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Phenomenology of turbulent mixing in variable viscosity and density flows – MUVAR

MUVAR

Phenomenology of turbulent mixing in variable viscosity and density flows

Fundamental study of the variable viscosity and density flows.

In variable viscosity or density flows, we will study the effect of the hydrodynamical (Reynolds number) and physico-chemical parameters (density ratio and viscosity) on the behaviour of the dynamical system (velocity and scalar field) at various scales (mean and fluctuating fields).

The approach will be triple: analytical, experimental and numerical, with the objective of better understanding the phenomenology of mixing. For each of the scales, energy budgets will be established in order to better understand the flow features. This kind of approach should, on the one hand, result in a better characterization of variable viscosity and density flows and, on the other hand, open new perspectives towards the development of new subgrid models for Large Eddy Simulations.

Given: the injection velocity, the geometry of the injector (nozzle), the two mixed fluids either with different densities, or viscosities and for each region of the flow, i.e. at a given downstream position from the injection, and a lateral position (on the jet axis, where only the decay and the turbulence production are present) or out of the axis (shear region), the aim of the project is to provide answers to the following questions, all of them being challenging through the way in which combined expertise (analytical, experimental and numerical) will be put together in order to answer them:
1) Which is the morphology of the velocity field and of mixing ? This consists in detecting the characteristic structures present in the flow (vortices and scalar sheets, their sizes and lengths).
2) How can be characterized the flow and mixing from a statistical viewpoint? Note that our main sight is on the scalar field, the dynamical field being studied only because both of them are coupled.

3) Which are the dynamical evolutions of second-and-third-order statistics? Starting from the already developed scale-by-scale energy budget equations for isotropic or anisotropic/axisymmetric turbulence (Danaila et al. 2004, Danaila, Antonia and Burattini 2011, Danaila et al. 2011 and ANR ‘ANISO’), these equations are to be written in the context of variable density/viscosity flows, by considering Favre averages and fluctuations of the viscosity, a first step has been done during the PhD of B. Talbot, Coria.
4) Which is the phenomenology of the mixing/flow associated with the dynamical transport equations of scale-by-scale energy?
5) Which are reliable closures for the third-order velocity-scalar terms?
6) Which is the mixing time at several representative positions in the flow, and for each injection velocity?
7) Which are the flow regimes, injector shape etc. which are most favourable to rapid mixing?

The present fundamental research proposal, which combines theory, experiments and computations creatively and innovatively, will make a significant contribution to the engineer’s ability to predict the mixing characteristics of turbulent flows encountered in industry and nature. The mixing of two fluid streams is of fundamental importance to a broad spectrum of engineering and environmental applications. In combustion systems, for example, the molecular mixing of fuel and oxidizer is a necessary precursor to chemical reaction. Focusing on how the small scale scalar fluctuations are destroyed- an important feature of this proposal- should lead to an improved understanding of turbulent non-premixed combustion as well as pollutant formation processes.
We have emphasized that the key for providing realistic engineering predictions of mixing in different turbulent flow types is the inclusion in the mathematical analysis of only the most relevant physical processes which control the large scale energy and scalar variance budgets in a particular flow or a specific region of this flow. This will then allow us to properly account for the effect of the large scales on the small scales by formulating the most appropriate mathematical form of the scale-by-scale energy and scalar variance budgets. These budgets can subsequently be used, by modelling the second-order terms, for yielding realistic predictions of the transfer rates of energy and scalar variance, thus allowing an intelligent assessment of the status of mixing by comparison to the asymptotic (infinite Reynolds number) results that have been available since the 1940s. In particular, we will be able to quantify the departures from the asymptotic inertial range behaviour for different flows or, alternately, in the same flow but over a range of Reynolds numbers.

Three publications and several participations at international congresses

Solving the 'theory of turbulence' supposes the ability to predict the statistical behavior of any turbulent field. The ideal solution would be a tractable quantitative theory, based on the Navier-Stokes equations. On the other hand, most of traditional turbulence studies concern homogeneous fluids flows. But, variable viscosity and density flows represent the most important part of real flows.
Therefore, it is important from both fundamental and economical viewpoints to understand, with the aim to predict, mixing in variable viscosity and density flows. The fluid composition is in this case an active scalar, since it modifies locally the value of the velocity field.
This study will be performed by considering two situations, depending on the values of the density ratio between the two mixed fluids and of their dynamical viscosity ratio:
1. fluids with the same density, but with different viscosity (propane/air, for which the dynamical viscosity ratio is 3.5),
2. fluids with the same viscosity, but with different densities (helium mixed with air, the ratio of densities is 7).
These two representative situations will be critically compared with the reference case for which both density and viscosity are the same, i.e. the passive scalar mixing (very slightly heated air, mixed with fresh air).
The final aim is to push forth our understanding of the active scalar mixing, with the aim to predict a part of its statistical properties. Therefore, our objectives are physical questions addressed on active scalar mixing. These objectives concern the characterisation of the phenomenology, understanding and predicting the active scalar mixing, without neglecting the dynamical field, in variable density and viscosity fluids.
All of the addressed questions are challenging through the way in which combined expertise (analytical, experimental and numerical) will be put together in order to answer them. The questions are:
1) Which is the morphology of the velocity field and of mixing ?
2) How can be characterized the flow and mixing from a statistical viewpoint?
3) Which are the dynamical evolutions of second-and-third-order statistics?
4) Which is the phenomenology of the mixing/flow associated with the dynamical transport equations of scale-by-scale energy? Closing reasonably these equations is equivalent to having correctly identified the phenomena characteristic of the flow and in particular the influence of variable density and/or viscosity.
5) Which are reliable closures for the third-order velocity-scalar terms?
6) Which is the mixing time at several representative positions in the flow, and for each injection velocity?
7) Which are the flow regimes, injector shape etc. which are most favourable to rapid mixing?

The issues raised above will be tackled by using, as interactively as is feasible, three kinds of tools: analysis/theory, experiments and simulations. The experimental study concern a round jet flow of one fluid, issuing in an ambient with another fluid. Nominally, two types of experiments will be performed:
-mixing of two fluids with nearly the same density, but with a different dynamical viscosity (e.g. propane/air), in CORIA;
-mixing of two fluids with nearly the same viscosity, but with a different densities (e.g. helium/air), at IRPHE.
In both cases, the experimental techniques concern planar measuremens of the velocity field (PIV) and of the scalar (either by Rayleigh scattering, or PLIF on acetone).

Whilst measurements will be done for several Reynolds numbers ranging from very low (Taylor microscale Reynolds number smaller than 100) to moderate/large Reynolds (larger than 100), numerical simulations of variable viscosity/density jets focus on the lowest velocities. The numerical database will bring an important information which is not available experimentally (the unmeasured velocity component, or several terms in the mean energy dissipation rate.

Project coordinator

Madame Luminita DANAILA (Complexe de Recherche Interprofessionnel en Aérothermochimie) – danaila@coria.fr

The author of this summary is the project coordinator, who is responsible for the content of this summary. The ANR declines any responsibility as for its contents.

Partner

CORIA Complexe de Recherche Interprofessionnel en Aérothermochimie
CNRS - IRPHE Centre National de Recherche Scientifique délégation Provence et Corse - Institut de Recherche sur les Phénomènes Hors Equilibre

Help of the ANR 358,966 euros
Beginning and duration of the scientific project: December 2012 - 36 Months

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