Modeling and Hydrodynamic Characteristics of Bionic Undulate Fin Propeller Driven by Hydraulic System

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1 Advances in Natural Science Vol 3, No 2, 2010, wwwcscanadanet ISSN [PRIN] ISSN [ONLINE] wwwcscanadaorg *he 3rd International Conference of Bionic Engineering* Modeling and Hydrodynamic Characteristics of Bionic Undulate Fin Proeller Driven by Hydraulic System XU Hai-jun 1 PAN Cun-yun 2 XU Xiao-jun 3 ZHOU Han 4 Abstract: he bionic undulating roeller driven by hydraulic system has different structure, kinematic and dynamic characteristics than that of the common bionic undulating roellers driven by other sources his aer highlights firstly the structure and driving mechanism of bionic undulating roeller with a hydraulic system, and then setu its kinematic model, based on ruled-surface equation Changing rules of dynamic mesh for bionic fin is designed based on kinetic model Later on, the changing courses of hydrodynamic force caused by the bionic undulating fin are calculated and studied with the CFD (Comutational Fluid Dynamics) method, as well as the changing characteristics of the fluid ressure field he analysis showed that while driven by hydraulic system, the bionic roeller could roduce full-baseline undulating motion, and has flexible start-u rocess, as well as doubled-frequency character he bionic undulating fin driven by hydraulic system uts u flexible characters on both kinematic and dynamics Key Words: Hydraulic Driven; Undulating Fin; Bionic Proeller; Dynamic Mesh; Hydrodynamics 1 INRODUCION 1 Lecturer, College of Mechatronics Engineering and Automation, National University of Defense echnology, Changsha, Hunan , China 2 College of Mechatronics Engineering and Automation, National University of Defense echnology, Changsha, Hunan , China 3 College of Mechatronics Engineering and Automation, National University of Defense echnology, Changsha, Hunan , China 4 College of Mechatronics Engineering and Automation, National University of Defense echnology, Changsha, Hunan ,China *Received 8 May 2010; acceted July

2 Bionic roelling technology has gained much attention from researchers around the world however, as for as the study of undulating mechanism and engineering technology, little work has been ut on existing bionic undulating roellers, which leads to the distance on motion and roelling ability between exected and actual bionic roellers, and bionic of fish (Maciver et al, 2004; LIU &HU, 2006; XIE et al, 2006) In order to enhance the flexible characteristics of structure and motion in bionic roeller, the aer designs a bionic undulating roeller with a um-valve controlled hydraulic system, called HBUP (Hydraulic Driven Bionic Undulating Proeller) he HBUP consisted of bracket, RDV (Rotational Direction Valve), several BSUs (Bionic Swaying Units) and bionic fin (ZHANG et al, 2008), as is shown in figure 1 Figure 1: Structure of Hydraulic driven Bionic Undulating Fin (1) Bionic Ribbing (2) Bionic Swaying Unit (3) Branch Oil Pie (4) Bracket (5) Bionic Fin (6) Rotational Direction Valve he RDV drives each BSU swaying to and fro, eriodically, and astricts several BSUs swaying in sequence, create undulating wave, with controlled sreading frequency and direction By changing oil flux, swaying range can be adjusted, and similarity is the undulating wave amlitude he HBUP could roduce variable wave length under different connection method between RDV and BSUs 2 KINEMAIC MODELING OF HBUP 21 Setu of Reference Frames o be convenient for modeling and analyzing, several reference frames are setu (YAN, 2005), as shown in figure 2 Figure 2: Setu of Reference Frames for HBUP Base-oint Frames Oxyz i i i i Origin O i is the base-oint of the BSU i, axis x i towards the tangent direction of base-line at oint O i, axis y i towards the main normal direction, and axis z i towards the sub-normal direction, then reference frames Oxyz are setu i i i i 278

3 HBUP Frame Oxyz It has suerosition to the first base-oint frame HBUP Accomanying Frame Oxyz r r r r It has suerosition to HBUP Frame at the initial time t 0s he Inertial Frame Oxyz e e e e Origin O e fixed to the ground, and axis xe, ye, z e arallel to axis xr, yr, z r 22 Kinematic Modeling of HBUP In figure 3, P is a common oint on bionic fin in HBUP Frame Oxyz, OP e stands for the ribbing across P from to-oint P e to base-oint O, with the coordinates ax ( ) [ xyx, ( ),0], and OP e hx ( ) According to the Base-oint Frames, base-oint frame Oxyz is setu for ribbing OP, e then ( x, t) is angle between OP e and axis y Figure 3: Ruled-surface Kinematic Model for Bionic Fin (HU et al, 2009) Defining the variable s [0,1] along ribbing, and OP shx ( ) hen coordinates of P in Oxyz can be deicted by following formula x 0 y sh( x) cos ( x, t) z sh( x) sin ( x, t) When baseline is suosed as a lanar curve, then OO in Oxyz can be described as follows x x 2 OO ax ( ) yx ( ) ax 1 ax 2 a 3 (2) 0 0 Where, ai ( i 1,2,3) are constant Letting the angle between tangent of baseline at O and axis x as ( x), then ( x) arctan y'( x) hus OP e can be exlained in Oxyz as follows: cos ( x) sin ( x) 0 x sh( x) cos ( x, t) sin ( x) OP e sin ( x) cos ( x) 0 y shx ( ) cos ( xt, ) cos ( x) (3) z sh( x) sin ( x, t) (1) 279

4 According to relative bionics study (DONG, 2003), changing rules of ribbing length can be summarized into the following form: 2 hx ( ) hx hx h (4) Where, hi ( i 1,2,3) are constant, and not all of them are zero Combined with equation (1) ~ (4), coordinates of P in Oxyz is shown as follows r ( x, s, t) a( x) sh( x) c( x, t) x cos ( xt, ) sin ( x) 2 2 ax 1 ax 2 a 3 s ( h1 x h2 x h3) cos ( xt, ) cos ( x) (5) 0 sin ( xt, ) Where, cxt (, ) is the transforming matrix from Oxyz to Oxyz When P moves freely on the whole bionic fin, equation (5) deicts the undulating motion shae of the whole bionic roeller at any time 3 HYDRODYNAMIC MODEL AND PARAMEER SEING OF HBUP 31 Parameter Setting of Hydrodynamic model A three-dimensional model of bionic fin is built, according to the arameters in table 1 able 1: Structure and Motion Parameters of Bionic Fin Parameter Height (H) Wavelength(λ) Frequency(f w ) Amlitude(θ max ) Unit m m Hz rad Value π/12 Suosing that non-sliage condition is ermitted on the undulating wave surface of bionic fin, which means that the velocity of fluid nearby the surface is equal to that of mesh grid node Besides, assumtions are made that fluid is uncomressible with infinite volume, and the fluid field is still until the bionic fin starts moving (HAN et al, 2004; WANG, 2008) Parameters of the calculating region for bionic fin are as follow: (1) Sizes of calculating region and dense region are set as follows LWH 4m2m2m (6) L1 W1 H1 16m 08m 08m (2) Entrance boundary conditions: initial velocity and ressure of fluid are zero V in vx vy v z (7) in 0 (3) Exit boundary conditions: velocity and ressure grads of fluid are zero V out V out V out 0 x y z (8) out out out 0 x y z Parameters of calculating region are shown in figure 4 280

5 Figure 4: Parameters Setting of Calculating Region 32 Mesh Grid Dividing of Calculating Region In order to cature effectively the fluid information while the bionic fin is undulating, mesh grid forming method with multi-sized function is used to make a balance between mesh grid size and number his can be exlained as follows: Dense region near bionic fin changes raidly and it is divided into tetrahedron mesh grid with tiny size However, calculating region far away from bionic fin can be divided into tetrahedron mesh grid too, but with larger size (ZHOU, 2009) With the mesh grid generating method above, mesh effect of calculating region is shown in figure 5, after a horizontal lane is used to intercet the calculating region Figure 5: Mesh grid dividing of Calculating Region 4 HYDRODYNAMICS ANALYZING OF HBUP 41 Analyzing of Hydrodynamic Forces and orques When calculating in the software Fluent, bionic fin model is fixed by its baseline, and the iterative time ste is 001s Starting and stable rocess is set as follows: during starting rocess, the undulating frequency kees fw 3Hz, and undulating amlitude increases from zero to 12 Within three motion cycles, the model kees undulating under constant motion arameters for another three motion cycles 281

6 According to the calculating results during the starting and stable rocess of bionic fin, curves of hydrodynamic forces in three directions of Oxyz are shown in figure F z F(N) t(s) F y Figure 6: Curves of Hydrodynamic Forces As is shown in figure 6, during the starting and stable rocesses (t = 0~2s), hydrodynamic forces generate along each axis of Oxyz, and aear eriodicity obviously Minus values mean that directions of hydrodynamic forces are oosite to that of undulating motion Proelling and lifting forces along axis x and amlitude until it achieves stability (t=1~2s), maximal values of F x y increase following the increase of undulating F x and F y are N and N resectively, eriodical average values are Fx 80682N and Fy 61412N resectively Changing cycle of roelling and lifting forces are nearly of the same magnitude, about 01626s, which is about half of the undulating cycle his means that the changing frequencies of roelling and lifting forces are twice in magnitude of that of undulating motion Periodical average value of lateral force along axis z is about Fz 01686N, far away from roelling and lifting forces However, changing cycle of lateral force is about 03184s, equal to that of undulating cycle he changing frequencies of roelling and lifting forces are twice in magnitude of that of undulating motion his henomena is called doubled-frequency effect of undulating Although eriodical average value of lateral force is very small and is disadvantage of undulating motion, since it exists all the time With the same calculating results, curves of hydrodynamic torques in three directions of Oxyz are shown in figure M y M z M(N m) M x t(s) Figure 7: Curves of Hydrodynamic orques 282

7 As is shown in figure 7, eriodical average value of rolling torque along axis x and yawing torque along axis y are nearly zero, and the changing cycles are about 03262s, nearly the same of undulating cycle his is because rolling and yawing torques come from the action of lateral force F z Maximal value and eriodical average value of itching torques along axis z are M z 22539N m and M z 10793N m resectively, the changing cycle is about 01607s, nearly half of the undulating cycle herefore, there is doubled-frequency effect for the itching torque two his is because itching torque mainly comes from F and F, where doubled-frequency effects exist x y 42 Characteristics of Pressure Field in Stable Process After visualization on the calculated results, changing course of ressure field on bionic fin is obtained, as shown in figure 8 It is obvious that there are both high and low ressure regions on bionic fin synchronously hese two kinds of ressure regions change and alternate regularly into one direction, along with the sreading of undulating wave x x y y O z O z (a) (b) y x y x O z O z (c) (d) y x y x O z O z (e) (f) Figure 8: Pressure Nehogram on Bionic Fin in an Undulating Cycle 283

8 he undulating waves sreads along axis x, followed by low and high ressure regions moving from front to back in sequence and eriodically, as shown in figure 8, and cause hydrodynamic forces and torques In a single undulating cycle, low and high ressure regions change their osition twice in turn, then form the doubled-frequency effect 5 CONCLUSIONS he bionic undulate roeller using hydraulic system as driving chain could generate an undulating motion with amlitude gradually increasing, so that the hydrodynamic forces and torques increase inchmeal his makes the bionic structure carry hydro-load gradually, which is uniform to that of nature fish Some of the hydrodynamic forces and torques are of doubled-frequency characteristic, because of the trade off between low and high ressure regions on undulating bionic fin It is obvious that hydraulic system rovides the bionic roeller unique flexible structure and dynamic characteristics, which are very imortant in underwater bionic roelling technology REFERENCES DONG Zengfu (2003) Matrix Analysis Course[M] HaErBin: HaErBin Industry University Press (In Chinese) HAN Zhanzhong, WANG Jing, LAN Xiaoing (2004) Calculating Examles and alication of Fluid Engineering Simulation in Fluent[M] Beijing: Beijing Institute of echnology Press (In Chinese) HU ianjiang, SHEN Lincheng, LIN Longxin, XU Haijun (2009) Biological insirations, kinematics modeling, mechanism design and exeriments on an undulating robotic fin insired by Gymnarchus niloticus Mechanism and Machine heory 44(3): (In Chinese) LIU J, HU H (2006) Biologically insired behaviour design for autonomous robotic fish[j] International Journal of Automation and Comuting 3(4): (In Chinese) Maciver M A, Fontaine E, Burdick J W (2004) Designing Future Underwater Vehicles: Princiles and Mechanisms of the Weakly Electric Fish[J] IEEE Journal of Oceanic Engineering 39(3): WANG Fujun (2008) Comutational Fluid Dynamics Analysis-CFD mechanism and alication[m] Beijing: singhua University Press (In Chinese) XIE Haibin, SHEN Lincheng, ZHANG Daibing (2006) Dynamic Analysis of Undulatory Proulsion of Long Flexible Fin Mechanics in Engineering 28(4): (In Chinese) YAN Weisheng (2005) Fish oredo Navigation Dynamics[M] Northwest University of echnology Press (In Chinese) ZHANG Daibing, XIE Haibin, SHEN Lincheng (2008) A Bionic Underwater hruster of Undulate Fin Driven by Hydraulic System China [P] (In Chinese) ZHOU Han (2009) Dynamics Behavior and Exerimental Research of Bionic Underwater Vehicle Proelled by Undulatory Fins[D] Changsha: National University of Defense echnology (In Chinese) 284