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In this answer I showed the schematic diagram of a basic de Laval nozzle and representative plots of how temperature, pressure and and velocity would behave.

It can be used as a rough representation of how these would vary from combustion chamber, through the expansion nozzle, and out into ambient space, but not an accurate example nor with any quantitative information.

I'd just written the comment:

@SteveLinton there's a ballpark estimate of 1500ºC in the linked "expansion of the ~100 atm chamber pressure..." answer, but if an answer with more details can't be found that would certainly make for an interesting new question by itself. Some quantitative plots of velocity, temperature, pressure as a function of position from chamber through nozzle and into ambient for a canonical modern engine.

Question: What might quantitative plots of velocity, temperature, pressure as a function of position from chamber through nozzle and into ambient for a few canonical modern engines examples look like? Plots should have units for the vertical axis(es).

below: "gas characteristics along a de Laval nozzle, T - absolute temperature; p - pressure; v - speed; M - Mach number" from here.

gas characteristics along a de Laval nozzle

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  • $\begingroup$ I can give some SSME plots at various power levels, but not for other engines. $\endgroup$ – Organic Marble Dec 19 '18 at 18:03
  • $\begingroup$ @OrganicMarble SSME is certainly a canonical engine. $\endgroup$ – uhoh Dec 19 '18 at 23:55
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For the SSME:

I took a shot at this; I had to make so many assumptions, it may just end up as a fun exercise for me without too much anchorage in reality.

I got the SSME thrust chamber and nozzle geometry from this paper: Performance predictions for an SSME configuration with an enlarged throat but I had to eyeball them from these low-quality plots:

enter image description here enter image description here

You will see some wobblies in the plots where I didn't eyeball them all that well.

Some of the assumptions and (why they are bad):

  • Isentropic flow throughout (not really isentropic throughout)
  • Used the ratio of specific heats aka gamma for steam (I calculated the exhaust was about 96% steam, 4% unburned H2; for this kind of analysis, 4% is not worth worrying about)
  • The fluid starts at rest in the combustion chamber (it really gets injected in at a non-trivial velocity)
  • The combustion process happens instantly after injection and requires zero length (it doesn't)

Calculation process:

  1. Pick a longitudinal (X) station and get its radius off the geometry plots
  2. Calculate area at that station and area ratio using the throat area
  3. Look up the Mach number, pressure ratio, and temperature ratio in the isentropic flow charts for that area ratio and gamma. I didn't expend a lot of effort interpolating here, I just picked the closest one...
  4. Multiply the stagnation pressure and temperature by the appropriate ratio to get the value at that station

So given all that, here are the results.

The X axis on both plots is the distance from the throat in inches.

The first one shows the geometry (radius) in green (left Y axis, units of inches) and the temperature in purple (right Y axis, units of deg R)

enter image description here

The second one shows the pressure in red (left Y axis, units of psi) and the velocity in blue (right Y axis, units of Mach number)

enter image description here

So, take it with a ton of salt. The trends should be representative, anyway.

Additional references:

Isentropic flow spreadsheet downloaded from Purdue's engineering website

Chamber properties from the SSME Orientation briefing.

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  • $\begingroup$ This is great! Thanks for adding some tangibility to the subject. $\endgroup$ – uhoh Dec 17 '19 at 1:17
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    $\begingroup$ It was fun to put together. $\endgroup$ – Organic Marble Dec 17 '19 at 1:32
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    $\begingroup$ Great answer. Cpropep the tool that I used in this answer is able to calculate the temperature and pressure for a given area ratio (supersonic and subsonic) even with respect to the shifting chemical equilibrium. Might not be too interesting for hydrolox engines but for hydrocarbons its usually quite relevant especially for low pressure engines. $\endgroup$ – Christoph Dec 17 '19 at 7:24
  • $\begingroup$ @Christoph thanks. I would be interested in going over this again later and making it more realistic, that tool will certainly help. $\endgroup$ – Organic Marble Dec 17 '19 at 13:54
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    $\begingroup$ @OrganicMarble I guess the most interesting result observed from these plots is the distribution of pressure. One can see how negligible the axial component of thrust (pressure over bell surface) becomes after the throat. I.e. majority of the thrust is due to the pressure in the chamber upstream the throat. $\endgroup$ – Sergiy Lenzion Dec 19 '19 at 7:24

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