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 ER: Turbulent Boundary Layers: High Reynolds Number |
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Chair: Javier Jimenez, Universidad Politecnica de Madrid Room: Hilton Chicago Stevens 3 |
Sunday, November 20, 2005 4:10PM - 4:23PM |
ER.00001: Reynolds Number Needed to Determine the von K\'{a}rm\'{a}n Constant Ronald Panton New precise measurement of velocity profiles and independent measurements of wall shear stress have allowed researchers to determine better values of the von K\'{a}rm\'{a}n constant, $\kappa$. The constant appears in the common part of the inner and outer velocity profiles; the log law. As the Reynolds number becomes high, the common part may be explicitly measured in the velocity profile. The question is how high does \textit{Re*} need to be before measurement will yield accurate values of the von K\'{a}rm\'{a}n constant. The answer is different for pipe flow, channel flow, boundary layers. A model of the inner flow velocity profile and Coles' wake function are combined in a composite expansion. For a given flow (wake parameter $\Pi$ and \textit{Re*} one can compute the ``Log Law Diagnostic'' function; $\gamma$ \textit{$\equiv$ y+ d u+ / d y+} and determine if 1 / $\gamma {\rm}$ becomes, for any $y+$, equal to the von K\'{a}rm\'{a}n constant. At low values of \textit{Re*} the inner and outer functions interact so strongly that 1 / $\gamma$ is never equal to $\kappa {\rm u}$ From a sequence of calculations one can determine the lowest Reynolds number for which $\kappa$ can be determined. The results depend on the wake parameter of the flow. At any Reynolds number one can determine the range of $y+$ values for which the log law should be observed. Of course, the calculated results are dependent on the assumed model. Although precise values are not accurate, they are useful as rough estimates and their trends with \textit{Re*} and $\Pi $ are to be expected. [Preview Abstract] |
Sunday, November 20, 2005 4:23PM - 4:36PM |
ER.00002: Non-Universality of K\'{a}rm\'{a}n Constant. Hassan Nagib, Kapil Chauhan, Peter Monkewitz Flat plate boundary layer experiments at high Reynolds numbers, Re$_{\theta }>$10,000, in presence of adverse and favorable pressure gradients are studied to evaluate the mean velocity profiles in the overlap region. The profiles exhibit logarithmic behavior analogous to the well documented case of zero-pressure gradient (ZPG). In contrast to the ZPG case, the pressure gradient cases exhibit systematic variations in the K\'{a}rm\'{a}n Coefficient $\kappa $ and the additive term B, which were believed to be constant based on classical arguments. The changes in $\kappa $ and B are also confirmed by very good agreement between the calculated skin friction coefficient calculated from velocity profiles utilizing relations for two-dimensional self similar flows, and that measured directly using oil-film interferometry. The variations in $\kappa $ and B are not only exhibited for the clearly non-equilibrium cases of strong favorable pressure gradient (SFPG; $\beta \approx $-0.15), but also for the mild adverse and favorable pressure gradient cases, APG ($\beta \approx $0.1 to 0.3) and FPG ($\beta \approx $-0.09 to -0.15) respectively, where the skin-friction coefficient behavior is equilibrium like. The conclusions are supported by the observed changes in the shape factor H and the Coles wake parameter $\Pi $. The variations for APG and FPG are opposite in nature when referenced to the equilibrium state of a ZPG. The results are also self-consistent and in agreement with fully developed pipe and channel flows where $\kappa $ values higher than in ZPG are found: $\kappa \approx $0.41 compared to 0.384. [Preview Abstract] |
Sunday, November 20, 2005 4:36PM - 4:49PM |
ER.00003: New Scales and Scaling Arguments in Boundary Layers. Kapil Chauhan, Hassan Nagib, Peter Monkewitz Flat plate turbulent boundary layers at high Reynolds numbers are studied based on experiments in the National Diagnostic Facility (NDF) and other measurements. The range of Reynolds number based on momentum thickness, Re$_{\theta }$, for the NDF zero-pressure gradient data is between 12,000 and 62,000. Experimental results for the mean flow are analyzed to reveal appropriate scale relations. It is found that the ratio of mean time scale, $x/U_{\infty }$, and turbulent time scale, \textit{$\delta $}$_{99}/u_{\tau }$, can be used as a significant flow parameter and not just for order of magnitude estimations. Then, the Reynolds number dependence of the wake parameter in the outer region is reevaluated and its strong dependence on the constants of the logarithmic law is assessed. Next, the behavior of the shape factor H for zero pressure gradient boundary layers is discussed in the limit of very large Reynolds numbers, where H approaches unity very slowly. Turning to the mean velocity profiles, the conventional outer scaling of the mean velocity defect is compared with other recently proposed velocity scales and it is concluded that u$_{\tau }$ is the proper velocity scale in the overlap and wake regions. Finally, a new outer length scale $\Lambda $, analogous to the outer scale used in pipes and channels, is proposed to clarify issues related to the limit of infinite Reynolds number. [Preview Abstract] |
Sunday, November 20, 2005 4:49PM - 5:02PM |
ER.00004: Some further thoughts on the zero-pressure-gradient turbulent boundary layer W.K. George In spite of its remarkable ability to describe recent friction and integral boundary layer thickness data, there have been consistent claims that power-law based theories of turbulent boundary layers are not viable. In particular it is argued that they do not properly describe the velocity data in the overlap region near the wall. These claims are examined in detail using recent experiments for which the data is publicly available. (Smith\footnote{Smith, R.\ W.\ , Ph.\ D.\ diss., Princeton, 1994.} and \"{O}sterlund\footnote{\"{O}sterlund, J.\ O.\ , Ph.D diss., KTH, 2000.}). The mean velocity data from both experiments are seen to be described by the George/Castillo/Wosnik\footnote{George, W.\ and Castillo,L. {Appl. Mech. Rev, 50},12, Pt 1, 689 - 729, 1997.}$^{,}$\footnote{Wosnik, M.\ , Ph.\ D. diss., SUNY/Buffalo, 2000.} theoretical profile to within fractions of a percent for $y^+ > 30$. [Preview Abstract] |
Sunday, November 20, 2005 5:02PM - 5:15PM |
ER.00005: Physical description of boundary layer velocity-vorticity products at high and low Reynolds numbers Paththage Priyadarshana, Joseph Klewicki The mean wall-normal gradient of the Reynolds stress is directly related to mean momentum transport and can be represented by velocity-vorticity products, $v\omega_z$ and $w\omega_y$. Here, $u$, $v$, and $w$ are streamwise, wall-normal and spanwise velocity components and, $\omega_y$ and $\omega_z$ are wall normal and spanwise vorticity components. Physical experiments were conducted to study the effects of scale separation associated with increasing Reynolds number on these velocity-vorticity products. The high Reynolds number data ($R_{\theta} \simeq O(10^6)$, $\theta$-momentum thickness) were acquired in the near neutrally stable atmospheric surface layer flow over a salt playa under both smooth and rough wall conditions. The low $R_{\theta}$ data were from a database acquired in a large scale laboratory facility at $1000< R_{\theta} < 5000$. Spectral analyses were conducted on $v\omega_z$ and $w\omega_y$ at wall normal locations, $y_p/2$ and $2y_p$, where, $y_p$ is the peak wall-normal position of Reynolds stress. The cospectra between velocity and vorticity indicate that there is a scale selection occuring at wavenumbers near the peak of the participating velocity and vorticity components. Physical interpretations are proposed to effectively identify these scale selections. \noindent This work was supported by the National Science Foundation~(grant monitor Dr. Michael W. Plesniak) and the Office of Naval Research~(grant monitor Dr. Ronald D. Joslin), respectively. [Preview Abstract] |
Sunday, November 20, 2005 5:15PM - 5:28PM |
ER.00006: Mean velocity statistics and turbulent structure in a very high Reynolds number boundary layer Scott Morris PIV measurements were acquired over a region of y+ up to 3000 in the atmospheric surface layer at the SLTEST site with a range of 6000 wall units in the streamwise direction. The surface roughness was k+=14, with a boundary layer thickness of order 100m. The thermal conditions were neutral for more than one hour prior to and after the measurement period. A total of 708 snapshots were acquired in a 25 minute period where the wind conditions were nearly stationary. In this talk, mean velocity statistics will be used in comparison to the log-law fit as well as a power law fit. RMS statistics and Reynolds stresses will be compared with lower Reynolds number data. Finally, the structure of the flow will be described both in terms of stochastic quantities, such as the two point correlation functions, as well as instantaneous visualizations of the vector field. [Preview Abstract] |
Sunday, November 20, 2005 5:28PM - 5:41PM |
ER.00007: Surface shear stress fluctuations in the atmospheric surface layer Jason Monty, Nick Hutchins, Ivan Marusic, Min Chong A lightweight, high frequency response ($25Hz$), floating element sensor was used to measure wall shear stress fluctuations in the atmospheric surface layer formed over a salt flat at the SLTEST site, Utah, USA. The sensor uses a laser position measurement system to track the motion of the floating element which consisted of a $50mm$ diameter foam disc, as described by Heuer \& Marusic (Meas. Sci. Tech., Vol. 16, 1644- -1649, 2005). The measurements were taken as part of an internationally coordinated experimental program designed to make extensive spatial and temporal measurements of velocity, temperature and wall shear stress of the surface layer. Velocity measurements were made with both a $30m$ high vertical array and a $100m$ wide horizontal array of sonic anemometers; 18 anemometers in total were employed. Cross-correlations of shear stress and streamwise velocity fluctuations were analysed in an attempt to identify structure angles in the flow. The results were also compared with experimental data from controlled, laboratory turbulent boundary layers having three orders of magnitude lower Reynolds number. [Preview Abstract] |
Sunday, November 20, 2005 5:41PM - 5:54PM |
ER.00008: Synchronous measurements of the streamwise velocity in a high Reynolds number boundary layer Beverley McKeon, Meredith Metzger Streamwise velocity measurements in the high Reynolds number turbulent boundary layer over the salt playa of Utah's western desert were made using thirty-one synchronously sampled single hot wires spaced up to a wall-normal height of 5m, or inner normalized distance $y^+ = O(10^4)$. Data were acquired under conditions of near-neutral stability, as verified by the Monin- Obukhov length, and varying wall roughness. Mean and rms velocity profiles and energy spectra will be used to illuminate the boundary layer physics and structure, with particular attention paid to identification of momentum equation scaling regions and high Reynolds number features. The support of a Royal Society Dorothy Hodgkin Fellowship (BJM) and ONR (MM) is gratefully acknowledged. [Preview Abstract] |
Sunday, November 20, 2005 5:54PM - 6:07PM |
ER.00009: Boundary layer surface vorticity flux measurements at high Reynolds number Joe Klewicki, David Kenney Under isothermal conditions vorticity enters a flow through a flux at the wall. If the walls are stationary, this flux is proportional to the pressure gradients in the plane of the surface. Wall vorticity flux measurements were acquired through the use of closely spaced microphones in arrays mounted flush with the surface. The measurements were acquired at $R_ {\theta} = O(10^6)$ under the near-neutral thermally stratified condition at the SLTEST site in Utah's west desert. Owing to the attributes of the flow at the SLTEST site, pressure measurements there are especially devoid of the noise sources found in wind tunnels. Through the use of a variety of microphones and microphone separations, the sensitivity of the measured vorticity flux is explored relative to the spatial and temporal resolution of the sensors. Spectra and pdfs of both the pressure and pressure gradients are presented. Comparisons of the normalized surface vorticity flux intensity are made with previous low $R_{\theta}$ laboratory based measurements. [Preview Abstract] |
Sunday, November 20, 2005 6:07PM - 6:20PM |
ER.00010: High Reynolds number turbulent pipe flow Rongrong Zhao, Alexander Smits Fully developed turbulent pipe is measured using a crossed-wire probe. Streamwise and wall-normal turbulence components are obtained over a Reynolds number range from $1.1\times 10^5$ to $9.8\times10^6$. Inner and outer scaling are applied to the broadband turbulence intensity and spectra. The results are evaluated in terms of Perry's attached eddy model prediction (for example, $k^{-1}$ law), and whether Townsend's `inactive' and `active' motions are interactive or not. Streamwise turbulence intensity measurements were compared to the earlier work of Morrison and found to be consistent to the previous one. For $v'_{rms}$, a constant region is found for the region $200\le y^+ \le 0.1R^+$ in inner and outer scaling for Reynolds numbers up to $1.0\times 106$. An increase in $v'_{rms}$ is observed closer to the wall at about $y^+\sim 100$, and is suggestive of the first maxima of streamwise turbulence intensity profile reported in Morrison \textit{et al.} (2004). This result is new, and is not expected from Townsend's `active' and `inactive' motion distinction and Perry's attached eddy model, may signal the existence of interaction between `active' and `inactive' motions, which will lead to the incomplete similarity argued in Morrison \textit{et al.} (2004). The wall-normal spectra are carefully examined, especially in the mean flow overlap region (where the logarithmic law applies). Collapse is found for the energy containing part with inner scaling, but for the low wave number region, a $y/R$ dependence is observed which also indicates an influence from the outer flow. [Preview Abstract] |
Sunday, November 20, 2005 6:20PM - 6:33PM |
ER.00011: Assessment of Scaling Laws in Fully Developed Turbulent Pipe and Channel Flows. E.-S. Zanoun, H. Nagib, F. Durst, L. Terentiev We investigated effects of Reynolds number (Re) on mean flow scaling for turbulent pipe and channel flows. Of particular interest are the streamwise mean velocity distribution, the Reynolds shear stress, and the turbulent kinetic energy production. For high Re, the $-u'_{1}u'_{2}$ collapsed when scaled with wall variables, indicating Re-independence close to the wall, i.e. y$^{+}<$100. This contradicts a conclusion by Gad-el-Hak and Bandyopadhyay, that inner scaling fails to collapse the $-u'_{1}u'_{2}$ profiles. However, in the core region of pipe and/or channel the $-u'_{1}u'_{2}$ data do not collapse using inner scaling. For high enough Re, the $-u'_{1}u'_{2}^{+ }$(i.e. $-u'_{1}u'_{2}$/u$_{\tau }^{2})$ approaches a maximum value outside the viscous sublayer and the location of its maximum was found to move away from the wall as Re increases. Better agreement was achieved for $-u'_{1}u'_{2}^{+}$ when utilizing Panton's formula with the new von K\'{a}rm\'{a}n constant obtained recently by present authors, $\kappa $=0.37 {\&} $\kappa $=0.38, for channel, and pipe respectively. Re-independence of turbulent kinetic energy production was obtained for Re$_{\tau }\ge $2$\times $10$^{3}$ when data are represented in wall units and a peak value of approximately 0.25 was obtained at a fixed distance from the wall, y$^{+}\approx $12. The position of the normalized maximum [$-u'_{1}u'_{2}^{+}$(\textit{dU}$^{+}$\textit{/dy}$^{+})$] was found to coincide with wall-normal position at which turbulent and viscous shear stresses are equal. [Preview Abstract] |
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