Does thrust depend on rocket chamber shape?

I mark with green part of rocket which produce forward thrust and with red backward thrust. integration of pressure around rocket walls gives total thrust,which always act in forward direction..

Does thrust depend on rocket chamber shape and what is optimum shape to get max thrust?

• Scroll about halfway down this page and it talks about nozzle design and such. Might have what you want. To much material there to quote in a post here.
– John K
Commented Jul 12, 2020 at 22:31
• Why would you believe that the red area generates backward thrust? There is no exit for the pressure at those locations, there is no equal and opposite reaction to force that does not involve an exit for the gases. Commented Jul 13, 2020 at 0:00
• @fred_dot_u The components of pressure force acting in the axial direction in the red area do reduce the delivered thrust. I would not call it "backward thrust" though. The pressure drops quickly through the throat, the pressure on the injector face is the major contributor. space.stackexchange.com/a/39939/6944 Commented Jul 13, 2020 at 0:19
• @Aeronautic Freek It is unlikely that there is a single optimum shape. If there were, all engines would use it. Thrust chamber design, like the design of most complex devices, is driven by many tradeoffs. Of course thrust depends on the shape, a poorly designed chamber would give minimal thrust. Commented Jul 13, 2020 at 0:34

Not really (see edit)

The primary driver behind chamber design is mixing. Complete combustion of the propellants is the ideal situation for any rocket, but is rarely achieved; it would require a chamber that was prohibitively long to give the propellant enough time to combust completely. Chamber volume is really the key and is defined in rocketry by the characteristic length (see combustion chamber sec.). The characteristic length is equal to the volume of the chamber (injector to throat) divided by the throat area. Different propellant combinations require different residence times and, therefore, different characteristic lengths for optimum performance. These values are typically in the realm of 50-150 cm, but actual engine designs tend to use slightly lower values, ~40cm.

In regards to flow properties, the chamber holds high pressure subsonic gas, which is pretty unpicky when it comes to duct geometry; there are practically no losses due to the contraction to the throat, and the geometry doesn't need to be subtle or particularly smooth (this being the geometry of the "reverse thrust" section in your drawing). Combustion chambers are essentially fancy tanks as far as geometric design is concerned, and there's not much performance increase to be yielded from changes in that design. The nozzle design, on the other hand, is very critical. Supersonic flow is very picky, and pressure losses are easy to collect if the geometry doesn't smoothly expand the flow.

In regards to your drawing, the "backward thrust" section is entirely canceled (see edit) by the forward thrust on the injector wall that is directly behind it. This leaves only the forward thrust from pressure on the nozzle and from a throat sized patch on the injector (everything you could see looking into the butt of an engine). This is further evidence that chamber design doesn't significantly impact thrust, at least in the way you're suggesting.

Important Edit:

The "backward thrust" section is NOT entirely canceled by the forward thrust on the injector wall that is directly behind it. It is almost entirely canceled.

The contraction does accelerate the flow and reduce the pressure in those regions which creates some extra thrust, this is why the thrust coefficient is not unity at an expansion ratio of 1, but rather ~1.2. As an example, a typical rocket engine thrust coefficient will be ~1.6, so a rough calculation gives:

62.5% of thrust provided by a throat sized patch on the injector face.

12.5% of thrust provided by the remaining area of the injector face (this is the area I mention above as being "directly behind" the "backward thrust" section.

25% of thrust provided by the expanding portion of the nozzle.

So you can see that the contraction is basically responsible for 10% of a rocket's thrust. And, indeed, this would be mostly lost if you had a chamber design with a plain orifice configuration instead of a gentle contraction. Though the points I make in the original answer are generally correct. These two broad points together would explain the prevalence of conical contractions and contoured expansions found in most rocket nozzles.