# Quantitative plots of v, T, p, vs position from chamber through nozzle to ambient for a few canonical modern engines?

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

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:

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