a Rankine-like vortex

 An experimental investigation of the three-dimensional boundary layer induced by a Rankine-like vortex with its axis normal to a stationary disk is described. The velocity field through the boundary layer was measured for Reynolds number Re (based on the tangential velocity and radius at the disk edge) ranging from 10 000 to 25 000 at various radial distances by means of a 4-beam, 2-component Laser Doppler Anemometer. Our results show that the nature of the boundary layer is affected by two factors: an inflexional instability caused by the crossflow velocity profile and a stability factor caused by the favorable pressure gradient. At lower Reynolds number, the radial pressure gradient has a very strong stabilizing effect on the boundary layer and acts to revert it to its laminar state upstream of the effusing core. At higher Re the inflexional instability caused by the crossflow velocity dominates while the stabilizing influence of the favorable pressure gradient recedes. As such, laminar reversion likely occurs closer to the effusion core. Thus, the point of laminar reversion moves closer to the effusion core as the Reynolds number is increased. Received 23 May 1996 / Accepted 29 July 1996     

Strong vortex/boundary layer interactions

Detailed measurements with hot-wires and pressure probes are presented for the interaction between a turbulent longitudinal vortex pair with common flow down, and a turbulent boundary layer. The interaction has a larger value of the vortex circulation parameter, and therefore better represents many aircraft/vortex interactions, than those studied previously. The vortices move down towards the boundary layer, but only the outer parts of the vortices actually enter the it. Beneath the vortices the boundary layer is thinned by lateral divergence to the extent that it almost ceases to grow. Outboard of the vortices the boundary layer is thickened by lateral convergence. The changes in turbulence structure parameters in the boundary layer appear to be due to the effects of extra-rate-of-strain produced by lateral divergence (or convergence) and by free-stream turbulence. The effect of the interaction on the vortices (other than the inviscid effect of the image vortices below the surface) is small. The flow constitutes a searching test case for prediction methods for three-dimensional turbulent flows.     

Strong vortex/boundary layer interactions

This is the second of two papers on the interaction between a longitudinal vortex pair, produced by a delta-wing at angle of attack, and a turbulent boundary layer developing on a flat plate. In the first paper only the outer parts of the vortices entered the boundary layer whereas in this paper the vortices merge with it. In the resultant interaction, the boundary layer between the vortices is kept thin by lateral divergence and a three-dimensional separation line is formed outboard of each vortex. Turbulent, momentum-deficient fluid containing longitudinal vorticity is entrained from the boundary layer along these lines and wrapped around the vortices. As a consequence, the turbulent region of the vortices increases in size and the circulation slowly decreases. It is shown that the flow near the separation line and in the vortices is complicated, and this interaction is expected to be more difficult to calculate than the first. Detailed mean flow and turbulence measurements are reported.     

Nonlinear interaction of a large vortex with a boundary layer

The nonlinear problem of boundary layer instability under the influence of a plane vortex is investigated for high Reynolds numbers. The vortex occupies the entire thickness of the boundary layer and has a longitudinal dimension of the order of the Tollmien-Schlichting wavelength. The initial vortex is rapidly swept away by the flow, inducing a Stokes layer near the surface of the plate. Expanding, this layer reaches the dimensions of the viscous sublayer of free interaction theory, where wave packet generation takes place. In the case in question a feature of the nonlinear stage of development of the disturbances is the formation of a concentrated vortex, which arises in the Stokes layer and grows rapidly, whereas the wave packet propagated ahead of it remains linear. From the calculations there emerges a tendency for the new vortex to be formed above the wail, whereas the maximum vorticity of the vortex generated in the Stokes layer corresponds to the wall itself.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.1, pp. 70–77, January–February, 1993.The authors are grateful to V. V. Kozlov for his interest in their work.     

Interaction of an oscillating vortex with a turbulent boundary layer

An oscillating vortex embedded within a turbulent boundary layer was generated experimentally by forcing a periodic lateral translation of a half-delta wing vortex generator. The objective of the experiment was to investigate the possibility that a natural oscillation, or meander, might be responsible for flattened vortex cores observed in previous work, which could also have contaminated previous turbulence measurements. The effect of this forced oscillation was characterized by comparison of measurements of the mean velocities and Reynolds stresses at two streamwise stations, for cases with and without forcing. The Reynolds stresses, especially w, were affected significantly by the forced oscillation, mainly through contributions from the individual production terms, provided the vortex was not too diffuse.List of Symbols a amplitude of forced vortex motion - f frequency of forced vortex generator motion - l vortex generator root chord - L flow length scale - R _Y , R _Z vortex core radial dimensions in vertical and spanwise directions, respectively - R_r vortex circulation Reynolds number R = / - u, v, w instantaneous velocity components in X, Y, Z directions - U, V, W mean velocities; shorthand notation for u, , w - X, Y, Z right-hand Cartesian streamwise, vertical, and spanwise coordinate directions - boundary-layer thickness - overall circulation - air kinematic viscosity - _x streamwise vorticity, _X = W/Y–V/d+t6Z - ( )₀ reference value (measured at X = 10 cm) - ( )c refers to vortex center - ( ) _max maximum value for a particular crossflow plane - ( ) (overbar) time average - ( ) (prime) fluctuating component, e.g., u=U+u     

The boundary layer on the free surface of a hollow vortex

Several problems are known which are associated with the circular motion of a viscous incompressible fluid with a rotating cylinder[l, 2]. In the present paper we consider the case of unsteady circular motion of a viscous fluid with a cavity in the fluid.     

Structure of a bathtub vortex: importance of the bottom boundary layer

A bathtub vortex in a cylindrical tank rotating at a constant angular velocity Ω is studied by means of a laboratory experiment, a numerical experiment and a boundary layer theory. The laboratory and numerical experiments show that two regimes of vortices in the steady-state can occur depending on Ω and the volume flux Q through the drain hole: when Q is large and Ω is small, a potential vortex is formed in which angular momentum outside the vortex core is constant in the non-rotating frame. However, when Q is small or Ω is large, a vortex is generated in which the angular momentum decreases with decreasing radius. Boundary layer theory shows that the vortex regimes strongly depend on the theoretical radial volume flux through the bottom boundary layer under a potential vortex : when the ratio of Q to the theoretical boundary-layer radial volume flux Q _b (scaled by ${2\pi R^2 ( \Omega \nu )^\frac{1}{2}}$ ) at the outer rim of the vortex core is larger than a critical value (of order 1), the radial flow in the interior exists at all radii and Regime I is realized, where R is the inner radius of the tank and ν the kinematic viscosity. When the ratio is less than the critical value, the radial flow in the interior nearly vanishes inside a critical radius and almost all of the radial volume flux occurs only in the boundary layer, resulting in Regime II in which the angular momentum is not constant with radius. This criterion is found to explain the results of the laboratory and numerical experiments very well.     

Receptivity of a flat plate boundary layer to a free stream axial vortex

A single free stream axial vortex of controlled strength and position was used to investigate a vortical receptivity of Blasius boundary layer. Excited boundary-layer disturbances were dominated by streamwise velocity perturbations, that grew downstream essentially linearly with the streamwise coordinate. It was shown that the disturbance characteristics are in agreement with data of previous experiments performed under natural and control conditions concerning the ‘by-pass’ transition initiated at high free stream disturbance levels. It was proved that the role of the leading edge in the receptivity process and disturbance growth under consideration is not dominant.     

Flow structure in a vortex chamber

The structure of a swirl flow in a vortex chamber is studied. Distributions of the azimuthal and axial components of velocity are obtained almost in the entire volume of the chamber. A pattern of streamlines of this flow is constructed, and the mechanism of the emergence of a reverse flow directed toward the closed end face of the chamber is identified.     

Numerical simulation of quasi-streamwise hairpin-like vortex generation in turbulent boundary layer

A mechanism for generation of near wall quasi-streamwise hairpin-like vortex （QHV） and secondary quasi-streamwise vortices （SQV） is presented. The conceptual model of resonant triad in the theory of hydrodynamic instability and direct numerical simulation of a turbulent boundary layer were applied to reveal the formation of QHV and SQV. The generation procedures and the characteristics of the vortex structures are obtained, which share some similarities with previous numerical simulations. The research using resonant triad conceptual model and numerical simulation provides a possibility for investigating and controling the vortex structures, which play a dominant role in the evolution of coherent structures in the near-wall region.     

Receptivity of the inclined-cylinder attachment-line boundary layer to vortex perturbations

The receptivity of the boundary layer in the neighborhood of the attachment line of a cylinder inclined to the flow with respect to periodic vortex perturbations frozen into the stream is investigated. The problem considered simulates the interaction between external turbulence and the leading-edge swept wing boundary layer. It is shown that if the direction of the external perturbation vector is almost parallel to the leading edge, then the external perturbations are considerably strengthened at the outer boundary layer edge. This effect can cause laminar-turbulent transition on the attachment line at subcritical Reynolds numbers.Translated from Izvestiya Rossiiskoi Academii Nauk, Mekhanika Zhidkosti i Gaza, No. 6, 2004, pp. 72–85. Original Russian Text Copyright © 2004 by Ustinov.     

Effect of air jet vortex generators on a shock wave boundary layer interaction

The effect of upstream injection by means of continuous air jet vortex generators (AJVGs) on a shock wave turbulent boundary layer interaction is experimentally investigated. The baseline interaction is of the impinging type, with a flow deflection angle of 9.5° and a Mach number M _e  = 2.3. Considered are the effects of the AJVGs on the upstream boundary layer flow topology and on the spatial and dynamical characteristics of the interaction. To this aim, Stereoscopic Particle Image Velocimetry has been employed, in addition to hot-wire anemometry (HWA) for the investigation of the unsteady characteristics of the reflected shock. The AJVGs cause a reduction of the separation bubble length and height. In addition, the energetic frequency range of the reflected shock is increased by approximately 50%, which is in qualitative agreement with the smaller separation bubble size.     

Turbulent wake and vortex shedding for a stack partially immersed in a turbulent boundary layer

The effect of the jet-to-cross-flow velocity ratio, R, on the turbulent wake and Kármán vortex shedding for a cylindrical stack of aspect ratio AR=9 was investigated in a low-speed wind tunnel using thermal anemometry. The cross-flow Reynolds number was Re_D=2.3×10⁴, the jet Reynolds number ranged from Re_d=7.6×10³ to 4.7×10⁴, and R was varied from 0 to 3. The stack was partially immersed in a flat-plate turbulent boundary layer, with a boundary layer thickness-to-stack-height ratio of δ/H=0.5 at the location of the stack. From the behaviour of the turbulent wake and the vortex shedding, the flow around the stack could be classified into three regimes depending on the value of R, which were the downwash (R<0.7), cross-wind-dominated (0.7R<1.5), and jet-dominated (R1.5) flow regimes. Each flow regime had a distinct structure to the mean velocity (streamwise and wall-normal directions), turbulence intensity (streamwise and wall-normal directions), and Reynolds shear stress fields, as well as the variation of the Strouhal number and the power spectrum along the stack height.     

Flow structure in a flat vortex chamber

We investigate a flow in a flat vortex chamber in which the distance between the end walls is smaller than the radius of the chamber. The study was mainly performed by optical methods: a Töpler device was employed, with the Foucault knife replaced by a diaphragm. It is shown that the flow in the chamber has a complicated spatial structure. In addition to the basic helical flow, an intense “transverse” rotation of the type of Taylor-Görtler vortices occurs. In contrast to previously studied flows, where these vortices were observed near a concave surface, in the motion considered transverse vortices occur in the entire working volume of the chamber. In this case, four parallel vortex filaments are formed. The high intensity of the vortices has allowed one to visualize them by the Töpler method and by “tinting” the flow by highly disperse particles. Quantitative dependences of the dimensions of the vortex cells on the flow regime, i.e., on the pressure of gas deceleration, were obtained.     

Evolution of vortex structure in boundary layer transition induced by roughness elements

The particle image velocimetry (PIV) and hydrogen-bubble visualization technique are used to investigate the flat-plate boundary layer transition induced by an array of roughness elements. The streamwise evolutions of the mean and fluctuation velocity are analyzed, and the critical Reynolds number Re _k,c is determined between 339 and 443 under current experimental setup. The hairpin vortices shed from supercritical roughness elements are visualized by swirling strength, in which two pairs of counter-rotating vortices can be observed: one vortex pair is the manifestation of the neck of the hairpin vortices shed from the top of the roughness; the other vortex pair, which originates from the lower part of the roughness, comes from the streamwise vortices that are constantly perturbed by the hairpin vortex shedding.     

Investigation of a fluidized bed in a vortex chamber

Results on the tangential velocity in a fluidized bed measured by a laser Doppler velocimeter and by a mechanical propeller are presented. The reasons for the difference in the bed rotation velocities obtained by these measurement techniques are analyzed on the basis of numerical calculations of the multiphase flow dynamics.