On mean flow universality of turbulent wall flows. I. High Reynolds number flow analysis

Stefan, Heinz G.

doi:10.1080/14685248.2019.1566736

Cited by 16 publications

(28 citation statements)

References 93 publications

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“…[57]) Recently, Heinz (Ref. [58], Fig. A.2d) provides a relation between the momentum thickness Reynolds number R θ and the Kármán number, i.e., R τ = 0.31R θ , which leads to the skin friction relation of the Coles-Fernholz type:…”

Section: Logarithmic Friction Lawsmentioning

confidence: 99%

Refinement of the logarithmic law of the wall

Laadhari

2019

Phys. Rev. Fluids

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Available direct numerical simulation of turbulent channel flow at moderately high Reynolds numbers data show that the logarithmic diagnostic function is a linearly decreasing function of the outer-normalized wall distance η = y/δ with a slope proportional to the von Kármán constant, κ = 0.4. The validity of this result for turbulent pipe and boundary layer flows is assessed by comparison with the mean velocity profile from experimental data. The results suggest the existence of a flow-independent logarithmic law U + = U /u τ = (1/κ) ln(y * /a), where y * = yU S /ν with U S = yS(y) being the local shear velocity and the two flow-independent constants κ = 0.4 and a = 0.36. The range of its validity extends from the inner-normalized wall distance y + = 300 up to half the outer-length scale η = 0.5 for internal flows, and η = 0.2 for zero-pressure-gradient turbulent boundary layers. Likewise, and within the same range, the mean velocity deficit follows a flow-dependent logarithmic law as a function of a local mean-shear-based coordinate. Furthermore, it is illustrated how the classical friction laws for smooth pipe and zero-pressure-gradient turbulent boundary layer are recovered from this scaling.

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Section: Logarithmic Friction Lawsmentioning

confidence: 99%

Refinement of the logarithmic law of the wall

Laadhari

2019

Phys. Rev. Fluids

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“…There + 12 = + 1 + + 2 is the inner flow contribution to the dimensionless mean strain rate + (4), disregarding wake effects, see Eq. ( 7) of [20] and the corresponding discussion. Precisely, the universal function…”

Section: Analysis: Exact Eddy-viscosity Formula and Transport Equatio...mentioning

confidence: 95%

“…The aim of this work is to offer a third way, at least for a relevant class of flows: fully developed channel and pipe flows, together with zero-pressure gradient boundary layers over a flat plate. For these three canonical flows, denoted hereafter 'turbulent wall flows', [20,21] proposed analytic models of the mean flow , Reynolds shear stress − and eddy viscosity , built after a thorough analysis of recent DNS, including those of [7,22,23], and experimental data, for instance those of [24]. Interestingly, these models are valid for friction-based Reynolds numbers 500:…”

Section: R -Amentioning

confidence: 99%

“…Following [20,21], we consider turbulent wall flows of incompressible fluids of mass density and kinematic viscosity . Locally, a cartesian system of coordinates O is used, such that points in the streamwise direction, and measures the distance to the closest wall.…”

Section: Analysis: Exact Eddy-viscosity Formula and Transport Equatio...mentioning

confidence: 99%

“…The second ingredient of the theory is the function , which is flow-dependent and in outer scaling, because it describes wake effects. With the notations of [20,21], = 1/ for channel and pipe flows, / for boundary layers, where and characterize the wake contribution + 3 to the dimensionless mean strain rate + (see Eqs. 7 and A.22 of [20]), characterizes the total stress in boundary layers (see Eq.…”

Section: Analysis: Exact Eddy-viscosity Formula and Transport Equatio...mentioning

confidence: 99%

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Exact Eddy-Viscosity Equation for Turbulent Wall Flows—Implications for Computational Fluid Dynamics Models

Plaut

Stefan

2022

AIAA Journal

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For turbulent channel flow, pipe flow and zero-pressure gradient boundary layer, Heinz (2018, 2019) yields analytical formulas for the eddy-viscosity as a product of a function of + (the wall-normal distance scaled in inner units) and a function of / (the same scaled in outer units). By calculating the eddy-viscosity turbulent diffusion term, we construct for those flows an exact high-Reynolds number equation with one production and two dissipation terms. One dissipation term is universal, peaks near the wall, and scales mainly with + . The second, smaller one, is flow-dependent, peaks in the wake, and scales mainly with / . The production term is flow-dependent, peaks in between, and scales similarly. The universal dissipation term implies a length scale analogous to the von Karman length scale used in the SAS models of Menter. This length scale also appears in the production term. This confirms the relevance of these length scales. An asymptotic analysis of all terms in the budget in the limit of infinite Reynolds numbers is provided. This yields a test bench of existing RANS models with a similar equation. We show that some models, e.g. the one of Spalart & Allmaras, do not respect the flow physics: they display a production peak in the near-wall region. We modify the most promising model, a SAS model. As a step forward towards a solution to the wall damping problem, the equation of our model behaves much more correctly in the near-wall region.

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Physics-Informed Minimal Error Simulation Methods for Turbulent Flow Predictions

Heinz

2024

Springer Proceedings in Physics

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On mean flow universality of turbulent wall flows. I. High Reynolds number flow analysis

Cited by 16 publications

References 93 publications

Refinement of the logarithmic law of the wall

Refinement of the logarithmic law of the wall

Exact Eddy-Viscosity Equation for Turbulent Wall Flows—Implications for Computational Fluid Dynamics Models

Physics-Informed Minimal Error Simulation Methods for Turbulent Flow Predictions

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