ENAE 488C – Computational Fluid Dynamics

Study of Air Flow over Two Side-By-Side

2-D Circular Cylinders

Mario Nirman Mondal

UID# 113269066

Department of Aerospace Engineering

University of Maryland, College Park, MD

Final Project, Spring 2015

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Study of Air Flow over Two Side-By-Side

2-D Circular Cylinders

Mario Nirman Mondal

UID# 113269066

Abstract

In this project, the air flow over two identical cylinders, which were placed side-by-side,

has been studied. The cylinders were represented in two-dimension by a circle, and flow domain

was created and discretized using the commercial grid generation software, Pointwise. The flow

was modeled as steady, viscous, turbulent and compressible. CFD++ was used as a CFD solver

to get the solution of the flow field. After solving the flow field, the qualitative analysis of

streamlines was done using Tecplot. The distance ratios between two cylinders, L/D (L = center

to center distance, D = Diameter of the single cylinder) were varied to study the flow behavior at

different distances. The variation of coefficient of lift (Cl) and the coefficient of drag (Cd) of the

two cylinders was examined. Lift-coefficient, Cl decreases for upper cylinder as the distance

increases. Conversely, Cl increases for the lower cylinder as the lower cylinder as the distance

increases. At some point, Cl of both the cylinders converges to same value, which means they

start to act like single cylinder and become free of the effect of the flow from the other cylinder.

The Reynolds number (Re) was also varied in each distant case. At different Reynolds numbers,

the flow pattern, the wakes behind the cylinders, vorticity contours and flow separation was

analyzed. The variation of coefficient of drag (Cd) as a function of Reynolds number was

examined, and it was plot with the analytical value of Cd to compare. As expected, Cd continues

to keep decreasing as Re increases. However, at critical Re=3 X 105, a drop in Cd is observed,

and it again increases afterwards. Unsteady flow behavior at low Reynolds number was also

simulated to get the idea of how the unsteady simulation works and the effect of unsteady

compared to steady flow was investigated. Finally, the grid resolution study was done in order to

observe the effectiveness of the baseline (1X) grid generation with the 2X and 4X grid points.

I. Introduction

Flow over cylinder is a fundamental fluid dynamics problem of practical importance.

Double circular side-by-side cylindrical configurations are widely used in engineering

applications e.g. the flow around bi-planes, twin-jet engine aircraft, wind turbine farms, electrical

poles, chimneystacks etc. The goal of the project is to investigate the flow behavior around two

side-by-side cylinders by varying the distances between two cylinders and also varying the

Reynolds number. Actually, the distance ratio L/D was varied, where L = center to center

distance, D = Diameter of the single cylinder/Characteristics length/Chord length. Because the

study was done from very low Mach (M=0.000043) region to subsonic region (M=0.43), the far

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field of the flow was placed 50 times far off the

characteristics length in each direction so that the

disturbance cannot migrate from upstream or downstream

of the flow.

The flow was modeled as steady, viscous,

turbulent and compressible flow. The flow field was

discretized and the grid was generated using grid

generation software, Pointwise. CFD++ was used as a

CFD solver to get the solution of the flow field. After

solving flow field, the qualitative and quantitative analysis

was done. The qualitative analysis was done by getting the

streamlines of flow using Tecplot, and the quantitative

analysis and plots were made using Microsoft Excel.

II. Theory and Equations

he relations between the coefficients and the forces are as follows:

;

Where, Cl = Coefficient of Lift

Cd = Coeffiient of Drag

L = Lift force

D = Drag force

q∞ = Dynamic Pressure

= Density of the fluid (in this case, Air)

S = Surface area of the body = Chord length (C) X Span (b)

Since a circle is being modeled, surface area S= , r = radius of the circle

Also, the equation that relates Reynolds number to free stream velocity is given below:

Reynolds number,

Where, d = characteristics length = diameter of the cylinder = 0.1m

μ = viscosity of air = 1.7894 x 10-5

kg/(m.s)

= Density of the fluid (in this case, Air) = 1.225 kg/m3

In order to vary the Reynolds number, the free stream velocity, V∞ was varied.

Figure 1: Basic Geometry

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III. Methods

1. Grid Generation:

The geometry was created in Pointwise: A circle of diameter 0.1m (which was mirrored

later to get the symmetrical flow domain of another 2-D cylinder).

For the baseline (1X) grid, 90 grid points were imposed on the circle (4° per point).

By default, the grid point distribution on the circle was d=0.00349 and it was kept as

the spacing distribution of the points on the connecting lines.

Wall spacing of s=0.0001 was chosen for all the grids.

Farfield boundary was placed approximately 50 chord lengths/diameter away from the

cylinders in all directions.

Structured O-grid was generated around one cylinder up to 5*D distance so that the

boundary layer effects can be captured as good enough as possible.

Points were clustered around the cylinder in order to resolve boundary layer.

After creating the O-grid, the whole domain was divided into 4 rectangles and H-grid was

generated around one cylinder up to farfield.

Then, the whole domain was mirrored about X-axis to get the flow grid domain of the

other cylinder.

Figure 2: Grid (Zoomed in) for L/D=3

Three different grids were generated to vary L/D (distance ratio of the two cylinders).

1.) L/D = 1.5 : Number of cells – 52,080

2.) L/D = 3 : Number of cells – 55,500

3.) L/D = 5 : Number of cells – 59,040

In order to do the grid resolution study, for L/D=3 two more grids were made as follows:

1.) Baseline (1X) grid points : Number of cells – 55,500

2.) 2X grid points : Number of cells – 206,276

3.) 3X grid points : Number of cells – 793,512

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2. CFD++ Solver Setup:

The Wizards was used to set the equation type, initialize the domain with given

quantities, set up turbulence model with k - , set up fluid properties of air and set up time

integration quantities.

Compressible perfect gas equation was used.

The solver was run at steady-state condition.

The dimension and units were used in S.I system.

Freestream X-velocity was varied to match with the desired Reynolds number according

to the equation of the Reynolds number.

Re = 100 X-velocity = 0.0146 m/s

Re = 200 X-velocity = 0.0292 m/s

Re = 10000 X-velocity = 1.4607 m/s

Re = 100000 X-velocity = 14.6073 m/s

Re = 1e+6 X-velocity = 146.0735 m/s

Initial condition of the domain was set at sea level condition (Altitude 0 Km).

Pressure = 101325 Pa Temperature = 288 Kelvin

Freestream turbulence intensity was set at 3%.

Simple turbulence model (2-equation model) was used.

Turbulent/laminar viscosity ratio was used as 50.0.

In all cases, turbulence was modeled from the first iteration.

Boundary conditions were set adiabetic viscous wall function for airfoil wall, and

characteristics-based inflow/outflow for the farfield.

Spatial order of accuracy – 2nd

order accurate

Simulations were run at different X-velocity of each of the L/D case. Therefore, 15

steady simulations were run.

Convergence criterion was fulfilled by residual drops of 6.0 orders of magnitude.

There was one unsteady flow was run for L/D=3 and Re=200. For the unsteady flow

parameters was selected as below:

→ Strouhal number was assumed to be 0.2

→ Vortex shedding frequency was calculated using the Strouhal equation:

Strouhal no, St = (f*D)/u

f = vortex shedding frequency; D=cylinder diameter; u = X-velocity

→ From the frequency, f, time period, ts was calculated.

→ 1000 time steps were wanted to resolve the time period, ts.

→ Therefore, time step size Dt was calculated as Dt = (ts)/1000

→ In order to run the unsteady simulation, up to 300 iterations were run as steady-state

so that the solution converges. Then, upto 1500 iterations were made to get the

unsteady solution.

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-0.05

-0.04

-0.03

-0.02

-0.01

0

0.01

0.02

0.03

0.04

0 1 2 3 4 5 6

Co

eff

of

Lift

, Cl

L/D

Cl vs L/D

Cl of Lower Cylinder

Cl of Upper Cylider

0

0.01

0.02

0.03

0.04

0.05

0.06

0 1 2 3 4 5 6

Co

eff

of

Dra

g, C

d

L/D

Cd vs. L/D

Cd of Lower Cylinder

Cd of Upper Cylinder

3. Flow visualization in Tecplot, Data collection and Plotting in Microsoft Excel:

After CFD++ ran the simulations, residual plots and the flow visualization plots were

observed and analyzed.

Streamlines of the flow were plotted in Tecplot.

Data was recorded for approximately last 50 iterations and average was calculated.

Entries for lift and drag coefficients were created in Microsoft Excel.

Plots of Cl vs. Re; Cl vs. L/D; Cd vs. L/D; Cd vs. Re, and Cl vs. Re as a function of L/D

were generated and compared.

For L/D=5 and L/D=3, Cd vs. Re was compared to the experimental value. Experimental

values were taken from “Fundamentals of Aerodynamics” by John D. Anderson Jr.

IV. Results and Discussion

1. Coefficient of lift (Cl) and Coefficient of drag (Cd) vs. Distance ratio (L/D):

When the cylinders were close (L/D=1.5),

flow past two side-by-side cylinders

interact with each other largely resulting

higher (+) ve lift on the upper cylinder

and higher (-)ve lift on the lower cylinder.

As the distance between the cylinders was

increased, the coefficient of lift (Cl) starts

to decrease because flow interactions

become less. As the flow interaction

decreases, the two cylinders starts to

behave as they were single cylinder.

On the other hand, coefficient of drag (Cd)

behaves differently. When the cylinder

were really close (L/D=1.5), the drag was

lower than when they were at L/D=3.

Also, when we increase the distance, as

we increase the L/D ratio, the drag starts

go down to the point as they were alone.

The reason behind that is when the

cylinders are really close because of the

flow interaction from both the cylinders

the force in the X-direction is higher, also

the wakes created past the cylinders

interact with each other causing lower

drag than at L/D=3.

Figure 4: Cl vs L/D

Figure 3: Cd vs L/D

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2. Coefficient of lift (Cl) and Coefficient of drag (Cd) vs. Distance ratio (L/D):

At low Reynolds number (Re) somewhat higher lift-coefficient (Cl) was observed than at higher.

However, at very high Re higher Cl is observed. As from figure 5, the result is clear enough.

Figure 5

At low Reynolds number, the flow is completely laminar. As the Re increases, turbulence starts

to affect and causes flow separation, which, in turn, decreases lift. However, at high Reynolds

number, the flow velocity becomes high enough to ignore the viscous effect and the pressure

gradient becomes high resulting high lift.

After examining the Cd vs. Reynolds

number plot, it can be seen that the

Reynolds number drops at Re=200 and

increases and stays close up to 100000, and

again drop after 1e+5 and starts increase. As

we expected, from 100<Re<200 flows

transition happens from laminar to

turbulent. For this reason drag drop around

at Re=200. Re=3 x 105 is called critical

Reynolds number where a significant drag

drop happens. At the flow separation point

of the cylinder transition to turbulent flow

takes place about 120° around the body.

This transition to turbulent flow and

corresponding thinner wake reduces

-5.00E-02

-4.00E-02

-3.00E-02

-2.00E-02

-1.00E-02

0.00E+00

1.00E-02

2.00E-02

3.00E-02

4.00E-02

5.00E-02

1.00E+00 1.00E+01 1.00E+02 1.00E+03 1.00E+04 1.00E+05 1.00E+06 1.00E+07

Reynolds Number

Cl vs Reynolds No.

Cl_Up_Cyl_L/D=1.5

Cl_Up_Cyl_L/D=3

Cl_Low_Cyl_L/D=3

Cl_Low_Cyl_L/D=1.5

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

1 10 100 1000 10000 100000 1000000

Cd

Reynolds Number

Cd vs. Reynolds No. for L/D=3 Cd Lower_Cyl

Cd Upper_Cyl

Figure 6

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pressure drag on the cylinder and is responsible for the precipitous drop in Cd at Re = 3 x 105.

The experimental result is compared with the computation value in figure 7.

Our CFD result predicted drag less than the experimental value. There might be several reasons:

1) Experimental data was for single cylinder, but the CFD results were done for side-by-side

cylinders. Though the cylinders were far, they were not free from flow interactions that

cause underestimation of coefficient of drag (Cd).

2) Boundary layer might need to be resolved more to achieve the solution accuracy.

3) Experimental results are for 3-D cylinder whereas the CFD result is for 2-D circle.

3. Vorticity study:

Vorticity is measure of the rationality of the flow. The more the flow is rotational, the higher the

vorticity. From figure 8, it can be easily understood that the vorticity doesn’t change much in

magnitude as the distance ratio (L/D) varies. However, vorticity clearly depends on Reynolds

number. At low Reynolds number, vortices form at the front face of the cylinders, and they die

away after passing the cylinder. However, at high Reynolds number, vorticity is really high at the

back face of the cylinders. Actually, at high Reynolds number flow separation occurs at 120° of

the body and the flow becomes highly turbulent. Because of turbulence in flow and the flow

separation at the body, vorticity is really higher than order of magnitude 4 at the flow separation

points. Vortices continue to move throughout the turbulent flow, but their strength decrease in

magnitude as they go far from the body. As shown in figure 8, when the cylinders are close (L/D

= 1.5) vortices are little affected by the vortices created by the other cylinder. When they are far

(L/D=3) vortices are unaffected.

0.01

0.1

1

10

100

0.1 1 10 100 1000 10000 100000 1000000 10000000

Cd

Reynolds No

Cd Vs. Reylonds No. Comparison

Cd vs Re : Experimental

Cd_Up_Cyl_L/D=5

Cd_Up_Cyl_L/D=3

Figure 7

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Re = 1e+6, L/D = 1.5

Re = 200, L/D = 3

Re = 1e+6, L/D = 3

Figure 8: Vorticity at different Re and L/D

4. Study of wake as L/D and Reynolds number varies:

The streamlines of the flow were plot using Tecplot, the wakes

of the flow were investigated qualitatively. When the L/D is

low at 1.5, the pattern of wakes were observed as expected.

The gap flow was biased to one side, resulting in the formation

of a narrower wake behind one cylinder and wider wake

behind the other. Steady and fluctuating fluid forces acting on

the cylinders were decomposed for the narrower wake and the

wider wake flow patterns. At higher distance, L/D=5, as

expected, two-street of vortex pattern are formed mostly

unaffected by each other (As shown in the picture next page).

At lower Reynolds number, large wake patterns are formed.

Conversely, at higher Reynolds number, small wake patterns

are formed. Wakes are the phenomena of laminar flow. At high

Reynolds number, flow becomes turbulent soon enough it

leaves the body. As a result, a very small wake patterns are

seen at high Reynolds number flow.

Re= 200 , L/D = 1.5

Re = 200, L/D = 1.5

Re = 100000, L/D = 1.5

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5. Failure of unsteady simulation:

At very low Reynolds number region, the flow is expected to be highly unsteady. In order to see

the unsteady effects and the Von Karman vortex street was run. However, the unsteady

simulation result wasn’t much different than the steady state simulation result. More experiment

and knowledge was needed to resolve the Strouhal number, vortex shedding frequency and the

time step size to get the visible unsteady solution.

6. Grid resolution study:

Grid resolution study was done at Re = 100000 and L/D=3 by increasing the number of points by

2X and 4X. The simulations were run and compared to the baseline data. The results are below:

Gridpoints No of cells Low_Cyl Up_Cyl Low_Cyl Up_Cyl

Cl Cl Cd Cd

Baseline (1X) 55,500 -3.50E-03 3.50E-03 5.30E-02 5.30E-02

2X 206,276 -4.69E-03 4.69E-03 5.55E-02 5.55E-02

4X 793,512 -4.59E-03 4.59E-03 5.51E-02 5.51E-02

Percent difference in Cl =

= 25.37%

Both the 2X and 4X yield the similar result. There was issue with wall spacing for the baseline

L/D=3. Most probably, grid solving wasn’t good enough to capture the boundary layer effect. If

we would have worked with 2X as baseline, the result might have been better. Because the

project timeline was reached, there wasn’t enough time to go back and redo the simulations.

Lack of grid refinement actually affected the results overall.

Re = 200, L/D = 5 Re = 100000, L/D = 5

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V. Conclusion

The goal of the project was to investigate the flow behavior around two side-by-side

cylinders by varying the distances between two cylinders and also varying the Reynolds number.

The goal has been achieved because a wide range of study of lift and drag coefficients, vorticity,

streamlines, wakes, flow pattern as a variation of the distance and Reynolds number. It was

found that how the coefficient of lift and drag are affected by the Reynolds number. Different

wake patterns at different distances of the cylinders were investigated. Grid generation and flow

simulation techniques were learned and practiced. Though the grid resolution wasn’t accurate,

the solution was converged so quickly (see figure). It can be said to conclude that the farther the

cylinders and the higher the Reynolds numbers, the better the results.

References

Anderson, Jr., John D. Fundamentals of Aerodynamics. Fifth Edition. New York: McGraw-Hill,

2011. Print.

Alam, Md. Mahbub, M. Moriya, and H.Sakamoto. “Aerodynamic characteristics of two side-by-

side circular cylinders and application of wavelet analysis on the switching phenomenon.”

Journal of Fluids and Structures 18.3-4 (2003): 325-346. ScienceDirect. Web. 20 May. 2015.

< http://www.sciencedirect.com/science/article/pii/S0889974603001075>

Chen, Bo, and Wan-Ping Li. “Near-wake flow characteristics of two side-by-side circular

cylinders close to a wall.” Acta Mechanica 222.3-4 (2011): 295-307. Springer International

Publishing AG. Web. 20 May. 2015. <http://link.springer.com/article/10.1007%2Fs00707-

011-0538-3>

Shao, J., and C. Zhang. “Numerical Studies of Flow Past Two Side-by-Side Circular Cylinders.”

New Trends in Fluid Mechanics Research (2009): 73. Springer International Publishing AG.

Web. 20 May. 2015. < http://link.springer.com/chapter/10.1007%2F978-3-540-75995-9_14>

Residual plot at Re = 100000 and L/D = 1.5