Efforts to Solve the Bathtub Vortex Problem

2012 ◽  
Vol 9 ◽  
pp. 10
Author(s):  
Takashi Noguchi
Keyword(s):  
Bathtub Vortex

scholarly journals Bathtub Vortex Profile and Flow Field Model with Circulation.

1998 ◽  
Vol 64 (620) ◽  
pp. 972-978 ◽  
Author(s):  
Seigo SAKAI ◽  
Haruki MADARAME ◽  
Koji OKAMOTO
Keyword(s):  
Flow Field ◽  
Field Model ◽  
Bathtub Vortex

A further note on the bathtub vortex

1964 ◽  
Vol 19 (4) ◽  
pp. 539-542 ◽  
Author(s):  
D. L. Kelly ◽  
B. W. Martin ◽  
E. S. Taylor
Keyword(s):  
Surface Waves ◽  
Alternative Explanation ◽  
Vortex Motion ◽  
Initial Direction ◽  
Flow Reversals ◽  
Bathtub Vortex

Using identical equipment, an attempt was made to reproduce the unexpected flow reversals obtained by Sibulkin (1962) in his study of the vortex motion associated with draining a liquid from a vessel through an orifice in its bottom. Reversal of the initial direction of rotation was found only for counter-clockwise filling with large initial heads and settling times, unless during settling or draining of the vessel a shock was applied to the system, in which case the tendency to reversal was generally more pronounced with clockwise filling. Re-reversal of the motion was also observed in a number of cases. An alternative explanation is proposed, based on a consideration of the surface waves generated by a shock.

Asymptotic theory for a bathtub vortex in a rotating tank

2014 ◽  
Vol 749 ◽  
pp. 113-144 ◽  
Author(s):  
M. R. Foster
Keyword(s):  
Vortex Core ◽  
Asymptotic Theory ◽  
Azimuthal Velocity ◽  
Velocity Variation ◽  
Cylindrical Tank ◽  
Short Cylinder ◽  
Rotating Table ◽  
Bathtub Vortex ◽  
Potential Vortex ◽  
Upper Boundary

AbstractFluid entering the periphery of a cylindrical tank mounted on a rotating table is pumped inwards toward a central, floor drain by a potential vortex that is established in the fluid interior. We present here an asymptotic theory for small Rossby and Ekman numbers, including detailed solutions in the vortex core. Results for azimuthal velocity variation with radius agree quite well with the experiments of Andersen et al. (J. Fluid Mech., vol. 556, 2006, pp. 121–146), in spite of their free upper boundary. Modifications of the flow are presented in the instance that a short cylinder is place on the tank axis as in the work of Chen et al. (J. Fluid Mech., vol. 733, 2013, pp. 134–157). The overall flow structure found here is exactly that noted by both Andersen et al. and Chen et al.

scholarly journals The bathtub vortex in a rotating container

2006 ◽  
Vol 556 ◽  
pp. 121 ◽  
Author(s):  
A. ANDERSEN ◽  
T. BOHR ◽  
B. STENUM ◽  
J. JUUL RASMUSSEN ◽  
B. LAUTRUP
Keyword(s):  
Bathtub Vortex

Speed of a surge in a bathtub vortex

1968 ◽  
Vol 34 (4) ◽  
pp. 651-656 ◽  
Author(s):  
Robert A. Granger
Keyword(s):  
Experimental Investigation ◽  
Experimental Evidence ◽  
Short Period ◽  
Salient Features ◽  
Bathtub Vortex

The surge studied in this paper is due to the sudden closure of the sink of a bathtub vortex. Experimental evidence established that the surge is not initially a wave but is in fact a slug of fluid which has, for a very short period of time, a distinctive motion of its own. The purpose of this paper is to present the salient features of an experimental investigation of the effect of circulation, geometry, and viscosity on the speed of the surge and to report some rather unexpected observations.

scholarly journals Structure of a bathtub vortex: importance of the bottom boundary layer

2009 ◽  
pp. 339-343
Author(s):  
Shinji Yukimoto ◽  
Hiroshi Niino ◽  
Takashi Noguchi ◽  
Ryuji Kimura ◽  
Frederic Y. Moulin
Keyword(s):  
Boundary Layer ◽  
Bottom Boundary Layer ◽  
Bottom Boundary ◽  
Bathtub Vortex

scholarly journals Measurement of Flow Distribution around a Bathtub Vortex.

1997 ◽  
Vol 63 (614) ◽  
pp. 3223-3230 ◽  
Author(s):  
Seigo SAKAI ◽  
Haruki MADARAME ◽  
Koji OKAMOTO
Keyword(s):  
Flow Distribution ◽  
Bathtub Vortex

Experimental Analysis of a Bathtub Vortex in a Simplified Cowl Box of Automotive Vehicles

2012 ◽  
Author(s):  
Yann Recoquillon ◽  
Emmanuelle Andrès ◽  
Azeddine Kourta
Keyword(s):  
Vortex Structure ◽  
High Speed ◽  
Numerical Models ◽  
Contour Detection ◽  
Measuring Devices ◽  
Capacitance Probe ◽  
Controlled Flow ◽  
Set Up ◽  
Physical Phenomena ◽  
Bathtub Vortex

On automotive vehicles, the cowl box is a volume located at the bottom of the windshield, under the cowl top grille. It provides external fresh air to the HVAC (Heating, Ventilating and Air Conditioning) unit and it is used to collect water coming from the windshield under rain conditions. This box is designed as a tranquillisation chamber to segregate water from air and avoid the ingress of rainwater into the HVAC unit. However, as the area is awkward to access with measuring devices, our knowledge about the physics of flow in the cowl box is limited. The present work aims to advance our knowledge through experimental work on the air/water flow in a simplified cowl box in order to optimize the box size and improve numerical models. This paper will focus on the analysis of the bathtub vortex, which is potentially responsible for insufficient draining of the water collected in the cowl box. The experimental set-up consists of a Plexiglas parallelepiped representing a simplified cowl box with top cowl grille, HVAC inlet and drain. A blower generates airflow through the HVAC inlet. A water sheet, with controlled flow rate, is created on an inclined plane representing the windshield. Velocity measurements of all components are obtained by PIV (Particle Image Velocimetry) in the liquid phase and the surface level is recorded by a capacitance probe near the drain. Moreover, contour detection of the vortex core is achieved using a high-speed camera. Results show a relationship between the pressure loss generated by the airflow in the cowl box, the water level and the vortex structure. The modification of the vortex structure as well as the modification of velocity components near the air core are visible only in transient stages. These experimental results give us today some insight to understand the physical phenomena occurring in the cowl box.

Switching Phenomenon of a Bathtub Vortex

1994 ◽  
Vol 61 (4) ◽  
pp. 850-854 ◽  
Author(s):  
M. Shiraishi ◽  
T. Sato
Keyword(s):  
Linear Relationship ◽  
Flow Rate ◽  
Oscillation Frequency ◽  
Design Parameters ◽  
Water Tank ◽  
Fluid Level ◽  
Rate Difference ◽  
Switching Phenomenon ◽  
Double Orifice ◽  
Bathtub Vortex

Switching phenomenon of the bathtub vortex in a double-orifice water tank is experimentally investigated. This alternation between “vortexflow” and “nonvortex flow” is caused by flow rate differences through the two orifices. The oscillation frequency is experimentally examined by changing the design parameters, such as the orifice size, the distance between two orifices, and the fluid level. A linear relationship is obtained between the frequency and the flow rate difference.

A bathtub vortex under the influence of a protruding cylinder in a rotating tank

2013 ◽  
Vol 733 ◽  
pp. 134-157 ◽  
Author(s):  
Yin-Chung Chen ◽  
Shih-Lin Huang ◽  
Zi-Ya Li ◽  
Chien-Cheng Chang ◽  
Chin-Chou Chu
Keyword(s):  
Vortex Structure ◽  
Stokes Equations ◽  
Finite Thickness ◽  
Ekman Pumping ◽  
Height Ratio ◽  
Coriolis Parameter ◽  
Ekman Number ◽  
Drain Hole ◽  
Bathtub Vortex ◽  
Taylor Column

AbstractNumerical simulations and laboratory experiments were jointly conducted to investigate a bathtub vortex under the influence of a protruding cylinder in a rotating tank. In the set-up, a central drain hole is placed at the bottom of the tank and a top-down cylinder is suspended from the rigid top lid, with fluid supplied from the sidewall for mass conservation. The cylinder is protruded to produce the Taylor column effect. The flow pattern depends on the Rossby number ($\mathit{Ro}= U/ fR$), the Ekman number ($\mathit{Ek}= \nu / f{R}^{2} )$ and the height ratio, $h/ H$, where $R$ is the radius of the cylinder, $f$ is the Coriolis parameter, $\nu $ is the kinematic viscosity of the fluid, $h$ is the vertical length of the cylinder and $H$ is the height of the tank. It is found appropriate to choose $U$ to be the average inflow velocity of fluid entering the column beneath the cylinder. Steady-state solutions obtained by numerically solving the Navier–Stokes equations in the rotating frame are shown to have a good agreement with flow visualizations and particle tracking velocimetry (PTV) measurements. It is known that at $\mathit{Ro}\sim 1{0}^{- 2} $, the central downward flow surrounded by the neighbouring Ekman pumping forms a classic one-celled bathtub vortex structure when there is no protruding cylinder ($h/ H= 0$). The influence of a suspended cylinder ($h/ H\not = 0$) leads to several findings. The bathtub vortex exhibits an interesting two-celled structure with an inner Ekman pumping (EP) and an outer up-drafting motion, termed Taylor upwelling (TU). The two regions of up-drafting motion are separated by a notable finite-thickness structure, identified as a (thin-walled) Taylor column. The thickness ${ \delta }_{T}^{\ast } $ of the Taylor column is found to be well correlated to the height ratio and the Ekman number by ${\delta }_{T} = { \delta }_{T}^{\ast } / R= {(1- h/ H)}^{- 0. 32} {\mathit{Ek}}^{0. 095} $. The Taylor column presents a barrier to the fluid flow such that the fluid from the inlet may only flow into the inner region through the narrow gaps, one above the Taylor column and one beneath it (conveniently called Ekman gaps). As a result, five types of routes along which the fluid may flow to and exit at the drain hole could be identified for the multi-celled vortex structure. Moreover, the flow rates associated with the five routes were calculated and compared to help understand the relative importance of the component flow structures. The weaker influence of the Taylor column effect on the bathtub vortex at $\mathit{Ro}\sim 1$ or even higher $\mathit{Ro}\sim 1{0}^{2} $ is also discussed.

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