Challenge

Flow over a cylinder

SSaurav Sankhe20 Jun 2020

Aim: Study the external flow behaviour over a cylinder and performing a Parametric study by changing the Reynold’s number using SOLIDWORKS Flow Simulation.

Objective: Perform CFD simulation and:

Calculate the Reynold’s number by running baseline simulation.
Calculate flow through time for 10%, 20% and 100% of Reynold’s number.
Calculate the velocity and pressure distribution in all the three cases.

Theory:

External flow is characterized by a freely growing boundary layer surrounded by an outer flow region that involves small velocity and temperature gradients. In internal flows, the entire flow field is dominated by viscous effects, while in external flow, the viscous effects are confined to a portion of the flow field such as the boundary layers and wakes. When a fluid moves over a solid body, it exerts pressure forces normal to the surface and shear forces parallel to the surface along the outer surface of the body. The component of the resultant pressure and shear forces that acts in the flow direction is called the drag force (or just drag), and the component that acts normal to the flow direction is called the lift force (or just lift).

Flow over cylinders and spheres is frequently encountered in practice. For example, the tubes in a shell-and-tube heat exchanger involve both internal flow through the tubes and external flow over the tubes, and both flows must be considered in the analysis of the heat exchanger. The characteristic length for a circular cylinder or sphere is taken to be the external diameter D. Thus, the Reynolds number is defined as `Re=(VD)/υ` where `V="the uniform velocity of the fluid as it approaches the cylinder"` The critical Reynolds number for flow across a circular cylinder or is about `Re_(cr)≅2×10^5`. That is, the boundary layer remains laminar for about `Re_(cr)≤2×10^5` and becomes turbulent for `Re_(cr)≥2×10^5`.

At very low upstream velocities `Re≤1`,the fluid completely wraps around the cylinder and the two arms of the fluid meet on the rear side of the cylinder in an orderly manner. Thus, the fluid follows the curvature of the cylinder. At higher velocities, the fluid still hugs the cylinder on the frontal side, but it is too fast to remain attached to the surface as it approaches the top (or bottom) of the cylinder. As a result, the boundary layer detaches from the surface, forming a separation region behind the cylinder. Flow in the wake region is characterized by periodic vortex formation and pressures much lower than the stagnation point pressure.

When a fluid separates from a body, it forms a separated region between the body and the fluid stream. This low-pressure region behind the body where recirculating and backflows occur is called the separated region. The larger the separated region, the larger the pressure drag. The effects of flow separation are felt far downstream in the form of reduced velocity (relative to the upstream velocity). The region of flow trailing the body where the effects of the body on velocity are felt is called the wake.

Flow separation occurs at about `theta = 80^0` (measured from the front stagnation point of a cylinder) when the boundary layer is laminar and at about `theta=140^0` when it is turbulent

CAD Model:

A cylinder was made in SolidWorks by the dimensions as shown in the below figure (all dimensions are in mm).

Performing a baseline Simulation

Using flow simulation Add-In in Solid works, baseline simulation was performed by carrying following steps:

Clicking on the Wizard tool from Flow Simulation toolbar, then giving the title of the project along with the comments (if any).
Selecting SI units for simulation then clicking next.
Analysis type was changed to external with time dependent (Total analysis time was set to 0.1 sec and output time step was set to 0.01 sec). The reason for selecting these times have been explained further.
Default fluid was set to air and then by clicking next, the velocity along X direction was set to 10 m/s in Initial and Ambient Conditions window.
This made a computational domain over the cylinder which can be seen in isometric view.
Then default mesh was set (automatic mesh with size of 3).
Then two cut plots were made for visualising velocity and pressure distribution, by inserting the cut plots from results tree in feature manager. The cut plots were made in XY direction at a distance of 0.03m from origin.
Finally, the setup was made to run. Some of the important snaps are shown below.

End Flow time (Simulation End time)

Usually while performing external flow simulation in solid works with time dependent analysis, the most important factor to consider is the end flow time.

It is nothing but how much time does it needs to record all the changes in the variation of parameter while making an animation.

End flow time or simulation end time is calculated as follows, `"End Flow time"=2×"Flow-through time"`.

where, `"Flow through time"= ("Length of Computational domain")/("Inlet Velocity")`.

For above set baseline simulation, Inlet velocity is 10 m/sec whereas the length of the domain along X direction is set to 0.5m.

Thus`"Flow through time is" 0.5/10=0.05 sec` and `"End flow time"=2×0.05=0.1 sec`.

Results of Baseline Simulation

Reynold’s number for the proposed flow is calculated as `Re=(10×0.06)/(1.48×10^(-5) )=40541`.

As the velocity flows along X direction, it can be seen in the graph that the pressure along X direction becomes maximum as soon as it strikes the cylinder. The second plot shows the minimum pressure which gives us the indication that at that point, the flow has been separated which is nearly at an angle between 80-90 degrees which also shows that the flow is still laminar.

Velocity Plot

As we can see that the velocity is maximum where pressure is minimum which also again gives us a clear indication of flow separation point.

Animation

Parametric Study

As Reynold’s number was to be increased to 10% 20% and 100% of the value obtained from the above baseline simulation, MATLAB code was generated that calculated both the Reynold’s number and Simulation end time which are shown as below:

%% FLOW OVER CYLINDER
close all
clear all
format shortG
format compact
clc
% INPUTS
D = 0.06;
V_i = 10;
nu = 1.48e-5;
 
Re_i = (V_i*D)/nu;
 
Re1 = 1.2*Re_i;
Re2 = 1.4*Re_i;
Re3 = 2*Re_i;
 
Re = [Re_i Re1 Re2 Re3]
 
V1 = (nu*Re1)/D;
V2 = (nu*Re2)/D;
V3 = (nu*Re3)/D;
V = [V_i V1 V2 V3]
 
% SIMULATION END TIME
Domain_length = 0.5;
Flow_time = Domain_length./V;
End_time = 2*Flow_time

Output

Re =
        40541        48649        56757        81081
V =
    10    12    14    20
End_time =
          0.1     0.083333     0.071429         0.05

A parametric study was created in solid works by changing the inlet velocity as follows.

End time was calculated in-order to record the animations separately.

Parametric Study	Design Point 1	Design Point 2	Design Point 3
Velocity in X direction (Initial and Ambient Conditions) [m/s]	12	14	20
Level of initial mesh (Automatic Mesh) [ ]	5	5	5

Results of Design Point 1

With increase in inlet velocity, there was an increase in wake region on both the plots, also the maximum velocity was changed. But there was not much difference in the change in the pressure.

Results of Design Point 2

Same trends were noted down from this condition. Also, the separation point is about 80-90 degrees from the X axis, giving an indication that the flow is still laminar.

Results of Design Point 3

With doubling the Reynolds number, the wake region has also increased with the same trends in parameter but with high magnitude were noted. Still there was no indication of change in the flow.

Conclusion

With increase in Reynolds number, wake region was increased.
Flow separation occurs at maximum velocity and minimum pressure.
Flow Separation occurs at around 80 degrees from the stagnation point in case of laminar flows.

Animation

Velocity and Pressure distribution at 10% of Reynolds number