Bulletin of the American Physical Society
2005 58th Annual Meeting of the Division of Fluid Dynamics
Sunday–Tuesday, November 20–22, 2005; Chicago, IL
Session LS: Boundary Layer Instabilities III |
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Chair: Peter Duck, University of Manchester Room: Hilton Chicago Stevens 4 |
Tuesday, November 22, 2005 8:00AM - 8:13AM |
LS.00001: Significant Surface Heat Transfer Rate Enhancement and Scalar Transport under Secondary Instabilities of Steady Longitudinal Vorticity Elements in Boundary Layers. J. T. C. Liu Nonlinear wavy secondary instability of steady longitudinal vortices in boundary layer flow, characterized by the sinuous mode, give rise to skin friction well above the local turbulent boundary layer values$^{1}$ because the Reynolds stress contributes to fluctuation momentum flux towards the wall$^{1}$. Measurements of time-averaged surface heat transfer rates in air show a similar behavior$^{2}$. Similarity between dimensionless total streamwise velocity and dimensionless temperature is valid for the steady problem$^{3}$ for Prandtl number unity, but is hampered here by the presence of fluctuation streamwise-pressure gradient which has no counterpart in the scalar transport equation. Estimates for not-so-long waves relative to the local conductivity scale length show that the fluctuation streamwise pressure gradient is small, thus making similarity approximately possible. We conclude that the normal-to-wall fluctuation heat flux contributes to transport towards the wall, squashing the iso-temperature lines and increasing the temperature gradient thus make plausible a mechanism for the overshoot of surface heat transfer rate. $^{1}$ J.T.C. Liu and I.G Girgis, Abstract in ICTAM'04 Proceedings, Warsaw (2004). $^{2}$ L. Momayez, P. Dupont and H. Peerhossaini, Int. J. Heat Mass Transfer \textbf{47}, 3783 (2004). $^{3 }$J.T.C. Liu and A.S. Sabry, Proc. Royal Soc. \textbf{A432}, 1 (1991). [Preview Abstract] |
Tuesday, November 22, 2005 8:13AM - 8:26AM |
LS.00002: Triad Resonance in Transition to Turbulence in Rotating Disk Boundary Layer Eric Matlis, Thomas Corke This work is a study of the resonant interaction between traveling cross-flow modes and low-mode-number stationary modes in transition to turbulence of the three-dimensional boundary layer flow over a rotating disk. A distributed array of ink dots are placed on the disk surface to enhance a narrow band of azimuthal and radial wave numbers of both stationary and traveling modes. The size of the dots is small ($d=1.6$mm, $h=0.06$ mm, $h(\omega / \nu)^{1/2}$ = 0.16) so that the disturbances they produce is linear. Two hot-wires are used to perform spatial correlation measurements giving the wavenumber vector. The time series were sorted in terms of the separate contributions of the traveling and stationary modes. Cross-bicoherence was used to identify triad phase locking between frequencies of traveling and stationary cross-flow modes. Frequencies that satisfied this condition were then shown to satisfy wave number matching required for a triad resonance. The triad resonance was found to be the dominant mechanism for spectral broadening during transition to turbulence. This mechanism can account for large wavelength stationary modes observed in flow visualization on disks and swept wings. [Preview Abstract] |
Tuesday, November 22, 2005 8:26AM - 8:39AM |
LS.00003: Experimental Investigation of Absolute Instability of a Rotating-Disk Boundary Layer Hesham Othman, Thomas Corke A series of experiments were performed to study the absolute instability of Type I travelling cross-flow modes in the boundary layer on a smooth disk rotating at constant speed. Controlled temporal disturbances were introduced by a short-duration air pulse from a hypodermic tube located above the disk and outside the boundary layer. The air pulse was positioned just outboard of the critical radius for Type I cross-flow modes. A hot-wire sensor was positioned at different spatial locations on the disk to document the growth of disturbances produced by the air pulses. Ensemble averages conditioned on the air pulses revealed wave packets that evolved in time and space. Two amplitudes of air pulses were used. The lower amplitude produced wave packets with linear amplitude characteristics that agreed with linear-theory wall-normal eigenfunction distributions and spatial growth rates. The higher amplitude pulse produced wave packets that had nonlinear amplitude characteristics. The space-time evolution of the leading and trailing edges of the wave packets were followed well past the critical radius for the absolute instability based on Lingwood (1995). With the linear amplitudes, the absolute instability was dominated by the convective modes, agreeing with the linear DNS simulations of Davies and Carpenter (2003). With the nonlinear amplitudes, the wave packet development resembled those of Lingwood (1996) suggesting the amplitudes in that case were finite. [Preview Abstract] |
Tuesday, November 22, 2005 8:39AM - 8:52AM |
LS.00004: Global stability of the rotating disk boundary layer and the effects of suction and injection Christopher Davies, Christian Thomas The von Karman boundary layer over a rotating disk is known to be absolutely unstable (Lingwood 1995). However, numerical simulations indicate that this absolute instability does not give rise to an unstable linear global mode, when account is taken of the radial dependence of the basic flow (Davies \& Carpenter 2003). Analogous behaviour can be found in solutions of the linearized complex Ginzburg-Landau equation, similar to those derived by Hunt \& Crighton (1991). These solutions show that detuning, arising from the radial variation of the local temporal frequency, may be enough to globally stabilize disturbances, even when local temporal growth rates increase with radius. Depending on the precise balance between the radial increase in growth rates and the corresponding shifts in frequency, it is possible for an absolutely unstable flow to remain globally stable. For the von Karman rotating disk boundary layer, the earlier numerical simulation results suggest that the balance in this case does in fact give rise to global stability. Similar behaviour has been identified in more recent numerical simulations that we have conducted, where mass injection was introduced at the disk surface. The modified flow still appears to be globally stable, despite the fact that injection is known to be locally destabilizing. More interestingly, it was also found that globally unstable behaviour was promoted when suction was applied. [Preview Abstract] |
Tuesday, November 22, 2005 8:52AM - 9:05AM |
LS.00005: Convective and absolute nature of boundary layer instabilities in an opened rotating cavity Bertrand Viaud, Eric Serre, Patrick Bontoux Direct Numerical Simulation of incompressible Navier-Stokes equations has been used to investigate the impulse response of a rotating boundary layer. The aim is to extend recent theoretical works of Pier [J. Fluid Mech. \emph{487}, 315 (2003)] and Davies \& Carpenter [J. Fluid Mech. \emph{486}, 287 (2003)] about the role played by the absolute instability in the occurence of turbulence. Thus, the identification of such a mode would open prospect in the developpement of efficient control strategy of transition. By the way of a highly accurate three dimensional spectral solver, spatio-temporal properties of convective type I (inviscid) and type II (viscous) instabilities have been studied, and the results appear to be in good agreement with experimental and theoretical works (Serre \& al. [Phys. Fluids, \emph{16 3} (2004)]). Computations at high Reynolds numbers, larger than the theoretical critical Reynolds number of absolute mode are in progress. In this prospect, the spectral solution enables precise determination of the spatial and frequential characterictics of this mode. [Preview Abstract] |
Tuesday, November 22, 2005 9:05AM - 9:18AM |
LS.00006: Three-Dimensional Instabilities of Laminar Flow in a Rough Channel Jerzy M. Floryan Flow in a channel with distributed surface roughness is considered. Results of the linear stability analysis show that the presence of the roughness destabilizes the traveling-wave instability as well as introducing a new instability that manifests itself in the form of streamwise vortices. The critical conditions for the occurrence of both instabilities are given for different classes of roughness shapes. It is shown that these conditions can be predicted with a reasonable accuracy in the case of an arbitrary (but Fourier transformable) roughness by considering only the leading Fourier mode (wavy-wall model). It is argued that the onset of any type of instability can be used to formally define the conditions that determine when the rough wall ceases to behave as hydraulically smooth wall. [Preview Abstract] |
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