Increase in Stability of an X-Configured AUV through Hydrodynamic Design Iterations with the Definition of a New Stability Index to Include Effect of Gravity
Abstract
:1. Introduction
2. Stability Indices
2.1. Controls Fixed Linear Dynamic Stability Index for the Horizontal Plane
2.2. Controls Fixed Linear Dynamic Stability Index for the Vertical Plane
3. CFD Simulations
- Planar motion mechanism;
- Turn-circle maneuver.
3.1. Planar Motion Mechanism
3.2. Turning Circle Maneuver
4. Baseline Design
5. Iterative Design Process
6. Results
6.1. Stability Indices
6.2. Investigation of the Sail
6.3. Investigation of the Skates
7. Assessment of Implications of Stability Analysis
7.1. Pitching/Yawing Maneuver for the Vertical and Horizontal Planes for Verification of Stability
7.2. Circular Maneuver for CFD Validation of Stability
8. Closing Remarks and Future Work
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Conflicts of Interest
References
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Index | Definition |
---|---|
G | stability criterion by Roddy [6] |
stability parameter traditionally defined for the vertical plane of submarines | |
stability parameter defined in this article accounting for hydrostatic force | |
, | non-dimensionalized first order derivative of yaw moment with respect to sway (v) and yaw (r) rate, respectively |
, | non-dimensionalized first order derivative of yaw moment with respect to heave (w) and pitch (q) rate, respectively |
, | non-dimensionalized first order derivative of sway force with respect to sway (v) and yaw (r) rate, respectively |
, | non-dimensionalized first order derivative of heave force with respect to heave (w) and pitch (q) rate, respectively |
non-dimensionalized mass | |
u, v, w | velocity components along x, y and z axes in the body reference frame |
, , | acceleration components along x, y and z axes in the body reference frame (BRF) |
, , | coordinates of center of gravity |
external components of force acting on the craft | |
external moments acting on the craft about the COG | |
rotation rate about the roll (x), pitch (y), and yaw (z) axes, respectively | |
, , | angular acceleration about roll (x), pitch (y), and yaw (z) axes, respectively |
vertical distance from COB to COG | |
COG | center of gravity |
COB | center of buoyancy |
NP | neutral point |
CP | critical point |
g | acceleration due to gravity |
coefficient of drag | |
mass moment of inertia with respect to specified axes ‘’ and ‘’ | |
A, B, C | coefficients of characteristic polynomial |
variable of characteristic polynomial |
Index | Recommended Range |
---|---|
0.2 to 0.4 | |
0 to 0.8 |
/D | 0.028 | 0.03 | 0.04 | 0.05 | 0.06 | 0.07 | 0.08 | |
---|---|---|---|---|---|---|---|---|
Fr No. | ||||||||
0.137 | 26 | 39 | 52 | 65 | 78 | 91 | 104 | |
0.27 | 7 | 10 | 13 | 16 | 20 | 23 | 26 | |
0.41 | 3 | 4 | 6 | 7 | 9 | 10 | 12 | |
0.55 | 2 | 2 | 3 | 4 | 5 | 6 | 7 | |
0.69 | 1 | 2 | 2 | 3 | 3 | 4 | 4 | |
0.82 | 1 | 1 | 1 | 2 | 2 | 3 | 3 | |
0.96 | 1 | 1 | 1 | 1 | 2 | 2 | 2 | |
1.10 | 0 | 1 | 1 | 1 | 1 | 1 | 2 | |
1.24 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | |
1.37 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | |
1.51 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | |
1.65 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | |
1.78 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | |
1.92 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | |
2.06 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
2.20 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
2.33 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
2.47 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
2.61 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | |
2.75 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
Design Number | CAD Image | Description |
---|---|---|
Design 1 | Baseline model | Baseline model: fully appended. The socket gap between control fins and fixed strakes is filled for CFD. |
Design 2 | Extended Strakes model | Extended strakes model: The control fins are extended lengthwise. |
Design 3 | T-Strakes model | T-strakes model: The control fins and fixed strakes are appended with a T at the edges to increase fin surface area. |
Design 4 | Vertical Fins model | Vertical Fins model: A vertical fin that is fixed, in addition to the four strakes, is added to the stern of the craft at the top and bottom. The added fins follow a NACA profile to minimize drag. |
Design 5 | Hybrid Narrow model | Hybrid narrow model: The fins are extended and have a T-shaped edge, making this model a combination of Designs 2 and 3. The T-shaped edge has a triangular leading edge to avoid stagnation. |
Design 5a | No-skates model | No-skates model: The skates are removed to understand the stability in the presence of the remaining appendages. |
Design 5b | No-appendages model | No-appendages model: The sail and skates are removed to understand the stability in the presence of the remaining appendages. |
Design 6 | T-Strakes Extended model | T-strakes extended model: The fins have been extended beyond those of the hybrid narrow model in the lengthwise dimension. |
Design 7 | Hybrid Wide model | Hybrid wide model: This model based on Design 5 and Design 6 has wider T-edges on the strakes to increase surface area and mass for the stern. |
Design 7.5a | No-sail model | No-sail model: No sail in the hybrid trapezoidal model. This model is a step before Design 8, the only difference being the triangular leading edge of the T strakes. |
Design 7.5b | Equal holes model | Equal holes model: Equally spaced holes of the same diameter placed along the skates. |
Design 7.5c | Unequal holes model | Unequal holes model: Holes of unequal diameter, evenly spaced, placed along the skates. |
Design 7.5d | Slots model | Slots model: Slot cut out in the front part of the skates, removing most material after Design 7.5a. |
Design 8 | Hybrid triangle model | Hybrid triangle model: The fins are extended and have T-shaped edges. The edge is shaped with a triangular leading edge and taper leading to its widest trailing edge. |
Parameter | Value |
---|---|
Length | L |
Diameter | 0.224 L |
Volume | 0.0284 L |
Wetted Surface Area | 0.571 L |
Cruise Speed | 4 kn |
0.0416 D |
Design | |
---|---|
Baseline | 0.0608 |
Hybrid wide T | 0.0879 |
Hybrid wide triangle | 0.0878 |
Hydrodynamic Coefficients | Design 1 | Design 2 | Design 3 | Design 4 | Design 5 | Design 6 | Design 7 | Design 8 |
---|---|---|---|---|---|---|---|---|
−0.0162 | 23.1 | −108 | −32.4 | −65.6 | −123 | −93.3 | −79.3 | |
0.0367 | 1.47 | −8.82 | 2.12 | −7.61 | −20 | −21.3 | −22 | |
−0.000673 | 40.1 | 56.6 | −7.41 | 56.4 | 102 | 172 | 132 | |
−0.0236 | 16.5 | −67.2 | −23.4 | −37.8 | −90.3 | −66.9 | −53.5 | |
−0.0233 | 1.69 | 19.9 | −4.44 | 21.8 | 49.4 | 52.4 | 55.7 | |
−0.0259 | 1.68 | 1.16 | −0.066 | 2.2 | 3.62 | 4.85 | 4.84 | |
−0.00573 | 74.5 | −47.1 | −12.7 | −22.8 | −43.7 | −19.2 | −14.2 | |
−0.00266 | 33.6 | 46.5 | 8.6 | 70.8 | 69.3 | 101 | 107 | |
−0.00105 | 11 | 6.02 | 0.816 | 11.8 | 11.8 | 20.1 | 20.7 | |
−0.014 | 72.9 | −49 | −8.53 | −25.2 | −48.4 | −25.2 | −19.4 | |
−0.00532 | 47.4 | 68.3 | 7.76 | 98.9 | 103 | 150 | 155 | |
−0.000218 | 109 | 110 | −1.9 | 135 | 144 | 283 | 240 |
Hydroplanes | Design 1 | Design 2 | Design 3 | Design 4 | Design 5 | Design 6 | Design 7 | Design 8 |
---|---|---|---|---|---|---|---|---|
neutral point at 4 kn | −0.765 | −0.763 | −0.581 | −0.817 | −0.580 | −0.409 | −0.395 | −0.383 |
critical point at 4 kn | 0.625 | 0.626 | 0.465 | 0.672 | 0.466 | 0.316 | 0.303 | 0.293 |
Rudder Deflection [] | Hybrid Triangle [m] | Baseline [m] |
---|---|---|
10 | 6.2 L | 3.4 L |
20 | 3.3 L | 2.3 L |
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Miller, L.; Brizzolara, S.; Stilwell, D.J. Increase in Stability of an X-Configured AUV through Hydrodynamic Design Iterations with the Definition of a New Stability Index to Include Effect of Gravity. J. Mar. Sci. Eng. 2021, 9, 942. https://doi.org/10.3390/jmse9090942
Miller L, Brizzolara S, Stilwell DJ. Increase in Stability of an X-Configured AUV through Hydrodynamic Design Iterations with the Definition of a New Stability Index to Include Effect of Gravity. Journal of Marine Science and Engineering. 2021; 9(9):942. https://doi.org/10.3390/jmse9090942
Chicago/Turabian StyleMiller, Lakshmi, Stefano Brizzolara, and Daniel J. Stilwell. 2021. "Increase in Stability of an X-Configured AUV through Hydrodynamic Design Iterations with the Definition of a New Stability Index to Include Effect of Gravity" Journal of Marine Science and Engineering 9, no. 9: 942. https://doi.org/10.3390/jmse9090942