What will be the pressure inside a small hydrogen peroxide rocket engine?

[guss]

Hello, I am designing a small hydrogen peroxide rocket engine. Hydrogen peroxide will be pumped into a combustion chamber where there will be a catalyst (manganese dioxide in this case) that will convert the peroxide into steam and oxygen. These byproducts will then exit through a nozzle.

I am designing the engine to put out 35 Newtons of thrust for 20 seconds, and use up .4 liters of 85%-90% pure hydrogen peroxide (all of these numbers are approximate). The combustion chamber is about 4cm long, and 2cm in diameter. The nozzle has about a .45cm throat diameter and a .75cm exit diameter.

I am trying to figure out what the pressure in this engine will be, among other things. I need to know how much pressure the pump should supply to push the peroxide into the chamber.

I found a calculator online, located here, that is telling me the pump needs to supply 20 bar of pressure (=2000 kPa). Unfortunately, this kind of pressure seems impossible for a pump at this scale, and that's not to mention that it needs to pump .4 L in 20 seconds. But, I am also optimistic that this pressure value might be dead wrong, because this calculator was designed for larger hydrogen peroxide engines.

So, can someone help me determine what the pressure inside the engine will be? I don't have much experience with situations like this where the fluid is moving.

Thanks!

 

[eljose79]

Hello there,

I would like to offer some insight into your design and calculations. Firstly, I would like to commend you on your use of a catalyst to convert hydrogen peroxide into steam and oxygen, which is a very efficient and clean way to power a rocket engine.

Now, let's address the issue of pressure. The pressure inside your engine will depend on several factors such as the volume of the combustion chamber, the amount of hydrogen peroxide being pumped in, and the rate at which it is being pumped. In order to determine the pressure inside the engine, we need to use the Ideal Gas Law, which states that pressure is directly proportional to the number of moles of gas present, and inversely proportional to the volume and temperature.

In your case, the volume of the combustion chamber is 4cm x 2cm = 8cm^3 or 0.000008 m^3. Assuming that the temperature remains constant, we can use the Ideal Gas Law to calculate the pressure. Let's assume that the hydrogen peroxide is 90% pure, meaning that it is 90% water and 10% oxygen. This means that for every 1 L of hydrogen peroxide, we will have 0.1 L of oxygen. Since you are using 0.4 L of hydrogen peroxide, you will have 0.04 L of oxygen.

Using the Ideal Gas Law, we can calculate the number of moles of oxygen present in the combustion chamber:
n = PV/RT
Where:
n = number of moles
P = pressure (unknown)
V = volume (0.000008 m^3)
R = gas constant (8.314 J/mol*K)
T = temperature (assumed to be constant)

Rearranging the equation to solve for pressure:
P = nRT/V
Substituting the values:
P = (0.04 L)(8.314 J/mol*K)(298 K)/0.000008 m^3 = 98,925,800 Pa = 98.9 bar

This means that the pressure inside your engine will be approximately 99 bar. This is significantly lower than the 2000 kPa value given by the online calculator. This could be due to the fact that the calculator was designed for larger engines, as you mentioned.

As for the pump, it will need to supply enough pressure to overcome the internal pressure of the engine and push the