Fuel injector surrounded by a coaxial air stream

[Clausius2]

Maybe you, chemical people could answer my question.

Imagine a fuel injector surrounded by a coaxial air stream. The fuel and air flow are parallel, coaxial and axisymmetric. Both fluids obey ideal gas equation. Let's consider steady and compressible flow, i.e, variations of $$\rho$$ are important.

At low Mach numbers, the flow velocity is small enough to allow both reactants to be mixed by means of molecular diffusion and convection, resulting in a diffusion flame that can be seen experimentally. I think chemical reaction takes place in the mixing region of both substances. The thickness of this mixing layer I think it will depend on how important is the diffusion mechanism in the transport phenomena.

But my question is about high Mach numbers, in particular M>>1 (supersonic). What would happen?. Will there be enough time for molecular diffusion?. If not, it would be possible to the reaction to take place?.

Moreover, what do you think it will happen if fuel stream is subsonic and air is supersonic?

Any help is welcomed.

 

[altered-gravity]

Hi spanish collegue,

Interesting. I cannot assure nothing about it.

I would say that yes, even at very high flux velocities in a conctrete direction, there is always a numer of molecules traveling in the transversal direction (in fact in all directions). So there would be allways diffusion mechanisms (i think). If combustion iniciates, it wolud create turbulences enhancing the mixturing process don´t you think so?

Molecular Brownian motions are about 1 km/s, are you talking of flux velotities higher than this? Then perhaps combustion wolud appear only after a long distance from the start of the fluxes. During this distance perhaps some molecules would react, but heat transfer in the transversal direction would be avoided by such a high velocity.

 

[Clausius2]

Thanks for your reply. I was searching for an answer before doing any numerical simulation. I was pretending to employ Euler equations (without the diffusion terms) in order to describe the flow. Euler equations assume that diffusion and heat transfer are negligible compared with convection phenomena. This is the same thing that saying mixing layer has a negligible thickness compared with the longitudinal variations at #Mach>>1.

I do not agree with you have just said:

"I would say that yes, even at very high flux velocities in a conctrete direction, there is always a numer of molecules traveling in the transversal direction (in fact in all directions). So there would be allways diffusion mechanisms (i think)"

There will be a convection of both reactants in transverse directions. It is enough for enhancing a mixing process (isn't it?). . I've just make up my mind... this is an interesting question: chemical reaction is not possible if diffusion does not exist?. I would say not. The reactive energy term in N-S equations is:

$$D_{a}\theta Y_{F}Y_{O2} e^{\frac{T}{1+T/\beta}}$$ (non-dimensional).

So that, the chemical reaction will take place in a space region with both fuel and oxidizer are present simultaneusly. This can be reached only by a convective process (do you agree??, I'm not sure of that).

Anyway, I was trying to program some simulation of this flow in Matlab. This is very interesting in supersonic combustion (have you ever heard about Scramjet engine?). If not, see the attached file below. I've found it in the web. It's a supersonic flame simulated with Fluent.

 

[altered-gravity]

Ok, I confess that i´ve never read about such rapid flows. If you´re talking about match 3 or even higher velocities, the flow itself is quicker than the brownian motions of the molecules, that wold mean that almost all the molecules are traveling in the direction of the flow right? then there´s not diffusion to the transverse direction, so you would be right.

I can´t help you.

 

[altered-gravity]

(have you ever heard about Scramjet engine?)

No, how does it work?

 

[Clausius2]

Ok. It doesn't matter. I really didn't hope anyone to read this thread, because it's a bit complex to solve. Anyway, thanks again for trying something.

The Scramjet engine is a supersonic engine. It breaths the air directly of a supersonic atmosphere. Thus, air into combustion chamber runs supersonically, also in the combustion process. But knowing this process is a very hard task due to flame unstabilities. By the way, NASA's sciencist are almost able now to build such engine at large scale. Some people say the next decade they'll get rid of the space shuttle and use this hypersonic spacecraft .