CFD Analysis of flow around 2D Circular Cylinder in Unsteady Flow Regime
Abstract:
Flow around circular 2D is simulated by creating the computational domain in GAMBIT 2.4.6 . CFD
analysis is performed in Fluent 6.3 for the flow around cylinder under laminar steady flow regime for
Re=20 and 40 and unsteady laminar flow regime for Re=100, 200 and 1000. Flow characteristics such as
lift and drag are compared with the values in literature. Unsteady turbulent simulations are performed
for Re=4000, 14000 and 34,000 and the corresponding curves and contours are plotted and compared.
Introduction:
Flow around circular cylinders is of great importance in many applications including off shore risers,
bridges, piers, chimneys, towers, antennas and wires. Several researchers have worked on the flow
around cylinders particularly in unsteady regime. It is known that as the Reynolds number increases, the
dynamics of flow around cylinder changes significantly. Experimental data suggests that for very small
Reynolds number the wake consists of steady recirculation region behind the cylinder. As the Reynolds
number gradually increases disturbance starts creeping in and finally at sufficiently high Reynolds
number the flow becomes turbulent.
The wake behind a circular cylinder has been extensively studied by numerous researchers because of
the significance of the two dimensional and periodic Von karman vortex street. The relation between
Strouhal number and the Reynolds number has been studied and reported extensively in the literature
and is well established. Roshko( 1954) studied variation of drag of circular cylinders at very high
Reynolds number and has proposed a model for flows. Braza(1986) studied the physical aspects of
vortex shedding and the interactions of velocity and pressure fields outside and inside the wake.
Wissink et al (2008) did a numerical study of near wake of cylinder for high Reynolds numbers to study
the influence of turbulence statistics near wake. Posdziech and Grundmannn(2007) studied flow around
an infinitely long circular cylinder at low Reynolds number using Spectral element method and different
computational domains were used to obtain asymptotic solutions in the steady and unsteady flow
regime. Bruno et al (2010) made a computational study around 3D cylinder and investigated by means
of orthogonal decomposition and coherence function of side surface fluctuating pressure field. C
Norberg (2003) presents experimental data concerning the fluctuating lift acting on a stationary circular
cylinder in cross flow and also presents data from literature and empirical solutions for the calculation
and of St over wide range of Reynolds number. S.Rajagopalan and Antonia (2005) investigated the
separated shear layer in the near wake of a circular cylinder using a single hot wire probe.
Governing Equations:
An incompressible Newtonian Flow past a circular 2D cylinder has been simulated by solving Navier-
Stokes Equation of motion
Under these conditions , the resulting dimensionless equations are
= 0
The flow domain is divided in to number of control volumes or cells. The general equation is modified to
boundary conditions for control volumes adjacent to domain boundary. The resulting linear algebraic
equations are solved to obtain the velocity and pressure distribution at each nodal point. Lift and drag
coefficients are calculated as given below
=
Where D and l represent drag and lift force
Also the pressure coefficient is defined as
( )
Where the subscripts P and v represents pressure and viscous forces. is the dimensionless wall
pressure and is the dimensionless wall vorticity as defined by
⁄
Also the dimensionless Strouhal number is expressed as
Where f is the frequency of vortex shedding, d is the diameter of the cylinder and is free stream
velocity.
Physical Model :
The flow around cylinder is modeled in two dimensions with the axes of cylinder perpendicular to the
direction of flows. The cylinder is modeled as a circle and computational domain is created surrounding
the cylinder. The computational domain consists of 10 times the radius of cylinder and downstream 40
times to that of the radius of cylinder and width of 20 times.
Fig1: physical Model of the computational domain
Meshing:
Boundary Conditions:
The wall boundary conditions used in the problem are of non- slip and impermeable. i.e.u=0, v=0. In the
physical domain the flow is not confined. An imaginary boundary of 20R is used to solve the governing
equations numerically. Uniform free stream velocity of = 1.0m/s is applied at the inlet boundary. The
density is taken as 1 ⁄ .The periodic conditions are considered at the lateral boundary. The flow
exit is treated as pressure outlet.
Results and Discussion
Flow simulation is performed for different Reynolds numbers ranging from Re=20 to Re=34000 in
different flow regimes. Primarily, the study of wakes is carried out for Re=20 and 40 and velocity
vectors and vorticity contours have been compared along with the drag values. In steady flow regime ,
the two symmetrical wakes are formed at the rear of the cylindrical which is in agreement with that of
experimental and theoretical studies and shown in Fig(1 &2). It is known that two symmetrical wakes
form at the rear of cylinder under steady regime and stream velocity contours shows the same. The
simulation is performed in unsteady flow regime for Re =20 and 40 to compare the reattachment length
L/a versus Reynolds number with that of Braza et al. A good comparison is found with that of the
simulated results. It is known that as Reynolds number becomes higher than 40, there will be a loss in
the symmetry of wakes and alternating eddies are formed which are convected and diffused away from
the cylinder forming vo
Strouhal numbers for Re=100 , 200 and 1000 are chosen form the Braza (1986) and compared with that
of the numerical values obtained from oscillations the lift curve. Simulations are performed for
unsteady laminar regime and the parameters like Cd, Cl and Strouhal number are compared with that of
Braza().good agreement of the St with that the literature for different Re. Similarly , a comparison is
done for Re with that of the values taken from Braza.
Re Theoretical St Numerical St Error
100 0.16 0.18 12.5%
200 0.20 0.19 -5%
1000 0.21 0.20 - 4%
An error of 10-15% has been found for these three Reynolds number which is infact a good agreement
with that of Braza.
The results of unsteady laminar flow for Re =20, 40 , 100, 200 and 1000 which includes velocity vectors ,
contours of vorticity magnitude are given below .Wall vorticity versus angle of separation has been
compared for Re=200 and 1000.
Contours of vorticity for the entire range of Reynolds number has been given. The contours shows how
the symeetry of wakes is changed as the Reynolds number increases gradually.
Contours of Vorticity magnitude
Re=20
Re=40
Re=100
Re=200
Re=1000
Re=4000
Re=14000
Re=34000
COefficent drag and Lift
Cd= 2.71 for Re=20
Cd= 1.99 for Re=40
The initial comparison of coefficient of drag values with that of the values taken form the plot sho a
considerable agreement with that of Braza.
y = 3.7236x-0.167 R² = 0.9524
0
0.5
1
1.5
2
2.5
3
0 10000 20000 30000 40000
Cd
Cd
Power (Cd)
Drag and Lift plots
Re=100
Cd= 1.58
Re=200
Cd= 1.45
Re=1000
Unsteady Turbulent Flows
-1.2
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
0 1 2 3 4 5 6 7
Wall voriticity vs Angle
ϴ
The simulation is performed in Unsteady turbulent regime for Re=4000, 14000 and 34000 using K-
Omega model and flow parameters such as drag , lift and contours of Turbulence Intensity and Vorticity
are found.
Re=4000
Cd= 0.939
Re=14000
Cd= 0.737
Re=34000
Norberg et al (2003) proposed empirical relation for calculating Strouhal number for a range of Reynolds
number . Strouhal number for Re=4000 , 1400 and 34000 are calculated using the relation
( )
Where ( ⁄ )
which gives us following Strouhal numbers
Re Theoretical St Numerical St Error
4000 0.19 0.20 5%
14000 0.19 0.20 5%
34000 0.1848 0.194 5%
Re100