Modulation of turbulence in forced convection by temperature-dependent viscosity

Zonta, Francesco; Marchioli, Cristian; Soldati, Alfredo

doi:10.1017/jfm.2012.67

Cited by 124 publications

(77 citation statements)

References 36 publications

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“…Table II lists the maximum grid spacing in terms of the Batchelor scale η θ = η/ √ Pr (with η the Kolmogorov scale) for all cases. The values are within the resolution requirements of x < 12η θ , y < 2η θ , z < 6η θ , as also reported in other DNS studies [13,29].…”

Section: Simulation Detailssupporting

confidence: 89%

“…In all such cases, the effects of thermophysical property variations can be strong enough to modulate turbulence and the traditional approach of treating temperature as a passive scalar no longer holds. Although turbulence modulation in a turbulent channel flow due to variable thermophysical properties has been investigated in great detail in high-Mach-number flows [9][10][11][12] and in low-Mach-number flows [13][14][15][16], the effect of property variations on scalar transport is not well understood. Lee et al [17] studied the influence of wall heating on turbulent thermal boundary layers with variable viscosity and observed variations in mean scalar, scalar fluctuation, and scalar flux, relative to a reference isothermal flow.…”

Section: Introductionmentioning

confidence: 99%

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Scalar statistics in variable property turbulent channel flows

2017

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Direct numerical simulation of fully developed, internally heated channel flows with isothermal walls is performed using the low-Mach-number approximation of Navier-Stokes equation to investigate the influence of temperature-dependent properties on turbulent scalar statistics. Different constitutive relations for density ρ, viscosity μ, and thermal conductivity λ as a function of temperature are prescribed in order to characterize the turbulent scalar statistics. It is shown that the dominant effect caused by property variations on scalar statistics can be parameterized by two nondimensional parameters, namely the semilocal Reynolds number Re τ ≡ Re τ √ (ρ/ρ w )/(μ/μ w ) (the bar and subscript w denote Reynolds averaging and wall value respectively, while Re τ is the friction Reynolds number based on wall values), and the local Prandtl number Pr = Pr w (μ/μ w )/(λ/λ w ) (Pr w is the molecular Prandtl number based on wall values). Near-wall gradients in Re τ modulate the turbulent heat flux generation mechanism because of structural changes in turbulence. However, the influence of these modulations on the inner scaling of turbulent heat conductivity normalized by local mean viscosity is shown to be weak. Using this observation, a temperature transformation is derived that is invariant of Re τ variations and only exhibits a Pr -dependent shift.

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Section: Simulation Detailssupporting

confidence: 89%

Section: Introductionmentioning

confidence: 99%

Scalar statistics in variable property turbulent channel flows

2017

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“…More complex stratified and rotating flows can also be envisaged in the future, with a wealth of new phenomena occurring, taking into consideration for example the effect of the walls on the energy budget [73], or the dependence of viscosity and diffusivity on temperature [74], leading in that case to intermittent bursts of heat transfer (see also [75] for strong intermittency in stratified flows). This opens the question of the validity of the assumption of a unit Prandtl number, at least in modeling approaches [74], the effect on thermal expansion seemingly being more important than that on viscosity [76].…”

Section: Discussionmentioning

confidence: 99%

Large-scale anisotropy in stably stratified rotating flows

et al. 2014

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We present results from direct numerical simulations of the Boussinesq equations in the presence of rotation and/or stratification, both in the vertical direction. The runs are forced isotropically and randomly at small scales and have spatial resolutions of up to 1024 3 grid points and Reynolds numbers of ≈ 1000. We first show that solutions with negative energy flux and inverse cascades develop in rotating turbulence, whether or not stratification is present. However, the purely stratified case is characterized instead by an early-time, highly anisotropic transfer to large scales with almost zero net isotropic energy flux. This is consistent with previous studies that observed the development of vertically sheared horizontal winds, although only at substantially later times. However, and unlike previous works, when sufficient scale separation is allowed between the forcing scale and the domain size, the total energy displays a perpendicular (horizontal) spectrum with power law behavior compatible with ∼ k −5/3 ⊥ , including in the absence of rotation. In this latter purely stratified case, such a spectrum is the result of a direct cascade of the energy contained in the large-scale horizontal wind, as is evidenced by a strong positive flux of energy in the parallel direction at all scales including the largest resolved scales.

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“…This forms the basis for an ideal setup to study turbulence modification due to variable properties, and to compare scaling laws with isothermal flows, as compared to a case where the bottom and top walls are at different temperatures and therefore at different Reynolds numbers. 14,25 The co-ordinates x, y, z represent the stream-wise, the wall-normal, and the span-wise directions, respectively; the corresponding velocity vectors are represented as u, v, w. The mean statistics are obtained by averaging with respect to time and in homogeneous directions (x and z) using Reynolds and Favre averaging. For a generic variable γ, the Reynolds averaged mean γ and its fluctuation γ ′ are defined as γ = γ + γ ′ , with γ ′ = 0.…”

Section: A Governing Equations and Computational Approachmentioning

confidence: 99%

Semi-local scaling and turbulence modulation in variable property turbulent channel flows

et al. 2015

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We theoretically and numerically investigate the effect of temperature dependent density and viscosity on turbulence in channel flows. First, a mathematical framework is developed to support the validity of the semi-local scaling as proposed based on heuristic arguments by Huang, Coleman, and Bradshaw ["Compressible turbulent channel flows: DNS results and modelling," J. Fluid Mech. 305, 185-218 (1995)]. Second, direct numerical simulations (DNS) of turbulent channel flows with different constitutive relations for density and viscosity are performed to assess and validate the semi-local scaling for turbulent statistics. The DNS database is obtained by solving the low-Mach number approximation of the Navier-Stokes equation. Finally, we quantify the modulation of turbulence due to changes in fluid properties. In the simulations, the fluid is internally heated and the temperature at both channel walls is fixed, such that the friction Reynolds number based on wall quantities is Re τ = 395 for all cases investigated. We show that for a case with variable density ρ and viscosity µ, but constant semi-local Reynolds number Re * τ ≡  (ρ/ρ w )/(µ/µ w )Re τ (where bar and subscript w, denote Reynolds averaging and averaged wall quantity, respectively), across the whole channel height, the turbulent statistics exhibit quasi-similarity with constant property turbulent flows. For cases where Re * τRe τ across the channel, we found that quasi-similarity is maintained for cases with similar Re * τ distributions, even if their individual mean density and viscosity profiles substantially differ. With a decrease of Re * τ towards the channel center (Re * τ < Re τ ), we show that the anisotropy increases and the pre-multiplied stream-wise spectra reveal that this increase is associated with strengthening of the large scale streaks in the buffer layer. The opposite effect is observed when Re * τ increases towards the channel center. The present results provide an effective framework for categorizing turbulence modulation in wall-bounded flows with variable property effects, and can be applied to any Newtonian fluid that is heated or cooled. C 2015 AIP Publishing LLC. [http://dx

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Modulation of turbulence in forced convection by temperature-dependent viscosity

Cited by 124 publications

References 36 publications

Scalar statistics in variable property turbulent channel flows

Scalar statistics in variable property turbulent channel flows

Large-scale anisotropy in stably stratified rotating flows

Semi-local scaling and turbulence modulation in variable property turbulent channel flows

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