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Before everyone responds that this has been asked before, I have read through every relevant post I could find here and believe my question has not been clearly covered.

I also understand that "Unfortunately there is no simple equation to calculate the chamber pressure." as stated here. I am not looking for a defining equation.

My question is:

Once a desired theoretical chamber pressure is determined for a liquid engine, how is the engine designed to reach that pressure? For example, chamber temperature can be determined and controlled based on the combustion temperature of your propellants, O/F ratio, etc. Is chamber pressure achieved purely by experimental design, or are there equations/models for determining rough values? (e.g. A company determines they want to design their engine to 2500 psia Pc. What design criteria are relevant to reaching the target value?)

The gap in previous explanations that I have found is that the mechanism by which chamber pressure builds up is not clearly explained. It is repeated that chamber pressure is generally an initial design parameter, but I am looking to understand how it actually physically develops.

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  • $\begingroup$ Welcome to Space SE! Someone has voted to close your question with the reason "Needs more focus: This question currently includes multiple questions in one. It should focus on one problem only" I think the quickest remedy would be to delete #2 here and change "My two questions are" to "My question is". You can ask as many questions as you like, but each question should strive to be answerable with a single answer (though it's not always possible). $\endgroup$
    – uhoh
    Commented Jan 12, 2022 at 22:56
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    $\begingroup$ Updated question to combine two separate questions. They were both asking essentially the same thing from different perspectives. $\endgroup$ Commented Jan 13, 2022 at 0:57
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    $\begingroup$ yeah, i'll submit another question if needed for more details $\endgroup$ Commented Jan 13, 2022 at 2:59
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    $\begingroup$ Sutton goes through this in Example 9-1 of the revered 4th edition: given a required thrust, propellant, and Pc, design the engine. It's quite lengthy and refers back to other quite lengthy sections. He starts out "No general rule can be given for designing thrust chambers...." $\endgroup$ Commented Jan 13, 2022 at 4:49
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    $\begingroup$ What chapter title is that? I have a different version (9) and can't find the corresponding example $\endgroup$ Commented Jan 13, 2022 at 5:41

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I'll make an attempt at this although it seems unclear whether you're asking (a) the theoretical ramifications of a certain chamber pressure or (b) the thermal and mechanical aspects of making it occur inside the chamber properly.

Before jumping into how one develops $p_c$, one should rigorously define it. This answer gives a good definition - that it is the static pressure within the chamber measured at or near the injector/chamber interface. In other words, it is the static pressure of the propellants immediately downstream of the injector, when they are first introduced to the engine.

In terms of how one arrives at a desired $p_c$, many of the answers are correct in that it is not a calculated parameter, but rather one which is arrived at by desiring a certain degree of performance. In general, increasing $p_c$ also increases $I_{sp}$ (albeit asymptotically) and decreases combustion chamber size. Increasing it also allows for larger nozzle ratios at a given exit pressure. These considered, there is a great impetus to run $p_c$ values as high as realistically achievable.

The determination of desired $p_c$ may be assisted by analytic tools such as NASA's Chemical Equilibrium with Applications or Ponomarenko's RPA, but there aren't (at least to my knowledge) straightforward means of calculating a $p_c$ operating point from performance levels. It is usually iteratively decided by setting a target, estimating performance, and adjusting. Certain values can be ruled out in specific cases by knowing other properties (i.e. RP-1 may go "sooty" below a certain pressure), but again, this is the land of "no general analytic rules" - many engine designs receive their first estimates from what has worked for similar engines in the past.

In terms of mechanically arriving at that pressure, once that value is set, one can define the factors used to develop the propellants to that pressure. In general, for pump-fed engines, one can simplistically model the propellant circuitry as a number of pressure drops*:

  1. The pressure drop of the injectors for fuel and oxidizer
  2. The pressure drop of the regenerative cooling jacket, if applicable
  3. The pressure drop of any ductwork and manifolds required to communicate the propellant between these areas

*This assumes a gas-generator cycle, as the pressure layout is most straightforward of all pump-fed engines. For staged-combustion and expander-cycle engines, the flow path is more complex.

In this case, the required outlet pressure of the propellant turbopumps equals the sum of the drops and the chamber pressure:

$$p_{op} = p_c + \Delta p_{inj} + \Delta p_{rg} + \Delta p_{\text{duct}}$$

Of course, this can quickly delve into a chicken-and-egg game whereby certain values which are not known require other values which may or may not be known. In that spirit, authors such as Sutton have developed rules of thumb for what these values should be - the general guidance for gas-generator cycles, for example, is that pump output pressure should be between 135% and 180% of $p_c$ (Sutton, 9e., Table 6-6).

As that allows definitions for $p_{op}$, one can now shape the other components (within limits, of course) to achieve the proper balance - the ductwork diameter can be driven to produce a certain $\Delta p_{\text{duct}}$, the injector orifice areas can be modified to give a desired $\Delta p_{inj}$, and the regenerative cooling channels can be sized similarly. It is intuitively reasonable that one wants these pressure drop taxes to be as low as possible, as this decreases both the required power of the pump and the mass of components. In practice, however, this may require a significant bit of iteration to make sure that reducing $p_{op}/p_c$ margins do not stress the mechanics of the overall system too greatly.

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