## 3 Results and Discussion
### Ultrasonic Fields  
Ultrasonic propagation through the above-designed waveguide rod and specimen was simulated with the COMSOL Multiphysics. Figure 9 shows the local enlargement of the ultrasonic field at \(y\)-\(z\) plane, which gives the ultrasonic distribution in the waveguide rod and the specimen at a different time. It can be seen from the simulation diagram that the ultrasonic wave propagates along the waveguide rod to the inside of the test piece (Figure 9a), reflects and generates an echo at the bottom of the test piece (Figure 9b-d), and the reflected echo returns to the waveguide rod along the original path (Figure 9e,f). It also can be found that the ultrasonic waveguide undergoes a complex waveform conversion,  
Figure 8: Comparison of calculated temperature buffer curve and measured temperature buffer curve. Figure 7: Electric heating device used in the test. including longitudinal, transverse, and surface waves. Furthermore, the ultrasonic-guided wave undergoes significant attenuation and dissipation in the specimen, which is inevitable in the propagation process. However, the energy of the ultrasonic-guided wave is mainly concentrated in the center. Figure 10 shows the time-domain plot monitored by three probe points. The coordinates of the three probe points are (0, 0, 150), (0, 3, 150), and (0, 6, 150), which are all located on the horizontal centerline of the waveguide rod, but the distance from the vertical centerline of the waveguide rod is 0 mm, 3 mm, and 6 mm. As can be seen from the figure, the degree of signal attenuation and dispersion at different locations is different. The closer the receiving point to the center, the clearer the ultrasound signal. More serious ultrasound signal attenuation and dispersion occur as it moves gradually far away from the center. Therefore, probe 1 monitors the clearest ultrasound signal, and probe 3 monitors the most disturbed ultrasound signal. This suggests a conclusion that in order to obtain a clear  
and discernible echo signal, the receiving point should be located on the centerline of the waveguide rod. With the designed waveguide structure, an ultrasonic testing device was developed, as shown in Figure 11. It includes a signal generator, oscilloscope, waveguide structure, and clamping device. The end of the waveguide structure was fixed on the specimen by the clamping device with a strong pressing force. Therefore, the ultrasonic wave can transport between the specimen and the waveguide structure. The specimen was put on the electric heating device and heated to a certain temperature. Then, the device transmitted and received the ultrasonic signal. Two plate specimens were tested with a thickness of 20 mm and 50 mm, respectively. Figure 12 displays the received wave signals, and the crests of the echo are very clear. The thickness can be obtained according to the wave path difference. Figure 13 shows the measured data of the thickness at different temperatures. If the wave velocity is set as a constant, the predicted thickness basically increases linearly with the temperature. A large error occurs at high temperatures, which may reach to 6.9% and 5.0% at 250 deg C, respectively. Therefore, the effect of temperature must be considered in detecting the thickness of high-temperature objects. Figure 10: Time-domain plot of three probe points at the centerline of the waveguide rod. (**a**) Probe 1, coordinates (0 mm, 0 mm, 150 mm); (**b**) Probe 2, coordinates (0 mm, 3 mm, 150 mm); (**c**) Probe 3, coordinates (0 mm, 6 mm, 150 mm); (**d**) Probe 1 (**Blue**); Probe 2 (**Green**); Probe 3 (**Red**). The specimen expands at high temperatures, and the thickness can be theoretically calculated based on the expansion coefficient. It is found that the theoretical thickness grows little below 250 deg C, which has a bigger difference with that measured at a constant wave velocity.