Gotowa bibliografia na temat „Transitional channel flow”

The redistribution of mean momentum and vorticity, along with the mechanisms underlying these redistribution processes, is explored for post-laminar 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 high-resolution 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 non-zero 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 sub-domain 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 post-laminar regime and those operative in the high Reynolds number regime are connected and describable within a single theoretical framework.

In line with Pomeau’s conjecture about the relevance of directed percolation (DP) to turbulence onset/decay in wall-bounded flows, we propose a minimal stochastic model dedicated to the interpretation of the spatially intermittent regimes observed in channel flow before its return to laminar flow. Numerical simulations show that a regime with bands obliquely drifting in two stream-wise symmetrical directions bifurcates into an asymmetrical regime, before ultimately decaying to laminar flow. The model is expressed in terms of a probabilistic cellular automaton of evolving von Neumann neighborhoods with probabilities educed from a close examination of simulation results. It implements band propagation and the two main local processes: longitudinal splitting involving bands with the same orientation, and transversal splitting giving birth to a daughter band with an orientation opposite to that of its mother. The ultimate decay stage observed to display one-dimensional DP properties in a two-dimensional geometry is interpreted as resulting from the irrelevance of lateral spreading in the single-orientation regime. The model also reproduces the bifurcation restoring the symmetry upon variation of the probability attached to transversal splitting, which opens the way to a study of the critical properties of that bifurcation, in analogy with thermodynamic phase transitions.

The transitional regime of plane channel flow is investigated above the transitional point below which turbulence is not sustained, using direct numerical simulation in large domains. Statistics of laminar-turbulent spatio-temporal intermittency are reported. The geometry of the pattern is first characterized, including statistics for the angles of the laminar-turbulent stripes observed in this regime, with a comparison to experiments. High-order statistics of the local and instantaneous bulk velocity, wall shear stress and turbulent kinetic energy are then provided. The distributions of the two former quantities have non-trivial shapes, characterized by a large kurtosis and/or skewness. Interestingly, we observe a strong linear correlation between their kurtosis and their skewness squared, which is usually reported at much higher Reynolds number in the fully turbulent regime.

AbstractDirect numerical simulations (DNS) are performed of a transient channel flow following a rapid increase of flow rate from an initially turbulent flow. It is shown that a low-Reynolds-number turbulent flow can undergo a process of transition that resembles the laminar–turbulent transition. In response to the rapid increase of flow rate, the flow does not progressively evolve from the initial turbulent structure to a new one, but undergoes a process involving three distinct phases (pre-transition, transition and fully turbulent) that are equivalent to the three regions of the boundary layer bypass transition, namely, the buffeted laminar flow, the intermittent flow and the fully turbulent flow regions. This transient channel flow represents an alternative bypass transition scenario to the free-stream-turbulence (FST) induced transition, whereby the initial flow serving as the disturbance is a low-Reynolds-number turbulent wall shear flow with pre-existing streaky structures. The flow nevertheless undergoes a ‘receptivity’ process during which the initial structures are modulated by a time-developing boundary layer, forming streaks of apparently specific favourable spacing (of about double the new boundary layer thickness) which are elongated streamwise during the pre-transitional period. The structures are stable and the flow is laminar-like initially; but later in the transitional phase, localized turbulent spots are generated which grow spatially, merge with each other and eventually occupy the entire wall surfaces when the flow becomes fully turbulent. It appears that the presence of the initial turbulent structures does not promote early transition when compared with boundary layer transition of similar FST intensity. New turbulent structures first appear at high wavenumbers extending into a lower-wavenumber spectrum later as turbulent spots grow and join together. In line with the transient energy growth theory, the maximum turbulent kinetic energy in the pre-transitional phase grows linearly but only in terms of ${u}^{\ensuremath{\prime} } $, whilst ${v}^{\ensuremath{\prime} } $ and ${w}^{\ensuremath{\prime} } $ remain essentially unchanged. The energy production and dissipation rates are very low at this stage despite the high level of ${u}^{\ensuremath{\prime} } $. The pressure–strain term remains unchanged at that time, but increases rapidly later during transition along with the generation of turbulent spots, hence providing an unambiguous measure for the onset of transition.

Velocimetry, heat transfer, and pressure drop experiments are reported for laminar/transitional air flow in a channel containing rectangular transverse ribs located along one channel wall. The geometry is intended to represent an array of low profile electronic packages. At fixed pumping power per unit channel volume, the heat transfer rate per unit volume is independent of rib-to-rib spacing and increases with decreasing wall-to-wall spacing. The fully developed, rib-average heat transfer coefficient is found to be linearly related to the maximum streamwise rms turbulence measured above the rib-tops. Linear correlations, in terms of a descriptor of the rms streamwise turbulence, are shown to unify heat transfer/pressure drop data for channels containing either two-or three-dimensional protrusions.