Kelvin-Helmholtz-like instabilities in turbulent flows over complex surfaces

Riblets are small surface protrusions aligned with the flow direction, which confer an anisotropic roughness to the surface [6]. We have recently reported that the transitional-roughness effect in riblets, which limits their performance, is due to a Kelvin–Helmholtz-like instability of the overlying mean flow [7]. According to our DNSs, the instability sets on as the Reynolds number based on the roughness size of the riblets increases, and coherent, elongated spanwise vortices begin to develop immediately above the riblet tips, causing the degradation of the drag-reduction effect. This is a very novel concept, since prior studies had proposed that the degradation was due to the interaction of riblets with the flow as independent units, either to the lodging of quasi-streamwise vortices in the surface grooves [2] or to the shedding of secondary streamwise vorticity at the riblet peaks [9]. We have proposed an approximate inviscid analysis for the instability, in which the presence of riblets is modelled through an average boundary condition for an overlying, spanwise-independent mean flow. This simplification lacks the accuracy of an exact analysis [4], but in turn applies to riblet surfaces in general. Our analysis succeeds in predicting the riblet size for the onset of the instability, while qualitatively reproducing the wavelengths and shapes of the spanwise structures observed in the DNSs. The analysis also connects the observations with the Kelvin–Helmholtz instability of mixing layers. The fundamental riblet length scale for the onset of the instability is a ‘penetration length,’ which reflects how easily the perturbation flow moves through the riblet grooves. This result is in excellent agreement with the available experimental evidence, and has enabled the identification of the key geometric parameters to delay the breakdown. Although the appearance of elongated spanwise vortices was unexpected in the case of riblets, similar phenomena had already been observed over other rough [3], porous [1] and permeable [11] surfaces, as well as over plant [5,14] and urban [12] canopies, both in the transitional and in the fully-rough regimes. However, the theoretical analyses that support the connection of these observations with the Kelvin–Helmholtz instability are somewhat scarce [7, 11, 13]. It has been recently proposed that Kelvin–Helmholtz-like instabilities are a dominant feature common to “obstructed” shear flows [8]. It is interesting that the instability does not require an inflection point to develop, as is often claimed in the literature. The Kelvin-Helmholtz rollers are rather triggered by the apparent wall-normal-transpiration ability of the flow at the plane immediately above the obstructing elements [7,11]. Although both conditions are generally complementary, if wall-normal transpiration is not present the spanwise vortices may not develop, even if an inflection point exists within the roughness [10]. REFERENCES [1] Breugem, W. P., Boersma, B. J. & Uittenbogaard, R. E. 2006 J. Fluid Mech. 562, 35–72. [2] Choi, H., Moin, P. & Kim, J. 1993 J. Fluid Mech. 255, 503–539. [3] Coceal, O., Dobre, A., Thomas, T. G. & Belcher, S. E. 2007 J. Fluid Mech. 589, 375–409. [4] Ehrenstein, U. 2009 Phys. Fluids 8, 3194–3196. [5] Finnigan, J. 2000 Ann. Rev. Fluid Mech. 32, 519–571. [6] Garcia-Mayoral, R. & Jimenez, J. 2011 Phil. Trans. R. Soc. A 369, 1412–1427. [7] Garcia-Mayoral, R. & Jimenez, J. 2011 J. Fluid Mech. doi: 10.1017/jfm.2011.114. [8] Ghisalberti, M. 2009 J. Fluid Mech. 641, 51–61. [9] Goldstein, D. B. & Tuan, T. C. 1998 J. Fluid Mech. 363, 115–151. [10] Hahn, S., Je, J. & Choi, H. 2002 J. Fluid Mech. 450, 259–285. [11] Jimenez, J., Uhlman, M., Pinelli, A. & G., K. 2001 J. Fluid Mech. 442, 89–117. [12] Letzel, M. O., Krane, M. & Raasch, S. 2008 Atmos. Environ. 42, 8770–8784. [13] Py, C., de Langre, E. & Moulia, B. 2006 J. Fluid Mech. 568, 425–449. [14] Raupach, M. R., Finnigan, J. & Brunet, Y. 1996 Boundary-Layer Meteorol. 78, 351–382.

Kelvin-Helmholtz-like instability of turbulent flows over riblets

The turbulent drag reduction due to riblets is a function of their size and, for different configurations, collapses well with a length scale l+g=(A+g)1/2, based in the groove cross-section Ag. The initially linear drag reduction breaks down for l+g≈11, which agrees in our DNS with the previously reported appearance of quasi-two-dimensional spanwise rollers immediately above the riblets. They are similar to those found over porous surfaces and plant canopies, and can be traced to a Kelvin-Helmholtz-like instability associated with the relaxation of the impermeability condition for the wall-normal velocity. The extra Reynolds stress associated with them accounts quantitatively for the drag degradation. An inviscid model for the instability confirms its nature, agreeing well with the observed perturbation wavelengths and shapes. The onset of the instability is determined by a length scale L+w that, for conventional riblet geometries, is proportional to l+g. The instability onset, L+w≥4, corresponds to the empirical breakdown point l+g≈11.

The transition mechanism of highly-loaded LP turbine blades

A detailed experimental investigation was conducted into the interaction of a converted wake and a separation bubble on the rear suction surface of a highly loaded low-pressure (LP) turbine blade. Boundary layer measurements, made with 2D LDA, revealed a new transition mechanism resulting from this interaction. Prior to the arrival of the wake, the boundary layer profiles in the separation region are inflexional. The perturbation of the separated shear layer caused by the converting wake causes an inviscid Kelvin-Helmholtz rollup of the shear layer. This results in the breakdown of the laminar shear layer and a rapid wake-induced transition in the separated shear layer.

The effects of a trip wire and unsteadiness on a high speed highly loaded low-pressure turbine blade

This paper presents the effect of a single spanwise 2D wire upon the downstream position of boundary layer transition under steady and unsteady inflow conditions. The study is carried out on a high turning, high-speed, low pressure turbine (LPT) profile designed to take account of the unsteady flow conditions. The experiments were carried out in a transonic cascade wind tunnel to which a rotating bar system had been added. The range of Reynolds and Mach numbers studied includes realistic LPT engine conditions and extends up to the transonic regime. Losses are measured to quantify the influence of the roughness with and without wake passing. Time resolved measurements such as hot wire boundary layer surveys and surface unsteady pressure are used to explain the state of the boundary layer. The results suggest that the effect of roughness on boundary layer transition is a stability governed phenomena, even at high Mach numbers. The combination of the effect of the roughness elements with the inviscid Kelvin-Helmholtz instability responsible for the rolling up of the separated shear layer (Stieger [1]) is also examined. Wake traverses using pneumatic probes downstream of the cascade reveal that the use of roughness elements reduces the profile losses up to exit Mach numbers of 0.8. This occurs with both steady and unsteady inflow conditions.

Lift and the leading edge vortex

Leading edge vortices are considered to be important in generating the high lift coefficients observed in insect flight and may therefore be relevant to micro-air vehicles. A potential flow model of an impulsively started flat plate, featuring a leading edge vortex (LEV) and a trailing edge vortex (TEV) is fitted to experimental data in order to provide insight into the mechanisms that influence the convection of the LEV and to study how the LEV contributes to lift. The potential flow model fits the experimental data best with no bound circulation, which is in accordance with Kelvin's circulation theorem. The lift-to-drag ratio is well approximated by the function 'cot α' for α > 15°, which supports the tentative conclusion that shortly after an impulsive start, at post-stall angles of attack, lift is caused non-circulatory forces and by the action of the LEV as opposed to bound circulation. Copyright © 2012 by C. W. Pitt Ford.

Lift and the leading-edge vortex

Flapping wings often feature a leading-edge vortex (LEV) that is thought to enhance the lift generated by the wing. Here the lift on a wing featuring a leading-edge vortex is considered by performing experiments on a translating flat-plate aerofoil that is accelerated from rest in a water towing tank at a fixed angle of attack of 15°. The unsteady flow is investigated with dye flow visualization, particle image velocimetry (PIV) and force measurements. Leading-and trailing-edge vortex circulation and position are calculated directly from the velocity vectors obtained using PIV. In order to determine the most appropriate value of bound circulation, a two-dimensional potential flow model is employed and flow fields are calculated for a range of values of bound circulation. In this way, the value of bound circulation is selected to give the best fit between the experimental velocity field and the potential flow field. Early in the trajectory, the value of bound circulation calculated using this potential flow method is in accordance with Kelvin's circulation theorem, but differs from the values predicted by Wagner's growth of bound circulation and the Kutta condition. Later the Kutta condition is established but the bound circulation remains small; most of the circulation is contained instead in the LEVs. The growth of wake circulation can be approximated by Wagner's circulation curve. Superimposing the non-circulatory lift, approximated from the potential flow model, and Wagner's lift curve gives a first-order approximation of the measured lift. Lift is generated by inertial effects and the slow buildup of circulation, which is contained in shed vortices rather than bound circulation. © 2013 Cambridge University Press.

Scaling of transitionally-rough flow structures in DNSes of channels with riblets up to Reτ=550

The linear, drag-reducing effect of vanishingly small riblets breaks down once their size is in the transitionally-rough regime. We have previously reported that this breakdown is caused by the additional Reynolds stresses produced by the appearance of elongated spanwise rollers just above the riblet surface. These rollers are related with the Kelvin--Helmholtz instability of free shear layers, and to similar structures appearing over other rough and porous surfaces. However, because of the limited Reτ=180 in our previous DNSes, it could not be determined whether those structures scaled in inner or outer units. Furthermore, it is questionable if results in the transitionally-rough regime at Reτ=180 can be extrapolated to configurations of practical interest. At such small Reynolds numbers, roughness of transitional size can perturb a large portion of the boundary layer, which is not the case in most industrial and atmospheric applications. To clarify these issues we have conducted a set of DNSes at Reτ=550. Our results indicate that the spanwise rollers scale in wall units, and support the validity of the extrapolation to configurations of practical interest.

Large eddy simulations in low-pressure turbines: Effect of wakes at elevated free-stream turbulence

The transition of a separated shear layer over a flat plate, in the presence of periodic wakes and elevated free-stream turbulence (FST), is numerically investigated using Large Eddy Simulation (LES). The upper wall of the test section is inviscid and specifically contoured to impose a streamwise pressure distribution over the flat plate to simulate the suction surface of a low-pressure turbine (LPT) blade. Two different distributions representative of a 'high-lift' and an 'ultra high-lift' turbine blade are examined. Results obtained from the current LES compare favourably with the extensive experimental data previously obtained for these configurations. The LES results are then used to further investigate the flow physics involved in the transition process.In line with experimental experience, the benefit of wakes and FST obtained by suppressing the separation bubble, is more pronounced in 'ultra high-lift' design when compared to the 'high-lift' design. Stronger 'Klebanoff streaks' are formed in the presence of wakes when compared to the streaks due to FST alone. These streaks promoted much early transition. The weak Klebanoff streaks due to FST continued to trigger transition in between the wake passing cycles.The experimental inference regarding the origin of Klebanoff streaks at the leading edge has been confirmed by the current simulations. While the wake convects at local free-stream velocity, its impression in the boundary layer in the form of streaks convects much slowly. The 'part-span' Kelvin-Helmholtz structures, which were observed in the experiments when the wake passes over the separation bubble, are also captured. The non-phase averaged space-time plots manifest that reattachment is a localized process across the span unlike the impression of global reattachment portrayed by phase averaging. © 2013 Elsevier Inc.

Electrostatic force microscopy and potentiometry of realistic nanostructured systems

We investigate the dependency of electrostatic interaction forces on applied potentials in electrostatic force microscopy (EFM) as well as in related local potentiometry techniques such as Kelvin probe microscopy (KPM). The approximated expression of electrostatic interaction between two conductors, usually employed in EFM and KPM, may loose its validity when probe-sample distance is not very small, as often realized when realistic nanostructured systems with complex topography are investigated. In such conditions, electrostatic interaction does not depend solely on the potential difference between probe and sample, but instead it may depend on the bias applied to each conductor. For instance, electrostatic force can change from repulsive to attractive for certain ranges of applied potentials and probe-sample distances, and this fact cannot be accounted for by approximated models. We propose a general capacitance model, even applicable to more than two conductors, considering values of potentials applied to each of the conductors to determine the resulting forces and force gradients, being able to account for the above phenomenon as well as to describe interactions at larger distances. Results from numerical simulations and experiments on metal stripe electrodes and semiconductor nanowires supporting such scenario in typical regimes of EFM investigations are presented, evidencing the importance of a more rigorous modeling for EFM data interpretation. Furthermore, physical meaning of Kelvin potential as used in KPM applications can also be clarified by means of the reported formalism. © 2009 American Institute of Physics.