I think contributions are very good, taking into account some very important points that are basic in engineer's heat transfer calculation; but when we take into account two-phase flow and heat transfer, things get very complicated. I'm not sure do we really need it; it can be justified only if accuracy gives you some tangible benefit.
I will try to approch from total practical side. This problem is safety problem. Safety is the most important, all other things come after that.
1. Not only thermal expansion of water, but water pressure. When water expand thermally in this case its pressure rises because it is confined by pipe. The water pressure is what we need to control!
2. You must have some data for working pressure of water pipe. In this case you simply set safety relief valve to 1,1-1,15 x working pressure and that's it! Pressure must not come beyond it anyhow. But this is SECOND safety measure!
3. FIRST safety measure is: you must block steam inflow when water side pressure reaches some point that is above working pressure but bellow relief valve set pressure (let us say 1, 05 x water working pressure). This way real purpose of safety relief valve is to protect water pipe only from accumulated heat. It means when FIRST safety measure block the source of trouble (steam), there will be further water heating and pressure rise for a while because of thermal accumulation. This can be one moment or "little more", depending on water and steam volumes and contact area, but this moment is critical for safety because pressure still rises although you switch off everything
4. Not earlier then now thermal expansion comes into play. You calculate critical thermal expansion to find minimal opening area for relief valve. This is where you must consult standards. In my little country there is mandatory standard for this (it is called "Safety Relief Valve Calculation"; there must be some equivalent ANSI stuff).
Regards