 Mechanical Engineering  Research Publications
Mechanical Engineering  Research Publications
Permanent URI for this collection
4 results
Filters
Reset filtersSettings
Statistics
Citations
Search Results
Now showing
1  4 of 4

ItemMean dynamics of transitional channel flowElsnab, J ; Klewicki, J ; Maynes, D ; Ameel, T (CAMBRIDGE UNIV PRESS, 20110701)The redistribution of mean momentum and vorticity, along with the mechanisms underlying these redistribution processes, is explored for postlaminar flow in fully developed, pressure driven, channel flow. These flows, generically referred to as transitional, include an instability stage and a nonlinear development stage. The central focus is on the nonlinear development stage. The present analyses use existing direct numerical simulation data sets, as well as recently reported highresolution molecular tagging velocimetry measurements. Primary considerations stem from the emergence of the effects of turbulent inertia as represented by the Reynolds stress gradient in the mean differential statement of dynamics. The results describe the flow evolution following the formation of a nonzero Reynolds stress peak that is known to first arise near the critical layer of the most unstable disturbance. The positive and negative peaks in the Reynolds stress gradient profile are observed to undergo a relative movement toward both the wall and centreline for subsequent increases in Reynolds number. The Reynolds stress profiles are shown to almost immediately exhibit the same sequence of curvatures that exists in the fully turbulent regime. In the transitional regime, the outer inflection point in this profile physically indicates a localized zone within which the mean dynamics are dominated by inertia. These observations connect to recent theoretical findings for the fully turbulent regime, e.g. as described by Fife, Klewicki & Wei (J. Discrete Continuous Dyn. Syst., vol. 24, 2009, p. 781) and Klewicki, Fife & Wei (J. Fluid Mech., vol. 638, 2009, p. 73). In accord with momentum equation analyses at higher Reynolds number, the present observations provide evidence that a logarithmic mean velocity profile is most rapidly approximated on a subdomain located between the zero in the Reynolds stress gradient (maximum in the Reynolds stress) and the outer region location of the maximal Reynolds stress gradient (inflection point in the Reynolds stress profile). Overall, the present findings provide evidence that the dynamical processes during the postlaminar regime and those operative in the high Reynolds number regime are connected and describable within a single theoretical framework.

ItemMean dynamics of transitional boundarylayer flowKlewicki, J ; Ebner, R ; Wu, X (CAMBRIDGE UNIV PRESS, 20110901)The dynamical mechanisms underlying the redistribution of mean momentum and vorticity are explored for transitional twodimensional boundarylayer flow at nominally zero pressure gradient. The analyses primarily employ the direct numerical simulation database of Wu & Moin (J. Fluid Mech., vol. 630, 2009, p. 5), but are supplemented with verifications utilizing subsequent similar simulations. The transitional regime is taken to include both an instability stage, which effectively generates a finite Reynolds stress profile, −ρuv(y), and a nonlinear development stage, which progresses until the terms in the mean momentum equation attain the magnitude ordering of the fourlayer structure revealed by Wei et al. (J. Fluid Mech., vol. 522, 2005, p. 303). Selfconsistently applied criteria reveal that the third layer of this structure forms first, followed by layers IV and then II and I. For the present flows, the fourlayer structure is estimated to be first realized at a momentum thickness Reynolds number Rθ = U∞ θ/ν ≃ 780. The firstprinciplesbased theory of Fife et al. (J. Disc. Cont. Dyn. Syst. A, vol. 24, 2009, p. 781) is used to describe the mean dynamics in the laminar, transitional and fourlayer regimes. As in channel flow, the transitional regime is marked by a nonnegligible influence of all three terms in the mean momentum equation at essentially all positions in the boundary layer. During the transitional regime, the action of the Reynolds stress gradient rearranges the mean viscous force and mean advection profiles. This culminates with the segregation of forces characteristic of the fourlayer regime. Empirical and theoretical evidence suggests that the formation of the fourlayer structure also underlies the emergence of the mean dynamical properties characteristic of the highReynoldsnumber flow. These pertain to why and where the mean velocity profile increasingly exhibits logarithmic behaviour, and how and why the Reynolds stress distribution develops such that the inner normalized position of its peak value, ym+, exhibits a Reynolds number dependence according to $y_m^+ {\,\simeq\,} 1.9 \sqrt{\delta^+}$.

ItemLargescale amplitude modulation of the smallscale structures in turbulent boundary layersMathis, R ; Hutchins, N ; Marusic, I (CAMBRIDGE UNIV PRESS, 20090610)In this paper we investigate the relationship between the large and smallscale energycontaining motions in wall turbulence. Recent studies in a highReynoldsnumber turbulent boundary layer (Hutchins & Marusic, Phil. Trans. R. Soc. Lond. A, vol. 365, 2007a, pp. 647–664) have revealed a possible influence of the largescale boundarylayer motions on the smallscale nearwall cycle, akin to a pure amplitude modulation. In the present study we build upon these observations, using the Hilbert transformation applied to the spectrally filtered smallscale component of fluctuating velocity signals, in order to quantify the interaction. In addition to the largescale logregion structures superimposing a footprint (or mean shift) on the nearwall fluctuations (Townsend, The Structure of Turbulent Shear Flow, 2nd edn., 1976, Cambridge University Press; Metzger & Klewicki, Phys. Fluids, vol. 13, 2001, pp. 692–701.), we find strong supporting evidence that the smallscale structures are subject to a high degree of amplitude modulation seemingly originating from the much larger scales that inhabit the log region. An analysis of the Reynolds number dependence reveals that the amplitude modulation effect becomes progressively stronger as the Reynolds number increases. This is demonstrated through three orders of magnitude in Reynolds number, from laboratory experiments at Reτ ~ 103–104 to atmospheric surface layer measurements at Reτ ~ 106.

ItemUnravelling turbulence near wallsMarusic, I (CAMBRIDGE UNIV PRESS, 20090710)Turbulent flows near walls have been the focus of intense study since their first description by Ludwig Prandtl over 100 years ago. They are critical in determining the drag and lift of an aircraft wing for example. Key challenges are to understand the physical mechanisms causing the transition from smooth, laminar flow to turbulent flow and how the turbulence is then maintained. Recent direct numerical simulations have contributed significantly towards this understanding.