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Catalyst design is central to the development of monopropellant thrusters and hence, ignoring its importance, as I have realised, is not very good practice. My question is if the mass flow rate, bed loading, chamber temperature and pressure are known, is there a simple hard-and-fast means to determine a rudimentary geometry?

Edit: I have since found two examples of equations used to determine catalyst pack length, both of which are a product of catalyst diameter.

The first example (equation 9) seems pretty straight forward however I am unsure what the variable R_u represents (it isn't mentioned anywhere else) and;

enter image description here

The second example-I have no idea what going on with this, all the values are there but I can't seem to get the right answer. I think the m^2 symbol implies that the answer is the square root but is still incorrect.

enter image description here

I have been struggling with this for some time so if anyone could tell me what I am doing incorrectly it would be greatly appreciated!

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    $\begingroup$ If we think of a very short catalyst bed with a small conversion ratio of about 10 %, doubling the length may rise the ratio to about 20 %. But how to increase the ratio from 80 to 95 % is not so easy. To find a good compromise between chamber length and conversion ratio seems to be very hard. I found an article medcraveonline.com/AAOAJ/AAOAJ-03-00076.pdf , the model looks very diificult , another paper core.ac.uk/download/pdf/84144819.pdf $\endgroup$
    – Uwe
    Jun 7, 2022 at 11:57
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    $\begingroup$ I think you are getting into trying to obtain manufacturer's proprietary design info. Lots of testing is involved in developing that technology. That's how they try to distinguish themselves in competitive bidding. $\endgroup$
    – tckosvic
    Jun 7, 2022 at 16:13
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    $\begingroup$ $R_u$ is the universal gas constant. It could be replaced in that equation with $R$ because the molar mass is in the denominator: $R=\frac{R_u}{\bar{m}}$ $\endgroup$
    – A McKelvy
    Jun 22, 2022 at 11:00
  • $\begingroup$ The link to the second example doesn't work. It seems to be a link to a file on your pc. Please provide a link to the source or at least say what it was. $\endgroup$
    – Organic Marble
    Jun 22, 2022 at 15:28
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    $\begingroup$ @OrganicMarble thank you very much I had no idea, I've just edited it now. $\endgroup$
    – R. Hall
    Jun 23, 2022 at 1:10

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Partial answer -

First equation:

As A McKelvy states in a comment, using Ru to be the universal gas constant of 8.314 J / mol-K will get you the answer given in the paper.

Second equation:

Given the numbers in the paper I got 8.96 cm which is pretty close to the 8.852 cm they give.

You have to convert the given values of stay time into seconds and the pressure into pascals. I believe the "m^2" at the end of the equation is an error, it should read "m", the answer comes out in meters. Then they quote it in cm.

Remember the fundamental definitions of newtons and joules when checking the units.

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