Bulletin of the American Physical Society
64th Annual Meeting of the APS Division of Fluid Dynamics
Volume 56, Number 18
Sunday–Tuesday, November 20–22, 2011; Baltimore, Maryland
Session A7: Turbulent Boundary Layers I |
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Chair: Yiannis Andreopoulos, City College of New York Room: 310 |
Sunday, November 20, 2011 8:00AM - 8:13AM |
A7.00001: Predictive wall model and LES applied to the flat-plate turbulent boundary layer M. Inoue, R. Mathis, I. Marusic, D.I. Pullin An empirical inner-outer wall model (Mathis {\it et al}, {\it JFM 2011}) is used, together with time series of stream-wise, resolved-scale velocities within the logarithmic region obtained from large-eddy simulations (LES), to calculate turbulence intensities $\overline{u'^2}/u_\tau^2$ in the inner region of the zero-pressure gradient turbulent boundary layer. Comparisons are made of the LES-wall-model results with both equivalent predictions using experimental time series, and also with direct experimental measurements at $Re_\tau = 7,300, 13,600$ and $19,000$. LES combined with the wall model are then used to extend the inner-layer predictions to Reynolds numbers within a gap in $\log(Re_\tau)$ space between laboratory measurements and surface-layer, atmospheric experiments. [Preview Abstract] |
Sunday, November 20, 2011 8:13AM - 8:26AM |
A7.00002: Low-order representation of turbulent pipe flow Jean-Loup Bourguignon, Beverley McKeon A simple model of pipe flow turbulence based on a forcing-response analysis of the Navier-Stokes equations (McKeon \textit{et al.} 2010) is presented and used to investigate the dynamics of the large-scale structures. The model is validated against pipe flow DNS data and naturally leads to a low-order representation of the flow as a sum of traveling waves corresponding to the response modes predicted by the model. The low-order flow representation captures a significant fraction of the turbulence intensity and Reynolds stress in the core of the pipe and is highly correlated to the large-scale structures observed in the DNS data. Furthermore, by considering the forcing modes associated with each response mode in the low-order flow representation the amplification mechanisms sustaining the large-scale structures can be identified. [Preview Abstract] |
Sunday, November 20, 2011 8:26AM - 8:39AM |
A7.00003: Classification of critical points in a converging-diverging turbulent channel flow Ra\'{u}l Bayo\'{a}n Cal, Murat Tutkun, {\O}yvind Waage Hanssen-Bauer, Anders Helgeland, {\O}yvind Andreassen, Jean-Philippe Laval Based on Direct Numerical Simulations of a channel with a bump,\footnote{M. Marquillie et al. (2008), J. Turbulence, vol 9, no 1, pp. 1-23.} a critical point generation and classification is performed. Topological features of the flow are found relating critical point type with the distribution of Jacobian Determinants as well as the behavior of skin friction. Eight different types of points are found within the flow and these are visualized using different forms of the Line Integral Convolution visualization technique as described by Aasen and Furuheim (2008).\footnote{M. Aasen and K. Furuheim (2008), M.Sc. thesis, Department of Informatics, University of Oslo, Oslo, Norway.} It is found that the determinant analysis can be a useful method for data reduction of critical points. Local minima and maxima of the skin friction coefficient, $C_f$, are reliable indicators of development of extreme determinants. Further explanation of the physics is done through the analysis of the velocity and pressure iso-surfaces. [Preview Abstract] |
Sunday, November 20, 2011 8:39AM - 8:52AM |
A7.00004: Spatial locality of turbulent fluxes: the filtering approach Scott Salesky, Marcelo Chamecki A number of methods exist for decomposing turbulent fluxes, including those that are local in scale (e.g. cospectra, structure functions) or in scale and space (e.g. wavelets). We propose a new spatially local decomposition of turbulent fluxes based on a filtering operation where the filter width $\Delta$ defines the scale of the local fluctuations. The Germano identity is used to show the ensemble average of the local flux recovers the Reynolds-averaged flux at any given scale $\Delta$. Properties of local flux-gradient relationships are investigated using atmospheric surface layer data from the Advection Horizontal Array Turbulence Study (AHATS). In atmospheric surface layer measurements, random error in measured turbulent fluxes occurs due to insufficient averaging times for the time mean to converge to the ensemble mean by the ergodic hypothesis. Maximum possible averaging times are limited due to nonstationary large scale atmospheric motions. A new method of estimating random error in atmospheric surface layer data based on local fluxes is evaluated, and other applications of local fluxes are considered. [Preview Abstract] |
Sunday, November 20, 2011 8:52AM - 9:05AM |
A7.00005: Turbulent Boundary Layers: An Energy Harvesting Perspective Pierre Lemaire, Huseyin Dogus Akaydin, Niell Elvin, Yiannis Anreopoulos A turbulent boundary layer (TBL) carries mechanical energy distributed over a range of temporal and spatial scales. The inherent unsteadiness in the TBL induces a strain field on a solid body immersed in it. The induced strain can be converted to electrical energy using a solid body of piezoelectric material. This energy harvesting method can be used for developing self-powered flow sensors. In the present work, we experimentally investigate the interaction of a TBL with a thin flexible beam. The vibration frequency and amplitude of the beam is measured using strain gages. Three relevant parameters are the length of the beam ($l)$, the distance of the beam from the wall ($h)$ and the free stream speed ($V_{\infty })$. While $V_{\infty }$ changes the TBL characteristics, $h$ and $l$ primarily affect the fluid-structure interaction. In our wind tunnel tests we traversed the piezoelectric beam across the TBL by varying these three parameters for the purpose of finding values maximizing the vibrations. We present a ``power map'' of the TBL indicating the optimal $h$ and $V_{\infty }$ values for a given value of $l$. We also discuss the effect of $l$ in flow-induced vibrations by presenting spectrum analysis of strain signals at various $h$ and $V_{\infty }$. [Preview Abstract] |
Sunday, November 20, 2011 9:05AM - 9:18AM |
A7.00006: A Multi-scale Approach for the Thermally Stratified Turbulent Boundary Layer Sam Notaro, Gustavo Rivera-Rosario, Luciano Castillo The governing equations have been established for the inner and outer regions of the turbulent boundary layer for thermally stratified flows subject to external pressure gradient. It was shown that the pressure gradient across the boundary layers contains the wall-normal Reynolds stress and the buoyancy term. Therefore, the streamwise momentum equation includes the buoyancy terms and can be employed to obtain the scales of the velocity and thermal fields. Furthermore, it has been clearly identified that single scaling analysis cannot satisfy the equations of motion while satisfying the boundary layers simplifications. Moreover, using a multi-scale similarity approach of the equations of motion a buoyancy parameter, $\beta_T$ has been derived and must be constant for an equilibrium flow to exist. From this new parameter a power law for the growth of the thermal boundary layer exists given as, $\delta_T \sim$ $\Delta {T_w}^{1/\beta_{T}}$, in which the growth is controlled by the strength of the stratification. In addition, it was shown that the outer mean temperature scales with the temperature difference, $\Delta T_{w}$, and the inverse of the Richardson number. [Preview Abstract] |
Sunday, November 20, 2011 9:18AM - 9:31AM |
A7.00007: Linear analysis of transient growth in stably-stratified, turbulent channel flow Juan Carlos del Alamo, Carlos Yanez, Manuel Garcia-Villalba We studied stably-stratified, fully-developed, turbulent channel flow using linear stability analysis. The analysis considered the mean velocity and density profiles extracted from DNS [1] calculations as base flow, and included a linear model to represent the energy dissipation and scalar diffusion felt at the large scales as a consequence of the small scales. The flow was found to be asymptotically stable in all cases but transient growth of initial perturbations was observed. The perturbations showing maximal transient growth corresponded well with spanwise waves in the center of the channel and with streaks in the near wall region, which were both observed in the DNS. In particular, their sizes and convection velocities were reasonably well predicted by the linear model. Component-wise analysis revealed that, while the streaks were formed by the vertical stirring of mean shear, the transient amplification of the spanwise waves was reminiscent of the Orr mechanism. \\[4pt] [1] M. Garc\'{\i}a-Villalba and Juan C. Del \'{A}lamo, Turbulence modification by stable stratification in channel flow. Phys. Fluids, 23:045104, 2011. [Preview Abstract] |
Sunday, November 20, 2011 9:31AM - 9:44AM |
A7.00008: Inverse Magnus effect on a rotating sphere Jooha Kim, Hyungmin Park, Haecheon Choi, Jung Yul Yoo In this study, we investigate the flow characteristics of rotating spheres in the subcritical Reynolds number ($Re$) regime by measuring the drag and lift forces on the sphere and the two-dimensional velocity in the wake. The experiment is conducted in a wind tunnel at $Re=0.6 \times 10^{5} - 2.6 \times 10^{5}$ and the spin ratio (ratio of surface velocity to the free-stream velocity) of 0 (no spin) - 0.5. The drag coefficient on a stationary sphere remains nearly constant at around 0.52. However, the magnitude of lift coefficient is nearly zero at $Re<2.0 \times 10^{5}$, but rapidly increases to 0.3 and then remains constant with further increasing Reynolds number. On the other hand, with rotation, the lift coefficient shows negative values, called inverse Magnus effect, depending on the magnitudes of the Reynolds number and spin ratio. The velocity field measured from a particle image velocimetry (PIV) indicates that non-zero lift coefficient on a stationary sphere at $Re>2.0 \times 10^{5}$ results from the asymmetry of separation line, whereas the inverse Magnus effect for the rotating sphere results from the differences in the boundary-layer growth and separation along the upper and lower sphere surfaces. [Preview Abstract] |
Sunday, November 20, 2011 9:44AM - 9:57AM |
A7.00009: A novel Lie-group analysis for wall-bounded turbulent flows Xi Chen, Zhen-Su She, Fazle Hussain Symmetry analysis based on the Lie-group method is the most effective method for solving nonlinear problems. Here, we present a novel Lie-group analysis for wall-bounded turbulent flow in following ways: First, the governing equation for symmetry analysis is inner and outer mean momentum equation, instead of the Navier-Stokes equation. Second, the dilation and Galilean transformations are applied to space variable, mean velocity, and in particular to the mixing length and its spatial gradient. Finally, a transition ansatz is formulated, as a special choice of the similarity solution, which accomplishes a composite solution across adjacent layers. With all of these, we achieve a rare occasion that symmetry is used to construct the complete solution: an analytic expression for the entire mixing length profile and then the mean velocity profile. Thus, a classical turbulence closure problem is analytically solved by combining multi-layer perturbation with Lie-group analysis. [Preview Abstract] |
Sunday, November 20, 2011 9:57AM - 10:10AM |
A7.00010: Accurate determination of Karman constant and mean velocity in high Reynolds number turbulent pipe Zhen-Su She, Xi Chen, You Wu, Fazle Hussain In 1904, Prandtl1 presented the boundary layer concept, which initiated a century old search for analytic solution of turbulent flow near a wall. Here, we present a theory combining multi-layer perturbation with Lie-group analysis, for a complete determination of the similarity solution in turbulent channel and pipe flows. In particular, we present a procedure enabling close interaction with empirical data, which accomplishes an objective determination of key parameters involved in the solution. A remarkable outcome is all data suggest a universal Karman constant, having the value of 0.45. Based on measured parameter, the predicted MVPs agree with experimental/simulation data within 1{\%} at all points for a wide range of Re covering nearly three decades. Because both multi-layer and Lie-group symmetry are general, this is a promising framework for mean flow solutions of a wide class of turbulent flows, including incompressible, compressible and rough-wall boundary layers, and Rayleigh-Benard convection. [Preview Abstract] |
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