In regards to the OP - I do not believe that a PWR (Pressurized Water Reactor), such as that used on NR-01, can be adapted to freefall.
Without getting into big details, the problem is that even though the coolant going through the core is supposed to remain a liquid at all times, a PWR uses a vessel called a Pressurizer to ensure that operating pressure for the reactor coolant is always far above saturation presure for the plant’s operating pressure. The way this is done is that the environment in the pressurizer is actually at saturation temperature for the plant’s operating pressure. Usually several hundred degrees warmer than the temperature in the plant’s core. Because the water in the Pressurizer is connected to the rest of the coolant system, it exerts that pressure through the whole system, without actually mixing with the coolant going through the core. In effect a PWR plant has two general temperature environments: The circulating loop, at an average operating temperature; and the pressurizer at a higher temperature, to ensure that the core never reaches saturation conditions to allow boiling.
In a gravity field, or even in a simulated gravity field, when any liquid is heated to a gas, the newly formed gas bubbles will rise to the top of the vessel it is in - in the pressurizer vessel, this means that there is a bubble of steam at the top of this vessel, that actually provides the pressure to keep the rest of the coolant well above saturation pressure.
In freefall, however, there is no reason for the less dense steam to move away from the heating elements. So what is more likely to happen is that the steam bubble will form around the heating elements, which would effectively insulate the elements from the heaters. The effect of this would be to mean that once a bubble is formed in the pressurizer it wouldn’t be able to raise the temperature of the surrounding water very easily… until the bubble collapsed again, allowing water into direct contact the heating elements. Which would remove one of the most important safety features of a PWR - the certainty that a properly operating plant won’t allow boiling in the core. Even here in our one-g field, it’s a bad thing for a PWR to experience boiling in the core. (In general - there are technical considerations I don’t think I can get into without having to hunt anyone who reads this thread down to kill 'em and eat their brains. I don’t believe they’re a secret to anyone with knowledge of thermodynamics, but I have to balance things out with my own oath to hold certain knowledge secret whether I think it’s useful, or not.) Because the channels going through the core in a PWR are so thin, it is devastating to have that insulating effect of steam bubbles keeping the core from transferring it’s heat into the coolant. It is relatively easy for these channels to get blocked by steam bubbles, and once that happens, the heat of fission being produced in the core can’t be removed from the core - and causes the temperature of the core materials to rise… until eventually, something fails.
And having your power plant fail - especially something in the core fail - is a bad thing[sup]tm[/sup].
This isn’t to say that there aren’t reactors that work in freefall, just that the Navy’s PWRs are not the sort of reactor for that environment.
I would also like to point out: there’s no real reason to insist than all the components in a space vessel are all in the same hull. In a submarine, because of the incredible pressures involved, it doesn’t make sense, to most naval designers, to have more than one pressure vessel. In short it’s cheaper to make one larger vessel that can withstand hundreds (perhaps even thousands) of pounds pressure per square inch, than to make several. Economies of scale. However, that sort of stress just doesn’t exist with vacuum work - there’s some concern about containing the internal pressure of the astronauts’ environment, but it’s not the same magnitude of concern. So, instead of having huge concerns about building the most powerful pressure hull possible for x amount of money, the biggest concern is going to be: what is the maximum mass we can lift in any single given launch? And while space borne construction is still a virgin field, I suspect that making a rigid frame that can withstand a moderate constant thrust is going to be easier to do than actually trying to connect seperate modules into a single pressure hull in orbit.
