Topic

Simulate the flow over a cylinder and explain the phenomenon of Karman vortex street.

A project

Submitted in partial fulfillment of the requirement for the award of the certificate

Of

Master Program

(CFD Masters)

By

Nitesh Negi

(Enrolment ID:3081)

Under the supervision of

CFD Team Leader Director of product

Pritam Goel Sarangarajan Iyengar

5th floor, Bristol IT Park
Main Rd, South Phase, Sathya Nagar, Gandhi Nagar, Chennai, Tamil Nadu 600032, +918939850851

CANDIDATE\'S UNDERTAKING

I, Nitesh Negi (Enrolment Id:3081) state that the contents and findings of the project entitled “Simulate the flow over a cylinder and explain the phenomenon of Karman vortex street using Ansys Fluent”, are original. To the best of my knowledge, the current project does not infringe upon anyone’s copyright nor violate any proprietary rights and that any ideas, techniques, quotations or any other material from the work of other people included in my project, published or otherwise, are fully acknowledged in accordance with the standard referencing practices. Even though later on in case of any complaint pertaining of plagiarism, I am solely responsible for the same and understand that as per norms.

ACKNOWLEDGEMENT

Primarily, I acknowledge this moment of time which has gone just forever but made up my mind to write the word for those who have been with me with their over-whelming gestures throughout this assignment. With deep gratitude, I express my earnest thanks to my respected guides Mr. Pritam Goel, CFD Team Leader, and Mr. Sarangarajan Iyengar, Director of product skilllync for his constant involvement, energetic efforts, and proficient guidance. Without his wise counsel and encouragement, it would have been impossible to complete the project work in this manner.

I would also thank all the members of Ansys Fluent Skill-Lync what are app group members for support and express my gratitude.

ABSTRACT

Flow over a cylinder is a simulation to study the Karman vortex street flow which is generated. A Von Karman vortex street is a repeating pattern of swirling vortices arising in the wake of flows around cylindrical objects. In fluid dynamics, vortex shedding is an oscillating flow that takes place when a fluid such as air or water flows past a bluff body at certain velocities, depending on the size and shape. In this flow, vortices are created at the back of the body and detach randomly from either side of the body. The fluid flow past the object creates alternating low-pressure vortices or eddies on the downstream side of the object. The object will tend to move toward the low-pressure zone and flow separation occurs results in vortex generally found above Reynolds no. 40.

The computational fluid dynamics (CFD) package FLUENT as a fluid flow analysis tool to solve the governing equations, prominently equations of continuity, motion, and energy. Numerical results can be compared with experimental results and which was done by research scholar since due to model setup and lab constraints we will only compare the simulation results of different cases as per our objective. The mesh size is selected to do that the numerical solution is taken considering the computation time and simulation processing time. The flow has Reynolds no. above 40 shows Karman vortex street as per simulation results.

Keywords: Karman vortex street, numerical simulation, Fluent, CFD, laminar model, Reynolds No.

CONTENTS

Candidate’s undertaking i

Acknowledgment ii

Abstract iii

Contents iv

List of figures v

List of table’s vi

Nomenclature vii

Contents

CHAPTER 1: INTRODUCTION

-Introduction

-History

-Application

- What is a cylindrical body/object?

CHAPTER 2: LITERATURE REVIEW

- Introduction

- Review of Literatures

- Objectives

CHAPTER 3: METHODOLOGY

-Flow chart for CFD simulation

-Procedure/Steps for the CFD simulation

CHAPTER 4: RESULT AND DISCUSSIONS

CHAPTER 5: CONCLUSIONS AND FUTURE SCOPE

REFERENCES

LIST OF FIGURES

Figure (1): Figure(56) contained in this report

LIST OF TABLES

Table (1): variation of flow at different Reynolds no.

Table (2): variation of flow at different Reynolds no. with coff. of drag and coff. of lift.

NOMENCLATURE

Symbols Significance

Re no. Reynolds No

d diameter of the cylinder

u free stream velocity

Cd. coff. of drag and

Cl. coff. of lift.

CHAPTER 1

INTRODUCTION

Figure(1): shows the Karman vortex effect at Re. No. 100 at transient state

A Von Karman vortex street is repeating patterns of swirling vertices that are arising in the wake of flows around the blunt objects. The phenomena of vortex shedding are shown on flow over a two-dimensional cylinder in the above image. The fluid flow past the object creates alternating low-pressure vortices on the opposite side of the object and the object low-pressure zone is created.

Figure(2): Shows Streamline flow at the Karman vortex effect at Re. No. 100 flow over a 2D cylindrical surface.

Vortex shedding is an oscillating flow that takes place when a fluid flows past a body at certain velocities, depending on the shape and size of the body and other factors. In this flow, the vortices are created at the back of the body and detach randomly from either side of the body generating a Von Karman vortex street in a flow.
The bluff body is not fixed and the frequency of vortex shedding matches the natural resonance frequency of the object, then the object can begin to resonate and start vibrating. These vibrations can cause more damage to the object.

Figure(3): Shows Streamline flow at the Karman vortex effect flow over a 2D cylindrical surface and the velocity variation.[1]

Strouhal No:[2]

The Strouhal number is the ratio of inertial force due to the local acceleration of the flow to the inertial forces due to the convective acceleration. Inflows characterized by a periodic motion, the Strouhal number is associated with the oscillations of the flow due to the inertial forces relative to the changes in velocity due to the convective acceleration of the flow field. Thus, periodic flows are given by the following expression.

St= F *L/U
F= the frequency at vortex shedding (Hz )
L = characteristic length of the body(here Dia. of the cylinder)
U = Flow Velocity (m/s).

Consider a stream of fluid flow past a circular cylinder. As the fluid passes from the two extreme ends of the cylinder, it finds itself unable to negotiate the rear half of the cylinder where there is an uphill pressure gradient. Hence the fluid separates from the leading surface and the flow is separate individually with highly organized and typically consists of two sequences of vortices, one from each point of the body, with circulations of opposite signs. Depending on the shape and motion of the body more random patterns of vortices may arise. In the wake of the cylinder ie low-pressure area, the flow pattern consists of an alternating system of vortices or regions of rotation, as shown in Figure is \'3\'. This repeating pattern of swirling vortices at the wake of the cylinder is known as Karman vortex street.
It is important to note that even if the incoming flow is steady (i.e, does not change with time), the unsteadiness is intrinsically generated and the Karman street is formed downstream of the body. Thus causes turbulence due to variation in pressure an velocity.
A vortex street can be observed only. Beyond Re ≈40 the flow becomes unsteady and the Kármán vortex street occurs due to low-pressure gradient and low high velocity and fluid properties.

Figure(4): Shows flow vector during the Karman vortex effect at Re. No. 100; flow over a 2D cylindrical surface.

To check the vortex nature it is important to know the Reynolds no. The Reynolds number is a measure of the ratio of inertial to viscous forces in the flow of a fluid and may be defined as:

Reynolds No.[3]

Re = ρVD/ μ
where:
ρ = Density,
D = the diameter of the cylinder around which the fluid is flowing,
V = the steady velocity of the flow upstream of the cylinder and
μ = the kinematic viscosity of the fluid.

Figure(5): Flow variation at different conditions; flow over a 2D cylindrical surface.[4]

Drag And Lift:

Figure(6): Define the drag and lift direction on an aerofoil shape.[5]

It is a common experience that a body meets some resistance when it is forced to move through a fluid. You experience the same feeling when you extend your arm out of the window of a moving car. A fluid may exert forces and moments on a body in and about various directions. The force a flowing fluid exerts on a body in the flow direction is called drag.
A stationary fluid exerts only normal pressure forces on the surface of a body immersed in it. A moving fluid, however, also exerts tangential shear forces on the surface because of the
no-slip condition caused by viscous effects. Both of these forces, in general, have components in the direction of flow, and thus the drag force is due to the combined effects
of pressure and wall shear forces in the flow direction. The components of the pressure and wall shear forces in the direction normal to the flow tend to move the body in that direction, and their sum is called lift.

The drag and lift forces depend on the density 𝜌 of the fluid, the upstream velocity V, and the size, shape, and orientation of the body, among other things, and it is not practical to list these forces for a variety of situations. Instead, it is more convenient to work with appropriate dimensionless numbers that represent the drag and lift characteristics of the body. These numbers are the drag coefficient CD, and the lift coefficient CL, and they are defined as a formula

The drag and lift forces themselves are not as interesting as the dimensionless drag and lift
coefficients. These depend only on the Reynolds number and an object’s shape, not its
size. The coefficients are defined as
using the following parameters:
• FD and FL are the drag and lift forces
•

is the fluid’s density
• Umean is the mean velocity
• A is the projected area (product of thickness and diameter of a cylinder)[6]

-History[7]

Zdravkovich [1], in an excellent monograph, has compiled almost all the experimental, analytical and numerical simulation data on flow past cylinders, available since 1938 and systematically classified this challenging flow phenomenon into five different flow regimes based on the Reynolds number. In the present study, the computation is restricted only to the first few regimes designated by Zdravkovich as (1) creeping laminar state (L1) of flow (0<Re<4)\">(0<Re<4), (2) laminar flow (L2) with steady separation (4<Re<48\">(4<Re<48) forming a symmetric contra-rotating pair of vortices in the near wake, (3) laminar flow (L3) with periodic vortex shedding (48<Re<180)\">(48<Re<180) and finally (4) part of the transition-in-wake (TrW) regime (180<Re<400)\">(180<Re<400) when the three-dimensional instabilities lead to the formation of streamwise vortex structure. Computations are carried out in the present work in the range of 0.1<Re<400\">0.1<Re<400 for comparison with available measurement data or other computation results for both steady and unsteady flow situations. All the computations use an implicit pressure-based finite volume Navier–Stokes algorithm (RANS3D) for time-accurate prediction of the flow. This flow solution algorithm, originally proposed by the last author [2], has been further developed [3], [4], [5] at the CTFD Division, NAL, Bangalore during the last 10 years. The whole flow domain covering the L1–TrW regimes has first been computed under the assumption of two-dimensional flow. Later, in order to understand the effect of the three-dimensional disturbances on the complex wake vortex dynamics, three-dimensional analysis have been carried out at five different Reynolds number covering part of the L3 and TrW regimes, already reported in unclassified literature by a few researchers [6], [7], [8], [9].

Table(1)TYPES OF FLOW OVER A CYLINDER AT DIFFERENT. REYNOLDS NO.[8]

-Application

Strouhal made the first measurements of the frequencies associated with the shedding of vortices by defining a Strouhals number (S)
S = fD/L
where, diameter (D), speed (U), frequency (f)
Note: As Strouhal Number deals with frequency, it can be only obtained for transient type problems. Both Renolds number and Strouhals number are nondimensional numbers. On the practical side, the Karman street can lead to unwanted noise or even cause the failure of structures when the vortex shedding frequency coincides with the natural frequency of the structure. This type of vortex-induced oscillations can occur in a variety of situations such as chimneys, bridges, heat exchanger tubes, overhead power cables, and marine structures. Therefore understanding the physics of the Karman vortex street is crucial to avoid disasters in these situations.

It is important to reduce vortex-induced vibrations, drag, and lift force acting on them in order to prevent structural damage. Therefore, it is necessary to adapt control techniques in flow past circular cylinder to reduce structural damage and improve the service life of cylinder used for the particular application

- What is a cylindrical body/object?

A cylinder (or disk) of diameter \'D\' is placed in a two-dimensional, incompressible, inviscid flow. The goal is to find the steady velocity and pressure p in a plane, subject to the condition that far from the cylinder.

.

CHAPTER 2:

LITERATURE REVIEW

- INTRODUCTION

To begin the proposed work it is required to make a review of research papers in order to discover what work has been done already about the related topic and which procedure or methodology has been adopted to perform the simulation/experiments and conclude the results.

A review of the various published literature on any specific topic is the first important step to be taken to get,

• Knowledge about the state of art.
• Familiarity with the established methods and procedures for conducting work.
• To stop duplication of work.

- LITERATURE REVIEW

There are several numbers of studies conducted by researchers regarding the Steady-state simulation on a TEE Geometry of Mixing fluid (air) from the turbulence model using Ansys Fluent, some of them are discussed below:-

1. B.N.Rajani^aA.Kandasamy^bSekharMajumdar. Numerical simulation of laminar flow past a circular cylinder[9]
2. AuthorP.W.Bearman; Circular cylinder wakes and vortex-induced vibrations[10]
   
3. R.M.Stringer^aJ.Zang^aA.J.Hillisb Unsteady RANS computations of flow around a circular cylinder for a wide range of Reynolds numbers[11]

-OBJECTIVE

Simulate the flow over a cylinder and explain the phenomenon of Karman vortex street.

PART-I

• Simulate the flow with the steady and unsteady case and calculate the Strouhal Number for Re= 100.

PART-II

• Calculate the coefficient of drag and lift over a cylinder by setting the Reynolds number to 10, 100, 1000, 10000 & 100000. (Run with steady solver)
• Discuss the effect of Reynolds number on the coefficient of drag.[Results should be validated with any standard literature & error must be within 5%.]

Note:- Vary the velocity of the flow to change the Reynold\'s number

Expected results:-

• In both approaches, show that the flow has converged. That is, what quantities or plots can be used to determine that the flow has converged?
• Plots of the coefficient of drag and lift.
• Plots to show vortex shedding behind the cylinder.
• Mention the preferred material at the end of the challenge page.

CHAPTER 3

-METHODOLOGY

The complete methodology that has been adopted to conduct the present project work is shown in the form of the flow chart in figure 3.1

Figure (6): Flow Chart for CFD simulation

-Procedure for CFD simulation of flow over a cylinder

Selection of material

The material property is not necessary in this simulation since we are not considering the heat transfer through the wall i.e. is approximate an adiabatic process, no heat transfer through the wall.

Further, we will know that in this type of simulation we consider the surface generation and that is extracted using the Space claim tool.

Cad Model Preparation

-Procedure for CFD simulation of Mixing Tee

Cad Model Preparation

Step1: Open the workbench & double click open Flow Fluent

Step2: Double click on geometry to open space claim> open the file from saved location/prepare.

Geometry :
To create the geometry we use Ansys Spaceclaim. Since this is a 2D flow simulation we consider a slice of the cylinder which in 2D plane represents a circle. The diameter of the
circle is 2m. To create a flow around the cylinder we introduce a computational domain. The inlet is at a distance of 10 times the diameter from the center of the circle. The outlet is at a distance of 20 times the diameter from the center of the circle. The walls will be having a symmetry boundary condition and are at a distance of 5 times the diameter from the center of the circle on either end. Finally, we create a surface using the pull option.

. Figure(7): Dimension of the profile.

Step4: Go to prepare tab and select the surface generation while eliminating the surface generation

Step5: Close space claim workbench and save files if required.

Preprocessing

Step6: Double click on Mesh from workbench>Generate Mesh by right-clicking the mesh icon and click generate mesh option and mesh will be generated; here you can change mesh size from element size option in the mesh tree.

Step7: Give a name to required parts by face section/edge selection>click update by right-clicking on the mesh>check the mesh metric matrix by select element quality should be not less than 5%.

Figure(8): Shows the quality of mesh and mesh generation on the profile.

Step8: Edit parameters

Meshing Element Type: TriangularElement size: 100 mm &50mm (for Re no. 10,000 & 100,000)
Inflation: First Layer Thickness
First layer height: 5 e-003m
Number of layers: 6
Growth rate:1.2
Sizing: Edge Sizing
Number of divisions:72
Number of Nodes:
Number of Elements:
Orthogonal Quality of Mesh: 0.968

Figure(9): Shows No. of division done on the circular geometry.

Inflation Layer and the number of divisions are used to capture the circular geometry so that nodes can calculate values and get better results.

Setup/Processing

Step9: Double click on setup to open the workbench

Step10: select for Time -steady-state solution, Solver Type -pressure-based solvers, Velocity Formulation - Absolute and Physics-energy from the model.>select the Viscous Model laminar based upon the condition.

Step11: setup the boundary condition as per the given data.

Fluent Setup:
Material Specification: Fluid - Air
Density(kg/m3):1
Viscosity(kg/m-s):0.02
Reynolds Number,Re = Form 1 to 100000

Step12: The velocity at inlet> Temperature of air>

Physical Model: Laminar
Boundary Conditions: Inlet - Velocity Inlet (1 to 1000 m/s)
Outlet - Pressure Outlet(Gauge Pressure = 0 Pa)
wall - symmetry
wall motion: stationary wall
shear condition: No-slip

Step13: In solution select the report for standard deviation temperature & average temperature.>initialize the solution>run for the calculation by entering the no.of iteration

Post-processing/Results

Step14: Open results workbench by double-clicking on the result option>Open the geometry by unchecking the named parameters>create XY plane to plot the contour of velocity and pressure.

Step15: Open the workbench & double click open Flow Fluent.

Step16: Double clicks on geometry to open space claim> open the file from saved location.

Step17: Go to prepare tab and select the volume generation tool and select the edges for complete volume generation from inlet to outlet.

Step18: Close space claim workbench and save files if required.

CHAPTER 4:

RESULT AND DISCUSSIONS

The results of various Simulation tests conducted for flow over a cylinder as well as are calculated and explained with the help of different graphs and charts which are plotted by using Ansys Fluent & MS-Excel software. Comparisons of results are also done Case I and Case II. The compared results are summarized as the following:-

• PART-I

  • Simulate the flow with the steady and unsteady case and calculate the Strouhal Number for Re= 100.

STEADY AND UNSTEADY FLOW OVER A CYLINDER FOR RE=100 GEOMETRY

Simulation of flow over a cylinder with the steady and unsteady case.

Re= (ρ*v*D) / μ.

*Inlet Velocity: 1 m/s rest parameters are fixed

Re = ( 1 * 1 * 2 ) / 0.02 = 100.

1. Residual Plot:

Figure(10): Shows Residual plot; flow over a 2D cylindrical surface for Reynolds No. 100 at steady-state.

After about 1250 iterations, the residuals started to give almost constant values.

2. Vertex Average of Velocity-Magnitude at Monitor Point:

Figure(11): Shows Velocity-Magnitude at Monitor Point; flow over a 2D cylindrical surface for Reynolds No. 100 at steady-state.

3. Coefficient of Drag plot:

Figure(12): Shows Coefficient of Drag plot; flow over a 2D cylindrical surface for Reynolds No. 100 at steady-state.

Coefficient of Drag=1.3759

4. Coefficient of Lift plot:

Figure(13): Shows Coefficient of Lift plot; flow over a 2D cylindrical surface for Reynolds No. 100 at steady-state.

Coefficient of lift=0.03636

5. Velocity Contour Plot:

Figure(14): Shows Velocity Contour Plot & vortex generated; flow over a 2D cylindrical surface for Reynolds No. 100 at steady-state.

6. Pressure Contour Plot:

Figure(15): Shows Pressure Contour Plot; flow over a 2D cylindrical surface for Reynolds No. 100 at steady-state.

Figure(16): Shows Velocity-pressure contour animation; flow over a 2D cylindrical surface for Reynolds No. 100 at steady-state.

UNSTEADY FLOW OVER A CYLINDER FOR RE=100 GEOMETRY

PART-1:
Simulation of flow over a cylinder with the steady and unsteady case.

Re= (ρ*v*D) / μ.

*Inlet Velocity: 1 m/s rest parameters are fixed

Re = ( 1 * 1 * 2 ) / 0.02 = 100.
In this case,we are going to simulate the flow over the cylinder using unsteady solver for a Reynold number of Re=100 and the Strouhal Number for Re=100 is calculated.

Unsteady case condition:
Time step size: 0.1
Time step: 1200
Max number of iteration per timestep:10

1 Residual Plot:

Figure(17): Shows Residual plot; flow over a 2D cylindrical surface for Reynolds No. 100 at unsteady-state.

After about 12000 iterations, the residuals started to give almost constant values.

2. Vertex Average of Velocity-Magnitude at Monitor Point:

Figure(18): Shows Velocity-Magnitude at Monitor Point; flow over a 2D cylindrical surface for Reynolds No. 100 at unsteady-state.

Vortex Shedding frequency:f=Number of cycles/Time for cycles(s)
= 3.5/20
= 0.175 Hz
We know that, Strouhal Number St = f*L/U
where, f=vortex shedding frequency
L= characteristic length over which the flow takes place
U=free stream velocity of flow
Therefore, St = 0.175*2/1
= 0.35

3. Coefficient of Drag plot:

Figure(19): Shows Coefficient of Drag plot; flow over a 2D cylindrical surface for Reynolds No. 100 at unsteady-state.

Coefficient of Drag=1.3890

4. Coefficient of Lift plot:

Figure(20): Shows Coefficient of lift plot; flow over a 2D cylindrical surface for Reynolds No. 100 at unsteady-state.

Coefficient of lift=0.014

5. Velocity Contour Plot:

Figure(21): Shows Velocity Contour Plot & vortex generated; flow over a 2D cylindrical surface for Reynolds No. 100 at unsteady-state.

6. Pressure Contour Plot:

Figure(22): Shows Pressure Contour Plot; flow over a 2D cylindrical surface for Reynolds No. 100 at unsteady-state.

Figure(23): Shows Velocity-pressure contour animation; flow over a 2D cylindrical surface for Reynolds No. 100 at unsteady-state.

From the residuals plot, as shown above, we could observe that the solution converged in about 350 iterations in the steady case and for almost about 12000 iterations in the unsteady case for a timestep size of 0.1, ie the residual shows a repeating pattern after some iterations. Hence we will be able to assume that the flow has to converge.
The vertex average of the velocity magnitude that was plotted shows an oscillating behavior after certain iterations, thus by seeing the variations in the
the velocity we can confirm that the flow has converged.

During the analysis of flow in steady simulation, we are not able to accurately predict the result during the intermediate phase of the flow whereas the unsteady case or the time-dependent flow helps us to obtain accurate results at any time of the flow. Thus the result obtained during the unsteady simulation
can be judged as accurate about the strouhal number which is .35.

PART II:

The Reynolds number is varied by changing the velocity of the inlet and all other parameters mentioned above like meshing remains unchanged.
Case 1.Re = 10.Since ,

Re = ρuL/μ

Re = 100 ( ρ= 1 kg/m , u= 1 m/s, L= 2 m)
Therefore, u = 0.1m/s.

1. Residual Plot:

Figure(24): Shows Residual plot; flow over a 2D cylindrical surface for Reynolds No. 10 at steady-state.

After about 1400 iterations, the residuals started to give almost constant values.

2. Vertex Average of Velocity-Magnitude at Monitor Point:

Figure(25): Shows Velocity-Magnitude at Monitor Point; flow over a 2D cylindrical surface for Reynolds No. 10 at steady-state.

3. Coefficient of Drag plot:

Figure(26): Shows Coefficient of Drag plot; flow over a 2D cylindrical surface for Reynolds No. 10 at unsteady-state.

Coefficient of Drag=3.3643

4. Coefficient of Lift plot:

Figure(27): Shows Coefficient of lift plot; flow over a 2D cylindrical surface for Reynolds No. 10 at steady-state.

Coefficient of lift=0.002888

5. Velocity Contour Plot:

Figure(28): Shows Velocity Contour Plot & vortex generated; flow over a 2D cylindrical surface for Reynolds No. 10 at steady-state.

6. Pressure Contour Plot:

Figure(29): Shows Pressure Contour Plot; flow over a 2D cylindrical surface for Reynolds No. 10 at steady-state.

Case: 2: Re = 100
Re = 100 ( ρ= 1 kg/m , u= 1 m/s, L= 2 m)
So, = (1 * 1 *2) / 0.02
= 100
All plots, regarding this case, for steady flow conditions, are ploted above.

Case 3: Re = 1000.
Here,u ie ,inlet velocity = 10m/s.

So, = (1 * 1 *2) / 0.02
= 1000

1. Residual Plot:

Figure(30): Shows Residual plot; flow over a 2D cylindrical surface for Reynolds No. 1000 at steady-state.

After about 400 iterations, the residuals started to give almost constant values.

2. Vertex Average of Velocity-Magnitude at Monitor Point:

Figure(31): Shows Velocity-Magnitude at Monitor Point; flow over a 2D cylindrical surface for Reynolds No. 1000 at steady-state.

3. Coefficient of Drag plot:

Figure(32): Shows Coefficient of Drag plot; flow over a 2D cylindrical surface for Reynolds No. 1000 at steady-state.

Coefficient of Drag=1.226

4. Coefficient of Lift plot:

Figure(33): Shows Coefficient of lift plot; flow over a 2D cylindrical surface for Reynolds No. 1000 at steady-state.

Coefficient of lift=0.3548

5. Velocity Contour Plot:

Figure(33): Shows Velocity Contour Plot; flow over a 2D cylindrical surface for Reynolds No. 1000 at steady-state.

6. Pressure Contour Plot:

Figure(34): Shows Pressure Contour Plot; flow over a 2D cylindrical surface for Reynolds No. 1000 at steady-state.

Figure(35): Shows Velocity-pressure contour animation; flow over a 2D cylindrical surface for Reynolds No. 1000 at steady-state.

Case 4: Re=10,000
The inlet velocity, u = 100m/s.
So, = (1 * 100 *2) / 0.02
= 10000

1. Residual Plot:

Figure(36): Shows Residual plot; flow over a 2D cylindrical surface for Reynolds No. 10000 at steady-state.

After about 750 iterations, the residuals started to give almost constant values.

2. Vertex Average of Velocity-Magnitude at Monitor Point:

Figure(37): Shows Velocity-Magnitude at Monitor Point; flow over a 2D cylindrical surface for Reynolds No. 10000 at steady-state.

3. Coefficient of Drag plot:

Figure(38): Shows Coefficient of Drag plot; flow over a 2D cylindrical surface for Reynolds No. 10000 at steady-state.

Coefficient of Drag=1.001

4. Coefficient of Lift plot:

Figure(39): Shows Coefficient of lift plot; flow over a 2D cylindrical surface for Reynolds No. 10000 at steady-state.

Coefficient of lift=0.34478

5. Velocity Contour Plot:

Figure(40): Shows Velocity Contour Plot; flow over a 2D cylindrical surface for Reynolds No. 10000 at steady-state.

6. Pressure Contour Plot:

Figure(41): Shows Pressure Contour Plot; flow over a 2D cylindrical surface for Reynolds No. 10000 at steady-state.

Figure(42): Shows Velocity-pressure contour animation; flow over a 2D cylindrical surface for Reynolds No. 10000 at steady-state.

Case 5: Re = 1,00,000:
inlet velocity,u=1000m/s.

1 Residual Plot: