The flexible composite tank (FCT) used in this research was an iso-proportional model of 2 m³, 1.6 m high, and a maximum diameter of 1.64 m. The 2D curves are shown in Supplementary Material, and the FCT model was obtained by converting the curve using 3D CAD software. The shape of the FCT was roughly spherical, and the tank was mainly composed of a steel center pipe and flexible membrane. The center pipe consisted of a main pipe and 16 struts, all spread around the main pipe, with a radius of 175 mm and a length of 1.2 m. The flexible membrane consisted of a sealing layer, an insulation layer, and an antileakage layer, each made of collapsible flexible materials (Figure 1). The density of the insulation layer was 0.064 g/cm³, and its thermal conductivity is shown in Table 1.

In this test, more heat-tracings with the same type of heating elements were installed to demonstrate that, whether the power was sufficient or not, additional heating elements were activated. A 20-m heat-tracing, which can supply 6.6 kW maximum heating power, was equipped to test the relationship between elevating temperature and heating power supply. Based on the structure of the FCT, two heat-tracing arrangements were designed. Plan 1 had all the heat-tracings laid along with the struts, as shown in Figure 2. Plan 2 had all the heat-tracings arranged within 0.5 m height from the bottom of the struts, as shown in Figure 3.

Thirty-three temperature sensors were deployed in the FCT to monitor all field temperatures. The temperature sensors were distributed in the whole tank, including five sensors on the center pipe, 16 sensors on the membrane, and 12 sensors suspended inside the FCT. The 3D layout is shown in Figure 4. The 33 sensors were distributed on two mutually perpendicular surfaces, and the relative position is shown in Figure 5. Each sensor number is shown in Figure 6. For the center pipe, the five sensors were numbered 71, 72, 73, 74, and 75 from the top to the bottom.

The medium used for the test was white oil (nonwaxy crude), and its properties are presented in Table 2. The FCT was placed in water to reduce the influence of changes in ambient conditions on the test results. The pool was 12 m in length, 7 m in width, and 6.5 m in depth (Figure 7). In accordance with recorded data, the water temperature fluctuated between 19°C and 25°C.

The switch and heating power adjustment of the heating system during the test were controlled using an automatic procedure and the data from each temperature sensor were recorded every 1 min. For plan 1, the heating power was 6600 W and the continuous heating time was 6 h. The measurements from the sensors inside the FCT were observed. The highest temperature point of 71.31°C was at the top area of the center pipe, the lowest temperature point of 33.38°C was at the bottom of the center pipe, and the temperature difference was 37.93°C. The entire system was allowed to cool down naturally, and the internal temperature of the FCT returned to ambient temperature after 46 h.

From the experimental results, the relatively high-temperature area inside the FCT was at the top and the relatively low temperature area was located at the bottom after heating for 6 h with the plan 1 layout (Figure 8). The maximum temperature deviation was 37.93°C. This phenomenon may be due to rising of the liquid heated by the bottom heating trace into the top zone under conditions of thermal convection, which is then added to the heating effect of the top trace, causing the heating efficiency of the top zone to be twice that of the bottom zone.

As shown in Figure 9, the temperature difference between the central region and the edge region was small within the same height range, with a maximum deviation of 6.87°C. The experimental results indicate feasibility of use of a central heating source combined with an edge insulation layer to achieve a relatively small temperature difference between the central and extreme edge areas of the container. However, improvement of the central heat source layout is needed. Considering thermodynamic convection characteristics, the heat source layout in the top area could be reduced, and the heat source in the bottom increased, to achieve more uniform temperature distribution in the system.

For plan 2, the heating duration was 8 h 20 min, heating power was 3400 W, holding time was 21 h 10 min, and the corresponding power was 540 W. The experimental results showed the highest temperature of 43.12°C near the heat source and the lowest temperature of 35.94°C at the top edge. The maximum temperature difference within the FCT was 7.18°C.

As shown in Figure 10, the temperature difference in the height range was insignificant in either the central or edge area. The maximum temperature at the center pipe near the top area was 41.7°C, and the minimum temperature in the upper central partial region (section B-B) was 37.1°C. No remarkable ladder change was observed in the temperature field distribution in the intermediate section between the central pipe and the boundary. The top region had a low temperature, and the bottom region had a higher temperature, with a minimum of 34.44°C and a maximum of 43.12°C. No remarkable ladder change was observed in the temperature field distribution in the boundary, with a minimum temperature of 34.44°C and a maximum of 42.56°C.

As shown in Figure 11, no obvious gradient change was observed in the temperature distribution from the center pipe to the boundary within the same height plane. The test results demonstrated that the plan 2 layout can produce a uniform heating effect on the entire FCT. The insulation led to well-maintained temperature inside the FCT throughout the 21 h 10 min test period, during which the temperature did not rise or fall remarkably, and the overall temperature was effectively maintained in a stable state under the combined action of the insulation layer and the insulation power of 540 W. The maximum temperature fluctuation at each point was 2.56°C, which shows that the plan 2 scheme provided effective insulation of the FCT system.

As shown in Figures 9B,C and Figures 11B,C, the heating power of plan 1 is 6600 W and that of plan 2 is 3400 W for the temperature field distribution at the same height (section B-B and C-C) inside the FCT. The heating efficiency of plan 2 is comparable to that of plan 1 at the same heating time. Plan 2 achieves the same heating effect as plan 1 with approximately half the heating power, as the temperature distribution from middle to edge is more uniform in the same height range. Plan 2 is preferred from both economic and practical perspectives.

To facilitate follow-up research, a corresponding finite element model was established based on plan 2, as shown in Supplementary Material. In view of the symmetry of the structure, only 1/4 models were built for heating analysis. Therefore, the heating power in the model was 850 W, and the holding power was 135 W.

The general finite element software FLUENT was used for analysis, and the properties of each material are summarized in Tables 1, 2. The distribution of the temperature field inside the FCT after heating for 10 h is shown in Supplementary Material. The highest temperature, 41.0°C, was located near the heating source, with a deviation of 4.92% from the experimental results. The lowest temperature, 38.0°C, was located at the top edge, with deviation from the experimental results of 5.73%. The distribution of temperature field was similar to the experimental results.

The variation curve of the average temperature inside the FCT during the heating and holding stages is shown in Supplementary Material. The comparison of computational fluid dynamics (CFD) analysis and the experimental results in Supplementary Material shows that the CFD model can accurately simulate the temperature variation trend. The comparison of results also demonstrates that the CFD model and algorithm can accurately predict the experimental results, indicating suitability for use in subsequent research.