水火箭飛行動態特性之研究

A study on water rocket dynamic characteristics in flight

張峰垚(Feng-Yao Chang)

指導教授 ： 翁輝竹

中原大學/工學院/機械工程研究所/碩士(2016年)

https://doi.org/10.6840/cycu201600786

摘要

本研究在理論探討水火箭飛行軌跡與動態特性。主要目的在分析箭體內氣壓及水量對水火箭垂直飛行高度、速度及加速度隨時間變化之影響。過程中，首先利用Reynolds傳輸定理以推導水火箭之動量守恆方程式。接著應用連續方程式、Bernoulli方程式及等熵程序關係式以推導噴口處流速及箭體內氣壓與水量間之變化關係。最後，透過數值求解箭體飛行之初始值問題以預測水火箭垂直飛行高度、速度及加速度等飛行軌跡與動態特性，並與實驗數據進行比較。
單節水火箭之研究結果發現，數值預測可得到與實驗數據相近之結果。進一步發現，在一定箭體內水量下，當箭體內氣壓越大，水火箭垂直飛行高度越高、最大速度越快、加速度越大；在一定箭體內氣壓下，當箭體內水量由少遞增，一開始水火箭垂直飛行高度增加、最大速度增快、加速度遞減，隨後高度降低、最大速度減慢、加速度持續遞減。雙節水火箭之研究結果發現，數值預測亦可得到與實驗數據相近之結果。逆止閥是影響雙節水火箭飛行軌跡與動態特性的重要因素。在一定箭體內水量及氣壓下，透過上下節箭體內水量之適當比例，可使水火箭達到最佳飛行效果。相較於單節水火箭，雙節水火箭之垂直飛行高度可明顯高於單節水火箭。

關鍵字

水火箭 ； Reynolds傳輸定理 ； 熱力學分析 ； 等熵程序

並列摘要

This study theoretically explores the flight trajectory and dynamic characteristics of water rockets. Its main purpose is to analyze the effects of the inner air pressure and water amount of water rockets on its change of vertical flight altitude, velocity and acceleration over time. The Reynolds transport theorem is first used in the analysis to deduce the momentum conservation equation of water rockets. Then the continuity equation, Bernoulli equation, and the isentropic process relation are applied to infer the outlet fluid velocity and the relationship between the inner air pressure and water amount. Finally, through a numerical solution method, the initial value problem for water rocket space flight and dynamics is solved to predict the flight trajectory and dynamic characteristics, like the vertical flight altitude, velocity and acceleration of water rockets. Moreover, the numerical predictions can be compared with experimental data.
The study results on a single-stage water rocket show that the numerical predictions can get the results close to the experimental data. The results further indicate that under a certain water amount in a single-stage water rocket, the greater the air pressure in the rocket, the higher the vertical flight altitude, the faster the maximum velocity and the bigger the maximum acceleration of the rocket. Moreover, under a certain air pressure in a single-stage water rocket, with the increase of water amount in the rocket, the vertical flight altitude increases, the maximum velocity becomes faster, but the maximum acceleration decreases at the beginning stage; however, after more than a certain amount of water, the vertical flight altitude reduces and the maximum velocity becomes slow. As to a double-stage water rocket, the numerical predictions can also get the results near to the experimental data. Furthermore, the capability of the one-way check valve between the upper part and lower part of the double-stage water rocket is an important factor to influence the flight trajectory and dynamic characteristics of the double-stage water rocket. Under a certain total water amount and air pressure, through an appropriate ratio of the water amount adjusted in the upper part and lower part of the double-stage water rocket, the best flight performance can be reached. Compared with the single-stage water rocket, the vertical flight height of the double-stage water rocket is significantly higher than that of the single-stage water rocket.

並列關鍵字

water rockets ； Reynolds transport theorem ； thermodynamic analysis ； isentropic process

參考文獻

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