Large Eddy Simulation of the Flow around a Generic Submarine under Straight-Ahead and 10° Yaw Conditions
Abstract
:1. Introduction
2. The Joubert BB2 Submarine Model
3. Numerical Methodology
3.1. Large Eddy Simulation
3.2. Computational Domain and Boundary Condition
3.3. Computation Mesh
4. Results and Discussion
4.1. Validation of the Numerical Approach
4.2. Analysis of the Evolution of the Flow
5. Conclusions
- (1)
- Three sets of grids under 10° yaw conditions were designed to examine the grid convergence and computational accuracy. As the grid number increased, the numerical dissipation decreased, and the capture of the vertical component of velocity, the cross-stream Reynolds stress, seemed to be more refined, especially for the extreme values, which were more representative of the experiments, with the relative error of the peak value in the region of core flow being relatively smaller. The numerical attenuation of the mean resultant velocity of the core flow inevitably existed in the LES simulations with the dynamic Smagorinsky model, which could be eliminated through the improvement in the grid’s spatial resolution. In the near sail-wake region, the numerical simulations for all grid sets could define the centers of the vortices well, but as they evolve downstream, the advantages of refining the grids are gradually reflected. Overall, through qualitative and quantitative comparison with experiments under 10° yaw conditions, the computational accuracy was verified and results shown are more representative of the experiments with the improvement in grid spatial resolution.
- (2)
- A comparison of the evolution of the flow under straight-ahead and 10° yaw conditions shows that in the core-flow region, the resultant velocity, vorticity magnitude, and TKE under straight-ahead conditions were somewhat smaller than those under 10° yaw conditions. The side-vortices on the leeward side of the sail occurred further forward, and the sail-tip and hydroplane-tip vortices were strong enough, relatively, to develop far downstream under 10° yaw conditions. Another obvious feature that distinguishes the straight-ahead conditions is the flow separation on the leeward side of the middle hull; the wake of the submarine becomes quite complicated, and the flow behind the stern is dominated by the mixing of various component vortex systems, including the tilted horseshoe-vortex system, the upper and lower hull vortices, the tip vortices, and the wake of the sail, hydroplanes, X-rudders, and the hull under 10° yaw conditions. But downstream, far away from the hull under straight-ahead conditions, all the tip vortices dissipated, and only the wake vortices, after complicated interaction, dynamically evolved, with the energy gradually weakening.
- (3)
- The tip vortex tracking under 10° yaw conditions exhibited significant three-dimensional characteristics compared to those under straight-ahead conditions. Under10° yaw conditions, sail-tip vortex tracking maintained an axial angle of approximately 8 degrees with the hull, and was almost stable vertically after experiencing a downwash immediately behind the sail. The port hydroplane-tip vortices developed and spiraled around the sail-tip vortices, while the core of the starboard hydroplane-tip vortices kept moving towards the leeward side, with the vertical position gradually rising away from the hull after passing through a valley at approximately x/L = 1.1, due to the repulsive interaction of the hull wake.
- (4)
- The resultant velocity, vorticity magnitude, and TKE showed a gradually decreasing trend as the wake of the cruciform appendage developed downstream. Under 10° yaw conditions, the core-flow exhibited a high-velocity characteristic, in which the peaks of mean vorticity magnitude were located on the windward side in the near wake region, while in the far wake region, the velocity was smaller than the freestream velocity and the valleys of mean vorticity magnitude were located on the windward side. The strongest TKE did not occur immediately behind the sail, but approximately in the range of x/L equal to 0.6 to 1.0, where the downwash of the sail-tip vortex was quite intense.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Nomenclature
CFD | Computational fluid dynamics | SUBOFF | Submarine Technology Program Office |
CSSRC | China Ship Scientific Research Centre | Filtered stress tensor | |
DARPA | Defense Advanced Research Projects Agency | Sub-grid-scale stress | |
DES | Detached eddy simulation | TKE, k | Turbulence kinetic energy, m2/s2 |
DNS | Direct numerical simulation | Mean streamwise velocity, m/s | |
DSTO | Defense Science and Technology Organization | <uxux> | Normal stress in the streamwise component, m2/s2 |
Exp. 1 | Experimental results with ReL = 4 × 106 | Mean resultant velocity, m/s | |
Exp. 2 | Experimental results with ReL = 8 × 106 | Mean horizontal velocity, m/s | |
Resultant of the body forces | <uyuy> | Normal stress in the horizontal component, m2/s2 | |
G1 | Most coarse grid set | <uyuz> | Cross-stream Reynolds stress, m2/s2 |
G2 | Median grid set | Mean vertical velocity, m/s | |
G3 | Most refined grid set | <uzuz> | Normal stress in the vertical component, m2/s2 |
Identity tensor | Freestream velocity, m/s | ||
L | Model length, m | Filtered velocity | |
LES | Large eddy simulation | x | Streamwise coordinate, m |
o | Coordinate origin | y | Horizontal coordinate, m |
ONR | Office of Naval Research | y+ | Dimensionless wall distance |
Filtered pressure | z | Vertical coordinate, m | |
PISO | Pressure implicit with splitting of operators | ||
PIV | Particle image velocimetry | Greek symbols | |
RANS | Reynolds averaged Navier–Stokes | Sub-grid scale turbulent viscosity | |
ReL | Reynolds number | Density | |
rm | Model radius, m | Mean streamwise vorticity,/s | |
ry | Radial distance, m | Mean vorticity magnitude,/s | |
Strain rate tensor | Mean horizontal vorticity,/s | ||
SPIV | Stereo particle image velocimetry | Mean vertical vorticity,/s |
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Measurement Plane | Grid Scheme | Sail Tip | Hydroplanes | ||||
---|---|---|---|---|---|---|---|
Windward | Leeward | ||||||
y/L | z/L | y/L | z/L | y/L | z/L | ||
G1 | −0.072 | 0.141 | −0.108 | 0.161 | −0.013 | 0.123 | |
x/L = 0.511 | G2 | −0.073 | 0.141 | −0.105 | 0.161 | −0.015 | 0.121 |
G3 | −0.072 | 0.141 | −0.105 | 0.159 | −0.014 | 0.123 | |
G1 | −0.079 | 0.136 | −0.095 | 0.173 | −0.027 | 0.109 | |
x/L = 0.650 | G2 | −0.080 | 0.136 | −0.092 | 0.171 | −0.028 | 0.109 |
G3 | −0.079 | 0.136 | −0.094 | 0.169 | −0.025 | 0.110 | |
G1 | −0.092 | 0.130 | −0.077 | 0.169 | −0.048 | 0.094 | |
x/L = 0.815 | G2 | −0.092 | 0.130 | −0.074 | 0.163 | −0.048 | 0.092 |
G3 | −0.090 | 0.130 | −0.077 | 0.165 | −0.044 | 0.093 |
Measurement Plane | Grid Scheme | Sail Tip | Hydroplanes | ||||
---|---|---|---|---|---|---|---|
Windward | Leeward | ||||||
y/L (%) | z/L (%) | y/L (%) | z/L (%) | y/L (%) | z/L (%) | ||
G1 | 4.3 | −1.9 | 5.3 | 1.6 | 2.7 | 0.3 | |
x/L = 0.511 | G2 | 5.3 | −1.8 | 2.2 | 1.9 | 9.2 | −1.6 |
G3 | 5.0 | −1.9 | 1.8 | 0.5 | 6.7 | −0.3 | |
G1 | 6.5 | −1.3 | 1.0 | 4.2 | 12.0 | 0.4 | |
x/L = 0.650 | G2 | 7.7 | −1.4 | −2.3 | 3.0 | 9.6 | −0.4 |
G3 | 6.1 | −1.1 | −0.1 | 2.0 | 4.8 | 1.2 | |
G1 | 9.0 | 0.4 | −3.7 | 3.3 | 7.5 | −0.5 | |
x/L = 0.815 | G2 | 9.2 | 0.3 | −7.0 | −0.4 | 6.2 | −1.8 |
G3 | 7.2 | −0.3 | −3.5 | 0.6 | −2.5 | −1.5 |
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Chen, M.; Zhang, N.; Sun, H.; Zhang, X. Large Eddy Simulation of the Flow around a Generic Submarine under Straight-Ahead and 10° Yaw Conditions. J. Mar. Sci. Eng. 2023, 11, 2286. https://doi.org/10.3390/jmse11122286
Chen M, Zhang N, Sun H, Zhang X. Large Eddy Simulation of the Flow around a Generic Submarine under Straight-Ahead and 10° Yaw Conditions. Journal of Marine Science and Engineering. 2023; 11(12):2286. https://doi.org/10.3390/jmse11122286
Chicago/Turabian StyleChen, Mo, Nan Zhang, Hailang Sun, and Xuan Zhang. 2023. "Large Eddy Simulation of the Flow around a Generic Submarine under Straight-Ahead and 10° Yaw Conditions" Journal of Marine Science and Engineering 11, no. 12: 2286. https://doi.org/10.3390/jmse11122286
APA StyleChen, M., Zhang, N., Sun, H., & Zhang, X. (2023). Large Eddy Simulation of the Flow around a Generic Submarine under Straight-Ahead and 10° Yaw Conditions. Journal of Marine Science and Engineering, 11(12), 2286. https://doi.org/10.3390/jmse11122286