Gebremeskel Eshetu Kebede, Paul D. Winger

Center for Sustainable Aquatic Resources, Fisheries and Marine Institute, Memorial University, 155 Ridge Rd, St. John's, Newfoundland and Labrador, A1C 5R3, Canada

Keywords:

Drag

Lift

Helix rope

Knotted netting

Knotless netting

Reynolds number

ABSTRACT

This study evaluated the hydrodynamic forces produced by whole panels of hand-made (geometrically different)rope meshes typically found in midwater trawls. Experimental treatments included both knotted and knotless meshes constructed of helix composite ropes, conventional braided nylon (PA) ropes, and twisted polyethylene(PE) ropes. Direct measurement of lift (L) and drag (D) forces were conducted using controlled flume tank experiments on panels oriented at 21°relative to the flow. For knotted netting, our results showed that the hydrodynamic forces (L and D) were statistically higher for helix ropes compared to conventional ropes of the same diameter. For knotless netting constructed of helix ropes, our primary finding is that the arrangement of helix ropes (S and Z lay) in individual meshes significantly affects the resulting D and Cd of whole netting panels.Arranging the mesh bars in the S-Z-S-Z lay pattern exhibited 29% and 32% lower drag (D) compared to S—S—S—S and S—S-Z-Z lay meshes, respectively. We also use computational fluid dynamics (CFD) to characterize the finescale flow- field around helix and conventional ropes. The resulting streamlines and pressure contours provide a functional explanation for the empirical measurements collected in the flume tank. These results can be useful in informing the design of midwater trawls.

1.Introduction

In a typical midwater trawl, the forward leading panels of the trawl are constructed using very large meshes. Due to the size of these meshes,they are commonly constructed by hand using individual ropes of varying length and diameter. The porosity of these meshes depends on the type of materials used, mesh size, mesh shape, and mesh orientation.The resulting shape and motion of the trawl during towing operations is governed by internal and external forces. Internal forces are due to the stiffness of the fabric material while the external forces are static(buoyancy and gravity), and dynamic (drag and lift). Dynamic lift and drag forces and their associated coefficients are of interest to fishing gear designers and engineers as they influence the shape and performance of the fishing gear (Lee, Lee, & Song, 2007). These hydrodynamic forces arise either from the movement of the fishing gear through the water or from the movement of the water with respect to the gear (Fridman &Carrothers, 1986). Adequate understanding of these forces is essential for the numerical modelling and simulation of trawls using various computer programs (see review by Nguyen & Winger, 2016). Moreover,knowledge of the change in drag under different scenarios can help gear technologists to design and construct fishing systems that minimize energy consumption and reduce emissions of greenhouse gases including nitrogen oxides and CO(Lee et al., 2018).

The resistance force of netting is mainly determined by netting solidity, mesh geometry, twine roughness, knot type and number, angle of attack to the direction of tow, and Reynolds number (O'Neill et al.,2017; Tsukrov, Drach, DeCew, Swift, & Celikkol, 2011; Zhou, Xu, Hu, &Qu, 2015). As much as 62% of the total drag of a trawl is attributed to the wires and netting (Balash & Sterling, 2012). Gansel et al. (2015)showed that netting obstructed with biofouling exhibited higher drag than similar (unobstructed) netting with the same solidity. At low solidity (～0.19), the relationship between drag coefficient (

C

) and Reynolds number (

Re

) show a similar trend to a cylinder of the same solidity, and the effect of

Re

on

C

decreases with increasing solidity(Tang et al., 2018). According to Tang, Dong, et al. (2018) and Tang, Xu,et al. (2018), knots can account for up to 15—25% of the total drag, and exhibit an increasing

C

with increasing solidity. As the knots in trawl netting are non-symmetric, they can be oriented in either a positive or negative angle of attack (AOA) to the tow direction. Broadhurst, Balash,Sterling, Millar, and Matsubara (2017) conducted a flume tank evaluation of full-scale prawn trawls constructed using different knot orientations in the top and bottom panels and reported that trawls constructed with both panels oriented with a negative AOA had 10% less total drag and nearly 27% lower headline height. Moreover, a trawl with top and bottom panels oriented in a negative AOA exhibited signi ficantly greater wingspread than a trawl with both horizontal panels in positive AOA orientations (Broadhurst, Sterling, & Millar, 2016). Mesh orientation also affects the hydrodynamic properties of netting panels.For instance, T45 mesh (i.e., diamond mesh 45°turned) exhibited lower drag than T0 meshes at increasing water velocities (Balash, Sterling,Binns, Thomas, & Bose, 2015). In another study, T90 mesh (i.e., diamond mesh 90°turned) produced a large increase in drag (approx. ～36%) compared to T0 standard-mesh (Balash & Sterling, 2012). Lee,Lee, Cha, Kim, and Lee (2005) demonstrated that the coefficient of lift(

C

) of diamond netting reached a maximum value of 0.6 at a 55°attack angle, and the drag coefficient (

C

) reached a maximum value of 1.2 at 90°attack angle.When netting is towed through the water at an angle of attack to the tow direction, it will alter the flow field, allowing a portion of the fluid to pass through the netting. The volume and velocity of fluid passing through the netting depends on the solidity ratio (Løland, 1993). Drag is unavoidably produced, and the extent of this drag is related to the velocity distribution upstream and downstream of the netting (i.e., at the front and rear side of the netting). Currently, there are a number of methods for measuring water velocities and flow fields around netting structures. Direct measurements can be made in flume tanks using impellor and electromagnetic current meters (e.g., Balash & Sterling,2012; Murphy, Bungay, Stern, Winger, & Robert, 2015, pp. 43—46),while less intrusive approaches include laser doppler velocimetry and particle image velocimetry (e.g., Cha, Kim, Bae, Yang, & Kim, 2013;Pichot, Germain, & Piour, 2009). Outputs from these instruments can help validate numerical models of fishing gears. A number of numerical models have been proposed by researchers to predict hydrodynamic forces in relation to solidity,

Re

, and angle of attack. Computational fluid dynamics (CFD) has proved particularly insightful in recent years. For example, Patursson et al. (2010) used CFD to investigate the fluid flow pattern around a net panel, Chen and Christensen (2016) used CFD to investigate porous resistance coefficients for fishing net structures,Germain et al. (2012) used CFD to describe velocity and pressure values around the knots of submerged fishnets, and most recently, Tang, Xu,Dong, Zhao, and Guo (2017) used CFD to simulate the flow field through a cultured fish cage.Previous research by Kebede et al. (2020) evaluated the hydrodynamic performance of helix ropes compared to traditional ropes used in the forward leading panels of midwater trawls. These innovative ropes were initially invented by Hjörtur Erlendsson in 1997, subsequently patented for midwater trawling (Safwat & Perevoshchikov, 2005), and then introduced into the global market (Hampidjan, 2018). Under controlled flume tank conditions, Kebede et al. (2020) demonstrated that helix ropes produce increased lift (

L

) compared to conventional ropes of the same diameter when subjected to water flow at various velocities and angles of attack. In this study, we build upon the results of Kebede et al. (2020) and evaluate the lift (

L

) and drag (

D

) forces produced by whole panels of hand-made rope meshes typically found in midwater trawls. The corresponding coefficients of lift (

C

) and drag (

C

)are also determined. Experimental treatments include both knotted and knotless meshes constructed of helix, nylon (PA), and polyethylene (PE)ropes. We also evaluate, for helix rope, different arrangements of S and Z-lay ropes within individual meshes and its effect on the resulting hydrodynamic forces and coefficients. Moreover, we use computational fluid dynamics (CFD) to characterize the fine-scale flow- field around helix and conventional ropes. The resulting streamlines provide functional explanations for the empirical measurements collected in the flume tank experiments.

2.Methods

2.1.Materials and setup

Hydrodynamic tests were carried out using a flume tank located at the Fisheries and Marine Institute of Memorial University, St. John's,NL, Canada. The facility holds 1.7 million liters of water circulating through a 3-story vertical hydraulic circuit (Fig. 1). The dimensions of the test chamber were 4 m deep, 8 m wide, and 22.25 m long. Water velocity is adjustable between 0 and 1.0 m/s (see Winger, DeLouche, &Legge, 2006 for more information).

Fig. 1.Schematic representation of the flume tank located at the Fisheries and Marine Institute, Canada.

Panels of handmade netting (typical of midwater trawls) were constructed using knotted and knotless meshes made of rope (Fig. 2).Knotted samples were constructed using helix S-lay, braided nylon (PA),and twisted polyethylene (PE) Z-lay ropes with a diameter of 6 mm(Table 1). Helix rope is a composite material in which the main rope is composed of polyamides and the spiral rope overlaid on top of the main rope is composed of polyethylene (Kebede et al., 2020). The spiral rope makes numerous Z or S turns along the length of the main rope with consistent pitch (i.e., gap between consecutive turns). Ropes with a low gap are called short pitched, whereas ropes with a larger gap are called high pitched. In general, high pitched helix ropes are less stiff than short pitched helix ropes. Helix ropes used in this experiment had a spiral overlaid rope with a pitch of 32 mm. Each sample was given a code based on its physical description. For example, PA6_Mesh represents polyamide netting with 6 mm diameter rope with knotted meshes. All samples had a mesh size of 423 mm long with 50% transversal hanging ratio.

Fig. 2.Experimental netting panels mounted on an aluminum frame. Knotted samples (a) were constructed using helix, nylon (PA), and polyethylene (PE) ropes.Knotless samples (b) were constructed using individual helix ropes, and assembled using three different S lay (red) and Z lay (green) arrangements (c). (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)

Table 1Physical properties of the knotted mesh panel samples.

In a separate experiment, knotless samples were constructed using helix ropes with a diameter of 8 mm, including different arrangements of S and Z lay ropes (Fig. 2c, Table 2). These samples were constructed by cutting individual lengths of rope (212 mm length) using a hot knife blade and boring small holes at both ends of the bars for discrete(knotless) connection to the other bars. Each sample was given a code based on its physical description. HE_SZSZ_8M represents Helix, Slay-Zlay-Slay-Zlay bars in a mesh, 8 mm twine diameter, and M-mesh of knotless net. Similar to above, all samples had a mesh size of 423 mm long with 50% transversal hanging ratio.

Table 2Physical properties of the knotless mesh panel samples.

The above mentioned samples were attached to an aluminum frame(1.524m wide by 1.524m long) in the manner similar to Lee et al.(2007), Madsen, Hansen, and Enerhaug (2011), Tsukrov et al. (2011),and Kebede et al. (2020). A Canon EOS Rebel T5 (IS) 18 MP Digital SLR Camera with 18—55 mm Lens Kit was used to capture images of the netting samples. Image J software was used to measure the projected area (

A

) of the netting within each image. The images were converted to grayscale, with a black background (Fig. 2ab). Known frame dimensions were used to scale the image. The software was then able to calculate the amount of gray within the image. The procedure was repeated for the frame only (without netting) to determine the projected area (

A

) of the netting within each sample.The aluminum frame was lowered into the center of the flume tank to minimize the effects of vortices and boundary layers near the wall surfaces (Winger et al., 2006; Balash et al., 2012, p. 92; Kok et al., 2010).The frame was suspended using two top bridles connected to a single rope, which hung vertically from an overhead crane to counter balance the weight of the frame and prevent it from sinking, similar to Kebede et al. (2020). The frame was instrumented with 22.7 kg and 45.4 kg load cells for measuring the drag (

D

) and lift (

L

) forces in kgf (Fig. 3). For each experimental condition, data from the load cells was recorded at 50 Hz for about 60 s. We used a 7 m long and 1 mm diameter stainless steel wire for measuring drag, with a breaking strength of 75 kgf (Prado et al.,1990). The remaining cables were composed of 0.9 mm diameter Kevlar rope, with a breaking extension of 3.5% and high modulus of 90 GPa(McKenna, Hearle, & O'Hear, 2004). Individual bridles were attached to each corner of the frame in a hen-footed pattern. Lengths of the two bridles on the starboard side were adjusted to orient the frame with a if xed angle of attack of 21°to the incoming water flow in order to mimic the wing of a midwater trawl. The motion of the frame was restricted with high tensile bridles which were composed 1 mm Kevlar monofilament and 2 mm stainless steel wire-rope. This attack angle was selected based on numerical simulation of a full-scale Gloria 480 midwater trawl for red fish at a towing speed of 2.6 kn using trawl simulation software (DynamiT, 2018). Both knotted and knotless samples were subjected to water velocities of 0.5—0.9 m/s at an interval of 0.1 m/s.

Fig. 3.3D view of experimental setup in the flume tank.

2.2.Calculation of coefficients

For each test, the hydrodynamic forces were resolved into two components: drag (

D

) and lift (

L

) forces (Fridman & Carrothers, 1986).The effect of the aluminum frame (no netting) was subtracted from the total recorded forces to determine the effect of the netting by itself,similar to Tsukrov et al. (2011). The corresponding drag coefficient (

C

)and lift coefficient (

C

) were determined by:

where

C

and

C

are the drag and lift coefficients,

D

and

L

are the measured drag and lift forces respectively (kgf),

ρ

is the density of the water in the flume tank which is 102 kgf-sec/mat 10 °C for water with 0—2‰ salinity,

V

is the water velocity (m/s), and

A

is the projected area(m) of the netting, which was obtained by image analysis using Image J software (see above). Reynolds number (

Re

) is a dimensionless value that describes the ratio of dynamic forces to viscous forces (Hoerner,1965). It is expressed as:

where

V

is the water velocity (m/s),

Ø

is the diameter of the rope (m),and

γ

is the kinematic viscosity of water at 10 °C which is about 1.33 ×10m/s (Fridman & Carrothers, 1986).The porosity of the netting samples is described by their solidity ratio. Solidity ratio (

S

) is defined as the ratio of the projected area of net to the area of the outline (Tsukrov et al., 2011; Zhou et al., 2015).

where

A

is the projected area of the net sample in mand

A

is the total area of the outline of the net sample in m. In this flume tank test, we attempted to make the porosity or solidity ratio of the netting similar for all knotless samples, as well as the same for all knotted meshes. We did this by ensuring the mesh size, diameter of the ropes, and mesh number in transversal and normal direction were the same within each group(Tables 1 and 2).

2.3.Numerical modelling

Computational fluid dynamics (CFD) modelling was used to characterize the fine-scale flow- field around helix and conventional ropes.Finite Volume Method (FVM) scheme for pressure-velocity coupling in steady flow and solved by with SIMPLE (Semi-Implicit Method for Pressure Linked Equation) algorithm using the software ANSYS 17.2(Versteeg et al., 2007). We treated conventional ropes (both braided and twisted ropes) as cylinders and helix ropes as cylinders wrapped with a mono filament thinner rope. All ropes were modelled with a length of 432 mm, diameter of 8 mm, and an attack angle to the incoming fluid of 21°, similar to the flume tank experiment. The volume of the fluid domain was 10mm. The governing Navier-Stokes equation for incompressible and non-viscous fluid is listed as follows (Anderson et al.,1995):

i. For conservation of mass or continuity, it is expressed as:

ii. Conservation of momentum, X, Y, and Z momentum are given respectively as:

iii. Conservation of Energy,

where

u

,

v

, and

w

are components of the fluid velocity

V

in XYZ coordinates,

ρ

for fluid density,

p

for pressure,

μ

for dynamic viscosity,

i

for internal energy, Ø for energy dissipation function,

k

for heat conductivity, and

T

for temperature.

2.4.Data treatment and statistical analysis

Millivolt signals generated by the load cells were processed using a signal-conditioning amplifier, which boosted the signal to a level (0—10 VDC) compatible with our data acquisition hardware. We logged the data at a frequency of 50Hz, producing 3000 data values each minute per load cell. Each load cell was calibrated prior to use using five standard weights (4, 6, 8, 14, and 20 kg). The resulting calibration equation for the best fitting regression was entered into the Dasylab V.12 data acquisition software, producing an automatic conversion of load cell responses into units of force (kgf) and saved as an ASCII file. The files were imported into MS Excel for further processing. Similar to Tsukrov et al. (2011), we removed outliers beyond plus or minus three times the standard deviation, as well as 15% of each data set near the boundary regions to homogenize the data set around the mean. Nearly 50% of the central dataset were extracted, of which 1250 values were considered to represent the true drag and lift forces. These were used to produce a single mean value for each test condition (sample x water velocity). The known force of the bare frame (without nets) for each test condition was then subtracted to determine the mean forces generated by the ropes themselves. The processed datasets were saved as text-tab delimited files for statistical analysis using R-studio software. Using this approach, we were able to determine the mean drag (

D

) and lift (

L

) force for each test condition (sample x water velocity) in the flume tank.Drag and lift forces for the various test conditions were compared using non-parametric Kruskal-Wallis tests (Currell, 2015). The relationship between hydrodynamic forces (

F

) and water velocity (

V

) were characterized using power regressions with zero intercepts.

where

a

and

b

are coefficients of power regression function. The resulting power-equations can be rewritten then into linear equations using logarithmic relation as:

For determination of the coefficients. In addition, the corresponding slopes were compared using a Two-sample t-test. Relationships between the hydrodynamic coefficients and

Re

were characterized using linear regression.

3.Results

3.1.Lift and drag forces

3.1.1.Knotted netting

Both lift (

L

) and drag (

D

) forces exhibited an increasing trend with increasing water velocity for each of the knotted netting samples(Fig. 4). Our results showed that the forces were proportional to the square of the water velocity. HES6_Mesh produced the highest lift forces at each water velocity of all knotted netting samples. For instance, at 0.6 m/s, 0.7 m/s, and 0.8 m/s, the mean lift forces of HES6_Mesh were 22.3%, 19.8%, and 25.6% higher than the corresponding values of PA6_Mesh respectively.

Fig. 4.Lift forces (a) and drag forces (b) produced by the knotted netting samples at increasing water velocity (V).

However, helix netting also produced the highest drag forces compared to the other netting samples. This difference increased with increased water velocity (Fig. 4b). For instance, at 0.6 m/s, 0.7 m/s, and 0.8 m/s, the mean drag forces of HES6_Mesh were 59.7%, 54.7%, and 63.9% higher than the corresponding values of PA6_Mesh respectively.

Results from the Kruskal-Wallis statistical test at 95% confidence interval revealed no significant difference among lift forces (χ=2.88,

p

=0.237), however a marginally significant difference between the drag forces was detected (χ=6.04,

p

=0.049). After converting the power equations into first order linear equations using logarithmic relation, a comparison of the slopes revealed no significant differences among the samples for either lift or drag (

p ＞

0.05).

3.1.2.Knotless netting

Similar to the knotted netting, the lift (

L

) and drag (

D

) forces for the knotless netting exhibited an increasing trend with increasing water velocity (Fig. 5). Our results showed that lift forces were almost identical among the samples at lower water velocities (0.5 and 0.6 m/s), however a modest but increasing deviation was exhibited at the higher velocities.At 0.9 m/s, the netting panel with the S-Z-S-Z lay bar arrangement produced the highest lift force. More variation among the samples was observed with regard to drag (Fig. 5b). For instance, HE_SZSZ_8M showed progressively 15%, 19%, 27%, 16%, and 27% less drag than HE_SSSS_8M for each of the increasing water velocities, respectively.Similarly, HE_SZSZ_8M exhibited progressively 16%, 23%, 31%, 22%,and 31% less drag than HE_SSZZ_8M for each of the increasing water velocities, respectively. Moreover, the fitted curve for HE_SZSZ_8M exhibited increasing deviation from the other curves with increasing water velocity, revealing a lower and lower drag force at higher flow rates.

Fig. 5.Lift forces (a) and drag forces (b) produced by the knotless netting samples at increasing water velocity (V).

Results from the Kruskal-Wallis statistical test revealed no significant difference among lift forces of the different netting samples (χ=0.11,

p

=0.949), however a statistically significant difference between the drag forces was detected (χ=6.81,

p

=0.033). Subsequent pairwise comparisons of the slopes for the drag: velocity relationships showed that the SZSZ and SSZZ lay arrangements were significantly different (

t

=7.73,

p＜ 0.001

). Similarly, the SZSZ and SSSS lay arrangements were also different (

t

=7.09,

p ＜ 0.001

). However, the SSZZ and SSSS lay arrangements were not statistically different (

t

=0.99,

p

=0.36).

3.2.Coefficients of lift and drag

3.2.1.Knotted netting

As our test conditions lie in the range of Reynolds number 2.5 ×10—6.5 × 10, which lie in subcritical regions and known to exhibit a slow declining trend for cylinders, drag coefficients were expected to reveal a linear relationship with Reynolds number (Re) for rope(Hoerner, 1965). Therefore, we used linear functions to characterize the trend of dynamic force coefficients with Re that best fit the observed values. Fig. 6 illustrates inverse relationships for the coefficients of lift(

C

) and drag (

C

) with increasing Re (2.5 × 10≤Re ≤ 6.5 × 10) for knotted meshes at 21°attack angle. In both cases, HES6_Mesh exhibited the highest

C

and

C

values. The mean

C

of HES6_Mesh, PA6_Mesh, and PEZ6_Mesh were 0.23, 0.21, and 0.20, respectively. The corresponding mean

C

values were 0.43, 0.30, and 0.26, respectively.

Fig. 6.Reynolds number (Re) plotted against lift coefficient (a) and drag coefficient (b) for the knotted netting samples. Cl, Cd, and Re stand for lift coefficient, drag coefficient and Reynolds number, respectively.

Results from the Kruskal-Wallis statistical test at 95% confidence interval revealed no significant difference among the

C

values for the different netting samples (χ=3.05,

p

=0.217), however a statistically significant difference between the

C

values was detected (χ=9.89,

p＜ 0.001

). Subsequent pairwise comparisons of the slopes of the fitted regression lines did not reveal any significant differences (

p ＞

0.05).

3.2.2.Knotless netting

Fig. 7 illustrates inverse relationships for

C

and

C

with increasing Re(2.5 × 10≤ Re ≤ 6.5 × 10) for the knotless meshes at 21° attack angle.Fitted relationships for

C

were almost identical for all mesh arrangements evaluated (Fig. 7a). Deviation among the fitted relationships for

C

were more noticeable (Fig. 7b), with HE_SZSZ_8M producing the lowest

C

values. The mean

C

of HE_SSSS_8M, HE_SSZZ_8M, and HE_SZSZ_8M were 0.24, 0.24, and 0.25, respectively. The corresponding mean

C

values were 0.29, 0.32, and 0.24, respectively.

Fig. 7.Reynolds number (Re) plotted against lift coefficient (a) and drag coefficient (b) for the knotless netting samples. Cl, Cd, and Re stand for lift coefficient, drag coefficient and Reynolds number, respectively.

Results from the Kruskal-Wallis statistical test revealed no significant difference among the

C

values for the different netting samples (χ=0.34,

p

=0.847), however a marginally statistically significant difference between the

C

values was detected (χ=6.134,

p

=0.047).Subsequent pairwise comparisons of the slopes of the fitted regression lines did not reveal any significant differences (

p ＞

0.05).

3.3.Numerical modelling

Fig. 8 illustrates the hydrodynamic properties of conventional rope(left panel) and helix rope (right panel) when oriented at 21°to an incoming water velocity of 0.9 m/s. Streamlines are used to illustrate the path of the water. The flow around the conventional rope is symmetrical, producing a similar water velocity above and below the rope.Without a difference in the pressure field, no lift (

L

) is produced.However in the case of helix ropes, the fluid is allowed to spin around the rope in either a clockwise or counter-clockwise direction depending on the alignment (lay) of the spiral rope. Above the rope, the spinning flows will join with the free flow producing a higher resultant velocity,resulting in a higher dynamic pressure.

Fig. 8.Flow visualization (streamlines) for conventional (left panel) and helix ropes (right panel) using Computational Fluid Dynamics (CFD) modelling.

Fig. 9 shows the corresponding pressure contours. A cross-sectional view is given for a conventional rope (left panel) and helix rope (right panel) when oriented at 21°to an incoming water velocity of 0.9 m/s.The stagnation point (0°), 90°upper, 90°lower, and 180°which is the rear side and exactly opposite to stagnation point. In both the conventional and helix ropes, the pressure is shown to be highest at the stagnation point (0°), with a lower pressure field noted at the rear side of the rope. The pressure field for conventional rope is shown to be symmetrical at the stagnation point (0°). By comparison, the pressure field for the helix rope is shifted downward as a result of the spiral rope. An area of low pressure (very light green) is also noticeable near the top of the rope (90°). This difference in pressure field in the vertical direction is responsible for an upward force called lift (

L

).

Fig. 9.Pressure contours for a conventional rope (left panel) and helix rope (right panel). In the simulation, both ropes are oriented 21°to the direction of incoming flow with a water velocity of 0.9 m/s. The small blue circle in the middle of each panel represents the cross-sectional profile of the rope. Coloured contours represent variation in the pressure field. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)

4.Discussion

In general, hydrodynamic forces are the result of total pressure force differentials, which is normal to the surface gradient, and skin frictions,which is tangent to the surface gradient around the entire surface of cylindrical ropes (Cengel, Turner, Cimbala, & Kanoglu, 2008, pp.833—874). Of the two dynamic forces, drag (

D

) is particularly important to fishing gear designers and engineers as it is the most prominent force and directly associated with fuel consumption. Flume tank experiments have shown that up to 62% of the total drag of a trawl is due to the wires and netting (Balash & Sterling, 2012). Therefore, studies on the geometry, material composition, and roughness of netting and wires is critical to the development of energy efficient trawling systems. Moreover,understanding the flow pattern around the meshes, bars, knots, and riggings has important implications for the engineering of fishing gears.Given that the porosity or the solidity ratio of netting affects the hydrodynamic property of the ropes/twines (Gansel, McClimans, & Myrhaug, 2012), the knotless and knotted nets used in this experiment were made to possess comparable solidity ratios as shown in Tables 1 and 2One of the primary findings of this study is that the arrangement of helical ropes (S and Z lay) in individual meshes (Fig. 2c) significantly affects the resulting

D

and

C

of whole panels of netting (Figs. 5 and 7).We attribute this finding to the unique spiral rope twisted over the surface of the main rope. This spiral acts as a channel for the flow field in the boundary region, guiding water to flow in either clockwise or counter-clockwise directions. Lowest drag forces were measured for the netting samples constructed using knotless mesh consisting of SZSZ lay arrangement. We speculate that the flow field in the boundary region would have flowed counter-clockwise along each of the S lay mesh bars.When it reached the tip, it was suddenly forced to change into an opposite or clockwise direction as it crossed from S to Z lay bars. This change in flow direction at each of the intersections resulted in a reduction of water velocity or reduced pressure drag on the rope surface.This collectively resulted in a reduction of the drag on the entire netting panel constructed with the SZSZ lay arrangement. We recommend a detailed hydrodynamic study using either laser doppler velocimetry or particle image velocimetry (e.g., Cha et al., 2013; Pichot et al., 2009) to properly characterize the fine-scale flow fields around helix rope meshes.Numerical modelling conducted in this study helps provide novel insight toward understanding the hydrodynamic observations collected in flume tanks (this study and Kebede et al., 2020). Using CFD modelling, we showed that helix ropes exhibit asymmetry in water flow(streamlines) above and below the rope. This results in asymmetry at the stagnation point and an area of low pressure visible in the contour map(Fig. 9). Since the modelling was carried out at high towing speed of 0.9 m/s or at Reynolds number (

＞

5 × 10), dynamic pressure is more dominant than static pressure. The presence of a spiral rope overlaid on top of a rope (i.e., helix ropes) allows the fluid to spin around the rope in either a clockwise or counter-clockwise direction depending on the alignment (lay) of the spiral rope. Above the rope, the spinning flows will join with the free flow producing a higher resultant velocity,resulting in higher dynamic pressure. Below the rope, the flows are moving in an opposite direction to the free flow producing a relatively lower velocity, resulting in a low dynamic pressure. This difference in pressure field in the vertical direction generates the lift (

L

) force recorded in the flume tank (Kebede et al., 2020).In conclusion, this study evaluated the drag and lift forces produced by whole panels of hand-made rope meshes (typical in midwater trawls),using both knotted and knotless meshes constructed of helix and conventional ropes. Results showed that the arrangement of helical ropes (S and Z lay) in individual meshes significantly affects the resulting

D

and

C

of whole netting panels. Using computational fluid dynamics (CFD),we demonstrate differences in the fine-scale flow- field around helix and conventional ropes. The resulting streamlines and pressure contours provide a functional explanation for the empirical measurements collected in the flume tank. Together, these results can be useful in informing the design of midwater trawls with large hand-made panels with low solidity.

CRediT authorship contribution statement

Gebremeskel Eshetu Kebede: Conceptualization, Methodology,Software, Formal analysis, Data curation, Writing - original draft,Visualization. Paul D. Winger: Funding acquisition, Resources, Project administration, Supervision, Methodology, Writing - review & editing.

Declaration of competing interest

The authors declare that there is no conflicts of interest.

Acknowledgements

This project was part of Module H of the Ocean Frontier Institute,funded by the Canada First Research Excellence Fund. Special thanks to George Legge and H. DeLouche for designing and building the test apparatus and Ryan Doody for his technical assistance during flume tank testing.