scholarly journals Numerical Computation of Low Reynolds Number Viscous Flow Past Bluff Bodies

2020 ◽  
Vol 25 (3) ◽  
pp. 133-157
Author(s):  
Md. Shahjada Tarafder ◽  
Miad Al Mursaline
Keyword(s):  
Reynolds Number ◽  
Circular Cylinder ◽  
Viscous Flow ◽  
Separation Angle ◽  
Total Drag ◽  
Functional Relationships ◽  
Square Cylinders ◽  
Length Separation ◽  
Bubble Length ◽  
Low Reynolds

AbstractThis article presents a two-dimensional steady viscous flow simulation past circular and square cylinders at low Reynolds numbers (based on the diameter) by the finite volume method with a non-orthogonal body-fitted grid. Diffusive fluxes are discretized using central differencing scheme, and for convective fluxes upwind and central differencing schemes are blended using a ‘deferred correction’ approach. A simplified pressure correction equation is derived, and proper under-relaxation factors are used so that computational cost is reduced without adversely affecting the convergence rate. The governing equations are expressed in Cartesian velocity components and solution is carried out using the SIMPLE algorithm for collocated arrangement of variables. The mesh yielding grid-independent solution is then utilized to study, for the very first time, the effect of the Reynolds number on the separation bubble length, separation angle, and drag coefficients for both circular and square cylinders. Finally, functional relationships between the computed quantities and Reynolds number (Re) are proposed up to Re = 40. It is found that circular cylinder separation commences between Re= 6.5-6.6, and the bubble length, separation angle, total drag vary as Re, Re−0.5, Re−0.5 respectively. Extrapolated results obtained from the empirical relations for the circular cylinder show an excellent agreement with established data from the literature. For a square cylinder, the bubble length and total drag are found to vary as Re and Re−0.666, and are greater than these for a circular cylinder at a given Reynolds number. The numerical results substantiate that a square shaped cylinder is more bluff than a circular one.

scholarly journals Experimental and numerical study of the separation angle for flow around a circular cylinder at low Reynolds number

2004 ◽  
Vol 515 ◽  
pp. 233-260 ◽  
Author(s):  
MING-HSUN WU ◽  
CHIH-YUNG WEN ◽  
RUEY-HOR YEN ◽  
MING-CHENG WENG ◽  
AN-BANG WANG
Keyword(s):  
Reynolds Number ◽  
Circular Cylinder ◽  
Numerical Study ◽  
Low Reynolds Number ◽  
Separation Angle ◽  
Low Reynolds

Steady separated flow past a circular cylinder at low Reynolds numbers

2009 ◽  
Vol 620 ◽  
pp. 89-119 ◽  
Author(s):  
SUBHANKAR SEN ◽  
SANJAY MITTAL ◽  
GAUTAM BISWAS
Keyword(s):  
Boundary Condition ◽  
Circular Cylinder ◽  
Steady Flow ◽  
Slip Boundary Condition ◽  
Separation Angle ◽  
Towing Tank ◽  
Slip Boundary ◽  
Length Separation ◽  
Bubble Length ◽  
Lateral Walls

The steady two-dimensional laminar flow around a stationary circular cylinder has been investigated via a stabilized finite-element method. The Reynolds number Re is based on the cylinder diameter and free-stream speed. The results have been presented for 6 ≤ Re ≤ 40 and the blockages between 0.000125 and 0.80. The blockage B is the ratio of the cylinder diameter to the domain width. There is large scatter in the value of Res, reported in the literature, marking the onset of the flow separation. From the present study the Res is found to be 6.29, approximately for B = 0.005. The effect of the blockage on the characteristic flow parameters is found to be insignificant for B ≤ 0.01. The bubble length, separation angle and Res exhibit non-monotonic variation with the blockage. It is for the first time that such a behaviour for the separation angle and Res is being reported. Two types of boundary conditions at the lateral walls have been studied: the slip wall and towing tank. In general for high blockage, the results from the slip boundary condition are closer to the ones for the unbounded flow. In that sense, the use of the slip boundary condition as opposed to the towing tank boundary condition on the lateral walls is advocated. The bubble length, separation angle, base suction, total drag, pressure drag, viscous drag and maximum vorticity on the cylinder surface for the steady flow are found to vary as Re, Re−0.5, Re−1, Re−0.5, Re−0.64, Re−0.60 and Re0.5, respectively. The extrapolated results for the steady flow, for higher Re, are found to match quite well with the other results from the literature.

Low Reynolds number flow around and heat transfer from a heated circular cylinder

2010 ◽  
Vol 1 (1-2) ◽  
pp. 15-20 ◽  
Author(s):  
B. Bolló
Keyword(s):  
Reynolds Number ◽  
Circular Cylinder ◽  
Lift Coefficient ◽  
Reynolds Numbers ◽  
Low Reynolds Numbers ◽  
Reynolds Number Flow ◽  
Two Dimensional Flow ◽  
Number Flow ◽  
Low Reynolds ◽  
Increasing Temperature

Abstract The two-dimensional flow around a stationary heated circular cylinder at low Reynolds numbers of 50 < Re < 210 is investigated numerically using the FLUENT commercial software package. The dimensionless vortex shedding frequency (St) reduces with increasing temperature at a given Reynolds number. The effective temperature concept was used and St-Re data were successfully transformed to the St-Reeff curve. Comparisons include root-mean-square values of the lift coefficient and Nusselt number. The results agree well with available data in the literature.

Steady approach of unsteady low-Reynolds-number flow past two rotating circular cylinders

2013 ◽  
Vol 736 ◽  
pp. 414-443 ◽  
Author(s):  
Y. Ueda ◽  
T. Kida ◽  
M. Iguchi
Keyword(s):  
Reynolds Number ◽  
Circular Cylinder ◽  
Stokes Equations ◽  
Low Reynolds Number ◽  
Vortex Method ◽  
The Self ◽  
Circular Cylinders ◽  
Far Field ◽  
Flow Past ◽  
Low Reynolds

AbstractThe long-time viscous flow about two identical rotating circular cylinders in a side-by-side arrangement is investigated using an adaptive numerical scheme based on the vortex method. The Stokes solution of the steady flow about the two-cylinder cluster produces a uniform stream in the far field, which is the so-called Jeffery’s paradox. The present work first addresses the validation of the vortex method for a low-Reynolds-number computation. The unsteady flow past an abruptly started purely rotating circular cylinder is therefore computed and compared with an exact solution to the Navier–Stokes equations. The steady state is then found to be obtained for $t\gg 1$ with ${\mathit{Re}}_{\omega } {r}^{2} \ll t$, where the characteristic length and velocity are respectively normalized with the radius ${a}_{1} $ of the circular cylinder and the circumferential velocity ${\Omega }_{1} {a}_{1} $. Then, the influence of the Reynolds number ${\mathit{Re}}_{\omega } = { a}_{1}^{2} {\Omega }_{1} / \nu $ about the two-cylinder cluster is investigated in the range $0. 125\leqslant {\mathit{Re}}_{\omega } \leqslant 40$. The convection influence forms a pair of circulations (called self-induced closed streamlines) ahead of the cylinders to alter the symmetry of the streamline whereas the low-Reynolds-number computation (${\mathit{Re}}_{\omega } = 0. 125$) reaches the steady regime in a proper inner domain. The self-induced closed streamline is formed at far field due to the boundary condition being zero at infinity. When the two-cylinder cluster is immersed in a uniform flow, which is equivalent to Jeffery’s solution, the streamline behaves like excellent Jeffery’s flow at ${\mathit{Re}}_{\omega } = 1. 25$ (although the drag force is almost zero). On the other hand, the influence of the gap spacing between the cylinders is also investigated and it is shown that there are two kinds of flow regimes including Jeffery’s flow. At a proper distance from the cylinders, the self-induced far-field velocity, which is almost equivalent to Jeffery’s solution, is successfully observed in a two-cylinder arrangement.

Sign in / Sign up

Export Citation Format

Share Document