Numerical Simulation of the Basketball Flight Trajectory based on FLUENT Fluid Solid Coupling Mechanics Yanhong Pan

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1 Applied Mechanics and Materials Submitted: ISSN: , Vols , pp Accepted: doi: / Online: Trans Tech Publications, Switzerland Numerical Simulation of the Basketball Flight Traectory based on FLUENT Fluid Solid Coupling Mechanics Yanhong Pan School of Physical Education, Hezhou University, Hezhou, China Keywords: FLUENT software; Fluid solid coupling; Basketball flight; Deformation curve; 3D modeling; Iteration Abstract. The calculation of basketball traectory involves the elastic-plastic mechanics and aerodynamics theory. Besides the deformation of basketball flight, the flight is a complex fluid solid coupling process. If wanting to simulate the flight traectory of basketball accurately, it must consider the effect of flow field and solid fluid solid coupling field. In order to calculate the flight traectory of basketball accurately and improve basketball shooting speed and posture training efficiency in the training process, this paper uses the FLUENT to simulate the basketball flight traectory. Combined with the aerodynamic theory we established the mathematical model of basketball flight. Through the numerical simulation we calculate the velocity field and the monitoring point deformation curve of basketball flight, it provides a new method for computer technical training for basketball players. Introduction Basketball is a very intense antagonism competition, in the course of the game, players should consume a lot of physical strength, also need flexible technical movements as the key to win success. The basketball movement is different from other sports, and it requests the athlete to have good bounce, amazing explosive force, the sensitive action and instant reaction ability, also requires athletes to have flexible basketball shooting skills and gesture [1, 2]. Therefore, based on the computer hardware and software technology as a strong technical support, from the mechanical properties of the basketball, we simulate the flight traectory of basketball shooting process, and obtain the good simulation results, which provide technical support for basketball players. Overview of FLUENT Basketball Flight Simulation Before the numerical simulation calculation of FLUENT, we first do numerical modeling. The numerical modeling approach can use the FLUENT GAMBIT software, and it can also use CAD, Solidworks and PROE software to import the model, and then do grid division [3]. This paper uses the GAMBIT direct modeling to establish basketball structure model and aerodynamic flow field, and simulates the basketball traectory under the different speeds. The main process is as follows: Fig. 1 Schematic diagram of FLUENT numerical simulation process Figure 1 shows the schematic diagram of FLUENT simulation process. The process is divided into four steps, including the basketball and air field model, grid division, iterative calculation and the results of after treatment [4]. Through calculating the flight track under different flight speeds, we summarize the different shooting speed, which provides technical reference for basketball players. All rights reserved. No part of contents of this paper may be reproduced or transmitted in any form or by any means without the written permission of Trans Tech Publications, (ID: , Pennsylvania State University, University Park, USA-12/05/16,06:23:36)

2 2348 Material Science, Civil Engineering and Architecture Science, Mechanical Engineering and Manufacturing Technology II Mechanics Modeling and UDF Program Design in the Basketball Flight Using computer methods to simulate the basketball flight, it needs to s to build basketball mechanical model, including basketball itself and air flow field. The solution on the air flow field consists of three equations, and one of the most commonly used is the conservation of mass and momentum conservation equations [5, 6]. By solving the three equations it realizes the coupling effect of flow field and solid field. For the air flow, air medium is basis of model. The matter conservation equation is as shown in formula (1). ρ ρ( u + t x ) = 0, = 1,2,3. (1) Among them, x is the axial coordinate, u is axis flow velocity, the momentum equation can be written: P τ i ( ρ ui) + ( ρuiu ) = + + ρgi + Fi. (2) t x x c p is static pressure, τ i is stress tensor, so it is: i u u i ul τ i µ 2 = + µ δi. (3) x x i 3 xl Three coordinate unit vector of basketball flight direction are respectively a, b, c, so basketball force F can be written as shown in formula (4): F = Fx a + Fb i + Fzc. (4) According to the Bernoulli equation, the air resistance of basketball can be expressed as the formula (5). 2 ( 1 / 2 ) C ρ SV F =. (5) C is the air resistance coefficient, ρ is air density, S is the basketball windward area, V is the relative velocity between basketball and air. This paper uses UDF programming to realize fluid solid coupling process of basketball and air. The basketball deformation and the air field programming coupling are as follows: Compute_Force_And_Moment(domain,tf,x_cg,f_glob,m_glob,TRUE); vn=v_body[1]; yn=b_ctr; Vn=vn+dtm*(K1+2*K2+2*K3+K4)/6; Yn=yn+dtm*vn+dtm*dtm*(K1+K2+K3)/6; v_body[1]=vn; b_ctr=yn; t+=dtm; } DEFINE_CG_MOTION(dynamic_cylinder,dt,vel,omega,time,dtime) { NV_S(vel,=,0.0); NV_S(omega,=,0.0); vel[1]=v_body[1]; }

3 Applied Mechanics and Materials Vols Fluid Solid Coupling Simulation of Basketball Flight Traectory In order to verify the reliability and effectiveness of basketball flight mechanics model and the FLUENT UDF program designed in the second part, this paper uses FLUENT to simulate the basketball flight traectory, and the FLUENT is FLUENT12.1.version. The interface is as shown in Figure 2. Fig. 2 The ANSYS-FLUENT12.1 interface Figure 2 shows the numerical simulation software of FLUENT. In the calculation process, if the model is complex, it can use advanced modeling software CAD and Solidworks, and then using GAMBIT to import into the model [7]. In this paper this model is simple, so we directly set up by GAMBIT Fig.3 The 3D model of basketball and the air flow field Figure 3 shows 3D model for basketball flight traectory simulation. The model includes basketball body part and the air flow field. In the simulation calculation process basketball and air field are respectively modeling and do grid division [8]. Grid division uses Gambit software. Fig. 4 2D cross section of basketball grid division Figure 4 shows a 2D cross-section basketball grid. In order to improve the precision of calculation, this paper uses a structured hexahedral mesh, and encrypts the grid around the basketball. In order to reduce the computational complexity, we use the progressive grid as shown in Figure 5.

4 2350 Material Science, Civil Engineering and Architecture Science, Mechanical Engineering and Manufacturing Technology II Fig. 5 2D cross section of basketball flight velocity field simulation Figure 5 shows 2D cross section of basketball flight velocity field simulation. From the chart we can see, during the flight, it produces vortex around the basketball, which is consistent with the actual flight conditions [9]. And it proves the validity and reliability of numerical simulation. Fig. 6 The curve changes with time for deformation during basketball flight Figure 6 shows the curve changes with time for deformation during basketball flight. The curve monitors a middle position of basketball, and simulates the deformation changes at different time. From the chart we can see, as time increases, the curve shows a symmetry change trend, suggesting that it produced a vortex during flight. The vortex can make the basketball be far away from the original track, so it must pay attention to the problem. Table 1. The monitoring deformation for different shooting speeds No. Shooting speed (m/s) Deformation monitoring (cm) Table 1 shows the monitoring deformation for different shooting speeds. From the table we can see, along with the increase of the shooting speed, monitoring deformation is increasing gradually

5 Applied Mechanics and Materials Vols [10]. Basketball deformation will affect the flight traectory of basketball, thus affecting the basketball shooting effect. Therefore, it needs to consider the factors of shooting speed and angle of shooting in basketball shooting process, adusting the shot, so as to improve the percentage of hits. Summary In this paper we use the differential equation theory and aerodynamics theory to establish the fluid solid coupling mechanics model of basketball flight, and use UDF to program the FLUENT. We use GAMBIT software of FLUENT to establish the mathematical model of basketball and the air flow field, and use the numerical simulation of FLUENT to calculate the air velocity field and the basketball deformation. By analyzing the monitoring point deformation under different speeds, we summarize the basketball flight traectory, and it provides theory reference for basketball shooting speed training. References [1] Kang Kai. The anaerobic ability analysis of free combat athletes in Shandong Province [J]. Journal of Shandong Sports Institute, 2011, 21(3): [2] Wu Hao, Feng Meiyun. Study on metabolism based on Wingate [J]. Journal of Beiing Sport University, 2012, 20(1): [3] Zhao Yongcai. Wingate and HUR force platform for anaerobic capacity test analysis between Physical education students and ordinary students [J]. Zheiang sports science, 2011, 32(1): [4] Li Yan. Study on the speed of 1500 meters sprint ability on the role of men athletes [J]. Chinese innovation of science and Education Journal, 2011, 30(14): [5] Zhang Bo, Wang Lina, Zhou Jinli, Bai Jie. Combination of strength training of the basketball players in vertical umping ability [J]. Journal of Hebei Institute of Physical Education, 2013, 5(1): [6] Liu Anqing. Research on status and development countermeasures of high level basketball coach teams in Universities in China [J]. Journal of Beiing Sport University, 2013, 2(11): [7] Song Zhenzhen. From the CUBA and NCAA discussing the development of high level sports teams in colleges and universities countermeasures [J]. Journal of Shanghai Institute of Physical Education, 2013, 5(11): [8] Yang Tieli. The occupation market theory of basketball [M]. Beiing: Beiing Sport University press, 2012: [9] Hao Guohua. work together for common development-the first A Club Association symposium Abstract [P]. China basketball version of CBA [10] Hu Anyi, Liu Jingyu. Construction and its application of uvenile basketball players material model [J]. Journal of Wuhan Sports Institute, 2012, 41(2):

6 Material Science, Civil Engineering and Architecture Science, Mechanical Engineering and Manufacturing Technology II / Numerical Simulation of the Basketball Flight Traectory Based on FLUENT Fluid Solid Coupling Mechanics /