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