Drag Reduction by Microvortexes in Transverse Microgrooves

Abstract

A transverse microgrooved surface was employed here to reduce the surface drag force by creating a slippage in bottom layer in turbulent boundary layer. A detailed simulation and experimental investigation on drag reduction by transverse microgrooves were given. The computational fluid dynamics simulation, using RNG k-ε turbulent model, showed that the vortexes were formed in the grooves and they were a main reason for the drag reduction. On the upside of the vortex, the revolving direction was consistent with the main flow, which decreased the flow shear stress by declining the velocity gradient. The experiments were carried out in a high-speed water tunnel with flow velocity varying from 17 to 19 m/s. The experimental results showed that the drag reduction was about 13%. Therefore, the computational and experimental results were cross-checked and consistent with each other to prove that the presented approach achieved effective drag reduction underwater.

1. Introduction

The drag is encountered in submerged vehicles or surface ship and pipeline transformation, which consists of pressure drag, wave making resistance, and skin friction drag. The turbulent flow shows randomness, which contains a coherent structure. The coherent structure is derived from the flow separation, which can induce the low pressure region. The low pressure induced by the vortex would contribute to the pressure drag [1]; for a moving body, the drag F_drag can be described as

F_{drag} = (p_{h} L_{h} - p_{l} L_{l}) + τ A,

(1)

where p_hL_h − p_lL_l and τA are the pressure drag and the skin friction drag of this body, respectively. p_h is the pressure of high pressure area; L_h is the area that the high pressure is acting upon due to the fact that the model in Figure 1 was simplified as a two-dimensional model and this area can be described as the height of this area when the simplified thickness was considered as 1; p_l is the pressure of low pressure area; L_l is the area that the low pressure is acting upon; τ is the shear viscous stress at the solid-liquid interface; A is the superficial area of the body.

Figure 1:

The drag of a body moving in liquid.

It is well known that the streamlined airfoil suffers from a lower drag than the object with other shapes when moving in liquid. According to (1), when the body moving in liquid was streamlined airfoil, the area of low pressure was remarkably reduced. Due to the fact that low pressure is a negative value (compared with the standard atmospheric pressure), the pressure drag (p_hL_h − p_lL_l) was reduced with the decreasing of the L_l. Although the streamlined shape increased the superficial area which induced the larger skin friction drag, the reduction of the pressure drag caused the declining of total drag. Dimples also caused local flow separation and triggered the shear layer instability along the separating shear layer, resulting in the generation of large turbulence intensity as shown in Figure 2 [2]. With this increased turbulence, the flow reattaches to the sphere surface with a high momentum near the wall and overcomes a strong adverse pressure gradient formed in the rear sphere surface. As a result, dimples delay the main separation and reduce drag significantly.

Figure 2:

Flow field and pressure distribution around a sphere. (a) Smooth surface and (b) dimpled surface.

Skin friction drag shares a very quotient in the total drag, even over 60% or 80% for the streamlined bodies and 100% for pipe transportation [3, 4]. Therefore, skin friction drag reduction is a key for drag reduction. While the reduction of pressure drag can contribute to the drag reduction, the declining of the skin friction (shear stress) also, even greater, achieves the drag reduction effect. The shear viscous stress τ is described as

τ = \frac{d u}{d y} μ,

(2)

where μ is the dynamic viscosity of fluid and du/dy is the velocity gradient. According to (2), it is essential to change the state of boundary layer to decrease the velocity gradient for an effective drag reduction rate.

Drag reduction is important for vehicles on or under water or in air to increase voyage and cruising speed and to decrease the consumption of energy, thermal damage, and serious noise. For underwater drag reduction, some methods appeared to influence the velocity gradient at or near wall, such as microstructures, traveling wave, polymer, microbubbles, and wall oscillation. Early in 1970s it has been found that the surface with riblets parallel to the streamwise direction could arrive at 8% drag reduction by Walsh [5]. The performance of riblets for viscous drag reduction has been proved in flight test. The aircraft (Airbus A320) covered with riblets film (manufactured by 3M company, USA) achieved drag reduction about 2% [6]. Bechert et al. [7] tested several kinds of riblets with different shapes and dimension and obtained a 5% skin friction drag reduction under a velocity of 1.3 m/s. In other experiments, Debisschop and Nieuwstadt [8] obtained a 13% drag reduction and Neumann and Dinkelacker [9] obtained 9% drag reduction of axial sample under 9 m/s. On the mechanics of drag reduction of riblets, Gallagher and Thomas [10] attributed the drag reduction to the increasing of thickness of the viscous sublayer; Choi and Orchard [11] indicated that the riblets delayed the turbulent transition; Bacher and Smith [12] and Walsh et al. [13] considered that a low-speed quiet flow was retained in the valley. Experiments by Wang et al. [4] showed that the thickness of the viscous sublayer, the region of buffer layer, and the integral constant C in the log-law of the riblet surface were greater than those of the smooth surface.

So far, some methods were suggested to control the structure of the turbulence boundary layer to decline the velocity gradient. In this paper, the method for skin friction drag reduction by microvortexes formed in transverse microgrooves on surfaces was proposed and confirmed by experimental measurements. Therefore, a detailed simulation is presented for viscous drag and pressure drag analysis when microvortexes exist in transverse grooves to determine possible key features and the mechanism of drag reduction.

2. Materials and Methods

2.1. Theory Analysis

According to (2), to achieve a lower skin friction drag, the velocity gradient must be reduced. In the near wall flow field, due to the different structures in different regions, the velocity profile in each region corresponds to its structure. The near wall flow field can be divided into three levels from the inside out under turbulent conditions [14]. In the bottom layer, owing to the influence of wall on the liquid, the laminar flow regime (laminar sublayer) stably exists. Therefore, the velocity profile can be described as [14]

u^{+} = y^{+},

(3)

where u⁺, a nondimensional number, is a function of flow velocity u, and y⁺, a nondimensional number, is a function of the distance from wall. The middle layer is a turbulent flow region, and the velocity profile can be described as [14]

u^{+} = 5.75 \log y^{+} + B,

(4)

where B is a value that depends on R₀ which is a function of Reynolds number R_x. R₀ can be described as [14]

R_{0} = {(84.5 \log R_{x} - 466)}^{2} .

(5)

The bottom laminar and the middle turbulent layer (turbulent sublayer) comprise the boundary layer, while there is a buffer layer between the two flow regimes. Beyond the boundary, the flow regime is also turbulent flow, but the velocity profile is different from the internal turbulent flow [14]:

u^{+} = 10.4 \log y^{+} - D,

(6)

where D is a value that depends on R₀ which is a function of Reynolds number R_x. The thickness of the bottom laminar layer can be confirmed by the intersection of (3) and (4) [14]:

y^{+} = \frac{1}{40} (\sqrt{R_{0}} + 341) .

(7)

According to (4) and (5), the thickness of the boundary layer can be achieved [14]:

\log y^{+} = 0.837 \log R_{0} - 0.372 .

(8)

As shown in Figure 3, the flow field can be divided into laminar sublayer, buffer layer, turbulent sublayer, and turbulent layer. When the velocity profile was affected, the skin friction drag was changed. In previous investigations, the turbulent sublayer was usually selected to enlarge the thickness of the boundary layer. Furthermore, the velocity gradient was declined. However, when the structure in the turbulent sublayer was modified, the extra energy was essential to enhance the thickness of the boundary layer, due to energy dissipation in turbulent flow. Therefore, the drag reduction by modifying the structure of the turbulent sublayer was limited. Here, we hope to change the velocity profile in the laminar layer to affect the structure of the turbulent boundary layer, which can achieve an effective drag reduction.

Figure 3:

Velocity profile on a smooth surface in flowing water.

2.2. The Design of Structures

To reduce the velocity gradient in bottom laminar layer, the slippage at the solid-liquid interface is an excellent method. For the structured surface, when liquid perpendicularly flowed over a groove, the microvortex was formed as shown in Figure 4. On the upside of the vortex, the revolving direction was consistent with the main flow, which decreased the flow shear rate, resulting in viscous drag reduction as described in (1). Therefore, the skin friction drag should be reduced by the microvortexes formed in transverse grooves of the surface. Additionally, the scale of flow regime affected by this grooved structure should be less than the thickness of the bottom laminar layer to modify the flow field in the laminar sublayer. Here, these grooved structures were designed in the scale of 10 μm within the surface (below the level of the surface, reducing the influence on the flow field).

Figure 4:

Microvortex in a transverse groove.

2.3. Numerical Simulation

The numerical simulation is of great help to understand the characteristics of flow field. For some complex problems, it is difficult to present the analytical solutions and numerical simulation is a kind of effective method [15, 16]. Here, the numerical simulation was chosen to study the boundary layer structure when liquid flows over the transverse microgrooved surface. In the computational fluid dynamics simulation, based on the geometric features of the transverse grooved structures, a three-dimensional problem is simplified into a two-dimensional one. One of a series of periodic grooves was selected to be object of this investigation as shown in Figure 5, but the periodic boundary condition was set to be close to the actual situation. In this model, the transverse microgrooved surface and smooth surface were located at up and down walls of a channel, respectively, in which the error induced by liquid flowing and the amount of calculation were reduced as much as possible.

Figure 5:

Demonstration of computational area with depth of groove h and height of channel H.

In the numerical simulation, the geometry of the transverse microgrooved surface could be simplified as shown in Figure 5. The scale of this structure was designed and used to guide the experiments. Here, the height of the microgroove was 15 μm and the slope angle of this structure was 40° on both sides of the microgroove. The distance between two neighbouring microgrooves (including a microgroove) was 75 μm. The fluid medium was set as water with the density of 998.2 kg/m³ and the viscosity of 0.001003 Pa·s. The grid spacing increased from the walls by aspect ratio of less than 1.1 to get a structured mesh. A renormalized group (RNG) k-ε model, which had an additional term in its ε equation that significantly improves the accuracy [15], was used for turbulence modeling [15, 16]. An implicit solution scheme was used in combination with an algebraic multigrid method to achieve faster convergence. The second-order upwind scheme was used in the discretization scheme for all equations to achieve higher accuracy in results. Velocity-pressure coupling was established by pressure-velocity correlation using a SIMPLE (Semi-Implicit Method for Pressure-Linked Equations) algorithm. Residuals were continuously monitored for continuity, x-velocity, y-velocity, z-velocity, k, and ε. Convergence of the solution was assumed when the values of all residuals went below 10⁻⁶. No-slip condition was given at wall boundaries. Velocity inlet (flow velocity 17 m/s, 18 m/s, and 19 m/s) and free stream turbulent intensity of 2.3% (corresponding to the experimental condition) were defined at inlet boundary and pressure outlet. Zero gauge pressure was defined at outlet boundary and others were set as default.

To ensure the accuracy of the calculation, the height of channel Hwas set to be no less than 10 times of the depth of grooves. Not only that, to confirm that our results are independent of the choice of mesh size, the mesh size was optimized until the results of calculation did not change with the increasing of mesh density. Additionally, the wall boundary conditions were set to be no-slip boundary conditions.

2.4. Experiments

Samples were cylindrical pipes with a length of 325 mm and a diameter of 39 mm. Sample #1 was a common pipe, that is, a slippery one. On the surface of sample #2, discontinuous wavy grooves were manufactured. The roughness of samples #1 and #2 excluding wavy grooves were the same and were about 0.6 μm. According to the scale of the structure in numerical simulation, as shown in Figure 6, the microgroove has a cross-section of a V-shape with the height of H, the slope angle in front of α, and the slope angle in rear of β. The width of the microgroove (W) can be achieved by

W = H (\frac{1}{\tan α} + \frac{1}{\tan β}) .

(9)

Here, the depth of the microgroove of sample #2 was about 15 μm, the slope angle in front was about 40°, the slope angle in rear was also 40°, and the width of the microgroove was about 30 μm. The density of the microgrooves could be described as the ratio of the width to the distance between two neighboring microgrooves; here this ratio is about 1: 2.5.

Figure 6:

Surface topography measurement of microgrooved surface. (a) Top view of the microgrooves and (b) the section curve of the line in (a).

The experiment was done with a high-speed water tunnel, which is a closed circulation system, as shown in Figure 7(a) [17, 18]. Water was driven by the pump and firstly flowed through the antirevolving part, which primarily prevented the revolving of the flow. The disturbances of flow perpendicular to streamwise direction were eliminated by the honeycomb. Water was accelerated by the contraction with a quintic curve. In the four corners, guide vanes were employed to decrease the flow separation and increase the uniformity. The purpose of all the methods was to improve the flow quality and prevent the flow separation.

Figure 7:

Schematic diagram of the water tunnel for the skin friction drag test. (a) Flow circulation system and (b) test section.

The test section of the water tunnel can measure the friction force of the sample directly [18] as shown in Figure 7(b). The sample was located at the middle of the tunnel and was supported through the center axle. Through the slipping pins, the friction force was transferred to the force sensor. The head and tail of the model were fixed on the center support. There were two small gaps between the sample and its front and back accessories [17, 18]. Therefore, the pressure force would transfer to the support and only the friction force was measured by the force sensor.

The fluid medium was tap water and the temperature was about 20°C (with a fluctuation of less than 2°C during test). The temperature shift of sensor was less than 1% in the range of 20 ± 2°C. In order to avoid cavitation of the water in the tunnel, the pressure at the inlet of the contraction section was maintained more than 3 atm. The signal of the force sensor was magnified by a strain gauge and the voltage was gained by a computer, which was proportional to the drag force. The sensor outputs were not affected by external circumstances, which ensures that the sensor outputs were only the response to force [17, 18]. A calibration was used to determine the relationship between the electrical output corresponding to the deflection and the sensor stress. The sensor stress (F) was linearly related to electrical output (voltage, E_v): F = E_v/0.2059; thus the drag could be achieved by electrical output [17, 18].

The data acquisition system collected sensor readout at 30 hertz for 100 seconds and the average of all data was considered as a tested result. In the calibration of drag test system, the method of multiple tests of smooth samples (10 samples) was used to check the reliability of the test result. The tested uncertainty level of smooth samples with the same surface roughness (Ra < 0.6 μm) was less than 3%, which demonstrated that the tested results of this drag test system were fairly reproducible and stable [17, 18].

3. Results and Discussion

When liquid (water) flows over a transverse microgrooved surface, the structure of flow field is at or near wall. The numerical computing results show that a microvertex also forms in microgrooves in flowing water. On the upside of the vortex formed in transverse microgrooves, the revolving direction was consistent with the main flow. Therefore, the velocity gradient near the wall can be reduced, which decreased the flow shear rate, resulting in viscous drag reduction compared with a smooth surface as shown in Figure 8(b). The contour of pressure in Figure 8(c) indicates that the pressure in microgroove will be changed by these microstructures in flowing water, which induced the increase of extra undesired pressure drag coefficient. Because of the existence of a microvortex, the wall shear stress can be reduced. Furthermore, the viscous drag can also be reduced by transverse microgrooves on a microgrooved surface. However, an extra undesired pressure drag is induced, resulting in increasing of the skin friction drag.

Figure 8:

The state of flow field is near the transverse microgrooved surface. (a) Streamline in microgroove, (b) contour of velocity, and (c) contour of pressure.

The decreasing of velocity gradient near the wall is beneficial to achieve an effective drag reduction rate, while extra desired pressure drag is a key negative contributor to the effect of drag reduction. In the computation of fluid dynamic, the flow conditions near the wall surface were studied in detail.

For the smooth surface, the flow field characteristic in the position of solid-liquid interface corresponded to a nonslip boundary condition which is set as the boundary conditions at all the walls. For the transverse microgrooved surface, the velocity profile in the flow direction at various altitudes indicates that there is a remarkable slippage at the position A in the insert of Figure 9, because the microvortex existed in microgrooves. There were distinctions between the velocity profiles of the smooth surface and the transverse microgrooved surface. After a simple calculation, there is a more than 30% velocity-slip at “solid-liquid interface” and the slip length is approximately 4 μm. This result shows that there is a relative velocity at the original solid wall replaced by water due to the existence of a vortex.

Figure 9:

Profile of velocity (denoted by ■) at the center of transverse microgroove as shown in position A in the insert.

The analysis of flow conditions near the wall surface explains that the viscous drag can be reduced, because of the decreasing of velocity gradient induced by the vortex. However, a pressure drag is induced when water flows over this transverse microgrooved surface, resulting in an increase of the skin friction drag. Considering the pressure drag induced by the structure, the total drag coefficient was studied by numerical simulation. To compare with the result, the total drag coefficient was also investigated.

The results in Figure 10 give us the detailed information for the drag coefficient of both microgrooved surface and smooth surface. Extra pressure drag coefficient appeared when water flowed over the microgrooved surface at a speed range from 17 to 19 m/s, but under the same conditions there was no pressure drag on the smooth surface. Though the extra pressure drag coefficient existed, the viscous drag coefficient decreased significantly, resulting in that the total coefficient is less than that of smooth surface at this speed. An effective drag reduction rate was achieved by means of the result of contrast calculation as follows:

R % = \frac{C_{d s} - C_{d t}}{C_{d s}} \times 100 %,

(10)

where R is the drag reduction rate, C_ds is the total drag coefficient of smooth surface, and C_dt is the total drag coefficient of transverse microgrooved surface. According to the drag coefficient calculated by numerical simulation, this proposed structured surface can achieve an effective drag reduction rate of about 13% in water flowing with the speed of 17–19 m/s.

Figure 10:

Drag and drag reduction rate calculated by using a comparative approach.

According to the results of simulation, the transverse microgrooved surface could achieve an effective drag reduction rate and the mechanism of drag reduction can be attributed to the formation of a vortex. To explain the points further, experiments were conducted in a water tunnel to investigate the effect of this microgrooved surface. The experiments were finished in a high-speed water tunnel which is shown in Figure 7. The experimental drag reduction rate was calculated by the means of the following comparison:

R_{\exp} % = \frac{F_{s} - F_{g}}{F_{s}} \times 100 %,

(11)

where R_exp is the experimental drag reduction rate, F_s is the skin friction drag of smooth surface (sample #1), and F_g is the skin friction drag of the transverse microgrooved surface (sample #2). The experimental results indicate that the underwater drag reduction rate of the transverse microgrooved surface was 13.33%, 13.28%, and 13.17% at the flow velocity of 17 m/s, 18 m/s, and 19 m/s, respectively. In the numerical simulation, the underwater drag reduction rate was 14.01%, 11.89%, and 12.78% at the flow velocity of 17 m/s, 18 m/s, and 19 m/s, respectively. According to these results, the experiment results were in good agreement with those of the calculations and they showed that the skin friction drag reduction was about 13% in water when the microgrooves were optimized.

4. Conclusions

A transverse microgrooved surface was employed to reduce the surface drag in the bottom laminar layer regime. A detailed simulation and experimental investigation on drag reduction by transverse microgrooves were given. In the experiment, a high-speed water tunnel with flow velocity varying from 17 to 19 m/s was employed. The experiment results showed that the drag reduction was about 13% at the test flow speed. From the computational fluid dynamics simulation, vortexes could be formed in the microgrooves, and on the upside of the vortex the revolving direction was consistent with the main flow, which induced the flow shear rate reduction. However, the simulation also showed that a pressure drag could appear by the waves. Therefore, the drag reduction in the experiment should be attributed to the fact that the viscous drag reduction was greater than the pressure drag enhancement. To sum up, the computational simulation qualitatively explained the experimental results. Because of the complexity of flow, the optimal shape and dimension of the wavy wall would change with the flow conditions which include the fluid medium, velocity, and object shape. More researches should be done for different conditions in the future.

Conflict of Interests

The authors declare that there is no conflict of interests regarding the publication of this paper.

Footnotes

Acknowledgment

This work was supported by the National Natural Science Foundation of China (Grant nos. 51375253, 51021064, and 51105223).

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