Departures from Ideal Performance for Conical Nozzles
This article covers departures from ideal performance for conical nozzles and bell nozzles, straight-cut throats and rounded throats; including nozzle thrust coefficient losses, and losses from the theoretical specific impulse to delivered specific impulse. Simple design modifications for straight-cut throats are presented which have the potential to increase the thrust, total impulse and specific impulse of most high power solid rocket motors, and almost all experimental/amateur solid rocket motors by 3.5% to 8%, a significant across-the-board increase in performance for two entire classes of rocket motors. The article contains extensive experimental test data, both for professional solid rocket motors and from instrumented tests of high power and experimental/amateur solid rocket motors. The experimental data, and the models based on the experimental data for performance losses from straight-cut throats are unique, and to the author’s knowledge the first published anywhere. Please note that there was an error in Equation 7 on Page 27 of the first part of this article. There is a formal Errata note at the end of the second half of the article with the corrected Equation 7.
Copyright ©2004 by
Charles E. Rogers. Where:
_{ ,act} =
l
C^{
0}_{F}Which is equivalent to assuming that the _{F}) is equal to 1.0. All of
these computer programs, software packages, spreadsheets, performance
charts, etc., can be easily updated to the Standard Method by simply
multiplying the ideal thrust coefficient (C^{
0}) and the nozzle divergence correction
factor (l) with the _{F}C efficiency factor
(h_{F}_{F}). _{ ,act} =
l
h_{F} C^{
0}_{F}The
article presents models for the C efficiency factor
models can be retrofitted into existing computer programs, software
packages, spreadsheets, etc., using the above equations._{F}
_{F} h_{q}
I^{
0}_{sp}This
is equivalent to assuming that the nozzle divergence correction factor
(l) = 1.0, the _{F}) = 1.0, and the c*
efficiency factor (h_{q}) = 1.0. Even if
correct values for the nozzle divergence correction factor and the
C efficiency
factor are used, representative values for the _{F}c* efficiency factor
are still required.Simply put the theoretical specific impulse is what comes out of programs such as PROPEP and the USAF ISP code. The delivered specific impulse is what the motor will actually deliver. The article provides details on how to make the corrections to the theoretical specific impulse to get the actual delivered specific impulse for a solid rocket motor. Smaller, shorter solid rocket motors using aluminized or
metallized propellants will have lower residence times in the motor, thus
reduced combustion efficiency, and hence producing a lower Based on representative data presented in the article, as the solid rocket motor size is increased from 1 lb propellant weight the delivered specific impulse can be increased by 5% for 50 lb propellant weight motors, and 7.5% for 350 lb propellant weight motors.
_{F})
= 1.0), the actual thrust coefficient loss from using a straight-cut
throat was found to be approximately 10% (a C
efficiency factor (h_{F}_{F}) = 0.90) for the straight-cut
throat lengths used on most high power and experimental/amateur rocket
motors. While the results were primarily based on historical Thiokol
solid rocket motor nozzle thrust coefficient data, static firings with
chamber pressure measurements for determining experimental values for
thrust coefficient were also performed for a large high power solid rocket
motor and a large experimental/amateur solid rocket motor, the test
results from which confirm the trends from the historical Thiokol
data.
C efficiency
factor, and hence the nozzle thrust coefficient as the straight-cut
throat L/D was reduced to less than 0.45. The summary plot of
_{F}C efficiency
factor versus straight-cut throat L/D is presented below, which
graphically shows the jump in _{F}C efficiency factor
when the straight-cut throat L/D is less than 0.45._{F}Copyright ©2004 by Charles E. Rogers. All rights reserved. Used with permission. The
For Conical Nozzles with Straight-Cut Throats:
_{
,act} = l h_{F} C^{
0}_{F}For Throat L/D < 0.45 High Performance:
h Low Performance:
h For Throat L/D ³ 0.45
h For Conical Nozzles with Rounded Throats:
_{
,act} = l h_{F} C^{
0}_{F}
h
Throat Design Criteria for Conical Nozzles with Straight-Cut Throats: Throat L/D £ 0.40 A
throat L/D £ 0.40 is used rather
than a throat L/D < 0.45, to provide extra margin to be sure that the
jump in nozzle performance indicated by the models based on the historical
Thiokol data and the high power and experimental/amateur solid rocket
motor experimental data, as shown in the plot of If there is a single conclusion that the reader should come away with from reading the article, it is that on straight-cut throats to make sure that the throat L/D £ 0.40.
C efficiency factor models presented above, with no
throat entrance rounding, but with the ability to be drilled to a wide
range of throat areas while still maintaining the same throat entrance
profile (a sharp throat entrance). Performance predictions for the
“optimal” and “universal” nozzles are presented based on the
_{F}C efficiency factor models and calculated nozzle
divergence correction factor._{F}This article was Parts 4 and 5 of
Parts 1 and 2 Part 3 Parts 4 and 5 Part 6 |