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浙江大学学报(工学版)
Journal of ZheJiang University (Engineering Science)  2023, Vol. 57 Issue (1): 81-91    DOI: 10.3785/j.issn.1008-973X.2023.01.009
    
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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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     
Received: 22 February 2022      Published: 17 January 2023
CLC:  TU 411  
Fund:  国家自然科学基金资助项目（51988101）
Corresponding Authors: Jian-jing ZHENG     E-mail: 21912219@zju.edu.cn;zhengjianjing@zju.edu.cn
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Tian-hao ZHAO
Jian-jing ZHENG
Jing-hua LING
Chang-yu SHI
Dao-sheng LING
Cite this article:

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.

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


离心超重力环境下流体中物体浮力与运动

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 
Fig.1 Coordinate system of centrifuge
Fig.2 Change of θ with N for ${\text{ }}{\phi _{\rm{G}}} = 1/5{\text{ }}$ and ${\text{ }}{\phi _{\rm{R}}} = 1/3$
Fig.3 Change of θ with $ {\text{ }}{\phi _{\rm{R}}}{\text{ }} $ for N = 5 and $ {\phi _{\rm{G}}} = 1/5 $
Fig.4 Change of εv and εh with R0 for different N
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 ${C_{\rm{D} } } = 0.19 - { {8 \times { {10}^4} } }/{ { {Re} } }$
Tab.1 CD expression under different Re
Fig.5 Solid falling trajectory with different $ \;{\beta _0} $ for N = 10
Fig.6 Change of $ {\delta _{\rm{r}}} $ with N for different $ \;{\beta _0} $
Fig.7 Change of sedimentation velocity with viscosity coefficient
Fig.8 Sphere trajectory for $ {\alpha _0}{\text{ = }}1 $
Fig.9 Change of f with τ for α0= 1 and ε= 2
Fig.10 Sphere trajectory for $ \;{\beta _0} = \pm 1 $ and $ {\alpha _0}{\text{ = }}{\gamma _0}{\text{ = 0}} $
Fig.11 Sphere trajectory for $ {\gamma _0} = \pm 1 $ and $ {\alpha _0}{\text{ = }}{\beta _0}{\text{ = 0}} $
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