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浙江大学学报(工学版)
浙江大学学报(工学版)  2023, Vol. 57 Issue (1): 81-91    DOI: 10.3785/j.issn.1008-973X.2023.01.009
土木工程     
离心超重力环境下流体中物体浮力与运动
赵天浩1(),郑建靖1,2,*(),凌靖华3,施昌宇1,凌道盛1,2
1. 浙江大学 建筑工程学院，浙江 杭州 310058
2. 浙江大学 超重力研究中心，浙江 杭州 310058
3. 浙江华艺建筑设计有限公司，浙江 杭州 310000
Buoyancy and motion of objects in fluid in centrifugal hypergravity environment
Tian-hao ZHAO1(),Jian-jing ZHENG1,2,*(),Jing-hua LING3,Chang-yu SHI1,Dao-sheng LING1,2
1. College of Civil Engineering and Architecture, Zhejiang University, Hangzhou 310058, China
2. Center for Hypergravity Experiment and Interdisciplinary Research, Zhejiang University, Hangzhou 310058, China
3. Zhejiang Huayi Architectural Design Limited Company, Hangzhou 310000, China
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摘要：

为了表征离心超重力环境下物体在流体中的运动规律，基于旋转非惯性系，考虑吊篮摆动遗留角的影响，推导由地球常重力和离心超重力共同产生的试验超重力场的重力势、静止流体压力及流体中物体承受流体浮力的表达式. 基于Newton第二定律建立离心模型试验中静止流体内物体运动的控制方程，编制并验证了数值求解程序. 流体中圆球运动的数值分析结果表明，当离心加速度较大时，吊篮摆动遗留角的影响可以忽略. 试验超重力等势面是以离心机主轴为轴线的旋转抛物面，随着离心加速度的增大，等势面形态受地球重力的影响逐渐减小，趋于圆柱面. 物体在流体中所受的浮力具有向心性和非均匀性. 物体在流体中运动时，科氏力的影响不可忽略.
关键词： 离心超重力;  重力势;  浮力;  科氏加速度;  运动轨迹    
Abstract:

The expressions of the test hypergravity potential generated by the earth gravity and the centrifugal hypergravity, the static fluid pressure and the buoyancy of an object in fluid were derived in the rotational non-inertial frame by considering the residual angle of the suspended basket in order to characterize the motion law of object in fluid under the centrifugal hypergravity environment. The motion equation of a rigid object in static fluid in centrifugal model test was established based on Newton’s second law, and its numerical solution program was compiled and verified. The numerical analysis results of sphere motion in fluid show that the residual angle of the suspended basket can be ignored under high centrifugal acceleration. The equipotential surface of test hypergravity is a rotating paraboloid with the centrifuge spindle as the axis. The influence of earth gravity on the equipotential surface is gradually reduced with the increase of centrifugal acceleration. The shape of the equipotential surface tends to be a cylindrical surface. The buoyancy is centripetal and non-uniform, and the influence of the Coriolis force cannot be ignored when the object moves in fluid.
Key words: centrifugal hypergravity    gravity potential    buoyancy    Coriolis acceleration    trajectory
收稿日期: 2022-02-22 出版日期: 2023-01-17
CLC:  TU 411  
基金资助: 国家自然科学基金资助项目（51988101）
通讯作者: 郑建靖     E-mail: 21912219@zju.edu.cn;zhengjianjing@zju.edu.cn
作者简介: 赵天浩（1997—），男，硕士生，从事离心超重力试验的研究. orcid.org/0000-0002-1898-375X. E-mail： 21912219@zju.edu.cn
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引用本文:

赵天浩,郑建靖,凌靖华,施昌宇,凌道盛. 离心超重力环境下流体中物体浮力与运动[J]. 浙江大学学报(工学版), 2023, 57(1): 81-91.

Tian-hao ZHAO,Jian-jing ZHENG,Jing-hua LING,Chang-yu SHI,Dao-sheng LING. Buoyancy and motion of objects in fluid in centrifugal hypergravity environment. Journal of ZheJiang University (Engineering Science), 2023, 57(1): 81-91.

链接本文:

https://www.zjujournals.com/eng/CN/10.3785/j.issn.1008-973X.2023.01.009    或    https://www.zjujournals.com/eng/CN/Y2023/V57/I1/81

图 1  离心机的坐标系
图 2   ${{\boldsymbol{\phi}} _{\bf{G}}} = {\bf{1/5 }}$， ${{\boldsymbol{\phi}} _{\bf{R}}} = {\bf{1/3}}$时，θ随N的变化曲线
图 3  当N = 5， ${{\boldsymbol{\phi}} _{\bf{G}}} = {\bf{1/5 }}$时，θ随 $ {{\boldsymbol{\phi}} _{\bf{R}}} $的变化曲线
图 4  不同N时εv、εh随R0的变化图
Re CD的表达式
Re < 0.01 ${C_{\rm{D}}} = 1/16+24/{Re}$
0.01＜ Re ≤20 ${C_{\rm{D} } } = \dfrac{ {24} }{ { {Re} } }(1+0.131 \;5{ {Re} ^{0.82 - 0.05B} })$
20 ≤ Re ≤ 260 ${C_{\rm{D}}} = \dfrac{ {24} }{ { {Re} } }(1+0.193 \;5{ {Re} ^{0.630 \;5} })$
260 ≤ Re ≤ 1500 $\lg {C_{\rm{D}}} = 1.643 \;5 - 0.124 \;2B+0.155 \;8{B^2}$
1.5×103＜Re≤1.2×104 $\begin{gathered} \lg {C_{\rm{D} } } = - 2.457 \;1+2.555 \;8B - 0.929 \;5{B^2}+ \\ {\text{ } }0.104 \;9{B^3} \\ \end{gathered}$
1.2×104＜Re≤4.4×104 $\lg {C_{\rm{D}}} = - 1.918 \;1+0.637 \;0B - 0.063 \;6{B^2}$
4.4×104＜Re≤3.38×105 $\lg {C_{\rm{D}}} = - 4.339 \;0+1.580 \;9B - 0.154 \;6{B^2}$
3.38×105＜Re≤4×105 ${C_{\rm{D}}} = 29.78 - 5.3B$
4×105＜Re≤106 ${C_{\rm{D}}} = 0.1B - 0.49$
Re > 10 6 ${C_{\rm{D} } } = 0.19 - { {8 \times { {10}^4} } }/{ { {Re} } }$
表 1  不同Re下CD的表达式
图 5  N = 10时，不同 $ \;{{\boldsymbol{\beta}} _{\bf{0}}} $下的物体运动轨迹
图 6  不同 ${{\boldsymbol{\beta}} _{\bf{0}}}$下 ${{\boldsymbol{\delta}} _{{{\bf{r}}}}}$随N的变化曲线
图 7  沉降速度随流体黏度的变化曲线
图 8   $ {\alpha _0}{\text{ = }}{\boldsymbol{1}} $时的圆球运动轨迹
图 9  当ε= 2，α0= 1时 $ f $随τ的变化曲线
图 10   $\;{{\boldsymbol{\beta }}}_{{\bf{0}}} = {\boldsymbol{\pm 1}}、{{\boldsymbol{\alpha}} }_{{\bf{0}}}\text{\;=\;}{{\boldsymbol{\gamma }}}_{{\bf{0}}}\text{\;=\;{\bf{0}}}$时的圆球运动轨迹
图 11   ${{\boldsymbol{\gamma}} }_{{\bf{0}}}={\boldsymbol{\pm 1}}、{{\boldsymbol{\alpha}} }_{{\bf{0}}}\text{\;=\;}{{\boldsymbol{\beta}} }_{{\bf{0}}}\text{\;=\;{\bf{0}}}$时的圆球运动轨迹
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