Reynolds and froude number effect on the flow past an interface-piercing circular cylinder

International Journal of Naval Architecture and Ocean Engineering.
2014.
Sep,
6(3):
529-561

This is an Open-Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/3.0) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

- Published : September 30, 2014

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Large-eddy simulation
;
Interface-piercing circular cylinder
;
Run-up
;
Wave breaking
;
Vortical structures

INTRODUCTION

The turbulent flow past a circular cylinder has been investigated extensively for a long time due to its importance in many engineering applications. It shows different features at different Reynolds numbers (
COMPUTATIONAL METHODS

CFDShip-Iowa version 6.2, a sharp interface orthogonal curvilinear grid solver for two-phase incompressible flows recently developed at IIHR (
Yang and Stern, 2009
;
Suh et al., 2011
) is used for all computations. The interface is tracked by a Coupled Level Set and Volume-of-Fluid (CLSVOF) method (
Wang et al., 2009
;
Wang et al., 2012
) instead of the level set method used in
Suh et al. (2011)
to capture detailed breaking waves.
- Mathematical model

An orthogonal curvilinear coordinate system is adopted for the governing equations. The Navier-Stokes equations for twophase, immiscible, incompressible flows have been written in the orthogonal curvilinear coordinates. The continuity equation is given as follows:
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- Numerical method

The finite-difference method is used to discretize the Navier-Stokes equations on a non-uniform orthogonal curvilinear grid. A staggered variable arrangement is adopted, i.e., the contravariant velocity components
SIMULATION CONDITIONS, VERIFICATION AND VALIDATION

- Grid, computational domain, and geometry

Body-fitted cylindrical grids were used for all cases and
Table 1
shows the number of grid points and distance of the first grid point from the cylinder wall (
Simulation conditions.

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- Flow conditions, boundary conditions, and initial conditions

The diameter of cylinder,
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- Verification and validation of integral variables

The time histories of the drag coefficient
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Verification study with caseRe= 458,000 /Fr= 1.64

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Iterative uncertainty using drag coefficient (CD).

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Validation study with caseRe= 458,000 /Fr= 1.64.

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- Flow field validation forRe=234,000/Fr=0.84

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REYNOLDS NUMBER EFFECT WITH FIXED FROUDE NUMBER = 0.84

Three different Reynolds numbers from sub-critical to post-critical (27,000, 234,000, and 458,000) with
- Mean separation pattern

Fig. 13
shows the separation pattern of the mean flow with vortex core lines, which is obtained using the approach discussed in
Kandasamy et al. (2009)
and
Sujudi and Haimes (1995)
. The separated shear layer was visualized approximately using the iso-surfaces of the stagnation
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- Vorticity

For a single-phase flow past a circular cylinder, the regular Karman vortex street and organized wake patterns are prominent for low
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- Reynolds stresses

The streamwise Reynolds stress (
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- Vorticity transport

Suh et al. (2011)
studied the mechanism of the vorticity generation at sub-critical
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- Overall Froude number effect with differentRe

There is little influence of Reynolds number at the air-water interface based on variables related to the air-water interface such as mean interface elevation, run-up height, and Kelvin wave patterns, etc. The instantaneous air-water interface elevations for all different Fr with different Re are shown in
Fig. 25
. For the lowest
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FROUDE NUMBER EFFECT ON FLOW STRUCTURES WITH RE = 458,000

Three different Froude numbers (0.84, 1.24, and 1.64) with
- Air-water interface structures at differentFr

The mean air-water interface elevation contours for all three
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- Vorticity and velocity at the interface

Three-dimensional instantaneous coherent vortical structures identified by the second invariant of the velocity gradient tensor (Hunt et al., 1998) for the three Fr are shown in
Fig. 31
. At
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- Wave breaking at differentFr

Fig. 34
shows the iso-surface of the air-water interface with slices of the wave profile orthogonal to the cylinder wall for the three
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CONCLUSIONS AND FUTURE WORK

The two-phase turbulent flow past an interface-piercing circular cylinder at different Reynolds and Froude numbers is studied numerically using large-eddy simulation with a Lagrangian dynamic subgrid-scale model. Verification and validation studies are performed to show the accuracy of the simulations with comparisons against available experimental data.
It is found that the variation in sub-critical
Acknowledgements

This work was sponsored by the Office of Naval Research (ONR) under Grant No. N000141-01-00-1-7, with Dr. Ki-Han Kim as the program manager. The simulations were performed at the Department of Defense (DoD) Supercomputing Resource Centers through the High Performance Computing Modernization Program (HPCMP).

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Citing 'Reynolds and froude number effect on the flow past an interface-piercing circular cylinder
'

@article{ E1JSE6_2014_v6n3_529}
,title={Reynolds and froude number effect on the flow past an interface-piercing circular cylinder}
,volume={3}
, number= {3}
, journal={International Journal of Naval Architecture and Ocean Engineering}
, publisher={The Society of Naval Architects of Korea}
, author={Koo, Bonguk
and
Yang, Jianming
and
Yeon, Seong Mo
and
Stern, Frederick}
, year={2014}
, month={Sep}