## 4 Regulation Method and Characteristics Analysis
### Valve Model and Control Characteristics  
On the basis of keeping the bus pressure difference constant, the electric valve is used to adjust the branch flow resistance in the rack so as to achieve the final flow distribution. In order to study the influence of the valve characteristics on the flow rate control performance of the rack, the physical model of the resistance components in each branch of the rack is simplified as shown in Figure 14; a flow path model consisting only of shunt components and loads is constructed. The flow resistance characteristics of the shunt components are only related to the valve opening \(K_{v}\) of the branch, assuming that the resistance coefficient \(\xi_{v}\) is independent of the \(Re\). Compared to the ideal characteristics of the valve, the actual flow characteristics of the flow path will have a significant change but also be related to the external pump characteristics, load flow resistance coefficient and number of parallel branches [25; 26]. For the flow system in Figure 14, the flow resistance characteristics can be expressed as:  
\[\Delta P_{t}=\xi_{t}\frac{\dot{m}_{t}^{2}}{2\rho A^{2}} \tag{11}\]  
where \(\xi_{t}\) is the system flow resistance coefficient, \(\rho\) is the density of the fluid medium, \(\dot{m}_{t}\) is the total flow rate of system and \(A\) is the total circulation area of pipe. \[\xi_{t}=\left(\sum_{j=1}^{3}\frac{1}{\sqrt{\xi_{j\
u}+\xi_{jL}}}\right)^{-2} \tag{12}\]  
where \(\xi_{j\
u}\) is the resistance coefficient of valve in branch \(j\) and \(\xi_{jL}\) is the resistance coefficient of other components in branch. Defines the ratio of flow resistance to total flow resistance when the valve is fully open as the valve resistance ratio (\(S\)):  
\[\frac{\xi_{v100\%}}{\xi_{v100\%}+\xi_{L}}=S \tag{13}\]  
where \(\xi_{v100\%}\) is the flow resistance when the valve is fully open; \(\xi_{L}\) is the flow resistance of other components. This paper analyzes the ideal control characteristics under different valve characteristics and the control methods of branch load for two kinds of limit pump characteristics; the ideal pump working mode is divided into the constant pressure difference type and the constant flow type; because of the existence of the load and the difference in the pump, the actual pump characteristics are between the two kinds of limit pump characteristics. Figure 14: Simplified flow model inside the payload rack. The ideal flow characteristics of valve refer to the relationship between flow rate \(\dot{n}_{\rm VP}\) and valve opening \(K_{v}\) when the pressure drop at both ends of the valve is fixed; the valve can be divided into linear, logarithmic and quick-open type as shown in Figure 15[27]. In the thermal control system presented in this paper, the pressure difference in the TCB outside the experimental module is kept constant. Figure 16 shows the flow rate of branch 1 as the opening \(K_{1v}\) for three different types of valves. Compared to ideal characteristics of ideal value, the actual flow characteristic curve will present upward convex trend, the linear valve will be close to the quick-open valve characteristic curve, the logarithm type valve will be close to the linear-type valve characteristic curve and the quick-open valve will have a more pronounced quick-open characteristic. Under the premise that the output pressure difference regarding the pump is constant, the actual flow characteristic curve is affected by the load characteristics; as the valve resistance ratio increases, the branch will be closer to the ideal valve characteristics. Because the pressure difference in the thermal bus outside the rack is limited, the increase in the valve resistance ratio will reduce the carrying capacity of the branch. On the other hand, excessive valve resistance ratio will lead to pressure drop consumption in the valve, resulting in lower efficiency of the whole system, leading to increased energy consumption. Based on the analysis of this simple flow system, the following conclusions can be drawn:  
1.