# Temperature Fluctuation Attenuation of Circulating Cooling Water Using Dynamic Thermal Filtering
## 4 Experiment and Discussion
### Results and Discussion  
The temperature fluctuation attenuation ratio of the DTFM attenuator is tested. Additionally, the temperature set values of the two CCW machines are 22.5 \({}^{\circ}\)C and 21.5 \({}^{\circ}\)C respectively. In actual CCW temperature control systems, the frequency of CCW temperature fluctuation is hardly over 0.1 Hz. Moreover, the CCW temperature fluctuation of frequency lower than 0.005 Hz can be directly eliminated by the temperature closed loop feedback control of the CCW temperature control system. Therefore, the switching frequencies of the two three-way valves are defined as 0.01 Hz, 0.02 Hz, and 0.05 Hz for three experiment times.  
It is hoped that a CCW stream with ideal square temperature waveform could be obtained. However, because of the thermal inertia between the outer header of the CCW machines and the inlet header of the DTFM attenuator, including thermal inertia of pipes, valves, and so on, the temperature waveform at inlet header of the DTFM attenuator is smoothed and distorted, as shown in Figure 6.  
Figure 5: Photo of experimental setup (First CCW flow loop: 1-3-6-4-1; Second CCW flow loop: 2-3-6-4-2. Signal loop: 7-5-3, 4).  
Therefore, the frequency analysis of CCW temperature waveforms is carried out to illustrate the performance of fluctuation attenuation in frequency domain, as shown in Figure 7. The main frequencies of distorted CCW temperature waveforms at inlet header of the DTFM attenuator are 0.01 Hz, 0.025 Hz, and 0.053 Hz, respectively, while the corresponding temperature fluctuation attenuation ratios are \(-3.47\) dB, \(-6.19\) dB, and \(-10.97\) dB, respectively. The temperature fluctuation attenuation ratio corresponding to 0.105 Hz is \(-15.28\) dB.  
Figure 6: Temperature waveforms of CCW at inlet header and outer header of the DTFM attenuator.  
Figure 7: Performance of temperature fluctuation attenuation in frequency domain.  
The comparison of experimental results with theoretical modeling results is shown in Figure 8. It can be seen that the values of experimental results are \(\sim\)5 dB worse than the theoretical results. There are many factors which may result in the difference between experimental and theoretical values, such as indispensable approximation in the transfer functions, thermal dissipation of the experimental set up and so on. Therefore, the difference of \(\sim\)5 dB is acceptable in this work, since the trend of the experimental results agrees well with the theoretical results.  
Conventional temperature fluctuation attenuation methods can provide a super large attenuating ratio, such as more than \(-\)60 [EMAIL_ADDRESS] Hz presented by [PERSON] [14], however, the thermal capacity medium in previous work are all non-updatable, which means that the temperature fluctuation attenuation is available around a fixed temperature. Thus, the conventional methods can not satisfy the demand of temperature fluctuation attenuation in dynamic temperature control system, since the dynamic performance of the system is sacrificed for better temperature stability by the introduced thermal inertia. Compared with conventional methods, the proposed DTFM can be applied for the applications demanding dynamic temperature control of CCW.