final Towed Hydrophone Array

Analyses of the Mechanical Design for a Towed Hydrophone Array

Presented to the

University of California, San Diego

Department of Mechanical and Aerospace Engineering

MAE 199: Professor Jan Kleissl and Dr. Gerald D’Spain

06/13/2014

Prepared by:

Sulaman Ahmed

Spring 2014

1

Abstract

To study the potential effects of man-made sound on odontocetes, particularly members

of the beaked whale family, a wide-band towed hydrophone array was designed and constructed.

Two candidate designs were created using the computer aided design program SolidWorks and

modeled in fluid flow using FloWorks. Results show that the Flooded Torpedo which had a drag

of 16 N, torque of 9 Nm, and a shear stress of 20 Pa, while the X-Array had a drag force of 52 N,

torque of 5 Nm, and a shear stress of 34 Pa. However, a modified X-Array with offset wing

struts was chosen to be built in order to provide aperture in 3 dimensions. In addition; the

Flooded Torpedo had no concrete method to allow water to flow through it, it had a higher

possibility of rotating, and the smaller distance between the hydrophones housed inside reduced

spatial resolution.

2

Table of Contents

1. Introduction 4

2. Theory 5

3. Experimental Procedure 6

4. Results 9

5. Discussion 15

6. Conclusion 16

7. Appendix A Surface and Cut plots 18

8. Appendix B Tables 41

9. Appendix C Drawings 50

3

1. Introduction

The objective of this project is to create a mechanical design for a towed passive

underwater acoustic array for detecting and localizing transient signals in the ultrasonic band,

greater than 20 kHz, from odontocetes, in particular members of the beaked whale family. The

array is designed to be deployed by two people, towed up to ten knots speed, resist rotating while

being towed, and hydrodynamically designed to minimize the noise on the hydrophones due to

turbulent pressure fluctuations. Two different designs were created, the “Flooded Torpedo” and

“X-Array”, and run through flow simulations to determine the final build design.

Ocean acoustics is the study of the underwater sound field in the ocean. Sound waves

travel underwater by pressure fluctuations that alternate between compressing and dilating the

water molecules. The sound waves radiate in all directions from the source. These pressure

changes caused by the sound waves can be detected by devices such as hydrophones.

Oceanographers are use hydrophones to study ocean sound, understand the sources, and

the potential effects of the sound on marine like, and the properties of the ocean environment.

Passive underwater acoustic monitoring has achieved better understanding of global warming,

earthquakes, movement of magma through the ocean floor from volcanic eruptions, and calls

from marine mammals.

San Diego is home to a large Navy base, which is equipped with vessels with active sonar

capabilities. Active sonar is an instrument used to image the underwater environment, by

emitting pulses of sound. These sounds are believed to be causing a disturbance in the behavior

of beaked whales. It is the goal of Southwest Fisheries Science Center and Scripps Institution of

Oceanography to determine the potential effects the Navy sonar and other man-made acoustic

4

sounds has on the marine mammals in the proximity of the acoustic source operations.

2. Theory

It is not viable to use optics-based devices such video recorders except over short ranges

in the ocean because the distance light can travel is reduced significantly due to absorption. On

the other hand, sound waves can travel much greater distances than light. Sound travels about

five times faster underwater than in air. Hydrophones are microphones designed for use

underwater, and multiple hydrophones can be arranged in an array. Using an array, signals from

desired directions can be enhanced and signals from undesired directions can be ignored. A

signal processing technique such as beamforming uses the relative locations of the hydrophones

to estimate the location of the sound source. The ship typically must travel in a straight line to

collect a reliable data samples in order for the positions of the hydrophones to stay relatively

constant. The spatial resolution of the beamforming is affected by the relative distances between

the hydrophones; larger distances between hydrophones increases the resolution. For the project,

the array will be towed 300 meters behind the ship to minimize any disturbances to the

hydrophones due to both the noise radiated by the ship and array vibrations and turbulence

caused by the propulsion.

Drag in fluid mechanics is the force in the opposite direction of an object’s velocity,

acting to oppose the object’s motion through a fluid medium. Two main types of drag exist, skin

friction and pressure (form) drag. Skin friction drag is caused by the friction of the fluid and the

surface of the object flowing through it. Pressure drag is caused by the shape of the object and

how the boundary layer separates creating a pressure gradient. If a drag coefficient CD can be

estimated, drag can be calculated using the equation

5

FD=12ρ υ2CD A⊥ (1)

In equation (1) ρ represents the density of the fluid, υ is the speed, and A is the cross-sectional

surface area. The coefficient depends on the shape of the object and the Reynolds number. The

Reynolds number is a non-dimension quantity estimated from the fluid properties, the speed, a

characteristic length. The Reynolds number is widely used to predict fluid flow patterns. The

power required to overcome drag is

PD=FD v=12ρ υ3 A⊥CD (2)

A minimum amount of power must be supplied for a body to move. Shear stress is the force from

friction acting on the body of the object by the fluid it is moving through. The equation for shear

stress from drag force is

τ=F DA∥

(3)

Where A now is the cross-sectional area parallel to the drag force. Shear stress is parallel to the

surface while normal stress is perpendicular. The stress on an object can create deformation or

make the object break in the areas of high stress. Stress is measured in units of Pascals, the same

units as for pressure.

3. Experimental Procedure

Two mechanical designs were modeled in Solidworks. The first one is called the Flooded

Torpedo Shell and the second design was named X-Array. Each model is designed to be towed

6

300 meters behind a ship at a maximum speed of 10 knots. Once the designs were assembled in

SolidWorks, they were run through the simulation program FloWorks.

The Flooded Torpedo Shell is a two stage design, the interior stage housing the

hydrophones attached to the exterior shell of a piece of pipe. The electrical wires are spliced into

the towing cable which runs through the center. The interior stage is flooded with seawater to

allow the hydrophones to take measurements. This design allows for the hydrophones to stay in a

relatively secure area and minimizes any damage that can occur to them or other equipment.

Figure 1 illustrates a computer aided design (CAD) drawing of the flooded torpedo shell design.

Figure 1: Flooded Torpedo Shell

The X-Array is a four winged pipe with cross-section in the shape of the letter “X”.

These wings are streamline aluminum struts from Carlson Aircraft Inc. The wings begin from the

same location on the array body and extending out at an angle of 30 degrees from the pipe. The

7

wings also are equally separated from each other, creating a shape that looks like a X-Wing

Starfighter from “Star Wars”. The hydrophones are mounted to the end of each of these wings

inside of capsules that are shaped to reduce drag. The towing cable can either run through the

pipe or be attached to the array through rings on the end. Since the array wing struts and

hydrophones capsules are freely flooded when deployed, the X-Array allows the hydrophones to

be unrestricted to the seawater by unlike the previous design, and improves accuracy of the

beamforming because the hydrophones are further spread apart, 0.5 meters between hydrophones

on opposite wings. Figure 2 is a CAD drawing of the X-Array design.

Figure 2: X-Array

A fluid flow simulation was done using the program FloWorks. Each design model was

run in the program using the same parameters. The parameters used in the simulation were the

external flow speed and direction with respect to the array, standard ocean temperature, and a

8

velocity of 5 m/s (about 10 knots). The designs were run at angles offset from the array body

(pipe): 0 degrees (parallel to the array body), 1 degree, 2 degrees, 4 degrees, and 8 degrees.

Using the Pythagorean theorem, the angles to the body were created by changing the speed in the

vertical direction. So if the arrays were traveling at 5 m/s, zero degrees to the array body would

have a no velocity component in the vertical direction and 4 degrees would have a velocity of

0.351 m/s in the vertical direction. A surface parameters excel sheet, found in Appendix A

Surface and Cut plots, was created from the simulation’s solution along with several surface

plots, Appendix B Tables.

4. Results

The two models’ FloWorks simulation plots are presented in Appendices A Surface and

Cut plots and B Tables. In the flow simulations, the positive Z axis is the direction the array is

being towed. The Y axis is perpendicular to the surface. The appendices also include three more

models, based on the X-Array with new configurations of the wing placement, which were

created after the simulations of the Flooded Torpedo and original X-Array.

Parameter Minimum Maximum Average Bulk Average Surface area [m^2]Pressure [Pa] -706895 529007 164165 1.25748Temperature [K] 293.198 293.203 293.201 1.25748Density [kg/m^3] 997.561 997.563 997.562 1.25748Velocity [m/s] 0 0 0 1.25748Shear Stress [Pa] 7.66431E-12 1673.18 19.9097 1.26585Fluid Temperature [K] 293.198 293.203 293.201 1.25748Normal Force [N] 2.67251 -0.53802 -0.1875 2.61106 1.26585Shear Force [N] 13.758 -0.02342 0.08625 13.7577 1.26585Force [N] 16.3787 -0.56144 -0.1013 16.3687 1.26585Torque [N*m] 9.95017 6.1264 -7.839 0.151464 1.26585Surface Area [m^2] 1.26585 -4.2E-05 -0.0001 3.3956E-06 1.26585Torque of Normal Force [N*m] 2.52825 1.55811 -1.9882 0.106866 1.26585Torque of Shear Force [N*m] 7.42317 4.5683 -5.8508 0.0445986 1.26585Uniformity Index [ ] 1 1.25748CAD Fluid Area [m^2] 1.28153 1.28153

Table 1: Flooded Torpedo Shell ( 0 degrees)

Parameter Minimum Maximu Averag Bulk Surface area

9

m e Average [m^2]

Pressure [Pa] 96359.5 105142 100649 0.500327

Temperature [K] 293.2 293.203293.20

3 0.500327

Density [kg/m^3] 997.562 997.562997.56

2 0.500327

Velocity [m/s] 0 0 0 0.500327

Shear Stress [Pa]2.92019E-

11 54.049533.729

5 0.500327

Fluid Temperature [K] 293.2 293.203293.20

3 0.500327

Normal Force [N] 35.9966 2.15824 -3.4519 -35.7657 0.500327

Shear Force [N] 16.8194 0.004680.0019

8 -16.8194 0.500327

Force [N] 52.7425 2.16293 -3.45 -52.5851 0.500327

Torque [N*m] 5.04599 -4.575611.6513

1 -1.34127 0.500327

Surface Area [m^2] 0.500327 5.4E-19 -7E-181.21973E-

19 0.500327

Torque of Normal Force [N*m] 3.75924 -3.333691.1035

9 -1.34183 0.500327

Torque of Shear Force [N*m] 1.35734 -1.241920.5477

20.00056019

6 0.500327

Uniformity Index [ ] 1 0.500327

CAD Fluid Area [m^2] 0.593678 0.593678

Table 2: X-Array ( 0 degrees)

The surface plots for pressure show how the hydrodynamic pressure on the arrays varies

over the entire body. This information is important because of the resulting forces acting on the

array and because the hydrophones record the sound waves, which is a pressure wave. The plots

of array found in Appendix A Surface and Cut Plots and the tables found in Appendix B Tables

show the areas of high pressure and the fluctuations due to the array being towed which could

potentially disturb the hydrophones or in the worst case damage the array. In the Flooded

Torpedo, the area with the highest pressure is the front and end cones, which cover the cable and

seal off the midsection of the body. The X-Array also exhibits higher pressure on the area of the

cones and along the ridges of the wings. The pressure over the hydrophone casings, for the X-

Array is low in comparison. The average pressure experienced by the Flooded Torpedo and the

X-Array are 164 kPa and 101 kPa respectively. For the Flooded Torpedo, the pressure fluctuates

from -706 to 529 kPa and for the X-Array from 96 kPa to 105 kPa. The pressure fluctuations, the

10

minimum and maximum pressure, are much more significant in the Flooded Torpedo than in the

X-Array.

The shear stress surface plots are useful to highlight the areas that will need attention

when the model will be assembled. These areas will have a higher possibility to break during use

and should be reinforced if necessary. The Flooded Torpedo will need care in the area where the

cones connect to the main body. The X-Array has high shear stress in the areas of where the

wing struts are attached. This concentration of shear stress can be problematic since all the wing

struts are attached in the same area of the body. The X-Array also has an average shear stress of

14 Pa higher than the Flooded Torpedo.

For the X-Array, the flow trajectories show the flow velocity around the hydrophones

does not reduce noticeably and for the Flooded Torpedo, the hydrophones are housed inside the

body so the water interacting with the hydrophones will be flowing as fast as the inlet and outlet

allow. Since the arrays are moving at constant velocity, the drag force will be equal to the net

force of the towing cable. From the surface parameters from Appendix B, the drag force on the

Flooded Torpedo is equal to about 16 N and for the X-Array the drag force is equal to about 52

N. The torque dictates how resistant to twisting the towing cables must be. If the cables cannot

resist the torque applied, the models will rotate while being towed. If they do rotate rapidly the

spatial information obtained from the beamforming may be miscalculated. The torque on the X-

Array is about 5 N and on the Flooded Torpedo is 9 N.

After further consideration, some tweaks were made to the original design of the X-Array

to create the first remodel, reference figure 3. The two wing strut pairs are now offset from each

other along the array body by a ½ meter. This change is helpful for the array design for several

11

reasons. Separation of the two pairs of struts along the main body of the array now provides

array aperture in the 3rd dimension, improving the directional information provided by the

measurements. The stress at the base of each wing strut which was focused on one area of the

pipe has now been spread out, therefore removing the need to reinforce the pipe at this location.

To reduce the probability for the array to rotate, changing buoyancy of individual wing

struts will be considered to keep the array steady and upright when being towed. The second and

third remodels to the X-Array, figures 4 and 5, have increased the angle between the center pipe

of the array and the wing struts to 60 degrees. The two models differ only by a 90-degree

rotation about the array body.

Figure 3: X-Array Remodeled 1 (wings offset)

Parameter MinimumMaximum

Average

Bulk Average

Surface area [m^2]

12

Pressure [Pa] 97209.5 103871 100959 0.480425

Temperature [K] 293.2 293.203293.20

30.480425

Density [kg/m^3] 997.561 997.562997.56

20.480425

Velocity [m/s] 0 0 0 0.480425

Shear Stress [Pa] 1.38E-07 52.017430.210

20.480425


30.480425

Normal Force [N] 42.5239 -13.6272 -17.765 36.1525 0.480425

Shear Force [N] 14.4792 -0.004160.0035

714.4792 0.480425

Force [N] 55.361 -13.6313 -17.761 50.6317 0.480425

Torque [N*m] 5.62004 -5.365160.2862

8-1.64861 0.480425

Surface Area [m^2] 0.480425 -0.00083 -0.0009 4.31E-06 0.480425


5-1.64921 0.480425

Torque of Shear Force [N*m] 0.785834 0.75057 -0.23280.00060326

10.480425


CAD Fluid Area [m^2] 0.606781 0.606781

Table 3: X-Array Remodeled 1 (wings offset)

Figure 4: X-Array Remodeled 2 (wider struts)

13


Average

Bulk Average

Surface area [m^2]

Pressure [Pa] 98189.1 103476 100791 0.512201

Temperature [K] 293.2 293.203293.20

3 0.512201

Density [kg/m^3] 997.561 997.562997.56

2 0.512201

Velocity [m/s] 0 0 0 0.512201


07 39.851315.927

3 0.512201


3 0.512201

Normal Force [N] 98.2045 9.16301 -9.1747 -97.3446 0.512201

Shear Force [N] 8.14699 0.000320.0010

5 -8.14699 0.512201

Force [N] 106.286 9.16333 -9.1737 -105.492 0.512201

Torque [N*m] 9.68034 -8.042431.3695

1 5.21083 0.512201

Surface Area [m^2] 0.512201 -0.00063 -0.00040.00012083

1 0.512201


5 5.21012 0.512201


60.00071362

7 0.512201


CAD Fluid Area [m^2] 0.641655 0.641655

Table 4: X-Array Remodeled 2 (wider struts)

Figure 5: X-Array Remodeled 3 (orientation rotated 90 degrees)

14

Parameter Minimum Maximum AverageBulk Average

Surface area [m^2]

Pressure [Pa] 98171.8 103143 100807 0.509449

Temperature [K] 293.2 293.203 293.203 0.509449

Density [kg/m^3] 997.562 997.562 997.562 0.509449

Velocity [m/s] 0 0 0 0.509449


08 98.9349 22.4727 0.509449

Fluid Temperature [K] 293.2 293.203 293.203 0.509449

Normal Force [N] 86.243 1.80078 -23.902 -82.845 0.509449

Shear Force [N] 11.4339 -0.00131 -0.2108 -11.4319 0.509449

Force [N] 97.3284 1.79946 -24.113 -94.277 0.509449

Torque [N*m] 10.3684 -10.2114 1.75987 -0.365351 0.509449

Surface Area [m^2] 0.509449 -0.00063 -0.0004 0.00012083 0.509449

Torque of Normal Force [N*m] 9.51814 -9.37847 1.58366 -0.362441 0.509449

Torque of Shear Force [N*m] 0.851402 -0.83296 0.17621-

0.00291011 0.509449


CAD Fluid Area [m^2] 0.641655 0.641655

Table 5: X-Array Remodeled 3 (wing position flipped)

The pressure fluctuations and the shear stress for the X-Array are reduced in the new

models in figure 4 and 5. The second and third remodeled of the X-Array do not differ much

between themselves in the results. They both experience only about half of the shear stress the

first remodel experiences. The pressure fluctuations are reduced by about 1 kPa. The torque is

almost the same as before and the drag force is increased to about 100 N.

5. Discussion

Although the simulations show that the Flooded Torpedo had a few better results in the

flow conditions, it was not enough to motivate further development. The largest hurdle the

Flooded Torpedo still had to encounter was the ability to allow water to enter and exit the model.

The two arrays were conceived to house hydrophones and record the most accurate data as

possible. A mechanism to allow water to flow in and out of the Torpedo Shell had not been

created yet. The disturbances from the entry and exit point could lead to significant degradation

in the hydrophones’ ability to record sound due to turbulence and flow noise. The accuracy for

the hydrophones for determining the sound source location depends on the distance between the

15

hydrophones in the array. The shell does not allow for significant distance in two directions

between the hydrophones. Also the Flooded Torpedo has higher torque then the X-Array by

almost a factor of 2, thus allowing for significant rotation during towing. These elements gave

significant cause for the Flooded Torpedo Shell approach to be shelved.

Out of the several X-Array models, the second and third remodels (figures 4 and 5) gave

the best results. They were able to reduce the shear stress of the X-Array by half and the pressure

fluctuations were also reduced, allowing higher fidelity acoustic recording. The torque for the

two models was about the same as the original X-Array. The simulations also show that

changing the orientation between remodels 2 and 3 does not have a significant effect.

The casing for the hydrophones used in the X-Array models cannot be purchased at any

retailer and are costly to fabricate. A fused deposition manufacturing (FDM) technique is used

for these hydrophone casings. FDM is advantageous because of the reduced cost for most

complicated designs and the ability to produce intricate designs, such as a hollow sphere, that are

impossible for a machine shop to fabricate. FDM is an additive 3-D printing technology. The

printer lays plastic filament or metal wire down in layers building up the specified model. The

extrusion nozzle is fed the material from coils, as the plastic or metal enters the nozzle they are

heated up to liquid state and deposited. The plastic or metal instantly hardens after deposition,

forming the solid model. A computer aided manufacturing (CAM) software using

stereolithography file format (STL) controls the FDM printer. These files can be created directly

from SolidWorks drawings.

6. Conclusion

16

Two mechanical designs were modeled in SolidWorks and run through simulations in

FloWorks. The simulations showed that the drag on the X-Array was 36 N greater, 52 N to 16 N,

but the torque was half that of the Flooded Torpedo, 5 N to 10 N. The Flooded Torpedo has

some better results in the simulations, but these results do not outweigh the problems: the

hydrophone placement being too close together, increased probability to rotate, and its inability

to allow water to flow in and out undisturbed. The X-Array design had refinements done to the

positions of the wing struts and this final design will be built with the aid of fused deposition

manufacturing (FDM) techniques. The engineering drawings for the design can be found in

Appendix C Drawings.

17

7. Appendix A

Plot 1: Velocity Cut Plot of X-Array at 5 m/s and 0 degrees

18

Plot 2: Pressure surface plot of X-Array at 5 m/s and 0 degrees

Plot 3: Flow trajectory plot of X-Array at 5 m/s and 0 degrees

19

Plot 4: Velocity Cut Plot of X-Array at 5 m/s and 1 degree

Plot 5: Flow Trajectory Plot of X-Array at 5 m/s and 1 degree

20

Plot 6: Pressure Surface Plot of X-Array at 5 m/s and 1 degree

Plot 7: Pressure Surface Plots of X-Array at 5 m/s and 1 degree

21

Plot 8: Shear Stress Surface Plot of X-Array at 5 m/s and 1 degree

22

Plot 9: Shear Stress Surface Plot of X-Array at 5 m/s and 1 degree


23

Plot 11: Flow Trajectory Plot of X-Array at 5 m/s and 2 degrees

Plot 12: Pressure Surface Plot of X-Array at 5 m/s and 2 degrees

24


Plot 14: Shear Stress Surface Plot of X-Array at 5 m/s and 2 degrees

25



26



27



28



29



30


31



32



33

Plot 29: Velocity Cut Plot of Flooded Torpedo Shell at 5 m/s and 0 degrees

34

Plot 30: Pressure Surface Plot of Flooded Torpedo Shell at 5 m/s and 0 degrees

35

Plot 31: Shear Stress Surface Plot of Flooded Torpedo Shell at 5 m/s and 0 degrees

36

Plot 32: Pressure Cut Plot of remodeled X-Array (wide wings)

37

Plot 33: Pressure Surface Plot of remodeled X-Array (wide wings)

Plot 34: Shear Stress Surface Plot of remodeled X-Array (wide wings)

38

Plot 35: Pressure Cut Plot of remodeled X-Array (wide wings rotated)

Plot 36: Pressure Surface Plot of remodeled X-Array (wide wings rotated)

39

Plot 37: Shear Stress Surface Plot of remodeled X-Array (wide wings rotated)

40

8. Appendix B Tables

Parameter Minimum Maximum Average Bulk Average Surface area [m^2]Pressure [Pa] -706895 529007 164165 1.25748Temperature [K] 293.198 293.203 293.201 1.25748Density [kg/m^3] 997.561 997.563 997.562 1.25748Velocity [m/s] 0 0 0 1.25748Shear Stress [Pa] 7.66431E-12 1673.18 19.9097 1.26585Fluid Temperature [K] 293.198 293.203 293.201 1.25748Normal Force [N] 2.67251 -0.53802 -0.1875 2.61106 1.26585Shear Force [N] 13.758 -0.02342 0.08625 13.7577 1.26585Force [N] 16.3787 -0.56144 -0.1013 16.3687 1.26585Torque [N*m] 9.95017 6.1264 -7.839 0.151464 1.26585Surface Area [m^2] 1.26585 -4.2E-05 -0.0001 3.3956E-06 1.26585Torque of Normal Force [N*m] 2.52825 1.55811 -1.9882 0.106866 1.26585Torque of Shear Force [N*m] 7.42317 4.5683 -5.8508 0.0445986 1.26585Uniformity Index [ ] 1 1.25748CAD Fluid Area [m^2] 1.28153 1.28153



Average

Bulk Average

Surface area [m^2]

Pressure [Pa] 96359.5 105142 100649 0.500327

Temperature [K] 293.2 293.203293.20

3 0.500327

Density [kg/m^3] 997.562 997.562997.56

2 0.500327

Velocity [m/s] 0 0 0 0.500327


11 54.049533.729

5 0.500327


3 0.500327

Normal Force [N] 35.9966 2.15824 -3.4519 -35.7657 0.500327

Shear Force [N] 16.8194 0.004680.0019

8 -16.8194 0.500327

Force [N] 52.7425 2.16293 -3.45 -52.5851 0.500327

Torque [N*m] 5.04599 -4.575611.6513

1 -1.34127 0.500327

Surface Area [m^2] 0.500327 5.4E-19 -7E-181.21973E-

19 0.500327


9 -1.34183 0.500327


20.00056019

6 0.500327


CAD Fluid Area [m^2] 0.593678 0.593678

Table 2: X-Array ( 0 degrees)


Average

Bulk Average

Surface area [m^2]

Pressure [Pa] 97209.5 103871 100959 0.480425

Temperature [K] 293.2 293.203293.20

30.480425

Density [kg/m^3] 997.561 997.562997.56

20.480425

Velocity [m/s] 0 0 0 0.480425

Shear Stress [Pa] 1.38E-07 52.017430.210

20.480425

41


30.480425

Normal Force [N] 42.5239 -13.6272 -17.765 36.1525 0.480425

Shear Force [N] 14.4792 -0.004160.0035

714.4792 0.480425

Force [N] 55.361 -13.6313 -17.761 50.6317 0.480425

Torque [N*m] 5.62004 -5.365160.2862

8-1.64861 0.480425

Surface Area [m^2] 0.480425 -0.00083 -0.0009 4.31E-06 0.480425


5-1.64921 0.480425

Torque of Shear Force [N*m] 0.785834 0.75057 -0.23280.00060326

10.480425


CAD Fluid Area [m^2] 0.606781 0.606781



Average

Bulk Average

Surface area [m^2]

Pressure [Pa] 98189.1 103476 100791 0.512201

Temperature [K] 293.2 293.203293.20

3 0.512201

Density [kg/m^3] 997.561 997.562997.56

2 0.512201

Velocity [m/s] 0 0 0 0.512201


07 39.851315.927

3 0.512201


3 0.512201

Normal Force [N] 98.2045 9.16301 -9.1747 -97.3446 0.512201

Shear Force [N] 8.14699 0.000320.0010

5 -8.14699 0.512201

Force [N] 106.286 9.16333 -9.1737 -105.492 0.512201

Torque [N*m] 9.68034 -8.042431.3695

1 5.21083 0.512201

Surface Area [m^2] 0.512201 -0.00063 -0.00040.00012083

1 0.512201


5 5.21012 0.512201


60.00071362

7 0.512201


CAD Fluid Area [m^2] 0.641655 0.641655

Table 4: X-Array Remodeled 2 (wider struts)


Surface area [m^2]

Pressure [Pa] 98171.8 103143 100807 0.509449

Temperature [K] 293.2 293.203 293.203 0.509449

Density [kg/m^3] 997.562 997.562 997.562 0.509449

Velocity [m/s] 0 0 0 0.509449


08 98.9349 22.4727 0.509449


Normal Force [N] 86.243 1.80078 -23.902 -82.845 0.509449

Shear Force [N] 11.4339 -0.00131 -0.2108 -11.4319 0.509449

Force [N] 97.3284 1.79946 -24.113 -94.277 0.509449

42

Torque [N*m] 10.3684 -10.2114 1.75987 -0.365351 0.509449

Surface Area [m^2] 0.509449 -0.00063 -0.0004 0.00012083 0.509449



0.00291011 0.509449


CAD Fluid Area [m^2] 0.641655 0.641655

Table 5: X-Array Remodeled 3 (wing position flipped)

Local parameters

Parameter MinimumMaximu

m AverageBulk

AverageSurface area

[m^2]

Pressure [Pa] 96359.5 105142 100649 0.500327

Temperature [K] 293.2 293.203 293.203 0.500327

Density [kg/m^3] 997.562 997.562 997.562 0.500327

Velocity [m/s] 0 0 0 0.500327

X-component of Velocity [m/s] 0 0 0 0.500327

Y-component of Velocity [m/s] 0 0 0 0.500327

Z-component of Velocity [m/s] 0 0 0 0.500327Heat Transfer Coefficient

[W/m^2/K] 0 0 0 0.500327


11 54.0495 33.7295 0.500327


Heat Flux [W/m^2] 0 0 0 0.500327

X-component of Heat Flux [W/m^2] 0 0 0 0.500327

Y-component of Heat Flux [W/m^2] 0 0 0 0.500327

Z-component of Heat Flux [W/m^2] 0 0 0 0.500327

Integral parameters

Parameter ValueX-

componentY-

componentZ-

componentSurface area

[m^2]

Heat Transfer Rate [W] 0 0 0 0 0.500327

Normal Force [N] 35.9966 2.15824 -3.45193 -35.7657 0.500327

Shear Force [N] 16.8194 0.00468336 0.00198134 -16.8194 0.500327

Force [N] 52.7425 2.16293 -3.44995 -52.5851 0.500327

Torque [N*m] 5.04599 -4.57561 1.65131 -1.34127 0.500327

Surface Area [m^2]0.50032

75.42101E-

19-7.12863E-

18 1.21973E-19 0.500327


Torque of Shear Force [N*m] 1.35734 -1.24192 0.54772

0.000560196 0.500327


43

CAD Fluid Area [m^2]0.59367

8 0.593678

Table 6: X-Array (0 degrees)

Local parameters

Parameter Minimum Maximum AverageBulk

AverageSurface area

[m^2]

Pressure [Pa] 94837.2 108103 100544 0.546729

Temperature [K] 293.2 293.203 293.203 0.546729

Density [kg/m^3] 997.561 997.562 997.562 0.546729

Velocity [m/s] 0 0 0 0.546729



Z-component of Velocity [m/s] 0 0 0 0.546729

Heat Transfer Coefficient [W/m^2/K] 0 0 0 0.547286


07 111.898 32.32 0.547286


Heat Flux [W/m^2] 0 0 0 0.547286




Integral parameters

Parameter ValueX-

componentY-

component Z-componentSurface area

[m^2]


Normal Force [N] 56.196 -5.83022 -26.5773 -49.1696 0.547286

Shear Force [N] 17.568 -0.0129863 -0.224603 -17.5666 0.547286

Force [N] 72.154 -5.8432 -26.8019 -66.7362 0.547286

44

Torque [N*m] 7.87662 -6.61542 3.12847 2.91377 0.547286


61.20617E-

18-1.02999E-

18-2.63529E-

17 0.547286

Torque of Normal Force [N*m] 6.61741 -5.32812 2.61574 2.92561 0.547286

Torque of Shear Force [N*m] 1.3857 -1.2873 0.512735 -0.0118467 0.547286



8 0.593678

Table 7: X-Array (1 degree)

Local parameters


mAverag

eBulk

AverageSurface area

[m^2]

Pressure [Pa] 94639.3 105180 100559 0.5478

Temperature [K] 293.2 293.203293.20

3 0.5478

Density [kg/m^3] 997.561 997.562997.56

2 0.5478

Velocity [m/s] 0 0 0 0.5478




[W/m^2/K] 0 0 0 0.548069


09 112.735 31.371 0.548069


3 0.5478

Heat Flux [W/m^2] 0 0 0 0.548069X-component of Heat Flux

[W/m^2] 0 0 0 0.548069Y-component of Heat Flux

[W/m^2] 0 0 0 0.548069Z-component of Heat Flux

[W/m^2] 0 0 0 0.548069

Integral parameters

Parameter ValueX-

componentY-

componentZ-


[m^2]


Normal Force [N] 60.067 -5.18182 -33.3063 -49.7181 0.548069

Shear Force [N] 17.07 0.00629764 -0.452712 -17.0639 0.548069

Force [N] 75.0086 -5.17552 -33.7591 -66.782 0.548069

Torque [N*m] 5.06812 -2.94312 3.06132 2.76627 0.548069


9-2.07015E-

186.17995E-

18-9.08697E-

18 0.548069Torque of Normal Force

[N*m] 4.16952 -1.77553 2.55201 2.77842 0.548069

Torque of Shear Force 1.2739 -1.16759 0.509309 -0.0121533 0.548069

45

[N*m]



8 0.593678


Local parameters


mAverag

eBulk

AverageSurface area

[m^2]

Pressure [Pa] 93721.2 107459 100548 0.54866

Temperature [K] 293.2 293.203293.20

3 0.54866

Density [kg/m^3] 997.561 997.562997.56

2 0.54866

Velocity [m/s] 0 0 0 0.54866




[W/m^2/K] 0 0 0 0.55103


06 118.182 30.762 0.55103


3 0.54866




[W/m^2] 0 0 0 0.55103

Integral parameters

Parameter ValueX-

componentY-

componentZ-


[m^2]


Normal Force [N] 92.2996 -13.6999 -76.1761 -50.2863 0.55103

Shear Force [N] 16.8218 0.0255533 -0.845331 -16.8005 0.55103

Force [N] 103.053 -13.6743 -77.0215 -67.0869 0.55103

Torque [N*m] 6.44397 -4.18744 4.85053 -0.680035 0.55103

Surface Area [m^2] 0.551033.27294E-

181.49078E-

19-7.87402E-


[N*m] 5.457 -3.21074 4.36407 -0.651803 0.55103Torque of Shear Force

[N*m] 1.09151 -0.976705 0.486453 -0.0282324 0.55103



8 0.593678


46

Local parameters


mAverag

eBulk

AverageSurface area

[m^2]

Pressure [Pa] 91764.3 108807 100533 0.549368

Temperature [K] 293.2 293.203293.20

3 0.549368

Density [kg/m^3] 997.561 997.562997.56

2 0.549368

Velocity [m/s] 0 0 0 0.549368




[W/m^2/K] 0 0 0 0.550984


06 147.22232.544

9 0.550984


3 0.549368




[W/m^2] 0 0 0 0.550984

Integral parameters

Parameter ValueX-

componentY-

component Z-componentSurface area

[m^2]


Normal Force [N] 171.09 -10.4778 -163.635 -48.842 0.550984

Shear Force [N] 17.7554 0.0185277 -1.93349 -17.6498 0.550984

Force [N] 178.727 -10.4592 -165.568 -66.4918 0.550984

Torque [N*m] 7.06934 -4.76638 5.10068 -1.11369 0.550984

Surface Area [m^2] 0.5509841.87025E-

18-3.34747E-

18-3.38136E-


[N*m] 6.05884 -3.83349 4.57277 -1.05057 0.550984

Torque of Shear Force [N*m] 1.07376 -0.932892 0.527912 -0.0631129 0.550984


CAD Fluid Area [m^2] 0.593678 0.593678


Local parameters


mAverag

eBulk

AverageSurface area

[m^2]

Pressure [Pa] -706895 529007 164165 1.25748

Temperature [K] 293.198 293.203293.20

1 1.25748

Density [kg/m^3] 997.561 997.563997.56

2 1.25748

Velocity [m/s] 0 0 0 1.25748




[W/m^2/K] 0 0 0 1.26585

47


12 1673.1819.909

7 1.26585


1 1.25748




[W/m^2] 0 0 0 1.26585

Integral parameters

Parameter ValueX-

componentY-

componentZ-


[m^2]


Normal Force [N] 2.67251 -0.538019 -0.187529 2.61106 1.26585

Shear Force [N] 13.758 -0.0234178 0.0862466 13.7577 1.26585

Force [N] 16.3787 -0.561437 -0.101282 16.3687 1.26585

Torque [N*m] 9.95017 6.1264 -7.83901 0.151464 1.26585

Surface Area [m^2] 1.26585-4.19403E-

05-

0.000111868 3.3956E-06 1.26585Torque of Normal Force

[N*m] 2.52825 1.55811 -1.9882 0.106866 1.26585

Torque of Shear Force [N*m] 7.42317 4.5683 -5.85082 0.0445986 1.26585


CAD Fluid Area [m^2] 1.28153 1.28153


Local parameters


mAverag

eBulk

AverageSurface area

[m^2]

Pressure [Pa] 97209.5 103871 100959 0.480425

Temperature [K] 293.2 293.203293.20

3 0.480425

Density [kg/m^3] 997.561 997.562997.56

2 0.480425

Velocity [m/s] 0 0 0 0.480425




[W/m^2/K] 0 0 0 0.480425


07 52.017430.210

2 0.480425


3 0.480425




[W/m^2] 0 0 0 0.480425

48

Integral parameters

Parameter ValueX-

componentY-

componentZ-


[m^2]


Normal Force [N] 42.5239 -13.6272 -17.7645 36.1525 0.480425

Shear Force [N] 14.4792 -0.00416424 0.00357378 14.4792 0.480425

Force [N] 55.361 -13.6313 -17.7609 50.6317 0.480425

Torque [N*m] 5.62004 -5.36516 0.28628 -1.64861 0.480425


5-

0.000832719-

0.000852222 4.31373E-06 0.480425Torque of Normal Force

[N*m] 6.35543 -6.11573 0.519047 -1.64921 0.480425

Torque of Shear Force [N*m]0.78583

4 0.750569 -0.232767 0.000603261 0.480425



1 0.606781


Local parameters


Surface area [m^2]

Pressure [Pa] 98189.1 103476 100791 0.512201

Temperature [K] 293.2 293.203 293.203 0.512201

Density [kg/m^3] 997.561 997.562 997.562 0.512201

Velocity [m/s] 0 0 0 0.512201



Z-component of Velocity [m/s] 0 0 0 0.512201Heat Transfer Coefficient [W/m^2/K] 0 0 0 0.512201


07 39.8513 15.9273 0.512201


Heat Flux [W/m^2] 0 0 0 0.512201




Integral parameters

Parameter Value

X-component

Y-component

Z-component

Surface area [m^2]


Normal Force [N] 98.2045 9.16301 -9.1747 -97.3446 0.512201

Shear Force [N] 8.14699 0.00032 0.00105 -8.14699 0.512201

Force [N] 106.286 9.16333 -9.1737 -105.492 0.512201

Torque [N*m] 9.68034 -8.04243 1.36951 5.21083 0.512201

Surface Area [m^2] 0.512201 -0.00063 -0.00040.00012083

1 0.512201

Torque of Normal Force [N*m] 9.31224 -7.62043 1.22535 5.21012 0.512201

Torque of Shear Force [N*m] 0.445944 -0.422 0.144160.00071362

7 0.512201


CAD Fluid Area [m^2] 0.641655 0.641655

49

Table 13: X-Array Remodeled 2 ( wide wings)

Local parameters


Surface area [m^2]

Pressure [Pa] 98171.8 103143 100807 0.509449

Temperature [K] 293.2 293.203 293.203 0.509449

Density [kg/m^3] 997.562 997.562 997.562 0.509449

Velocity [m/s] 0 0 0 0.509449



Z-component of Velocity [m/s] 0 0 0 0.509449Heat Transfer Coefficient [W/m^2/K] 0 0 0 0.509449


08 98.9349 22.4727 0.509449


Heat Flux [W/m^2] 0 0 0 0.509449




Integral parameters

Parameter Value

X-component

Y-component

Z-component

Surface area [m^2]


Normal Force [N] 86.243 1.80078 -23.902 -82.845 0.509449

Shear Force [N] 11.4339 -0.00131 -0.2108 -11.4319 0.509449

Force [N] 97.3284 1.79946 -24.113 -94.277 0.509449

Torque [N*m] 10.3684 -10.2114 1.75987 -0.365351 0.509449

Surface Area [m^2] 0.509449 -0.00063 -0.0004 0.00012083 0.509449



0.00291011 0.509449


CAD Fluid Area [m^2] 0.641655 0.641655

Table 14: X-Array Remodeled 3 ( wide wings rotated)

50

9. Appendix C Drawings

Figure 1: Flooded Torpedo Shell

Figure 2: X-Array

51

Figure 3: X-Array Remodeled 1 (wings offset)

Figure 4: X-Array Remodeled 2 (wider struts)

52

Figure 5: X-Array Remodeled 3 (orientation rotated 90 degrees)

Figure 6: Original hand drawing of X-array

53

Figure 7: Original hand drawing of Flooded Torpedo Shell

Figure 8: X-Array Wing drawing

54

Figure 8: X-Array Hydrophone drawing

Figure 8: X-Array Array Body drawing

55

Figure 8: X-Array End Cones drawing

56

Documents

final Towed Hydrophone Array