Flow over a cylinder

Flow Simulation over a Cylinder using SolidWorks

1. AIM : To simulate the flow over a cylinder in SolidWorks.

2. OBJECTIVE:

• To run a baseline simulation (inlet velocity = 10 m/s) and to calculate the Reynolds number for the same.
• To run the transient flow simulation after increasing the baseline Reynolds number as follows –
  1. By a factor of 20%
  2. By a factor of 40%
  3. By a factor of 100%

• To create animations for all the three Reynolds number for the –
  1. Velocity
  2. Pressure

Note: - Make sure that end time is set to 2 times the flow through time.

3. INTRODUCTION :

3.1 FLUID: - A fluid is any substance that flows or deforms under applied shear stress. Or, The substances which have the tendency to flow is also called as fluid.

3.2 Fluid Flow Simulation: - Carrying out fluid flow simulation in a virtual environment is a better suited approach. This allows the engineers to model the fluid’s behavior at every stage in the process and accurately predict how it will react in an actual casting environment. In doing so, it greatly reduces the time it takes to create a working design, which can then be manufactured in the real world. Because of the work that has been done in the virtual world, the chances of this unit performing as excepted are greatly increased and the overall cost of development is substantially reduced.

3.3 Types of Fluid Flow :

• Laminar and Turbulent fluid flow : - This laminar fluid flow is defined as the type of flow in which the fluid particles move along well-defined paths or streamline and all the streamlines are straight and parallel.

Thus, the particles move in laminas or layers gliding smoothly over the adjacent layer. This type of fluid is also called as streamline flow or viscous flow.

This Turbulent fluid flow is defined as the type of flow in which the fluid particles move in a zig-zag way, the eddies formation takes place which is responsible for high energy loss.

For pipe flow, the type of flow is determined by a non-dimensional number called the Reynolds number.

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.

3.4 Reynolds Number: - Reynolds number is a dimensionless value which is applied in fluid mechanics to represent whether the fluid flow in a duct or pat a body is steady or turbulent. This value is obtained by comparing the inertial force with the viscous force.

The Reynolds number is denoted by Re.

Reynolds number is given by,

`"Reynolds Number =" "Inertial force" /"Viscous force"`

The Reynolds number formula is expressed by,

`"Re = " (ρuD)/μ = (uD)/ν`

Where,

• ρ is the density of the fluid (SI units: kg/m³)
• u is the inlet flow speed (m/s)
• D is the diameter of the cylinder (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).

Reynolds number formula is used to determine the velocity, diameter and viscosity of the fluid.

The Kind of flow is based on the value of Re,

1. If Re < 2000, the flow is called Laminar flow
2. If Re > 4000, the flow is called Turbulent flow
3. If 2000 < Re < 4000, the flow is called transition.

4. BODY OF CONTENT :

For performing flow simulation inside pipe, we will need the 3D model of cylinder.

So, first we need to design 3D model of cylinder. And for designing any 3D model, we have to design 2D sketch of the model first, after that we can proceed for designing 3D model.

fig.1: 2D sketch of circular part of the cylinder

• All dimensions are in the unit system of MKS (i.e. meter, kilogram, seconds).
• Front plane is used here for 2D sketch of cylinder.

Now going to extrude the circle to form a solid cylinder structure.

Dimensions taken for the Cylinder –

1. Diameter = 0.02 m
2. Length = 0.05 m

3D Model -

fig.2: 3D model of cylinder

Now, we will go to the flow simulation in SolidWorks.

As we have to perform a flow simulation so, we need to consider a gas/fluid which will flow over the cylinder for our flow simulation study.

Here, we are considering air as a gas for our flow simulation study.

Characteristics of Air (at `15℃`) –

Density of water (ρ) = `1.225 " kg/" "m" ^3`

Dynamic viscosity of water (μ) = `1.81×10^(-5) " kg/" ("m-s" )`

Here, we are going to do Time-dependent simulation. As, whenever we want to simulate the behaviour of a system as a function of time, then it is better to choose ‘transient analysis (simulation)’ rather than ‘steady-state analysis’.

• Transient simulation (or, analysis) is also called as ‘Time-dependent simulation’.

As we are going to perform flow over a cylinder i.e. an external flow. So, going for an external analysis type and assigning time-dependent there as –

• For this, over the duration of simulation; we will get 10 outputs.

After that, for a flow simulation there must be some velocity for the fluid or, gas.

For Baseline simulation –

Here, going to take the inlet velocity of air = 10 m/s

As we know that,

`"Re =" (ρuD)/μ`

Where, Diameter of cylinder (D) = 0.02 m

Then, by substituting the values we get –

Re = 13535.91

Now, going to assign mesh to the cylinder. This is an important thing with aspect for getting more accurate result and also in better visualization.

So, here assigning mesh from ‘global mesh’ at a level of initial mesh = 3.

fig.3: mesh and computational domain (at a level of initial mesh = 3)

After that, we will make cut plot along XY plane at middle of the cylinder length (i.e. at a distance of 0.025 m), this will give us a better visualization.

And after completing all above steps, now we are ready to perform the Parametric Study. Doing so, we need to run our simulation,

After that, we get the followings as result for –

Velocity simulation –

fig.4: Velocity plot at 10 m/s (baseline simulation)

b. Pressure simulation –

fig.5: Pressure plot at 10 m/s (baseline simulation)

For performing animation, we selected ‘Scenario’ for the type of the animation as, it gives the animation of the development of flow field distribution in time,

5. CALCULATIONS :

Increasing the Reynolds number of baseline simulation as follows -

By a factor of 20%	By a factor of 40%	By a factor of 100%
New Re = 16243.092 By using formula for Re, we get – `u` = 12 m/s	New Re = 18950.274 By using formula for Re, we get – `u` = 14 m/s	New Re = 27071.82 By using formula for Re, we get – `u` = 20 m/s

6. RESULTS :

6.1 Study-1: Flow over a cylinder with Reynolds number increased by a factor of 20%

(i.e. Re= 16243.092 & = 12 m/s)

a. Velocity simulation –

fig.6: Velocity plot at 12 m/s

b. Pressure simulation –

fig.7: Pressure plot at 12 m/s

6.2 Study-2: Flow over a cylinder with Reynolds number increased by a factor of 40%

(i.e. Re= 18950.274 & `u` = 14 m/s)

a. Velocity simulation –

fig.8: Velocity plot at 14 m/s

b. Pressure simulation –

fig.9: Pressure plot at 14 m/s

6.3 Study-3: Flow over a cylinder with Reynolds number increased by a factor of 100%

(i.e. Re= 27071.82 & `u` = 20 m/s)

a. Velocity simulation –

fig.10: Velocity plot at 20 m/s

b. Pressure simulation –

fig.11: Pressure plot at 20 m/s

Drive link for 3D models, Results :-

https://drive.google.com/file/d/1ZmwYxO_l71wWZAth9CWO9GPGt0oKJAC5/view?usp=sharing

7. OBSERVATIONS & CONCLUSIONS :

1. The velocity increases with the same proportion as the Reynolds number because the other parameters than these two are constant.
2. No significant variation in the pressure plot because pressure is dependent on area which remains the same here. Also, pressure is maximum at the rare face of cylinder, which is the point of impact of the flow with the cylinder.
3. The velocity is approximately zero near the surface, at the side not in contact with the inlet flow. For larger value of Reynolds number (larger inlet velocity), velocity profile is longer behind the cylinder, i.e. on the side facing the flow.