On the Gradient Diffusion Hypothesis and Passive Scalar Transport in Turbulent Flows

Combest, Daniel P.; Ramachandran, P.A.; Duduković, Milorad P.

doi:10.1021/ie200055s

Cited by 86 publications

(32 citation statements)

References 29 publications

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“…These results confirmed that one single value of Sc t is unable to represent the physical processes in the entire domain and that Sc t may need to be calibrated on a case by case basis. Thus, it would be of interest to better represent the effects of hydrodynamic unsteadiness and turbulence anisotropy on the scalar transport [25] through refined turbulence and algebraic GDH models as highlighted by Combest et al [97]. For the contact tank, it would be interesting to determine whether inaccuracies can be attributed solely to the inadequacy of the particular turbulence model (in this case, the standard k-ε) chosen or whether an improved calculation of the turbulent diffusivity, e.g., by a locally-varying value of Sc t or a departure from the standard GDH would allow more reliable, ideally uncalibrated, predictions.…”

Section: Discussionmentioning

confidence: 99%

On the Values for the Turbulent Schmidt Number in Environmental Flows

Gualtieri

Angeloudis

Bombardelli

et al. 2017

Fluids

166

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Computational Fluid Dynamics (CFD) has consolidated as a tool to provide understanding and quantitative information regarding many complex environmental flows. The accuracy and reliability of CFD modelling results oftentimes come under scrutiny because of issues in the implementation of and input data for those simulations. Regarding the input data, if an approach based on the Reynolds-Averaged Navier-Stokes (RANS) equations is applied, the turbulent scalar fluxes are generally estimated by assuming the standard gradient diffusion hypothesis (SGDH), which requires the definition of the turbulent Schmidt number, Sc t (the ratio of momentum diffusivity to mass diffusivity in the turbulent flow). However, no universally-accepted values of this parameter have been established or, more importantly, methodologies for its computation have been provided. This paper firstly presents a review of previous studies about Sc t in environmental flows, involving both water and air systems. Secondly, three case studies are presented where the key role of a correct parameterization of the turbulent Schmidt number is pointed out. These include: (1) transverse mixing in a shallow water flow; (2) tracer transport in a contact tank; and (3) sediment transport in suspension. An overall picture on the use of the Schmidt number in CFD emerges from the paper.

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Section: Discussionmentioning

confidence: 99%

On the Values for the Turbulent Schmidt Number in Environmental Flows

Gualtieri

Angeloudis

Bombardelli

et al. 2017

Fluids

166

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“…The concern expressed by Combest, Ramachandran & Dudukovic (2011) regarding the lack of availability of reliable values of the turbulent Prandtl number (Pr T ), later addressed in Darisse, Lemay & Benaïssa (2013a), is but one implication. In spite of that, reliable measurements of the passive scalar field of round jets evolving in still air (without a co-flow) are few and far between (Gouldin et al 1986).…”

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confidence: 99%

Budgets of turbulent kinetic energy, Reynolds stresses, variance of temperature fluctuations and turbulent heat fluxes in a round jet

2015

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The self-preserving region of a free round turbulent air jet at high Reynolds number is investigated experimentally (at x/D = 30, Re D = 1.4 × 10 5 and Re λ = 548). Air is slightly heated (20 • C above ambient) in order to use temperature as a passive scalar. Laser doppler velocimetry and simultaneous laser doppler velocimetry-cold-wire thermometry measurements are used to evaluate turbulent kinetic energy and temperature variance budgets in identical flow conditions. Special attention is paid to the control of initial conditions and the statistical convergence of the data acquired. Measurements of the variance, third-order moments and mixed correlations of velocity and temperature are provided (including vw 2 , uθ 2 , vθ 2 , u 2 θ, v 2 θ and uvθ ). The agreement of the present results with the analytical expressions given by the continuity, mean momentum and mean enthalpy equations supports their consistency. The turbulent kinetic energy transport budget is established using Lumley's model for the pressure diffusion term. Dissipation is inferred as the closing balance. The transport budgets of the u i u j components are also determined, which enables analysis of the turbulent kinetic energy redistribution mechanisms. The impact of the surrogacy vw 2 = v 3 is then analysed in detail. In addition, the present data offer an opportunity to evaluate every single term of the passive scalar transport budget, except for the dissipation, which is also inferred as the closing balance. Hence, estimates of the dissipation rates of turbulent kinetic energy and temperature fluctuations ( k and θ ) are proposed here for use in future studies of the passive scalar in a turbulent round jet. Finally, the budgets of turbulent heat fluxes (u i θ) are presented.

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“…However, it is clearly seen that the chemical source terms are important at x/d = 10 compared with the production terms because of the large reaction rate in this region. In the eddy viscosity model (Combest et al 2011), the Reynolds stress is given by…”

Section: Resultsmentioning

confidence: 99%

“…One of the most practical and widely used models for u i γ α is the gradient diffusion model (e.g. Tominaga & Stathopoulos 2007;Combest, Ramachandran & Dudukovic 2011), in which u i γ α is modelled by…”

Section: Introductionmentioning

confidence: 99%

Turbulent Schmidt number and eddy diffusivity change with a chemical reaction

Watanabe¹,

Sakai²,

Nagata³

et al. 2014

J. Fluid Mech.

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We provide empirical evidence that the eddy diffusivity D tα and the turbulent Schmidt number Sc tα of species α (α = A, B or R) change with a second-order chemical reaction (A + B → R). In this study, concentrations of the reactive species and axial velocity are simultaneously measured in a planar liquid jet. Reactant A is premixed into the jet flow and reactant B is premixed into the ambient flow. An optical fibre probe based on light absorption spectrometry is combined with I-type hot-film anemometry to simultaneously measure concentration and velocity in the reactive flow. The eddy diffusivities and the turbulent Schmidt numbers are estimated from the simultaneous measurement results. The results show that the chemical reaction increases Sc tA ; Sc tB is negative in the region where the mean concentration of reactant B decreases in the downstream direction, and is positive in the non-reactive flow in the entire region on the jet centreline. It is also shown that Sc tR is positive in the upstream region whereas it is negative in the downstream region. The production terms of axial turbulent mass fluxes of reactant B and product R can produce axial turbulent mass fluxes opposite to the axial gradients of the mean concentrations. The changes in the production terms due to the chemical reaction result in the negative turbulent Schmidt number of these species. These results imply that the gradient diffusion model using a global constant turbulent Schmidt number poorly predicts turbulent mass fluxes in reactive flows.

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On the Gradient Diffusion Hypothesis and Passive Scalar Transport in Turbulent Flows

Cited by 86 publications

References 29 publications

On the Values for the Turbulent Schmidt Number in Environmental Flows

On the Values for the Turbulent Schmidt Number in Environmental Flows

Budgets of turbulent kinetic energy, Reynolds stresses, variance of temperature fluctuations and turbulent heat fluxes in a round jet

Turbulent Schmidt number and eddy diffusivity change with a chemical reaction

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