Flow Simulation over a Cylinder using Solidworks.

Aim:- Flow Simulation over a Cylinder using Solidworks.

Objective:-

1. Run a baseline simulation and then calculate the Reynolds number. Then increase the Reynolds number by a factor of 20%, 40%, and 100% then run the transient flow simulation.
2. Simulation end time should be calculated properly
3. Create animations for pressure-velocity for all the three Reynolds number

Introduction:-

Potential flow around a circular cylinder is a classical solution for the flow of an inviscid, incompressible fluid around a cylinder that is transverse to the flow. Far from the cylinder, the flow is unidirectional and uniform. The flow has no vorticity and thus the velocity field is irrotational and can be modeled as a potential flow. Unlike a real fluid, this solution indicates a net-zero drag on the body, a result known as d'Alembert's paradox.

Reynolds number

The Reynolds number (Re) is an important dimensionless quantity in fluid mechanics used to help predict flow patterns in different fluid flow situations. At low Reynolds numbers, flows tend to be dominated by laminar (sheet-like) flow, while at high Reynolds numbers turbulence results from differences in the fluid's speed and direction, which may sometimes intersect or even move counter to the overall direction of the flow (eddy currents). These eddy currents begin to churn the flow, using up energy in the process, which for liquids increases the chances of cavitation. The Reynolds number has wide applications, ranging from liquid flow in a pipe to the passage of air over an aircraft wing. It is used to predict the transition from laminar to turbulent flow and is used in the scaling of similar but different-sized flow situations, such as between an aircraft model in a wind tunnel and the full-size version. The predictions of the onset of turbulence and the ability to calculate scaling effects can be used to help predict fluid behavior on a larger scale, such as in local or global air or water movement and thereby the associated meteorological and climatological effects.

With respect to laminar and turbulent flow 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

where:

• ρ is the density of the fluid (SI units: kg/m³)
• u is the flow speed (m/s)
• D is the diameter of the tube (m)
• μ is the dynamic viscosity of the fluid (Pa·s or N·s/m² or kg/(m·s))
• ν is the kinematic viscosity of the fluid (m²/s).

In general, if Re < 2300, the fluid experiences laminar flow. If Re > 4000, its flow is turbulent. If the value of Reynolds number lies in between these two boundaries, it is a case of transitional flow.

Procedure:-

1. A new part model created using a circle of diameter 0.03 m and extruded it to 0.05 m.
2. Created a new project under the wizard, and specified the input data by defining the general settings by selecting the type of fluid and the flow type.
3. Define the cut plots in the XY plane(perpendicular to the longitudinal axis) for the velocity and pressure at the middle of the cylinder(0.025m)
4. The animation is obtained from the results menu for the velocity and pressure simulation.
5. Similarly, more new studies are done by varying the velocity according to the objective and then a comparison of all studies is done.

Specifications and Calculations:-

The diameter of cylinder = 0.03 m

The length of cylinder = 0.05 m

Air flow direction = X-axis

Mesh index = 3

At STP( temperature=0 degree celcius/ 273.15k and pressure = 101325 pascal):

The density of air = 1.229 kg/m^3

Viscosity of air = 1.73*10^-5 kg/m.s

Using Reynolds formula, Reynold's number for respective velocity is calculated.

For Velocity = 10 m/s, Re = 21312.138 (Baseline study)

For Velocity = 12 m/s, Re = 25574.566

For Velocity = 14 m/s, Re = 29836.993

For Velocity = 20 m/s, Re = 42624.276

Simulation end time calculation:

Speed=Distance/Time

Therefore, Time=Distance/Speed

Here, distance means the length of the computational domain that is 0.27m in the direction of airflow.

Actually, end time is always 3-4 times of flow-through time, but here we are considering it only twice.

Flow-through time is the time taken by the fluid/gas to flow through the entire domain from inlet to outlet whereas End time is the total time to run the simulation.

For Velocity = 10 m/s, FTT = 0.27/10 = 0.027 sec

Therefore, End time=2*FTT = 0.054 sec

For Velocity = 12 m/s, FTT=0.27/12 = 0.0225 sec

Therefore, End time=2*FTT = 0.045 sec

For Velocity = 14 m/s, FTT=0.27/14 = 0.0193 sec

Therefore, End time=2*FTT = 0.038 sec

For Velocity = 20 m/s, FTT=0.27/20 = 0.0135 sec

Therefore, End time=2*FTT = 0.027 sec

Descriptions of study:-

Study 1- Baseline study at an inlet velocity of 10m/s and Re = 21312.138

Velocity Plots/Graphs:-

For inlet velocity of 10m/s, the minimum velocity is 0.723 m/s at zero degrees to the cylinder and the maximum velocity(red zone) is 12.235 m/s.

Pressure Plots/Graphs:-

For the inlet velocity of 10m/s, the minimum pressure is 101288.22 pascal which is represented as a blue region in the graph and the maximum pressure(red zone) is 101382.26 pascal which at the surface of the cylinder where the air is striking and this point the velocity of air is minimized.

Velocity Simulation:- https://drive.google.com/file/d/10N_i1jds9xGihzBbM4M0OjCLAdSxutCF/view?usp=sharing

Pressure Simulation:- https://drive.google.com/file/d/1lP2pgfGQcvCiWWPSE4jRoPy26n01S-Rg/view?usp=sharing

Study 2- Air inlet velocity of 12m/s and Re = 25574.566

Velocity Plots/Graphs:-

For inlet velocity of 12m/s, the minimum velocity is 0.882 m/s at zero degrees to the cylinder and the maximum velocity(red zone) is 14.673 m/s.

Pressure Plots/Graphs:-

For the inlet velocity of 12m/s, the minimum pressure is 101272.24 pascal which is represented as a blue region in the graph and the maximum pressure(red zone) is 101407.49 pascal which at the surface of the cylinder where the air is striking and this point the velocity of air is minimized.

Velocity Simulation:- https://drive.google.com/file/d/1ygYsdSMoRoE8f7QP3eYXu1_s3Y5GNyNQ/view?usp=sharing

Pressure Simulation:- https://drive.google.com/file/d/1MnlZJqJohlDeXucbz4Cza6cUGWaKVvK9/view?usp=sharing

Study 3- Air inlet velocity of 14m/s and Re = 29836.993

Velocity Plots/Graphs:-

For the inlet velocity of 14m/s, the minimum velocity is 1.074 m/s at zero degrees to the cylinder and the maximum velocity(red zone) is 16.774 m/s.

Pressure Plots/Graphs:-

For the inlet velocity of 14m/s, the minimum pressure is 101235.89 pascal which is represented as a blue region in the graph and the maximum pressure(red zone) is 101389.76 pascal which at the surface of the cylinder where the air is striking and this point the velocity of air is minimized.

Velocity Simulation:- https://drive.google.com/file/d/1yu20D_WGgqWMBD47Vy-fjnDeaXmAUjOM/view?usp=sharing

Pressure Simulation:- https://drive.google.com/file/d/1tOmtfsIFzNSsVnUCo3ftNiq54ai4AbLK/view?usp=sharing

Study 4- Air inlet velocity of 20m/s and Re = 42624.276

Velocity Plots/Graphs:-

For the inlet velocity of 20m/s, the minimum velocity is 1.483 m/s at zero degrees to the cylinder and the maximum velocity(red zone) is 24.503 m/s.

Pressure Plots/Graphs:-

For the inlet velocity of 20m/s, the minimum pressure is 101177.48 pascal which is represented as a blue region in the graph and the maximum pressure(red zone) is 101554.13 pascal which at the surface of the cylinder where the air is striking and this point the velocity of air is minimized.

Velocity Simulation:- https://drive.google.com/file/d/1R7hYrQCXl0trWi_C4oTt3gUfcMpPcIFX/view?usp=sharing

Pressure Simulation:- https://drive.google.com/file/d/1tYyriwHC3aUxU2UVmz670uIRDT64hALt/view?usp=sharing

Conclusion:-

1. On the surface of the cylinder, Pressure varies from a maximum (shown in the graph in red) at the stagnation points at θ = 0 and θ = 180 degrees to a minimum (shown in blue) on the sides of the cylinder, at θ = 90 degrees and θ = 270 degrees. Likewise, Velocity varies from minimum at the stagnation points (that is θ = 0 and θ = 180 degrees) to maximum on the sides (at 90 and 270 degrees), in the low pressure.

2. Velocity and pressure are inversely proportional to each other.
3. As the Reynolds number increases, velocity also increases according to the varying factor that is velocity increases proportionally to the Reynolds number.

4. The dynamic pressure at the upstream stagnation point has a value that is needed to decelerate the free stream flow of speed. This same value appears at the downstream stagnation point, this high pressure is again needed to decelerate the flow to zero speed. This symmetry arises only because the flow is completely frictionless. The low pressure, which must be present to provide the centripetal acceleration, will also increase the flow speed as the fluid travels from higher to lower values of pressure. Thus we find the maximum speed in the flow in the low pressure on the sides of the cylinder.

5. From the above studies(1-4), we can say that Study1 is of laminar flow (Re<2300); Study 2&3 is of transitional flow (2300<Re<4000) and Study4 is of turbulent flow.

6. The point at which the air strikes the cylinder represents the region of maximum pressure and minimum velocity whereas the upstream and downstream side of the cylinder is the region of minimum pressure and maximum velocity.

Google drive link- https://drive.google.com/drive/folders/1_lBjftSVFQ5-sY_v6gOp8nGpuQgx-LQN?usp=sharing

Reference:-

https://en.wikipedia.org/wiki/Potential_flow_around_a_circular_cylinder

https://en.wikipedia.org/wiki/Reynolds_number