Asymptotic analysis of initial flow around an impulsively started circular cylinder using a Brinkman penalization method

2021 ◽  
Vol 929 ◽  
Author(s):  
Y. Ueda ◽  
T. Kida
Keyword(s):  
Circular Cylinder ◽  
Asymptotic Solution ◽  
Asymptotic Analysis ◽  
Drag Coefficient ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Cylinder Surface ◽  
Initial Flow ◽  
Penalization Method ◽  
Brinkman Penalization Method

The initial flow past an impulsively started translating circular cylinder is asymptotically analysed using a Brinkman penalization method on the Navier–Stokes equations. The asymptotic solution obtained shows that the tangential and normal slip velocities on the cylinder surface are of the order of $1/\sqrt {\lambda }$ and $1/\lambda$ , respectively, within the second approximation of the present asymptotic analysis, where $\lambda$ is the penalization parameter. This result agrees with the estimation of Carbou & Fabrie (Adv. Diff. Equ., vol. 8, 2003, pp. 1453–1480). Based on the asymptotic solution, the influence of the penalization parameter $\lambda$ is discussed on the drag coefficient that is calculated using the adopted three formulae. It can then be found that the drag coefficient calculated from the integration of the penalization term exhibits a half-value of the results of Bar-Lev & Yang (J. Fluid Mech., vol. 72, 1975, pp. 625–647) as $\lambda \to \infty$ .

Computation of Vortex Lock-In in the Laminar Wake of a Circular Cylinder Using Unsteady Monopole Sources

1995 ◽  
Vol 117 (2) ◽  
pp. 227-233 ◽  
Author(s):  
Dartzi Pan ◽  
Yu-Chi Chin ◽  
Chih-Hao Chang
Keyword(s):  
Circular Cylinder ◽  
Flow Field ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Finite Volume Scheme ◽  
Cylinder Surface ◽  
Navier Stokes Equations ◽  
Laminar Wake ◽  
Lock In ◽  
Flux Difference

The vortex lock-in in the laminar wake behind a circular cylinder induced by the unsteady monopole source is numerically simulated in this paper. The artificial compressibility method is employed to solve the incompressible Navier-Stokes equations. A high-order accurate upwind flux-difference finite-volume scheme is used to discretize the flow field. The unsteady monopole source is simulated by a pulsating volume flux through the cylinder surface at a prescribed forcing frequency and amplitude. The forcing amplitude is set to a fixed value while the frequency is varied to search for the lock-in region. The flow field of the periodic lock-in state is examined in detail. Finally, the effects of a higher amplitude and a different source location are briefly investigated.

Simulation of Unsteady Flow Around a Cylinder

2015 ◽  
Vol 3 (2) ◽  
pp. 28-49
Author(s):  
Ridha Alwan Ahmed
Keyword(s):  
Stokes Equations ◽  
Lift Coefficient ◽  
Reynolds Numbers ◽  
Mean Value ◽  
Navier Stokes ◽  
Cylinder Surface ◽  
Navier Stokes Equations ◽  
Flow Around A Cylinder ◽  
Numerical Grid ◽  
Good Agreement

       In this paper, the phenomena of vortex shedding from the circular cylinder surface has been studied at several Reynolds Numbers (40≤Re≤ 300).The 2D, unsteady, incompressible, Laminar flow, continuity and Navier Stokes equations have been solved numerically by using CFD Package FLUENT. In this package PISO algorithm is used in the pressure-velocity coupling.        The numerical grid is generated by using Gambit program. The velocity and pressure fields are obtained upstream and downstream of the cylinder at each time and it is also calculated the mean value of drag coefficient and value of lift coefficient .The results showed that the flow is strongly unsteady and unsymmetrical at Re>60. The results have been compared with the available experiments and a good agreement has been found between them

ON THE ASYMPTOTIC ANALYSIS OF THE BGK MODEL TOWARD THE INCOMPRESSIBLE LINEAR NAVIER–STOKES EQUATION

2010 ◽  
Vol 20 (08) ◽  
pp. 1299-1318 ◽  
Author(s):  
A. BELLOUQUID
Keyword(s):  
Asymptotic Analysis ◽  
Stokes Equations ◽  
Strong Solutions ◽  
Navier Stokes ◽  
Uniqueness Theorems ◽  
Bgk Model ◽  
Navier Stokes Equation ◽  
Navier Stokes Equations ◽  
Stokes Systems ◽  
Global Strong Solutions

This paper deals with the analysis of the asymptotic limit for BGK model to the linearized Navier–Stokes equations when the Knudsen number ε tends to zero. The uniform (in ε) existence of global strong solutions and uniqueness theorems are proved for regular initial fluctuations. As ε tends to zero, the solution of BGK model converges strongly to the solution of the linearized Navier–Stokes systems. The validity of the BGK model is critically analyzed.

Numerical solution of the early stage of the unsteady viscous flow around a circular cylinder: a comparison with experimental visualization and measurements

1985 ◽  
Vol 160 ◽  
pp. 93-117 ◽  
Author(s):  
Ta Phuoc Loc ◽  
R. Bouard
Keyword(s):  
Circular Cylinder ◽  
Flow Structure ◽  
Stokes Equations ◽  
Early Stage ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Grid Systems ◽  
Unsteady Viscous Flow ◽  
Vorticity Transport ◽  
New Phenomena

Early stages of unsteady viscous flows around a circular cylinder at Reynolds numbers of 3 × 103 and 9.5 × 103 are analysed numerically by direct integration of the Navier–Stokes equations – a fourth-order finite-difference scheme is used for the resolution of the stream-function equation and a second-order one for the vorticity-transport equation. Evolution with time of the flow structure is studied in detail. Some new phenomena are revealed and confirmed by experiments.The influence of the grid systems and the downstream boundary conditions on the flow structure and the velocity profiles is reported. The computed results are compared qualitatively and quantitatively with experimental visualization and measurements. The comparison is found to be satisfactory.

CFD Analysis of Vortex Shedding in a Circular Cylinder: Flow Induced Vibration Design

2006 ◽  
Author(s):  
Nadeem Ahmed Sheikh ◽  
M. Afzaal Malik ◽  
Arshad Hussain Qureshi ◽  
M. Anwar Khan ◽  
Shahab Khushnood
Keyword(s):  
Circular Cylinder ◽  
Vortex Shedding ◽  
Stokes Equations ◽  
Boundary Layer Separation ◽  
The Body ◽  
Navier Stokes ◽  
Structural Vibrations ◽  
Flow Induced Vibration ◽  
Navier Stokes Equations ◽  
Implicit Approach

Flow past a blunt body, such as a circular cylinder, usually experiences boundary layer separation and very strong flow oscillations in the wake region behind the body at a discrete frequency that is correlated to the Reynolds number of the flow. The periodic nature of the vortex shedding phenomenon can sometimes lead to unwanted structural vibrations. The effect of vibrating instability of a single cylinder is investigated in a uniform flow using the power of computational methods. Fluid structure coupling procedure predicts the fluid forces responsible for structural vibrations. An implicit approach to the solution of the unsteady two-dimensional Navier-Stokes equations is used for computation of flow parameters. Calculations are performed in parallel using a domain re-meshing/deforming technique with efficient communication requirements. Results for the unsteady shedding flow behind a circular cylinder are presented with experimental comparisons, showing the feasibility of accurate, efficient, time-dependent estimation of shedding frequency and resulting vibrations.

Heat Transfer From a Circular Cylinder at Low Reynolds Numbers

1998 ◽  
Vol 120 (1) ◽  
pp. 72-75 ◽  
Author(s):  
V. N. Kurdyumov ◽  
E. Ferna´ndez
Keyword(s):  
Circular Cylinder ◽  
Energy Equation ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Order Unity ◽  
Navier Stokes Equations ◽  
Wide Range ◽  
Prandtl Numbers ◽  
High Degree

A correlation formula, Nu = W0(Re)Pr1/3 + W1(Re), that is valid in a wide range of Reynolds and Prandtl numbers has been developed based on the asymptotic expansion for Pr → ∞ for the forced heat convection from a circular cylinder. For large Prandtl numbers, the boundary layer theory for the energy equation is applied and compared with the numerical solutions of the full Navier Stokes equations for the flow field and energy equation. It is shown that the two-terms asymptotic approximation can be used to calculate the Nusselt number even for Prandtl numbers of order unity to a high degree of accuracy. The formulas for coefficients W0 and W1, are provided.

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