Does engine purging in a liquid rocket engine cause dry run of the turbopump? If so, does that have any implication for the design, health, maintenance, or operation of the pump?
How do we calculate the purging pressure?
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1$\begingroup$ You do not want to run your turbo pump without something in it. That can cause pump failure which is unlikely to be acceptable in a rocket application. And purging is often done with a pressurized gas, probably the same you use to pressurize your propellant tanks. Havn't got sources so no answer from me (: $\endgroup$– GittingGudMay 16, 2019 at 6:32
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No, it doesn't. There is always a valve between the purging circuitry and the turbopump, preventing the turbopump from going dry (which, as @GittingGud points out in a comment) is highly undesirable. The valve is closed by the same gas as the one used to purge. For a nice description, see p. 60 of Huzel and Huang, "Design of Liquid-Propellant Rocket Engines" dealing with a (hypothetical!) engine using fluorine for an oxidizer.
To answer the second part of your question: if a dry run ever occurs, the turbopump will spin up to rpms well above its specification, and eventually some material fault will make one of the impeller blades break by centrifugal force. The pieces of the blade will shatter the pump encasing, just before or at the moment the rest of the impeller flies apart because the centre of mass is not on its axis anymore. The impeller debris will fly, at very high speeds, through the various parts of your rocket. Depending on the stage the rocket is in (pre-launch, ignition, flight) this may lead to what the Brits call, tongue-in-cheekishly, accelerated self-disintegration (an explosion).
At engine burnout, the propellant remaining behind in the turbopump is part of the engine's so-called wet mass.
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$\begingroup$ There is no such valve in the SSME. $\endgroup$ Aug 26, 2019 at 12:15
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$\begingroup$ Also, page 60 of the book you reference has nothing to do with purging or turbopumps, but is part of the "Selection of Materials"chapter. ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19710019929.pdf If you mean a different edition, please provide a link. $\endgroup$ Aug 26, 2019 at 21:21
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1$\begingroup$ Those valves you mention don't 'prevent the turbopump from going dry' in the SSME. They allow helium to be injected into the feedlines postMECO, blowing the residual prop out through the engine including the turbopumps. They are specifically intended to dry out the engine! $\endgroup$ Aug 27, 2019 at 11:58
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9$\begingroup$ A dry run is a problem if the turbopump is being driven (e.g. by the preburner) while it goes dry. Then the driving torque causes the pump to speed up. During a purge, the only driving force is caused by the purging gas, and you can control that to limit the pump speed to a safe value. $\endgroup$– HobbesSep 25, 2019 at 6:22