I found a nice write up by David Shultz titled "
Parachute Bay Pressure Vents" that describes how to model compartment venting using a simple system that behaves like and RC filter.
Apparently, Bob Krech had posted a formula for computing the time constant for an altimeter bay vent on Rocketry Online but it is lost due to a server crash.
The Altimeter Bay Time Constant formula is:
T = L*((D/d)^2))/4000
L is the length of the compartment
D is the inside diameter of the compartment
d is the diameter of the circular vent hole
The write up, see link above, goes on to show how a first order digital filter can be used to model this and provides a link to a nice little C program. While the original C program was written to work with RockSim, I modified it to work with exported data from OpenRocket consisting of time, altitude, velocity, pressure, and time step. The output is a csv text file. Here's a short sample of the output file:
#Compartment Diameter = 3.900000
#Compartment Length = 27.000000
#Vent Diameter = 0.132580
#TC = 5.840863
time (s), altitude (ft), velocity (ft/s), pressure (psi), filtered pressure (psi), pressure difference (psi), force (lbs)
0.010000, 0.000000, 0.000000, 14.700000, 14.700000, 0.000000, 0.000000
...
0.250000, 7.503700, 77.613998, 14.697099, 14.699971, 0.002872, 0.034314
I manually crop the output file after apogee deployment events at peak altitude.
The payload section of my Frenzy will need to vent the payload tube volume plus the nosecone volume. For vent calculations, I used L = 27 inches for the payload compartment, and D = 3.90 inches. After careful consideration, I've decided to use three 3/32 diameter vent holes in my Payload Compartment, with the holes just below the nosecone coupler, spaced 120 degrees apart and aligned with the fins to minimize flow disturbance over the altimeter bay vent holes. As I'm using 3 holes, I calculated an "effective diameter" for the three 3/32" vent holes using the following equation:
d = EffectiveVentDiameter = 2*sqrt((n*A)/pi)
n is the number of holes
A is the area for a single hole
This "effective diameter" is what I used to input vent hole diameter into the simulation program for multiple vent hole configurations.
Thus d = 0.16238" for n=3 3/32" vent holes
I ran the simulation for multiple scenarios, assuming that one or two of the three vent holes could be blocked. The vent diameters used where: d=0.16238 (3 holes), d=0.13258 (2 holes), d = 0.09375 (1 hole).
It's interesting to see how much additional force due to trapped internal pressure can be created by blocked vent holes. Here are my results for the Payload/Main Parachute Compartment where I've plotted the output/results using Google Sheets:
I'll be using three 4-40 shear pins to secure the nosecone to the payload tube. They were sized primarily for potential shock load upon the kevlar cord snapping tight during the apogee drogue deployment, but they must also withstand the added stress due to any trapped pressure within the payload compartment. Three 3/32" diameter vent holes will be a good size and number for the Payload Compartment, even if one or two holes are completely blocked by recovery gear.
For the Booster/Drogue Parachute Compartment, I used L = 22 inches, D = 3.9 inches and d=0.16238 (3 holes), d=0.13258 (2 holes), d = 0.09375 (1 hole), where d is the effective diameter for the number of 3/32" diameter vent holes being simulated.
I'll be using three 2-56 shear pins to secure the booster section to the lower avionics bay. These pins will combat separation forces due to internal pressure as well as drag deceleration forces after motor burnout. The three 3/32" diameter vent holes look to be a good size for the Booster Compartment. Similar to the Payload shear pins, the Booster shear pins should be able to tolerate one or two vent holes becoming blocked by recovery gear.
I've plotted the output/results using Google Sheets.