# How to calculate catalyst bed geometry (length/radius) for a monopropellant thruster?

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; 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. 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!

• 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
– Uwe
Jun 7, 2022 at 11:57
• 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. Jun 7, 2022 at 16:13
• $R_u$ is the universal gas constant. It could be replaced in that equation with $R$ because the molar mass is in the denominator: $R=\frac{R_u}{\bar{m}}$ Jun 22, 2022 at 11:00
• 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. Jun 22, 2022 at 15:28
• @OrganicMarble thank you very much I had no idea, I've just edited it now. Jun 23, 2022 at 1:10