Calculating NTR performance curves

[Hlynkacg]

So i'm working on accurately modeling a NERVA engine for my Reusable Nuclear Shuttle Addon.

NASA's Nuclear Flight definition study gives nominal tempratures/flow-rates for different phases of operation but is rather vague about the steps in between.

For instance, from reading the definition study I know that...

...the reactor is rated for 1125 mwt at max output.

...stable idling temp was to be around 411 K (280 F) and that under full-power the reactor would reach 2500 K.

...With a propellent (LH2) flow rate of 40 kg/s this would result in an internal chamber pressure of 600+ PSI (4.13 Mpa), 75,000 lbs-f (333 Kn) of thrust, and an impulse of around 800 seconds.

...I also know that the cooldown phase would consume .66 kg/s of propellant until the reactor reached 800 K at which point active cooling would no longer be neccesary.

Now if the relationships were linear knowing the start and points would between temp, prop flow, pressure, etc.. would be enough, unfortunatly they are not.

I need an equation into which I can plug Reactor Temp and Prop Flow and get Pressure or ISP.

Likewise I need an Idea of how to calculate reactor temp based on power setting (0-100%) and propellant/coolant flow. Unfortunatly this requires data on NERVA's heat rejection capability/rates that I do not have.

If anyone has any data or sources that can fill in the gaps, the help would be much appreciated.

Heck, I'd settle for some best guesses that I could use in the interim.

Thank you and

 

[Sky IsNoLimit]

Hello, maybe I can help you, but I am not sure. What exactly do you mean with "performance curves"?

There are some fundamental relationships between power (P), thrust (F), mass flow rate (mdot) and effective exhaust velocity (ve) for every rocket engine:

(1) F = mdot * ve

(2) P = 1/2 * ve^2 * mdot

(3) F = 2*P / ve ........ - follows directly from (1) and (2)

P is the so called "jet power", the power of the exhaust stream. This equals the reactor power if all the power from the reactor is transferred into the propellant.


Using your example from the definition study: mdot = 40kg/s and ve = (800 * 9.81)m/s and putting this in Eq. (1) results in a thrust of 313.92kN (not 333kN), so the data you have does not seem to fit all to well.


About the relatonship between temperature (T) and effective exhaust velocity (ve):

ve^2 = C * T ..... with C being a constant dependent on the type of the used propellant and the performance of the nozzle.

Assuming you have a set of reference temperature T1 and reference effective exhaust velocity ve1, you can calculate the effective exhaust velocity at a different temperature:

ve1^2 / T1 = ve2^2 / T2

=> ve2 = ve1 * SQRT(T2/T1)

You must keep in mind that T is the temperature of the propellant at the exit of the reactor, the so called plenum, and not the temperature of the core itself. The temperature of the reactor core must be higher to alow a high enough heat transfer into the propellant (200 - 300 degrees K if I remember correctly).

You may also be interested to take a look into the final report of the ROVER program if you haven't done already:
http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19920005899_1992005899.pdf

I hope this helps as a starting point. :tiphat:

 

[Hlynkacg]

Ok, just to make sure I understood.

If my referance point is an exhaust velocity of 7848 m/s (800 * 9.81) at a Temprature of 2500 k the equation should look something like...

CurrentVE = 7848 * SQRT(CurrentTEMP/2500)

Correct?

Using your example from the definition study: mdot = 40kg/s and ve = (800 * 9.81)m/s and putting this in Eq. (1) results in a thrust of 313.92kN (not 333kN), so the data you have does not seem to fit all to well.

Some form of mechanical inefficiency perhapse?

You may also be interested to take a look into the final report of the ROVER program if you haven't done already:
http://ntrs.nasa.gov/archive/nasa/ca...1992005899.pdf

I hope this helps as a starting point. :tiphat:

I hadn't seen that, It'll take some time to read and digest but thank you for the assistance

 

[Sky IsNoLimit]

If my referance point is an exhaust velocity of 7848 m/s (800 * 9.81) at a Temprature of 2500 k the equation should look something like...

CurrentVE = 7848 * SQRT(CurrentTEMP/2500)

Yes, that is correct!

Quote:
Originally Posted by Sky IsNoLimit

Using your example from the definition study: mdot = 40kg/s and ve = (800 * 9.81)m/s and putting this in Eq. (1) results in a thrust of 313.92kN (not 333kN), so the data you have does not seem to fit all to well.

​

Some form of mechanical inefficiency perhapse?

No, because Eq(1) is the definition of the effective exhaust velocity: Thrust created per unit of used propellant, these numbers MUST always fit 100%.

After thinking about it, the only explanation that comes to mind is that the Isp of 800s maybe not the specific impulse when the engine is thrusting, but an Isp that is averaged over the whole time of the engine burn sequence: engine startup - burn - cooldown. The specific impulse is reduced considerably during the cooldown phase as the reactor temperature goes down. So the Isp of 800s could only be used for the calculation of the delta v and not for the thrust. But this is only a guess. :hmm:

 

[Hlynkacg]

After thinking about it, the only explanation that comes to mind is that the Isp of 800s maybe not the specific impulse when the engine is thrusting, but an Isp that is averaged over the whole time of the engine burn sequence: engine startup - burn - cooldown. The specific impulse is reduced considerably during the cooldown phase as the reactor temperature goes down. So the Isp of 800s could only be used for the calculation of the delta v and not for the thrust. But this is only a guess. :hmm:

That would make sense.

Now that I know how temprature effects ISP I just need to calculate temprature. ???

As it stands it's just a function of time. ie 50 seconds to go from idle to operation temp, and 180 s to cool back down.

This works well enough for testing but it is linear where it should be logarithmic and ignores the cooling effect of the propellant.

Idealy there'd be an equation that could give chamber temprature as a function of propellant flow and reactor power (control-rod position).

There may be something in the Project ROVER report you linked but if so I have yet to find it.

Once again, thank you for the assistance. :tiphat:

---------- Post added 01-21-12 at 01:55 AM ---------- Previous post was 01-20-12 at 07:38 PM ----------

Found Aerojet's Manufacturing report on the NX reactor.

http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19770069903_1977069903.pdf

It looks promising.

 

[Sky IsNoLimit]

It's good to know that I could help and the manufacturing report is quite interesting. Thank you for the link! It is dated from 1962, so it cannot be the final version of the NERVA engine or what do you think? Anyway, if I find some more information, I will post it here.