Does hero's engine have an upper limit for the rotational speed under ideal conditions?

This is a simple hero’s engine. The source of the gas and the rotating part is seperated by a frictionless bearing. So only the upper part rotates. My question is this:

Given ideal conditions ( no friction / air drag, unlimited gas ) is there an upper bound for the rotational speed of the upper part (in newtonian mechanics)?

I have done some calculations and it seems there indeed is an upper bound. Assuming the gas is released at a constant speed $v$ wrt the edge of the pipe the released gas produces a torque $frac{Delta m v r} {Delta t} $ where $∆m$ is the mass of the released gas in small time $Delta t$ and $r$ is the radius of the upper part. If the edge of the upper part was rotating at speed $V$ at that time wrt ground then to make the gas left inside the pipe travel to the edge (filing the void left by the released gas) $∆m V r$ amount of angular momentum is needed. Angular momentum is conserved here.

So,

-Change in angular momentum of the released gas = Change in angular momentum of the gas left inside the tube in the upper part + Change in angular momentum of the upper part (the metal part)

$$impliesDelta m v r = Delta m V r + I Delta omega$$ where I is the moment of inertial of the upper part (the metal part only)

$$ impliesfrac{dm}{dt}r v = frac{dm}{dt} r V + I frac{frac{dV}{dt}}{r} $$

$$ impliesfrac{dV}{dt} = C (v – V) $$

here $C$ is a constant
This means that $V$ eventually settles at $v$

Are my calculations right ?