Bulletin of the American Physical Society
72nd Annual Meeting of the APS Division of Fluid Dynamics
Volume 64, Number 13
Saturday–Tuesday, November 23–26, 2019; Seattle, Washington
Session C10: Turbulent Boundary Layers I |
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Chair: Hassan Nagib, IIT, Chicago Room: 3A |
Sunday, November 24, 2019 8:00AM - 8:13AM |
C10.00001: Intermediate scaling for streamwise mean velocity and variance in a turbulent boundary layer Sourabh Diwan, Jonathan Morrison In this work, we use an intermediate length scale ($y_{m}^{+})$ proportional to the square root of friction Reynolds number and an associated velocity scale ($u_{m})$ to scale the streamwise mean velocity and variance in the intermediate region of a turbulent boundary layer (TBL; Diwan and Morrison TSFP-11, 2019). Towards this we make use of the high-Reynolds-number TBL data available in the literature. The mean velocity is plotted in defect formulation, i.e., $U-U(y_{m})/u_{m}$. The intermediate-scaled mean velocity and variance exhibit Reynolds-number invariance over a certain region around $y/y_{m}=$1. This implies existence of a Reynolds-number independent log law in terms of the intermediate variables for the mean velocity and variance. The classical ``Karman constant'' and ``Townsend-Perry constant'' are expressed in terms of the log-law constants obtained from the intermediate scaling and their dependence on Reynolds number examined. The present work suggests a three-layer asymptotic structure for the TBL, with each layer governed by distinct length and velocity scales, which results in two overlap layers (Afzal, Ing.-Arch. 1982). We discuss the relevance of the power/log law behavior of the mean velocity in the overlap layers, based on the ratio of the velocity scales of the adjacent layers. . [Preview Abstract] |
Sunday, November 24, 2019 8:13AM - 8:26AM |
C10.00002: Log-law \& power-law: local self-similarity of a flat-plate boundary layer Joseph Ruan, Guillaume Blanquart A large controversy in the previous decade for flat-plate boundary layers was on the scaling of the defect layer with respect to different velocity scales, made prominent by George \& Castillo (1997). The lack of enough large Reynolds number experiments and simulations makes the choice of appropriate velocity scale rather difficult. We show mathematically that the differences between the scaling descriptions (using the free-stream velocity or the friction velocity as a scaling parameter) may in fact be negligible for local regions of the boundary layer. We verify from a variety of simulation frameworks that the differences between the two scalings are in fact small for flat-plate boundary layers. Furthermore, we identify scalings of the wall-normal velocity profile as providing contributions of a similar order to the flat-plate boundary layer. [Preview Abstract] |
Sunday, November 24, 2019 8:26AM - 8:39AM |
C10.00003: A Spectral-Scaling Based Extension to the Attached Eddy Model of Wall-Turbulence Dileep Chandran, Jason Monty, Ivan Marusic An extension to the attached eddy model (AEM) for the logarithmic region of turbulent boundary layers is presented here. The extension is driven by the scaling of two-dimensional (2-D) spectra of the streamwise velocity component, measured at friction Reynolds numbers ranging from 2400 to 26000. The conventional AEM assumes the boundary layer to be populated with hierarchies of self-similar wall-attached ($Type\,A$) eddies alone. While $Type\,A$ eddies represent the dominant energetic large-scale motions at high Reynolds numbers, the scales that are not represented by such eddies are observed to carry a significant proportion of the total kinetic energy. Therefore, in the present study, we propose an extended AEM that incorporate two additional representative eddies. These eddies, named $Type\,C_A$ and $Type\,SS$, represent the self-similar but wall-detached low-Reynolds number features, and the non-self-similar wall-attached superstructures, respectively. The extended AEM is observed to predict reasonably well a greater range of energetic length scales and capture the low- and high-Reynolds number scaling trends in the 2-D spectra of all three velocity components. [Preview Abstract] |
Sunday, November 24, 2019 8:39AM - 8:52AM |
C10.00004: Spatio-Temporal Characteristics of Coherent Structures in Shear-Dominated Flows Taygun Recep Gungor, Ayse Gul Gungor, Yvan Maciel, Mark Phil Simens The energy and Reynolds stress carrying structures are investigated using three direct numerical simulation databases. The first and second databases are non-equilibrium adverse gradient pressure (APG) turbulent boundary layers (TBLs) with $Re_\theta$ reaching 8000. In the second case, the turbulent activity in the inner layer ($y/\delta<0.1$) is artificially eliminated to examine outer of layer APG TBLs in the absence of near-wall turbulent activity. The last one is a homogeneous shear flow (HSF) database that provides information about a shear dominated flow without a wall. The turbulence statistics and structures in three flow cases are compared to understand similarities and differences between the outer layer of APG TBLs and HSF. Results of the manipulated APG TBL indicate that outer layer turbulence sustains itself when there is no turbulence activity in the inner layer and the spatial-temporal characteristics of the energetic structures are similar to the structures found in the original APG TBL. Furthermore, Reynolds stress carrying structures in the APG TBLs resemble the ones in HSF when their dimensions are scaled with the Corrsin length scale. [Preview Abstract] |
Sunday, November 24, 2019 8:52AM - 9:05AM |
C10.00005: Reynolds number dependence of turbulence statistics near the turbulent/non-turbulent interfacial layer in turbulent boundary layer Xinxian Zhang, Tomoaki Watanabe, Koji Nagata Direct numerical simulations (DNS) of a temporally developing turbulent boundary layer (TBL) are performed for investigating the Reynolds dependence of the turbulent/non-turbulent interfacial layer (TNTI layer). The Reynolds number based on the momentum thickness ranges from 2000 to 13000 in the present DNS. The outer edge of the TNTI layer, called irrotational boundary, is detected as an isosurface of vorticity magnitude, and the conditional statistics are calculated conditioned on the distance from the irrotational boundary. The results show that the mean thickness of the TNTI layer divided by the Kolmogorov scale is almost constant for different Reynolds numbers when the Kolmogorov scale is taken near the TNTI layer. On the other hand, the mean thickness normalized by Taylor microscale decreases as the Reynolds number increases. Influence of the wall on the statistics near the TNTI layer are shown to be stronger for a lower Reynolds number. Geometry of the irrotational boundary is also studied for the mean curvature and surface area. It is shown that the mean curvature normalized by the Kolmogorov scale has a similar probability density function for all the Reynolds numbers while the surface area increases with the Reynolds number. [Preview Abstract] |
Sunday, November 24, 2019 9:05AM - 9:18AM |
C10.00006: Where is the wall? Ricardo Garcia-Mayoral, Joseph Ibrahim, Garazi Gomez-de-Segura Textured surfaces with small texture size can increase or reduce turbulent drag, compared to a smooth wall, by imposing different virtual origins for the different velocity components, as proposed by Luchini et al. (1991) for the streamwise and spanwise components. We extend this idea by imposing different virtual origins for all three velocities using Robin, slip-length-like boundary conditions in direct numerical simulations. We show that the change in drag depends only on the offset between the virtual origin for the mean velocity profile, typically set by the streamwise slip length, and the virtual origin for turbulence (embodied by the quasi-streamwise vortices of the near-wall cycle), set by the wall-normal and spanwise slip lengths. We demonstrate that, other than by the offset between these origins, turbulence remains essentially smooth-wall-like, and show how to obtain the position of the virtual origins for the mean velocity and for turbulence from the three slip-length coefficients, and from them the change in drag. [Preview Abstract] |
Sunday, November 24, 2019 9:18AM - 9:31AM |
C10.00007: Quantifying Reynolds stresses in the planar transitional T3-serious flows Fan Tang, Wei-Tao Bi, Zhen-Su She The transitional flow with a rapid change of friction coefficient in the streamwise direction is a subject of enormous technological impact, but difficult to quantify, even for simple geometry such as flow passing a smooth flat plate. Recently, a comprehensive theory of turbulent boundary layer is constructed via a Lie-group symmetry approach, yielding a multi-layer description of four stress lengths in the wall-normal direction. Here, we report its extension to transitional TBL, with a unified quantitative description for both the Reynolds shear stress and normal stresses (turbulence intensities) throughout the transition region. Specifically, the transition and subsequent evolution to fully developed TBL are quantified with a streamwise multilayer description (starting from the leading edge) of two key parameters (a near-wall eddy length, and kappa -- a bulk flow parameter), which display a scaling change from laminar to turbulent regime. For the T3-serious planar transitional flows with varying incoming turbulence intensity and pressure gradient covering both natural and bypass transitions, the new theory predicts simultaneously, for the first time, the friction coefficient and wall-normal mean (velocity and turbulent kinetic energy) profiles throughout the entire flow domain. In summary, all four Reynolds stress components are successfully predicted for transitional planar boundary layer, promising future simpler and more accurate transitional model for engineering applications. [Preview Abstract] |
Sunday, November 24, 2019 9:31AM - 9:44AM |
C10.00008: Near-asymptotics overlap solutions for transport moments in turbulent channesl and boundary layers William George, Jean-Marc Foucaut, Jean-Philippe Laval The log profile overlap solutions for turbulent channel have been complemented recently by solutions for the dissipation$^{1}$, $\varepsilon$ and the kinetic energy$^2$, $\langle q^2 \rangle/2$. The dissipation varies as $1/y^+$, while the turbulence kinetic energy varies logarithmically. The Reynolds shear stress is nearly constant. We show from similar arguments that the transport moments, $T =-\langle p v \rangle/\rho - \langle q^2 v \rangle/2 +2 \nu \langle u_i s_{ij} \rangle$, also vary logarithmically. So all the terms in the kinetic energy balance in overlap region, $[\partial T/\partial y - \langle uv \rangle dU/dy - \varepsilon]=0$, vary inversely with $y^+$. Boundary layer results are the power-law equivalents, but indistinguishable. Both are shown to be consistent with recent experimental and DNS data. This presents a problem for the usual eddy viscocity models for this region, $\nu_t \propto \langle q^2 \rangle^2 / \varepsilon$, since both cannot be true. References: 1) Wosnik, M. {\it etal} (2000) JFM 421, 115; 2) Hultmark, M. (2012) JFM 707,575 [Preview Abstract] |
Sunday, November 24, 2019 9:44AM - 9:57AM |
C10.00009: Revealing Some Roots to Our Uncertainty Regarding Values of Von K\'arm\'an Constants Hassan Nagib, Lucia Mascotelli, Gabriele Bellani, Alessando Talamelli Three different fits of logarithmic dependence of centerline velocity, $U^+_{CL}$, in pipe flow at CICLoPE, with nearly equal representation of experimental data over range $8,000 < Re_\tau < 40,000$ have been used to generate synthetic data that are densely spaced with Reynolds number. A higher order term proportional to inverse of $Re_\tau$ was incorporated into one. Two approaches to uncertainty analysis of three sets of synthetic data were used to study dependence of uncertainty of extracted values of $\kappa_{CL}$: Random Sampling of Full Range of Uncertainty and All Possible Permutations of Extreme Uncertainties. Role of low Reynolds number data and accuracy of pressure transducer used to measure pressure gradient along pipe were examined. Results reveal following mean values and uncertainties from measurements by the multiple-transducer pressure scanner that was used: $\kappa_{CL} = 0.44 \pm 0.062$ for all Reynolds numbers, and $\kappa_{CL} = 0.45 \pm 0.038$ for data with $Re_\tau > 12,000$. More significantly, we conclude that CICLoPE requires a more accurate pressure scanning method for determining $dp/dx$; e.g., using a Scanivalve connected to a single more accurate pressure transducer. Such an approach has potential of reducing uncertainty by an order of magnitude. [Preview Abstract] |
Sunday, November 24, 2019 9:57AM - 10:10AM |
C10.00010: Turbulent flow field in the viscous sublayer: statistics and structures. Santosh Kumar Sankar, Jiarong Hong The study of wall-bounded turbulence has largely focused on the buffer and logarithmic regions above the wall. However, the need to unravel the effects of sublayer roughness structures on turbulence (Evans \textit{et al.} PNAS 2018, 115, 1210-1214) requires measurements that can fully resolve the sublayer flow, which are challenging with current state-of-art techniques. Specifically, the spatial averaging effects of hot-film probes (along probe length) as well as particle image velocimetry (PIV) based experiments (across light sheet thickness) lead to large uncertainties when approaching the wall. Using digital Fresnel reflection holography (DFRH) introduced in Kumar \textit{et al.} [Opt. Express 2018, 26(10), 12779-12789] which records backscattered signal from tracers, we can measure 3D flow fields within the viscous sublayer at high resolution. Such measurements enable us to observe and quantify meandering particle trajectories below 1 wall unit which indicating strong spanwise acceleration and an instantaneously linear streamwise velocity profile with varying slopes. In addition, the streamwise velocity PDF shows a positive skewness decreasing with wall normal distance and the limiting value of the streamwise turbulence intensity is higher than the ones reported from prior studies. [Preview Abstract] |
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