## 2 Design of Molten Salt Swing Check Valve
### Dynamics Model of the Opening Process of Molten Salt Swing Check Valve  
#### 2.2.1 Opening Process Dynamics Model  
To address the fact that a high-temperature molten salt transport system molten salt swing check valve opening process will appear difficult to open under conditions of low pressure difference, and to deal with the opening process valve oscillation, pressure fluctuations and other problems, an analysis of the opening process valve motion components  
Figure 1: Tower-type molten salt cogeneration system.  
Figure 2: Structure of molten salt swing check valve.  
force can be performed, as shown in Figure 3. Based on the valve moment balance and considering the molten salt density, this model will allow the researchers to establish a molten salt check valve opening process dynamics model, to make predictions and, in actual operations, to avoid the above problems.  
When the molten salt medium flows through the check valve, the disc rotates about the rotating shaft under the action of the resultant force or is in a state of equilibrium. The main torque affecting disc rotation are torque by jet impingement on the disc and the torque by pressure difference, gravity moment, buoyancy moment, and friction moment, among which the friction moment at the rotating axis is usually very small and can be ignored. The dynamic model of the valve opening process is established as follows, and the opening characteristic parameters of the molten salt check valve are analyzed.  
The angular momentum equation of the opening process can be expressed as:  
\[I_{disc}\frac{d\omega}{dt}=T_{V}+T_{P}+T_{W} \tag{1}\]  
where \(I_{disc}\) is the rotational inertia of the valve motion components with respect to the rotating shaft; \(\omega\) is the angular velocity of the valve motion components opening; \(T_{V}\) is the torque induced by jet impingement; \(T_{P}\) is the torque induced by pressure difference; \(T_{W}\) is the combined moment of gravity and buoyancy of the valve motion components.  
The torque induced by jet impingement \(T_{V}\) is caused by the relative velocity of the valve motion components to the molten salt medium. Define the relative flow velocity as [29]:  
\[v_{rel}=v-L_{c}\omega\cos\theta \tag{2}\]  
where \(v\) is the molten salt inlet flow velocity; \(L_{c}\) is the distance from the valve shape center to the rotating axis; \(\theta\) is the valve opening angle, taking the value range of 0\({}^{\circ}\)\(\sim\)61.5\({}^{\circ}\).  
The medium impact moment can be expressed as follows [30]:  
\[T_{V}=\int R\times\mathrm{d}F=\rho A_{disc}v_{rel}|v_{rel}|L_{c}\cos\theta \tag{3}\]  
The pressure difference moment, caused by the inlet and outlet pressure difference, can be defined as:  
\[T_{P}=\Delta pA_{disc}L_{c}\cos\theta \tag{4}\]  
where \(\Delta p\) is the upstream and downstream pressure difference of the valve motion components; \(A_{disc}\) is the area of the valve disc.  
Figure 3: Force analysis of valve motion components.  
The combined moment of gravity and buoyancy of the valve motion components can be defined as:  
\[T_{W}=-V_{disc}\Big{(}\rho_{disc}-\rho_{fluid}\Big{)}gL_{g}\sin\theta \tag{5}\]  
where \(V_{disc}\) is the volume of valve motion components; \(\rho_{disc}\) and \(\rho_{fluid}\) are valve motion component material density and molten salt medium density, respectively; \(L_{g}\) is the distance from the center of gravity of the valve motion components to the rotating axis.