Research Papers: Flows in Complex Systems

Numerical Investigation of Trajectory and Attitude Robustness of an Underwater Vehicle Considering the Uncertainty of Platform Velocity and Yaw Angle

[+] Author and Article Information
Guihui Ma

School of Energy Science and Engineering,
Harbin Institute of Technology,
Harbin 150001, Heilongjiang, China
e-mail: 15B902026@hit.edu.cn

Fu Chen

School of Energy Science and Engineering,
Harbin Institute of Technology,
Harbin 150001, Heilongjiang, China
e-mail: chenfu@hit.edu.cn

Jianyang Yu

School of Energy Science and Engineering,
Harbin Institute of Technology,
Harbin 150001, Heilongjiang, China
e-mail: yujianyang@hit.edu.cn

Kun Wang

School of Energy Science and Engineering,
Harbin Institute of Technology,
Harbin 150001, Heilongjiang, China
e-mail: 17b902040@stu.hit.edu.cn

1Corresponding author.

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received March 7, 2018; final manuscript received July 13, 2018; published online August 16, 2018. Assoc. Editor: Moran Wang.

J. Fluids Eng 141(2), 021106 (Aug 16, 2018) (11 pages) Paper No: FE-18-1157; doi: 10.1115/1.4040930 History: Received March 07, 2018; Revised July 13, 2018

The vertically launched underwater vehicle always suffers various hydrodynamic disturbances in its water-emerging process due to the uncertainty of the launch platform motion. Based on the nested sparse grid based stochastic collocation method (NSSCM) and nonintrusive polynomial chaos method, the effect of uncertainty of platform velocity and yaw angle on robustness of vehicle's trajectory and attitude is numerically studied. Results indicate that the uncertainty stemming from platform motion propagates along vehicle's water-emerging process. As the negative horizontal velocity of vehicle gradually changes to positive direction, the uncertainty bar of horizontal velocity presents contracting-expanding mode with an “hourglass” shape while the uncertainty bar of horizontal displacement experiences a “spindle-shaped” one (expanding-contracting-expanding), which is a half cycle later compared with the velocity. The uncertain motion of platform enlarges the uncertainty bar of bottom force via its impact on the gas-leakage process of trail bubble, resulting in the increasing of uncertainty of vertical velocity. Pitching angle (attitude of vehicle) and pitching angular velocity of vehicle persist getting worse driven by the pressure difference between vehicle's front and back sides especially on head part. And their continuous increasing uncertainty bars are formed mainly due to the condition that pressure uncertainty of front side is larger than that on back side, which also leads to the increasing of uncertainty of horizontal force.

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Fig. 1

Typical water-emerging process of a vertically launched underwater vehicle

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Fig. 2

(a) Geometry model, (b) computational domain and boundary conditions, (c) definition of yaw angle in top view

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Fig. 3

(a) Schematic of water tank with gas ejection system and horizontal moving platform and (b) experimental and numerical displacements of the projectile and their trail bubbles at some typical moments

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Fig. 4

Comparison of nondimensional pressure among different amounts of mesh at T¯=1.0 and the computational mesh

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Fig. 5

The extending process of collocation points with two-dimensional stochastic variables

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Fig. 6

Cumulative distribution function of pitching angle when bottom of vehicle leaves water surface with different orders of PCE

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Fig. 7

Probability density function (third-order PCE), CDF and frequency distribution (collocation points) of pithing angle when bottom of vehicle leaves water

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Fig. 8

Mean values and uncertainty bars of 2D-trajectorys along different directions and the relevant velocity profiles

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Fig. 9

Mean values and uncertainty bars of 3D-trajectory and pitching angle as well as the schematic of uncertain trajectory

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Fig. 10

Mean values and uncertainty bars of horizontal force and the corresponding horizontal velocity

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Fig. 11

Mean values and uncertainty bars of attack angle and schematic of attack angle when vehicle rotates

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Fig. 12

Mean values and uncertainty bars of the vertical force and the corresponding vertical velocity

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Fig. 13

Evaluation process of vehicle's trail bubble when platform moves with a Vsub platform velocity and 0 deg yaw angle

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Fig. 14

Mean values and uncertainty bars of pitching moment and the corresponding pitching angular velocity

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Fig. 15

Statistical parameters on the symmetry plane of vehicle at typical y position: (a) mean value of phase volume fraction α and nondimensional pressure P¯, (b) standard deviation of phase volume fraction α, and (c) standard deviation of nondimensional pressure P¯

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Fig. 16

Mean values and uncertainty bars of nondimensional pressure on vehicle's exterior along axial direction at typical y position



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