Validation and application of a coupled xenon-transport and reactor dynamic model of Molten-salt reactor experiment

Abstract

Liquid-fueled molten-salt reactors have dynamic features that distinguish them from solid-fueled reactors, such that conventional system-analysis codes are not directly applicable. In this study, a coupled dynamic model of the Molten-Salt Reactor Experiment (MSRE) is developed. The coupled model includes the neutronics and single-phase thermal-hydraulics modeling of the reactor and validated xenon-transport modeling from previous studies. The coupled dynamic model is validated against the frequency-response and transient-response data from the MSRE. The validated model is then applied to study the effects of xenon and void transport on the dynamic behaviors of the reactor. Plant responses during the unique initiating events such as off-gas system blockages and loss of circulating voids are investigated.

Appendix

The derivation begins with the one-dimensional heat conduction equation:

$$\begin{aligned} \frac{\partial T(t,x)}{\partial t} = \alpha _\text {th}\frac{\partial ^2T}{{\partial x}^2}. \end{aligned}$$

(15)

The measurement point was located at $x=0$, whereas the boundary was located at $x=L$. The boundary conditions are as follows:

$$\begin{aligned} \frac{\partial T}{\partial x}\Bigr \vert _{x=0}&= 0 \end{aligned}$$

(16)

$$\begin{aligned} \Bigr [k \frac{\partial T}{\partial x}\Bigr \vert _{x=L} + hT(t,L) - hT_{\infty }(t) \Bigr ]&= 0. \end{aligned}$$

(17)

By applying a Laplace transform on Eq.  (15), Eq. (16), and Eq.  (17), the following equations were obtained in the frequency domain:

$$\begin{aligned} \frac{\partial ^2{\tilde{T}}}{{\partial x}^2} - \frac{s}{\alpha _\text {th}} {\tilde{T}}&= 0, \end{aligned}$$

(18)

$$\begin{aligned} \frac{\partial {\tilde{T}}}{\partial x}\Bigr \vert _{x=0}&= 0 \end{aligned}$$

(19)

$$\begin{aligned} \Bigr [k \frac{\partial {\tilde{T}}}{\partial x}\Bigr \vert _{x=L} + h\tilde{T(L)} - h{\tilde{T}}_{\infty }(s) \Bigr ]&= 0. \end{aligned}$$

(20)

Equation (18) has a common solution when considering the boundary condition at $x=0$,

$$\begin{aligned} {\tilde{T}} = {\tilde{C}}(s)\cosh \Bigl (\sqrt{\frac{s}{\alpha _\text {th}}} \Bigr ), \end{aligned}$$

(21)

Next, Eq. (21) is substituted into the boundary condition at $x=L$ to obtain

$$\begin{aligned} \begin{aligned} -k{\tilde{C}}\sqrt{\frac{s}{\alpha _\text {th}}}\sinh \Bigl (\sqrt{\frac{s}{\alpha _\text {th}}}L\Bigr ) + h{\tilde{C}}\cosh \Bigl (\sqrt{\frac{s}{\alpha _\text {th}}}L\Bigr )&\\ = h{\tilde{T}}_\infty (s)&. \end{aligned} \end{aligned}$$

(22)

Now we rearrange Eq. (22) and note that ${\tilde{T}}(s,0)={\tilde{C}}(s)$, which is the temperature measurement in the frequency domain; thus, we have

$$\begin{aligned} & {\tilde{M}}(s) = \frac{{\tilde{C}}}{{\tilde{T}}_\infty }\nonumber \\ & =\Bigl [\cosh \Bigl (\sqrt{\frac{s}{\alpha _\text {th}}}L\Bigr ) - \frac{k}{h}\sqrt{\frac{s}{\alpha _\text {th}}} \sinh \Bigl (\sqrt{\frac{s}{\alpha _\text {th}}}L\Bigr )\Bigr ]^{-1} \end{aligned}$$

(23)

By replacing s with jw, the transfer function between the measured temperature and surrounding temperature is obtained.