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 PA: Turbulent Boundary Layers: Computational Studies |
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Chair: Yoshi Kimura, Nagoya University Room: 001A |
Tuesday, November 25, 2008 11:35AM - 11:48AM |
PA.00001: Application of the Sensitivity Equation Method to Examine Low-Reynolds Number Effects in Turbulent Channel Flow Richard Kirkman, Meredith Metzger The sensitivity equation method (SEM) has been implemented in the context of direct numerical simulations of fully-developed turbulent channel flow to explore low Reynolds number effects on the profiles of the mean velocity and Reynolds stresses. Simulations were performed at Reynolds numbers of 100, 150, and 180, based on the friction velocity and channel half-width. In SEM, the governing equations are differentiated with respect to the parameter of interest, in this case the Reynolds number, yielding a set of sensitivity equations, which are subsequently discretized and numerically solved concurrently with the discretized equations for the primitive variables (i.e., velocity and pressure). The present study utilizes a finite-volume, fractional step computational scheme to solve both the governing equations and the sensitivity equations. Turbulent velocity statistics compare very well to others in the literature (Kim et al., 1987; Kuroda et al., 1989). The results from SEM correctly predict the Reynolds number trend in the wall shear stress. The SEM method also provides quantitative information about the rate of change of the mean streamwise velocity profile with respect to Reynolds number. Finally, wall-normal profiles of the higher order moments of the sensitivity of all velocity components were calculated, along with the sensitivity profiles of the Reynolds stresses. [Preview Abstract] |
Tuesday, November 25, 2008 11:48AM - 12:01PM |
PA.00002: Theory and numerical computation of the von Karman constant in two-dimensional turbulent flows Nicholas Guttenberg, Nigel Goldenfeld, Jason Larkin, Alisia Prescott, Hamid Kellay, Walter Goldburg We present a calculation of the velocity profile in two-dimensional (2D) turbulent flows. The method is based upon the momentum-transfer theory for the friction factor, proposed by Gioia and Chakraborty, and when fitted to a putative law of the wall profile yields a value for the von K\'{a}rm\'{a}n constant which is in satisfactory agreement with direct numerical simulations at width Reynolds numbers between 20,000 and 80,000. We compare the theoretical results with experimental results on turbulent 2D soap films, taking into account the effects of air resistance. Our findings indicate that the von K\'{a}rm\'{a}n constant in 2D is significantly less than the accepted value in 3D. [Preview Abstract] |
Tuesday, November 25, 2008 12:01PM - 12:14PM |
PA.00003: Turbulent pipe flow drag reduction by discrete counter-rotating strips. Markus Schwaenen, Travis Thurber, Andrew Duggleby, Kenneth S. Ball Spanwise wall oscillations have been shown to result in as much as 45{\%} drag reduction in turbulent channel flows, as widely reported in the literature. A recent study [Duggleby et al., Phys. Fluids \textbf{19}, 125107 (2007)] has shown that in turbulent pipe flow with $Re_\tau =150$, a 27{\%} increase in mean velocity, corresponding to reduced drag, results when the entire pipe wall is oscillated about the axis of the pipe. In the current study, we show that significant drag reduction still occurs when a series of discrete circumferential strips, placed at finite intervals along the axis of the pipe, are rotating in alternating directions. Results for this new method of drag reduction are presented for a turbulent pipe flow with $Re_\tau =150$. Computations were performed with two separate codes: a finite volume Large Eddy Simulation (LES) code and a spectral element Direct Numerical Solution (DNS) code. Both methods show a flow rate increase of about 10{\%} when the flow is driven by a constant pressure gradient. The effect of strip width and spacing between strips is examined. [Preview Abstract] |
Tuesday, November 25, 2008 12:14PM - 12:27PM |
PA.00004: Composite Expansions for Active and Inactive Motions in the Streamwise Reynolds Stress of Turbulent Boundary Layers Robert McKee, Ronald Panton Proper scaling of streamwise Reynolds stress in turbulent
boundary layers has been controversial for more than a decade as
its Reynolds Number dependence can not be removed by normal
scaling. One issue that explains the behavior of the streamwise
Reynolds stress is that it is affected by both active and
inactive motions per Townsend's hypothesis. The goal of this
research is to develop a composite expansion for the streamwise
Reynolds stress that considers active and inactive motions,
explains various Reynolds Number dependencies, and agrees with
available data. Data from four sources are evaluated. A new
asymptotic representation for the Reynolds shear stress,
$<$uv$>$+, that meets the requirements for a proper composite
expansion is developed. The streamwise Reynolds stress,
$<$uu$>$+, can be separated into active and inactive parts with
Reynolds shear stress as the active part. An outer correlation
equation with the correct asymptotic limits for the inactive
streamwise Reynolds stress is developed and shown to fit the
outer $<$uIuI$>$\# data. A separate correlation equation for
$<$uIuI$>$\# is developed and fit to data. These two equations
form a composite expansion for the inactive streamwise Reynolds
stress. This composite expansion can be combined with the |
Tuesday, November 25, 2008 12:27PM - 12:40PM |
PA.00005: DNS of turbulent channel flow subject to a model dynamically rough wall Beverley McKeon While there is an extensive literature on the influence of surface roughness on wall turbulence, the influence of a spatially-distributed roughness with a time-varying amplitude, a ``dynamically rough'' wall, has not been so extensively explored. There are fundamentally interesting questions about the influence of a roughness timescale and structured energy addition on the development of the near-wall flow as well as potential applications in flow control for this kind of wall actuation. Results from a Direct Numerical Simulation of a linearized model of dynamic wall roughness in a turbulent channel flow with $Re_{\tau} \sim 500$ are presented. The channel flow DNS of Flores \& Jimenez (2006) was modified to incorporate a time-dependent boundary condition in which the no-slip and impermeability constraints are replaced with a specific temporally-harmonic distribution of streamwise and wall-normal velocities at the wall, which can be considered as a crude linearized approximation to boundary conditions corresponding to dynamic roughness linearized about the turbulent mean velocity profile. It is shown that a global response to this forcing occurs when the first harmonic of the forcing frequency is excited. This work was performed as part of the CTR Summer program 2008. The generosity of Javier Jimenez in allowing the use of the DNS code is gratefully acknowledged. [Preview Abstract] |
Tuesday, November 25, 2008 12:40PM - 12:53PM |
PA.00006: A formula for the von K\'arm\'an constant in terms of the flow structure of wall bounded turbulence Vassilios Dallas, Christos Vassilicos, Geoffrey Hewitt We perform Direct Numerical Simulations (DNS) of turbulent channel flows with and without several types of simulated wall activation. These DNS support our theoretical prediction that the von K\'arm\'an constant can be calculated from the formula $1/\kappa = C_s (B_2/B_1^2) \mathcal{D}$ where $B_1$ is the constant of proportionality between the Taylor microscale and the average distance between stagnation points (both of which depend on height from the wall without $B_1$ depending on it in the log-layer), $C_s$ is a number of stagnation points of the fluctuating velocity field at the upper edge of the buffer layer, $B_2$ tends to 1 as $Re_\tau >> 1$ and $ \mathcal{D}$ characterises the anisotropy of the fluctuating velocity field in the log-layer. This formula accounts for the possibility of non-universality of $1/\kappa$ in the sense of Reynolds number and wall-flow type dependencies. [Preview Abstract] |
Tuesday, November 25, 2008 12:53PM - 1:06PM |
PA.00007: Entropy generation in a transitioning boundary layer Edmond J. Walsh, Donald M. McEligot, Brian Egan, Luca Brandt, Philipp Schlatter, Dan S. Henningson Insight into entropy generation is a key to increasing efficiency. For viscous wall layers, it is reasonably understood and predictable for laminar and developed turbulent flows. However, results apparently are not yet available for the pointwise entropy generation rate for transitional boundary layers, even for zero pressure gradients, except with an approximate treatment. The present study applies the numerical simulations of Brandt et al. [JFM 2004] to address this deficiency. Predicted spatial distributions are presented for an initial Reynolds number (Uinf,in x delta,star,in/nu) of 300, a length scale (L/delta,star,in) of five and a moderate turbulence level of 4.7 per cent; they are compared to approximate predictions/measurements. [Preview Abstract] |
Tuesday, November 25, 2008 1:06PM - 1:19PM |
PA.00008: The structures of the momentum transfer in turbulent channels Oscar Flores, Javier Jim\'enez We analyze the geometry and the spatial distribution of structures with $-uv > 1.75 u'v'$, in a turbulent channel with $Re_{\tau}=10^3$. Even if they cover less than 10\% of the wall-parallel area, they contribute up to 60\% of the mean Reynolds stresses. Most of them are wall-attached, forming a self-similar family in which the objects lengths and widths are proportional to their heights. They are classified into Q2 ejections ($v>0, u<0$) and Q4 sweeps ($v<0, u>0$), usually forming side by side pairs, several (3--4) of which tend to be aligned in the streamwise direction, with a weak tendency for larger objects to be downstream of smaller ones. While the geometric and spatial characteristics of Q2s and Q4s are very similar, the velocity fields conditioned to them show higher log-layer streaks associated with the Q4s. The streak length decreases when conditioned only to isolated objects, suggesting that the observed very long streaks are due to the streamwise grouping of the pairs. A special class is formed by events with heights of the order of the channel half-width, with ``packets lengths'' of the order of the full simulation domain $(25 h)$. Funded by CICYT. [Preview Abstract] |
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