I know the upper stage of the Falcon 9 can be restarted once, thus allowing an additional thrust for some circumstances that might require it. However, I don't really understand the mechanism that limits the number of restarts. What limits the number of restarts that a liquid fueled rocket can perform?
Per this old usenet thread, there are a lot of design choices, but the main problems are in getting the fuel to the engines while in free-fall, and igniting non-hypergolic propellants.
To get the fuel into the pumps / engines, you can use:
- bladder pressurization (which is a materials problem with cryo fuels)
- piston pressurization (difficult to do on a large scale)
- small solid-fuel ullage rockets (which you'd have a limited number of)
- small liquid-fuel ullage rockets (which has the same fuel supply issues, but on a smaller and more easily solvable scale)
- boiloff venting of cryo propellants for ullage!
- a mesh or membrane system to hold sufficient amounts of fuel at the pump inlet via capillary action
To ignite non-hypergols, you can use:
- hypergolic chemical igniters (which you'd have a limited number of)
- electric spark igniters (which might dirty up or wear down)
- solid fuel pyrotechnics (which you'd have a limited number of, and in turn require electric igniters)
There is no SENSIBLE upper limit in terms of the likely requirements in the next few decades. Increasing restart capability adds complexity and a certain amount of mass but you can soon get to a system which is essentially reliability limited. Tens to hundreds of restarts would readily be achievable with existing technology.
As one only example
You can use cold gas thrusters to achieve ullage location of main tank fuel and if desired replenish the gas reservoirs from main fuel or oxidiser once the contents are stable.
Anywhere outside a permanent shadow (which are rather hard to find usually) you can use photovoltaic panels to recharge electrical system energy stores. Existing battery technologies have calendar and cycle lifetimes well in excess of what is sensibly needed.
Lack of hypergolicity is a challenge but, if the need exists, small igniters running on main fuel mixes heated to combustion point electrically are an entirely realistic solution.
It's likely that dozens of restarts could be achieved by such systems, and unlikely that more than that number would be required in any likely application short term. Extension to say hundreds of restarts is "just a matter of engineering" with increased need for maintaining reliability as restarts increased.