If a nozzle is underexpanding you more/less do not cash-in the aditional
isp you could have gotten with a ideally expanding nozzle. Nevertheless
you still get aditional pressure-thrust from the pressure differential
times nozzle exit area (therefore increasing with altitude). This is
less than you could get with ideal expansion but not negledgible.
For example Rasaero(HPR simulation tool) is accunting for
pressure-thrust while Openrocket is not. Among other things this is one
of the reasons for more optimistic results from Rasaero(e.g. manual page
75 second last paragraph).
This is not analog for overexpansion where more komplex flow
disturbances come into play.
m.
Am 27.10.2016 um 22:34 schrieb Ed Kelleher:
I have some time and am updating my rocket flight simulator.
One thing I was looking at adding was the performance change of a
booster thrust chamber (TC), with altitude.
I've heard it described as an increase of ISP with altitude.
RPA will give you an altitude analysis that shows ISP increasing with
altitude.
But that seems a little misleading because I use ISP for determining
exhaust velocity for the rocket equation and propellant mass flow for
tank sizing.
When I look at the thrust equations (e.g. in Sutton RPE) I see that
these elements (Ve, Mdot) aren't functions of altitude; i.e., decreasing
ambient pressure outside the TC exit nozzle.
They don't change with altitude. What changes is the thrust due to the
exit nozzle, the final term in the Cf equation.
(P2 - P3) * A2
P2 = design pressure at the nozzle exit for optimum expansion
P3 = ambient pressure
A2 = Area of nozzle exit
At the design altitude P2 = P3 and this term is 0.
So for a particular TC I would use that equation to compute the
difference in thrust at an altitude (P3 ambient pressure) different from
the design pressure for optimum expansion (P2)?
Am I understanding this correctly?
Where do you account for inefficiencies of under expansion?
Something doesn't seem right here?
Also, at less than design altitude you have less than design thrust, a
problem for boosters which have low initial accelerations.
And with low chamber pressures, you have larger nozzle exit areas, and
thus a larger variation with altitude than an equivalent thrust TC with
a higher Pc.
I expect if I play with RPA some I'll see that larger expansion ratios
(Ae/At - with lower values of P2) give more thrust at optimum altitude
than the (P2 - P3) * A2 equation would give for an under expanded nozzle.
Sutton shows a graph of thrust for a particular TC (V2 or H1/RS27)
increasing with altitude in every edition of RPE (even #5) usually in
the fundamentals section, which I didn't think too much of before.
Ed Kelleher
