The Numerical Simulation of a Submarine Based on a Dynamic Mesh Method
Abstract
:1. Introduction
2. Numerical Model
2.1. Governing Equations
2.2. Turbulence Model
3. Model Verification
3.1. Computational Domain and Grids
3.2. Dynamic Mesh Method and Boundary Conditions
3.3. Convergence Study
3.4. Validation of the Numerical Results
4. Results and Discussion
4.1. Analysis of the Wake Waves
4.1.1. Comparison between the Inflow Method and Dynamic Mesh Method
4.1.2. Wake Waves of the Steady Turning Motion
4.2. Influence of the Velocity
4.2.1. Pressure Coefficient Acting on the Submarine
4.2.2. Influence of the Velocity on the Pressure Coefficient
4.2.3. Influence of the Velocity on the Force
4.3. Influence of the Rotation Rate
5. Conclusions
- (1)
- The steady turning motion of the submarine causes the pressure difference between the port side and starboard side, which results from the difference in the velocity field distribution and the flow separation on both sides of the submarine. The velocity vector field on the plane of z = 0 reflects the characteristics of the flow field around the submarine during its turning motion. It can explain the surface pressure variation precisely through the analysis of the velocity vector field based on Bernoulli’s equation.
- (2)
- In the steady turning period, under the condition of the same rotation rate, the influences of the velocity on the wake waves, pressure coefficient and force are significant. The force components in both the tangential direction and normal direction increase as the velocity increases. This indicates that the forward velocity affects the flow field in terms of the pressure gradient, viscous shear stress gradient and wave-making intensity.
- (3)
- When the submarine retains the same velocity but changes in the rotation rate, the force component in the normal direction changes significantly. Decreasing the rotation rate will decrease the normal force. Thus, the normal force is strongly affected by the rotation rate. The tangential force tends to remain constant at the same time, indicating that it is independent of the rotation rate.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
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Basic Size(m) | Net Increase in Cells (Thousand/s) | Total Resistance Rt (N) | Error of Rt (%) |
---|---|---|---|
0.042 | 412.528 | 70.465 | —— |
0.063 | 324.429 | 70.461 | 0.006 |
0.084 | 206.963 | 69.984 | 0.683 |
0.126 | 128.653 | 69.404 | 1.507 |
Time Step (s) | Number of Steps (Step) | Total Resistance Rt (N) | Error of Rt (%) |
---|---|---|---|
0.005 | 1000 | 70.829 | —— |
0.01 | 500 | 70.461 | 0.520 |
0.02 | 250 | 69.291 | 2.172 |
0.05 | 100 | 68.568 | 3.193 |
Basic Size(m) | Net Increase in Cells (Thousand/s) | Total Resistance Rt (N) | Error of Rt (%) |
---|---|---|---|
0.0315 | 225.763 | 71.749 | —— |
0.042 | 170.822 | 71.342 | 0.568 |
0.063 | 115.586 | 70.653 | 1.529 |
0.084 | 83.421 | 69.976 | 2.471 |
Time Step (s) | Number of Steps (Step) | Total Resistance Rt (N) | Error of Rt (%) |
---|---|---|---|
0.005 | 1000 | 71.816 | —— |
0.01 | 500 | 71.342 | 0.660 |
0.02 | 250 | 70.388 | 1.989 |
0.05 | 100 | 69.720 | 2.918 |
Froude Number Fr (-) | Rotational Radius R (m) | Rotation Rate γ = L/R (-) | Tangential Force Ft (N) | Normal Force Fn (N) | Resultant Force Rt (N) |
---|---|---|---|---|---|
0.5 | 3 L | 0.333 | 69.305 | 19.665 | 72.041 |
5 L | 0.200 | 69.938 | 9.575 | 70.590 | |
7 L | 0.143 | 69.970 | 3.441 | 70.216 |
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He, G.; Zhang, C.; Xie, H.; Liu, S. The Numerical Simulation of a Submarine Based on a Dynamic Mesh Method. J. Mar. Sci. Eng. 2022, 10, 1417. https://doi.org/10.3390/jmse10101417
He G, Zhang C, Xie H, Liu S. The Numerical Simulation of a Submarine Based on a Dynamic Mesh Method. Journal of Marine Science and Engineering. 2022; 10(10):1417. https://doi.org/10.3390/jmse10101417
Chicago/Turabian StyleHe, Guanghua, Cheng Zhang, Hongfei Xie, and Shuang Liu. 2022. "The Numerical Simulation of a Submarine Based on a Dynamic Mesh Method" Journal of Marine Science and Engineering 10, no. 10: 1417. https://doi.org/10.3390/jmse10101417