物體碰撞水面之流固耦合現象探討—以打水漂為例

Simulation on fluid - solid coupling phenomenon of an object impacting the water surface – A case study of stone skipping

林世平(Shih-Ping Lin)

指導教授 ： 趙聖德

國立臺灣大學/工學院/應用力學研究所/碩士(2019年)

https://doi.org/10.6342/NTU201901507

摘要

小時候在池塘邊打水漂，依照經驗會挑選較扁平的石頭，盡可能使用最大的力量投擲出去。然而石頭運動速度極快，無法對於提升彈跳次數的各項因素有微觀的分析。
本研究使用有限元素軟體LS-PrePost針對影響彈跳次數的幾項因素作探討，例如石頭與水面的夾角，速度與水面的夾角，自轉速度，目標為找到最佳的彈跳次數的影響因素及預測彈跳次數。除此之外，本研究中可以由模擬驗證出水速度與入水速度的比值大約等於石頭與水面夾角加上入射速度與水面夾角的餘弦值，以預測每一次彈跳後的速度損失，配合能發生彈跳的最低速度，預測彈跳次數。
出水速度與入水速度的比值越大，代表每次彈跳後的能量損失越少，會影響此比值的有石頭與水面的夾角和速度與水面的夾角，經模擬分析得到速度與水面的夾角越小越好。石頭與水面的夾角在也是角度小時會有較好的彈跳表現。
在投擲前我們會設定一個石頭與水面的夾角，為了使每一次彈跳不因為水面造成的力矩使得此角度改變，故我們會給予石頭初始自轉速度，使其有陀螺效應足以穩定角度，而隨著轉速提升，角度變化量會越趨近零。另外，我們由模擬得到如果入射速度提升，轉速也須依照入射速度提升的倍數放大，方能使此角度變化量很小。
本研究藉由定義的恢復係數為石頭與水面夾角加上入射速度與水面夾角的餘弦值得到預測彈跳次數的方程式，即會影響彈跳次數的因素中，找到最佳組合使其有最多彈跳次數。

關鍵字

有限元素 ； 水漂 ； 恢復係數 ； 彈跳次數 ； LS-DYNA ； 納維爾－斯托克斯方程 ； 流固耦合

並列摘要

When we were young,most of us had experience of skipping stones at a pond.Past experience has taught us that we should choose a flat stone,and throw it obliquely.While stones skipping,it moves very fast.We can’t analyze directly by our eyes.
In this thesis,we used finite element analysis—LS-PrePost to discuss factors(e.g.,angle between stones and water surface,angle between stones and initial velocity,spin velocity,velocity)which effect the number of bounces.Finding the best number of bounces and predicting number of bounces are our target.Besides,we derive the relation between the ratio of outbound velocity and incidence velocity is cosine of the angle between stones and water surface plus angle between stones and initial velocity.Here we define cosine of the angle between stones and water surface plus angle between stones and initial velocity as a coefficient of restitution.By this coefficient of restitution,it’s easily to know the velocity after richocheting.The velocity after richocheting go with minimum velocity for bouncing can predict the number of bounces.
If the the ratio of outbound velocity and incidence velocity is large,it means less energy dissipation after each bounce.The ratio of outbound velocity and incidence velocity is affected by angle between stones and water surface, angle between stones and initial velocity.After analyzing our data,We found out it’s better to choose angle as small as you can.
We set an angle between stones and water surface before throwing.In order to prevent angle change,we will give spin velocity at the beginning to offer gyroscopic effect.Gyroscopic effect can stabilize angle.If we want to get more bounces,intuitively we speed up the incident velocity.We have to keep angle as a constant,so we also speed up angular velocity.The angular speed must increase in accordance with the multiple of the incidence speed increase.
In this thesis,we derive the equation of predicting the number of bounces.We also found out the best factors to achieve the most number of bounces.

並列關鍵字

finite element analysis ； stone-skipping ； coefficient of restitution ； number of bounces ； LS-DYNA ； Navier-Stokes equations ； fluid solid interaction

參考文獻

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