Structure function tensor equations in inhomogeneous turbulence

Gatti, Davide; Chiarini, Alessandro; Cimarelli, Andrea; Quadrio, Maurizio

doi:10.1017/jfm.2020.399

Cited by 26 publications

(80 citation statements)

References 59 publications

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“…11. It is worth noting (Gatti et al 2020) that, since uv is not positive-definite, interpreting P 12 , Π 12 and 12 in terms of production or dissipation requires to account for the sign of uv . Negative values of P 12 are observed everywhere-except in a flat region very close to the cylinder side where it is slightly positive-with a global minimum within the primary vortex at (− 0.59, 1.03) and a local minimum in correspondence of the shear layer separating from the trailing edge at (2.65, 0.5).…”

Section: Single-point Budget Of the Reynolds Stressesmentioning

confidence: 99%

“…Along the shear layer Π 22 > Π 33 , so that uu preferentially provides energy to vv ; the opposite occurs in the core of the recirculating region, where ww is the largest receiver. Following Gatti et al (2020), the bottom left panel visualises this concept, by plotting in red (or blue) the areas where energy is preferentially transferred from uu to ww (or vv ). In fact, the incompressibility constraint mandates that:…”

Section: Single-point Budget Of the Reynolds Stressesmentioning

confidence: 99%

“…The line set is attracted by the large sink region with ξ 12 < 0 placed in the shear layer, and approach the leading edge corner. Again, when discussing these field lines, fluxes of uv should not be interpreted in terms of energy transfer, as uv is not a positive-definite quantity (Gatti et al 2020).…”

Section: Single-point Budget Of the Reynolds Stressesmentioning

confidence: 99%

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The Turbulent Flow over the BARC Rectangular Cylinder: A DNS Study

Chiarini

Quadrio

2021

Flow Turbulence Combust

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A direct numerical simulation (DNS) of the incompressible flow around a rectangular cylinder with chord-to-thickness ratio 5:1 (also known as the BARC benchmark) is presented. The work replicates the first DNS of this kind recently presented by Cimarelli et al. (J Wind Eng Ind Aerodyn 174:39–495, 2018), and intends to contribute to a solid numerical benchmark, albeit at a relatively low value of the Reynolds number. The study differentiates from previous work by using an in-house finite-differences solver instead of the finite-volumes toolbox OpenFOAM, and by employing finer spatial discretization and longer temporal average. The main features of the flow are described, and quantitative differences with the existing results are highlighted. The complete set of terms appearing in the budget equation for the components of the Reynolds stress tensor is provided for the first time. The different regions of the flow where production, redistribution and dissipation of each component take place are identified, and the anisotropic and inhomogeneous nature of the flow is discussed. Such information is valuable for the verification and fine-tuning of turbulence models in this complex separating and reattaching flow.

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Section: Single-point Budget Of the Reynolds Stressesmentioning

confidence: 99%

Section: Single-point Budget Of the Reynolds Stressesmentioning

confidence: 99%

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The Turbulent Flow over the BARC Rectangular Cylinder: A DNS Study

Chiarini

Quadrio

2021

Flow Turbulence Combust

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“…The present work comprehensively addresses the interscale exchanges across the wall-normal direction in a turbulent plane Couette flow, and builds upon a recent extension of the GKE (Gatti et al. 2020) that enables the observation of each component of the Reynolds stress tensor in the compound space of scales and wall distances. This extended tool, the anisotropic generalized Kolmogorov equations or AGKE, will be used here to study a Couette flow computed with DNS at , the highest considered by Kawata & Alfredsson (2018).…”

Section: Introductionmentioning

confidence: 99%

Ascending–descending and direct–inverse cascades of Reynolds stresses in turbulent Couette flow

et al. 2021

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The interaction between small- and large-scale structures and the coexisting bottom-up and top-down processes are studied in a turbulent plane Couette flow, where space-filling longitudinal rolls appear at relatively low values of the Reynolds number $Re$ . A direct numerical simulation database at $Re_\tau =101$ is built to replicate the highest $Re$ considered in recent experimental work by Kawata & Alfredsson (Phys. Rev. Lett., vol. 120, 2018, 244501). Our study is based on the exact budget equations for the second-order structure function tensor $\left \langle {\delta u_i \delta u_j} \right \rangle$ , i.e. the anisotropic generalized Kolmogorov equations (AGKE). The AGKE study production, redistribution, transport and dissipation of every Reynolds stress tensor component, considering simultaneously the physical space and the space of scales, and properly define the concept of scale in the inhomogeneous wall-normal direction. We show how the large-scale energy-containing motions are involved in the production and redistribution of the turbulent fluctuations. Both bottom-up and top-down interactions occur, and the same is true for direct and inverse cascading. The wall-parallel components $\left \langle {\delta u \delta u} \right \rangle$ and $\left \langle {\delta w \delta w} \right \rangle$ show that both small and large near-wall scales feed the large scales away from the wall. The wall-normal component $\left \langle {\delta v \delta v} \right \rangle$ is different, and shows a dominant top-down dynamics, being produced via pressure-strain redistribution away from the wall and transferred towards near-wall larger scales via an inverse cascade. The off-diagonal component shows a top-down interaction, with both direct and inverse cascades, albeit the latter takes place within a limited range of scales.

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“…The Karman–Howarth–Monin–Hill (KHMH) equation 54 is a general model without the need for making any assumptions about inhomogeneity and anisotropy. There are several works where the various terms of the KHMH equation are assessed (by post‐processing either DNS 51,55 or experimental 56 data) for their respective contributions to the evolution of the structure functions and to the turbulence cascade.…”

Section: Energy Spectrum—structure Function Model Based On Turbulence Anisotropymentioning

confidence: 99%

Modeling drop breakage using the full energy spectrum and a specific realization of turbulence anisotropy

et al. 2021

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The assumption of homogeneous isotropic turbulence when modeling drop breakage in industrially relevant geometries is questionable. We describe the development of an anisotropic breakage model, where the anisotropy is introduced via the inclusion of a perturbed turbulence spectrum. The selection of the perturbed spectrum is itself motivated by our previous large‐eddy simulations of high‐pressure homogenizers. The model redistributes energy from small to large scales, and assumes that the anisotropic part of the Reynolds stresses is confined to the energy‐containing range. The second‐order structure function arising from the perturbed spectrum is used in the standard framework of Coulaloglou and Tavlarides to calculate breakage frequency. While the base model exhibits non‐monotonic behavior (by predicting a maximum value for a certain drop size), the effect of anisotropy is shown to increase breakage frequency in length scales larger than this peak, thereby reducing non‐monotonicity. This effect is more pronounced for small turbulence Reynolds numbers.

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Structure function tensor equations in inhomogeneous turbulence

Cited by 26 publications

References 59 publications

The Turbulent Flow over the BARC Rectangular Cylinder: A DNS Study

The Turbulent Flow over the BARC Rectangular Cylinder: A DNS Study

Ascending–descending and direct–inverse cascades of Reynolds stresses in turbulent Couette flow

Modeling drop breakage using the full energy spectrum and a specific realization of turbulence anisotropy

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