Hi all,

I want to do CFD of laminar reactive liquid flow. The chemistry is represented by a system of two parallel competitive reactions, one quasi-instantaneous and the other one still very fast as compared to mixing time; the yield of this reaction system is sensitive to micro-mixing. There's a lot about micro-mixing models for TURBULENT reactive GAS flow, but what about models for LAMINAR reactive LIQUID flow? All I could find was a model for "striation-thinning" by Ottino but it seems to be quite impractical. Any ideas/hints where to look for more information?

Many thanks in advance,

Ingo Meisel

Hi,

I think there may be a confusion on what is micro-mixing. I will try to clarify:

- for turbulent reactive gas, the mixing is mainly performed by the turbulent process that occurs at small scales (modeled by the turbulence).

- in laminar cases, the mixing is performed by species convection and diffusion.

Can you describe more accurately the configuration you are aiming for and what kind of accuracy you expect?

What do you mean by "micro-mixing"?

One solution might be to solve the reaction using the full or reduce system of reaction and solve all species using appropriate models to account for molecular diffusion.

Hoppe being helpfull Julien

Hello jdc,

thank you for your quick reply.

In chemical engineering jargon, micro-mixing means the diffusional mixing on the molecular length scale; only after this process is completed (reactand molecules "see" their respective reaction partners in their immediate vicinity) can chemical reactions occur.

I am trying to simulate a system of two parallel-competitive reactions (1. A + B -> P, 2. A + C -> S, i.e. reactands B and C compete for limited reactand A) ,isothermal, with no chemistry feedback on the flow. Since the first reaction occurs extremely fast (quasi-instantaneous), and the second reaction is "only" very fast, for the case of a homogeneous mixture of A, B and C ("well micro-mixed"), only the first reaction will occur such that only (desired) product P is generated whereas (unwanted) by-product S will not occur. This is due to the fact that all A is consumed instantaneously by reaction 1 even though A is surrounded by B as well as C, and there will be no A left for reaction 2. On the other hand, if A and B/C are completely "segregated", half of the amount of A will be consumed by reaction 1 to produce P, and half of A will be consumed by reaction 2 to produce S. Therefore, measuring the amount of S produced in an experiment gives a measure of the degree of "micromixedness" in the reacting flow system; this is a method to characterize e.g. stirred-tank reactors for their mixing efficiency.

Since I come from the CFD side, it's my first time to deal with "micromixing" as defined in the chemical engineering sense. In the literature several approaches have been published on how to deal with the subgrid-scale phenomenon of mixing on the molecular scale since CFD cannot resolve all the length scales down to the Batchelor scale. These models include presumed/full probability density function (PDF) approaches, scalar-dissipation/scalar-variance/scalar-flux/reaction-rate closures, flamelets, linear-eddy models, conditional-moment-closure, to name just a few. Unfortunately, all these methods were derived assuming turbulent flow conditions, and involving gas flows. Looking for information about LAMINAR flow of liquids involving chemical reactions, I got the impression that either one might not need such a subgrid-scale model for diffusional mixing on the molecular length scale (but if so, why?) or I just didn't look for it in the appropriate journals. Or is it o.k. to use the above-mentioned models for laminar flow of reactive liquids? I don't think so because looking through the FLUENT manuals (that's the code I'm supposed to use) I found that all the provided models for reactive flows are restricted to turbulent gas flows.

Hope this helps to clarify my problem,

thank you again,

Ingo Meisel

Are A, B,C,P,S all liquids? I guess how are initially positioned and dynamically driven are important factors. Even at Laminar flow, there are significant "mixing" (not on molecular scale) by vortex motion that enhance contacting areas for species.

Hi versi,

thank you for your comment.

Yes, the reactands and products are all liquids dissolved in water as a carrier liquid (i.e. dilute approximation holds, and no precipitation processes occurs).

The problem is not how global flow features such as vortices, backflow regions and so forth affect the mixing (or rather, "convective stirring", as "mixing" here refers to diffusional processes only) on the macroscopic length scale. I wonder wether it is necessary to include some model to take subgrid-scale mixing (i.e. length scales that are not resolved by the numerical grid) into account. CFD results will eventually suggest that everything is well-mixed within a computational cell; one merely has to wait long enough to have all concentration gradients smeared out within this grid cell. But as I understand from the literature, in reality there could still be significant differences in concentration on the length scale of the computational grid and below, i.e. the reaction partners could still be segregated to a finite degree on the grid cell length scale and below - which will affect the product yield considerably, resulting in false predictions (often, an overestimation) from the simulation.

I found some more papers that might be related to this topic; if I find something new I did not mention so far or that could clarify my not-too-clear explanations, I'll post it here in this thread.

Again, thank you all for your comments and suggestions.

Yours sincerely,

Ingo Meisel

Hi Ingo,

From what I understand of your description, the mixing is ONLY due to molecular diffusion (and NOT from turbulent mixing). In this context, you can forget all combustion modeling such as PDF, variance, flamelets.... The more straightforward way (to my opinion) seems to: - set the flow as laminar - define reactants A, B, C and products P and S - and solve for the laminar mixing (eg, convection and molecular diffusion) of A, B, C, P and S

The two hard points are:

1) How to account for the molecular diffusion? Have a close look on all modeling for laminar flames. A starting point could be the manual of EGlib library. In short, the coarse modeling is constant Lewis number. More accurate is polynomial coefficient. Even more accurate is based on the kinetic theory.

My advice: use Lewis=1 for all species as a first approximation (unless you know the diffusion coefficients).

2) How to model for the chemical reaction? It seems you have an approximate idea of the chemical reaction times. Since all phenomena happens in laminar flow, you could just set the reactions:

A + B -> P \dot{w} = f(???) A + C -> S \dot{w} = f(???) with the appropriate way of specifying the reaction rate (it will be according to your chemical time)

My advice: this will be the hard point. Try to write the theory as clearly as possible and if you have the opportunity, have a chat with someone doing CFD of laminar flames.

I have no experience with fluent but I assume they will probably be able to do laminar combustion using "complex or simplified chemical reaction schemes".

Good luck, Julien