increasing Isp of temperature limited rockets

Sometime in the past I was entertaining myself by asking the question "normally higher chamber pressure gives better rocket performance. Is there ever a case where lower pressure gives better performance?" Well, there are some conventional reasons for using lower pressure like making simpler, more reliable engines, but I came up with an interesting idea that relates to microwave (or nuclear, or antimatter, etc.) thermal rockets.

When you have a rocket that is temperature limited, but not energy limited, and it is operating in vacuum you can increase Isp by lowering the chamber pressure.

Low chamber pressure normally steals performance in two ways. First, atmospheric pressure on the outside of the nozzle acts like a regressive tax. If your chamber pressure is 10 bars and atmospheric pressure is 1 bar it steals 10% of your thrust. If your pressure is 100 bars it only steals 1% of your thrust. In vacuum this effect does not occur. The tax rate is 0%.

The second way low pressure steals performance is chemical dissociation. At high temperature a certain fraction of your propellant spontaneously un-burns. This effect is reduced at high pressure because the un-burned atoms find a new partner and re-burn more quickly.

In a chemical rocket launcher where the amount of chemical energy available is fixed, having unburned propellant steals some of that energy and results in lower temperatures and thus lower Isp. But what about a rocket where you are allowed to add as much energy as you want until your propellant reaches a certain temperature?

Well, if you have hydrogen propellant and you heat it up some of the molecules will dissociate into hydrogen atoms. Atomic hydrogen is an even better propellant than molecular hydrogen at the same temperature. If you assume frozen flow then the hydrogen atoms have lower molecular weight. If you assume shifting flow the recombination of hydrogen atoms provides an additional resevoir of energy and keeps the temperature higher through the nozzle.

So low pressure hot hydrogen with lots of atomic hydrogen in it should be a better propellant than high pressure hot hydrogen that is mostly molecules if you are limited only by temperature, and have an unlimited supply of energy. The idea seems to check out on this propellant calculator I found on the web. Maybe someone could double check with some other method to make sure I am right.

http://rocketworkbench.sourceforge.net/equil.phtml

There are some disadvantages. Lower pressure will mean less mass flow through the same sized engine and thus less thrust to weight. Also, it will take more energy to reach the same temperature which means a larger microwave transmitter and larger receiver area.

This may never turn out to be the best design due to other fators like needing high thrust to limit transmission range, but I thought I would put it out there and see if anyone sees any obvious problems that I'm missing.

That's an intriguing point.

A quick Google search suggests to me that this would work for in-space propulsion and perhaps even an upper stage provided you can get the nozzle geometry right. The hydrogen rate constants aren't known accurately and that introduces a large uncertainty in the performance.

Performance assessment of low pressure nuclear thermal propulsion

Hydrogen recombination kinetics and nuclear thermal rocket performance prediction

I see it's been thought of before. I suppose not a lot of attention has been paid to it because thermal type rockets haven't been worked on much recently.

I bet the atomic hydrogen would chemically degrade any conceivable nozzle material pretty quickly. I wonder if there is any information available about bombarding materials with hot atomic hydrogen.

Thanks for those links. I've been looking into the possibility of using atomic hydrogen propellant.


Bob Clark

That is a pretty big "if" and an even bigger "and". The #2 and #1 show stopper I would think.