## 3 Experimental Results
### Steady-State Tests  
In the steady-state tests, the hot recuperated air (above 500 \({}^{\circ}\)C) of the T100 unit is used to heat the particles. In such tests, the particles are circulated through the bypass loop, i.e., no solar energy is being added. It is important to emphasize that the T100\({}^{\prime}\)s air always enters the heat exchanger with steady-state conditions, i.e., constant flow rate, constant temperature, and constant pressure. Table 6 summarizes some of the conducted tests in which the particle flow rate was varied. These experimental data were collected when air and particles temperatures along the heat exchanger and the whole facility reach steady-state conditions for a sufficient period. The temperatures were obtained by averaging the readings of the thermocouples installed at the corresponding locations. Figure 9 shows the air and particle temperatures at the inlet and outlet of the heat exchanger during one of the conducted steady-state tests. \begin{table}
\begin{tabular}{c c c c c c c} \hline \multirow{2}{*}{**Test**} & \(\hat{m}_{a}\) & \(\hat{m}_{p}\) & \(T_{a,i}\) & \(T_{a,o}\) & \(T_{p,i}\) & \(T_{p,o}\) \\  & [kg/s] & [kg/s] & [\({}^{\circ}\)C] & [\({}^{\circ}\)C] & [\({}^{\circ}\)C] & [\({}^{\circ}\)C] \\ \hline
1 & 0.542 & 0.666 & 555.9 & 502.0 & 491.6 & 523.3 \\
2 & 0.539 & 0.847 & 556.0 & 502.9 & 495.5 & 523.7 \\
3 & 0.543 & 1.020 & 556.1 & 503.5 & 497.6 & 522.7 \\
4 & 0.540 & 1.188 & 556.3 & 503.4 & 498.7 & 521.1 \\
5 & 0.518 & 1.314 & 555.4 & 499.2 & 495.7 & 517.0 \\
6 & 0.520 & 1.498 & 556.3 & 505.3 & 502.5 & 519.9 \\
7 & 0.518 & 1.661 & 553.9 & 504.1 & 501.7 & 517.2 \\
8 & 0.530 & 1.825 & 553.8 & 505.5 & 503.2 & 517.3 \\
9 & 0.518 & 1.988 & 555.4 & 505.7 & 504.3 & 517.1 \\ \hline \end{tabular}
\end{table} 
Table 6: Steady-state tests measurements. Figure 8: Air and particles temperatures across the heat exchanger during an on-sun test. The thermal performance of the heat exchanger can be represented by the overall heat transfer coefficient and the effectiveness. These parameters can be estimated using the following equations:  
\[\dot{Q}=U\ A_{s}\ LMTD \tag{3}\]  
\[\varepsilon=\frac{\dot{Q}}{\dot{Q}_{max}} \tag{4}\]  
where \(\dot{Q}\) is the heat transfer rate, \(U\) is the overall heat transfer coefficient, \(A_{s}\) is the total heat transfer area, \(LMTD\) is the log mean temperature difference, \(\varepsilon\) is the heat exchanger effectiveness, and \(\dot{Q}_{max}\) is the maximum possible heat transfer rate. The heat supplied by the air and that captured by the particles, inside the heat exchanger, can be estimated by incorporating a control volume on each medium and applying energy balance  
\[\dot{Q}_{supplied}=\dot{Q}_{a}=\dot{m}_{a}\ \Delta h_{a}=\dot{m}_{a}\ c_{p,avg} \Delta T_{a} \tag{5}\]  
\[\dot{Q}_{captured}=\dot{Q}_{p}=\dot{m}_{p}\ \Delta h_{p}=\dot{m}_{p}\int c_{p}dT \tag{6}\]  
where \(\dot{m}\) is the mass flow rate, \(\Delta h\) is the specific enthalpy difference between the inlet and outlet, \(c_{p}\) is the specific heat, and \(\Delta T\) is the temperature difference. The specific heat of the Carbobead CP particles, according to [6], can be obtained from  
\[c_{p_{p}}=0.365\ T^{0.18} \tag{7}\]  
The log mean temperature difference and the maximum possible heat transfer rate are obtained as  
\[LMTD=\frac{\left(T_{a,i}-T_{p,\rho}\right)-\left(T_{a,\rho}-T_{p,j}\right)}{ \ln\left(\frac{T_{a,i}-T_{p,\rho}}{T_{a,\rho}-T_{p,j}}\right)} \tag{8}\]  
\[\dot{Q}_{max}=C_{min}\left(T_{a,i}-T_{p,j}\right) \tag{9}\]  
Figure 9: Air and particle temperatures at the inlet and outlet of the heat exchanger, Test no. 8.  
where \(T_{a,i}\) and \(T_{a,\rho}\) are the inlet and outlet temperatures of air, respectively, \(T_{p,i}\) and \(T_{p,\rho}\) are the inlet and outlet temperatures of particles, respectively, and \(C_{min}=\min\left[\dot{m}_{a}c_{p_{a}},\dot{m}_{p}c_{p_{p}}\right]\) is the minimum heat capacity rate.