Relationship between Unsteady Fluid Force and Vortex Behavior around a Discoid Airfoil Simulating a Hand of Swimmer

Transcription

1 45 * Relationship between Unsteady Fluid Force and Vortex Behavior around a Discoid Airfoil Simulating a Hand of Swimmer Hiroaki HASEGAWA, Department of Mechanical Engineering, Akita University Jun WATANABE, Graduate School of Systems & Information Engineering, University of Tsukuba Kazuo MATSUUCHI, Graduate School of Systems & Information Engineering, University of Tsukuba (Received 16 May 2008; in revised form 26 December 2008) For predicting the hand force in swimming, the quasi-steady-state approach led to errors in predicting the fluid forces acting on a hand in unsteady conditions. The actual motion of a hand in swimming is obviously unsteady, and the time-dependent fluid forces have to be taken into account. It is presumable that the unsteady fluid forces are closely related to the generation of large vortices. In the present study, in order to investigate unsteady effects on propulsion during front crawl swimming, unsteady fluid forces acting on a discoid airfoil simulating a human hand and the vortical field were measured in the pitching motion for the wind tunnel test. The wind tunnel test has the advantage to enable many unsteady parameters to be changed easily. The flow structures due to the behavior of vortices shedding from the airfoil edge during the pitching motion were strongly affected by the reduced frequency. At high reduced frequency, the significant vortices were formed close to the airfoil s trailing edge, and large scale vortices were generated in the wake of the airfoil. (KEY WORDS): Unsteady Flow, Vortex, Fluid Force, Lift, Drag, Pitching Motion, PIV, Swimming 1 * hhasegaw@mech.akita-u.ac.jp

2 46 8 1) 2 2) 3, 4, 5) 6) 7) NACA 0012 S S S S 8, 9) mm 150 mm NACA mm NACA mm 2 FRP Flow Drag force sensor 1 Schematic of experimental set-up. (a) Discoid airfoil Potentiometer Lift forcesensor Stepping motor y z 2 Test model. x (b) NACA0012 (Dimensions in mm)

3 47 1/ ) 2.2 S S S in-sweep out-sweep S In-Sweep Out-Sweep Flow 3 3(b) in-sweep out-sweep 10) θ cos 90 in-sweep out-sweep S α α=α c α a cos(2πft) (1) α c 86.8 α a 10.0 f f= Hz x U 0 U 0 c (a) Cartoon depicting of swimmer s motion (b) Trajectory of hand movements 3 S-shaped pull. 4 Schematic diagram of PIV configuration.

4 48 (a) f=1.0hz (k=0.063) (b) f=6.0 Hz (k=0.38) 5 Hysteresis loop of dynamic drag for discoid airfoil (Re= ). (a) f=1.0hz (k=0.063) (b) f=6.0 Hz (k=0.38) 6 Hysteresis loop of dynamic drag for NACA0012 (Re= ). 11) 3 7 Drag ratio between dynamic and stationary conditions (Re= ). PIV: Particle Image Velocimetry 4 PIV PIV PIV 9) PIV α=86.8 7

5 49 (a) t =0.0 (b) t =0.4 (c) t =0.6 (d) t =0.9 8 Density map of vorticity for discoid airfoil in x-z plane (f=1.0 Hz, k=0.063, Re= ). (a) t =0.0 (b) t =0.4 (c) t =0.6 (d) t =0.9 9 Density map of vorticity for discoid airfoil in x-z plane (f=7.2 Hz, k=0.45, Re= ). (a) t =0.0 (b) t =0.25 (c) t =0.4 (d) t =0.6 (e) t =0.75 (f) t = Density map of vorticity for discoid airfoil in x-z plane (f=7.2 Hz, k=2.7, Re= ). 1 k(=πfc/u 0 ) ω x z u w u w (2) z x

6 50 t t 1 T f=7.2 Hz f=1.0 Hz 9 t t 0.4 t y=0 x-z mm 1 x u f=7.2 Hz m/s f=1.0 Hz m/s x Re 2 10 Re f=7.2 Hz Re t 0 t 0.25 t 0.7~0.8 t =0.6 t t = t = t = t = Re= f 7.2 Hz 1 12)

7 51 (a) t =0.0 (b) t =0.4 (c) t =0.6 (d) t = Density map of vorticity for NACA0012 in x-z plane (f=1.2 Hz, k=0.45, Re= ). (a) t =0.0 (b) t =0.4 (c) t =0.6 (d) t = Density map of vorticity for NACA0012 in x-z plane (f=7.2 Hz, k=2.7, Re= ). (a) Discoid airfoil (x/c=0.1) (b) Discoid airfoil (x/c=0.4) z/c z/c z/c z/c (c) NACA0012 (x/c=0.1) (d) NACA0012 (x/c=0.4) 13 Mean-velocity profiles in the streamwise direction (y/c=0, Re= ).

8 f= Hz 12(c) 1 13 x u z x/c=0.4 z=0 z=0 -x -x x 1 z f=7.2 Hz 6(b) y/c=0.3 x-z y/c=0 y/c=0 1 1 y/c=0 (a) t =0.0 (b) t =0.4 (c) t =0.6 (d) t = Density map of vorticity for discoid airfoil at y/c=0.3 in x-z plane (f=7.2 Hz, k=2.7, Re= ).

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