Lars wrote:
Suppose we have Thot_in at 704C, Thot_out at 593C, fuel salt at 4.4e6 J/m^3-K, and a 2.4e9 Watt (thermal) reactor. To move the heat the salt flow must be 4.9 M^3/sec. Suppose that the core is 3m in diameter, has a 1 m thick blanket, and a 0.3m thick neutron absorber. Further imagine that the ideal flow rate inside of the HX is 2m/s (I really don't know what it is for this HX). We then need 2.46m^2 cross-sectional area for the fuel salt in the HX. If the HX is 3m high then the fuel salt volume is 7.4 m^3. If 30% of the total HX cross-section is fuel salt area and the HX hugs the reactor then the HX is around 0.5m thick.
So a key question is what is the ideal flow rate for the HX with 2mm spacings between plates? And what would the pressure drop be for 2-3 meters of such a HX? We may be lucky and get an acceptable answer with simple top to bottom fuel flow (and bottom to top for the coolant).
In order to keep a reasonable pressure drop, flow must be in the laminar regime throughout the HX. Transition Reynolds number (where flow begins to become turbulent) is around 2000-2300, so I have used 2000 to stay conservative. Just to be clear, this analysis needs to be done on one single channel. From there, the total flow rate needed can be divided among N number of channels to remove the requisite amount of heat.
Re = (rho*V*Dh)/Mu where rho is the density of the fluid, V is the velocity of the fluid, Dh is the hydraulic diameter of the channel (4*channel area / channel perimeter), and Mu is the viscosity of the fluid.
This gives us a maximum velocity, which can then easily give us a maximum mass flow rate.
As for the pressure drop, I am going to rely on CFD results as well as known correlations. General results for any internal flow can be found using the Fanning friction factor, density, hydraulic diameter, and some constants.
Correlations are available for compact heat exchangers using microchannels and for rectangular channels. Numerous papers have been written solely on the validity of those correlations and sensitivity analyses. I can look through my notes tomorrow and post some of these if you’re interested. This will actually be good for me too, as I’ve been meaning to look back at some of those books that had really interesting information.
I also have an Excel document that I have been using for my simple calculations. I can post it if you’d like to take a look. Everything is labeled nicely, but it still may take some work to fully understand all the formulas and such that are at work behind the scenes. The dimensions I am using for my CFD simulations are based on results from that Excel document, where I tried to keep the pressure drop approximately equal to that of the MSBR shell-and-tube design, and calculated the SA/Vol and other characteristics. It's pretty useful and interesting to be able to change the channel height, channel width, number of channels, channel spacing, and other characteristics to see the sensitivity of each variable.