Passive separation control of shortfin mako shark skin in a turbulent boundary layer

Highlights

• Passive mechanism to control the flow.

• Shark skin scales are able to eliminate turbulent flow separation.

• Shark scales bristle to inhibit reversing flow.

• Effect of shark skin scales on turbulent boundary layer separation.

Abstract

This experimental investigation discusses the effectiveness of shortfin mako shark skin to passively control turbulent boundary layer separation. Experiments were conducted in a water tunnel facility with the shark skin specimens mounted on a smooth flat plate subjected to an adverse pressure gradient. The two skin specimens have shark scales with different sizes, shapes, and bristling angles. The flank region scales (B2) are slender, tall, and can bristle at 50°, while the scales in the region between flank and dorsal fin (B1) are wide, short, and can bristle at 30°. The adverse pressure gradient on the plate was generated by a rotating cylinder. DPIV measurements indicate that unpainted scales B2 can fully control or delay boundary layer separation and reduce the fraction of time the flow is reversed. The bristling of the scales caused fluctuation in the skin friction curve and the single spike intensity of the normal stress very close to the wall. These capabilities are directly related to the scale bristling angle. In contrast, the low bristling angle of the scales from region B1 did not impede the reversing flow, and therefore separation was enhanced. The increase in Reynold’s stress fluctuations away from the wall indicated that the separation region increased in size due to vortex structures further from the wall. Once the bristling mechanism of the B2 scales was eliminated by painting over the skin, the scales functioned as a rough surface but still promoted separation delay. In addition, the streamwise Reynolds stress profile for the flow over the painted scales measured after separation occurred, along with the high intensity of the normal stress near the surface are both characteristics of a flow over a rough surface. In summary, the shark skin surface showed an ability to both delay and increase flow separation depending on the capabilities of the scale bristling to inhibit reversing flow.

Introduction

Shark scales have been studied over the years to aid in the development of flow control mechanisms and to understand their biophysical purpose. Previous investigations primarily focused on the role of the riblet structures on top of the scales as a mechanism to reduce skin-friction drag [1], [2], [3], [4], [5], [6], [7], [8], [9], [10], [11], [12], [13], [14], [15], [16], [17], [18], [19], [20], [21], [22]. These studies established that the riblets (defined as ridges aligned in the flow streamwise direction) reduce the skin-friction drag and that the plausible mechanism for reducing the momentum transfer and shear stress involves hampering the turbulence fluctuations of the cross-flow near the wall [9]. In addition to the proven skin-friction drag reductions in laboratory experiments, riblets have also been shown beneficial in real-world applications [9], [22].

More recently, research focus has been directed to the potential of shark scales to interact dynamically with the flow to prevent flow separation [2], [8], [10], [12], [13], [15]. This research is driven by the observations that the bristling capability of shark scales varies over different regions of the body due to different flow conditions. As sharks continuously move around, the flow conditions over different regions over the body vary with time, especially when executing sharp maneuvers. This high agility gives more importance to controlling flow separation than reducing skin-friction drag. The scales on shark skin, especially on the shortfin Mako shark, which is considered the fastest shark in the ocean, can be manually bristled on dead specimens to large angles (Fig. 1) and will return to the original position upon release [23].

The scales on the shark skin, known as dermal denticles, are aligned with the flow direction and are composed of a riblet covered crown on a neck and an embedded base that can pivot in the dermis [23], [24]. Scale morphology differs among shark species, likely depending on the swimming speed [23]. The size and shape of the scales also vary over different regions of the shark body suggesting their relationship to flow control [1], [8], [23], [24]. In addition to their flow control purposes, the denticles serve as body armor to prevent biofouling [1], [2], [7], [23].

A detailed study examined the scale morphology and flexibility [23] for three species of fast sharks. It was found that the most flexible scales are on the Mako shark at the flank region (region B2 in Fig. 2). Scales in region B2 can be bristled manually to over 50° above the dermal skin and rest at around 45° when released (Fig. 1). B2 scales have shorter bases than scales in region B1, and a higher bristled angle (Figs. 3, 4). Scales from the B1 region were selected because they are subjected to approximately the same pressure gradient but have less flexibility. When the scales are at rest, tips of scales from one row overlap the base of the following row [23]. The flank region is subjected to high curvature as the body undulates during swimming making it the most prone region to flow separation. Flow separation is also promoted in this region as the pressure increases from the gills (point of minimum static pressure) to the tail due to the decreasing girth of the shark. The correspondence of the region of the most flexible scales with the region most prone to flow separation introduces the hypothesis that the scales act as a flow separation control mechanism.

One hypothesis previously proposed is that the scales act as vortex generators to increase the momentum transfer between the high momentum fluid in the free stream and the low momentum fluid near the wall [10]. The enhanced momentum exchange leads to an increased flow velocity near the wall making the boundary layer capable of tolerating higher pressure gradients and less prone to flow separation [25]. But this hypothesis requires the scales to be actuated upstream of the region of separation in order for them to protrude up into the flow and generate streamwise vortices downstream that enhance flow mixing [3]. However, a similar momentum exchange can also be achieved by the vortices forming inside the cavities created by the bristling of the scales [13]. As the scales bristle by any external forces [24], they create transverse cavities that reach 0.2 mm in size when the scales bristle at 48° [13], [14], [15].

Our primary hypothesis of the flow separation control mechanism of the shark skin scales is similar to the bird feathers hypothesis on controlling flow separation [9] with some differences. This hypothesis admits that the reverse flow developing upon the start of separation causes the light feathers to rise and prevent the spreading of flow separation towards the leading edge [9]. This hypothesis was the foundation for using movable flaps on the upper surface of an airfoil where the reverse flow actuates the movable flap as the flow starts to separate. The high-speed flow above the separation wake pushes the flap back to a lower elevation. The slightly elevated flap changes the effective shape of the airfoil and creates a lower effective angle of attack. This leads to an adjusted pressure distribution on the airfoil with a reduced tendency to separate allowing for an attached flow at higher angles of attack; thus, higher lift [10].

We hypothesize that as flow separation begins to develop at the wall within the boundary layer, the reversing flow reaches a sufficient magnitude to cause the scales to passively bristle, which then eventually get pushed back down by the higher momentum flow located above the wall. The amount of the bristle and recoil of the scales depends on flow parameters, such as the reverse flow magnitude and the boundary layer edge velocity which are both functions of the pressure gradient and depend on the flexibility of the scales. Both the pressure gradient and the flexibility of the scales are functions of the location on the shark body. The scales fully return to their original location (i.e., un-bristled) which results in flow separation at the original angle of attack. This scenario produces cyclic separation/reattachment even in steady flow conditions. Nonetheless, cyclic behavior is expected, which suggests a relationship between the time scale of the unsteady nature of steady turbulent flow separation [26] and the dampening rate of the scales.

There is also a relationship between the size of the low speed streaks in turbulent boundary layers and the width of the scales. For a shark swimming at 10 m.s⁻¹, the Reynolds number at a flank location of × = 1 m from the nose is approximately 1 × 10⁷. The estimated turbulent boundary layer thickness at this location is 1.6 cm, and the friction velocity is estimated for a turbulent boundary layer with zero pressure gradient as 0.37 m.s⁻¹. The scales in the flank region bristle to higher angles and protrude to 160 μm which is 1% of the boundary layer corresponding to y⁺ = 59. These values place the bristled scales into the log-law region.

Low speed streaks form between pairs of stretched counter-rotating vortices [17], [18], [27], [28], [29] with an average spanwise spacing of greater than 100 viscous length scales (u_τ/ν) for a flow with a strong adverse pressure gradient [28], [30]. The estimated width of the low speed streaks on a shark swimming at 20 m.s⁻¹ would be approximately 139.6 μm [31], which corresponds to the width of the scales (189 μm in B1 and 167 μm in B2). The velocity range to induce bristling is between 0.77 and 3.1 m.s⁻¹ [31], which corresponds to a range of 8–30% of a typical shark swimming speed of 10 m.s⁻¹. This lower end of this range corresponds to the backflow velocities of 0.1U_o near turbulent separation [32], [33] while the upper end corresponds to the reversing flow speeds of 0.2–0.3U_o found in the low-speed streaks of a turbulent flow over a flat plate [32]. The relationship between the time scale of the flow separation time and the dampening rate of the scales and the relationship between the width of the low speed streaks and the width of the scales will be discussed in subsequent papers.

The purpose of the present study is to examine the effects of the shark-skin scale flexibility on turbulent flow separation and its control that has been previously reported. This experimental investigation involved DPIV measurements of the flow over a flat plate covered with shark skin specimens with imposed adverse pressure gradient. Specifically, we used specimens from the flank region of the shark (most flexible scales (B2)), from a region with less flexible scales (B1), and painted scales to maintain surface roughness but inhibit the bristling mechanism. These additional experiments have most importantly further corroborated the ability of shark skin to act as a separation control mechanism while also permitting a finer resolution of the flow field with a more in-depth analysis of the Reynolds stresses and skin friction coefficient. In addition, results were obtained over a skin sample where flow control was not observed and an explanation is offered as to why this was not the case given the fact that the skin is being tested at speeds far below that obtainable by a swimming shark. Finally, samples were painted over for cases where the scales showed evidence of separation control to further understand the bristling effect on the flow control mechanism.