Numerical Investigation of the Stress on a Cylinder Exerted by a Stratified Current Flowing on Uneven Ground
2. Numerical Models
2.1. Governing Equations
2.2. Scalar Transport Equation
2.3. Turbulence Model
2.4. Establishment of a Numerical Tank
2.5. Numerical Model Verification
2.5.1. Verification by Physical Model Test
2.5.2. Grid Independence Test
3. Result and Analysis
3.1. Coupled Influence of Terrain and IWs on the Forces on the Cylinder
3.2. Comparison of the Vertical Distribution of the Force on the Cylinder in Different Cases
3.3. Variation in the Flow Field around the Cylinder under Different Cases
3.4. Influence of the Amplitudes on the IWs Forces and the Flow Field over the Terrain
3.4.1. Influence on the IWs Forces
3.4.2. Influence on the Flow Field
- The topographic factors of the terrain significantly affect the IW forces on the cylinder. There is a strong distinction between the SC case and the three terrain cases: in the SC case, the maximum resultant forces on the cylinder are positive, and the maximum resultant forces are negative in the terrain cases.
- Compared with the SC case, the shallow-water effect caused by the IW-terrain coupled environment enhances the strength of the flow field around the cylinder, so that the lower parts of the cylinder are subjected to larger forces in the reverse wave direction.
- Compared with the SC case, when the IWs propagate over the terrain, the interactions between the IWs and the terrain make the flow field around the cylinder more complex and changeable. As a result, the complex hydrodynamic environment compels the cylinder to experience larger forces.
- A percentage parameter RFn-max is applied in this research to specify the differences of CFn-max between the SC case and the terrain case. RFn-max decreases as the IW amplitude increases when the amplitude is relatively small, but it sharply increases when amplitude is large enough. It is can be explained by the shallow-water effect. When IWs with large amplitude propagate to the bottom terrain, the interaction between the IW and the terrain is intensified and the shallow-water effect occurs, which strengthens the flow field strength near the terrain in the lower layer.
- With the increase of IW amplitude, the interaction between the IW and the terrain is enhanced. Vortices can be found on the bank slope in all the cases, but the size of the vortices is obviously different when amplitude changes. The vortex size increases with the amplitude, and more than one vortex appears when the amplitude is large enough.
- With the increase of the IW amplitude, the IW pattern is more strongly disturbed by the terrain. IW propagating over the bank slope is partially reflected, causing a “blockage” near the terrain and a “elevation” in the reverse wave propagation direction. Therefore, the intensification of the interaction strength between the IWs and the terrain could not only cause greater horizontal forces on the lower parts of the cylinder, but also make the flow field around the terrain more complex.
Data Availability Statement
Conflicts of Interest
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|No.||Case||∆t (s)||CFn-max||Elements Number|
|1||T1 (low density)||0.02||0.0810||525,454|
|2||T2 (moderate density)||0.01||0.0857||2,384,640|
|3||T3 (high density)||0.006||0.0862||3,318,278|
|1||Single cylinder (N1)||0.33||0.0575||0.0857|
|2||Bottom-step terrain (N2)||0.33||0.0575||−0.0683|
|3||Flat-top-knoll terrain (N3)||0.33||0.0575||−0.0692|
|4||Flat-top-knoll terrain (N4)||0.33||0.0575||−0.0753|
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Wang, Y.; Xu, M.; Wang, L.; Shi, S.; Zhang, C.; Wu, X.; Wang, H.; Xiong, X.; Wang, C. Numerical Investigation of the Stress on a Cylinder Exerted by a Stratified Current Flowing on Uneven Ground. Water 2023, 15, 1598. https://doi.org/10.3390/w15081598
Wang Y, Xu M, Wang L, Shi S, Zhang C, Wu X, Wang H, Xiong X, Wang C. Numerical Investigation of the Stress on a Cylinder Exerted by a Stratified Current Flowing on Uneven Ground. Water. 2023; 15(8):1598. https://doi.org/10.3390/w15081598Chicago/Turabian Style
Wang, Yin, Ming Xu, Lingling Wang, Sha Shi, Chenhui Zhang, Xiaobin Wu, Hua Wang, Xiahui Xiong, and Chunling Wang. 2023. "Numerical Investigation of the Stress on a Cylinder Exerted by a Stratified Current Flowing on Uneven Ground" Water 15, no. 8: 1598. https://doi.org/10.3390/w15081598