Numerical simulation of cricket ball swings using OpenFOAM

17th Annual CFD Symposium, August 11-12, 215, Bangalore Numerical simulation of cricket ball swings using OpenFOAM Ajit Kumar ajit.kumar@snu.edu.in Department of Mathematics, Shiv Nadar University NH91, Tehsil Dadri, Gautam Buddha Nagar, Uttar Pradesh - 21314 India July 17, 215 Abstract Cricket ball swings are sideways deections of ball generally observed in high speed balls. Wind tunnel experiments suggest asymmetry in smoothness of ball to be the primary cause of swings. This paper presents a simple two dimensional model of an unevenly smooth cricket ball. The LES capability of OpenFOAM, an open source CFD package, is demonstrated through several examples of airow simulations around this cricket ball model. Simulation results are in good agreement with wind tunnel experiments. The ball model is generated using Gmsh. Keywords: Cricket Ball Swings, OpenFOAM, LES, Gmsh, CFD 1 Introduction Cricket ball swings are sideways deviation of ball, generally observed in high speed balls. Swings were scientically investigated for the rst time in [5]. This study claimed the presence of seam to be the cause of swing. To get a perfect wing ball needs to be thrown in such a way that keeps seam always at an oblique angle with the ball's direction. The presence of swing breaks the symmetry of ball and hence the ow of air around it. At high speed this asymmetry creates enough dierence in pressure to deect the ball sideways. Wind tunnel experiments conrm the role of seam in swings, but only when the ball is new [9, 8, 4]. Experiments on older balls suggest dierence in smoothness of two sides of ball separated from the seam to be the main reason for swings. Regardless of the seam direction, balls tend to go towards the rough side. A very thorough classication of dierent kinds of swings and conditions in which they are observed are given in [9, 8]. The ndings in [9] are summarized in Fig. 1. Basically we have three kinds: conventional, reverse, and contrast swings. A swing is conventional if ball deviates in the direction pointed by seam. Swing is said to be reverse if deviation is perpendicular to the seam. Contrast swings are those swings in which seam is aligned with the ball's direction but the ball still swings, most likely because of dierence in smoothness of two sides of the ball. This paper aims to study swings computationally. Some recent articles have investigated aerodynamics of sports ball using Computational Fluid Dynamics (CFD) tools [12, 14, 3, 1, 2, 7, 13]. All reported studies so far use only commercial CFD packages and generally don't provide enough details for cross checking of simulation results. In this paper ecacy OpenFOAM, an open source CFD package, is demonstrated. A simple two dimensional model of a cricket ball is presented. The model aims to study only those balls which are rough on one side and smooth on the other. This model is created in a free software 1

Smooth or Rough Smooth Conventional Swing Seam is at an angle with the pitch direction and ball deflects in the direction of the seam. Observed when one side is smooth. Other side may or may not be smooth but the side which is faciing the direction of pitch must be smooth. This swing is observed if the ball speed is between 3 to 7 mph. Smooth Rough Reverse Swing Seam is at an angle with the pitch direction and ball deflects in the OPPOSITE direction of the seam. Observed when one side is smooth and other side is rough. The side which is faciing the direction of pitch must be rough. This swing is observed if the ball speed is above 85 mph. Rough Contrast Swing Seam is aligned with the ball direction. One side is smooth and other side is rough. Ball deflects towards smooth side. Smooth This swing is observed if the ball speed is above 7 mph. Rough Contrast Swing Seam is aligned with the ball direction. One side is smooth and other side is rough. Ball deflects towards rough side. Smooth This swing is observed if the ball speed is below 7 mph. Figure 1: Various types of cricket ball swing [9] Gmsh. Airow around cricket ball are simulated in OpenFOAM with turbulence modeled by LES. The simulation results are qualitatively in good agreement with wind tunnel experiment reported in [9]. The paper begins with the description of problem geometry and mesh (Sec. 2). Key settings in OpenFOAM are listed next in Sec. 3. The analysis of simulation results and comparison with wind tunnel experiments are discussed in Sec. 4. 2 Geometry and mesh The wind tunnel is modeled as a rectangle, 4 m long and 2 m wide in xy plane, with corners A(-3,-1,), B(1,-1,), C(1,1,) and D(-3,1,) (See Fig. 2b). Line BC is the inlet, and line DA is the outlet. A disc of diameter 7.28 cm, centered at origin (,,) is the ball. This CAD model is generated in Gmsh [6]. Ball is modeled to be rough on one half and smooth on the other. The roughness is modeled by multiple tiny protrusions (See Fig. 2a). Line separating the rough side and smooth side is the seam line. All OpenFOAM algorithms assume problem geometry to be given in three dimension. Two dimensional problems are simulated in OpenFOAM by extruding 2D models in third dimension ( (z direction in our case), and telling OpenFOAM not to resolve any ow variable in the direction of extrusion. Fig. 2c and 2d are showing extruded ball and the extruded environment around the ball. Suppose the extruded points of A, B, C, D are E, F, G, H respectively. Theoretically our airow ow inlet is the line BC but for OpenFOAM purpose, our inlet is the patch BFGC. Similarly the patch DHEA is the outlet, DCGA the top, AEFB the bottom. Of course the boundary part labeled ball is the extrusion of two dimensional ball in the z direction. Because of extrusion new boundary patches ABCD and EHGF are created. These are grouped together in a new boundary label frontandback. We need to inform OpenFOAM to ignore the direction perpendicular to frontandback patch. This will have the eect of simulating two dimensional problem with our three dimensional geometry. The Gmsh le that generates the geometry of this problem in the Appendix (See Listing 1). Fig. 3 shows a typical mesh used for simulations in this work. Mesh around the ball is much ner then near wall. Average size of elements near the inlet, outlet, top and bottom ball are.8 m where as 2

D (-3,1,) C (1,1,) top outlet inlet ball bottom A (-3,-1,) B (1,-1,) (a) Ball in two dimension (b) Wind tunnel in two dimension H D top G outlet C E ball inlet fro fronta ntandback ndbac k A botto m F (a) Extruded ball (b) Extruded wind tunnel B Figure 2: A two dimensional model and of a cricket ball. The ball is modeled to be rough on one half by multiple tiny protrusion. The model is generated using Gmsh. The sub gure (c) and (d) are extrusions of 2d model. Extrusion is a technical requirement needed to implement 2d problems in OpenFOAM. average size of elements near the ball is kept as.2 m. 3 OpenFOAM details Simulations were conducted on OpenFOAM version: Foam-extend-3.1. Seam angles of 1o, 2o, 3o, 4o, 5o, 6o, 7o and 8o were tested. For each choice of seam angle, air ow around the ball was generated using inlet speed: 5, 1, 2 m/s. OpenFOAM has features for introducing uctuation in the inlet speed so that turbulence is modeled more realistically. A transient solver for incompressible isothermal ow, namely pisofoam was used, with ν = 1 5 m2 /s as the kinematic viscosity. OpenFOAM o ers a range of methods to simulate turbulence: Reynolds Average Simulations (RAS), Large Eddy Simulations (LES), Detached Eddy Simulations (DES), and Direct Numerical Simulations (DNS). Furthermore, multiple models are available to implement both RAS and LES. For simulations related to cricket ball swings, RAS was not helpful. The LES methods produced more realistic results. Di erent models of LES such as, oneeqeddy, SpalartAllmaras, Smagorinsky were tried and observation from all were found to be similar. The results reported here are generated using Smagorinsky LES model [1, 11]. The primary variables in Navier Stoke's equations are uid velocity u and pressure p. The use of LES models may require use of some intermediate variables: SubGrid Scale (SGS) turbulent kinetic energy k, SGS viscosity nusgs, and SGS stress tensor B. Because of heavy uctuations in turbulent ows, it is helpful if we can calculate time averages of ow variables. OpenFOAM o ers convenient methods to do that. The analysis of simulation output heavily depends on time averages of pressure pmean and velocity UMean. 3

zoom in zoom in Figure 3: Discretization of the PDE domain 4 Simulation Result and Analysis Air ow around the ball with several di erent seam angles and air inlet speed were simulated. The qualitative behaviour of the solution did not change too much with seam angles. The plots of simulations based on seam angle 3o are presented here. Overall four kinds of swings have been reported: conventional swing, reverse swing, contrast swing at low ball speed, and contrast swing at high ball speed [9]. The ball model presented in this work and LES simulation on OpenFOAM does reproduce all these swings. 4.1 Conventional and Reverse Swing simulation Fig. 4 are plots from a simulation which can be viewed as a two dimensional conventional and a reverse swing. 4.1.1 Conventional Swing The subplots C1, C2, and C3 in Fig. 4 represent data from one simulation. The seam angle was taken to be 3o. Rough side is on the top. Wind inlet speed is be 1 m/s. The sub gure C1 is plot of pressure distribution on the ball patch averaged over time pmean. Note that top and rough part of the ball experience lower pressure compared to lower smooth part of the ball. This indicated that ball would have de ected upward if we were looking at a real ball. The sub gure C2 is a snap shot of wind speed around the ball. We can see that a wake is being formed at the lower left of ball which again indicates ball being de ected upward. The sub gure C3 is average speed of the wind around the ball. This gure also indicates that a wake is present in the lower left side of the ball which con rms the conclusion from top two sub gures that ball will get pushed upward. 4.1.2 Reverse Swing The subplots (R1), (R2), and (R3) in Fig. 4 represent data from a simulation which can be viewed as a reverse swing. The seam angle is again 3o but this time rough side is on the bottom. Wind inlet speed was taken to be 1 m/s. The top gure (R1) shows the pressure distribution on the ball patch averaged over time. This time we observe that lower rough part of the ball experience low pressure. This indicates ball should be de ected downward. In this case as well as the conventional swing case the ball is de ecting towards the rough side. The reason this case is called reverse swing because the de ection is away from the direction in which the seam line is pointing. The sub gure (R2) is a snapshot of air 4

12 (C1) (R1) pmean 288 28 24 2 16 pmean 288 28 24 2 16 84.5 95.5 12 (C2) (R2) U Magnitude 24.4 2 1 U Magnitude 24.4 2 1 (C3) (R3) 2.2 UMean Magnitude 2 2.2 UMean Magnitude 2 1 1 Conventional Swing Reverse Swing Figure 4: Simulation of Conventional and Reverse Swing speed around the ball and (R3) is plot of time averaged speed of the air around the ball. Wind speed distribution is not saying much in this case but the pressure distribution indicates that this simulation can be considered a reverse swing. 4.2 Contrast Swings Fig. 5 shows result of two simulation which can be considered contrast swings. In both of these experiments the seam is horizontal, i.e. aligned with the direction of the ball. In both the experiments rough side is on the top. Dierence between two experiments is in the wind inlet speed. The left three gures (CL1), (CL2) and (CL3) are plots from the same experiment of inlet speed 5 m/s. (CL1) is showing that on average smooth side of the ball experience lower pressure so ball would be deected towards smooth side. The same interpretation is being suggested by (CL2) which is a snapshot of speed distribution around the ball, and (CL3) which is the time average of speed around the ball. The right three gures (CH1), (CH2), and (CH3) showing data from simulation with wind inlet speed 2 m/s. The gure (CH1) is showing that this time rough side of the ball experiences lower pressure than the smooth side. This indicates that ball will deect towards the rough side. This conclusion is conrmed in gure (CH2) which is a snapshot of speed distribution around the ball. We can see that wake is going down in the left. The gure (CH3) which is the time average of speed and this also indicates wake in lower left which implies ball should deect upward. Readers should notice that simulations in this paper predicts dierent direction of ball deection from the one reported in [9]. The Fig. 5 shows that at low speed ball will deect towards smooth side where as at high speed ball will deect towards rough side. Where as Fig 1 reports exactly opposite. It is not a purpose of this paper to get exact match between wind tunnel experiments and simulation. A qualitative simulation of swings was aimed using OpenFOAM and that purpose seems to have fullled. The ne tuning of simulation cases to get better agreement with wind tunnel experiments will be left for future work. 5

(CL1) (CH1) pmean 95.3 9 8 7 pmean 766 6 4 2 56.9 6-1.3 (CL2) (CH2) U Magnitude 9.39 8 6 4 2 U Magnitude 52.5 4 2 (CL3) (CH3) UMean Magnitude 8.55 8 6 4 2 UMean Magnitude 37 3 2 1 Contrast swing at low speed. Ball deflects towards smooth side Contrast swing at high speed. Ball deflects towards rough side Figure 5: Simulation of Contrast Swing 5 Conclusion A two dimensional model was presented which can be used to simulate various kind of swings observed in the game of cricket. Complete description of simulation setting for OpenFOAM was explained. Since OpenFOAM is open source and free, any person can easily reproduce the results of this article. Good qualitative agreement between wind tunnel experiments and simulations was observed for conventional and reverse swings. For contrast swings, simulation results and wind tunnel experiments seem to disagree. The resolution of this disagreement is being left for future work. Simulation of swing with dynamic mesh in three dimension is in progress. Three dimensional simulation becomes necessary if we wish to simulated the realistic bowling action which also involves some backspin. 6 Appendix: Source les Listing 1 is a the gmsh le used to generate the CAD of the ball, and the wind tunnel around the ball. // ----- cricketball2dcad. geo -----------------------------------// cl1 =.8; // average size of elements around the wall cl2 =.2; // average size of elements around the ball seamangle = 3; // in degrees Point (1) = { -3, -1,, cl1 ; // A Point (2) = {1, -1,, cl1 /1.5; // B Point (3) = {1, 1,, cl1 /1.5; // C Point (4) = { -3, 1,, cl1 ; // D Point (5) = {,,, cl2 ; // O : ball center Point (6) = {.364,,, cl2 ; Point (7) = {,.364,, cl2 ; Point (9) = {, -.364,, cl2 ; Listing 1: cricketball2dcad.geo Rotate {{,, 1, {,,, Pi /18 { 6

Duplicata { Point {6; Rotate {{,, 1, {,,, -Pi /18 { Duplicata { Point {6; Translate {.6,, { Duplicata { Point {6; Rotate {{,, 1, {,,, -Pi /36 { Point {12; Rotate {{,, 1, {,,, Pi /18 { Duplicata { Point {12; Line (1) = {11, 12; Line (2) = {12, 13; Line (3) = {13, 1; Rotate {{,, 1, {,,, Pi /2 { Duplicata { Point {1; Circle (4) = {1, 5, 14; Rotate {{,, 1, {,,, 11* Pi /18 { Duplicata { Line {1, 2, 3, 4; Rotate {{,, 1, {,,, 11* Pi /9 { Duplicata { Line {1, 2, 3, 4, 5, 6, 7, 8; Rotate {{,, 1, {,,, 11* Pi /45 { Duplicata { Line {16, 15, 14, 13, 12, 11, 1, 9, 8, 7, 6, 5, 4, 3, 2, 1; Rotate {{,, 1, {,,, 11* Pi /45 { Duplicata { Line {17, 18, 19, 2, 21, 22, 23, 24, 25, 26, 27, 28, 29, 3, 31, 32, 16, 15, 14, 13, 12, 11, 1, 9, 8, 7, 6, 5, 4, 3, 1, 2; Rotate {{,, 1, {,,, 11* Pi /45 { Duplicata { Line {33, 34, 35, 36, 37, 38, 39, 4, 41, 42, 43, 44, 45, 46, 47, 48; Rotate {{,, 1, {,,, 11* Pi /18 { Duplicata { Line {49, 5, 51, 52; Circle (69) = {247, 5, 11; Line (7) = {2, 3; Line (71) = {3, 4; Line (72) = {4, 1; Line (73) = {1, 2; Line Loop (74) = {71, 72, 73, 7; Line Loop (75) = {69, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 11, 12, 13, 14, 15, 16, 32, 31, 3, 29, 28, 27, 26, 25, 24, 23, 22, 21, 2, 19, 18, 17, 48, 47, 46, 45, 44, 43, 42, 41, 4, 39, 38, 37, 36, 35, 34, 33, 64, 63, 62, 61, 6, 59, 58, 57, 56, 55, 54, 53, 52, 51, 5, 49, 68, 67, 66, 65; Rotate {{,, 1, {,,, seamangle * Pi /18 { Line {69, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 11, 12, 13, 14, 15, 16, 32, 31, 3, 29, 28, 27, 26, 25, 24, 23, 22, 21, 2, 19, 18, 17, 48, 47, 46, 45, 44, 43, 42, 41, 4, 39, 38, 37, 36, 35, 34, 33, 64, 63, 62, 61, 6, 59, 58, 57, 56, 55, 54, 53, 52, 51, 5, 49, 68, 67, 66, 65; Plane Surface (76) = {74, 75; Physical Surface (77) = {76; Extrude {,,.5 { Surface {76; Layers {1; Recombine ; Physical Surface (" ball ") = {439, 435, 431,427,423, 419, 415, 411, 47, 43, 399,395, 391, 387, 383, 379, 375, 371, 367, 363, 351, 355, 359, 347, 335, 339, 343, 331, 319, 323, 327, 315, 33, 37, 311, 299, 287, 291, 295, 283, 271, 275, 279, 267, 255, 259, 263, 251, 239, 243, 247, 235, 223, 227, 231, 219, 27, 211, 215, 23, 191, 195, 199, 187, 183, 179, 175, 171, 443 ; Physical Surface (" inlet ") = {167; Physical Surface (" outlet ") = {159; Physical Surface (" top ") = {155; Physical Surface (" bottom ") = {163; Physical Surface (" frontandback ") = {444,76; Physical Volume (447) = {1; // ---------------------------------------------------// References [1] S Barber, SB Chin, and MJ Carré. Sports ball aerodynamics: a numerical study of the erratic motion of soccer balls. Computers & Fluids, 38(6):19111, 29. 7

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