Hobby rocket engine experiments

[Raddy13]

I've started making my own sugar-based hobby rocket engines and I want to work on creating a de Laval nozzle for the specific fuel type and configuration I'm using. I don't have the resources to measure things like chamber pressure and exhaust temperature, so I wanted to try and develop an experiment to figure out at what point the exhaust velocity hits Mach 1 and where the nozzle should begin to diverge.

If I understand the principle, at the optimal throat diameter is the largest diameter where the exhaust reaches Mach 1 and past that, the flow is choked and only the mass flow rate will increase. My idea was to build a series of engines with converging only nozzles and increasingly smaller throat diameters and to measure the thrust of each design. My hypothesis is that as the nozzles get smaller, I should see the thrust increase until the optimal throat diameter is reached, after which the thrust will plateau, or at least the delta-thrust will be significantly smaller. Is my thinking on this correct?

 

[anorlunda]

I expect that there must be forums dedicated to amateur rocketry that could give you much more specific help than is likely here. On the other hand, PF members have amazing knowledge, so perhaps one of them can answer directly.

Good luck.

 

[boneh3ad]

If I understand the principle, at the optimal throat diameter is the largest diameter where the exhaust reaches Mach 1 and past that, the flow is choked and only the mass flow rate will increase.

No, once the flow is choked, the mass flow rate does not change unless you increase the upstream pressure. Downstream conditions do not affect the mass flow rate at that point, and by definition, it is constant throughout the nozzle (mass isn't created or destroyed). Choking a flow has more to do with getting the pressure ratios right rather than a specific area. For a given pressure ratio, any throat area will be choked. It's just a matter of how fast you use up your upstream pressure (since a larger throat will pass more mass and drain pressure faster).

In other words, your goal should be to try to determine what sort of pressure your combustion chamber achieves so that you can design the nozzle accordingly.

 

[Raddy13]

But if the combustion chamber pressure is dependent on the nozzle design, then aren't we back to slowly reducing throat area until the flow is choked?

 

[boneh3ad]

In some sense. The chamber pressure will depend on the characteristics of the fuel burn as well as how fast mass is expelled through the nozzle. So in that sense, I suppose it's a matter of dropping the size down low enough that the chamber can sustain a pressure suitable to choke the flow and your proposal would work in that regard. That won't be the ideal pressure for operating the nozzle, though. Just because the flow is choked does not mean that you will actually start a supersonic nozzle. In fact, you will need quite a bit more pressure ratio in order to start the nozzle once you add the diverging section, otherwise you will still choke the flow but a shock will form in the nozzle and you will get a very low velocity.

So, just shrinking the nozzle down repeatedly until the flow is choked won't tell you much. Additionally, your thrust won't plateau because, as you keep shrinking the converging nozzle, it chamber pressure will likely keep increasing, and therefore so will the mass flux through the nozzle. Instead, you probably want to figure out how the chamber pressure varies as a function of the throat diameter and then use that to pick a throat diameter that allows you to start a supersonic nozzle.

 

[Raddy13]

Okay, I think I have a better understanding now. I'll have to figure out a cost-effective way to measure the pressure. Thanks!