Bulletin of the American Physical Society
68th Annual Meeting of the APS Division of Fluid Dynamics
Volume 60, Number 21
Sunday–Tuesday, November 22–24, 2015; Boston, Massachusetts
Session G22: Turbulent Boundary Layers II |
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Chair: Anthony Leonard, California Institute of Technology Room: 210 |
Monday, November 23, 2015 8:00AM - 8:13AM |
G22.00001: On the scaling of velocity and vorticity variances in turbulent channel flow A. Leonard The availability of new DNS-based statistics for turbulent channel flow (Lee \& Moser, JFM 2015) along with previous results (e.g., Hoyas \& Jim\'{e}nez, Phys. Flu. 2006) has provided the opportunity for another look at the scaling laws for this flow. For example, data from the former (fig. 4(e)) for the streamwise velocity variance in the outer region clearly indicate a modified log law for that quantity at $Re_{\tau} = 5200$, i.e., $ ^+ = C_0 - C_1 ln(y/\delta) - C_2 ln(y/\delta)^2 $ where $\delta$ is the channel half height. We find that this result fits the the data very well for $ 0.1 < y/\delta < 0.8$. The Reynolds number (5200) is still apparently too low to observe the much-discussed log law (above with $C_2 = 0$), which, presumably, would appear for roughly $ y/\delta < 0.1$, as it does in high $Re_{\tau}$ pipe flow (Hultmark et al., PRL 2012) with $\delta$ replaced by $R$. On the other hand, the above modified log law with the same values for $C_1$ and $C_2$ is a good fit for the pipe data at $Re_{\tau} = 98 \times 10^5$ for $y/R > 0.12$ (fig. 4 of Hultmark et al.). [Preview Abstract] |
Monday, November 23, 2015 8:13AM - 8:26AM |
G22.00002: Turbulent inertia and the onset of log region in pipe flows Jimmy Philip, Cheng Chin, Joseph Klewicki, Andrew Ooi, Ivan Marusic The wallnormal ($y$)-location where the log-region begins in wall-turbulence is the same location where the turbulent inertia or TI (${\rm d}\left<-uv\right>/{\rm d}y $) and the pressure gradient terms from the mean-momentum equation start balancing each other. This location is closely followed by the location, $y_m^+$ where TI vanishes (before becoming negative in the log-region). Dynamics of TI is elucidated using DNS data of pipe flow at $\delta^+ \approx$ 500, 1000 and 2000. We decompose TI as (i) velocity-vorticity correlations ($\left< v \omega_z \right> + \left<- w \omega_y \right>$) and their co-spectra, and (ii) wall-normal gradient of the Reynolds shear stress co-spectra (${\partial \Phi_{-uv}}/{\partial y}$). One interesting result is that the onset of the log-region moves outward with increasing Reynolds number as $ \sim \sqrt{\delta^+}$ because the eddies located close to $y_m^+$ are influenced by large scale accelerating motions of the type $\left<- w \omega_y \right>$ related to vorticity stretching. [Preview Abstract] |
Monday, November 23, 2015 8:26AM - 8:39AM |
G22.00003: Role of large scale motion in high $Re$ channel flow Myoungkyu Lee, Robert D. Moser Direct numerical simulations (DNS) of turbulent channel flow at Reynolds numbers up to $Re_\tau \approx 5200$ have been performed to study high Reynolds number wall-bounded turbulence. DNS result have shown that $Re_\tau \approx 5200$ is high enough to exhibit scale separation between the near-wall and outer regions. [Lee \& Moser, \textit{J. Fluid Mech.}, vol 774, 2015]. In this presentation we focus on the role of large scale motion on the transport of turbulent kinetic energy, $u^\prime_i u^\prime_i/2$, and Reynolds stress, $u^\prime v^\prime$. Spectral analysis of the evolution equation for the two-point correlation is performed to investigate the contribution of motions at different length scales to transport. It is shown that only the turbulent transport terms show significant $Re$ dependencies. Furthermore, the turbulent transport terms can be decomposed into two parts, one that contributes to transport in the wall-normal direction and one that is responsible for transfer between length scales. The results show that the large scale motion in the outer region has direct effects on the flow in the near-wall region through transport of turbulent kinetic energy and Reynolds stress. [Preview Abstract] |
Monday, November 23, 2015 8:39AM - 8:52AM |
G22.00004: Experiments on low Reynolds number turbulent flow through a square duct Bayode Owolabi, Robert Poole, David Dennis Previous experimental studies on square duct turbulent flow have focused mainly on high Reynolds numbers for which a turbulence induced eight-vortex secondary flow pattern exists in the cross sectional plane. More recently, Direct Numerical Simulations (DNS) have revealed that the flow field at Reynolds numbers close to transition can be very different; the flow in this marginally turbulent regime alternating between two states characterised by four vortices. In this study, we experimentally investigate the onset criteria for transition to turbulence in square ducts. We also present experimental data on the mean flow properties and turbulence statistics in both marginally and fully turbulent flow at relatively low Reynolds numbers using laser Doppler velocimetry. Results for both flow categories show good agreement with DNS. The switching of the flow field between two flow states at marginally turbulent Reynolds numbers is confirmed by bimodal probability density functions of streamwise velocity at certain distances from the wall as well as joint probability density functions of streamwise and wall normal velocities which feature two peaks. [Preview Abstract] |
Monday, November 23, 2015 8:52AM - 9:05AM |
G22.00005: Structural organization of uniform momentum core in turbulent channel flow Jongmin Yang, Jinyul Hwang, Hyung Jin Sung The coherent structures across the boundary of the quiescent core region are explored using the direct numerical simulation data of a turbulent channel flow at Re$_{\mathrm{\tau }}=$930. The quiescent core is the region where the streamwise momentum is relatively uniform with low-level turbulence in channel flow. Across the boundary of this region, the turbulence intensity and the Reynolds shear stress decrease suddenly. The mean velocity profile shows a significant jump which indicates a strong mean shear layer at the boundary of the uniform core region. Due to the strong mean shear, the prograde vortices are dominantly distributed along the boundary with the retrograde vortices below them. The prograde and retrograde vortices are distributed in a pair with a uniform wall-normal distance. Large-scale low- and high-speed structures are characterized by the positions of the core boundary, revealing that the core boundary is modulated by the large-scale structures. [Preview Abstract] |
Monday, November 23, 2015 9:05AM - 9:18AM |
G22.00006: Multiscale dynamics of the strain and enstrophy in turbulent channels Adrian Lozano-Duran, Markus Holzner, Javier Jimenez The invariants of the velocity gradient tensor, Q and R, and their enstrophy and strain components are studied in the log-layer of a turbulent channel. The velocities are filtered in the three spatial directions and the results analyzed at different scales. We show that the Q--R plane does not capture the changes undergone by the flow as the filter width increases, and that the enstrophy/enstrophy production and strain/strain-production planes are better choices. We also show that the conditional mean trajectories may differ significantly from the instantaneous behavior of the flow since they are the result of an averaging process where the mean is 3-5 times smaller than the corresponding standard deviation. Our final goal is to test whether the dynamics of the flow are self-similar in the inertial range and the answer turns out to be no. The mean shear is found responsible for the absence of self-similarity and progressively controls the dynamics of the eddies observed as the filter width increases. However, a self-similar behavior emerges when the calculations are repeated for the fluctuating velocity. Finally, the turbulent cascade in terms of vortex stretching is considered by computing the alignment of the vorticity at a given scale with the strain at a larger one. [Preview Abstract] |
Monday, November 23, 2015 9:18AM - 9:31AM |
G22.00007: Role of large-scale motions to turbulent inertia in turbulent pipe and channel flows Jinyul Hwang, Jin Lee, Hyung Jin Sung The role of large-scale motions (LSMs) to the turbulent inertia (TI) term (the wall-normal gradient of the Reynolds shear stress) is examined in turbulent pipe and channel flows at $Re_{\tau } \approx 930$. The TI term in the mean momentum equation represents the net force of inertia exerted by the Reynolds shear stress. Although the turbulence statistics characterizing the internal turbulent flows are similar close to the wall, the TI term differs in the logarithmic region due to the different characteristics of LSMs ($\lambda_{x} >3\delta )$. The contribution of the LSMs to the TI term and the Reynolds shear stress in the channel flow is larger than that in the pipe flow. The LSMs in the logarithmic region act like a mean momentum source (where TI \textgreater 0) even the TI profile is negative above the peak of the Reynolds shear stress. The momentum sources carried by the LSMs are related to the low-speed regions elongated in the downstream, revealing that momentum source-like motions occur in the upstream position of the low-speed structure. The streamwise extent of this structure is relatively long in the channel flow, whereas the high-speed regions on the both sides of the low-speed region in the channel flow are shorter and weaker than those in the pipe flow. [Preview Abstract] |
Monday, November 23, 2015 9:31AM - 9:44AM |
G22.00008: The inertial subrange in turbulent pipe flow: centre line Jonathan Morrison, Margit Vallikivi, Alexander Smits The inertial subrange scaling of the axial velocity component is examined for the centre line of turbulent pipe flow for Reynolds numbers in the range $249\le Re_\lambda \le986$. Measurements were performed in the Princeton/ONR Superpipe using NSTAP probes of length, $\ell = 30~ \mu$m or 60 $\mu$m, with temporal resolution up to 300 kHz. Estimates of the dissipation rate, $\epsilon$, are made by both integration of the one-dimensional dissipation spectra and the third-order moment of the structure function. It is noticeable that neither dissipation estimate provides values of $A=\frac{\epsilon}{u_{\tau}^3/R}$ that asymptote to a constant: rather $A$ increases almost linearly with $Re_\lambda$. We show that complete similarity of the inertial range spectra is not evident: there is little support for K41, and effects of Reynolds number are not well represented by Kolmogorov's ``extended similarity hypothesis,'' K62. The second-order moment of the structure function does not show a constant value, even when compensated by K62. Direct effects of viscosity appear at the centre line where correction of the ``${4}/{5}$ths'' constant for finite Reynolds number (Lundgren 2002) yields values of $0.80~\pm0.01$ [Preview Abstract] |
Monday, November 23, 2015 9:44AM - 9:57AM |
G22.00009: Amplitude modulation of vorticity and dissipation by large-scale motions in turbulent channel flow Yi-Chen Yao, Bing-Qing Deng, Wei-Xi Huang, Chun-Xiao Xu Amplitude modulation of both vorticity and dissipation by large-scale out-layer structures is studied using the DNS data of turbulent channel flow at Reynolds numbers up to \textit{Re}$_{\tau }=$1000. Carrier and modulated signals are scale decomposed in both streamwise and spanwise directions, and small-scale envelop is extracted by Hilbert transformation. Two-point amplitude modulation correlation is calculated at a range of wall-normal locations. The modulation strength on the vorticity and the dissipation rate of turbulent kinetic energy is found to be much stronger than on all the three components of velocity fluctuations. Distinct peak value of correlation is observed when large-scale signals are extracted from center log region and the corresponding modulated information from below $y^{\mathrm{+}}=$10. Also the strength of this peak value increases with Reynolds number, thus supporting the top-down mechanism that the near-wall layer is becoming more influenced by the large-scale structures which gradually emerge as Reynolds number increases. [Preview Abstract] |
Monday, November 23, 2015 9:57AM - 10:10AM |
G22.00010: Fully developed turbulence in slugs of pipe flows Rory Cerbus, Chien-chia Liu, Jun Sakakibara, Gustavo Gioia, Pinaki Chakraborty Despite over a century of research, transition to turbulence in pipe flows remains a mystery. In theory the flow remains laminar for arbitrarily large Reynolds number, Re. In practice, however, the flow transitions to turbulence at a finite Re whose value depends on the disturbance, natural or artificial, in the experimental setup. The flow remains in the transition state for a range of Re $\sim 0(1000)$; for larger Re the flow becomes fully developed. The transition state for Re $> 3000$ consists of axially segregated regions of laminar and turbulent patches. These turbulent patches, known as slugs, grow as they move downstream. Their lengths span anywhere between a few pipe diameters to the whole length of the pipe. Here we report Stereo Particle Image Velocimetry measurements in the cross-section of the slugs. Notwithstanding the continuous growth of the slugs, we find that the mean velocity and stress profiles in the slugs are indistinguishable from that of statistically-stationary fully-developed turbulent flows. Our results are independent of the length of the slugs. We contrast our results with the well-known work of Wygnanski \& Champagne (1973), whose measurements, we argue, are insufficient to draw a clear conclusion regarding fully developed turbulence in slugs. [Preview Abstract] |
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