0
Research Papers

Diagnostic-Photographic Determination of Drag/Lift/Torque Coefficients of a High Speed Rigid Body in a Water Column

[+] Author and Article Information
Peter C. Chu, Chenwu Fan

Naval Ocean Analysis and Prediction Laboratory, Naval Postgraduate School, Monterey, CA 94025

Paul R. Gefken

Polter Laboratory, SRI International, Menlo Park, CA 94025

J. Appl. Mech 77(1), 011015 (Oct 05, 2009) (15 pages) doi:10.1115/1.3173767 History: Received August 25, 2008; Revised May 12, 2009; Published October 05, 2009

Prediction of a rigid body falling through water column with a high speed (such as Mk-84 bomb) needs formulas for drag/lift and torque coefficients, which depend on various physical processes such as free surface penetration and bubbles. A semi-empirical method is developed in this study to determine the drag/lift and torque coefficients for a fast-moving rigid body in a water column. The theoretical part is to derive the relationships (called diagnostic relationships) between (drag, lift, and torque) coefficients and (position and orientation) of the rigid body from the three momentum equations and the three moment of momentum equations. The empirical part is to collect data of trajectory and orientation of a fast-moving rigid body using multiple high-speed video cameras (10,000 Hz). Substitution of the digital photographic data into the theoretical relationships leads to semi-empirical formulas of drag/lift and torque coefficients, which are functions of the Reynolds number, attack angle, and rotation rate. This method was verified by 1/12th Mk-84 bomb strike experiment with various tail configurations (tail section with four fins, two fins, and no fin and no-tail section) conducted at the SRI test site. The cost of this method is much lower than the traditional method using the wind tunnel. Various trajectory patterns are found for different tail configurations.

Copyright © 2010 by American Society of Mechanical Engineers
Your Session has timed out. Please sign back in to continue.

References

Figures

Grahic Jump Location
Figure 1

Position vectors rh, rt, and the unit vector e

Grahic Jump Location
Figure 2

Attack angle (α), angles (β,γ), center of volume (ov), center of mass (om), and drag and lift forces (exerted on ov). Note that σ is distance between ov and om with positive (negative) value when the direction from ov to om is the same (opposite) as the unit vector e.

Grahic Jump Location
Figure 3

Illustration of unit vectors (eu,euψ,euγ, and euxy) with evxy the projection of eu on the xy plane

Grahic Jump Location
Figure 4

Axial and cross-axial velocity (uaf,ucf), associated hydrodynamic forces on a pair of fins (Faf,Fcf) and the distance between of and om (i.e., σf) with positive (negative) value when the direction from of to om is the same (opposite) as the unit vector e

Grahic Jump Location
Figure 5

Illustration of Ω, Mtr, and Mc

Grahic Jump Location
Figure 6

Drag coefficient versus Reynolds number for a circular cross section (after Ref. 10)

Grahic Jump Location
Figure 7

Photography of 1/12th scale model Mk-84 bomb: (a) warhead with tail section and four fins and (b) sabot

Grahic Jump Location
Figure 8

Overview experimental arrangement

Grahic Jump Location
Figure 9

Two HSV images for Launch-3 (Type-I) at water-entry velocity of 295 ms−1: (a) initial water entry, (b) t=22.8 ms, and (c) t=44.4 ms

Grahic Jump Location
Figure 10

Dependence of Cd on the Reynolds number (Re) and attack angle (α) for three different values of Ω: (a) −5 s−1, (b) 0 s−1, and (c) 5 s−1

Grahic Jump Location
Figure 11

Dependence of Cl on the Reynolds number (Re) and attack angle (α) for three different values of Ω: (a) −5 s−1, (b) 0 s−1, and (c) 5 s−1

Grahic Jump Location
Figure 12

Dependence of Cm on the Reynolds number (Re) and attack angle (α)

Grahic Jump Location
Figure 13

Comparison between predicted and observed trajectories for Mk-84 warhead with tail section and four fins (Type-1) with initial water-entry speed: (a) 132 ms−1, (b) 297 ms−1, (c) 295 ms−1, (d) 302 ms−1, (e) 227 ms−1, (f) 219 ms−1, and (g) 119 ms−1

Grahic Jump Location
Figure 14

Two HSV images for Launch-11 (Type-II) at water-entry velocity of 290 ms−1: (a) initial water entry, (b) t=21.6 ms, (c) t=48.0 ms, (d) t=75.6 ms, (e) t=116.4 ms, and (f) t=344.4 ms

Grahic Jump Location
Figure 15

Comparison between predicted and observed trajectories for Mk-84 warhead with tail section and two fins (Type-1I) with initial water-entry speed: (a) 295 ms−1, (b) 290 ms−1, and (c) 297 ms−1

Grahic Jump Location
Figure 16

Two HSV images for Launch-17 (Type-III) at water-entry velocity of 298 ms−1: (a) initial water entry, (b) t=22.8 ms, (c) t=55.2 ms, (d) t=99.0 ms, (e) t=211.2 ms, and (f) t=376.2 ms. Note that for time longer than 99.0 ms, only one HSV camera got the pictures.

Grahic Jump Location
Figure 17

Comparison between predicted and observed trajectories for Mk-84 warhead with tail section and no fin (Type-1II) with initial water-entry speed: (a) 304 ms−1, (b) 298 ms−1, and (c) 291 ms−1

Grahic Jump Location
Figure 18

Two HSV images for Launch-13 (Type-IV) at water-entry velocity of 296 ms−1: (a) initial water entry, (b) t=30.0 ms, (c) t=51.6 ms, (d) t=155.4 ms, and (e) t=418.2 ms

Grahic Jump Location
Figure 19

Comparison between predicted and observed trajectories for Mk-84 warhead with no-tail section (Type-1V) with initial water-entry speed: (a) 296 ms−1, (b) 301 ms−1, and (c) 301 ms−1

Grahic Jump Location
Figure 20

Time-evolutions between predicted (solid) and observed (dotted) for Launch-13: (a) horizontal position (y) of om, (b) depth position (z) of om, (c) bomb speed (U), (d) angle γ, (e) angle β, and (f) attack angle α

Grahic Jump Location
Figure 21

Time-evolutions between predicted (solid) and observed (dotted) for Launch-14: (a) horizontal position (y) of om, (b) depth position (z) of om, (c) bomb speed (U), (d) angle γ, (e) angle β, and (f) attack angle α

Grahic Jump Location
Figure 22

Time-evolutions between predicted (solid) and observed (dotted) for Launch-15: (a) horizontal position (y) of om, (b) depth position (z) of om, (c) bomb speed (U), (d) angle γ, (e) angle β, and (f) attack angle α

Grahic Jump Location
Figure 23

Trajectories for Mk-84 warhead with different tail configurations

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In