Unified description of turbulent entrainment

Reeuwijk, Maarten van; Vassilicos, J. C.; Craske, John

doi:10.1017/jfm.2020.836

Cited by 15 publications

(22 citation statements)

References 69 publications

(168 reference statements)

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“…and van Reeuwijk, Vassilicos & Craske (2021). This definition, (4.12), is consistent with the unified description of the turbulent entrainment(van Reeuwijk et al 2021) and has been adopted by a number of temporally developing flows, for exampleJonker et al (2013) for a shear-driven flow with buoyancy stratification andKrug et al (2017) for a planar plume. With the definition of the top-hat characteristic velocity and length scales (3.4), the entrainment coefficient is obtained in terms of the integral quantities,…”

mentioning

confidence: 82%

High Grashof number turbulent natural convection on an infinite vertical wall

Williamson

Armfield

et al. 2021

J. Fluid Mech.

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The present study concerns a temporally evolving turbulent natural convection boundary layer (NCBL) adjacent to an isothermally heated vertical wall, with Prandtl number 0.71. Three-dimensional direct numerical simulations (DNS) are carried out to investigate the turbulent flow up to $\textit {Gr}_\delta =1.21\times 10^8$ , where $\textit {Gr}_\delta$ is the Grashof number based on the boundary layer thickness $\delta$ . In the near-wall region, there exists a constant heat flux layer, similar to previous studies for the spatially developing flows (e.g. George & Capp, Intl J. Heat Mass Transfer, vol. 22, 1979, pp. 813–826). Beyond a wall-normal distance $\delta _i$ , the NCBL can be characterised as a plume-like region. We find that this region is well described by a self-similar integral model with profile coefficients (cf. van Reeuwijk & Craske, J. Fluid Mech., vol. 782, 2015, pp. 333–355) which are $\textit {Gr}_\delta$ -independent after $\textit {Gr}_\delta =10^7$ . In this Grashof number range both the outer plume-like region and the near-wall boundary layer are turbulent, indicating the beginning of the so-called ultimate turbulent regime (Grossmann & Lohse, J. Fluid Mech., vol. 407, 2000, pp. 27–56; Grossmann & Lohse, Phys. Fluids, vol. 23, 2011, 045108). Solutions to the self-similar integral model are analytically obtained by solving ordinary differential equations with profile coefficients empirically obtained from the DNS results. In the present study, we have found the wall heat transfer of the NCBL is directly related to the top-hat scales which characterise the plume-like region. The Nusselt number is found to follow $\textit {Nu}_\delta \propto \textit {Gr}_\delta ^{0.381}$ , slightly higher than the empirical $1/3$ -power-law correlation reported for spatially developing NCBLs at lower $\textit {Gr}_\delta$ , but is shown to be consistent with the ultimate heat transfer regime with a logarithmic correction suggested by Grossmann & Lohse (Phys. Fluids, vol. 23, 2011, 045108). By modelling the near-wall buoyancy force, we show that the wall shear stress would scale with the bulk velocity only at asymptotically large Grashof numbers.

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confidence: 82%

High Grashof number turbulent natural convection on an infinite vertical wall

Williamson

Armfield

et al. 2021

J. Fluid Mech.

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“…Understanding this process is of great significance to various disciplines, including meteorology and oceanography (Mellado 2017). The entrainment has been detailed described from a global and a local perspective (van Reeuwijk, Vassilicos & Craske 2021). Globally, the integral entrainment velocity is proportional to the typical velocity scale in the turbulent region, and is not related to viscosity (Turner 1986; van Reeuwijk & Holzner 2014; Cafiero & Vassilicos 2020).…”

Section: Introductionmentioning

confidence: 99%

Universal modulations of large-scale motions on entrainment of turbulent boundary layers

2022

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The modulations of high/low-speed large-scale motions (H/L-SMs) on the turbulent/non-turbulent interface (TNTI) and turbulent entrainment are investigated in turbulent boundary layers via both experimental and numerical studies. The spanwise locations of large-scale motions can be locked by the spanwise heterogeneity, so the boundary layers over such a configuration are investigated first as an instructive case. In the engulfment process, it is found that irrotational ‘bubbles’ near the TNTI are more likely to originate from engulfment, while bubbles far from the TNTI could be produced by the local turbulence itself. Additionally, H-SMs are found to enhance the engulfment by the sweep flow. In the nibbling process, a competition relationship is observed: L-SMs induce stronger instantaneous ‘nibbling’ events by transporting more fluids towards the TNTI, while the H-SMs induced a more distorted TNTI. Consequently, the integral nibbling flux is greater above H-SMs. Furthermore, the explored mechanisms are verified to be insensitive to the wall shapes such as smooth and homogeneous roughness walls, which demonstrates that these modulations are universal for turbulent boundary layers. Finally, a conceptual modulation model is proposed to illustrate the entrainment process above the large-scale motions.

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“…where ∂Ω denotes the plume boundary, N = (N s , N y , N η ) T denotes the three-dimensional inward-pointing normal along ∂Ω, N ⊥ = (N y , N η ) T and u ⊥ = (u y , u η ) T are the vector components in the ( y, η) plane and n = N ⊥ /|N ⊥ | is the inward-pointing two-dimensional normal in the ( y, η) plane. As the plume boundary will be detected via the average buoyancy field b (see § 4), N is defined as N = ∇ b/|∇ b| (see also van Reeuwijk et al 2021). The factor 1/π in the definition of L[φ] and E[φ] is introduced for consistency with the convention in plume theory of dividing the integral quantities through by π (see (2.7)).…”

Section: Integral Equationsmentioning

confidence: 99%

“…Integration of (A1) over the plume area, whose domain is denoted Ω, expressed in the (s, y, η) coordinate system results in (using identity (2.5) for a steady state (v = 0) from van Reeuwijk et al (2021))…”

Section: Appendix a Derivation Of The Integral Identitymentioning

confidence: 99%

Under pressure: turbulent plumes in a uniform crossflow

et al. 2021

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Direct numerical simulation is used to investigate the integral behaviour of buoyant plumes subjected to a uniform crossflow that are infinitely lazy at the source. Neither a plume trajectory defined by the centre of mass of the plume $z_c$ nor a trajectory defined by the central streamline $z_{U}$ is aligned with the average streamlines inside the plume. Both $z_c$ and $z_{U}$ are shown to correlate with field lines of the total buoyancy flux, which implies that a model for the vertical turbulent buoyancy flux is required to faithfully predict the plume angle. A study of the volume conservation equation shows that entrainment due to incorporation of ambient fluid with non-zero velocity due to the increase in the surface area (the Leibniz term) is the dominant entrainment mechanism in strong crossflows. The data indicate that pressure differences between the top and bottom of the plume play a leading role in the evolution of the horizontal and vertical momentum balances and are crucial for appropriately modelling plume rise. By direct parameterisation of the vertical buoyancy flux, the entrainment and the pressure, an integral plume model is developed which is in good agreement with the simulations for sufficiently strong crossflow. A perturbation expansion shows that the current model is an intermediate-range model valid for downstream distances up to $100\ell _b$ – $1000 \ell _b$ , where $\ell _b$ is the buoyancy length scale based on the flow speed and plume buoyancy flux.

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Unified description of turbulent entrainment

Abstract: Abstract

Cited by 15 publications

References 69 publications

High Grashof number turbulent natural convection on an infinite vertical wall

High Grashof number turbulent natural convection on an infinite vertical wall

Universal modulations of large-scale motions on entrainment of turbulent boundary layers

Under pressure: turbulent plumes in a uniform crossflow

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