Numerical simulations of a swimmer’s head and cap wearing different types of goggles

The aim of this study was to analyse the effect of swimming goggles on swimming hydrodynamics by numerical simulations. An elite swimmer volunteered for this research. The swimmer’s head was scanned both without goggles, and while wearing 3 different types of goggles (Nikko, Ankor and Swedish). Numerical simulations were conducted at 2 m/s with the Fluent code. The condition without goggles showed the highest viscous drag (1.65 N), followed by the Ankor (1.64 N), Swedish (1.63 N) and Nikko (1.62 N) goggles, respectively. The highest pressure drag was found in the situation without goggles (11.34 N), followed by the Ankor (10.87 N), Nikko (10.78 N) and Swedish (10.20 N) goggles. The condition without goggles presented the highest total drag (12.99 N), followed by the Ankor (12.52 N), Nikko (12.40 N) and Swedish (11.83 N) goggles. Thus, Swedish goggles yields the best hydrodynamics, followed by the Nikko and Ankor goggles and lastly without goggles. Thus, goggles minimise the swimmer’s drag comparing to not wearing any. The design of the goggles may impose varying drag forces and therefore it is advised to use goggles at least in competition.


Introduction
Swimming performance is dependent on the swimmer's propulsive and resistive forces (Barbosa et al., 2018).To improve the performance, researchers have been looking for different strategies to minimise drag (Barbosa, Morais, Marques, et al., 2015).It is possible to monitor drag forces by analytical procedures, experimental techniques and numerical simulations by computational fluid dynamics (CFD) (Marinho et al., 2009;Mollendorf et al., 2004;Naemi et al., 2010).CFD enables measuring hydrodynamic parameters with a good control of environmental features as well as controlling between and within-subject variations (Barbosa et al., 2015(Barbosa et al., , 2018;;Bixler & Schloder, 1996;Marinho et al. 2009).CFD has become a standard and readily available technique to assess fluid mechanics in the past years (Marinho et al., 2009;Marinho, Barbosa, Rouboa, & Silva, 2011;Mantha et al., 2014).Numerical simulations are able to provide accurate and insightful details on the flow around the swimmer (Bixler et al., 2007).Additionally, CFD is often more affordable and less time-consuming than experimental testing (Gordon & Imbabi, 1998).
Goggles are a mainstream piece of sportswear in competitive swimming.Its role is to protect the eyeballs and enable a sharper vision accuracy underwater (Morgan et al., 2008).However, as far as the authors' understanding goes, no research studying the effect of goggles on the swimmer's hydrodynamics was yet conducted.One may argue that different goggles models could impose varying amounts of drag force acting on the swimmer.Nevertheless, we failed to find a study reporting whether this is indeed the case and, in such circumstances, how much the drag increase would be.Such a study would require the selection of an analysis technique that could provide a good control of environmental conditions, besides the within-subject variability (i.e., the best way to have insight on the effect of goggles on the swimmer's hydrodynamics would be to run numerical simulations by CFD).This procedure assesses the fluid flow behaviour and provides information about drag and pressure zones (Forte et al., 2020).
The aim of this study was to analyse the effect of swimming goggles on swimming hydrodynamics by numerical simulations.It was hypothesised that the use of goggles would affect the swimmer's hydrodynamics and this would vary based on the goggles models to be worn.

Subject and scanning the model
A 30 year old elite swimmer (1.71 m height, 66 kg of body mass, 21 years of training experience, best performance of 865 FINA points) was recruited for this research.All the procedures were in accordance with the Helsinki declaration and an informed written consent was obtained beforehand.The approval was granted by the Ethics Committee of the University of Beira Interior (Portugal) under registration number R-1857-S.
The swimmer was scanned wearing a competition swimming cap.Scans were made under 4 different conditions (Figure 1): (1) not wearing goggles; (2) wearing Nikko goggles (with an oval-shape, featuring a double rim at the edges; this is the largest of all models under study); (3) wearing Ankor goggles (its main feature is the narrow height); and (4) wearing Swedish goggles (the most popular model among swimmers, the shape lines closely fit the face anatomy).The goggles were painted in white to enhance the sports equipment scanning procedure and obtain a better portrait of its geometry.
The swimmer's head was scanned (Artec 3D scanner, 3D Artec TDSL (2011-08), M size type) to collect the geometry of the anatomical unit (Forte et al., 2016(Forte et al., , 2017)).The 3D scanner was fixed to a table and an anatomical unit (head, chest, neck and shoulders) spun 360º.The swimmer was sitting and scans were made under dim light to enhance the scanning procedure (Forte et al., 2016(Forte et al., , 2017)).Multiple scans from different angles, both horizontally and vertically, were made.Artec Studio Software was used to clean each scan.After aligning all the scans, the files were merged into 1 mesh (Forte et al., 2018).Upon that, a final edit consisting of filling holes, smoothing edges and applying mesh simplification was done to get the extracted geometry (Forte et al., 2018).
Subsequently, the scan files were imported into Geomagic Studio (3D Systems, USA) software.Through the use of this software, the remaining holes were filled in, noise data were deleted, and spikes and anatomical structures were smoothed (Forte et al., 2020c).After this procedure, the files were converted to points to create uniform node distances and reduce noise data.Four 3D files were created in stereolithography (

Boundary conditions
The swimmer's human head model resembles a sphere-like geometry.To conform to this shape, a cylindrical domain was created (radius of 0.5 m and 2.5 m length) (Moreira et al., 2006).For the mesh generation, the automatic meshing option available in the Ansys Fluent 15.0.7 commercial software was used.The automatic mesh generator implemented in the Ansys software is able to create both structured and unstructured grids of good quality.Manually creating a 3D grid with the same or even better quality would be too time-consuming.Moreover, developing a structured mesh manually can be very complex on curved and detailed anatomical geometries, such as a human face (Marinho et al., 2010).
For identical imported head geometries, 3 different grid generation techniques were tested: (1) the polyhedral meshing; (2) the tetrahedron assembly meshing; and (3) the cut cell assembly meshing.The Relevance Center settings were chosen in such a way that a sufficiently detailed grid was created for the head geometry, while still keeping acceptable computation times.A coarse relevance centre was created with polyhedral meshing and a fine relevance centre was used for both the tetrahedron and cut cell assembly meshing (Blocken et al., 2013).
The meshes were analysed by computing the skewness, orthogonal quality, number of elements and Y+ wall turbulence values (Peters, 2009).The CutCell assembly meshing method was able to generate the best quality grid.As this method creates a highly structured grid, the element count of approximately 600,000 cells was significantly lower than for the more unstructured polyhedral grids of around 1 million cells.The tetrahedron cell count was similar to that of the CutCell meshing.Also, a blockstructured approach often guarantees a better quality mesh, providing more accuracy than a highly unstructured mesh (Peters, 2009).
The generated mesh was fine near the head and coarser towards the outer edges of the domain (Figure 3).This especially enables accurate flow results near the head and goggles, simulating reliable boundary layers and near-surface water flows.Also, 'proximity and curvature' were selected for the grid generation.For the best quality mesh, sharp changes in the size of adjacent mesh cells should be prevented.In all cases, the 'smoothing' was set to 'high' and a programme-controlled 'inflation' setting was imposed on the mesh.

Numerical simulations
All CFD simulations were run with 3D double-precision settings.For the near-wall treatment, non-equilibrium wall functions were selected (Forte et al., 2018).These give improved predictions for fluid flows in the case of strong separation and large adverse pressure gradients compared to the standard wall-functions (Bakker, 2006).For the turbulence modelling, the viscous Realizable k-epsilon model was selected.The k-epsilon turbulence model is a 2-equation model with good predictions for turbulent flows.The model has been used successfully and extensively for industrial applications (Raiesi et al., 2011) and has shown good accuracy in modelling human swimming (Bixler et al., 2007;Bixler & Riewald, 2002;Moreira et al., 2006).
The head model without goggles presented Reynolds number of 4.14 × 10 7 .For the model with Swedish goggles, the Re was 4.22 × 10 7 .The model with Ankor goggles presented a Re of 4.46 × 10 7 .Finally, the model with Nikko goggles presented a Re of 4.46 × 10 7 .Thus, in all situations, the flow is considered turbulent.
The following boundary conditions were used (Figure 4): Cylinder top face = 'velocity inlet', normal to boundary; Cylinder bottom face = 'pressure outlet'; Cylinder sidewalls = 'symmetry' (d/dy = 0, viscosity ν = 0) to avoid water flow congestion; Head = 'noslip wall' (speed v = 0, viscosity ν = 0).The head model's vertex point was perpendicular with the velocity inlet face.Thus, the head angle of attack with the flow inlet velocity was 90º with an aligned head.Based on a previous study by CFD, this was considered as the best hydrodynamic position (Popa et al., 2014;Zaidi, Taiar, Fohanno, & Polidori, 2008).This aligned position presented the lowest drag in a previous study.The inlet velocity at the top of the cylinder domain was set to a steady-state flow of 2.0 m/s, representing a realistic average swimming velocity in competitive short-distance swimming.Assessing different body parts, several authors have used speeds near 2 m/s that are typically used during some sets in training and racing events (Marinho et al., 2009b;Marinho, Barbosa, et al., 2011, 2012;Rouboa et al., 2006).
At the velocity inlet and pressure outlet, the turbulence intensity and length scale were set to 1% and 0.1 m.These are realistic physical values for close to standstill low turbulence water present in a swimming pool (Bixler & Riewald, 2002).The incompressible fluid in the CFD domain was given the characteristics of water (density of 998.2 kg/m 3 and dynamic viscosity of 0.001003 kg/m•s −1 ) (Bixler & Riewald, 2002).Turbulent kinetic energy and turbulent dissipation rate were set to second-order upwind (Rouboa & Silva, 2007) and residual convergence criteria of the flow parameters were set to 10 × 10 −6 for the most accurate results.Residuals of the flow velocity components in the x-, y-and z-directions were monitored.When the residual and drag values remained close to constant, showing only small fluctuations, the simulation was deemed as converged (around 1500 iterations needed).

Drag force
Viscous drag, pressure drag, total drag and surface area were extracted from the Ansys Fluent Software (Ansys Fluent 15.0.7,Ansys Inc., Pennsylvania, USA).The total drag is defined as where F d is the drag force, C d represents the drag coefficient, v is the velocity, A is the cross-section surface area and ρ is the water density (998.2 kg/m 3 ).It is possible to obtain the effective surface area (AC d ) by multiplying A by C d .This variable encompasses the head surface area and the fluid flow around it.
The pressure drag (F dp ) and the viscous drag (F dv ) are given by (2) Pressure contours were also obtained from the code for qualitative analysis.These images depict the head geometry zones with higher pressure during the fluid flow.

Drag
Table 1 presents the pressure, viscous and total drag, and the percentual contribution to the total drag as found in the CFD simulations.Obviously, the pressure drag values are higher than the viscous forces.The computed viscous drag force was different across all 4 models (partial differences between 1% and 2%).Not wearing goggles had the highest viscous drag (1.65 N), followed by the Ankor (1.64 N), Swedish (1.63 N) and Nikko (1.62 N) goggles, respectively.The pressure drag force is different in the 4 studied situations (partial differences ranging from 4% to 10%).While wearing the 3 goggles models, the swimmer's head experienced less pressure drag than without goggles.The Swedish goggles showed the best hydrodynamics, followed by the Nikko and Ankor models.The condition without goggles had the largest pressure drag (11.34 N), followed by the Ankor (18.87 N), Nikko (10.78 N) and Swedish (10.20 N) goggles, respectively.A similar trend was found in the total drag force.The condition without goggles showed the lowest magnitude (12.99 N) of the total drag, followed by the Ankor (12.51 N), Nikko (12.40 N) and Swedish (11.83 N), respectively.For the effective surface area (AC d ) the same order applied.Altogether, the Swedish goggles decreased the drag force on the head model by 9% compared to the control condition (not wearing goggles).The 2 other goggles models also decreased the drag force, but just by 5% and 4%, respectively.

Pressure maps
In all the conditions, the highest-pressure zone is located on the top of the head (Figure 5).The tip part of the nose is also a high-pressure zone.The main lowpressure zones are the eyes or goggles, nostrils and ala (borders) of the nose, and the mandible (notably mental protuberance).At these locations, water is forced to flow around curved geometries, causing negative pressure gradients and imposing a fluid acceleration.
Depending on the shape of the goggles, the surface area around the eye regions has different geometries.Curved obstacles, whether a certain type of goggles or cavity of the human eye socket, induce a forced normal acceleration of the streaming water.The curved water flows cause pressure gradients on the surface of the model.Besides differences in eyepiece geometry, the goggles slightly vary the shape of the noseband, head strap and flat surface area.

Discussion and implications
The current study aimed to assess the hydrodynamic characteristics of a swimmer's head model wearing different swimming goggles.It was hypothesised that by wearing goggles the pressure, viscous and total drag change.The main results demonstrated that without goggles the swimmer's head model experiences a larger drag force than when wearing goggles.Comparing the 3 goggles models, the largest force was found while wearing the Ankor model, then with the Nikko model and the smallest force using the Swedish model.
Without goggles the head experienced a drag force of 12.99 N at 2.0 m/s, whereas with the goggles it varied between 11.83 and 12.51 N. In other studies, at 2.0 m/s, assessing the head influence position in the upper trunk, limbs and head geometry (Cortesi & Gatta, 2015) and full-body gliding position (Barbosa et al., 2018), the drag values were near 100 N.However, the authors (Barbosa et al., 2018;Cortesi & Gatta, 2015) ran the simulations to a larger body area (upper-body and full-bodied geometries), whereas in the present study, only the flow around the head was simulated, which represents only a small part of the total drag of the body during swimming.In the current study, the pressure drag contribution to the total drag at the same speed was between 86.22% and 87.29%.This is in accordance with Barbosa et al. (2018) who calculated a pressure drag contribution to the total drag of 83.14% at 2.0 m/s.The swimmer's head surface area ranged between 0.025 and 0.029 m 2 .However, no study was found in the literature reporting the swimmer's head surface area.The head model without goggles had the lowest surface area (0.025 m 2 ), followed by the head with the Swedish goggles (0.026 m2), Niko and Ankor goggles (0.029 m 2 ).This increases the hydrodynamic relevance of the goggles, reducing drag to a larger surface area.
Wearing goggles reduced the total drag force exerted over the swimmer's head by 4-9%, depending on the model.The viscous drag differences were between 1% and 2%, whereas the pressure drag differences were between 4% and 10%.These results show that the pressure drag is the main factor in the drag reduction when wearing goggles.The goggles design may enhance the shape, diminishing the pressure drag by improving the water flow around the face.The goggles design and the used materials allow the water to pass over the goggles more efficiently due to its frame portions being formed by a smooth and continuous surface (Van Atta et al., 2009).The smooth surfaces of the goggles materials minimise the viscous drag (Forte et al., 2020d;Schlichting, 1979).Another concern regarding the equipment design is the depth and profile of eyepiece reduction, which allows a smoother flow from the forehead over the goggles rather than the swimmer's eyes (Van Atta et al., 2009).The design of the goggles may justify the reason why the head without goggles experienced a higher drag and lower surface area compared to the situation with the goggles.
Altogether, the goggles were found to reduce the pressure, viscous and total drag.The goggles fill in a region near the eyes (the eye cavities) which without a piece of swimwear, change the water flow, increasing the drag force.The pressure drag is caused by differences of pressure between the front and back boundaries.Upon that, as higher the magnitude differences in pressure maps in the head regions, higher the pressure drag (Schlichting, 1979).For this specific case, the pressure drag is mainly reduced by the anterior-posterior depth profile of the goggles frames.As presented in Figure 5, the pressure is diminished by the goggles design between the head and the chin part.In the model without goggles (Figure 5) the forehead section has less pressure (blue colour) and the area around the eyes has higher pressure (yellow/light green colour); whereas with the goggles, the above part has more regions with lower pressure (blue colour), and the centre and/or the goggles below area has green colour.The viscous drag is reduced by the smooth surface of the goggles.Therefore, swimmers might wear customised goggles based on their eye depth profile.
No previous study was found assessing the head contribution to total drag.However, Mantha et al. (2014) assessed the swimmer's total drag without goggles in the gliding position and the drag was near 80 N. In our study, the differences between the model without and with the goggles are up to 1.16 N. Hence, a swimmer with a total drag of 80 N wearing the Swedish goggles (less drag imposed) may possibly reduce the drag to 78.84 N. It is expected that in a freestyle competition, and assuming that the race environment is the same as the experimental environment, for the same propulsion, the swimmer's goggles may improve the speed from 2.00 to 2.03 m/s.Thus, in a 100 m freestyle competition, it is expected that a swimmer with a total drag of 80 N and at 2 m/s may end the race in 50 s.Hence, with goggles (the Swedish goggles decrease the head drag in 1.16 N), it might be possible to improve winning time by about 0.73 s or 1% (2.00 m/s = 50.00s; 2.03 m/s = 49.28 s) for the same propulsion.However, this performance simulation is based on a different swimmer's model (Mantha et al., 2014).Consequently, the differences may vary with different swimmers.
The following limitations in the present study should be noted: (1) only 1 head position (attack angle) was tested; (2) the effect on the full-body hydrodynamics was not assessed; (3) 1 single participant took part in this research and different eye anatomies (e.g., eye orbital depth) may vary from person to person; (4) slight differences on head geometry following 4 successive scans of the same subject with different goggles may residually affect the results.

Conclusion
Wearing goggles diminishes the drag force as compared to not wearing them.Wearing this piece of swimwear enhances the head geometry shape/form, improving the water flow over the eye orbit cavities.Among the 3 tested models, the Swedish goggles showed the least drag force, followed by the Nikko and Ankor goggles.Viscous drag was reduced due to the smoother surface of the material used to make the equipment.Pressure drag reduces the anterior-posterior depth profile around the eye orbits.A swimmer may improve the head drag with goggles in approximately 4-9%.

Figure 3 .
Figure 3. Fine mesh near the head (left) and coarser towards the outer edges of the domain (right).

Figure 4 .
Figure 4. Boundary conditions within the entire domain geometry.

Figure 5 .
Figure 5.The pressure maps for the following situations: without goggles (left above), wearing Nikko (right above), Ankor (left below) and Swedish goggles (right below).

Table 1 .
Drag forces acting on the swimmer's head model.