Wake induced by an undulating elephant seal whisker
Abstract
Certain species of seals are able to faithfully detect minute disturbances in ambient water solely using their whiskers, which is attributed to the whiskers’ undulating three-dimensional (3D) morphology. While previous studies have examined effects of key morphology parameters on the wake using scaled-up whisker models, it is unclear how the wake behaves when induced by a real undulating seal whisker. Real seal whiskers usually have a diameter of about one millimeter and present variation in size and bending curvature along the length, which are not being considered in designing scaled-up whisker-like models. In addition, how the whisker orientation affects the induced wake and vortex shedding needs to be clarified. This work examines the wake flow characteristics generated by a real elephant seal whisker (of undulating morphology) and a California sea lion whisker (of smooth morphology) in laboratory water channels at Reynolds numbers of 110 and 390, using snapshot particle image velocimetry (PIV) and time-resolved PIV methods. Results indicate that the reversed flow region is remarkably reduced and turbulence intensities are greatly suppressed behind the undulating whisker compared to that of the smooth whisker, when the major axis of the whisker cross-section is parallel with the incoming flow (i.e., the angle of attack or AOA is 0\(^{\circ }\)). While the vortex shedding frequency is reduced for both the undulating and smooth whiskers, the power spectral density is substantially increased at an \(\mathrm{AOA} = 90^{\circ }\) in comparison to \(\mathrm{AOA} = 0^{\circ }\). Regardless of the AOA, the power spectral density is approximately 40% lower in the wake of the undulating whisker than that of the smooth whisker, indicating the favorable hydrodynamic feature of the undulating whisker. The extraordinary hydrodynamic traits of undulating seal whiskers is promising for renovating aero-propulsion flow components and designing high-sensitivity underwater flow sensors.
Graphical abstract
Keywords
Seal whisker Vortex shedding Vortex-induced vibration (VIV) Biomimicry Whisker-inspired applications1 Introduction
Seals with whiskers (vibrissae) of undulating morphology, which are the majority of true seals (Phocids), can trace even minute disturbance caused by prey fish in the ambient flow using only sensory input from their whiskers (Dehnhardt and Kaminski 1995; James and Dykes 1978; Renouf and Gaborko 1982). The superior sensing capability of harbor seal whiskers is attributed to the suppression or augmentation of vortex induced vibration (VIV), generated by bluff-bodies in air or water flow paths. In particular, the capability of seal whiskers to suppress the VIV and reduce drag is of great interest. Mimicking the beaded whisker morphology can be adopted as a passive flow control strategy in broad spectra of engineering applications, including structures in consistent flow paths such as wind turbine towers, light posts, high-rise buildings, sensor mounting supports on aircraft frames, and offshore oil drilling rigs. Research efforts have been made to design whisker-like high-sensitivity flow sensors (Beem 2015) and to modify the geometry of gas-turbine blades for enhanced aerodynamic performance in off-design conditions (Shyam et al. 2015). Applications of biomimetic flow control in engineered propeller have also been considered (Fish et al. 2008).
While experiments have been conducted with seals to understand how their whiskers function in a controlled environment, there are only limited studies that directly measure the wake flow generated by real whisker samples. Hanke et al. (2010) and Witte et al. (2012) reported experimental results of flow in a very small region adjacent to a real whisker using a micro-particle imaging velocimetry (\(\mu\)PIV). The work relied on detailed numerical simulations to demonstrate the wake hydrodynamics, such as drag and lift coefficients and vortex shedding. Murphy (2013) measured a cantilever-mounted whisker’s shaft vibration by laser vibrometry; no wake flow information was reported. While it is a bit surprising that no distinct difference in vibration frequency and amplitude is found for the undulating and smooth whiskers, the work revealed the noticeable effects of the angle of attack (AOA) on whisker vibration frequency and amplitude. Their recent follow-up in-situ experiment revealed a broader range of the whisker vibration, frequencies of 100–300 Hz, of living seals while swimming. The vibrations of seal whiskers may provide information about hydrodynamic events and enable sophisticated wake-tracking abilities of these animals (Murphy et al. 2017).
Limited studies about the wake flow around a real whisker have been conducted. Challenges may arise owing to variations related to biology species and the small physical size, approximately 0.5–1 mm, of the nominal diameter of the whisker. Research also showed that the bio-mechanics characteristics of seal whiskers may change after being removed from living seals (Hans et al. 2014). Instead, by employing scaled-up whisker-like rigid models, extensive experimental research has been done to examine the effects of key whisker morphology parameters (Wang and Liu 2016). This line of research is well aligned with the passive flow control using modified surface geometry of cylindrical cylinders or wavy cylinders (Lin et al. 2016; Zhang et al. 2005). The ability of modified geometries to suppress vortex-induced vibrations and reduce the drag forces acting upon them has been the central subject of various experimental and numerical studies (Morrison et al. 2016; Kim and Yoon 2017; Lin et al. 2016; Wang and Liu 2016). The flow properties of these modified cylinder geometries, along with the resulting forces, are generally comparable to those observed for the undulating seal whiskers (Morrison et al. 2016).
Measurements of the vibration forces acting on the whisker in a uniform flow by Miersch et al. (2011) show that self-induced vibration by a vortex street is about ten times lower for a harbor seal whisker. Recognizing that current flows can vary in direction with respect to the whisker, the AOA could be a critical factor when adopting the whisker-like morphology parameters. Unfortunately the effect of the AOA has not been extensively studied for the wake flow induced by a whisker. Miersch et al. (2011) tested the whisker vibration at three typical angles of attack (\(\mathrm{AOA} = 0^{\circ }\), \(45^{\circ }\) and \(90^{\circ }\)) without providing wake flow information. Kim and Yoon (2017) applied numerical simulation to analyze instantaneous 3-D vortex structures, drag and lift coefficients, as well as the vortex shedding at the AOA range of \(0^{\circ }\)–\(90 ^{\circ }\) for a Reynolds number of 500. To our best knowledge, no experimental studies have been conducted to understand the interaction of the vortex shedding and the coupled vibration.
This study aims to characterize the wake flow and the vortex shedding induced by a real undulating seal whisker in well-controlled water channels. Two different real seal whiskers are used: one is the elephant seal whisker with typical undulating morphology and the other is a similar-size California sea lion whisker of smooth morphology. We first described the PIV measurements of the wake flow induced by real undulating and smooth whiskers. In particular, the challenges of locating the light-sheet at desired planes and handling the unique bending curvature of the whisker are discussed (Sect. 2). Then we showed flow statistics of the wake induced by the undulating and the smooth whiskers in two orthogonal planes at an \(\mathrm{AOA} = 0^{\circ }\) (Sect. 3). We further evaluated the strength and frequency of the vortex shedding behavior using the high-speed PIV data at \(\mathrm{AOA} = 0^{\circ }\) and \(90^{\circ }\), which revealed the significant effect that the flow direction has on the vortex shedding (Sect. 3). The contribution is primarily twofold: (1) This work provided a detailed characterization of the wake flow and vortex shedding induced by single isolated real undulating and smooth whiskers, which is different from related studies which used scaled-up whisker-like models that commonly do not allow a full capture of the whisker morphology. The observed wake flow statistics and vortex shedding are expected to well reflect what occurs in nature. (2) The effects of the AOA on vortex shedding are illustrated between the undulating and smooth whiskers. The finding reveals a distinctly lower strength of the vortex shedding by the undulating whisker compared to the smooth whisker, consistent with statistics of wake flow.
2 Experimental setup and measurement methods
2.1 Laboratory water channels
Two water channels of similar flow quality are employed in this study, Fig. 2. The water channel at Cleveland State University (CSU) has a test section of 0.14 m (W)\(\times\) 0.20 m (H) \(\times\) 0.61 m (L). The flow is conditioned by six one-inch thick honeycombs spaced one-inch apart with 6.35 mm openings, 0.2 m upstream from the test section. Another water channel, at the Biofluid and Biomimic Research Center (BBRC) of Pohang University of Science and Technology (POSTECH) in Pohang, South Korea, has a test section of 0.30 m (W) \(\times\) 0.25 m (H) \(\times\) 1.2 m (L). The flow properties in the test sections of both water channels were characterized using PIV data prior to studying the whisker wake flow. In the CSU water channel, the free-stream velocity, \(U_0\), was constant at 0.12 m/s, yielding the Reynolds number of about 110 (based on \(U_0\) and the whiskers hydraulic diameter \(D_h\) defined in Eq. 1). In the POSTECH water channel the free-stream velocity was set at a \(U_0\) of 0.49 m/s, yielding the Reynolds number of about 390. Depending on the seals swimming speed and the whiskers hydraulic diameter, the Reynolds number is usually in the order of 10\(^2\) to 10\(^{3}\) (Wang and Liu 2016). As the seal engages active hunting, its swimming speed reaches the order of 1,m/s (James and Dykes 1978). The present two Reynolds numbers are determined based on the capacity of flow facilities but still within the reasonable seals’ swimming speed range (0.15–0.5 m/s used in Miersch et al. 2011; Witte et al. 2012 and Murphy et al. 2017).
It is also noted that, both water channels generate a uniform flow in the test section, where the real whisker is mounted for testing. The boundary-layer thickness on the smooth bottom and side walls is estimated to be 1–1.5 cm (less than 5% of the channel depth) at the half length downstream of the inlet, for a fully-developed boundary layer. The streamwise turbulence intensity in both water channels is at a similar level of 3–5%.
2.2 Real seal whiskers
The whisker samples are provided by the Marine Mammal Center, and previously used by Rinehart et al. (2017). The key parameters of an elephant seal whisker (of undulating morphology) and a California sea lion whisker (of smooth morphology) are listed in Table 1. It is noted that the angle of incidence \(\alpha\) and \(\beta\), of elliptical cross-sections along the whisker length are not measured for the specific whiskers. However, they are assumed to fall into the range of \(-15^{\circ }\) to \(15^{\circ }\) with a higher probability of being between \(-5^{\circ }\) and \(5^{\circ }\) (Rinehart et al. 2017).
Morphology parameters of the elephant seal whisker (ES) and the Californian sea lion whisker (CSL)
Parameters | 2a | 2b | 2k | 2l | \(D_{h}\) | \(D_{h,\mathrm{peak}}\) | \(D_{h,\mathrm{trough}}\) | a / b | k / l |
---|---|---|---|---|---|---|---|---|---|
mm | mm | mm | mm | mm | mm | mm | |||
ES | 0.978 | 0.521 | 0.826 | 0.495 | – | 0.650 | 0.601 | 1.88 | 1.67 |
CSL | 0.991 | 0.686 | – | – | 0.797 | – | – | 1.44 | – |
ES (mean) | 1.233 | 0.583 | 1.099 | 0.642 | 0.890 | – | – | 2.12 | 1.71 |
2.3 Particle image velocimetry (PIV) measurements
Wake behind the real whiskers is measured by a two-dimensional two-component (2D2C) snap-shot PIV and a high-speed PIV system (see Fig. 2b). The former allows us to acquire converged turbulence statistics and the latter enables us to capture vortex shedding behavior induced by a seal whisker with sufficient temporal resolution.
The 2D2C snap-shot PIV system (LaVision GmbH) was used to measure random instantaneous velocity fields and evaluate the turbulence statistics. A laser light sheet was formed from a laser beam of an Evergreen dual-pulsed ND:Yag laser at 15 Hz and carefully aligned to the desired area of interest. The water was seeded with hollow glass spheres of 10 \(\upmu\)m in diameter. The particle images were captured with a Pro-Imager SX 5MP CCD camera (of 2456 pixels \(\times\) 2058 pixels) fitted with a Nikon AF Micro-Nikkor 60 mm lens. A total of 1200 image pairs were captured in each measurement plane for both whiskers. Calibration of the 2D2C PIV measurements was conducted by taking multiple images of a scale in the center of the field of view (FOV). The FOV is 35.38 mm by 12.98 mm in the horizontal planes and 79.85 mm by 66.91 mm in the vertical plane in the CSU water channel. The conversion factor of 69.41 pixels/mm (for the horizonal planes) and 30.76 pixels/mm (for the vertical plane) is used, respectively, to transform the data from image plane to the physical coordinates. The FOV covers 25–30 \(D_h\) downstream of the whisker in the horizontal planes and 60–70 \(D_h\) in the vertical central plane.
Properly aligning the light sheet with a real whisker sample is critical to get data at the desired measurement planes and interpret the results faithfully. Due to the real whiskers having a natural bending curvature, challenges emerge when aligning the laser light sheet to the whisker in the vertical central plane. The whisker was first attached to a 1.58 mm diameter rigid rod and then mounted on a thin plate at the bottom of the water channel. The coordination of the optics tube, laser mounting mechanism, and the modeling clay allowed the light sheet to cover the majority of the mid-section of the whisker in the vertical plane. For the horizontal planes, the light sheet was aligned with a peak or trough or selected location. Alignment was monitored using a secondary camera with a telephoto lens to ensure proper placement of a light sheet at each peak and trough location.
Instantaneous vector fields from the snap-shot PIV tests were obtained with a window-based cross-correlation algorithm (DaVis 8.3, LaVision GmbH). A two-pass procedure was employed: initial interrogation window of 32 by 32 pixels followed by a reduced window of 16 by 16 pixels with 50% overlap in each pass. Convergence history of the mean streamwise velocity and the streamwise turbulence intensity at selected location of wake flow is examined with samples of 200, 300, 400, 600, 800, 1000 and 1200. The mean streamwise velocity reaches convergence at 400 instantaneous velocity fields, while the streamwise turbulence intensity needs 1000 samples for convergence. All 1200 instantaneous velocity fields were ensemble-averaged to ensure convergence of computing the mean velocity and turbulence statistics of the wake flow.
2.4 PIV measurement uncertainty
The total PIV measurement uncertainty is contributed collectively by various possible error sources, including the experimental setup, data acquisition, particle image quality, and data processing/post-processing (Adrian and Westerweel 2011; Raffel et al. 2007). Measurement uncertainty is also dependent on the specific flow features under investigation. Significant bias errors can be minimized by following PIV experimental guidelines and the random errors for a standard planar PIV are primarily determined by how accurately the cross-correlation peaks can be measured (Raffel et al. 2007). In both snap-shot PIV and high-speed PIV measurements, the correlation peaks were estimated to be about 0.1 pixel accuracy with the multi-iteration cross-correlation algorithm (Keane and Adrian 1993). The particle displacements were nominally 7–8 pixels in the far wake and the free stream but reduced to be about 2–3 pixels in the near wake region. Hence, the random error in the 2C PIV measurements is roughly 1.4 and 5% of full scale. Ensemble-averaging 1200 instantaneous velocity fields will result in the mean flow statistics in the near and far wakes below 1% of the full scale (by dividing it with \(\sqrt{1200}\), Tavoularis 2005). The other option under consideration is to use the correlation statistics method to obtain the map of the random error by image matching (Wieneke 2015).
Another aspect of measurement uncertainty is the interaction of whisker vibration and the induced wake. Since the single whisker sample is mounted as a cantilever, it is subjected to VIV. Subsequently, the wake structure and vortex shedding is affected by the whisker vibration. To evaluate the effects of whisker vibration on flow statistics, several cases in the high-speed PIV tests are utilized to identify displacement of profiles of the whisker cross-section in horizontal planes (Re \(=\) 390). Results show that the whisker displacement in the streamwise direction is much less than that in the spanwise direction, thus only the displacement perpendicular to the inflow is considered. The smooth whisker displacement is \(0.043\,D_h\) at an \(\mathrm{AOA} = 0^{\circ }\) and increased to \(0.86\,D_h\) at an \(\mathrm{AOA} = 90^{\circ }\). For the peak location of the undulating whisker, the displacement is \(0.7\,D_h\) at an \(\mathrm{AOA} = 90^{\circ }\). The magnitude of the whisker vibration agrees well with the strength of the vortex shedding (see Sect. 3.3). We conclude that the whisker vibration will have an influence on the flow statistics within \(1D_h\) around the whisker at an \(\mathrm{AOA} = 90^{\circ }\) while this effect can be safely neglected at an \(\mathrm{AOA} = 0^{\circ }\).
3 Results and discussion
3.1 Flow statistics of the wake: vertical central plane
3.2 Flow statistics of the wake: horizontal planes
The separated shear layers are indicated by the vertical vorticity (\(\omega _{y}\)) contours, in Fig. 7. Compared with the symmetric vorticity contours of slow-dissipated vorticity, the strong vorticity is closer to the whisker. The undulating whisker shows a longer region of high vorticity, extending for 10 \(D_h\), but then quickly dissipates to minor levels by 20 \(D_h\) downstream. While dissipating quickly in the streamwise direction, the vorticity in the wake of the undulating whisker also spreads out in the z-direction, an indicator of enhanced mixing in the wake. A clear difference is also seen in the peak and trough locations for the undulating whisker’s wake.
3.3 Vortex shedding
Vortex shedding behavior is directly associated to the VIV of a bluff body in a flow path. Instantaneous velocities acquired at 5000 Hz in the horizontal planes are sufficient in temporal resolution to quantify the strength of vortex shedding. In particular, two cases of the AOA, 0\(^{\circ }\) and 90\(^{\circ }\), are inspected for the effects of whisker orientation with respect to the incoming flow. The instantaneous streamwise velocities and vorticities at an AOA of 0\(^{\circ }\), Figs. 9 and 10, show a consistent trend with the previous ensemble-averaged results, Figs. 6 and 7. The wake region is significantly reduced at the peak location of the undulating whisker, compared to that of the smooth whisker. Furthermore, vertical vorticity remains at high magnitude up to 10 \(D_h\) at the peak and about 15 \(D_h\) at the trough location, versus 25 \(D_h\) downstream of the smooth whisker. The flow pattern observed from the high-speed PIV data confirms the wake suppression by the undulating whisker at \(\mathrm{AOA} = 0^{\circ }\).
Spectral analysis was performed to examine the distribution of turbulent kinetic energy across a range of frequencies in the wake of the smooth and undulating whiskers, Fig. 13. The spectra were calculated by taking the fast Fourier transform (FFT) of the instantaneous streamwise velocity at several locations of the separated shear layers. Localized high-energy signatures can be seen clearly at frequencies corresponding to periodic vortex shedding. A concentration of turbulent energy is indicated by the primary peak at the frequency of 108 Hz behind the smooth whisker, 150 and 158 Hz at the peak and trough of the undulating whisker at an AOA \(= 0^{\circ }\). Miersch et al. (2011) reported the frequency of seal and sea lion whiskers fall in the range of 47–193 Hz for a free-stream flow speed between 0.17 and 0.52 m/s. Our results appears to be aligned with this work. In addition, the power spectral density is found to be 50% lower for the case of the undulating whisker, indicating reduced strength of vortex shedding. This result is consistent with suppressed wake generated by the undulating whisker, as well as recent work of Morrison et al. (2016), Kim and Yoon (2017).
4 Conclusions and outlook
Experiments of the wake flow of a real undulating elephant seal whisker and a smooth sea lion whisker are conducted under well-controlled laboratory water channels. The turbulent statistics are achieved by a snap-shot PIV and the vortex shedding behavior is quantified by a high-speed PIV method.
The ensemble-averaged flow properties show a reduced reversed flow region with quickly dissipated vorticity and significantly reduced turbulence levels in the wake of the undulating whisker. In spite of the naturally presented variation in whisker diameter and curvature, the distinct flow feature of wake suppression by the undulating whisker at an AOA of \(0^{\circ }\) is clear from observation of two orthogonal views. In particular, promoted mixing in the wake induced by the undulations may push the area of high-magnitude turbulence intensities away from the whisker itself, thus reduce the VIV.
Spectral analysis of high-speed PIV data indicates the reduced power spectra density behind the undulating whisker, compared to that of the smooth whisker, regardless of the AOA. However, changing the AOA from \(0^{\circ }\) to \(90^{\circ }\) substantially increases the power spectral density, thus augmenting the vortex shedding significantly.
Ongoing work is to directly measure the smooth and undulating whisker vibration from the high-speed PIV images and to examine the relation of the dominant whisker vibration frequency to the frequency of the vortex shedding in the wake. New experimental data will be obtained at a higher Reynolds number of 2000, based on the seal swimming speed and the whisker hydrodynamic diameter. This will help to further understand the effect the Reynolds number has on the wake flow and the vortex shedding behavior, as well as provide further insights into whisker-inspired engineering applications.
Notes
Acknowledgements
This research is supported by the Faculty Startup Funds from the Office of Research at the Cleveland State University. The Authors would like to acknowledge Mr. David Epperly for assistance in experimental setup and the Civil Engineering Department for the access to the water channel. The authors also thank the NSF East Asia and Pacific Summer Institute for U.S. Graduate Students Program (NSF EAPSI 1515471) for the great opportunity to conduct high-speed PIV experiments at the Biofluid and Biomimic Research Center (BBRC) of the Pohang University of Science and Technology, Republic of Korea.
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