Flow Past Cylinder In 2D At Different Reynolds Numbers

Report on
“Flow past cylinder (in 2D) at different Reynolds numbers” 1

Contents
1

Abstract ............................................................................................................................................................ 3

2

Introduction ................................................................................................................................................... 3

3

Theory............................................................................................................................................................... 3
3.1

Unsteady state flow around a circular cylinder immersed in a uniform flow ............. 3

3.2

Lift Coefficient, Drag Coefficient and Vortex flow ................................................................... 4

4

Problem Description ................................................................................................................................... 6

5

Results .............................................................................................................................................................. 6

6

7

5.1

Graph of Drag Coefficient for Re 1, 25, 75 and 150 ................................................................ 6

5.2

Graph of Lift Coefficient for Re 1, 25, 75 and 150 ................................................................... 9

5.3

Pressure and Velocity Contours for Re 1, 25, 75 and 150 ................................................ 11

5.4

Velocity Vector components for Re 1, 25, 75 and 150 ....................................................... 15

5.5

Velocity Streamlines for Re 1, 25, 75 and 150....................................................................... 18

Summary and Discussion ....................................................................................................................... 20
6.1

Effect on geometry of the flow field change with Reynolds number............................ 20

6.2

Relation between Drag force and Reynolds number .......................................................... 21

References .................................................................................................................................................... 23

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1 Abstract
In this report we are analyzing the effect of unsteady fluid flow over a cylinder by using ANSYS Fluent Workbench Platform. We are provided with a 2 Dimensional
Dimens
model of cylinder of 1 meter in centimeter for the software,, for which we will define def the value of U; this will provide the velocity component to our fluid or indirectly indirectl we are providing the Reynolds Number
Number. Then output utput will be taken in the form of lift and drag forces on the same model for different values of Reynolds number, number these outputs uts are for pressure and velocity contour contour, vector component of velocity and streamline function.

2 Introduction
In this experiment, it involves the study of flow past a circular cylinder in a uniform stream.
This experiment is done with the application of computational fluid dynamics tool i.e.
Fluent.. The objective here is to give you experience of the broad range rang of flow measurement designing techniques that is available for the aeronautical or marine engineering.. The flow past a two two-dimensional cylinder inder is one of the most important studies in the field of aeronautics. This study is re relevant for many engineering g applications. The flow obtained and the value of drag force on a cylinder is functions of the Reynolds number, which is based on the measurements parameters like cylinder diameter D and the undisturbed free-stream stream velocity.

3 Theory
3.1 Unsteady state flow around a circular cylinder immersed in a uniform flow The Navier-Stokes
Stokes equation for the motion of the fluid, for the unsteady flow i.e. incompressible and viscous flow is given below:

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Where ρ is the density of the fluid fluid, u is the velocity vector, t is the time step, p is the pressure energy, and μ is the coefficient of the viscosity for the fluid.
This equation states that the inertia force is the summation of pressure force and viscous force. The analysis of fluid flow give givess us the relation between pressure energy and flow velocity by using equation 1. These results depend on the boundary condition, or the interface surface formed between solid object and the fluid. Practically unavoidable distributed roughness is present on the surface of the object, therefore particles of the fluid completely captures the surface of solid object because of viscosity of the fluid. Hence due to this property an important assumption can be made called as condition of zero fluid velocity (i.e., no slip) is achieved completely on the surface of solid object.
The other relative important ratio of the inertia forces to the viscous forces for the unsteady(or transient) flow conditions is given by taking L representing the characteristic scale of the flow and U represents the characteristic velocity of the flow; D/Dt ≈ L/U , Δ
≈1/L2 this can further written as as: In equation 2 Re is a dimensionless number called the Reynolds number. If the equation 1
i.e. Navier-Stokes is converted d to a dimensionless form, then this dimensionless equation depends only on the Reynolds number. Then
Then, if the value of Reynolds numbers is approximately equal, thus overall field with every individual flow having similar geometrical boundary shapess to each other, can also be concluded as similar values overall.
Also we can say that to increase velocity, higher density, lower viscosity, or a large body size of solid body responsible for increase in the Reynolds number, therefore it equally affects the flow field equally.. Accord
Accordingly, we can also say thatt the Reynolds number gives us a dimensionless number for flow velocity.

3.2 Lift Coefficient, Drag Coefficient and Vortex flow
Lift Coefficient: The lift coefficient is a number which is used by aerodynamicists to model all of the complex dependencies of shape, inclination, and some flow conditions on lift.
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The lifting force acting on a body in fluid flow can be expressed as:
FL = 1/2 CL ρ v2 A
Where FL is Lifting force, CL is lift coefficient, ρ is density of the fluid, v is flow velocity and A is body area.
Drag Coefficient: Any solid object moving through a fluid media experiences a drag; the net force in the direction of flow due to pressure and shear stress forces on the surface of the object. Drag force can be expressed as:
FD = 1/2 CD ρ v2 A
Where FD is Drag force, CD is drag coefficient, ρ is density of the fluid, v is flow velocity and A is characteristic frontal area of the body. The drag coefficient depends on several parameters like shape of the body, Reynolds Number for the flow, Froude number, Mach number and Roughness of the Surface.
Vortex Flow: In fluid flow, a vortex is a region, in a fluid medium, in which the flow is mostly rotating on an axis line, the vortical flow occurs either on a straight-axis or a curved-axis. In this type of flow streamlines are concentric circles and the component of tangential velocity is directly proportional to the radius of curvature of the circular flow.
Vortex in a fluid flow usually forms because of obstruction occur in the boundary layer flow of fluid.

Figure 1: Generation of Vortex Flow

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4 Problem Description
The analysis model in this study is shown in Figure 2. The fluid was assumed to be water with the density was ρ = 1000 kg/m3 and the coefficient of viscosity was μ = 0.001 kg/m3.
The diameter off the cylinder is D = 1 centimeter. Naturally,, an analysis of the drag and lift coefficient should begin with two two-dimensional dimensional behaviors of the flow around the circular cylinder. Figure 2: Given Case of cylinder for 2D analysis.
For the given case of 2D cylinder, the analysis is performed with pressure pressure-velocity velocity coupling scheme (PISO) for good quality of result. For time step 0.2 and flow time 600 and taking no. of iteration as 30. The simulation is performed for different values of Reynolds number i.e.
1, 25, 75 and 150; to set the inlet boundary condition we will take the flow velocity as
0.0001,
01, 0.0025, 0.0075 and 0.0150 for respective Reynolds number.

5 Results
For the different values of Reynolds number we give input value of velocity component in
Fluent. Therefore four times simulation is performed for the respective Reynolds number.
The obtained ined results are in the form of plot of Lift and Drag coefficient to the flow time.
Also we obtain the graphics of pressure contours, velocity contours, velocity vector and velocity streamlines.

5.1 Graph of Drag Coefficient for Re 1, 25, 75 and 150
Graph 1, 2,, 3 and 4 are showing us change in the value of drag coefficient with increase in the flow time.

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Graph 1: Drag Coefficient graph for Re=1

Graph 2: Drag Coefficient graph for Re 25
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Graph 3: Drag Coefficient graph for Re=75

Graph 4: Drag Coefficient graph for Re=150
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5.2 Graph of Lift Coefficient for Re 1, 25, 75 and 150
Graph 5, 6, 7 and 8 are showing us change in the value of lift coefficient with increase in the flow time.

Graph 5: Lift Coefficient graph for Re=1

Graph 6: Lift Coefficient graph for Re=25
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Graph 7: Lift Coefficient graph for Re=75

Graph 8: Lift Coefficient graph for Re=150
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5.3 Pressure and Velocity Contours for Re 1, 25, 75 and 150
Figure 3, 4, 5 and 6 are showing us value of pressure region or pressure contour for different values of Reynolds number and figure 7, 8, 9 and 10 are showing us value of velocity region or velocity contour for different values of Reynolds number. From the
Bernoulli’s principle, we can obtain a relationship between flow velocity and pressure, which states that with increasing flow velocity results in decrease in pressure. The resultant static pressure distributions or pressure contours can be explained through this principle as the flow moves down-stream and therefore the respective velocities were gradually reduced due to the effects of viscosity and the value of pressure gradient in that region, thus the flow can no longer travel along the surface of the solid object i.e. cylinder in this case. This phenomenon is can be defined as separation point; at this point the flow gets separated from the surface of cylinder.
In the figure 3, 4, 5, and 6 we can see the pressure contours formed with the fluid flow here we can see that the pressure value is maximum in the front of the cylinder and minimum at the rear. Also for lower Reynolds number the pressure value is equal at top and bottom with symmetry.

Figure 3: Pressure Contour for Re=1
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Figure 4: Pressure Contour for Re=25

Figure 5: Pressure Contour for Re=75
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Figure 6: Pressure Contour for Re=150
In figure 7, 8, 9 and 10 we can see that the value of velocity magnitude is lower where the pressure is high, this proves the Bernoulli’s principle. Especially the value is minimum in front because of stagnation condition and also in the wake region of the cylinder.

Figure 7: Velocity Contour for Re=1
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Figure 8: Velocity Contour for Re=25

Figure 9: Velocity Contour for Re=75
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Figure 10: Velocity Contour for Re=150

5.4 Velocity Vector components for Re 1, 25, 75 and 150
Figure 11, 12, 13 and 14 are showing us value of velocity vector region or velocity for different values of Reynolds number. The behavior of the flow separation is traced; the distributions of the velocity vectors around the cylinder are plotted. As the stagnation point is located at the front of the cylinder, the velocity in this region is zero. The velocity of fluid in the cylinder’s front flow accelerates, whereas the velocity of the fluid flow in the rear decreases. P.T.O
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Figure 11: Velocity Vector for Re=1

Figure 12: Velocity Vector for Re=25
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Figure 13: Velocity Vector for Re=75

Figure 14: Velocity Vector for Re=150
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5.5 Velocity Streamlines for Re 1, 25, 75 and 150
Figure 15, 16, 17 and 18 are showing us value of velocity streamlines for different values of
Reynolds number. These figures correspond to flows with different Reynolds number, and the streamlines are obtained symmetrically, from front to rear. When the Reynolds number exceeded 1 to 25, the symmetry was lost in the front and rear flows. However, no separation of fluid flow occurred. Figure 17 and 18 correspond to a Reynolds number 75 and 150, here a pair of upper and lower vortices was generated within the wake of the cylinder. With the increase in Reynolds number, the vortex region expands and length gets increased. Figure 15: Velocity Streamline for Re=1

P.T.O
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Figure 16: Velocity Streamline for Re=25

Figure 17: Velocity Streamline for Re=75
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Figure 18: Velocity Streamline for Re=150

6 Summary and Discussion
6.1 Effect on geometry of the flow field change with Reynolds number
Figure 19, 20, 21 and 22 shows a flow for different Reynolds number. The shape of velocity streamline is symmetrical around the cylinder’s upper to lower side, but also equal around its front to rear for the Reynolds number 1 as we can see in figure 19. With the increase in
Reynolds number, the symmetry from front to rear disappears, and the interval of the velocity streamlines of the cylinder’s rear flow widens. Further increment in the Reynolds number to 25, a closed region for the velocity streamline generates within the cylinder’s rear flow as we can see in figure 20, the fluid present in the upper half of this region rotates clockwise and the fluid present in the lower half rotates counter clockwise. This result in vortex formation or this phenomenon is known as vortices. With the increase in Reynolds number, the length of the vortex increases. When the Reynolds number reaches 75, the rear flow becomes unstable as shown in Figure 21, and the vortex starts oscillating in an up20

down direction. When Reynolds number reaches 150
150, the vortices starts to mix together; and the fluid flow behind the cylinder or wake region starts behaving very irregularly in time and space scale. A free stream with a distance from the wake region maintains steady state during the flow, and these se streamlines are held in smooth and regular shapes. shapes This phenomenon is known as laminar flow.

Figure 19: Effect on Flow Field Geometry for Re=1

Figure 20: Effect on Flow Fi
Field Geometry for Re=25

Figure 21: Effect on Flow Field Geometry for Re=
Re=75

Figure 22:: Effect on Flow Field Geometry for Re=150

6.2 Relation between Drag force and Reynolds number
As a fluid moves over a fluid, the drag force will change under different flow conditions. For unsteady fluids flow it is important to consider the Reynolds number of the flow field.
Considering cylinder, as with above results; we can see the variation in the drag coefficient with the change in Reynolds number in the table below. Drag force is the summation of
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pressure force and viscous force acting on the cylinder due to fluid flow over cylinder.
Hence from the simulation values for the total drag force can be obtained. This is given in the Table number 1.
Reynolds
Number

Drag
Force

1

8.33E-07

25

6.06E-05

75

0.000354664

150

0.001285288

Table 1: Value of Drag force for Different Reynolds number
By using the values from table 1, we will plot a graph of Reynolds number against Drag force. This graph is given in Graph no. 9.

Reynolds Number Vs Drag Force
1.40E-03
1.20E-03

Drag Force

1.00E-03
8.00E-04
6.00E-04
4.00E-04
2.00E-04
0.00E+00
0

50

100

150

200

Reynolds Nimber

Graph 9: Reynolds number Vs Drag Force
These sorts of forces are derived experimentally and tables for the determination of value for different flow conditions can be observed in calculation in fluid mechanics. Hence from the graph number 9, we can see that the value of Drag increases with the increase in the value of Reynolds number.
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7 References
[1] Catalano, P., Wang, M., Iaccarino, G., & Moin, P. (2003). Numerical simulation of the flow around a circular cylinder at high Reynolds numbers. International Journal of Heat and
Fluid Flow, 24(4), 463-469.
[2] Fornberg, B. (1985). Steady viscous flow past a circular cylinder up to Reynolds number
600. Journal of Computational Physics, 61(2), 297-320.
[3] Mandiyano, F., & Fabi, R. P. (2005). On the viscous steady flow around a circular cylinder. Revista mexicana de física, 51(1), 87-99.
[4] Sato, M., & Kobayashi, T. (2012). A fundamental study of the flow past a circular cylinder using Abaqus/CFD. In 2012 SIMULIA Community Conference. 1-15.

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References: [1] Catalano, P., Wang, M., Iaccarino, G., & Moin, P. (2003). Numerical simulation of the flow around a circular cylinder at high Reynolds numbers. International Journal of Heat and Fluid Flow, 24(4), 463-469. [2] Fornberg, B. (1985). Steady viscous flow past a circular cylinder up to Reynolds number 600. Journal of Computational Physics, 61(2), 297-320. [3] Mandiyano, F., & Fabi, R. P. (2005). On the viscous steady flow around a circular cylinder. Revista mexicana de física, 51(1), 87-99. [4] Sato, M., & Kobayashi, T. (2012). A fundamental study of the flow past a circular cylinder using Abaqus/CFD. In 2012 SIMULIA Community Conference. 1-15. 23