Flow over hydrofoils with varying hydrophobicity

Accepted Manuscript Flow over hydrofoils with varying hydrophobicity P. Sooraj, Shital Jain, Amit Agrawal PII: DOI: Reference:

S0894-1777(18)30897-5 https://doi.org/10.1016/j.expthermflusci.2018.12.021 ETF 9686

To appear in:

Experimental Thermal and Fluid Science

Received Date: Revised Date: Accepted Date:

13 May 2018 22 November 2018 13 December 2018

Please cite this article as: P. Sooraj, S. Jain, A. Agrawal, Flow over hydrofoils with varying hydrophobicity, Experimental Thermal and Fluid Science (2018), doi: https://doi.org/10.1016/j.expthermflusci.2018.12.021

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Flow over hydrofoils with varying hydrophobicity P Sooraj, Shital Jain, Amit Agrawal1 Department of Mechanical Engineering, Indian Institute of Technology Bombay, Powai, Mumbai 4000076, India

Abstract The effect of the shape of a hydrofoil on its force characteristics is well documented; however, the role of the surface on the ensuing flow is not yet understood. Here, we report the effect of hydrophobicity on the flow dynamics of NACA0015 hydrofoil based on more than 100 particle image velocimetry based experiments. Acrylic, Cellophane tape, Teflon coated, and superhydrophobic painted surfaces are studied for Reynolds number range of 6500-30800 at five angles of attack (0o-20o) in this work. The static contact angle varies from 70o to 152o for these surfaces. The superhydrophobicity helps to reduce the range of Reynolds number where the flow separation occurs. We observe up to 40% reduction in drag at 15o angle of attack for Re = 30800, and superior hydrodynamic performance for the superhydrophobic painted surface as compared to the bare Acrylic surface. The superhydrophobic painted surface is also found to delay flow separation and stall angle (by up to 5o based on the gliding ratio), which is attributed to a reduction in the separation bubble size (by up to 56%). The Teflon coated surface behaves similar to the superhydrophobic painted surface until an angle of attack of 5o. The vortex strength is reduced for the superhydrophobic painted surface at 15o angle of attack compared to the Acrylic surface. The results of this study show that the hydrodynamic efficiency can be increased and also sustained over a relatively large range of angle of attack by employing superhydrophobic surfaces. Keywords: Hydrophobicity; Drag reduction; Flow separation; Separation bubble

1. Introduction 1

Corresponding Author: Professor Amit Agrawal,

Department of Mechanical Engineering, Indian Institute of Technology Bombay, Powai, Mumbai 4000076, India Email: [email protected]; Phone: + (91) (22)2576-7516; Fax: + (91) (22)2572-6875 1

Superhydrophobicity is a property of a surface with contact angle greater than 150 o that can be obtained by reducing the surface energy or by increasing the surface roughness. The air pockets inside the micro-nano pores on the surface create air-water interfaces which helps to increase the contact angle. Water repellent property of lotus leaf and other plants inspired researchers to study superhydrophobic surfaces in order to understand the unique properties of these surfaces (Bhushan & Jung, 2006). Recently researchers have employed different types of nano-micro textures on various materials to achieve a superhydrophobic surface. Lithographic technique is one possible technique to fabricate such textures (Bixler & Bhushan, 2012). Most lithographybased fabrication techniques, however, provide texturing over relatively small surface areas (a few mm2). There is, therefore, enough scope to extend the benefits of employing superhydrophobicity to applications involving large surface area (of order m2). Here, we experimentally study three grades of hydrophobic hydrofoil and compare their performance with a bare hydrofoil. A hydrophobic surface attains superhydrophobicity when the surface has good amount of roughness on it. Fukagata et al. (2006) theoretically predicted the pressure drop reduction rate obtained by using superhydrophobic surface in turbulent channel flow. Laminar and turbulent channel flows over superhydrophobic surfaces have also been investigated (Ou et al. 2004; Daniello et al. 2009; Jung & Bhushan 2009; Gaddam et al. 2015). Min & Kim (2004) and Martell et al. (2009; 2010) numerically investigated the effect of superhydrophobic surface on pressure drop reduction in turbulent channel flows. It was found that superhydrophobic surfaces induce slip and reduction in pressure drop depends on the slip length. The wall shear stress reduces nearly by 40% for channel flow while the slip velocity reaches up to 75% of the bulk velocity (Martell et al. 2009). Experimental studies conducted on turbulent channel flows with superhydrophobic surface by Henoch et al. (2006), Daniello et al. (2009), Balasubramanian et al. (2004) showed significant reduction in pressure drop. Henoch et al. (2006) observed that the reduction rate decreases as the flow changes from laminar to turbulent. The longevity of the superhydrophobic surface immersed in water is one of the main concerns for underwater applications (Bobji et al. 2009; Samaha et al. 2011). The effective slip length mainly depends upon the trapped air pockets (Govardhan et al. 2009). Surface moves from Cassie (non-wetted) state to Wenzel (wetted) state when the trapped air is released from the air 2

pockets. Superhydrophobic surfaces may face many different failure mechanisms such as fluctuating pressure and velocity especially from turbulent flow, expel the air from the cavities and surface elevated pressure may compress the air in the pockets. The trapped air may diffuse into water if it is not already saturated (Ling et al. 2017).

Samaha et al. (2012) used fibrous

superhydrophobic coatings which can resist the loss of air from the surface at elevated pressure. The same group studied the longevity at different flow velocities and concluded that at higher velocities the trapped air dissolves in water and thereby it attains the wetted state. Jones et al. (2015) noticed that sub-micron level roughness is important to keep the surface dry under water. The above and many other works not reviewed here cover internal flows, whereas the subject of this study is external flow. Unlike internal flows, external flows are not driven by an externally imposed streamwise pressure gradient. Under external flows, studies are available on circular cylinder with hydrophobic coating (You & Moin 2007; Muralidhar et al. 2011; Legendre et al. 2009). These studies show a change in flow behavior and reduction in drag in presence of surface modification. Legendre et al. (2009) numerically simulated and explained the delay in onset of recirculation and vortex shedding into the wake as the magnitude of slip increases. Kim et al. (2015) experimentally showed a delay in flow separation for a circular cylinder with an increase in hydrophobicity. Their study shows that uniform size of the surface roughness boosts delay in flow separation and drag reduction. Slip length increases as the air-fraction increases which is attained by increasing the width and gap ratio of the surface textures (Aljallis et al. 2013). As a result, superhydrophobic surface delays the separation point further downstream and also reduces the base suction pressure (You & Moin 2007). The studies of You & Moin (2007) and Kim et al. (2015) further showed that there is a reduction in lift coefficient with an increase in the value of slip. Gogte et al. (2005) observed 18% drag reduction in a superhydrophobic Joukowski hydrofoil for a Reynolds number range 1500- 11000 and zero angle of attack. However, the effect of angle of attack and detailed study of flow field is absent in their study. The above literature survey shows that only limited studies have explored the effect of hydrophobicity on streamline bodies. Further, the effect of slip when the surface is kept at an angle, such that the flow is between a streamline and a bluff body, has not been explored. It is important to explore the effect of slip on flow behavior on streamline bodies near the stall angle, where both viscous and form drags are significant. In the present work, the effect of 3

hydrophobicity on flow past NACA0015 hydrofoil is studied, since hydrofoil shapes are important for underwater engineering applications. Surfaces of different hydrophobicities have been chosen for this study and hydrofoil at different angles of attack and different Reynolds number are considered.

2. Materials and methods Details about the experimental technique employed and the data reduction procedures are discussed in this section. A brief discussion on the uncertainty in the measurements is also presented. 2.1. Experimental setup The experiments are conducted in a closed-loop water tunnel with a working section of 400  400 mm2 cross-section and a length of 1500 mm (Fig. 1a). The velocity range in the tunnel is 0.008 to 2 m/s with turbulent intensity of less than 2%. Note that there are no free interfaces in the tunnel. Borosilicate glass particles of size 8-10 μm with a specific gravity of 1.1 are used for seeding. The particles trace the flow well since the Stokes number for the particles employed in the flow is much less than unity (2.7×10-4). The particles are illuminated by double pulse Nd:YAG lasers (Beamtech, China; wavelength: 532 nm, pulse-widths: 7.7 ns and 6.8 ns, energy: 200 mJ/pulse, repetition rate: 15 Hz). A CCD camera (PCO Pixefly, Germany; image size: 1392×1024 pixels) is used for capturing the images (Sewatkar et al. 2012). The images are captured at a frequency of 5 Hz. The delay time between a pair of images is varied from 1.8-7.0 ms depending on the flow speed. A Matlab based PIV Software is used to analyze the images (Thielicke & Stamhuis 2014; Hashiehbaf et al. 2015; Khan et al. 2017). The Matlab package uses cross-correlation as the interrogation method. The images are analyzed using an interrogation window size of 32×32 pixels with 50% overlap. The spatial resolution of the velocity field enables identification of about 5400 (63×86) velocity vectors with the separation space between adjacent velocity vectors being 1.6 mm, in an instantaneous frame. The field size is 10.09 cm×13.76 cm. A mirror has been used during the experimentation to avoid the shadow region from the edge of the hydrofoil, and the rejected vectors are mostly in the shadow and reflected regions.

4

NACA0015 hydrofoil (chosen as a representative shape for the hydrofoil) having a chord length (C) of 50 mm, made of Acrylic, is considered without and with three types of surface modifications: Cellophane tape (Polypropylene based transparent tape), Teflon tape (polytetrafluroethylene), and superhydrophobic paint. The experiments were therefore conducted for these four different surfaces. The different surfaces are created by winding Cello tape and Teflon tape around an Acrylic hydrofoil. The winding process is manual and some overlap in winding is unavoidable. However, the readings taken from multiple planes including the plane with double layered taping showed no difference in the flow behavior. The effect of the manner of winding on the ensuing flow is therefore deemed to be insignificant. The maximum thickness of the hydrofoil changes by less than 0.4% after applying these coatings. No significant variation in the force coefficients is expected owing to this small change in the thickness, as further confirmed by the results discussed below. The Cello tape is manufactured by ANSIO and Teflon tape by DIY crafts. The thickness of the Cello tape is 70 μm and the Teflon tape is of 90 μm. The superhydrophobic nature of the hydrofoil was achieved by using a surface protection paint ‘Ultra Ever Dry’ (UltraTech International, Inc., Florida). This commercial paint provides a superhydrophobic and oleophobic coating that repels most water-based and some oil-based liquids. Ultra-Ever Dry uses proprietary omniphobic technology to coat an object and creates a surface chemistry and texture with reduced surface energy. The superhydrophobic surface is obtained by manual spray painting of Acrylic surface. There is no correction performed on the measured data since the blockage ratio is less than 10% (Boutilier and Yarusevych 2012). The experiments are performed for five angles of attack ranging from 0 o-20o at intervals of 5o. The angle of attack is defined as the angle made by the chord line with the direction of freestream flow. The Reynolds number (Re, based on chord length and mean velocity) is in the range of 6765 to 30800. 520 statistically independent frames are acquired for each case. It was found that the number of frames is more than sufficient for the convergence of r.m.s. velocity value. The flow velocity ranges from 110 to 520 mm/s. Effect of five different angles of attack (α = 0o, 5o, 10o, 15o and 20o) is studied in the present work since previous studies show that the aerodynamic performance based on gliding ratio is better at low angles of attack compared to higher angles of attack. The streamwise velocity (u) and lateral velocity (v) are normalized using free stream velocity (u∞) and axial and lateral distances are normalized using chord length (C) to obtain U, V, X and Y respectively. 5

Front View

Side View

(a)

(b)

C= 50 mm

(c)

6

Figure 1: (a) Schematic of the water tunnel facility, (b) Schematic of PIV setup, and (c) Schematic of NACA 0015 hydrofoil employed in the measurements. 2.2. Force Estimation The mean drag force is calculated using the modified wake survey method which essentially solves the integral form of streamwise momentum equation. The contributions of fluctuating velocity and pressure terms are suitably accounted for in the analysis for the control volume chosen around the body. Bohl and Koochesfahani (2009) suggested an equation by adding the fluctuating components which also accounts for the lateral momentum deficit in the wake survey method. The streamwise component of momentum flux through the lateral control surface affects the total momentum on the control volume. This becomes more important when the control surfaces are close to the body. The velocity along the control surface lies between where

is the freestream velocity and

and

,

is the velocity at the downstream end of the control

volume. The average of these velocities is taken as the effective velocity and represented as

, where  is found to be adequately smaller than unity. The mean drag coefficient

equation can therefore be written as (Bohl and Koochesfahani, 2009): (1)

where C is the chord length,

is mean velocity of the control volume, H is distance of lateral

surfaces from the center of the viewframe,

and

are the fluctuating components of

streamwise and lateral velocity respectively. The integration is performed on the outlet of the control surface at a distance of 2C from the leading edge. The values obtained by this method is compared with the literature value for Acrylic surface in Fig. 2a. Lift is calculated using the Kutta-Joukowski theorem, which is expressed as (2) where

is density of water,

is freestream velocity, and

is circulation. The value of

circulation required in the above equation is calculated as (3)

7

where

is velocity of the flow, and

is the elemental length (boldface denotes vector quantity).

Line integration is performed around the body along the periphery of the view frame. Coefficient of lift is obtained by normalizing the value of lift by

. The obtained lift coefficient

values are compared with the literature value in Fig. 2b.

(a)

(b)

Figure 2: Comparison of (a) mean drag coefficient and (b) mean lift coefficient with Zhou et al. (2011). The values of drag and life coefficients obtained from the above procedure are compared with that given by Zhou et al. (2011). Zhou et al. obtained the force coefficient values using load cells. Their measurements are on NACA0012 hydrofoil; therefore, another set of measurements were conducted with NACA0012 hydrofoil for the purpose of validation. Figure 2 shows good agreement for both values of Reynolds number and angle of attack. This validation enhances our confidence in the procedure of force estimation employed here. 2.3. Uncertainty analysis We have considered four important factors which are important for determining the uncertainty in PIV measurements as suggested Raffel et al. (1998), Wang et al. (2008) and Lazar et al. (2010). These factors are: uncertainty related to equipment, uncertainty in particle lag, sampling,

8

and image processing. Uncertainty with equipment is estimated based on the uncertainty in calibration scaling magnification, timing accuracy and uncertainty with CCD. Uncertainty with processing is calculated based on the procedure in Raffel et al. (1998). The maximum uncertainty in velocity measurement is between ±2.1% with processing uncertainty in the algorithm as 0.5% and uncertainty in equipment as 0.6%. By combining the uncertainty with equipment, particle lag, sampling error and processing error we calculated the uncertainty with velocity measurement (Yadav et al. 2015). We also estimated the uncertainty in individual parameters involved the formula for lift and drag coefficients. These parameters are:

,

, C,

,

,

and . We estimated the

uncertainty in each of these parameters, which were ultimately combined using the standard uncertainty propagation method, to obtain the uncertainty in drag and lift coefficients. The uncertainty values in drag coefficient and lift coefficient are estimated to be ±4.4% and ±3.6% respectively. The actual uncertainty in the force coefficient is however expected to be smaller than the above estimate, because the process of integration helps reduce the overall uncertainty. A sensitivity analysis for the size and location of the control surface with respect to the hydrofoil was also carried out. It was found that the values converge provided that the downstream distance is at least 0.8 C and lateral distance is 0.5 C away from the surface. These conditions are satisfied by the control surfaces in the present measurements.

3. Results In this section, we first present contact angle measurements in order to characterize the surfaces employed. The flow behavior over these surfaces is presented in subsequent sections. Flow around four different surfaces are studied at five different Reynolds numbers (6765, 11700, 16800, 23000 and 30800) and five different angles of attack (0o, 5o, 10o, 15o and 20o) for each of the four surfaces considered in this study. The flow behavior is examined mainly using instantaneous and time-averaged streamline and vorticity contour plots. The force coefficients (lift and drag) are also calculated for all the cases. 3.1. Roughness estimation

9

The surface roughness of the superhydrophobic painted surface is measured using Alicona infinite focus microscope. This is an optical microscopy which uses focus variation to obtain three-dimensional surface morphology and information about the depth of the surface with a resolution of 10 nm. 250 linear profiles are taken over a sampling length of 178 μm. A 3-D contour image of the surface profile obtained from the Alicona infinite focus microscope is shown in Fig. 3. Mainly, three parameters are used to characterize the roughness; arithmetic ) estimated to be 10.40 μm, average root-mean-square height (

) is 11.85 μm

with a skewness of 0.69 and mean peak to trough roughness height (

) is 14.98 μm

roughness (

(Hokmabad and Ghaemi 2016). Lee et al. (2018) studied the effect of roughness on the flow around a superhydrophobic painted NACA0012 airfoil with arithmetic roughness of 12 μm. They found that the enhanced turbulence level due to pure roughness stands between those of smooth surface and superhydrophobic surface and air pockets in the superhydrophobic surface help to reinforce the hydrodynamic effects of roughness. Kim et al. (2015) observed that the effect of roughness on the flow dynamics around a circular cylinder with arithmetic roughness 12 μm is negligible at low Reynolds number (Re < 104). Hokmabad and Ghaemi (2016) studied the effect of wetted superhydrophobic surface with arithmetic roughness 7.9 μm in turbulent channel flow. They noticed that the wetted superhydrophobic surface is hydrodynamically smooth if the surface roughness is lesser than the viscous sublayer thickness. As in these earlier works, the effect of surface on the flow is attributed to change in hydrophobicity of the surface rather than the effect of roughness.

10

Figure 3: Three-dimensional contour of the surface profile obtained from Alicona infinite focus microscope.

3.2. Contact angle measurement and Surface patterns For each surface, contact angle measurement is undertaken (Fig. 3). Contact angle of each surface is measured using tangent method and a high speed camera (Redlake, Motion Pro X series) is used to capture the images. The contact angle values are summarized in Table 1. For each surface, 10 images are taken; the error in the table corresponds to the standard deviation of these readings. Figure 4 shows that the highest contact angle is obtained for superhydrophobic painted surface while the lowest contact angle is obtained for Acrylic surface. A surface is said to be superhydrophobic if the contact angle is greater than 150o. This has been achieved here by coating the hydrofoil using a commercial paint. Other coatings lead to an increase in hydrophobicity of the surface, as apparent from an increase in contact angle: 70o, 93o, and 138o for Acrylic, Cello tape, and Teflon coated surfaces respectively. The present measured values compare well with those from Kim et al. (2015) (Table 1). The advancing and receding contact angles are also obtained for the superhydrophobic painted surface and they are found to be 155o and 144o respectively and for Teflon the values are 143o and 127o respectively. In order to characterize the surfaces further, SEM images of the surfaces have been presented in Fig. 5. Notice that the hydrophobic surfaces have nano-micro textures which trap air inside and 11

the viscosity difference between air and water is known to create slip on the surface. It is evident from Fig. 5 that the textures on superhydrophobic painted surface are in nanoscales, while for Teflon surface they are in microscales. The difference in the size of the textures play an important role on the hydrophobic effect. The other two surfaces Acrylic and Acrylic with Cello tape do not have any textures on their surfaces.

Normal (Acrylic)

With Cello tape

With Teflon tape

With Paint: Superhydrophobic

Figure 4: Images of droplet on different surfaces used for the contact angle measurement.

Table 1: Contact angle measured using tangent method for the four surfaces employed in the present measurements. The corresponding values from Kim et al. (2015) is also included for comparison. (Symbol ‘W’ is chosen for Acrylic surface to show that the surface is ‘without’ any coating). Surface

Symbol

Contact

Contact angle (in o)

angle (in o)

(Kim et al. 2015)

Acrylic

W

70±2

72

Acrylic with Cello tape

C

93±2

-

Acrylic with Teflon tape

T

138±2

140

Acrylic with Superhydrophobic Paint

S

152±2

160

12

(a)

(b)

Figure 5: SEM images of (a) superhydrophobic painted surface and (b) Teflon surface. 3.3. Time averaged flow behavior Flow over surface modified hydrofoil is studied in order to understand the hydrodynamics of superhydrophobic surfaces. Time-averaged streamlines are plotted for the superhydrophobic painted and Acrylic surfaces at different angles of attack and different Reynolds numbers. The flow is found to be attached to the body until angle of attack 5o for all four surfaces (results not shown). Further, the streamline patterns for the different surfaces are similar at angles of attack 0o and 5o over the given range of Reynolds numbers. However, differences in employing superhydrophobic painted surface versus Acrylic surface shows up at higher angle of attack. The streamlines are found to be attached to the superhydrophobic painted surface at Re = 6765 for angle of attack 10o (Fig. 6a). On the other hand, there is formation of a small separation bubble at Re = 6765 and angle of attack 10o for all other surfaces (Fig. 6b). The separation bubble is formed when the flow reattaches to the surface. Interestingly, the laminar boundary layer is not getting separated for the superhydrophobic painted surface and the flow remains attached. This could possibly be due to slip on the superhydrophobic painted surface which leads to a non-zero value of momentum at the surface, which helps overcome the adverse pressure gradient; thereby preventing the formation of separation bubble. Flow separation occurs for all four surfaces near the trailing edge at angle of attack 10o as the Reynolds number increases to 11700. However, for α = 10o and Reynolds number of 1680030800, the streamlines are found to be attached to the surface with a thin boundary layer. All the 13

four surfaces show the same behavior in this parameter range. Formation of separation bubble is observed upon increasing the angle of attack to 15o for all Reynolds numbers and all surfaces studied in the present work. There is a substantial change in the flow behavior at Re = 30800 and angle of attack of 15 o for the superhydrophobic painted surface (Fig. 6c). The streamlines follow the surface for almost 70% of the hydrofoil surface and then the separation occurs, as shown in Fig. 6c leading to a reduction in drag as quantified in a later section. This point is discussed further in the next section. Acrylic, Cello tape and Teflon coated surfaces generate almost same size separation bubble, as that shown in Fig. 6d. Hydrofoil acts as a bluff body at an angle of attack 20o and there is no significant difference in the streamline pattern for this value of α over the entire range of Reynolds number studied in the present work. The streamline pattern at Re = 30800 for superhydrophobic painted and Acrylic surfaces are shown in Figs. 6e-f. From the similarity in flow pattern, it is inferred that the hydrophobic effect of the surface on the flow behavior has diminished (slight difference in the separation bubble size) as the angle of attack increases to 20o. That is, the effect of superhydrophobicity is confined to a certain range of angle of attack. Therefore, we only consider angle of attack less than 20o for further comparisons.

(a)

(b)

14

(c)

(d)

(e)

(f)

Figure 6: Variation of time-averaged streamline patterns for (a, c, e) superhydrophobic painted surface and (b, d, f) Acrylic surface; at (a, b) Re = 6765 and α = 10o, (c, d) Re = 30800 and α = 15o, (e, f) Re = 30800 and α = 20o.

In order to obtain better idea about the size of the separation zone and boundary layer thickness, the streamwise component of velocity is plotted at different streamwise distances (Fig. 7). The velocity profile shown in Figs. 7b-d corresponds to the streamline plots of Fig. 6. The flow is inferred to be separated for negative values of streamwise velocity. The velocity recovery along the lateral direction is faster for Teflon at angle of attack 5 o and Re = 30800 (Fig.7a). But the superhydrophobic painted surface shows some interesting differences from the other surfaces (Fig. 7b-c). Since the flow is attached for 00 and 50 for all cases, the streamwise velocity value reaches the freestream value very close to the body itself.

15

16

Figure 7: Streamwise variation of mean streamwise velocity at different streamwise locations for (a) Re = 30800 and α = 5o, (b) Re =6765 and α = 10o, (c) Re = 30800 and α = 15o and (d) Re = 30800 and α = 20o. The flow over Acrylic, Cello and Teflon surfaces get separated at Re = 6765 and angle of attack 10o (Fig. 7b); however, the flow remains attached for superhydrophobic painted surface (Fig. 7b). The velocity value is negative near the trailing edge for other three surfaces except superhydrophobic painted surface which indicates the formation of separation bubble near the trailing edge. Whereas the velocity value is positive throughout for superhydrophobic painted surface. The velocity gain is faster for superhydrophobic painted surface which is evident from the velocity profile at X= 2C (Fig.7b). Even if the flow is attached to the body for superhydrophobic painted surface, the velocity profile at Y= 0.2C shows the same trend as other three surfaces. This implies that the effect of surface property is mainly on the fluid nearby the surface. At angle of attack 10o, as Re increases to 11700, the flow gets separated for all surfaces. However, at Re = 16800, the flow remains attached to the surface for all cases.

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At angle of attack 15o, Flow reversal occurs around 0.7 C for superhydrophobic painted surface whereas it happens at an earlier location (around 0.4 C) for other three surfaces (Fig. 7c). This shows that as the Reynolds number increases to 30800, the delay in separation also increases. The variation in velocity around the body suggests slip near the surface for superhydrophobic painted surface (Fig. 6c). Figure 7d shows that there is no considerable difference in the variation in streamwise velocity profile along the streamwise distances at α = 20 o and Re = 30800 for all surfaces. The boundary layer thickness around the hydrofoil, plotted in Fig. 8, is defined as the distance at which 95% of the freestream velocity is attained by the flow. The curves are not smooth since the images are limited by the resolution of the PIV measurements. The superhydrophobic painted hydrofoil possesses smaller boundary layer compared to other hydrofoils in all the mentioned cases. The maximum difference in the boundary layer thickness between Acrylic and superhydrophobic painted surface is 28% seen at angle of attack 5o and Re = 30800 (Fig. 8a). Interestingly, the Teflon surface has the least value of boundary layer thickness towards the trailing edge at angle of attack 5o and Re = 30800. A maximum reduction of 62% in boundary layer thickness is observed for angle of attack 10o and Re = 6760 with superhydrophobic painted hydrofoil compared to Acrylic hydrofoil (Fig. 8b), where the flow is attached to the surface for the former. The difference in the boundary layer thickness between superhydrophobic painted surface and other surfaces reduces to 38% at angle of attack 15 o and Re 30800 (Fig. 8c). The effect of superhydrophobicity is diminished as the angle of attack increases to 20o and the reduction in the boundary layer thickness reduces to 6% at Re = 30800 for superhydrophobic painted surface compared to Acrylic surface. The Teflon and Cello tape surfaces behave similar to Acrylic surface beyond angle of attack 10o for these Reynolds numbers.

18

19

Figure 8: Boundary layer thickness around the hydrofoil at (a) Re = 30800 and α = 5o, (b) Re =6765 and α = 10o, (c) Re = 30800 and α = 15o and (d) Re = 30800 and α = 20o.

3.4. Instantaneous vorticity In order to better understand the mechanism of vortex generation and its movement over the surface, we examine instantaneous vorticity patterns and trace their evolution over a cycle of events. A sequence of instantaneous vorticity contours at Re = 30800 and angle of attack 15o is shown in Fig. 9 for superhydrophobic painted surfaces. It is clear from the figure that flow separation occurs near the leading edge (Fig. 9a). The point of separation then moves continuously towards the trailing edge (Figs. 9b-d) and the flow becomes attached to the surface (Fig. 9d). The flow again becomes separated (Figs. 9e-f) and attached (Fig. 9g), the cycle repeats itself. Figures 6a and 6b show time independent attached flow and separated flow respectively. The slip effect aids in the tendency of the flow to get attached to the surface, whereas the adverse pressure gradient tends to separate the flow. Therefore, at Re = 30800 and α =15o, the flow around the superhydrophobic painted surface displays a separated/attached behavior. The time period of this sequence of events, upon following over several cycles, is found to be irregular. The duration of the attached flow regime is greater than that of the separated regime on an average over many cycles. For Acrylic, Cello tape and Teflon coated surfaces, flow separation occurs near the leading edge and the behavior remains independent of time (not shown). The vortices roll up due to the adverse pressure gradient on the surface. However, they are not able to stay on the 20

superhydrophobic painted surface due to slip. Since the velocity gradient normal to a superhydrophobic painted surface is comparatively less, shear stress value will be lower compared to the Acrylic surface where the no-slip condition applies. Therefore, the adverse pressure gradient becomes weaker for the superhydrophobic painted hydrofoil as the fluid slips over the surface. Slip on the surface tries to make the flow further attached due to non-zero momentum of the fluid at the surface. Whenever the slip effect reduces, vortices roll-up on the surface (Figs. 9a-b). However, when the slip effect dominates near the separation point, the separation point moves further towards the trailing edge (Figs. 9c-e) by inducing velocity to overcome the adverse pressure gradient. The flow velocity on the surface is therefore found to vary with time, leading to a variation in the points of flow separation and attachment. The flow is attached from t = 1.4 s (Fig. 9d) to t = 2.2 s (Fig. 9e), after which the flow separates from the surface and remains so until t = 3 s (Fig. 9f). The mean flow for this case is already shown in Fig. 6c. Notice that on average, the separation point is very near to the trailing edge which implies that the number of cycles of attached flow dominates over separated flow. Apparently, the terminal phase of the cycle is a shift in the separation point from the trailing edge back to the leading edge. The separation takes place near the leading edge for Fig. 9f, which is similar to the flow behavior shown in Fig. 9a. The flow is attached and the shear layer follows the hydrofoil surface in Fig. 9g. The separated flow is clearly seen in Figs. 9a-c. Notice that the vortices have reasonably high strength as they shed towards the wake. The flow separation can be explained using vorticity dynamics, as the shedding of oversaturated vorticity generated at the wall via boundary vorticity flux can cause flow separation (Zhu et al. 2014). The strength of the shear layer on the top surface reduces towards the trailing edge.

21

(a) 0.0 s

(b) 0.2 s

(c) 0.6 s

(d) 1.4 s

(e) 2.2 s

(f) 3.0 s

(g) 5.4 s Figure 9: Instantaneous normalized vorticity contours at Re = 30800 and angle of attack = 15o for the superhydrophobic painted surface. 3.5. Variation of separation bubble size In order to quantify the amount of separation observed in the various cases, the characterization of the separation bubble is performed at an angle of attack 15o where the variation of the bubble size is significant (Fig. 10). The leading-edge vortex formation length (Lf) and bubble width (hb) of the separation bubble is estimated from the r.m.s. of the streamwise velocity field and the mean velocity field respectively as estimated by Alam et al. (2010) for NACA0012. The bubble width is defined as the maximum lateral distance of the region enclosed by u = 0 where reversed flow occurs and the leading edge vortex formation length is defined as the streamwise distance 22

from the leading edge to the maximum

in the upper half of the wake. The vortex formation

length and bubble width are normalized by the chord length. It is evident from Fig. 10 that both the vortex formation length and the bubble width decrease with increase in Reynolds number beyond 16800. The decrease is however more drastic for superhydrophobic painted surface as compared to Teflon, Cello and Acrylic surfaces, with the difference between the Acrylic and superhydrophobic painted surfaces being largest at Re = 30800. Cello tape surface behaves in a similar way as Acrylic surface. Notice that Teflon and superhydrophobic painted surfaces show approximately the same value at low Reynolds number; the behavior for Teflon surface switches to that of Acrylic surface with an increase in Reynolds number. This transition in behavior for Teflon surface occurs at around Re = 23000. A good agreement in the value of both vortex formation length and bubble width for two independent conditions (Teflon and superhydrophobic painted surfaces at low Re, and Teflon and Acrylic surfaces at high Re), helps induce lot of confidence in the force coefficient data analysis. The size of the recirculation bubble depends mainly upon the flow separation point. The bubble size increases as the separation point moves towards the leading edge. Superhydrophobic painted surface forms smaller recirculation bubble because of the delay in separation. The reduction in bubble size is rather severe at high Reynolds number. There is about a reduction of 38% in vortex formation length (Fig. 10a) and 48% in the bubble width (Fig. 10b) at Re = 30800 for superhydrophobic painted surface as compared to Acrylic surface, whereas Teflon exhibits a maximum bubble width reduction of 5% at Re = 11700. Slip is however comparatively less for Teflon surface since its hydrophobicity is lesser than superhydrophobic surface, as is evident by its smaller contact angle in Table 1 and Fig. 7. The hydrophobic effect of Teflon surface reduces as the Reynolds number increases. This essentially does not help to attach the flow at higher Reynolds numbers and higher angles of attack. Lee et al. (2018) observed delayed oscillation of shear layer and rolling up into Karman vortex for superhydrophobic painted surface compared to smooth surface when the angle of attack increases beyond 5o. Because of the delayed rolling up of the shear layer, the nucleus of the separation bubble moves closer to the leading edge for the superhydrophobic painted surface as shown in Fig. 6b, leading to a reduction in the size of the separation bubble for the superhydrophobic painted surface. 23

Figure 10: Variation of time-averaged separation bubble size for different Reynolds numbers at α =15o (W: Acrylic, C: Cello, T: Teflon, S: superhydrophobic painted).

3.6. Variation of Drag Coefficient Mean drag values are calculated using the modified wake survey method (Eq. 1). The results for all the angles of attack and Reynolds numbers are presented in Fig. 11. The value of mean drag

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coefficient increases with angle of attack owing to change in flow behavior around the body from streamline to bluff. There is a considerable reduction in the value of mean drag coefficient for superhydrophobic painted surface with respect to an Acrylic surface (Figs. 11a-e). The reduction is more prominent at higher Reynolds number and higher angle of attack. Note that Teflon and superhydrophobic painted surfaces exhibit approximately same value of mean drag coefficient until 5o and as the angle of attack increases Teflon follows the Acrylic surface characteristics. The difference is due to an earlier onset of flow separation in the case of Teflon unlike superhydrophobic painted surface, and hence Teflon has a drag value which is same as Acrylic surface. This result is therefore well correlated to the bubble size result of Fig. 10. Cello tape and Acrylic surfaces follow the same trend at all angles of attack and Reynolds numbers.

Figure 11: Mean drag coefficient for different surfaces (S: superhydrophobic painted, W: Acrylic, C: Cello tape, T: Teflon) versus angle of attack, at (a) Re = 6765, (b) Re = 11700, (c) Re = 16800, (d) Re = 23000 and (e) Re = 30800. 25

The amount of reduction in mean drag value with respect to Acrylic surface is explicitly noted in order to quantify the benefit of coating a surface. There is 38% reduction in mean drag at 10o, and 40% reduction at 15o for high Reynolds numbers. The flow either remains attached or separation is delayed for superhydrophobic painted surface, which helps reduce its value of drag coefficient. The sudden drop in the slope of the drag curve for all surfaces at Re = 16800 and α = 10 o is due to the change in the flow behavior. The flow is attached to the surface and there is no formation of separation bubble on the top surface of the hydrofoil for Re ≥ 16800 for NACA 0015 hydrofoil. However, the superhydrophobic painted surface has lower mean drag compared to other surfaces for these Reynolds numbers.

3.7. Variation of Lift Coefficient The lift coefficient is calculated using the Kutta-Joukowski theorem (Eq. 2) and the results are plotted in Fig. 12. The mean lift coefficient is expected to be zero at 0o angle of attack because of symmetric hydrofoil; the measurements are in agreement with this expected value. Further mean lift coefficient is not varying much at lower angle of attack and lower Reynolds number. The variation is clearer as the Reynolds number increases and at angles of attack of 5o and 10o. The lift coefficient values are comparatively lower for Teflon and superhydrophobic painted surface at Re = 30800 and α = 15 o (Fig. 12e). It is found that the velocity values near the surface is comparatively higher for Teflon surface and superhydrophobic painted surface (Fig. 7a). Therefore, the shear layer strength is lower which results in the reduction of lift. Of all the surfaces, at 10o, the superhydrophobic painted shows the least mean lift coefficient with an exception at Re = 6765 (Fig. 12a) where it has the highest value as the flow is not separated. Teflon and superhydrophobic painted surfaces have almost similar values until 5o. The mean lift coefficient value for superhydrophobic painted surface with respect to Acrylic surface at Re = 30800 and α = 15o (Fig. 12e) is almost 36% higher. The mean lift coefficient value at α = 15o is higher for superhydrophobic painted surface compared to all other surfaces; which shows that the superhydrophobicity delays the stall. There is a reduction in lift at all other small angles of attack for superhydrophobic painted surface. 26

The temporal variation in instantaneous lift coefficient is shown in Fig. 13, in order to understand the effect of vortex formation and its slipping on the surface on the instantaneous value of lift coefficient. Figure 9 shows that the flow can be attached or separated over a surface. Therefore, two different cases are considered in Fig. 13: flow over superhydrophobic painted surface (blue solid curve) and separated flow over Acrylic surface (green dash curve), to understand the effect of flow attachment/ separation from the surface. Note that the instantaneous vorticity corresponding to the blue curve are already shown in Fig. 9; whereas the instantaneous streamlines and vorticity corresponding to Acrylic surface have not been presented.

Figure 12: Mean lift coefficient for different surfaces at different angles of attack and Reynolds numbers at (a) Re = 6765, (b) Re = 11700, (c) Re = 16800, (d) Re = 23000 and (e) Re = 30800. (S: superhydrophobic painted, W: Acrylic, C: Cello tape, T: Teflon).

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The flow is fully attached from flow time 1.4 s – 2.2 s for superhydrophobic painted surface and the fluctuation in instantaneous lift value is comparatively less in this time span. Interestingly, the instantaneous values of lift coefficient for the separated flow over both Acrylic and superhydrophobic painted surfaces are of the same order (Fig. 13). Evidently, the fluctuation in instantaneous lift values is more for separated flow than that for attached flow. The mean lift coefficient for superhydrophobic painted surface is higher than that of Acrylic surface and the corresponding time averaged streamline plots shown in Figs. 6c, 6d are in good qualitative agreement with the result. The variation in lift coefficient for separated flow is mainly due to vortex shedding. This result reveals that the separation increases the fluctuation in instantaneous lift. You and Moin (2007) pointed out that the reduction in r.m.s. lift is due to the reduction in base suction coefficient, and can be explained based on vortex shedding.

Figure 13: Instantaneous lift coefficient for different surfaces at angle of attack 15 o and Re = 30800. 3.8. Variation of gliding ratio Gliding ratio is defined as the ratio of mean lift coefficient to mean drag coefficient. Figure 14 shows that the gliding ratio is a non-monotonic function of angle of attack – with the highest 28

value at 10o angle of attack. In general, the value of gliding ratio increases with Reynolds number, over the range investigated. At lower angles of attack (0o and 5o), the gliding ratio is more for Acrylic and Cello tape surfaces at higher Reynolds numbers. That is, the benefit of employing a superhydrophobic painted surface is not apparent at lower angle of attack. For superhydrophobic painted surface, the gliding ratio is very high at 10o and 15o for all Reynolds numbers. There is approximately a 5 o shift in the stall angle (based on gliding ratio) as the hydrophobicity increases (Fig. 14e). The gliding ratio can improve by an increase in value of lift coefficient or a decrease in drag coefficient (or both). It is apparent from the results in the previous sections that comparatively small drag values at 10o makes the gliding ratio very high for superhydrophobic painted surface.

Figure 14: Variation of gliding ratio for different surfaces at different angles of attack and Reynolds numbers (a) Re = 6765, (b) Re = 11700, (c) Re = 16800, (d) Re = 23000 and (e) Re = 30800. (S: superhydrophobic painted, W: Acrylic, C: Cello tape, T: Teflon). 29

4. Discussion Two different aspects of flow around superhydrophobic painted surface is discussed in this section. The changes in the flow behavior due to slip effect is discussed in the first subsection. The variation of force coefficient with respect to hydrophobicity is discussed in the second subsection. 4.1. Slip effect on the flow behavior The effect of superhydrophobicity on the flow is seen at low Reynolds number and angle of attack of 10o where the laminar separation is found to be delayed (Fig. 7b). That is, superhydrophobicity helps to reduce the Reynolds number regime where flow separation occurs. Another advantage of superhydrophobic painted surface on hydrofoil is that it delays stall. Stall occurs due to flow separation and is delayed if the flow separation is delayed. The gliding ratio is found to be comparatively higher for superhydrophobic painted surface over a reasonably large parameter range especially for angles of attack 10o and 15o (Fig. 14). The difference in flow behavior is mainly due to slip on the surface which leads to a finite velocity at the surface (Lee et al. 2018). Such surfaces are also known for their self-cleaning mechanism in animals (fish scales) and plants (lotus leaves). Figs. 7b show that the velocity reaches almost 90% of the freestream value for the superhydrophobic painted surface, while the Acrylic surface is having almost 50% of the freestream velocity value at X= 1C and Y= 0.1C. This suggests that the boundary layer thickness is smaller for the superhydrophobic painted surface compared to other surfaces. The boundary layer thickness is associated with wall shear stress. Here, the wall shear stress apparently reduces because of slip on the surface and leads to a reduction in drag. The slip velocity on a superhydrophobic painted surface leads to a reduction in the strength of the shear layer. The vorticity in the shear layer, therefore takes longer to get saturated enough to shed vortices into the wake. Legendre et al. (2009) and Muralidhar et al. (2011) also observed that the intensity of vortcity reduces, the length of the shear layer shortens, and the vortex shedding frequency increases for a superhydrophobic circular cylinder. The results obtained in this study therefore show that the hydrodynamic efficiency can be increased and at the same time sustained for angles of attack 10o and 15o over the entire range of 30

Reynolds number studied in the present work by employing superhydrophobic painted surfaces. The slip induced by superhydrophobic painted surface can potentially have a huge impact on the design of miniature underwater vehicles. 4.2. Effect of slip on force coefficients Viscous component of drag reduces since the surface is a low shear region under slip condition. The viscous drag contributes more to the total drag since the pressure recovery in streamline body is very high at low angles of attack. But the pressure component becomes significant at higher angle of attack (α ≥ 15o). Slip on the surface tries to reduce the base suction pressure (You and Moin 2007; Kim et al. 2005) and also increases the vortex shedding frequency (Legendre et al. 2009; Muralidhar et al. 2011) for a circular cylinder. Muralidhar et al. (2011) further noted that the shed vortices get elongated in the streamwise direction. Form drag contributes the major part of the total drag in bluff bodies. Streamlined bodies at higher angles of attack will have both pressure and viscous components. In the present work, the viscous drag component will be less significant since the slip condition applies on the surface. Also a reduction in vortex strength is observed and the recirculation bubble is found to move closer to the body compared to Acrylic surface. The observations on the vorticity field suggest an increased vortex shedding frequency. The shedding frequency is however not calculated here due to insufficient temporal resolution of the PIV data. A reduction in pressure component of drag is also expected with superhydrophobic painted surface because of reduction in the strength of vortices formed on the suction side (and downstream end) of the hydrofoil.

The lift coefficient of hydrofoil at lower angles of attack mainly depends upon the pressure distribution around the hydrofoil. It is noticed that superhydrophobic painted surface has comparatively lower lift coefficient until 10o. This is because the flow remains attached and the strength of vortices is less and therefore the reduction in pressure on the suction surface is lesser here, leading to relatively small value of lift coefficient, which is consistent with the observation of Legendre et al. (2009). The maximum reduction in lift coefficient for superhydrophobic surface is almost 10% compared to Acrylic surface. The Teflon surface is seen to have the lowest

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lift coefficient until 10o. The superhydrophobic painted surface exhibits the highest lift at 15o amongst all surfaces for Re ≥ 11700 because of delay in flow separation. 5. Conclusions A particle image velocimetry based study of hydrofoils of different hydrophobocities is conducted in this work. The objective is to understand the effect of surface modification on the flow behavior around the hydrofoil and the ensuing values of lift and drag coefficients. The measurements are conducted on four different types of surfaces (Acrylic, Cello tape, Teflon and Superhydrophobic painted surface) at five angles (0o- 20o) of attack over a large range of Reynolds number (Re = 6500– 31000). A number of variables, including instantaneous and mean streamlines, vorticity, velocity, lift and drag coefficients, and gliding ratio are computed over this parameter range in order to glean information about the flow. The main observation noticed during this study is the highly unsteady separation of the flow when a superhydrophobic painted surface is used. The measurements reveal a reduced tendency for the flow to separate over the superhydrophobic painted surface and a reduction in the boundary layer thickness. The mean lift coefficient is found to reduce, and the same mechanism which leads to a reduction in mean drag also leads to a reduction in mean lift. The gliding ratio (ratio of lift to drag coefficients) is however better for superhydrophobic painted surface. The r.m.s. of lift coefficient is related to the formation and movement of vortices on the surface. The r.m.s. of lift coefficient of superhydrophobic painted surface is comparatively less than Acrylic surface since the flow is more or less attached until angle of attack of 15o. This study reveals that there is a range of angle of attack where the superhydrophobic painted surface performs better than a bare Acrylic surface. At very low angles of attack, the flow is attached for both bare and superhydrophobic painted surfaces. On the other hand, at very high angles of attack (α ≥ 20o), flow is separated and the hydrofoil behaves as a bluff-body. The present results are interesting because this understanding can pave the way for employing superhydrophobic painted surfaces in various applications. Most of the results presented here are not previously available. Measuring the integral momentum and slip lengths directly will aid in understanding the flow physics better, which will be attempted in a future work.

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Acknowledgement The water tunnel facility utilized in these measurements was funded from a project by the Naval Research Board. We would like to acknowledge the helpful comments from the anonymous reviewers, which helped to greatly improve the manuscript.

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Conflict of Interest The authors declare that there is no conflict of interest in publishing this work.

Highlights

- The role of hydrofoil surface on the ensuing flow is systematically studied - Superhydrophobicity helps to reduce the range of Reynolds number where flow separation occurs

- Up to 40% reduction in drag for superhydrophobic surface as compared to bare Acrylic surface - A reduction in the separation bubble size noted for superhydrophobic surface - Teflon coated surface behaves similar to the superhydrophobic surface at low angle of attack