Modelling of Drag Forces on a Closed Flexible Fish Cage

9th IFAC Conference on Control Applications in Marine Systems The International Federation of Automatic Control September 17-20, 2013. Osaka, Japan

Modelling of Drag Forces on a Closed Flexible Fish Cage Ida Marlen Strand ∗ Asgeir J. Sørensen ∗ P˚ al Lader Zsolt Volent ∗∗ ∗

∗∗

Centre for Autonomous Marine Operations and Systems (AMOS) Department of Marine Technology Norwegian University of Science and Technology,NTNU NO-7491 Trondheim, Norway ∗∗ SINTEF Fisheries and Aquaculture NO-7465 Trondheim, Norway

Abstract: To cope with ecological challenges in the aquaculture industry, Closed Flexible Fish Cages (CFC) are proposed used in the sea. However, the existing knowledge about how the CFC will respond to external sea loads are limited. More knowledge is needed to understand the response of the cage if this technology is to be utilized in an industrial scale. In this paper a new method for mathematical modelling of the increase in drag, for decreasing filling level of a CFC is proposed. A model for a filling-level-dependent drag coefficient is presented. Experimental data are analysed related to forces and deformations on the bag for different filling levels. The analysed bag showed an increased tendency to deform for decreasing filling levels, leading to an increase in drag coefficient. Keywords: Aquaculture, drag, hydro-elastic 1. INTRODUCTION By use of open net structures in the sea, Norway have become the worlds biggest producer of Atlantic salmon. However while the aquaculture facilities have grown in size and number, the industry challenges related to escapes, sea-lice, diseases and pollution have increased (Rosten et al., 2013). One possible solution to the aquaculture industry challenges is to make a closed floating fish production system in the sea. In a closed system, the control of flow and quality of the water entering and leaving the bag is possible. One way of making a closed fish production system is as a Closed Flexible Cage (CFC). A CFC is not far from the currently used net cage systems, and may therefore be easier to put directly into operation. D Floater Membrane

H

Bacteria and sea-lice Organic waste removal Water inlet

Wild fish

Figure 1. Closed Flexible Cage with salmon. The CFC is made of a membrane material, in the form as a cylindrical bag with a cone at the bottom as illustrated in figure 1. 978-3-902823-52-6/2013 © IFAC

340

The existing knowledge about how a CFC will respond to external sea loads is limited. The hydrodynamic drag forces on the structure are expected to increase compared to a net based structure. The bag is flexible and expected to behave hydro-elastically, meaning that the deformation of, and hydrodynamic forces on the bag are closely coupled. Due to the hydroelasticity of the structure, the hydrodynamic loads and responses of the CFC are expected to be more complex, than those of rigid structures (Rosten et al., 2013). The ability of the bag to deform is expected to increase with decreasing filling level λ, which is given in percent as: λ=

Vf · 100% , V0

(1)

where Vf is the actual amount of water in the bag in litres, and V0 is the theoretical full filling level. It is crucial to secure the cage against escapes and structural collapse, therefore the forces on the bag must be at a minimum. To limit the forces on the structure, the flexibility of the bag is planed actively used, by controlling the filling level of the bag. The forces will decrease if the structure deforms in a favourable way, either passively, or by active control of the shape. To control the cage with needed stability and performance more knowledge is needed to understand the response. The object of this paper is to investigate drag forces on, and the response of a Closed Flexible Cage, from analysis of experimental data making a simplified mathematical model of how the loads, deformation and resulting response are dependent on the internal filling level of the bag. 10.3182/20130918-4-JP-3022.00014

IFAC CAMS 2013 September 17-20, 2013. Osaka, Japan

2. CURRENT FORCES AND DEFORMATIONS The drag force on a structure in uniform flow can be expressed as: 1 FD = ρACD Vc2 , (2) 2 where ρ is the fluid density equal to 1000 kg/m3 for fresh water, Vc is the current velocity, A is the projected frontal area and CD is a dimensionless drag coefficient. CD is dependent of the shape of the body and the flow regime around the body. The Reynolds number, given as Re = VνD is used as a non-dimensional measure of the characteristics of the flow regime, where D is a chariaristic length of the body, here the diameter, and ν is the kinematic viscosity of the fluid, for fresh water ν = 1·10−6 . The flow is typically turbulent for high velocities, large Re and laminar for very low velocities, low Re. If a membrane structure after a transient period adapt to a stationary form, this form can be compared to the form of a rigid structure. Theoretical models for drag for the deformed shape of the body for a rigid structure may then be applied. The CFC can be approximated, when the bottom part is neglected, as a rigid 3D cylinder. Blevins (1984) gives the theoretical drag coefficient closest to our H/D relation as CDc = 0.64. Rudi and Solaas (1993) modelled the environmental forces on a bag pen, which is an early type of the CFC. Global current forces were modelled and hydroelastic deformations of the bag were estimated. The global vertical deformation of the bag pen was approximated based on moment equilibrium, the deformations are shown in figure 2(b). Local deformations of the bag

wall were assumed originating from the varying pressure distribution around the bag in current. This pressure distribution was estimated using a rigid circular cylinder in steady flow as a basis. The local deformations are shown in figure 2(a). Due to the pressure variations the bag was pressed inwards in an area of two times 30 deg upstream, drawing the contour of a hemispherical cup deformation. The drag coefficient for a thin hemispherical cup is given in Blevins (1984) as CDe = 1.42. 3. EXPERIMENTAL SETUP To better understand how current loads affect the CFC for different filling levels and current velocities, model experiments were conducted. The model experiments took place in the small towing tank at US Naval Academy in Annapolis from July 30th to August 17th 2012. The model was made of a nylon parachute material, in scale 1:50, with dimensions as shown in table 1. Table 1. Full scale and model scale dimensions Full scale Model scale

Diameter 38.20 [m] 0.76 [m]

Height cylinder 15.00 [m] 0.30 [m]

Height cone 15.00 [m] 0.30 [m]

The model was rigidly attached to a circular bagholder as shown in figure 3. The bagholder was connected to the carriage. Approx. 80 cm Load cell 60 cm

The main contribution of the paper is the analysis and formulation of drag forces for closed flexible cages with varying filling levels.

Bag holder

Bag modell

Figure 3. Model set-up Current

Vertical and horizontal forces were measured with a load cell. Drag forces were found by taking the average of the measurement time series over 30 seconds of the horizontal forces for each run. To get the best measurements and steady state velocity, the carriage was run for at least 15 seconds before time averaging started.

180o

0o

90o (a) Local deformation of bag in current. The deflection is magnified for illustration purposes.

Current

Table 2. Full scale current (Vc ) and model towing velocities (Vm ) with connected Reynolds numbers

10o

(b) Global horizontal deformation of bag pen.

Figure 2. Deformations of a bag pen in current, adapted from Rudi and Solaas (1993). 341

Full scale Vc [m/s] Re [−] 0.15 5·106 0.20 7·106 0.30 10·106 0.40 13·106 0.50 16·106 0.60 20·106 0.70 23·106 0.80 26·106 0.90 29·106

Model scale Vm [m/s] Re [−] 0.021 1·104 0.028 2·104 0.042 3·104 0.057 4·104 0.071 5·104 0.085 6·104 0.099 6·104 0.113 7·104 0.127 8·104

IFAC CAMS 2013 September 17-20, 2013. Osaka, Japan

Nine different current velocities were tested by towing the carriage. The quality (accuracy) of the carriage speed were poor for speeds below 0.02 m/s, limiting the possible minimum current. Full scale and model scale velocities with connected Reynolds number are found in table 2.

A1 (y3 , z3 )

A3 (y7 , z7 ) Figure 5. Illustration of placement of coordinates used for area calculation 1 A1 = (y2 − y1 + y4 − y3 )(z3 − z1 + z4 − z2 ) , 4 1 A2 = (y4 − y3 + y6 − y5 )(z5 − z3 + z6 − z4 ) , 4 z5 + z6 1 ), A3 = (y6 − y5 )(z7 − 2 2 A = A1 + A2 + A3 . (3) 4. EXPERIMENTAL RESULTS

Table 3. Filling levels of the bag 90 % 165.1 l

80 % 146.7 l

(y6 , z6 )

(y5 , z5 )

To test the influence of different filling levels on the forces and deformation of the bag, the bag were subjected to four different filling levels λ. The filling levels are given in table 3.

100 % 183.4 l

(y4 , z4 ) A2

For model scale velocities we see from table 2 that Re is in the area of Re ≈ 104 , which is the subcritical flow regime, giving a laminar boundary layer. For the full scale current velocities we are around the supercritical and the transcritical flow regime, giving a turbulent boundary layer (Faltinsen, 1990). The change from subcritical to transcritical flow regime will affect CD , for an undeformed circular cylinder. However, the bag is expected to deform for decreasing filling levels, introducing changes in the bag geometry. If sharp corners are introduced, Blevins (1984) states that the drag coefficient is independent of Re for Re > 104 , making the drag coefficient scalable.

Filling level Volume

(y2 , z2 )

(y1 , z1 )

4.1 Drag force

70 % 128.4 l

Measured drag force for all filling levels were plotted and compared to (2) in figure 6. The amount of water filled into and emptied out of the bag were measured for control.

6

To measure/observe the deformations of the bag, a system of four cameras were put up as shown in figure 4.

×105 Exp. drag, 100% filling Exp. drag, 90% filling Exp. drag, 80% filling Exp. drag, 70% filling Theoretical drag

5

x z Cam1

Cam2

FD [N]

4 Cam3

3

Current 2 1

Cam4

0 0.1

Figure 4. Side view of camera location Pictures were taken of the structure from tree different angles to capture the deformations of the bag. To avoid disturbing the incoming current, no camera was placed in front of the bag. To estimate the exposed area of the bag, coordinates of the images from the third camera were translated to real world coordinates by a image calibration, using known coordinates in calibration pictures. Coordinates of the edges of the geometry were found, placed as illustrated in figure 5. The top cylinder formed exposed area were approximated as two trapezoids and the cone bottom as a triangle. The estimated error of the placement of the coordinates are in the order of ±5 cm. The exposed area A was found according to: 342

0.2

0.3

0.4

0.5 0.6 Vc [m/s]

0.7

0.8

0.9

1

Figure 6. Drag force on the bag for different filling levels as a function of current velocity Looking at figure 6 we see that the drag forces on the structure increases with decreasing λ. Equation (2) with constant area A and the drag coefficient of a circular cylinder CDc = 0.64 is accurate for the 100% filling level. However as the filling level decreases, (2) underpredicts to an increasing extent, the drag forces on the bag. Relating the increase in drag for decreasing filling levels to (2), three main hypothesis may be suggested: (1) The projected exposed area A of the structure increases as the filling level decreases.

IFAC CAMS 2013 September 17-20, 2013. Osaka, Japan

(2) As the filling level decreases, the body deforms causing the drag coefficient CD to increase. (3) A combination of the former. The hypothesis were examined successively. 4.2 Exposed area 860 840 Exposed area [m2 ]

820 800 780 760 740 (a) Deformation pattern for 70% filled cylindrical bag, for Vc ≤ 0.3 m/s. Undeformed borders for 100% full bag at 0 m/s indicated in red.

720 700 680 660 0

100% filling 90% filling 80% filling 70% filling A0 teoretical 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Vc [m/s]

1

Figure 7. Full scale measured exposed area of bag. From measurements of exposed area A shown in figure 7, no significant increase in the exposed area was observed, for decreasing filling levels. The measurements of the 70% filling level area indicates the opposite, a decrease in exposed area. All the measured areas were smaller than the theoretical exposed area A0 . The under prediction of the exposed areas by the measurements related to A0 is assumed mostly due to distortion in the images. Due to the nature of the measurement technique and calculations of the area estimates, an uncertainty of approximately ± 10% is assumed. Despite the errors in the measurement technique, the data indicate that there is no significant increase in exposed area for decreasing filling level. 4.3 Deformations Qualitative analysis of the images from the experiment were done to see if the body showed signs of deformations that could effect the drag coefficient CD . The image material showed a clear tendency that the body deformed when the bag was less than 100% full. These deformations increased with decreasing filling level. For Vc ≤ 0.3 m/s the body did not appear much affected by the current as shown in figure 8(a), the deformations show only small changes related to the deformed form as it appear for only static pressure. As for Vc > 0.3 m/s the bag displayed similar deformation of the front wall as described in Rudi and Solaas (1993), shown in figure 2(a). When the bag was exposed to current, 343

(b) Deformation pattern for 70% filled cylindrical bag, for Vc > 0.3 m/s. Undeformed borders for 100% full bag at 0 m/s indicated in red. The hemispherical cup deformation is indicated with a dotted black line.

Figure 8. Deformation patterns for 70% filled bag. a hemispherical cup was seen forming at the front. The deformation increased in size for decreasing filling levels. The deformation is shown for the 70% filling level in figure 8(b), and the hemispherical cup is indicated with the black dotted line. For the 70% filling level the bottom was observed to be deformed, this could explain the decrease in measured area for this filling level. The back and sides perpendicular to the current were not observed to deform, even for low filling levels and high current velocities, as can be seen in figure 8(b), where the back wall of the bag follows the borders of the undeformed bag. No deformation of the back wall is contrary to the global current deformations described by Rudi and Solaas (1993) and shown in figure 2(b). The reason for the lack of global deformation is most probably that the local deformation patterns become so pronounced. It was observed that the bag had an increasing tendency to deform for increasing velocities and decreasing filling

IFAC CAMS 2013 September 17-20, 2013. Osaka, Japan

levels, it is plausible that the observed deformations could effect CD .

turbulent. CD for λ < 100% is therefore expected to be valid for full-scale.

4.4 Drag coefficient 1.8

5. MODELLING OF FILLING LEVEL DEPENDENT DRAG COEFFICIENT

100% filling 90% filling 80% filling 70% filling

1.6

From the model experiments on the closed flexible cage a large increase in drag force on the bag was experienced for λ <100%. Analysis of the exposed area, deformations and drag coefficient on the bag clearly indicates that the increase in drag is caused by an increase in drag coefficient originating from a deformation of the bag. Since the passive deformations of the cage were unfavourable active control of the form of the cage is probably needed to keep the forces at a minimum. However to be able to control the cage, it is crucial to understand the response of the uncontrolled cage. To estimate the correct drag forces, a model for the drag coefficients dependency of the filling level is needed.

CD [−]

1.4 1.2 1 0.8 0.6 0.4

1

2

3

4

5 6 Re[-]

7

8

9 10 ×104

Figure 9. Model scale drag coefficient CD as a function of Reynolds number Re.

CD (λ) was used as a basis for modelling a filling level dependent drag coefficient CD (λ). Based on table 4, the data indicates that CD (100%) ≈ CDc = 0.64 and will for decreasing filling level, down to λ ≤ 70% increase to CD (70%) ≈ CDe = 1.42, see figure 10. 1.5

CD was found from the drag force measurements with constant area A0 according to: FD . (4) CD = 1 2 ρA 0 Vm 2

1.2 1.1 1

Figure 9 indicates a significant increase in drag coefficient for Re ≤ 4 · 104 . This is consistent with the deformation patterns observed in section 4.3. For Re > 4 · 104 the bag is unaffected by the current, it appear almost static, while for Re ≤ 4 · 104 the characteristic hemispherical cup have appeared.

0.9

Mean drag coefficients CD (λ) are calculated for the different filling levels for Re ≤ 4 · 104 , according to:

0.5 65

CD (λ) =

CD CD (λ)

1.3

CD [-]

CD for model scale were plotted against Reynolds number in figure 9 for all the filling levels.

CDe =1.42

1.4

0.8 0.7 0.6

CDc =0.64 70

75

80

85 90 λ [%]

95

100

Figure 10. Drag coefficient model

9 1 X · CD (λ)i . 6 i=3

(5) A simple relation is proposed for the transition from CDc → CDe :

The resulting CD (λ) are given in table 4. Table 4. Mean experimental drag coefficient λ [%] CD (λ) [ - ]

100 0.66

90 0.85

80 1.34

70 1.41

CD (λ) = CDe − (CDe − CDc ) · ec(100−λ) n

= 1.42 − 0.78 · ec(100−λ) ,

From table 4 it is observed that the drag coefficient for 100% filling, CD (100) is not far from the drag coefficient of the circular cylinder CDc = 0.64, while when the bag is 70% full, CD (70) indicates that CD proceeds towards the drag coefficient of the hemispherical cup CDe = 1.42. For decreasing λ the body deforms to a such extent that it is expected that the flow behind the body is fully 344

n

(6)

where n is a real integer, describing the form of the function, and c is an unknown coefficient found from fitting of the equation to the experimental data. c is found by solving (6) for a known filling level λk and an experimentally known drag coefficient CD (λk ), and n is found by minimizing the error  between the model and CD for 1 ≤ n ≤ 4.

IFAC CAMS 2013 September 17-20, 2013. Osaka, Japan

6

×105 Exp. drag 100% Exp. drag 90% Exp. drag 80% Exp. drag 70% Theoretical drag, CD = 0.64 Fitted drag model , CD (λ)

5 FD [N]

Using λk = 90% and CD (90%) = 0.85, yields:   C e −CD (λk ) ln D CDe −CDc , c= (100 − λk )n 0.319 =− n , 10 4 X n = |CD (λi ) − CD (λi )n | .

4 3

(7) (8)

i=1

2

The resulting c and n for 1 ≤ n ≤ 4 ,are given in table 5.

1

Table 5. Calculated c, for different n

0 6

n c n

5

2 −3.19 · 10−3 0.20

3 −3.19 · 10−4 0.05

4 −3.19 · 10−5 0.11

The least error is found for n = 3. By applying n = 3 and the associated c, the resulting model yields:

4 FD [N]

1 −3.19 · 10−2 0.65

−4

CD (λ) = 0.64 + 0.78 · e−3.19·10

3

(100−λ)3

(9)

Equation (9) is used in (2) and compared to the experimental results, and (2) with a constant CD = CDc in figure 11. From figure 11 it is now seen that (2) with CD (λ) predicts the increase in drag on the bag for decreasing λ.

2 1

6. CONCLUSION 0 6

2

To utilize Closed Flexible Cage technology at an industrial level more knowledge is needed to understand the sea loads on the structure. Drag forces on a Closed Flexible Cage for different filling levels have been experimentally studied, and a significant increase in drag was experienced as the filling level decreased. This drag increase was found to be due to a large deformation of the front wall facing the current, leading to a significant increase in the drag coefficient. A filling level dependent drag coefficient model have been proposed.

1

7. ACKNOWLEDGEMENTS

0 6

This work have been financed by the industry project ”External Sea Loads and Internal Hydraulics of Closed Flexible Cages” a knowledge-building project for the aquaculture business sector, in cooperation with SINTEF Fisheries and Aquaculture and NTNU, and the Norwegian Research Council.

5

FD [N]

4 3

5

FD [N]

4 3

The authors would also like to thank the professional and technical staff at the U.S. Naval Academy Hydromechanics Laboratory for their support.

2

REFERENCES

1 0

0

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Vc [m/s]

1

Figure 11. Drag forces on the bag for 100% , 90% , 80% and 70% filling as a function of current velocity. Experimental results plotted together with the theoretical model with constant drag coefficient CD = 0.64 and the fitted drag model CD (λ). 345

R. D. Blevins. Applied fluid dynamics handbook. Van Nostrand, New York, 1984. O.M Faltinsen. Sea Loads on ships and offshore structures. Cambridge University Press, 1990. T Rosten, B. F. Terjesen, Y. Ulgenes, K. Henriksen, E. Biering, and U. Winther. Lukkede oppdrettsanlegg i sjø- økt kunnskap er nødvendig. Vann, (1), 2013. H. Rudi and F Solaas. Floating fish farms with bag pens. In International Conference on Fish Farming Technology, 1993.