3 results
A heat transfer model of fully developed turbulent channel flow
- Alireza Ebadi, Juan Carlos Cuevas Bautista, Christopher M. White, Gregory Chini, Joseph Klewicki
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- Journal:
- Journal of Fluid Mechanics / Volume 884 / 10 February 2020
- Published online by Cambridge University Press:
- 17 December 2019, R7
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Experimental and numerical studies over the past two decades indicate that as the Reynolds number becomes large the turbulent boundary layer is increasingly composed of zones of uniform streamwise momentum, segregated by narrow regions of high shear. Recent experimental evidence suggests that passive scalar fields (for example, temperature) in turbulent boundary layers at high Reynolds number show similar characteristics; namely, large uniform temperature zones (UTZs) separated by narrow regions of high gradient, which we term thermal fissures (TFs). Herein, a model informed by analysis of the mean scalar transport equation, and that leverages the dynamical model recently developed by the authors (Cuevas Bautista et al., J. Fluid Mech., vol. 858, 2019, pp. 609–633), is formulated to predict passive scalar transport using the UTZ/TF concept. First, a finite number of TFs are distributed across the boundary layer. In analogy with the aforementioned dynamical model, the wall-normal positions of the TFs and their characteristic temperatures are then perturbed to generate independent ensembles, from which statistical moments are computed. The model successfully reproduces the statistical profiles of the temperature field as well as the streamwise turbulent heat flux. Lastly, the Prandtl number dependency of the empirically chosen parameters is investigated. It is concluded that the higher-order statistics, especially the kurtosis, produced by the model are sensitive to the Prandtl number, while the mean temperature and turbulent heat flux do not show noticeable Prandtl number dependency.
Mean dynamics and transition to turbulence in oscillatory channel flow
- Alireza Ebadi, Christopher M. White, Ian Pond, Yves Dubief
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- Journal:
- Journal of Fluid Mechanics / Volume 880 / 10 December 2019
- Published online by Cambridge University Press:
- 18 October 2019, pp. 864-889
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The mean dynamics in oscillatory channel flow is examined to investigate the dynamical mechanisms underlying the transition to turbulence in oscillatory wall-bounded flow. The analyses employ direct numerical simulation data acquired at three Stokes Reynolds numbers: $Re_{s}=648$, 801 and 1009, where the lower $Re_{s}$ flow is transitional over the entire cycle and the two higher $Re_{s}$ flows exhibit flow characteristics similar to steady turbulent wall-bounded flow during part of the cycle. The flow evolution over a half-period of oscillation for all three $Re_{s}$ is as follows: near-wall streamwise velocity streaks develop during the early accelerating portion of the cycle; then at some later point in the cycle that depends on $Re_{s}$, the near-wall streaks breakdown (demarking the onset of the nonlinear development stage), and the near-wall Reynolds stress grows explosively; the Reynolds stress remains elevated for part of the cycle before diminishing (yet remaining finite) during the late decelerating portion of the cycle. This process is then repeated indefinitely. The present findings demonstrate that transition to turbulence occurs when the nonlinear development stage begins during the accelerating portion of the cycle. This crucially leads to the diminishing importance of the centreline momentum source, the emergence of a locally accelerating/decelerating internal layer centred about the edge of the Stokes layer and the wall-normal rearrangement of the mean forces prior to the start of the decelerating portion of the cycle. The rearrangement of mean forces culminates in a four layer structure in the mean balance of forces. This is significant on a number of accounts since empirical and theoretical evidence suggests that the formation of a four layer structure is an important characteristic of a self-similar hierarchal structure that underlies logarithmic dependence of the mean velocity profile in steady turbulent wall-bounded flows (Klewicki et al., J. Fluid Mech., vol. 638, 2009, pp. 73–93). When the nonlinear development stage begins during the decelerating portion of the cycle (i.e. at $Re_{s}=648$), a four layer structure is not observed in the mean balance of forces and the flow remains weakly transitional over the entire cycle.
A uniform momentum zone–vortical fissure model of the turbulent boundary layer
- Juan Carlos Cuevas Bautista, Alireza Ebadi, Christopher M. White, Gregory P. Chini, Joseph C. Klewicki
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- Journal:
- Journal of Fluid Mechanics / Volume 858 / 10 January 2019
- Published online by Cambridge University Press:
- 06 November 2018, pp. 609-633
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Recent studies reveal that at large friction Reynolds number $\unicode[STIX]{x1D6FF}^{+}$ the inertially dominated region of the turbulent boundary layer is composed of large-scale zones of nearly uniform momentum segregated by narrow fissures of concentrated vorticity. Experiments show that, when scaled by the boundary-layer thickness, the fissure thickness is $\mathit{O}(1/\sqrt{\unicode[STIX]{x1D6FF}^{+}})$, while the dimensional jump in streamwise velocity across each fissure scales in proportion to the friction velocity $u_{\unicode[STIX]{x1D70F}}$. A simple model that exploits these essential elements of the turbulent boundary-layer structure at large $\unicode[STIX]{x1D6FF}^{+}$ is developed. First, a master wall-normal profile of streamwise velocity is constructed by placing a discrete number of fissures across the boundary layer. The number of fissures and their wall-normal locations follow scalings informed by analysis of the mean momentum equation. The fissures are then randomly displaced in the wall-normal direction, exchanging momentum as they move, to create an instantaneous velocity profile. This process is repeated to generate ensembles of streamwise velocity profiles from which statistical moments are computed. The modelled statistical profiles are shown to agree remarkably well with those acquired from direct numerical simulations of turbulent channel flow at large $\unicode[STIX]{x1D6FF}^{+}$. In particular, the model robustly reproduces the empirically observed sub-Gaussian behaviour for the skewness and kurtosis profiles over a large range of input parameters.