Flow over a cylinder

FLOW OVER A CYLINDER

AIM – Run an external flow simulation to obtain velocity and pressure variation of fluid flowing over cylinder.

OBJECTIVES-

1. Create 3D model of pipe.
2. Run base line flow simulation with initial velocity 10 m/s.
3. Run flow simulations by increasing Reynolds number by factor 0.2, 0.4 and 1 respectively.
4. Create animations for Cut plot of pressure and velocity for all simulations.

INTRODUCTION-

In fluid mechanics, external flow is such a flow that boundary layers develop freely, without constraints imposed by adjacent surfaces. Accordingly, there will always exist a region of the flow outside the boundary layer in which velocity, temperature, and/or concentration gradients are negligible. It can be defined as the flow of a fluid around a body that is completely submerged in it. The behaviour of external fluid is governed mainly by the effects of viscosity and gravity relative to the inertial forces of the flow. Depending on the effect of viscosity relative to inertia, as represented by the Reynolds number, the flow can be either laminar or turbulent.

With respect to laminar and turbulent regimes:

• Laminar flow occurs at low Reynolds numbers, where viscous forces are dominant, and is characterized by smooth, constant fluid motion.
• Turbulent flow occurs at high Reynolds numbers and is dominated by inertial forces, which tend to produce chaotic eddies, vortices and other flow instabilities.

The Reynolds number is defined as Re = ρ u D / μ = u D / ν{\displaystyle \mathrm {Re} ={\frac {\rho uD}{\mu }}={\frac {uD

• ρ is the density of the fluid
• u is the flow speed
• D is the diameter of the tube
• μ is the dynamic viscosity of the fluid
• ν is the kinematic viscosity of the fluid.

CALCULATIONS:

Let diameter of pipe = 0.02 m

Our working fluid is taken to be air. Following table gives variation of viscosity of air with temperature.

So, let us carry out our simulation at 20°C. So, Kinematic viscosity of air ν = 1.516 *10^-6 m²/s.

Base Line Simulation: Inlet velocity u = 10 m/s. Putting values in formula we get

Reynolds Number Re = 13192.612

Case 1: Reynolds Number Re = 13192.612 * 1.2 = 15831.344

Putting values in formula we get, Inlet velocity u = 12 m/s

Case 2: Reynolds Number Re = 13192.612 * 1.4 = 18469.6568

Putting values in formula we get, Inlet velocity u = 14 m/s

Case 3: Reynolds Number Re = 13192.612 * 2.0 = 26385. 224

Putting values in formula we get, Inlet velocity u = 20 m/s

Calculating end simulation time

Length of domain in X direction = 0.18m

Time = Distance/ Velocity

Also, flow through time is twice of end simulation time.

Base Line Simulation: End simulation time = 0.018 sec

Case 1: End simulation time = 0.015 sec

Case 2: End simulation time = 0.0129 sec

Case 3: End simulation time = 0.009 sec

PROCEDURE-

1. Click on New > Part. Sketch a circle of diameter 0.02 m in Front plane. Exit Sketch.
2. Clink on Extrude Boss/Base and put length 0.05 m. Now click on Shell. So, now we get our pipe. Save the part.
3. Click on Wizard in Flow Simulation. Select flow type external. Use SI units.
4. In Physical features> Time-dependent. Put Total analysis time = 0.1 sec and Output time step = 0.01 sec.
5. Select Gases> Air. Click on Add. In Parameter definition, see Velocity parameters. Put velocity in X direction = 10 m/s
6. In result resolution drag slider to 5. Click on finish
7. Click on Results>Cut Plot and insert a cut plot parallel to front plane.
8. Click on Run. Wait for Solver to finish.
9. Right click on legend of cut plot of Velocity. Set it to Global Maximum and Global Minimum Value.
10. Now, Click on Animation>Insert Animation. Click on Animation Wizard. Set time to 10 seconds. Select Scenario. Click finish.
11. Similarly, make animation of cut plot of Pressure.
12. Change the inlet velocity values according to different cases and repeat above steps.

RESULTS -

Base Line Simulation: Inlet velocity u = 10 m/s. Reynolds Number Re = 13192.612

Velocity animation -

Pressure Animation-

Case 1: Inlet velocity u = 12 m/s, Reynolds Number Re = 15831.344

Velocity animation

Pressure Animation

Case 2: Inlet velocity u = 14 m/s, Reynolds Number Re = 13192.612 * 1.4 = 18469.6568

Velocity animation

Pressure Animation

Case 3: Inlet velocity u = 20 m/s Reynolds Number Re = 13192.612 * 2.0 = 26385. 224

Velocity animation-

Pressure animation-

CONCLUSIONS & EXPLANATIONS-

1. To verify correctness of the results from analysing cut plots in all cases, select legend to stay between Global Maximum and Global Minimum value.
2. Increase in Reynolds number leads to increase in velocity which results in less flow through time.
3. Increasing the Reynolds number results in steadier value in case 3 when compared with case1 or case 2.
4. Plot of pressure doesn’t show large variation when compared with velocity plot.
5. As velocity increases the length of boundary layer increases and velocity varies for a longer distance after cylinder.
6. Also, the regions near to cylinder converge as we increase velocity.