Loading…

Touring UC-Berkeley’s CIET Facility

Kirk Sorensenblog, Strategy

For many years now I have been interested in the work being done at UC-Berkeley in the modeling of molten-salt reactors using a simulant fluid.

Prandtl number matching between salt and simulant fluid:

(1)   \begin{equation*} \text{Pr} = \frac{\mu C_p}{k} \end{equation*}

Dynamic viscosity $\mu$ is often a strong function of temperature while specific heat $C_p$ and thermal conductivity $k$ are generally weak functions of temperature.

There is no guarantee that the Prandtl number range of the salt mixture will correspond with the Prandtl number range of the simulant fluid over the desired temperature range.

This matching requirement will determine the suitable simulant fluid as well as the proper temperature for the simulation.

(2)   \begin{equation*} \text{Re}_\text{salt} = \text{Re}_\text{fluid} \end{equation*}

One begins by choosing the fluid temperature to match Prandtl number:

    \begin{displaymath} \text{Pr (salt, }600.0^{\circ}\text{C)} = \frac{(0.0145\text{ kg/m\textperiodcentered s}) (2300.0\text{ J/kg\textperiodcentered K})}{1.400\text{ W/m\textperiodcentered K}} = 23.902 \end{displaymath}

    \begin{displaymath} \text{Pr (Dowtherm, }54.3^{\circ}\text{C)} = \frac{(0.0019\text{ kg/m\textperiodcentered s}) (1671.0\text{ J/kg\textperiodcentered K})}{0.133\text{ W/m\textperiodcentered K}} = 23.906 \end{displaymath}

In this case, Dowtherm at 54.3$^\circ$C has the same Prandtl number as Li$_2$BeF$_4$ at 600$^\circ$C.

With matched Prandtl numbers, then the scaled length ratio can be calculated:

(3)   \begin{equation*} \frac{\ell_s}{\ell_d} = \left(\frac{\nu_s}{\nu_d}\right)^{2/3} \end{equation*}

    \begin{displaymath} \text{Pr (salt, }600.0^{\circ}\text{C)} = \frac{(0.0110\text{ kg/m\textperiodcentered s}) (920.0\text{ J/kg\textperiodcentered K})}{1.050\text{ W/m\textperiodcentered K}} = 9.615 \end{displaymath}

    \begin{displaymath} \text{Pr (Dowtherm, }149.0^{\circ}\text{C)} = \frac{(0.0006\text{ kg/m\textperiodcentered s}) (1937.2\text{ J/kg\textperiodcentered K})}{0.118\text{ W/m\textperiodcentered K}} = 9.616 \end{displaymath}

Scaled length ratio

(4)   \begin{equation*} \frac{\ell_s}{\ell_d} = \left(\frac{\nu_s}{\nu_d}\right)^{2/3} \end{equation*}

Scaled velocity ratio

    \begin{displaymath} \text{Pr (salt, }600.0^{\circ}\text{C)} = \frac{(0.0149\text{ kg/m\textperiodcentered s}) (2400.0\text{ J/kg\textperiodcentered K})}{1.100\text{ W/m\textperiodcentered K}} = 32.618 \end{displaymath}

    \begin{displaymath} \text{Pr (Dowtherm, }37.2^{\circ}\text{C)} = \frac{(0.0027\text{ kg/m\textperiodcentered s}) (1622.1\text{ J/kg\textperiodcentered K})}{0.136\text{ W/m\textperiodcentered K}} = 32.630 \end{displaymath}

Scaled length ratio

(5)   \begin{equation*} \frac{\ell_s}{\ell_d} = \left(\frac{\nu_s}{\nu_d}\right)^{2/3} \end{equation*}

Scaled velocity ratio

Table: Scaling parameters

Salt mixture properties Fuel Blanket Coolant Unit
Lithium fluoride 68.5 71.0 66.0 mole %
Beryllium fluoride 31.3 2.0 34.0 mole %
U/Th tetrafluoride 0.2 27.0 0.0 mole %
Temperature 600.00 600.00 600.00 $^\circ$C
Dynamic visc. (pred) 14.549 10.974 14.950 centipoise
Dynamic viscosity 14.549 10.974 14.950 centipoise
Density 1970.5 4475.6 1944.7 kg/m$^3$
Kinematic viscosity 7.3833 2.4519 7.6873 m$^2$/s $\times$ 10$^6$
Specific heat 2300.0 920.0 2400.0 J/(kg $\times$ K)
Thermal conductivity 1.4000 1.0500 1.1000 W/(m $\times$ k)
Prandtl number 23.902 9.615 32.618
Scaling with Dowtherm Fuel Blanket Coolant Unit
Temperature 54.32 148.99 37.18 $^\circ$C
Prandtl number 23.906 9.616 32.630
Prandtl number ratio 0.9998 0.9999 0.9996
Dynamic viscosity 1.906 0.586 2.735 centipoise
Density 1032.3 953.1 1046.1 kg/m$^3$
Kinematic viscosity 1.8461 0.6149 2.6144 m$^2$/s $\times$ 10$^6$
Specific heat 1671.0 1937.2 1622.1 J/(kg $\times$ K)
Thermal conductivity 0.1332 0.1181 0.1360 W/(m $\times$ K)
Kin. viscosity ratio 3.9995 3.9875 2.9404
Length ratio 0.3969 0.3977 0.4872
Velocity ratio 0.6300 0.6306 0.6980
Time ratio 0.6300 0.6306 0.6980
Reynolds and Froude number ratio 1.0000 1.0000 1.0000

 

Leave a Reply