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Research on Claw Motion Characteristics and Cavitation Bubbles of Snapping Shrimp

Research on Claw Motion Characteristics and Cavitation Bubbles of Snapping Shrimp Hindawi Applied Bionics and Biomechanics Volume 2020, Article ID 6585729, 12 pages https://doi.org/10.1155/2020/6585729 Research Article Research on Claw Motion Characteristics and Cavitation Bubbles of Snapping Shrimp 1 2 3 1 1 1 Yuliang Yang, Shimu Qin , Changchun Di, Junqi Qin, Dalin Wu, and Jianxin Zhao Shijiazhuang Campus, Army Engineering University, Hebei 050003, China China Aerodynamics Research and Development Center, Mianyang Sichuan 621000, China Unit 63961 of PLA, Beijing 100020, China Correspondence should be addressed to Shimu Qin; qshimu@126.com Received 12 February 2020; Revised 16 June 2020; Accepted 8 July 2020; Published 21 September 2020 Academic Editor: Francesca Cordella Copyright © 2020 Yuliang Yang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Snapping shrimp produces a high-speed jet through the rapid closure of the snapper claw, which stimulates the formation of cavitation bubbles of various shapes. In order to explore the fast motion characteristics of snapper claw, the formation and change process of cavitation, and the physical principles underlying the biological phenomena, the equivalent model of snapper claw was constructed through CT scanning technology. A high-speed camera was used to capture the claw’s motion characteristics, thereby simulating the production of cavitation bubbles by snapping shrimp. The results show that the rotation speeds of different species of snapping shrimps are different, as well as their motion characteristics. Cavitation is formed by the interaction of the pressure drop caused by the vortex at the nozzle with the inertia of the liquid inside the socket. Under the influence of the jet, the shapes of bubbles change from ring to cone, and eventually collapse into bubble clouds. 1. Introduction The snapper claws exhibit extremely high closing veloci- ties, with a measured value of 3500 rad/s [8]. The rapid closure mechanism is closely related to the structure of the Snapping shrimp is a member of the Alpheidae family. It has asymmetrical claws, the larger of which can grow to about half claw. The cocking pivot joints and cocking slip joints evolve its body size [1]. The claw has a protruding plunger (pl) on the on the claw between the dactyl and the propus [9, 10], which dactyl (d) and a matching socket (s) on the immobile propus facilitates the rapid closure of the claw. The cone-shaped (p) [2]. During predation, the snapping shrimp rapidly closes micropapillae units on the dactyl also have the effect of reducing underwater resistance, which facilitates the rapid the larger claw [3], draining the water into the socket and forming a high-speed water jet of 32 m/s [4]. Among them, closure motion of the snapper claw [11]. the speed of the water jet is related to the sex of the shrimp The cavitation generated by snapping shrimp is a kind and the size of the claw [5]. Because the high-speed water jet of vortex cavitation [12]. The original vortex with a cavita- injection causes cavitation due to the strong pressure reduc- tion ring is located in front of the claw. The volume of the tion effect of water and the rupture of the cavitation bubbles bubble is related to the closure velocity [13]. The reason in front of the claw, the snapping shrimp generates a loud why the high-speed jet is generated is not because the cracking noise of up to 210 dB at the source [6]. The shock axial momentum is large, but the momentum is converted wave released by the collapse of cavitation bubbles is about into the maximum strength of the leading vortex. 80 kPa at a distance of 4 cm [1], which is enough to stun and However, these findings are based on a simplified nozzle even kill the prey. When the claw is closed [7], there is an model, which can differ from the mechanism used by real angular offset between the dactyl and the propus, which pre- shrimp. The collapsed cavitation produces high pressures vents physical contact between these parts, indicating that and temperatures [4], thereby effectively forming a plasma the noise is caused by the bubble collapse. with photons and shock waves through energy focusing 2 Applied Bionics and Biomechanics above and vertical to the animals were both set to [14]. In order to avoid the destruction of the claw struc- ture by high-energy movement, it was found that the 99000 fps, 10 μs exposure time, and 512 ∗ 512 pixels. After materials of the claw have good temperature resistance the experiment, the calibration plate with a resolution of [15] and are subjected to more intense contact stresses [7]. 2 mm was placed on the plane perpendicular to the claw of The previous investigations mainly focused on the the camera to provide a reference for calculating the size, mechanical properties, surface morphology, snapping sound, distance, and angle during image postprocessing. and evolution of the snapper claw. However, the studies The actual size of the image was determined based on the about the mechanism of cavitation generated by snapping pixel coordinates of the picture and the length of the calibration shrimps and the characteristics of snapper claw motion are plate. The length of 4 mm on the calibration plate corresponds still blank. In order to elucidate the biophysical characteris- to the average value of 56 pixels, so the length of each pixel is tics of these small shrimps, this paper studied the structure 71.43μm. The contour of the snapper claw was obtained of snapper claw through CT scanning and established a 3D according to the gray value of the image through MATLAB, model of snapper claw, which was then used to simulate and the angles between the dactyl and the propus were deter- the formation of cavitation bubbles. A high-speed camera mined. Through curve fitting, the relationship between the was applied to capture and record the entire process of snap- angle and the time was obtained. Moreover, the relationship per claw rapid closure and the formation and development between the angular velocity and the angular acceleration was process of cavitation bubbles to analyze its motion character- also obtained through the derivative with time. istics and cavitation mechanism. Based on the combination Because the motion characteristics of No.1 shrimp of the above, the simulation results and the images captured (Alpheus macroskeles) was better than other samples, cavita- by the high-speed camera can provide insight into the gener- tion research was carried out by carrying out CT scanning ation and development of cavitation bubbles of the snapper and CFD simulation on it. claw. 2.3. Computed Tomography of the Snapper Claw. The snap- per claw was removed with scissors, and then cleaned with 2. Materials and Methods an ultrasonic cleaner (KQ-200KDE, Kunshan ultrasonic instruments CO., Ltd.) for 30 minutes to remove salt resi- 2.1. Preparation of Snapping Shrimp. In this experiment, dues, and then frozen in a vacuum freeze-drying machine samples were collected from the coastal area of Fujian, China, (FD-1C-50, Beijing Bo Kang laboratory instruments CO., in July 2018. A total of 6 adult male snapping shrimps that Ltd.). The dried snapper claw was tightly fixed with tape, had molted for over one week were selected for the experi- and then observed on a CT machine (nanoVoxel-3000, ment. According to the category of snapping shrimps, the Tianjin Sanying Precision Instruments CO., Ltd) with a scan- species and sizes of the shrimps used in the experiment are ning accuracy of 6.52 μm. as follows: Sample No.1 (Alpheus macroskeles, 44 mm with body length, and 8 mm with snapper claw size), Sample 2.4. Computational Fluid Dynamics Simulation. The stack of No.2 (Alpheus brevicristatus, 50 mm with body length, and CT slices was imported into the visualization software (Avizo 10 mm with snapper claw size), Sample No.3 (Alpheus brevi- 8.1) and then the claw is rendered in 3D visualization. The cristatus, 62 mm with body length, and 9 mm with snapper reconstructed 3D surface data of the claw was then exported claw size), Sample No.4 (Alpheus brevicristatus, 48 mm with to the CAD software (UG NX10). The main functional body length, and 8 mm with snapper claw size), Sample geometries of the claw were separated into the moving part No.5 (Alpheus acutocarinatus, 68 mm with body length, (dactyl), the stationary part (propus), and the connection and 12 mm with snapper claw size), Sample No.6 (Alpheus part to the pivot axis. According to the measurement results acutocarinatus, 74 mm with body length, and 11 mm with of high-speed photography, the angle of the claw was set to snapper claw size). The snapping shrimps were housed in ° 82.4 , as shown in Figure 1(b). seawater (temperature: 25 ± 1 C, salinity: 1.024) and were Since the jet and the cavitation bubble generated by the fed frozen shrimp every three days. Before the experiment, snapping shrimp were positioned close to the snapper claw, the snapping shrimps were numbered with small labels. in order to optimize the calculation accuracy and time, the CFD simulation mesh model containing internal and exter- 2.2. Measurement of Snapper Claw Motion Characteristics. nal parts was established, in which tetrahedral meshes with The use of high-speed cameras (V2512, Phantom) ensures the size of 30 μm were used in the internal part, and hexahe- that the movement of the snapper claw and the formation dron meshes with the size of 1 mm were used in the external and development of cavitation bubbles can be accurately part. The mesh size expansion ratio between the internal and captured and recorded. The experimental system consists of external parts was 1.2 : 1. After verification of grid indepen- a 50 ∗ 25 ∗ 30 cm aquarium, a vibration-isolated platform, dence, the number of cells met the calculation requirements. and two high-speed cameras. Snapping shrimp was fixed on The Reynolds number redefined the ratio of inertial the vibration-isolated platform by covering its carapace and forces to viscous forces in the fluid [16], which can determine claw with plasticene. The positions of the claw and cameras the flow type. need to be adjusted to the center of the camera’s field of view. Through the stimulation of a soft brush, the claw made a ρvd raising and rapid closure of the dactyl, and then the high- Re = , ð1Þ speed cameras were triggered to shoot. The cameras located Applied Bionics and Biomechanics 3 Camera Fixed nuts above Adjustable crossbeam Sensor fix rods Light sources Snapping shrimp Vibration-isolated Vertical platform camera 5 mm Pressure Aquarium sensors (a) (b) (c) 1 mm 1 mm 1.5 mm (d) (e) (f) Figure 1: (a) Schematic view of the experimental device. The vibration-isolated platform is placed in the center of the aquarium, and the sensors are fixed at a distance of 3 cm in front of the snapper claw. (b) Gray value image of the snapper claw from the side. The inflection points of the claw are marked by circles, and the opening angle is measured to be 82.4 . (c) 3D reconstructed model of snapper claw with a scale of 1 : 1. (d) CT slices of shrimp claw in the x-y direction. The dactyl is inserted into the socket to form a cavity closed on both sides. (e) CT slices of shrimp claw in the x-z direction. The red rectangle indicates the cavity and nozzle structure. (f) CT slices of shrimp claw in the y-z direction. The dactyl is tightly surrounded by socket, representing a fine hermetic seal. tive solutions of the pressure field and velocity field. The where v is the jet velocity, ρ is the fluid density, μ is the viscosity, and d is the characteristic size of the claw nozzle. selected solvers and predefined parameters in the simulation are listed in Table 1. With the typical values of v ≈ 32 − 70 m/s, ρ = 1024 kg/m , μ =1:003e − 03 kg/ðm ∗ sÞ, d ≈ 0:2mm, the Reynolds A dynamic mesh was used to simulate the movement of the dactyl, which is essential to accurately simulate the number is about 6534-14293, indicating that the type of jet process. According to the high-speed photography results, produced by snapping shrimp is turbulence. the closure velocity of the claw was accelerated, from the The FLUENT software package was used for the CFD initial velocity of 70 rad/s to the final velocity of simulation. In the simulation, the Navier-Stokes equations 4392 rad/s, and the total time was only about 885 μs. Sub- were used to simulate a Newtonian fluid whilst maintaining sequently, the claw motion information was written to a mass, momentum, and energy. In addition, the achievable profile to command the dactyl movement. For dynamic k-e turbulent model and VOF model were selected. The mesh, the smoothing and remeshing mesh methods were application of the PISO method was to determine the itera- 4 Applied Bionics and Biomechanics Table 1: Parameters of fluent simulation. Parameters Predefined value Solver Pressure-based Transient Solution methods PISO PRESTO, second order upwind Multiphase flow model VOF Realizable k − ε, Standard Wall function Cavitation model Zwart-Gerber-Belamri 3540 pa Primary phase Water-liquid Second phase Water-vapor 3 3 Density 1024 kg/m Density 0.02558 kg/m Materials 1:003e − 03 kg/ðÞ m ∗ s 1:26e − 06 kg/ðÞ m ∗ s Viscosity Viscosity Table 2: Settings of the dynamic mesh. Smoothing method Parameters Remeshing method Parameters Spring constant factor 0.01 Minimum length scale (m)0 Convergence tolerance 0.001 Maximum length scale (m)0 Number of iterations 20 Maximum cell skewness 0.7 Laplace node relaxation 1 Size remeshing interval 1 selected. The settings of the dynamic mesh are listed in in Figure 1(e). In the process of closing the claw, the dactyl Table 2. moves around the axis on the propus. The velocity reaches its maximum value at the moment when the dactyl is completely closed. The plunger on the dactyl provides the 3. Results initial liquid velocity by replacing the liquid in the socket. Due to the sealing of the socket and the propus, the liquid 3.1. Movement Characteristics of the Snapper Claw. The can only flow out of the socket through the orifice on the side high-speed camera accurately observed the movement of of the claw, resulting in a high-speed jet similar to the func- the snapper claw. In response to the stimulation, the snap- tion of the nozzle structure. ping shrimp tilted its dactyl to the maximum angle and stayed in that position for about a second, then the dactyl moved to close the claw at an extreme rapid velocity around 3.3. Formation and Development of Cavitation Bubbles. the joint. The curve of the snapper claw motion angle is The simulation results of the snapper claw model are rd shown in Figure 2(a). The 3 order polynomial can fit the shown in Figure 3. In the simulation and calculation of relationship between the angle of the claw motion and time cavitation bubbles, the isosurface shows bubbles with a well, as shown in Figure 2(b). The parameters of the curve volume fraction of 50% (the green part in the figure). 3 2 fitting (f ðxÞ = p1 ∗ x + p2 ∗ x + p3 ∗ x + p4) were shown When the claw is closed from the maximum angle (Figure 3(a)), the angular velocity gradually increases. in Table 3. Taking the derivative of the angle gave the angular veloc- With the movement of the claw, bubbles are first formed ity, which is an acceleration process from less than 100 rad/s in the corners of the socket (Figure 3(b)). When the claw to more than 1000 rad/s finally, as shown in Figure 2(c). is about to close, a toroidal bubble appears around the Using the same method, the angular acceleration was derived orifice formed by the dactyl and propus (Figure 3(c)). When the claw motion stops, the bubble continues to as follows. The No.1 shrimp (Alpheus macroskeles) had the highest angular velocity of about 4500 rad/s, and the angular grow and moves in the direction of the jet (Figure 3(d) 7 2 acceleration continued to increase to nearly 10 rad/s . The and (e)). Afterwards, under the influence of the ambient maximum angular velocity of the No. 2-4 shrimps (Alpheus pressure, the bubble begins to shrink and eventually col- brevicristatus) was about 1000 rad/s, and the angular acceler- lapses (Figure 3(f)–(h)) and disappears (Figure 3(i)). 6 2 ation almost remained unchanged at 10 rad/s . The maxi- mum angular velocity of the No. 5 and No. 6 shrimps 4. Discussion (Alpheus acutocarinatus) was about 1400 rad/s, and the angular acceleration continued to decrease, from the initial 4.1. Analysis of the Movement Characteristics of the Snapper 6 2 4×10 rad/s to 0 or even negative value. Claw. According to the law of conservation of energy, the larger the volume, the more water is contained in the socket, 3.2. Characterization of Claw Structure. The images pre- so more kinetic energy is required to drive the liquid. In addi- sented in Figures 1(c) and 1(d) show the 3D reconstructed tion, the larger the volume of the claw, the greater the area of model and the slices of the snapper claw in different direc- contact with water during movement, so the greater the resis- tions. When the claw is closed, a cavity is formed between tance. Taking into account the above two reasons, the move- the dactyl and the propus, as indicated by the red rectangle ment characteristics of different types of snapping shrimps in Applied Bionics and Biomechanics 5 1.5 2.5 1.5 0.5 0.5 0 0 0 0.5 1 1.5 2 2.5 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 –3 –3 Time (s) × 10 Time (s) × 10 No.4 No.1 No.4 No.1 No.2 No.5 No.2 No.5 No.3 No.6 No.3 No.6 (a) (b) 6000 6 × 10 3000 6 –1000 –2 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 –3 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Time (s) × 10 –3 Time (s) × 10 No.1 No.4 No.1 No.4 No.2 No.5 No.2 No.5 No.3 No.6 No.3 No.6 (c) (d) Figure 2: Motion information of the claw. (a) Curve of claw angle and time. (b) Angle of claw as a function of time. (c) Angular velocity of claw as a function of time. (d) Angular acceleration of claw as a function of time. the resistance they suffered when moving in the water was also greater, resulting in a slower closure velocity. However, Table 3: Curve fitting parameters of angle with time. due to the small volume of the socket cavity of this type of Sample p1 p2 p3 p4 R shrimp, its water storage capacity was small, and the resis- 1 1.24E+09 9.25E+05 -136.1 0.026 0.9962 tance of the liquid to the dactyl was low during squeezing. Combining two points, the closure angular acceleration of 2 -1.13E+08 6.53E+05 -78.79 0.02616 0.9973 the claw of this type of shrimp did not change much. Among 3 -9.46E+06 3.97E+05 -98.84 0.0232 0.9976 the test samples, the Alpheus acutocarinatus (No.5-6) had the 4 -2.23E+06 3.91E+05 27.61 0.01768 0.999 largest volume with an average dactyl length of 12 mm. Due to 5 -6.82E+08 1.91E+06 -454.4 0.02831 0.9926 their slender and flat contour of the dactyls, which can reduce 6 -5.83E+08 1.50E+06 -13.16 0.01602 0.9991 resistance, the closure velocity of snapper claw was faster than the second kind of shrimps, about 1400 rad/s. On the other hand, due to the large volume of the socket cavity, higher the experiment are different. Among the samples, the smal- energy was required to squeeze out the stored liquid, resulting lest snapping shrimp, Alpheus macroskeles (No. 1), had a tiny in insufficient energy provided by muscle contraction to over- snapper claw that was only about 8 mm long, so the resis- come the resistance of the liquid, so the angular acceleration of tance it received when moving in the water was small, and the claw motion continued to decrease. the energy provided by its muscle contraction was enough to squeeze out the fluid in the socket cavity. Therefore, both 4.2. Cavitation Inception. The contour of the cavitation the angular velocity and acceleration increased when the inception of the snapper claw is shown in Figure 4. The shrimp closed its claw. The Alpheus brevicristatus (No. 2-4) velocity of the jet generated by the claw flow through the noz- had larger snapper claws than those of the No.1 shrimp, so zle is about 70 m/s in the center (Figure 4(a)), which is much Angular velocity (rad/s) Angle (rad) 2 Angle (rad) Angular acceleration (rad/s ) 6 Applied Bionics and Biomechanics Vapor volume fraction Vapor 9.730e-001 7.298e-001 (a) (b) (c) 4.865e-001 (d) (e) (f) 2.433e-001 0.000e-000 (g) (h) (i) Figure 3: Indicative instances of the snapper claw model closure. The green part represents the cavitation bubble with the vapor volume of 50%. faster than the velocity of the surrounding flow. Under the where p is the pressure at the vortex radius, and p is the R C squeezing of the plunger, the liquid in the socket cavity is pressure at the vortex core. The liquid density ρ is ejected, so that the jet kinetic energy increases inside the 1024 kg/m , and the vortex radius R is about 0.15 mm. The cavity. When the liquid reaches the nozzle, the jet will con- vorticity is twice the instantaneous principal axis angular tinue to move along the wall of the claw. Under the influence velocity of the strain-rate tensor of the fluid element, so the of the inverse pressure gradient (dp/dx > 0), the jet velocity angular velocity Ω is about 150000 rad/s, with an average near the wall gradually decreases. At this time, the boundary pressure drop of 259200 Pa (about 2.5 atm). Since the layer begins to increase in thickness, and separates from the pressure at the vortex core is sufficiently lower than the satu- nozzle to form a vortex, and finally merges into the main- rated vapor pressure of 3540 Pa, this pressure difference stream. As shown in Figure 4(b), the vortex structures C1 between the two can lead to cavitation. and C2 are first formed around the nozzle, and the directions When the dactyl stops moving, the socket is not filled by of the two vortices are opposite, with the vortex of about the plunger, and the liquid in the cavity continues to flow 300,000. According to Bernoulli’s law, the pressure in the outward along the nozzle due to inertia, resulting in cavita- region with high velocity can be decreased and the presence tion inside the cavity, as shown in Figure 4(d). The formula of the vortex causes a pressure drop. The pressure at the core for calculating the pressure drop in the channel is [18]: of the vortex is the lowest, accompanied by cavitation incep- tion. Cavitation bubbles V1 and V2 appear around the nozzle l dϕ Δp = ρ , ð3Þ and are connected to the dactyl and the propus, as shown in S dt Figure 4(c). The induced liquid depressurization caused by the vortex can be expressed as [17]: where l and S are the length and the cross-sectional area of the channel, and ϕ is the flow rate. After the bubble in the cavity leaves the socket, it enters 2 2 ρR Ω the low-pressure area of the nozzle and then merges with p − p = , ð2Þ R C 2 the toroidal bubble generated by the vortex. For snapping Applied Bionics and Biomechanics 7 Velocity curl Velocity 7.065e+01 1.591e+06 6.693e+01 1.508e+06 6.321e+01 1.424e+06 5.949e+01 1.340e+06 5.577e+01 1.256e+06 5.205e+01 1.173e+06 Dactyl 4.834e+01 1.089e+06 4.462e+01 1.005e+06 C1 4.090e+01 9.214e+05 3.718e+01 8.376e+05 3.346e+01 7.538e+05 2.975e+01 6.701e+05 2.603e+01 5.863e+05 2.231e+01 5.026e+05 1.859e+01 4.188e+05 1.487e+01 3.350e+05 1.115e+01 Propus 2.513e+05 C2 1.675e+05 7.436e+00 8.376e+04 3.718e+00 1.054e–03 0.000e+00 0 0.0015 0.003 (m) 0 0.0015 0.003 (m) X Y X Y 0.00075 0.00225 0.00075 0.00225 (a) (b) Vapor volume fraction Vapor volume fraction 9.981e+01 9.981e+01 9.456e+01 9.456e+01 8.931e+01 8.931e+01 8.405e+01 8.405e+01 7.860e+01 7.860e+01 7.355e+01 7.355e+01 6.829e+01 6.829e+01 6.304e+01 V1 6.304e+01 5.779e+01 5.779e+01 5.253e+01 5.253e+01 4.728e+01 4.728e+01 4.203e+01 4.203e+01 3.677e+01 3.677e+01 3.152e+01 3.152e+01 2.627e+01 2.627e+01 2.101e+01 2.101e+01 1.576e+01 V2 1.576e+01 Bubble 1.051e+01 1.051e+01 5.253e+02 5.253e+02 0.000e+00 0.000e+00 0 0.0015 0.003 (m) 0 0.0015 0.003 (m) X Y X Y 0.00075 0.00225 0.00075 0.00225 (c) (d) 907. 2 𝜇 s 5 mm 967. 8 𝜇 s 5 mm 1301. 1 𝜇 s 5 mm (e) (f) (g) Figure 4: (a) The contour of jet velocity. The core velocity is much higher than the surroundings, forming a submerged jet in water. (b) The contour of vortex. Vortices are formed around the orifice of the nozzle, causing the pressure drop. (c) The contour of vapor. At the position of the vortex, cavitation incepts and the initial shape is toroidal. (d) The cavitation bubble in the socket cavity due to inertia. (e) Vortex core regions are indicated in grey. It gradually develops into a ring structure close to the dactyl. (f) The development of the cavitation bubble. The bubble is formed first at the nozzle orifice, and then changes from a toroidal bubble to a more conical one. (g) The pictures of cavitation bubbles generated by snapper claw. 8 Applied Bionics and Biomechanics Brush Bubble 5 mm 0 𝜇s +87.7 𝜇s +175.4 𝜇s +263.1 𝜇s (a) Dactyl Nozzle Propus 5 mm +350.8 𝜇s +438.5 𝜇s +526.2 𝜇s +613.9 𝜇s (b) Figure 5: High-speed images from the top of the claw. (a) The pictures of the compression of cavitation bubbles. The volume of the conical bubble reduces to is the minimum. (b) The pictures of the rebound of cavitation bubbles. The bubbles rebound many times without a specific shape and eventually disappear. shrimp, these two sources of cavitation work together to form initial cavitation bubble appears as a ring structure, which the bubble. continuously expands and stretches to a conical structure in contour along the direction of the jet under the impact of a 4.3. Development of Vortex Cavitation. After cavitation starts high-speed jet. Sadovskii et al. [21] studied the morphological at the nozzle, the vortex moves with the flow of the jet. changes in cavitation bubbles produced by high-speed Figure 4(e) shows the contour of the vortex at the nozzle submerged jets. At the moment of jet generation, a cavity when the claw is closed, where the grey parts represent the appeared as a narrow hollow torus in the plane perpendicular vortex regions. The vortex first appears around the nozzle to the jet direction. The transverse diameter of the cavity was orifice, and then develops into a ring structure close to the much larger than the jet diameter. When the jet was ejected dactyl in a similar manner to the air vortex cannon [19]. from the nozzle, the cavity surface evolved into an approxi- The core velocity of the jet produced by the claw is about mately cylindrical surface that grew in the direction of jet 70 m/s initially, and then gradually decreases. The vortex ring motion. After the jet was generated, the closure of the bottom structure is formed around the jet. As the jet develops, its surface of the cavity resulted in the formation of an axial jet radius gradually increases. According to the jet theory, under inside the cavity. The ever-evolving reentrant jet traversed the influence of the viscosity of the liquid, the boundary the cavity along its axis of symmetry to form a new conical layers of the jet continuously fall off, resulting in the vortex cavity, which had a convex surface as it penetrated into the filling of the area of the jet boundary. The vortex will cause liquid. The bottom surface of the cavity where the jet was turbulence, which will entrain any fluid in the static state into generated advanced in the direction of the jet. Therefore, the jet. With the development of turbulence, the entrained the cavitation bubbles generated by the snapping shrimp fluid increases, and the boundary of the jet gradually expands evolved from the initial ring-shaped bubbles into more coni- to both sides. The flow rate q increases along the path [20]. cal bubbles and moved in the direction of the jet. A high- speed camera was used to photograph the process of cavita- rffiffiffi q x tion bubbles produced by the claw of snapping shrimp. As ∝ , ð4Þ q d can be seen from Figure 4(g), after the claw was closed, the toroidal bubble overflowed from the side of the claw and where q is the flow at the nozzle, and d is the feature size of continuously expands in the cone structure. In addition, the the nozzle. Therefore, the vortices form a large vortex ring direction of its motion is at an angle relative to the claw. structure around the jet, and its size continues to increase. Therefore, the high-speed imaging confirms the validity of The bubble morphology is simulated and shown in the theoretical and simulation results. It can be concluded that there are two main functions of the jet. One is to transfer Figure 4(f), in which the orange part represents the contour of 20% vapor volume fraction. The bubble is ejected from the axial momentum of the jet to the vortex. The enhanced the nozzle on the side of the claw, and there is a certain angle vortex forms a low-pressure zone, which advances with the between the moving direction of the bubble and the claw. The vortex, causing continuous expansion of cavitation bubbles. Applied Bionics and Biomechanics 9 Pressure Dactyl 2.944e+004 2.274e+004 1.605e+004 9.352e+003 2.656e+003 –4.040e+003 –1.074e+004 –1.743e+004 –2.413e+004 –3.082e+004 –3.752e+004 –4.422e+004 Reference plane –5.091e+004 –5.761e+004 –6.430e+004 Propus –7.100e+004 –7.770e+004 –8.439e+004 –9.109e+004 –9.779e+004 Z 0 0.002 0.004 (m) 0 0.0005 0.001 (m) [Pa] 0.00025 0.00075 0.001 0.003 (a) (b) Vapor volume fraction Velocity 8.250e–001 1.320e+001 7.816e–001 Head 7.381e–001 6.947e–001 6.513e–001 9.901e+000 6.079e–001 5.645e–001 5.210e–001 4.776e–001 Nozzle 4.342e–001 6.601e+000 3.908e–001 3.474e–001 3.039e–001 2.605e–001 Bottom 2.171e–001 3.300e+000 1.737e–001 1.303e–001 X X 8.684e–002 4.342e–002 Y Y 0.000e+000 0.000e+000 0 0.0005 0.001 (m) 0 0.0005 0.001 (m) 0.00025 0.00075 0.00025 0.00075 (c) (d) Vapor volume fraction 9.989e–001 7.491e–001 Dactyl Vapor 4.994e–001 Jet 2.497e–001 Propus Vapor X Y 0 0.0015 0.000 (m) 0.000e+000 0.00075 0.00225 5 mm (e) (f) Figure 6: Continued. 10 Applied Bionics and Biomechanics Vapor volume fraction Vapor volume fraction 9.981e–01 9.981e–01 9.456e–01 9.456e–01 8.931e–01 8.931e–01 8.405e–01 8.405e–01 B–B 7.880e–01 7.880e–01 7.355e–01 7.355e–01 A–A 6.829e–01 6.829e–01 6.304e–01 6.304e–01 5.779e–01 Vapor 5.779e–01 5.253e–01 5.253e–01 4.728e–01 4.728e–01 4.203e–01 4.203e–01 3.677e–01 3.677e–01 3.152e–01 3.152e–01 2.627e–01 2.627e–01 2.101e–01 Jet 2.101e–01 1.576e–01 1.576e–01 1.051e–01 1.051e–01 5.253e–02 5.253e–02 0.000e+00 Z 0.000e+00 0 0.0005 0.000 (m) 0 0.001 0.002 (m) X Y 0.00025 0.00225 0.0005 0.0015 (g) (h) Figure 6: (a) Reference plane for the simulation results, showing the flow field of the snapper claw along the nozzle. (b) Contour of the pressure on the claw side when the bubble collapses. The pressure on both sides of the bubble is different, and the pressure on the bottom is higher. (c) When it is about to burst, the bubble is compressed into a concave shape, pointing to the head of the bubble. (d) Speed vector of the flow field. When the bubble bursts, the fluid on both sides moves toward the middle of the bubble, and the jet velocity from the bottom of the bubble pointing to the head is greater. (e) Picture of the cavitation bubble in the maximum state. The nonspherical bubble includes the jet in the middle and vapor around. (f) Simulation result of cavitation bubble with vapor volume fraction of 50%. (g) Contour of vapor volume fraction along the axis of the bubble. (h) Contour of vapor volume fraction along the radial cross-section of the bubble. The other is to guide the movement of the vortex ring and p are the liquid pressure at the interface and far away from cavitation bubbles. the bubble, respectively. According to the R-P equation, it can be inferred that the 4.4. Collapse of Cavitation Bubbles. There are two stages of collapse process of the nonspherical bubble is related to the the bubble collapse, namely, the compression stage and the local curvature radius of the initial shape of the bubble [24]. rebound stage [22]. During the compression stage, due to According to the simulation results, when the bubble bursts, the decrease in vortex intensity, the pressure outside the the forces on both ends of the bubble are different. The pres- bubble is greater than the internal pressure, causing the sure in the head area is lower than the pressure in the tail bubble to start compressing. At this stage, the bubbles are area, which causes the bubble to collapse from the bottom relatively stable and the disturbance increases slowly. There to the head, and generates a micro jet directed to the head, is a highly unstable nonspherical disturbance in the rebound as shown in Figures 6(a). stage, which is manifested by the fierce breakup of bubbles Therefore, it is estimated that the cavitation bubbles and the formation of many small bubbles. Under the contin- generated by the shrimps are directional. When the snapping uous rupture and rebound, the bubbles form a visible cloud. shrimp is hunting, its claw aims at the prey, and the shock wave Through the high-speed camera, the collapse process of the and the microjet generated by the collapse of the bubble both act bubbles generated by snapping shrimp is recorded. Through on the target, which has little effect on the snapping shrimp itself. careful observation, it can be found that the nonspherical bubbles begin to shrink after expanding to the maximum 4.5. Structure Characteristics of Cavitation Bubbles. volume. During the shrinkage process, the outline of the Figure 6(e) shows the maximum volume of cavitation bubble remains clear and the shape remains unchanged, indi- bubbles produced by the claw. It can be seen from the outline cating that it is in the compression stage, as shown in that the cavitation bubble is conical, in which the bottom sur- Figure 5(a). After the bubble shrinks to its minimum volume, face is elliptical and the front surface is elongated. The main it begins to rebound and expand, changing from a single body of the bubble is transparent, and there is an opaque jet conical bubble to many cloud bubbles. These bubbles burst inside. In the simulation results shown in Figure 6(f), along and rebound continuously, and then the cloud disappears the axis of the bubble (A-A), the inside of the bubble was gradually. This process is the rebound stage, as shown in not all water vapor, but there was a conical cavity structure Figure 5(b). as shown in Figure 6(g). The bubble is not the initial ring The Rayleigh-Plesset equation is widely used to describe structure, but a symmetrical nonspherical shape. The dimen- the collapse of a bubble [23]. sionless parameter σ was applied to describe the cavitation. 2 2 p − p p − p d R 3 dR 4ν dR 2S ∞ v g ∞ σ = , ð6Þ = R + + + , ð5Þ 1/2ρV ρ 2 dt R dt ρR dt ∞ where R is the radius of the bubble, ρ is the density of the liq- where p is the absolute pressure, and p represents the ∞ v uid, ν is the dynamic viscosity, S is the surface tension, p and vapor pressure of the liquid. V is the jet velocity, and ρ is g Applied Bionics and Biomechanics 11 nutritious food and a suitable living environment for ani- the liquid density. The cavitation number describes the possibility that the fluid cavitates or not when the high- mals. The snapping claw was removed with scissors, which speed flow reaches such low pressure. Where p =0:103 is safe for snapper claw because the other claw would grow to the lager one and the broken part could grow to a small MPa, V = 32 ~ 70 m/s, p = 3540 Pa, and ρ = 1024 kg/m . ∞ v claw. And this fast operation can reduce animal pain as well. Therefore, the cavitation number of bubbles generated by To prevent interspecific conflict, the animals without snap- the snapping shrimp is σ =0:04 ~ 0:19. When the cavitation per claw are kept separately. number is less than or equal to 0.2, the submerged jet will produce asymmetric cavitation, accompanied by the axial reentrant flow [25], which is consistent with the principle References of cavitation bubbles generated by the snapper claw. As shown in Figure 6(h), along the radial cross-section of [1] M. Versluis, B. Schmitz, A. von der Heydt, and D. Lohse, “How snapping shrimp snap: through cavitating bubbles,” Science, the bubble (B-B), the vapor volume fraction presents an vol. 289, no. 5487, pp. 2114–2117, 2000. annular distribution with a lower center, and liquid is the [2] W. K. Brooks, F. H. Herrick, and National Academy of main component. The vapor volume fraction in the middle Sciences, The Embryology and Metamorphosis of the is relatively higher, with dominant vapor. When external Macroura, Memoirs of the National Academy of Sciences, bubbles come into contact with water, the vapor volume National Academy of Sciences, Washington, 1891. fraction gradually decreases. [3] B. Schmiz and J. Herberholz, “Snapping movements and laser doppler anemometry analysis of water jets in the snapping 5. Conclusions shrimp Alpheus heterochaelis,” in Proceedings of the 26th Gottingen Neurobiol. Conf, vol. 2, p. 241, Gottingen, Germany, This paper reviewed the research status of snapping shrimps and analyzed the movement characteristics of several kinds [4] D. Lohse, B. Schmitz, and M. Versluis, “Snapping shrimp of snapping shrimps and the dynamic changes of cavitation make flashing bubbles,” Nature, vol. 413, no. 6855, pp. 477- bubbles, which provide a useful reference for biomimetic 478, 2001. research on the movement mechanism and cavitation mech- [5] J. Herberholz and B. Schmitz, “Flow visualisation and high anism of snapping shrimp. speed video analysis of water jets in the snapping shrimp ( This study investigated the motion characteristics and Alpheus heterochaelis ),” Journal of Comparative Physiology. the cavitation mechanism of the snapper claw, as well as A, vol. 185, no. 1, pp. 41–49, 1999. the development and structure of cavitation bubbles. Cavita- [6] B. Schmitz, The Crustacean Nervous System, Springer, Berlin tion bubbles are generated by the snapping shrimp through Heidelberg, 2002. the rapid closure of the snapper claw. This is an acceleration [7] S. Amini, M. Tadayon, J. Q. I. Chua, and A. Miserez, “Multi- process with velocity ranging from 1000-4500 rad/s, which is scale structural design and biomechanics of the pistol shrimp relevant to the structure of the snapper claw. The average snapper claw,” Acta Biomaterialia, vol. 73, pp. 449–457, 2018. pressure drop at the claw nozzle is about 2.5 atm, which is [8] J. Herberholz and B. Schmitz, “The visible water jet: flow visu- sufficient to cause cavitation. The cavitation bubble is based alisation in snapping shrimp (Alpheus heterochaelis),” in New neuroethology on the move. Pro-ceedings of the 26th Gottingen on both Bernoulli’s law and inertia. When the cavitation neurobiology conference, vol. 2, p. 242, Thieme, Stuttgart, 1998. number of the bubbles generated by the snapping shrimp is [9] S. N. Patek and S. J. Longo, “Evolutionary biomechanics: the less than 0.2, an asymmetric cavitation vortex is generated. pathway to power in snapping shrimp,” Current Biology, Under the influence of the flow jet, the cavitation bubble vol. 28, pp. R115–R117, 2018. deforms from the initial toroidal bubble to a conical one. [10] T. Kaji, A. Anker, C. S. Wirkner, and A. R. Palmer, “Parallel When it is about to burst, the bubble is compressed into a saltational evolution of ultrafast movements in snapping concave shape, accompanied by a micro jet directed toward shrimp claws,” Current Biology, vol. 28, no. 1, pp. 106– the head of the bubble. 113.e4, 2018. [11] Z. Qian, M. Yang, L. Zhou et al., “Structure, mechanical Data Availability properties and surface morphology of the snapping shrimp claw,” Journal of Materials Science, vol. 53, no. 15, The data used to support the findings of this study are avail- pp. 10666–10678, 2018. able from the corresponding author upon request. [12] D. Hess, C. Brücker, F. Hegner, A. Balmert, and H. Bleckmann, “Vortex formation with a snapping shrimp claw,” PLoS One, Conflicts of Interest vol. 8, no. 11, article e77120, 2013. [13] P. Koukouvinis, C. Bruecker, and M. Gavaises, “Unveiling the The authors declare no conflict of interest. physical mechanism behind pistol shrimp cavitation,” Scientific Reports, vol. 7, no. 1, article 13994, 2017. Acknowledgments [14] X. Tang and D. Staack, “Bioinspired mechanical device generates plasma in water via cavitation,” Science Advances, This work was supported by grants from the National vol. 5, no. 3, article eaau7765, 2019. Defense Science and Technology Innovation Fund. All the [15] P. Alam, I. Sanka, L. P. Alam et al., “The snapping shrimp experiments in this manuscript follow the 3R principle dactyl plunger: a thermomechanical damage-tolerant (Reduction, Refinement, Replacement), and we provide sandwich composite,” Zoology, vol. 126, pp. 1–10, 2018. 12 Applied Bionics and Biomechanics [16] S. Vogel, Life in moving fluids: the physical biology of flow, Princeton University Press, 1996. [17] J. P. Franc and J. M. Michel, Fundamentals of Cavitation, Kluwer Academic Publishers, 2005. [18] T. Bourouina and J. P. Grandchamp, “Modeling micropumps with electrical equivalent networks,” Journal of Micromecha- nics and Microengineering, vol. 6, no. 4, pp. 398–404, 1996. [19] S. B. Perry and K. L. Gee, “The acoustically driven vortex cannon,” The Physics Teacher, vol. 52, no. 3, pp. 146-147, 2014. [20] Z. Y. Dong, Jet Mechanics, Science Press, Beijing, 2005. [21] M. A. Sadovskii, V. N. Rodionov, and G. V. Belyakov, Doklady Akademii Nauk SSSR, vol. 325, p. 42, 1992. [22] C. E. Brennen, Cavitation and Bubble Dynamics, Oxford University Press Inc., New York, 1995. [23] L. van Wijngaarden, “Mechanics of collapsing cavitation bubbles,” Ultrasonics Sonochemistry, vol. 29, pp. 524–527, [24] W. Lauterborn, “Cavitation bubble dynamics—new tools for an intricate problem,” Applied Scientific Research, vol. 38, no. 1, pp. 165–178, 1982. [25] G. V. Belyakov and A. N. Filippov, “Cavitating vortex genera- tion by a submerged jet,” Journal of Experimental and Theoret- ical Physics, vol. 102, no. 5, pp. 862–868, 2006. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Bionics and Biomechanics Hindawi Publishing Corporation

Research on Claw Motion Characteristics and Cavitation Bubbles of Snapping Shrimp

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Hindawi Applied Bionics and Biomechanics Volume 2020, Article ID 6585729, 12 pages https://doi.org/10.1155/2020/6585729 Research Article Research on Claw Motion Characteristics and Cavitation Bubbles of Snapping Shrimp 1 2 3 1 1 1 Yuliang Yang, Shimu Qin , Changchun Di, Junqi Qin, Dalin Wu, and Jianxin Zhao Shijiazhuang Campus, Army Engineering University, Hebei 050003, China China Aerodynamics Research and Development Center, Mianyang Sichuan 621000, China Unit 63961 of PLA, Beijing 100020, China Correspondence should be addressed to Shimu Qin; qshimu@126.com Received 12 February 2020; Revised 16 June 2020; Accepted 8 July 2020; Published 21 September 2020 Academic Editor: Francesca Cordella Copyright © 2020 Yuliang Yang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Snapping shrimp produces a high-speed jet through the rapid closure of the snapper claw, which stimulates the formation of cavitation bubbles of various shapes. In order to explore the fast motion characteristics of snapper claw, the formation and change process of cavitation, and the physical principles underlying the biological phenomena, the equivalent model of snapper claw was constructed through CT scanning technology. A high-speed camera was used to capture the claw’s motion characteristics, thereby simulating the production of cavitation bubbles by snapping shrimp. The results show that the rotation speeds of different species of snapping shrimps are different, as well as their motion characteristics. Cavitation is formed by the interaction of the pressure drop caused by the vortex at the nozzle with the inertia of the liquid inside the socket. Under the influence of the jet, the shapes of bubbles change from ring to cone, and eventually collapse into bubble clouds. 1. Introduction The snapper claws exhibit extremely high closing veloci- ties, with a measured value of 3500 rad/s [8]. The rapid closure mechanism is closely related to the structure of the Snapping shrimp is a member of the Alpheidae family. It has asymmetrical claws, the larger of which can grow to about half claw. The cocking pivot joints and cocking slip joints evolve its body size [1]. The claw has a protruding plunger (pl) on the on the claw between the dactyl and the propus [9, 10], which dactyl (d) and a matching socket (s) on the immobile propus facilitates the rapid closure of the claw. The cone-shaped (p) [2]. During predation, the snapping shrimp rapidly closes micropapillae units on the dactyl also have the effect of reducing underwater resistance, which facilitates the rapid the larger claw [3], draining the water into the socket and forming a high-speed water jet of 32 m/s [4]. Among them, closure motion of the snapper claw [11]. the speed of the water jet is related to the sex of the shrimp The cavitation generated by snapping shrimp is a kind and the size of the claw [5]. Because the high-speed water jet of vortex cavitation [12]. The original vortex with a cavita- injection causes cavitation due to the strong pressure reduc- tion ring is located in front of the claw. The volume of the tion effect of water and the rupture of the cavitation bubbles bubble is related to the closure velocity [13]. The reason in front of the claw, the snapping shrimp generates a loud why the high-speed jet is generated is not because the cracking noise of up to 210 dB at the source [6]. The shock axial momentum is large, but the momentum is converted wave released by the collapse of cavitation bubbles is about into the maximum strength of the leading vortex. 80 kPa at a distance of 4 cm [1], which is enough to stun and However, these findings are based on a simplified nozzle even kill the prey. When the claw is closed [7], there is an model, which can differ from the mechanism used by real angular offset between the dactyl and the propus, which pre- shrimp. The collapsed cavitation produces high pressures vents physical contact between these parts, indicating that and temperatures [4], thereby effectively forming a plasma the noise is caused by the bubble collapse. with photons and shock waves through energy focusing 2 Applied Bionics and Biomechanics above and vertical to the animals were both set to [14]. In order to avoid the destruction of the claw struc- ture by high-energy movement, it was found that the 99000 fps, 10 μs exposure time, and 512 ∗ 512 pixels. After materials of the claw have good temperature resistance the experiment, the calibration plate with a resolution of [15] and are subjected to more intense contact stresses [7]. 2 mm was placed on the plane perpendicular to the claw of The previous investigations mainly focused on the the camera to provide a reference for calculating the size, mechanical properties, surface morphology, snapping sound, distance, and angle during image postprocessing. and evolution of the snapper claw. However, the studies The actual size of the image was determined based on the about the mechanism of cavitation generated by snapping pixel coordinates of the picture and the length of the calibration shrimps and the characteristics of snapper claw motion are plate. The length of 4 mm on the calibration plate corresponds still blank. In order to elucidate the biophysical characteris- to the average value of 56 pixels, so the length of each pixel is tics of these small shrimps, this paper studied the structure 71.43μm. The contour of the snapper claw was obtained of snapper claw through CT scanning and established a 3D according to the gray value of the image through MATLAB, model of snapper claw, which was then used to simulate and the angles between the dactyl and the propus were deter- the formation of cavitation bubbles. A high-speed camera mined. Through curve fitting, the relationship between the was applied to capture and record the entire process of snap- angle and the time was obtained. Moreover, the relationship per claw rapid closure and the formation and development between the angular velocity and the angular acceleration was process of cavitation bubbles to analyze its motion character- also obtained through the derivative with time. istics and cavitation mechanism. Based on the combination Because the motion characteristics of No.1 shrimp of the above, the simulation results and the images captured (Alpheus macroskeles) was better than other samples, cavita- by the high-speed camera can provide insight into the gener- tion research was carried out by carrying out CT scanning ation and development of cavitation bubbles of the snapper and CFD simulation on it. claw. 2.3. Computed Tomography of the Snapper Claw. The snap- per claw was removed with scissors, and then cleaned with 2. Materials and Methods an ultrasonic cleaner (KQ-200KDE, Kunshan ultrasonic instruments CO., Ltd.) for 30 minutes to remove salt resi- 2.1. Preparation of Snapping Shrimp. In this experiment, dues, and then frozen in a vacuum freeze-drying machine samples were collected from the coastal area of Fujian, China, (FD-1C-50, Beijing Bo Kang laboratory instruments CO., in July 2018. A total of 6 adult male snapping shrimps that Ltd.). The dried snapper claw was tightly fixed with tape, had molted for over one week were selected for the experi- and then observed on a CT machine (nanoVoxel-3000, ment. According to the category of snapping shrimps, the Tianjin Sanying Precision Instruments CO., Ltd) with a scan- species and sizes of the shrimps used in the experiment are ning accuracy of 6.52 μm. as follows: Sample No.1 (Alpheus macroskeles, 44 mm with body length, and 8 mm with snapper claw size), Sample 2.4. Computational Fluid Dynamics Simulation. The stack of No.2 (Alpheus brevicristatus, 50 mm with body length, and CT slices was imported into the visualization software (Avizo 10 mm with snapper claw size), Sample No.3 (Alpheus brevi- 8.1) and then the claw is rendered in 3D visualization. The cristatus, 62 mm with body length, and 9 mm with snapper reconstructed 3D surface data of the claw was then exported claw size), Sample No.4 (Alpheus brevicristatus, 48 mm with to the CAD software (UG NX10). The main functional body length, and 8 mm with snapper claw size), Sample geometries of the claw were separated into the moving part No.5 (Alpheus acutocarinatus, 68 mm with body length, (dactyl), the stationary part (propus), and the connection and 12 mm with snapper claw size), Sample No.6 (Alpheus part to the pivot axis. According to the measurement results acutocarinatus, 74 mm with body length, and 11 mm with of high-speed photography, the angle of the claw was set to snapper claw size). The snapping shrimps were housed in ° 82.4 , as shown in Figure 1(b). seawater (temperature: 25 ± 1 C, salinity: 1.024) and were Since the jet and the cavitation bubble generated by the fed frozen shrimp every three days. Before the experiment, snapping shrimp were positioned close to the snapper claw, the snapping shrimps were numbered with small labels. in order to optimize the calculation accuracy and time, the CFD simulation mesh model containing internal and exter- 2.2. Measurement of Snapper Claw Motion Characteristics. nal parts was established, in which tetrahedral meshes with The use of high-speed cameras (V2512, Phantom) ensures the size of 30 μm were used in the internal part, and hexahe- that the movement of the snapper claw and the formation dron meshes with the size of 1 mm were used in the external and development of cavitation bubbles can be accurately part. The mesh size expansion ratio between the internal and captured and recorded. The experimental system consists of external parts was 1.2 : 1. After verification of grid indepen- a 50 ∗ 25 ∗ 30 cm aquarium, a vibration-isolated platform, dence, the number of cells met the calculation requirements. and two high-speed cameras. Snapping shrimp was fixed on The Reynolds number redefined the ratio of inertial the vibration-isolated platform by covering its carapace and forces to viscous forces in the fluid [16], which can determine claw with plasticene. The positions of the claw and cameras the flow type. need to be adjusted to the center of the camera’s field of view. Through the stimulation of a soft brush, the claw made a ρvd raising and rapid closure of the dactyl, and then the high- Re = , ð1Þ speed cameras were triggered to shoot. The cameras located Applied Bionics and Biomechanics 3 Camera Fixed nuts above Adjustable crossbeam Sensor fix rods Light sources Snapping shrimp Vibration-isolated Vertical platform camera 5 mm Pressure Aquarium sensors (a) (b) (c) 1 mm 1 mm 1.5 mm (d) (e) (f) Figure 1: (a) Schematic view of the experimental device. The vibration-isolated platform is placed in the center of the aquarium, and the sensors are fixed at a distance of 3 cm in front of the snapper claw. (b) Gray value image of the snapper claw from the side. The inflection points of the claw are marked by circles, and the opening angle is measured to be 82.4 . (c) 3D reconstructed model of snapper claw with a scale of 1 : 1. (d) CT slices of shrimp claw in the x-y direction. The dactyl is inserted into the socket to form a cavity closed on both sides. (e) CT slices of shrimp claw in the x-z direction. The red rectangle indicates the cavity and nozzle structure. (f) CT slices of shrimp claw in the y-z direction. The dactyl is tightly surrounded by socket, representing a fine hermetic seal. tive solutions of the pressure field and velocity field. The where v is the jet velocity, ρ is the fluid density, μ is the viscosity, and d is the characteristic size of the claw nozzle. selected solvers and predefined parameters in the simulation are listed in Table 1. With the typical values of v ≈ 32 − 70 m/s, ρ = 1024 kg/m , μ =1:003e − 03 kg/ðm ∗ sÞ, d ≈ 0:2mm, the Reynolds A dynamic mesh was used to simulate the movement of the dactyl, which is essential to accurately simulate the number is about 6534-14293, indicating that the type of jet process. According to the high-speed photography results, produced by snapping shrimp is turbulence. the closure velocity of the claw was accelerated, from the The FLUENT software package was used for the CFD initial velocity of 70 rad/s to the final velocity of simulation. In the simulation, the Navier-Stokes equations 4392 rad/s, and the total time was only about 885 μs. Sub- were used to simulate a Newtonian fluid whilst maintaining sequently, the claw motion information was written to a mass, momentum, and energy. In addition, the achievable profile to command the dactyl movement. For dynamic k-e turbulent model and VOF model were selected. The mesh, the smoothing and remeshing mesh methods were application of the PISO method was to determine the itera- 4 Applied Bionics and Biomechanics Table 1: Parameters of fluent simulation. Parameters Predefined value Solver Pressure-based Transient Solution methods PISO PRESTO, second order upwind Multiphase flow model VOF Realizable k − ε, Standard Wall function Cavitation model Zwart-Gerber-Belamri 3540 pa Primary phase Water-liquid Second phase Water-vapor 3 3 Density 1024 kg/m Density 0.02558 kg/m Materials 1:003e − 03 kg/ðÞ m ∗ s 1:26e − 06 kg/ðÞ m ∗ s Viscosity Viscosity Table 2: Settings of the dynamic mesh. Smoothing method Parameters Remeshing method Parameters Spring constant factor 0.01 Minimum length scale (m)0 Convergence tolerance 0.001 Maximum length scale (m)0 Number of iterations 20 Maximum cell skewness 0.7 Laplace node relaxation 1 Size remeshing interval 1 selected. The settings of the dynamic mesh are listed in in Figure 1(e). In the process of closing the claw, the dactyl Table 2. moves around the axis on the propus. The velocity reaches its maximum value at the moment when the dactyl is completely closed. The plunger on the dactyl provides the 3. Results initial liquid velocity by replacing the liquid in the socket. Due to the sealing of the socket and the propus, the liquid 3.1. Movement Characteristics of the Snapper Claw. The can only flow out of the socket through the orifice on the side high-speed camera accurately observed the movement of of the claw, resulting in a high-speed jet similar to the func- the snapper claw. In response to the stimulation, the snap- tion of the nozzle structure. ping shrimp tilted its dactyl to the maximum angle and stayed in that position for about a second, then the dactyl moved to close the claw at an extreme rapid velocity around 3.3. Formation and Development of Cavitation Bubbles. the joint. The curve of the snapper claw motion angle is The simulation results of the snapper claw model are rd shown in Figure 2(a). The 3 order polynomial can fit the shown in Figure 3. In the simulation and calculation of relationship between the angle of the claw motion and time cavitation bubbles, the isosurface shows bubbles with a well, as shown in Figure 2(b). The parameters of the curve volume fraction of 50% (the green part in the figure). 3 2 fitting (f ðxÞ = p1 ∗ x + p2 ∗ x + p3 ∗ x + p4) were shown When the claw is closed from the maximum angle (Figure 3(a)), the angular velocity gradually increases. in Table 3. Taking the derivative of the angle gave the angular veloc- With the movement of the claw, bubbles are first formed ity, which is an acceleration process from less than 100 rad/s in the corners of the socket (Figure 3(b)). When the claw to more than 1000 rad/s finally, as shown in Figure 2(c). is about to close, a toroidal bubble appears around the Using the same method, the angular acceleration was derived orifice formed by the dactyl and propus (Figure 3(c)). When the claw motion stops, the bubble continues to as follows. The No.1 shrimp (Alpheus macroskeles) had the highest angular velocity of about 4500 rad/s, and the angular grow and moves in the direction of the jet (Figure 3(d) 7 2 acceleration continued to increase to nearly 10 rad/s . The and (e)). Afterwards, under the influence of the ambient maximum angular velocity of the No. 2-4 shrimps (Alpheus pressure, the bubble begins to shrink and eventually col- brevicristatus) was about 1000 rad/s, and the angular acceler- lapses (Figure 3(f)–(h)) and disappears (Figure 3(i)). 6 2 ation almost remained unchanged at 10 rad/s . The maxi- mum angular velocity of the No. 5 and No. 6 shrimps 4. Discussion (Alpheus acutocarinatus) was about 1400 rad/s, and the angular acceleration continued to decrease, from the initial 4.1. Analysis of the Movement Characteristics of the Snapper 6 2 4×10 rad/s to 0 or even negative value. Claw. According to the law of conservation of energy, the larger the volume, the more water is contained in the socket, 3.2. Characterization of Claw Structure. The images pre- so more kinetic energy is required to drive the liquid. In addi- sented in Figures 1(c) and 1(d) show the 3D reconstructed tion, the larger the volume of the claw, the greater the area of model and the slices of the snapper claw in different direc- contact with water during movement, so the greater the resis- tions. When the claw is closed, a cavity is formed between tance. Taking into account the above two reasons, the move- the dactyl and the propus, as indicated by the red rectangle ment characteristics of different types of snapping shrimps in Applied Bionics and Biomechanics 5 1.5 2.5 1.5 0.5 0.5 0 0 0 0.5 1 1.5 2 2.5 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 –3 –3 Time (s) × 10 Time (s) × 10 No.4 No.1 No.4 No.1 No.2 No.5 No.2 No.5 No.3 No.6 No.3 No.6 (a) (b) 6000 6 × 10 3000 6 –1000 –2 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 –3 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Time (s) × 10 –3 Time (s) × 10 No.1 No.4 No.1 No.4 No.2 No.5 No.2 No.5 No.3 No.6 No.3 No.6 (c) (d) Figure 2: Motion information of the claw. (a) Curve of claw angle and time. (b) Angle of claw as a function of time. (c) Angular velocity of claw as a function of time. (d) Angular acceleration of claw as a function of time. the resistance they suffered when moving in the water was also greater, resulting in a slower closure velocity. However, Table 3: Curve fitting parameters of angle with time. due to the small volume of the socket cavity of this type of Sample p1 p2 p3 p4 R shrimp, its water storage capacity was small, and the resis- 1 1.24E+09 9.25E+05 -136.1 0.026 0.9962 tance of the liquid to the dactyl was low during squeezing. Combining two points, the closure angular acceleration of 2 -1.13E+08 6.53E+05 -78.79 0.02616 0.9973 the claw of this type of shrimp did not change much. Among 3 -9.46E+06 3.97E+05 -98.84 0.0232 0.9976 the test samples, the Alpheus acutocarinatus (No.5-6) had the 4 -2.23E+06 3.91E+05 27.61 0.01768 0.999 largest volume with an average dactyl length of 12 mm. Due to 5 -6.82E+08 1.91E+06 -454.4 0.02831 0.9926 their slender and flat contour of the dactyls, which can reduce 6 -5.83E+08 1.50E+06 -13.16 0.01602 0.9991 resistance, the closure velocity of snapper claw was faster than the second kind of shrimps, about 1400 rad/s. On the other hand, due to the large volume of the socket cavity, higher the experiment are different. Among the samples, the smal- energy was required to squeeze out the stored liquid, resulting lest snapping shrimp, Alpheus macroskeles (No. 1), had a tiny in insufficient energy provided by muscle contraction to over- snapper claw that was only about 8 mm long, so the resis- come the resistance of the liquid, so the angular acceleration of tance it received when moving in the water was small, and the claw motion continued to decrease. the energy provided by its muscle contraction was enough to squeeze out the fluid in the socket cavity. Therefore, both 4.2. Cavitation Inception. The contour of the cavitation the angular velocity and acceleration increased when the inception of the snapper claw is shown in Figure 4. The shrimp closed its claw. The Alpheus brevicristatus (No. 2-4) velocity of the jet generated by the claw flow through the noz- had larger snapper claws than those of the No.1 shrimp, so zle is about 70 m/s in the center (Figure 4(a)), which is much Angular velocity (rad/s) Angle (rad) 2 Angle (rad) Angular acceleration (rad/s ) 6 Applied Bionics and Biomechanics Vapor volume fraction Vapor 9.730e-001 7.298e-001 (a) (b) (c) 4.865e-001 (d) (e) (f) 2.433e-001 0.000e-000 (g) (h) (i) Figure 3: Indicative instances of the snapper claw model closure. The green part represents the cavitation bubble with the vapor volume of 50%. faster than the velocity of the surrounding flow. Under the where p is the pressure at the vortex radius, and p is the R C squeezing of the plunger, the liquid in the socket cavity is pressure at the vortex core. The liquid density ρ is ejected, so that the jet kinetic energy increases inside the 1024 kg/m , and the vortex radius R is about 0.15 mm. The cavity. When the liquid reaches the nozzle, the jet will con- vorticity is twice the instantaneous principal axis angular tinue to move along the wall of the claw. Under the influence velocity of the strain-rate tensor of the fluid element, so the of the inverse pressure gradient (dp/dx > 0), the jet velocity angular velocity Ω is about 150000 rad/s, with an average near the wall gradually decreases. At this time, the boundary pressure drop of 259200 Pa (about 2.5 atm). Since the layer begins to increase in thickness, and separates from the pressure at the vortex core is sufficiently lower than the satu- nozzle to form a vortex, and finally merges into the main- rated vapor pressure of 3540 Pa, this pressure difference stream. As shown in Figure 4(b), the vortex structures C1 between the two can lead to cavitation. and C2 are first formed around the nozzle, and the directions When the dactyl stops moving, the socket is not filled by of the two vortices are opposite, with the vortex of about the plunger, and the liquid in the cavity continues to flow 300,000. According to Bernoulli’s law, the pressure in the outward along the nozzle due to inertia, resulting in cavita- region with high velocity can be decreased and the presence tion inside the cavity, as shown in Figure 4(d). The formula of the vortex causes a pressure drop. The pressure at the core for calculating the pressure drop in the channel is [18]: of the vortex is the lowest, accompanied by cavitation incep- tion. Cavitation bubbles V1 and V2 appear around the nozzle l dϕ Δp = ρ , ð3Þ and are connected to the dactyl and the propus, as shown in S dt Figure 4(c). The induced liquid depressurization caused by the vortex can be expressed as [17]: where l and S are the length and the cross-sectional area of the channel, and ϕ is the flow rate. After the bubble in the cavity leaves the socket, it enters 2 2 ρR Ω the low-pressure area of the nozzle and then merges with p − p = , ð2Þ R C 2 the toroidal bubble generated by the vortex. For snapping Applied Bionics and Biomechanics 7 Velocity curl Velocity 7.065e+01 1.591e+06 6.693e+01 1.508e+06 6.321e+01 1.424e+06 5.949e+01 1.340e+06 5.577e+01 1.256e+06 5.205e+01 1.173e+06 Dactyl 4.834e+01 1.089e+06 4.462e+01 1.005e+06 C1 4.090e+01 9.214e+05 3.718e+01 8.376e+05 3.346e+01 7.538e+05 2.975e+01 6.701e+05 2.603e+01 5.863e+05 2.231e+01 5.026e+05 1.859e+01 4.188e+05 1.487e+01 3.350e+05 1.115e+01 Propus 2.513e+05 C2 1.675e+05 7.436e+00 8.376e+04 3.718e+00 1.054e–03 0.000e+00 0 0.0015 0.003 (m) 0 0.0015 0.003 (m) X Y X Y 0.00075 0.00225 0.00075 0.00225 (a) (b) Vapor volume fraction Vapor volume fraction 9.981e+01 9.981e+01 9.456e+01 9.456e+01 8.931e+01 8.931e+01 8.405e+01 8.405e+01 7.860e+01 7.860e+01 7.355e+01 7.355e+01 6.829e+01 6.829e+01 6.304e+01 V1 6.304e+01 5.779e+01 5.779e+01 5.253e+01 5.253e+01 4.728e+01 4.728e+01 4.203e+01 4.203e+01 3.677e+01 3.677e+01 3.152e+01 3.152e+01 2.627e+01 2.627e+01 2.101e+01 2.101e+01 1.576e+01 V2 1.576e+01 Bubble 1.051e+01 1.051e+01 5.253e+02 5.253e+02 0.000e+00 0.000e+00 0 0.0015 0.003 (m) 0 0.0015 0.003 (m) X Y X Y 0.00075 0.00225 0.00075 0.00225 (c) (d) 907. 2 𝜇 s 5 mm 967. 8 𝜇 s 5 mm 1301. 1 𝜇 s 5 mm (e) (f) (g) Figure 4: (a) The contour of jet velocity. The core velocity is much higher than the surroundings, forming a submerged jet in water. (b) The contour of vortex. Vortices are formed around the orifice of the nozzle, causing the pressure drop. (c) The contour of vapor. At the position of the vortex, cavitation incepts and the initial shape is toroidal. (d) The cavitation bubble in the socket cavity due to inertia. (e) Vortex core regions are indicated in grey. It gradually develops into a ring structure close to the dactyl. (f) The development of the cavitation bubble. The bubble is formed first at the nozzle orifice, and then changes from a toroidal bubble to a more conical one. (g) The pictures of cavitation bubbles generated by snapper claw. 8 Applied Bionics and Biomechanics Brush Bubble 5 mm 0 𝜇s +87.7 𝜇s +175.4 𝜇s +263.1 𝜇s (a) Dactyl Nozzle Propus 5 mm +350.8 𝜇s +438.5 𝜇s +526.2 𝜇s +613.9 𝜇s (b) Figure 5: High-speed images from the top of the claw. (a) The pictures of the compression of cavitation bubbles. The volume of the conical bubble reduces to is the minimum. (b) The pictures of the rebound of cavitation bubbles. The bubbles rebound many times without a specific shape and eventually disappear. shrimp, these two sources of cavitation work together to form initial cavitation bubble appears as a ring structure, which the bubble. continuously expands and stretches to a conical structure in contour along the direction of the jet under the impact of a 4.3. Development of Vortex Cavitation. After cavitation starts high-speed jet. Sadovskii et al. [21] studied the morphological at the nozzle, the vortex moves with the flow of the jet. changes in cavitation bubbles produced by high-speed Figure 4(e) shows the contour of the vortex at the nozzle submerged jets. At the moment of jet generation, a cavity when the claw is closed, where the grey parts represent the appeared as a narrow hollow torus in the plane perpendicular vortex regions. The vortex first appears around the nozzle to the jet direction. The transverse diameter of the cavity was orifice, and then develops into a ring structure close to the much larger than the jet diameter. When the jet was ejected dactyl in a similar manner to the air vortex cannon [19]. from the nozzle, the cavity surface evolved into an approxi- The core velocity of the jet produced by the claw is about mately cylindrical surface that grew in the direction of jet 70 m/s initially, and then gradually decreases. The vortex ring motion. After the jet was generated, the closure of the bottom structure is formed around the jet. As the jet develops, its surface of the cavity resulted in the formation of an axial jet radius gradually increases. According to the jet theory, under inside the cavity. The ever-evolving reentrant jet traversed the influence of the viscosity of the liquid, the boundary the cavity along its axis of symmetry to form a new conical layers of the jet continuously fall off, resulting in the vortex cavity, which had a convex surface as it penetrated into the filling of the area of the jet boundary. The vortex will cause liquid. The bottom surface of the cavity where the jet was turbulence, which will entrain any fluid in the static state into generated advanced in the direction of the jet. Therefore, the jet. With the development of turbulence, the entrained the cavitation bubbles generated by the snapping shrimp fluid increases, and the boundary of the jet gradually expands evolved from the initial ring-shaped bubbles into more coni- to both sides. The flow rate q increases along the path [20]. cal bubbles and moved in the direction of the jet. A high- speed camera was used to photograph the process of cavita- rffiffiffi q x tion bubbles produced by the claw of snapping shrimp. As ∝ , ð4Þ q d can be seen from Figure 4(g), after the claw was closed, the toroidal bubble overflowed from the side of the claw and where q is the flow at the nozzle, and d is the feature size of continuously expands in the cone structure. In addition, the the nozzle. Therefore, the vortices form a large vortex ring direction of its motion is at an angle relative to the claw. structure around the jet, and its size continues to increase. Therefore, the high-speed imaging confirms the validity of The bubble morphology is simulated and shown in the theoretical and simulation results. It can be concluded that there are two main functions of the jet. One is to transfer Figure 4(f), in which the orange part represents the contour of 20% vapor volume fraction. The bubble is ejected from the axial momentum of the jet to the vortex. The enhanced the nozzle on the side of the claw, and there is a certain angle vortex forms a low-pressure zone, which advances with the between the moving direction of the bubble and the claw. The vortex, causing continuous expansion of cavitation bubbles. Applied Bionics and Biomechanics 9 Pressure Dactyl 2.944e+004 2.274e+004 1.605e+004 9.352e+003 2.656e+003 –4.040e+003 –1.074e+004 –1.743e+004 –2.413e+004 –3.082e+004 –3.752e+004 –4.422e+004 Reference plane –5.091e+004 –5.761e+004 –6.430e+004 Propus –7.100e+004 –7.770e+004 –8.439e+004 –9.109e+004 –9.779e+004 Z 0 0.002 0.004 (m) 0 0.0005 0.001 (m) [Pa] 0.00025 0.00075 0.001 0.003 (a) (b) Vapor volume fraction Velocity 8.250e–001 1.320e+001 7.816e–001 Head 7.381e–001 6.947e–001 6.513e–001 9.901e+000 6.079e–001 5.645e–001 5.210e–001 4.776e–001 Nozzle 4.342e–001 6.601e+000 3.908e–001 3.474e–001 3.039e–001 2.605e–001 Bottom 2.171e–001 3.300e+000 1.737e–001 1.303e–001 X X 8.684e–002 4.342e–002 Y Y 0.000e+000 0.000e+000 0 0.0005 0.001 (m) 0 0.0005 0.001 (m) 0.00025 0.00075 0.00025 0.00075 (c) (d) Vapor volume fraction 9.989e–001 7.491e–001 Dactyl Vapor 4.994e–001 Jet 2.497e–001 Propus Vapor X Y 0 0.0015 0.000 (m) 0.000e+000 0.00075 0.00225 5 mm (e) (f) Figure 6: Continued. 10 Applied Bionics and Biomechanics Vapor volume fraction Vapor volume fraction 9.981e–01 9.981e–01 9.456e–01 9.456e–01 8.931e–01 8.931e–01 8.405e–01 8.405e–01 B–B 7.880e–01 7.880e–01 7.355e–01 7.355e–01 A–A 6.829e–01 6.829e–01 6.304e–01 6.304e–01 5.779e–01 Vapor 5.779e–01 5.253e–01 5.253e–01 4.728e–01 4.728e–01 4.203e–01 4.203e–01 3.677e–01 3.677e–01 3.152e–01 3.152e–01 2.627e–01 2.627e–01 2.101e–01 Jet 2.101e–01 1.576e–01 1.576e–01 1.051e–01 1.051e–01 5.253e–02 5.253e–02 0.000e+00 Z 0.000e+00 0 0.0005 0.000 (m) 0 0.001 0.002 (m) X Y 0.00025 0.00225 0.0005 0.0015 (g) (h) Figure 6: (a) Reference plane for the simulation results, showing the flow field of the snapper claw along the nozzle. (b) Contour of the pressure on the claw side when the bubble collapses. The pressure on both sides of the bubble is different, and the pressure on the bottom is higher. (c) When it is about to burst, the bubble is compressed into a concave shape, pointing to the head of the bubble. (d) Speed vector of the flow field. When the bubble bursts, the fluid on both sides moves toward the middle of the bubble, and the jet velocity from the bottom of the bubble pointing to the head is greater. (e) Picture of the cavitation bubble in the maximum state. The nonspherical bubble includes the jet in the middle and vapor around. (f) Simulation result of cavitation bubble with vapor volume fraction of 50%. (g) Contour of vapor volume fraction along the axis of the bubble. (h) Contour of vapor volume fraction along the radial cross-section of the bubble. The other is to guide the movement of the vortex ring and p are the liquid pressure at the interface and far away from cavitation bubbles. the bubble, respectively. According to the R-P equation, it can be inferred that the 4.4. Collapse of Cavitation Bubbles. There are two stages of collapse process of the nonspherical bubble is related to the the bubble collapse, namely, the compression stage and the local curvature radius of the initial shape of the bubble [24]. rebound stage [22]. During the compression stage, due to According to the simulation results, when the bubble bursts, the decrease in vortex intensity, the pressure outside the the forces on both ends of the bubble are different. The pres- bubble is greater than the internal pressure, causing the sure in the head area is lower than the pressure in the tail bubble to start compressing. At this stage, the bubbles are area, which causes the bubble to collapse from the bottom relatively stable and the disturbance increases slowly. There to the head, and generates a micro jet directed to the head, is a highly unstable nonspherical disturbance in the rebound as shown in Figures 6(a). stage, which is manifested by the fierce breakup of bubbles Therefore, it is estimated that the cavitation bubbles and the formation of many small bubbles. Under the contin- generated by the shrimps are directional. When the snapping uous rupture and rebound, the bubbles form a visible cloud. shrimp is hunting, its claw aims at the prey, and the shock wave Through the high-speed camera, the collapse process of the and the microjet generated by the collapse of the bubble both act bubbles generated by snapping shrimp is recorded. Through on the target, which has little effect on the snapping shrimp itself. careful observation, it can be found that the nonspherical bubbles begin to shrink after expanding to the maximum 4.5. Structure Characteristics of Cavitation Bubbles. volume. During the shrinkage process, the outline of the Figure 6(e) shows the maximum volume of cavitation bubble remains clear and the shape remains unchanged, indi- bubbles produced by the claw. It can be seen from the outline cating that it is in the compression stage, as shown in that the cavitation bubble is conical, in which the bottom sur- Figure 5(a). After the bubble shrinks to its minimum volume, face is elliptical and the front surface is elongated. The main it begins to rebound and expand, changing from a single body of the bubble is transparent, and there is an opaque jet conical bubble to many cloud bubbles. These bubbles burst inside. In the simulation results shown in Figure 6(f), along and rebound continuously, and then the cloud disappears the axis of the bubble (A-A), the inside of the bubble was gradually. This process is the rebound stage, as shown in not all water vapor, but there was a conical cavity structure Figure 5(b). as shown in Figure 6(g). The bubble is not the initial ring The Rayleigh-Plesset equation is widely used to describe structure, but a symmetrical nonspherical shape. The dimen- the collapse of a bubble [23]. sionless parameter σ was applied to describe the cavitation. 2 2 p − p p − p d R 3 dR 4ν dR 2S ∞ v g ∞ σ = , ð6Þ = R + + + , ð5Þ 1/2ρV ρ 2 dt R dt ρR dt ∞ where R is the radius of the bubble, ρ is the density of the liq- where p is the absolute pressure, and p represents the ∞ v uid, ν is the dynamic viscosity, S is the surface tension, p and vapor pressure of the liquid. V is the jet velocity, and ρ is g Applied Bionics and Biomechanics 11 nutritious food and a suitable living environment for ani- the liquid density. The cavitation number describes the possibility that the fluid cavitates or not when the high- mals. The snapping claw was removed with scissors, which speed flow reaches such low pressure. Where p =0:103 is safe for snapper claw because the other claw would grow to the lager one and the broken part could grow to a small MPa, V = 32 ~ 70 m/s, p = 3540 Pa, and ρ = 1024 kg/m . ∞ v claw. And this fast operation can reduce animal pain as well. Therefore, the cavitation number of bubbles generated by To prevent interspecific conflict, the animals without snap- the snapping shrimp is σ =0:04 ~ 0:19. 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Applied Bionics and BiomechanicsHindawi Publishing Corporation

Published: Sep 21, 2020

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