## Novel Transient Calorimeter (NTC)  
### Principe and Characteristic of the Novel Transient Calorimeter  
The structural diagram of the novel transient calorimeter (NTC) is shown in Figure 1. CVD diamond is selected as the calorimeter element. Firstly, the platinum film resistance is sputtered on the back of the diamond as the sensitive temperature measurement element. Subsequently, the calorimeter element is attached to the sensor base. The platinum film wire extends from the back of the calorimeter, and the bottom is filled with air or insulation material, which is usually epoxy. The measurement principle of the transient calorimeter assumes that the back and side of the calorimeter element are adiabatic; namely, there is no heat loss from the calorimeter element. Thus, the heat introduced into the calorimeter element at certain time intervals should be equal to the heat accumulated by the calorimeter element:  
\[q=\int_{0}^{L}\rho c\frac{\partial T}{\partial t}dx \tag{1}\]  
where \(\rho\) and \(c\) are the density and specific heat of the calorimetric element material (CVD diamond in the present study), respectively; \(L\) is the thickness of the calorimetric element. As the density and specific heat are assumed constant, the following equation can be obtained:  
\[q=\rho cL\frac{\partial T_{a}}{\partial t} \tag{2}\]  
where \(T_{a}\) is the average temperature of the calorimetric element. The heat flux can be obtained by measuring the average temperature change rate of the calorimeter. In practical measurement, the average temperature of the calorimeter is difficult to measure. Thus, the back temperature is generally measured. Instead of using thermocouples to measure the temperature in traditional calorimeters, the new transient calorimeter uses the platinum film resistance to measure the back temperature of the CVD diamond with relatively high output sensitivity. The thermal response time of the calorimeter element is mainly related to the thermal response characteristics of the calorimeter material. The response time \(t_{R}\) of the calorimeter was calculated as follows by [PERSON] [34]:  
\[t_{R}=\frac{L^{2}}{\alpha\pi^{2}}\ln\left(\frac{2}{1-\frac{q_{b}}{q_{0}}}\right) \tag{3}\]  
where \(q_{b}\) is the heat flux calculated by the back temperature of the calorimeter element; \(q_{0}\) is the heat flux loaded on the surface, and \(\alpha=k/pc\) is the thermal diffusion coefficient of the calorimeter material. Table 1 shows the thermal physical parameters of a natural diamond, CVD diamond, and copper, which is the common calorimetric material. The physical parameters of the CVD diamond are determined by the Physical Property Measurement System (PPMS) of the diamond film used in this design. The physical parameters of other materials, which will be used in subsequent numerical calculations, are also listed here. Figure 1: Structural diagram of the NTC heat flux sensor (not to scale). The response time \(t_{R0.99}\) (99%) is selected as the characteristic response time of the sensor, which means that the heat flux at the back of the calorimeter element reaches 99% of the surface heat flux loading. Figure 2 shows the relationship between the characteristic response time and the thickness of the calorimeter element. It is observed that the characteristic thermal response time of the natural diamond is the fastest at the same thickness, followed by the CVD diamond and copper. At a thickness of 0.2 mm, the characteristic response time of copper is 186 us, whereas that of the CVD diamond is only 59 us. Although the response time of the natural diamond is faster (21 us at 0.2 mm), its cost is much higher. However, the CVD diamond meets the response time requirement at a relatively low cost. Due to the high resistivity of diamonds, the platinum film can be directly plated on the back of the calorimeter element without special insulation between them. The platinum film resistance is hidden on the back of the calorimeter element, thus protecting it from disturbances or erosion of the high-velocity gas flow.