Bulletin of the American Physical Society
61st Annual Meeting of the APS Division of Fluid Dynamics
Volume 53, Number 15
Sunday–Tuesday, November 23–25, 2008; San Antonio, Texas
Session EA: Turbulent Boundary Layers: Theory |
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Chair: Kenneth S. Ball, Virginia Polytechnic Institute and State University Room: 001A |
Sunday, November 23, 2008 4:10PM - 4:23PM |
EA.00001: Near-wall behavior of turbulent wall-bounded flows Mohamed Gad-el-Hak, Matthias Buschmann A data base compiling a large number of results from direct numerical simulations and physical experiments is used to explore the properties of shear and normal Reynolds stresses very close to the wall of turbulent channel/pipe flows and boundary layers. Three types of scaling are mainly investigated:\ classical inner, standard mixed, and pure outer scaling. The study focuses on the near-wall behavior, the location and the value of the peak Reynolds shear stress and the three normal stresses. A primary observation is that all of these parameters show a significant K\'{a}rm\'{a}n number dependence. None of the scalings investigated works in an equal manner for all parameters. It is found that the respective first-order Taylor series expansion satisfactorily represents each stress only in a surprisingly thin layer very close to the wall. In some cases, a newly introduced scaling based on $u_{\tau}^{3/2}u_{e}^{1/2}$ offers a remedy. [Preview Abstract] |
Sunday, November 23, 2008 4:23PM - 4:36PM |
EA.00002: Recent developments in scaling of wall-bounded flows Matthias H. Buschmann, Mohamed Gad-el-Hak Proper scaling of a fluid flow permits convenient, dimensionless representation of experimental data, prediction of one flow based on a similar one, and extrapolation of low-Reynolds-number, laboratory-scale experiments to field conditions. This is a particularly powerful technique for turbulent flows where analytical solutions derived from first principles are not possible. We extend in this presentation our recent work on scaling of turbulent wall-bounded flows ({\it Prog.\ Aerospace Sciences} {\bf 42}, p.\ 419--467, 2007) with respect to the most topical developments. The actual research tendencies in scaling go more and more toward investigating boundary layers under the influence of pressure gradient and/or of wall-roughness. Additionally, some new ideas employing local Kolmogorov scales arose. All together four main groups of questions are formulated that hopefully will be answered by future research. [Preview Abstract] |
Sunday, November 23, 2008 4:36PM - 4:49PM |
EA.00003: $2D/3C$ Model of Turbulence in Plane Couette Flow Dennice Gayme, Beverley McKeon, Antonis Papachristodoulou, John C. Doyle Given the consensus that turbulent flow is characterized by coherent structures and observations of streamwise-elongated structures in numerical simulations and experiments (in the near wall region), we model the mean behavior of fully developed turbulent plane Couette flow using a streamwise constant projection of the Navier Stokes (NS) equations, (the so-called $2D/3C$ model). The unforced $2D/3C$ model has been analytically shown to have a single globally stable solution. This property lends to analysis of the system using tools from robust control theory where one can represent model uncertainties or experimental errors through the addition of noise forcing. In the present work this nonlinear $2D/3C$ model is driven with small amplitude stochastic noise to produce fully developed turbulent plane Couette flow with low order statistics that are qualitatively consistent with experiments. The large scale features of the resulting flow are compared to both experiments (Kitoh and Umeki 2008) and DNS data (Tsukahara, Kawamura and Shingai 2006). [Preview Abstract] |
Sunday, November 23, 2008 4:49PM - 5:02PM |
EA.00004: Correlation of Fluctuating Vorticity in Turbulent Wall Layers Ronald Panton It is commonly known that Reynolds shear stress $$ scales with the friction velocity $u_{\ast }^{2}$. On the other hand, Degraaff and Eaton ( JFM, \textbf{422, }p 319 ) and Metzger and Klewicki ( P of F, \textbf{13}, p 6 92 ) have shown that the streamwise Reynolds stress \textit{$<$uu$>$} scales more nearly as $U u_{\ast }$. Townsend proposed that motions were ``active'' if they contributed to the Reynolds shear stress and ``inactive'' otherwise. Here, Townsend's definition is modified to say that motions are ``active'' if they scale with $u_{\ast }$; the same scaling as the Reynolds stress. A fluctuation that does not scale with $u_{\ast }$ is ``inactive.'' Vorticity profiles from the DNS (described in the various papers of Del Alamo, Jimenez, Zandonade, Moser, and Hoyas (P of F \textbf{15}, L-41; JFM, \textbf{500},p135, P of F, \textbf{18}, 011702) ) are reviewed. It is found that, in the limit of high Reynolds number, the outer region is free of vorticity. In the inner region the vortcity $<${\_}$_{y}${\_}$_{y}>$ is active with no inactive component. The other components, $<${\_}$_{x}${\_}$_{x}>$ and$<${\_}$_{z}${\_}$_{z}>$, have active components that scale as $<${\_}{\_}{\_}${\rm g}{\rm v}{\rm g}{\rm o} u_{\ast }^{4}$\textit{/{\_}}$^{{\rm y}}) $and inactive components that scale as $<${\_}{\_}{\_}${\rm g}{\rm v}{\rm g}{\rm o}{\rm o} u_{\ast }$\textit{/{\_}${\rm p}$}$^{{\rm y}} u_{\ast }U. $Since at the wall the vorticity and shear stress are proportional, the wall stress fluctuations are found to be: $<${\_}$_{x{\rm w}}{\rm g}${\_}$_{x{\rm w}}>$ / ${\rm o}$\textit{{\_}}$^{{\rm y}} u_{\ast }^{3}U)=0.007$and $<${\_}$_{z{\rm w}}{\rm g}${\_}$_{z{\rm w}}>$ / ${\rm o}$\textit{{\_}}$^{{\rm y}} u_{\ast }^{3}U)=$ 0.0038. [Preview Abstract] |
Sunday, November 23, 2008 5:02PM - 5:15PM |
EA.00005: The Reynolds shear stress in zero pressure gradient turbulent boundary layers derived from log-law asymptotics Peter A. Monkewitz, Hassan M. Nagib The Reynolds shear stress (RS) in zero pressure gradient turbulent boundary layers is established using recently developed composite mean velocity profiles based on the ``log-law'' in the overlap region between inner and outer profiles. The contribution of the normal stress difference is discussed and considered to be of secondary importance. From this analysis, an asymptotic expansion for the maximum RS and its location is developed. The hypotheses underlying this analysis are discussed and the results are compared with experiments and DNS. Using the friction velocity as scale, the analytic approximation of the RS agrees reasonably well with low-Re experimental results. However, when comparing with high-Re experiments, the agreement is generally limited as the experimental accuracy and resolution becomes problematic near the wall. Comparison with DNS, on the other hand, is shown to be affected by the delicate numerical treatment of the free stream boundary condition. Finally, the present asymptotics will be compared to the results of Sreenivasan, Panton and others for channels and pipes. [Preview Abstract] |
Sunday, November 23, 2008 5:15PM - 5:28PM |
EA.00006: Optimal transient growth and very large scale structures in turbulent boundary layers G. Pujals, C. Cossu, S. Depardon We compute the optimal energy growth sustained by a turbulent boundary using the mean flow proposed by Monkewitz et al. (Phys. Fluids 2007) and the associated eddy viscosity as recently done for channel flows (del \'Alamo \& Jim\'enez, J. Fluid Mech. 2006). Large transient energy growths are obtained for streamwise vortices evolving into streamwise streaks. For sufficiently large Reynolds numbers two distinct optimal spanwise walengths exist. The first, $\lambda^+ \sim 80 $, scales in inner units and is associated with most probable buffer layer streaks. The second, $\lambda \sim 8\,\delta$ scales in outer units and corresponds to optimal vortices centred near the boundary layer edge and to optimal streaks spreading in the whole boundary layer. These streaks scale in outer variables in the outer region and in wall units in the inner region of the boundary layer. [Preview Abstract] |
Sunday, November 23, 2008 5:28PM - 5:41PM |
EA.00007: Modified law of the wall leading to turbulent channel flow universal velocity profiles valid down to $Re_{\tau}=395$ Gregoire Winckelmans, Laurent Bricteux Velocity profile modeling is revisited using the results from databases of turbulent channel flow DNS at $Re_{\tau}=u_{\tau}\,h/ \nu= 2000$, $950$, $550$, and $395$. We consider the turbulent region: $y^+ = Re_{\tau}\,\eta$ (with $\eta=y/h$) larger than $70$). A new model for the effective turbulent viscosity, $\nu_t=-\overline{u'v'}/\frac{d\overline{u}}{dy}$, is proposed, that fits well the DNS results all the way to the channel center. The velocity profile is then obtained by integration: it corresponds to a ``modified law of the wall,'' $\frac{1} {\kappa}\left(\log(y^+ + y_0^+) -\eta\right) + C$, with the added classical ``law of the wake,'' $D\,g(\eta)$. The new $- \eta$ term in the modified law of the wall is really required in such still limited Reynolds number channel flows, as an important correction to the usual log term: both terms ``work together,'' as both are multiplied by the same $\frac{1}{\kappa} $ value (recall that $D$ is not related to $\kappa$). Only at the highest Reynolds numbers does this correction become negligible. As to the $y_0^+$ shift in the log term itself (value around 6), something also recently proposed by Spalart et al (Phys. Fluids in press), it too is required as a consequence of the $\nu_t$ near wall behavior. The present velocity profile is quite universal: it fits very well, with the same value of all constants, all $Re_{\tau}$ cases. In particular, the von K\`arm\`an constant is obtained as $\kappa=0.37$: same as Zanoun et al (Phys. Fluids 15 (10):3079, 2003), and close to $0.38$ as Spalart et al. [Preview Abstract] |
Sunday, November 23, 2008 5:41PM - 5:54PM |
EA.00008: Further insight into physics of rough-wall turbulent boundary layer Kiran Bhaganagar, Vejapong Juttijudata, Mehmet Sen To get a good understanding of the effect of surface-roughness in altering the flow in a turbulent boundary layer it is important to understand the alterations in the dynamical activity of the flow. For this purpose direct proper orthogonal decomposition (POD) has been used as a tool. The data used for the POD has been obtained from direct numerical simulation of flow in a channel with egg-carton roughness elements. In this talk the effects of surface-roughness on the temporal flow dynamics such as bursting frequency of the energetic structures in the flow will be discussed. VITA detection technique has been used to obtain the bursting frequency. It has confirmed that rough-wall has a shorter bursting period and a higher turbulence activity compared to the smooth-wall. The results have confirmed the existence of roll and propagating modes for flow over rough-wall. In addition to the turbulent kinetic energy, the concept of entropy that has been introduced in this study within the context of degree of distribution of energy over range of scales, is a useful metric to categorize the rough-wall flow dynamics. [Preview Abstract] |
Sunday, November 23, 2008 5:54PM - 6:07PM |
EA.00009: Advection, diffusion \& dispersion: effective diffusion for transient mixing vs. stirring with steady sources \& sinks Charles R. Doering, Zhi Lin The effective diffusion coefficient $\kappa_{eff}$ of a flow is often defined in terms of passive tracer particle dispersion. For some high P\'eclet number flows $\kappa_{eff}$ may be as large as $\kappa_{molec} \times Pe^{2}$ where $\kappa_{molec}$ is the molecular diffusion coefficient and the P\'eclet number $Pe = U\ell/\kappa_{molec}$ is defined in terms of characteristic velocity ($U$) and length ($\ell$) scales in the flow. On the other hand for stirring in the presence of steady sources and sinks an equivalent diffusion coefficient $\kappa_{eq}$ may be defined in terms of (statistical steady state) passive scalar concentration variance suppression. A theorem states that $\kappa_{eq} \le \kappa_{molec} \times Pe \times (L/\ell)$ as $Pe \rightarrow \infty$ where $L$ is a characteristic length scale of the sources-sink distribution. We discuss the origin and resolution of this discrepancy: effective diffusion coefficients proportional to $Pe^{2}$ arise in the large time asymptotic limit of particle dispersion while equivalent diffusion coefficients defined by concentration variance suppression for scalars sustained by steady sources are dominated by short-time transport characteristics of the flow. The theories may be reconciled by considering a time dependent effective diffusion coefficient that includes the transient---and not just time asymptotic---tracer particle dispersion. [Preview Abstract] |
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