Liu 2023a - Revision history

Rimni at 12:26, 13 November 2023

2023-11-13T12:26:11Z

Rimni at 12:25, 13 November 2023

2023-11-13T12:25:44Z

Rimni at 12:24, 13 November 2023

2023-11-13T12:24:50Z

Rimni at 11:28, 9 November 2023

2023-11-09T11:28:40Z

Rimni at 11:12, 6 October 2023

2023-10-06T11:12:02Z

Rimni: /* References */

2023-09-22T12:41:44Z

‎References

Rimni at 12:01, 22 September 2023

2023-09-22T12:01:43Z

Rimni: /* 3.3 Simulation study under different filling rates */

2023-09-22T11:59:58Z

‎3.3 Simulation study under different filling rates

Rimni: /* 4. Conclusion */

2023-09-22T11:56:31Z

‎4. Conclusion

Rimni: /* 3.3 Simulation study under different filling rates */

2023-09-20T14:23:19Z

‎3.3 Simulation study under different filling rates

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 <div id='img-6'></div>
-{| class="wikitable" style="margin: 0em auto 0.1em auto;border-collapse: collapse;width:90%;"
+{| class="wikitable" style="margin: 0em auto 0.1em auto;border-collapse: collapse;width:70%;"
 |-style="background:white;"
 |style="text-align: center;padding:10px;"| [[File:Liu_2023a_2266_Fig6.png]]

← Older revision		Revision as of 12:25, 13 November 2023
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−	From [[#img-6\|Figure 6]], the following conclusions can be drawn: at a=0.1g, the maximum pressure occurs at <math display="inline">t=2</math>s, amounting to 8,289 Pa; at <math display="inline">a=0.2</math>g, the maximum pressure occurs at <math display="inline">t=1.5</math>s, reaching 8,426 Pa; at <math display="inline">a=0.3</math>g, the maximum pressure occurs at <math display="inline">t=1</math>s, with a value of 13,791 Pa; at <math display="inline">a=0.4</math>g, the maximum pressure occurs at t=1s, registering 18,958 Pa; and at <math display="inline">a=0.5</math>g, the maximum pressure occurs at <math display="inline">t=0.5</math>s, totaling 99,200 Pa. Under varying steering accelerations, the liquid's agitation causes the maximum pressure inside the tank to rise in correlation with increasing steering acceleration, with greater acceleration resulting in a shorter time for the pressure to reach its maximum value.	+	From [[#img-6\|Figure 6]], the following conclusions can be drawn: at <math display="inline">a=0.1</math>g, the maximum pressure occurs at <math display="inline">t=2</math>s, amounting to 8,289 Pa; at <math display="inline">a=0.2</math>g, the maximum pressure occurs at <math display="inline">t=1.5</math>s, reaching 8,426 Pa; at <math display="inline">a=0.3</math>g, the maximum pressure occurs at <math display="inline">t=1</math>s, with a value of 13,791 Pa; at <math display="inline">a=0.4</math>g, the maximum pressure occurs at t=1s, registering 18,958 Pa; and at <math display="inline">a=0.5</math>g, the maximum pressure occurs at <math display="inline">t=0.5</math>s, totaling 99,200 Pa. Under varying steering accelerations, the liquid's agitation causes the maximum pressure inside the tank to rise in correlation with increasing steering acceleration, with greater acceleration resulting in a shorter time for the pressure to reach its maximum value.

	[[#img-7\|Figure 7]](a) and [[#img-7\|Figure 7]](b) display the run charts of the impact force generated by liquid sloshing in the tank on the tank body in the <math display="inline"> y</math> and <math display="inline"> z </math> directions over time, under a filling rate of 0.85 and differing steering accelerations. The figures indicate that the trends of impact force on the tank body in the <math display="inline"> y</math> and <math display="inline"> z </math> directions over time are generally consistent, with both the amplitude and extreme values increasing as steering accelerations rise. This suggests that the greater the steering acceleration during the tank car's turning, the larger the maximum lateral impact force on the tank body. The primary reason for this is the increased inertial and centripetal forces on the tank body during turning, which cause intensified liquid sloshing and an increased maximum force. Moreover, it is observed that when the steering acceleration is 0.5g, the impact force in the <math display="inline"> y</math>-direction on the tank body changes significantly over time compared to accelerations ranging from 0.1g to 0.4g, while in the <math display="inline"> z </math>-direction, the variation is relatively larger. This implies that the overall direction of the impact force on the tank body at 0.5g is more likely to be oriented in the <math display="inline"> z </math>-direction as opposed to accelerations between 0.1g and 0.4g. Hence, when the tank car turns with a steering acceleration of 0.5g, its safety is comparatively lower, and rollover risk is present. This finding aligns with the rollover threshold for heavy-duty liquefied natural gas trucks specified in [[#tab-2\|Table 2]].		[[#img-7\|Figure 7]](a) and [[#img-7\|Figure 7]](b) display the run charts of the impact force generated by liquid sloshing in the tank on the tank body in the <math display="inline"> y</math> and <math display="inline"> z </math> directions over time, under a filling rate of 0.85 and differing steering accelerations. The figures indicate that the trends of impact force on the tank body in the <math display="inline"> y</math> and <math display="inline"> z </math> directions over time are generally consistent, with both the amplitude and extreme values increasing as steering accelerations rise. This suggests that the greater the steering acceleration during the tank car's turning, the larger the maximum lateral impact force on the tank body. The primary reason for this is the increased inertial and centripetal forces on the tank body during turning, which cause intensified liquid sloshing and an increased maximum force. Moreover, it is observed that when the steering acceleration is 0.5g, the impact force in the <math display="inline"> y</math>-direction on the tank body changes significantly over time compared to accelerations ranging from 0.1g to 0.4g, while in the <math display="inline"> z </math>-direction, the variation is relatively larger. This implies that the overall direction of the impact force on the tank body at 0.5g is more likely to be oriented in the <math display="inline"> z </math>-direction as opposed to accelerations between 0.1g and 0.4g. Hence, when the tank car turns with a steering acceleration of 0.5g, its safety is comparatively lower, and rollover risk is present. This finding aligns with the rollover threshold for heavy-duty liquefied natural gas trucks specified in [[#tab-2\|Table 2]].

@@ Line 402: / Line 402: @@
 {| class="wikitable" style="margin: 0em auto 0.1em auto;border-collapse: collapse;width:90%;"
 |-style="background:white;"
-|style="text-align: center;padding:10px;"| [[File:Review 455397141911-image24.jpg|700px]]
+|style="text-align: center;padding:10px;"| [[File:Liu_2023a_2266_Fig6.png]]
 |-
 | style="background:#efefef;text-align:left;padding:10px;font-size: 85%;"| '''Figure 6'''. Cloud plots of maximum pressure inside the tank at different turning accelerations. (a) <math display="inline">a=0.1</math>g (<math display="inline">t=2</math>s); (b) <math display="inline">A=0.2</math>g (<math display="inline">t=1.5</math>s); (c) <math display="inline">A=0.3</math>g (<math display="inline">t=1</math>s); (d) <math display="inline">A=0.4</math>g (<math display="inline">t=1</math>s); (e) <math display="inline">A=0.5</math>g (<math display="inline">t=0.5</math>s)

@@ Line 429: / Line 429: @@
 |style="text-align: center;padding:10px;"| [[Image:Review_455397141911-image26.png|600px]]
 |-
-| style="background:#efefef;text-align:left;padding:10px;font-size: 85%;"| '''Figure 8'''. Cloud chart of the maximum pressure change in the tank under different filling rates. (a) <math display="inline">K=0.6 (t=1s)</math>. (b) <math display="inline">K=0.8 (t=3s)</math>. (c) <math display="inline">K=0.85 (t=4s)</math>. (d) <math display="inline">K=0.9 (t=5s)</math>
+| style="background:#efefef;text-align:left;padding:10px;font-size: 85%;"| '''Figure 8'''. Cloud chart of the maximum pressure change in the tank under different filling rates.<br> (a) <math display="inline">K=0.6 (t=1s)</math>. (b) <math display="inline">K=0.8 (t=3s)</math>. (c) <math display="inline">K=0.85 (t=4s)</math>. (d) <math display="inline">K=0.9 (t=5s)</math>
 |}

@@ Line 463: / Line 463: @@
 [2] Rees W.D.  Static hazards during the top loading of road tankers with highly insulating liquids: flow rate limitation proposals to minimize risk. J. Electrostat., 11(1):13-25, 1981.
-[3] Beiyou G.V., Cowley L.T., Smalletal M.L.  Fire engulfment of LPG tanks: Heatup, a Predictive model. J. Hazard Mater., 20(2):227-238, 1988.
+[3] Beiyou G.V., Cowley L.T., Smalletal M.L.  Fire engulfment of LPG tanks: Heatup, a predictive model. J. Hazard Mater., 20(2):227-238, 1988.
 [4] Birk A.M. Modelling the effects of a torch-type fire impingement on a rail or highway tanker. Fire Safety J., 15(4):277-296, 1989.

@@ Line 457: / Line 457: @@
 ==References ==
-[1] Xu, JX, Lin, WS, Chen, X; Zhang, H (2022) Review of unconventional natural gas liquefaction processes. Front Energy Res 10, 915893.
+[1] Xu J.X., Lin W.S., Chen X., Zhang H. Review of unconventional natural gas liquefaction processes. Front Energy Res., 10, 915893, 2022.
-[2] Rees WD (1981) Static hazards during the top loading of road tankers with highly insulating liquids:flow rate limitation proposals to minimize risk. J Electrostat 11(1),13-25.
+[2] Rees W.D.  Static hazards during the top loading of road tankers with highly insulating liquids: flow rate limitation proposals to minimize risk. J. Electrostat., 11(1):13-25, 1981.
-[3] Beiyou GV, Cowley LT, Smalletal ML (1988) Fire engulfment of LPG tanks: Heatup, a Predictive model. J Hazard Mater 20(2), 227-238.
+[3] Beiyou G.V., Cowley L.T., Smalletal M.L.  Fire engulfment of LPG tanks: Heatup, a Predictive model. J. Hazard Mater., 20(2):227-238, 1988.
-[4] Birk AM (1989) Modelling the effects of a torch-type fire impingement on a rail or highway tanker. Fire Safety J 15(4), 277-296.
+[4] Birk A.M. Modelling the effects of a torch-type fire impingement on a rail or highway tanker. Fire Safety J., 15(4):277-296, 1989.
-[5] Lloyd N, Vaiciurgis E, Langrish TAG (2002) The effect of baffle design on longitudinal liquid movement in road tankers: an experimental. Process Saf Environ 80(4),181-185.
+[5] Lloyd N., Vaiciurgis E., Langrish T.A.G. The effect of baffle design on longitudinal liquid movement in road tankers: an experimental. Process Safety and Environmental Protection,  80(4):181-185, 2002.
-[6] Shimanovsky AO, Kuznyatsova MG, Pleskachevskii YM (2012) The strength analysis of the partitions in road tank reservoirs. Procedia Eng 48, 607-612.
+[6] Shimanovsky A.O., Kuznyatsova M.G., Pleskachevskii Y.M. The strength analysis of the partitions in road tank reservoirs. Procedia Eng., 48:607-612, 2012.
-[7] Zakaria MS, Osman K, Saadun MNA, Manaf MZA, Mohd Hanafi MH (2013) Computational simulation of boil-off gas formation inside liquefied natural gas tank using evaporation model in ansys fluent. Appl Mech Materials 393(5), 839-844.
+[7] Zakaria M.S., Osman K., Saadun M.N.A., Manaf M.Z.A., Mohd Hanafi M.H. Computational simulation of boil-off gas formation inside liquefied natural gas tank using evaporation model in ansys fluent. Appl. Mech. Materials, 393(5):839-844, 2013.
-[8] Sun LN, Zhou GF (2012) Numerical simulation for liquid sloshing process of a tank truck. J Vib Shock 31(22), 147-150.
+[8] Sun L.N., Zhou G.F. Numerical simulation for liquid sloshing process of a tank truck. J. Vib. Shock, 2012(22):147-150, 2012.
-[9] Kolaei A, Rakheja S, Richard MJ (2014) Effects of tank cross-section on dynamic fluid slosh loads and roll stability of a partly-filled tank truck. Eur J Mech B-Fluid 46, 46-58.
+[9] Kolaei A., Rakheja S., Richard M.J. Effects of tank cross-section on dynamic fluid slosh loads and roll stability of a partly-filled tank truck. Eur. J. Mech. B-Fluid, 46:46-58, 2014.
-[10] Hu XM, Li WL, Zhao ZG, Sun L (2013) A study on the lateral sloshing of liquid in the tank body of a liquid tank truck. Chin J Appl Mech 30(5), 641-646.
+[10] Hu X.M., Li W.L., Zhao Z.G., Sun L. A study on the lateral sloshing of liquid in the tank body of a liquid tank truck. Chin. J. Appl. Mech., 30(5):641-646, 2013.
-[11] Yu D (2016) Research on Liquid Sloshing Non-linear Model and Driving
+[11] Yu D. Research on liquid sloshing non-linear model and driving stability of partially-filled tank trucks. Jilin University, 2016.
-−
-Stability of Partially-Filled Tank trucks. Jilin University.

@@ Line 437: / Line 437: @@
 [[#img-9|Figures 9]](a) and [[#img-9|9]](b) present the run charts of the impact force generated by liquid sloshing in the tank on the tank body in the <math display="inline">  y</math> and <math display="inline"> z</math> directions over time, under a steering acceleration of 0.2g and varying filling rates. The figures show that the force on the tank body in the <math display="inline">  y</math>-direction sharply increases during the initial period, then gradually decreases after achieving the first peak, followed by a rapid increase in the positive direction, decrease, and so forth. This occurs because, when the tank car initiates turning, the liquid within the tank oscillates due to the centripetal acceleration. The maximum force on the tank body corresponds to the most violent liquid sloshing. Concurrently, it can be observed that the impact force in the <math display="inline">  y</math>-direction diminishes as the filling rate increases. This is due to the larger available space inside the tank at smaller filling rates, which, when the tank car starts to turn, results in greater liquid sloshing amplitude and thus a larger force on the tank body.
-[[Image:Review_455397141911-image27.png|600px]]
+<div id='img-9'></div>
-From [[#img-9|Figures 9]](b), it is observed that the force on the tank body in the <math display="inline"> z</math>-direction remains minimal in the initial period and subsequently increases gradually, with the force fluctuating in both positive and negative directions of <math display="inline"> z</math>. This is because during the tank car's turning process, the liquid in the tank initially moves primarily in the ''x''-direction due to inertia force, causing the force in the <math display="inline"> z</math>-direction to approach zero. As the inertia force dissipates, the liquid in the tank generates an impact force on the tank in the <math display="inline"> z</math>-direction under centripetal force. When the filling rate is less than 0.85, the impact force rises with increasing filling rate, reaching its peak at a 0.85 filling rate. In contrast, for filling rates above 0.85, the impact force on the tank body decreases with increasing filling rate. This indicates that when the liquid filling rate of the tank exceeds 0.85, the tank car exhibits the least liquid sloshing during turning and driving, resulting in the minimal <math display="inline"> z</math>-direction impact force on the tank body.
+From [[#img-9|Figures 9]](b), it is observed that the force on the tank body in the <math display="inline"> z</math>-direction remains minimal in the initial period and subsequently increases gradually, with the force fluctuating in both positive and negative directions of <math display="inline"> z</math>. This is because during the tank car's turning process, the liquid in the tank initially moves primarily in the <math display="inline"> x</math>-direction due to inertia force, causing the force in the <math display="inline"> z</math>-direction to approach zero. As the inertia force dissipates, the liquid in the tank generates an impact force on the tank in the <math display="inline"> z</math>-direction under centripetal force. When the filling rate is less than 0.85, the impact force rises with increasing filling rate, reaching its peak at a 0.85 filling rate. In contrast, for filling rates above 0.85, the impact force on the tank body decreases with increasing filling rate. This indicates that when the liquid filling rate of the tank exceeds 0.85, the tank car exhibits the least liquid sloshing during turning and driving, resulting in the minimal <math display="inline"> z</math>-direction impact force on the tank body.
 ==4. Conclusions==

@@ Line 435: / Line 435: @@
 [[#img-8|Figure 8]] reveals that under different filling rates: at <math display="inline">K=0.6</math>, the maximum pressure occurs at t=1s with a value of 25,438 Pa; at <math display="inline">K=0.8</math>, the maximum pressure occurs at t=3s, amounting to 1,412 Pa; at <math display="inline">K=0.85</math>, the maximum pressure occurs at t=4s, totaling 369 Pa; and at <math display="inline">K=0.9</math>, the maximum pressure occurs at t=5s, registering 286 Pa. These results suggest that the maximum pressure inside the tank decreases as the filling rate increases, and it takes longer for the pressure to attain its maximum value. The highest maximum pressure is observed at <math display="inline">K=0.6</math>, signifying the most pronounced liquid sloshing. Conversely, when the filling rates are <math display="inline">K=0.85</math> and 0.9, the maximum pressure values inside the tank are considerably low, indicating minimal liquid sloshing amplitude.
-Fig. 9(a) and Fig. 9(b) present the run charts of the impact force generated by liquid sloshing in the tank on the tank body in the ''y'' and ''z'' directions over time, under a steering acceleration of 0.2g and varying filling rates. The figures show that the force on the tank body in the ''y''-direction sharply increases during the initial period, then gradually decreases after achieving the first peak, followed by a rapid increase in the positive direction, decrease, and so forth. This occurs because, when the tank car initiates turning, the liquid within the tank oscillates due to the centripetal acceleration. The maximum force on the tank body corresponds to the most violent liquid sloshing. Concurrently, it can be observed that the impact force in the ''y''-direction diminishes as the filling rate increases. This is due to the larger available space inside the tank at smaller filling rates, which, when the tank car starts to turn, results in greater liquid sloshing amplitude and thus a larger force on the tank body.
+[[#img-9|Figures 9]](a) and [[#img-9|9]](b) present the run charts of the impact force generated by liquid sloshing in the tank on the tank body in the <math display="inline">  y</math> and <math display="inline"> z</math> directions over time, under a steering acceleration of 0.2g and varying filling rates. The figures show that the force on the tank body in the <math display="inline">  y</math>-direction sharply increases during the initial period, then gradually decreases after achieving the first peak, followed by a rapid increase in the positive direction, decrease, and so forth. This occurs because, when the tank car initiates turning, the liquid within the tank oscillates due to the centripetal acceleration. The maximum force on the tank body corresponds to the most violent liquid sloshing. Concurrently, it can be observed that the impact force in the <math display="inline">  y</math>-direction diminishes as the filling rate increases. This is due to the larger available space inside the tank at smaller filling rates, which, when the tank car starts to turn, results in greater liquid sloshing amplitude and thus a larger force on the tank body.
 [[Image:Review_455397141911-image27.png|600px]]
@@ Line 442: / Line 442: @@
 Fig. 9 Changes in force on the tank body in different directions under different filling quantities: (a) ''y''-direction; (b) ''z''-direction</div>
-From Fig. 9(b), it is observed that the force on the tank body in the ''z''-direction remains minimal in the initial period and subsequently increases gradually, with the force fluctuating in both positive and negative directions of ''z''. This is because during the tank car's turning process, the liquid in the tank initially moves primarily in the ''x''-direction due to inertia force, causing the force in the ''z''-direction to approach zero. As the inertia force dissipates, the liquid in the tank generates an impact force on the tank in the ''z''-direction under centripetal force. When the filling rate is less than 0.85, the impact force rises with increasing filling rate, reaching its peak at a 0.85 filling rate. In contrast, for filling rates above 0.85, the impact force on the tank body decreases with increasing filling rate. This indicates that when the liquid filling rate of the tank exceeds 0.85, the tank car exhibits the least liquid sloshing during turning and driving, resulting in the minimal ''z''-direction impact force on the tank body.
+From [[#img-9|Figures 9]](b), it is observed that the force on the tank body in the <math display="inline"> z</math>-direction remains minimal in the initial period and subsequently increases gradually, with the force fluctuating in both positive and negative directions of <math display="inline"> z</math>. This is because during the tank car's turning process, the liquid in the tank initially moves primarily in the ''x''-direction due to inertia force, causing the force in the <math display="inline"> z</math>-direction to approach zero. As the inertia force dissipates, the liquid in the tank generates an impact force on the tank in the <math display="inline"> z</math>-direction under centripetal force. When the filling rate is less than 0.85, the impact force rises with increasing filling rate, reaching its peak at a 0.85 filling rate. In contrast, for filling rates above 0.85, the impact force on the tank body decreases with increasing filling rate. This indicates that when the liquid filling rate of the tank exceeds 0.85, the tank car exhibits the least liquid sloshing during turning and driving, resulting in the minimal <math display="inline"> z</math>-direction impact force on the tank body.
 ==4. Conclusions==

@@ Line 444: / Line 444: @@
 From Fig. 9(b), it is observed that the force on the tank body in the ''z''-direction remains minimal in the initial period and subsequently increases gradually, with the force fluctuating in both positive and negative directions of ''z''. This is because during the tank car's turning process, the liquid in the tank initially moves primarily in the ''x''-direction due to inertia force, causing the force in the ''z''-direction to approach zero. As the inertia force dissipates, the liquid in the tank generates an impact force on the tank in the ''z''-direction under centripetal force. When the filling rate is less than 0.85, the impact force rises with increasing filling rate, reaching its peak at a 0.85 filling rate. In contrast, for filling rates above 0.85, the impact force on the tank body decreases with increasing filling rate. This indicates that when the liquid filling rate of the tank exceeds 0.85, the tank car exhibits the least liquid sloshing during turning and driving, resulting in the minimal ''z''-direction impact force on the tank body.
-==4. Conclusion==
+==4. Conclusions==
 In this study, Fluent software is employed to simulate and analyze the impact force generated by the liquid sloshing inside the tank during the turning of a tank car, with a focus on the comparison and analysis of impact forces produced under different lateral accelerations and filling rates. The primary findings are as follows:
-(1) Under a constant tank filling rate, an increase in steering acceleration results in more intense liquid sloshing within the tank. Both the vertical and lateral impact forces on the tank body fluctuate over time, with trends remaining largely consistent. The changing amplitude and extreme values grow as the steering acceleration increases. When the steering acceleration reaches 0.5g, the impact force in the y-direction on the tank body undergoes a marked change in comparison to accelerations within the range of 0.1g-0.4g, while in the z-direction, it is considerably larger. This finding implies that the overall direction of the impact force on the tank body at 0.5g is more likely to be oriented in the z-direction as opposed to accelerations between 0.1g-0.4g. Consequently, the safety of a tank car cornering with a steering acceleration of 0.5g is relatively lower, resulting in a potential rollover risk.
+(1) Under a constant tank filling rate, an increase in steering acceleration results in more intense liquid sloshing within the tank. Both the vertical and lateral impact forces on the tank body fluctuate over time, with trends remaining largely consistent. The changing amplitude and extreme values grow as the steering acceleration increases. When the steering acceleration reaches 0.5g, the impact force in the <math display="inline">y</math>-direction on the tank body undergoes a marked change in comparison to accelerations within the range of 0.1g-0.4g, while in the <math display="inline">z</math>-direction, it is considerably larger. This finding implies that the overall direction of the impact force on the tank body at 0.5g is more likely to be oriented in the <math display="inline">z</math>-direction as opposed to accelerations between 0.1g-0.4g. Consequently, the safety of a tank car cornering with a steering acceleration of 0.5g is relatively lower, resulting in a potential rollover risk.
 (2) When the tank car turns at a specific turning acceleration, the vertical impact force on the tank body caused by liquid sloshing within the tank decreases as filling rate increases. The lateral impact force on the tank body increases with the rise in filling rate when the rate falls between 0.6 and 0.85; however, it diminishes as the rate increases between 0.85 and 0.9. A filling rate within the range of 0.85-0.9 is most favorable for the secure transportation of tank cars.

@@ Line 422: / Line 422: @@
 ===3.3 Simulation study under different filling rates===
-With a steering acceleration of a=0.2g, the tank car maintains a constant speed prior to turning and commences the turn at time t=0. The pressure distribution cloud maps showcasing the maximum pressure inside the tank under four different filling rate conditions (0.6, 0.8, 0.85, and 0.9) are simulated and depicted in Fig. 8.
+With a steering acceleration of <math display="inline">a=0.2</math>g, the tank car maintains a constant speed prior to turning and commences the turn at time <math display="inline">t=0</math>. The pressure distribution cloud maps showcasing the maximum pressure inside the tank under four different filling rate conditions (0.6, 0.8, 0.85, and 0.9) are simulated and depicted in [[#img-8|Figure 8]].
-[[Image:Review_455397141911-image26.png|600px]]
+<div id='img-8'></div>
-Fig. 8 reveals that under different filling rates: at ''K''=0.6, the maximum pressure occurs at t=1s with a value of 25,438 Pa; at ''K''=0.8, the maximum pressure occurs at t=3s, amounting to 1,412 Pa; at ''K''=0.85, the maximum pressure occurs at t=4s, totaling 369 Pa; and at ''K''=0.9, the maximum pressure occurs at t=5s, registering 286 Pa. These results suggest that the maximum pressure inside the tank decreases as the filling rate increases, and it takes longer for the pressure to attain its maximum value. The highest maximum pressure is observed at ''K''=0.6, signifying the most pronounced liquid sloshing. Conversely, when the filling rates are ''K''=0.85 and 0.9, the maximum pressure values inside the tank are considerably low, indicating minimal liquid sloshing amplitude.
+[[#img-8|Figure 8]] reveals that under different filling rates: at <math display="inline">K=0.6</math>, the maximum pressure occurs at t=1s with a value of 25,438 Pa; at <math display="inline">K=0.8</math>, the maximum pressure occurs at t=3s, amounting to 1,412 Pa; at <math display="inline">K=0.85</math>, the maximum pressure occurs at t=4s, totaling 369 Pa; and at <math display="inline">K=0.9</math>, the maximum pressure occurs at t=5s, registering 286 Pa. These results suggest that the maximum pressure inside the tank decreases as the filling rate increases, and it takes longer for the pressure to attain its maximum value. The highest maximum pressure is observed at <math display="inline">K=0.6</math>, signifying the most pronounced liquid sloshing. Conversely, when the filling rates are <math display="inline">K=0.85</math> and 0.9, the maximum pressure values inside the tank are considerably low, indicating minimal liquid sloshing amplitude.
 Fig. 9(a) and Fig. 9(b) present the run charts of the impact force generated by liquid sloshing in the tank on the tank body in the ''y'' and ''z'' directions over time, under a steering acceleration of 0.2g and varying filling rates. The figures show that the force on the tank body in the ''y''-direction sharply increases during the initial period, then gradually decreases after achieving the first peak, followed by a rapid increase in the positive direction, decrease, and so forth. This occurs because, when the tank car initiates turning, the liquid within the tank oscillates due to the centripetal acceleration. The maximum force on the tank body corresponds to the most violent liquid sloshing. Concurrently, it can be observed that the impact force in the ''y''-direction diminishes as the filling rate increases. This is due to the larger available space inside the tank at smaller filling rates, which, when the tank car starts to turn, results in greater liquid sloshing amplitude and thus a larger force on the tank body.