AIM: Steady and unsteady analysis of external flow over a cylinder

Methodology

• Karman vortex street
• Part 1

Case 1 flow over cylinder for the steady-state system (RE 100)

Case 1(a) flow over cylinder for Transient system (RE 100)

• Part 2

Calculation of coefficient of drag & lift for Reynolds number 10, 100, 1000, 10000 & 100000 for steady-state solver

Effect of Reynolds number on the coefficient of drag & lift

• Karman vortex street
• Karman vortex street is a phenomenon That occurs anywhere if a flow disturbed by an object. Hungarian scientist Karman vortex was first to describe this pattern that occurs behind the flow, which produces long eddies as shown in the figure, which is also called Karman vortex.

Source: google

• The frequency of vortex shedding can be determined by strouhal number (St). The St number is dependent on the cross-section of the object in which flow passes over, and is also dependent on the velocity of the flow, or the Reynolds number.
• St=(D.f)v
• Here st is strouhal number, D is the depth of the object, f is the frequency of vortex shedding,v is the flow speed.

• Drag force:
• A drag force is the resistance force caused by the motion of a body through a fluid, such as water or air. A drag force acts opposite to the direction of the oncoming flow velocity. This is the relative velocity between the body and the fluid.
• Lift force
• the lift is an upward-acting force on any blunt or streamline body.

• Case 1:

STEADY STATE CONDITION

• Here, for flow over a cylinder, the 2D model is considered for stability purpose, flow is considered incompressible.
• External flow analysis is to be done on the cylinder , For external flow analysis, Reynolds number above 5e+5 is considered turbulent.
• All setup is considered in Ansys fluent. Dimension of model is given below.

• 2m of diameter cylinder and some boundary box is considered for flow inlet and outlet purpose.
• For meshing purposes, the trial mesh is considered, element size is chosen 0.25 after mesh refinement.
• The growth ratio is considered 1.2 with 5 inflation layers.

• Boundary conditions are set as per following image with one inlet , outlet , symmetry and walls.
• .Re > 100 will gives a vortex shedding profile due to form and pressure force.Therefore from the origin inX+ direction at 8 m the monitor point is considered for the velocity data.
• Fluent setup:
• In pressure-based segregated solver, a simple method is considered, the material is user-defined with 1 kg/m# density and 0.02 kg/m-s viscosity.

• Plot a report of velocity magnitude, drag and lift coefficient, and contour velocity profile.
• Initializing the solution and running for 1000 iteration.

Residuals plot

• Flow is converged at around 240 iterations
• Velocity magnitude at a marker point

• Velocity contour profile

• From the profile, we can see that for any bluff or Blunt body due to the large angle of attack Drag force is created and behind the cylinder low-pressure zone is created, due to low-pressure zone and Higher pressure gradient, small vortex will be created.This is also called as Karman vortex phenomena, Due to steady-state problem we can not find strohual number due to absence of time.

• Case 1(a) flow over cylinder for Transient system (RE 100)
• Duplicating the Project and Changing the setup to transient from the steady-state.
• Time step size is taken 0.1 for 2000 time steps.

• Residuals

• Velocity contour graph

• From steady-state and transient velocity contour graph we can compare that Transient state is giving more accurate solution as the time is playing the most important role
• we can find strouhal number from monitor velocity graph.

• Monitor point velocity graph.

• Lift coefficient graph

Consider time between 140s and 160s there are around 1.5 cycles between this time .

Therefore frequency will be f=1.5160-140">f=1.5160−140f=1.5160-140

f=0.075">f=0.075f=0.075

The formula for strouhal number St=f.dv">St=f.dvSt=f.dv

St=0.075⋅2=0.15">St=0.075⋅2=0.15St=0.075⋅2=0.15

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• Case 2
• For each case velocity are changed for different Reynolds number
• For Re 10 (steady-state simulation) all the plots are shown below

Residual plots

Flow is converged around 1000 iterations, as values are going down below 1e-3

• Drag coefficient

• Lift coefficient

• Value of lift coefficient and drag coefficient

• Monitor point velocity

• For Re 100 (steady-state simulation) all the plots are shown below
• Lift coefficient

• Drag coefficient

• Lift coefficient & drag coefficient

• For Re 1000 (steady-state simulation) all the plots are shown below
• Residual plots

• Flow is converged after 200 itetrations.

• Monitor point velocity plot

• Lift coefficient

• Drag coefficient

• Lift coefficient & drag coefficient value

Velocity contour

• For Re 10000 (steady-state simulation) all the plots are shown below
• Residual plot

• Monitor point velocity plot

• Lift coefficient

• Drag coefficient

• Velocity contour plot

• Drag and lift coefficient

• For Re 100000 (steady-state simulation) all the plots are shown below
• Residuals plot

• Monitor point velocity

• Drag coefficient

• Lift coefficient

• Velocity contour

• Drag and lift coefficient

• Drag and lift coefficient value for different Reynolds number

• Effect of the drag coefficient on the body.
• As we notice the once Reynolds number is increasing Drag coefficient is decreasing. In technical language If the drag force is increasing the flow can be easily pass through surrounding with this shape of the body. which means it will require lower resistance to pass over the body. That is the reason why the bluff body has a higher drag in comparison to a streamlined body. If body dimensions are constrained and if the lower drag is a priority, That means velocity or density of fluid should be changed.

• Effect of lift coefficient on the body.
• Lift is the force that directly opposes the weight of a body and holds the body in the air. A negative value of lift means it is working on the opposite side, The higher the lift value the body will be easily lifted. which is also depends on the angle of attack. For airplane AoA is 18 to 22 degree after that loss of lift drag will happen and drag will increase.
• We can observe that once the Reynolds number is increasing, vortex shedding is increasing. Flow is slowly transferring to turbulent from laminar. at the starting of fluid is separated by a long distance and can be brought close together by eddies, by exchanging mass, momentum & energy.

• Learning outcome
• Process of flow over a cylinder
• Drag and lift coefficient importance on body
• Strouhal number & Karman vortex street phenomena

Reference Research Paper:- https://www.sciencedirect.com/science/article/pii/S0307904X08000243