# What is a realistic useful life of a calcium carbonate pulse jet deflagration chamber?

My jet-propelled squid uses a scavenged shell for its pulse jet deflagration chamber, I am trying to determine how often he’ll have to replace it.

Including the shell it’s a 5 kg animal using a hydrogen-fueled pulse jet in 2-second bursts. The shell needs to absorb 9.6j/s (9.6 Watts) of heat energy over that 2 second period.

The fluted tube shell chamber, scavenged from another mollusk, is lined with heavy nacre (CaCO$$_3$$) using the ideal zig-zag nacre pattern of the conch having Young’s modulus of 75 GPa, a fracture toughness of 35 MPa, and an exterior calcium carbonate base with hardness of 900 on the Vickers scale, density of 950kg/m3.

Most other dimensions are dependant on what is necessary to release 320 J/s from a hydrogen-oxygen reaction, within an acoustically resonant pulse jet deflagration chamber. This means I don’t know the fuel consumption required for this energy release, which I believe would determine the size of the chamber.

The chamber diameter and length for example depends on these pulse jet specifications based on a valveless pulse jet. I found a spreadsheet calculator for valved jet engines but not for valveless.

The constraint is that the shell can’t weigh more than 2 kg because the animal weighs 3kg, and the fluting expands the mean radius by 10%. This means the formula for the shell length and inside and outside radii will be: $$2 kg = \frac{950 kg}{m^3}[1.1\pi l(r_2^2 - r_1^2)]m^3$$

My thoughts are that the shell is structurally sound for repeated use but how heating and cooling will wear on the shell are my key concerns.

Useful life would be the time it takes to fracture. Materials of equivalent characteristics are acceptable for approximations (such as ceramics with similar densities and hardness having known stress fracture limits).

I feel I’ve covered the required variables, I hope my squid can fly soon!

# What is the approximate range of 2-second uses this chamber can endure before failure?

• I don’t think heating and cooling are going to be your strongest driver of damage. Pitting caused by high energy impacts of combustion products is a significant factor. Remember that the velocity of gases in a plasma follow a poisson distribution and, at the upper end, can be significantly higher than the mean. This results in both energetic chemical and mechanic damage. – EDL Jan 9 '20 at 2:07
• The problem with using a scavenged shell is that shells aren't pure CaCO3. They're a complex microstructure of CaCO3 plates in a protein matrix. Heating the shell burns the protein. Burned shells were once (and may still be, in some places) a way of producing quicklime for concrete, e.g. en.wikipedia.org/wiki/Tabby_concrete – jamesqf Feb 24 '20 at 4:28
• @jamesqf Looks like proteins may be easily denaturated but are surprisingly hard to decompose pubs.acs.org/doi/suppl/10.1021/acs.est.7b00434/suppl_file/… - somewhere around 400eV to see pyrolytic nitrogen flying away from proteins. Whether or not denaturation imply a loss in mechanical integrity is debatable, up to a certain amount of denaturation may even improve the toughness of cements - eggs were mentioned as use in construction of walls/bridges in antiquity; a patent for impermeable mortar with lime and egg yolk patents.google.com/patent/DE4017623A1/en – Adrian Colomitchi Feb 24 '20 at 5:07

The shell needs to absorb 9.6j/s (9.6 Watts) of heat energy over that 2 second period.
...
but how heating and cooling will wear on the shell are my key concerns.

Calcite specific heat capacity: 0.8343 J/g*K
So a max of 20J for those 2 secs? At that energy as heat, a 200g (a tenth of those 2kg) mass of calcite will heat up by: 20/(200*0.8343) = 0.12K.

A burst of 12 pulses without cooling in between will result in a temperature increase of 1.44K. I don't actually think this ΔT by itself going to create a problem for the structural integrity of the shell.
It's more likely that ΔP during the deflagration to affect it.