Transcript 低雷諾數圓形及多邊形水躍的研究

Rotating Hydraulic Jump
轉動的水躍
輔導教授：楊宗哲
指導老師：李文堂
學生：呂軒豪
Introduction

1-1
When a fluid jet falling vertically strikes a
horizontal plate, fluid is expelled radially, and the layer
generally thins until reaching a critical radius at which
the layer depth increase abruptly. This phenomenon is
called the Circular Hydraulic Jump .
1-2
 Predictions for the jump radius based on
inviscid theory were presented by Lord
Rayleigh(1914).
 The dominant influence of fluid viscosity on the
jump radius was elucidated by Watson(1964).
 Ellegaard(1998)identified that a striking in
stability may transform the circular hydraulic
jump into regular polygons.
1-3
 We find when a fluid jet strikes to a
container, at the moment when the flow
over the container’s boundary the
circular hydraulic jump transform into
rotating polygons, this is referred to as
Rotating Hydraulic Jump.
影片
影片(慢放)
Background
2-1
 Rayleigh regarded hydraulic jump as a
discontinuity (shock). Close to the jet
the fluid layer is thin
and the motion is
rapid, further away
it is an order of
magnitude thicker
and moves correspondingly slower.
2-2
 Rayleigh’s shock conditions imply that
the fluid before and after jump are
respectively “supercritical” and
“subcritical” , which means the average
velocity is respectively larger and
smaller than the small amplitude wave
gh .
2-3
 When a jet of viscous ethylene glycol strikes a
container, a circular hydraulic jump is formed.
 As height of hext is increased, vertical rollers are
formed surrounding the jump.
 The roller is formed owing to velocity gradient of
the fluid layer.
 The vertical structure of flow now plays a crucial
role, it produces multiple vortices around the jump.
 The vortex produces a horizontal pressure gradient
p 
2 R 2
2
:
angular velocity of the roller. ;
R= hext/2 ,  =density of the fluid .
2-4
 液體旋轉示意圖：
上層液體向外流
下層液體向外流且受到較大的黏滯阻力
2-5
2/3秒後
2/3秒後
影片1
影片2
2-6
 控制濃度固定(及黏滯係數固定)、流量固定，
改變液深hext ，探討邊數和hext 關係。影片
 控制流量固定、液深固定，改變溶液濃度，探
討邊數和黏滯係數的關係。
 控制液深固定、濃度固定，探討邊數和流量的
關係。
2-7
 We measure the Reynold number of
Rotating Hydraulic Jump.
 We assume that N  k aQb hc

N: the polygon number.
 : kinematical viscosity of fluid.
Q: flow rate.
We do experiment to find a,b,c. And
know the dependence of number of
polygon.
ext
最近準備進行工作
 用可以改變高度的容器，重做深度對邊數的
實驗，在每一個穩定的多邊形旁放入膠片量
出v，求出Vortex之 p ，算出Vortex大小
對邊數的關係。
 架高盤子(透明盤)，液體中加入鋁粉(不起
化學變化)由底端拍出較清晰的Vortex。
 數據分析整理。
References
 彭黃勝、范治明、蔡國棟和李志強：水牆，中華民國
中小學科學展覽第二十一屆至三十屆優勝作品專輯
國立台灣科學教育館編印，頁301-307
 周雨剛等四人：利用因次分析法研究圓形水躍的變因，
中華民國第四十六屆中小學科學展覽會作品說明書。
 Clive Elligard, “Creating corners in kitchen sinks”,
Nature, Vol.392, P767-768, 1998.
 Thomas R. N. Jansson, “Polygons on a rotating fluid
surface”, Physics Review Letters,174502, 2006(May)