Flow over a cylinder
"Simulating Flow over a Solid Cylinder."
1. Objective:
i. To Run a baseline simulation and then calculate the
Reynolds number
ii. Increase the Reynolds number by a factor of 20%,
40%, and 100% then run the transient flow simulation.
iii. Create animations for pressure-velocity for all the three Reynolds number.
2. Concepts:
Before doing the simulation first we need to understand some basic terms related to the fluid flow over the body, the basic terms are as follows.
2.1 Basic Terms:
i. Stagnation point:
In fluid dynamics, a stagnation point is a point in a flow field where the local velocity of the fluid is Minimum (or) zero and static pressure acting on the body is maximum. Stagnation points exist at the surface of objects in the flow field, where the fluid is brought to rest by the object.
ii Separation point and Wake Region:
The position at which the boundary layer leaves the surface of a solid body. It may occur with the laminar flow (laminar separation) or when the boundary layer is turbulent (turbulent separation). Separation is sometimes followed by reattachment of the flow.
The thickness of this layer is smallest at the stagnation point and increases towards the backside of the obstacle. However, at some point on the backside, the boundary layer separates from the obstacles surface to form a vortex-filled wake whose transverse dimensions are similar to those of the obstacle itself. This phenomenon is known as boundary layer separation.
the flow separates from the surface and creating a
highly turbulent region behind the cylinder called the
wake.
iii. Vortex Shedding:
The boundary layer separates from the surface forms a free shear layer and is highly unstable. This shear layer will eventually roll into a discrete vortex and detach from the surface (a phenomenon called vortex shedding). Another type of flow instability emerges as the shear layer vortices shed from both the top and bottom surfaces interact with one another. They shed alternatively from the cylinder and generates a regular vortex pattern (the Karaman vortex street) in the wake. The vortex shedding occurs at a discrete frequency and is a function of the Reynolds number. The dimensionless frequency of the vortex shedding, the shedding Strouhal number, St = f D/V, is approximately equal to 0.21 when the Reynolds number is greater than 1,000
2.2 Equations:
The type of flow is decided based on Reynold's number which is based on the density of fluid, Velocity of fluid, diameter and viscosity.
Re=p. V. D/u
Where:
p = Density
V = Velocity
D = Diameter of pipe
u= Viscosity
In our Problem, we need the help of Reynold's number and increase it to the factor of 20%, 40% and 100% and do simulation according to it. After that,We need to calculate the time duration for flow through time, the time calculation based on the following formula.
Time =Distance/Velocity
Where:
Time = flow-through time;
Distance = Length of the computational domain;
Velocity = calculated velocity for each case.
Other than These we need to understand some other
basic terminology which is as follows.
2.3 Basic Terminology:
i. Computational Domain and its Dimensions:
The computational Domain is the simplified form of a physical domain which is sufficient to consider the geometry in the simulation and also to impose the boundary conditions this simplified form should retain all physically important features of the problem. considering this as the environment to the system the boundary condition are provided accordingly, here thegeometry is cylindrical. also, the basic dimension provided for the computational domain is as shown
below.
ii. Transient Simulation
transient simulation is where the time derivative of the variable are also taken into account, hence the magnitude of the values of the system can be monitored at any particular instant of time but in steady-state simulation, only the initial values and steady-state values can be obtained.
In this project, we are approaching the solution through a transient simulation in order to observe the flow variables at each and every timestep. this will also help us in monitoring the frequency of the vortex shedding with respect to various Reynolds number.
iii. Total Analysis time(THAT) - The total analysis time defines the physical time period until which the simulation will be run from its initial instant of time.
iv. Flow-through time(FTT):-The time required for the flow to pass through the domain.
v. Output time steps(OTS):- Time step is used intransient solving which denotes the time interval for which the simulation will progress between each iteration/step. in our simulation the time step is 10 for each case.
3. Calculations:
Total time
In All the cases of simulation, we took the Diameter of the cylinder as 0.04m and length of the cylinder 0.05m. Also, the working fluid is air with density
1.225Kg/m^3 and viscosity as 18*10^-6 N.sec/m^2.
3.1 Baseline:
In the baseline simulation, we took the Velocity as 10m/s and doing the simulation with the total analysis time with 0.1 sec and output time step 0.01 sec. The calculation of the Reynolds number as follows.
Reynold's number calculation:
from equation (1)
Re=1.225 * 10* 0.04/18 * 10^-6
Re = 27222.22
After calculating Reynold's number for the baseline
we need to increase it with a factor of 20%, 40% and
100% and calculating the velocity and effective time
duration for the simulation as follows.
3.2 Increasing (Re) factor of 20 Percentage:
Increasing the Re:
Re=1.20 *27222.22
Re = 32666.66
Velocity calculation:
From Equation (1)
32666.66=1.225 * V*0.04/18*10^-6
V = 11.999 m/s
Time calculation:
from equation (ii)
T=11.999/0.8
T = 0.067 sec
OTS=0.0067 sec
Similarly, We can calculate other Parameters for the
remaining cases.
3.3 Increasing (Re) factor of 40 Percentage:
Increasing the Re:
Re = 1.40*27222.22
Re = 38111.11
Velocity calculation:
3811111 =1.225*V*0.04\18 × 10^-6
V=13.999 m/s
Time calculation:
T=13.999\0.8
T=0.0571 sec
OTS = 0.00571 sec
3.4 Increasing (Re) factor of 100 Percentage:
Increasing the Re:
Re =2*27222.22
Re = 54444.44
Velocity calculation
54444.44=1.225* V*0.04/18*10^-6
V = 19.999 m/s
Time calculation:
T=19.999\0.8
T = 0.0400 sec
OTS =0.00400 sec
Where:
CFTT = flow-through time; TAT = Total Analysis time; OTS = Output time steps.
4. Procedure:
After doing calculation we proceed further as
follows.
Step 1: Making a Cylinder with 0.04m diameter and 0.05m length in Solidworks.
Step 2: Setting Wizard in flow simulation with the required data such as type of flow, fluid type, directional velocity and etc. Here we are taken external flow time-dependent study with the varying time with respect to the calculated Reynolds number for each case. Also, the flowing fluid is air and velocity is in the x-direction (different for each case) and y and z-direction velocities are taken to be zero.
Step 3: Setting Computational Domain As discussed in the Basic. i.e 0.8m in the positive x-direction, -0.4m in the negative x-direction, 0.25m in the positive y direction, -0.25m in the negative y-direction.
Step 4: Setting Mesh to automatic. also on the surface of the cylinder, we need a finer mesh to get a better result at surface. hence, to do that we are inserted local mesh with refinement valve of 3.
Step 5: Setting Cut plot on the XY plane and adjusting it to the middle of the cylinder.
Note: Here we are taken solid cylinder.
5. Simulation & Analysis: -
5.1 Baseline:
In the baseline simulation, we took the Velocity as 10m/s and doing the simulation with the total analysis time with 0.1 sec and output time step 0.01 sec.
Pressure and velocity
5.2 factor of 20%
In the baseline simulation, we took the Velocity as 10m/s and doing the simulation with the total analysis time with 0.1 sec and output time step 0.01 sec.
Pressure and velocity
5.3 factor of 40%:
In the baseline simulation, we took the Velocity as 10m/s and doing the simulation with the total analysis time with 0.1 sec and output time step 0.01 sec.
Pressure and velocity
5.4 factor of 100%
In the baseline simulation, we took the Velocity as 10m/s and doing the simulation with the total analysis time with 0.1 sec and output time step 0.01 sec.
Pressure and velocity
OBSERVATION:
Note:- Here we are taking the image of only one case as a reference to represent the observations for basic understanding. because the Approach of observations done here is applicable for all the cases.
The Observation is as follows.
i. Reynold's number increases the velocity increases and the flow-through time is decreased in all the cases. While in all the animation of the pressure, we can observe that the pressure changes are very small.
ii. In all the cases the surface exposed in the direction of the fluid flow experiences the large pressure force which is indicated as a red zone in the animation, the green zone shows the lower pressure on the cylindrical surface exposed in the flow direction of the fluid, the red zone is shown smaller because of the smaller area of impact while the green zone is larger due to the separation of the fluid from the surface of the cylinder.
iii. Stagnation Point:- In the pressure view, we can see that the Red zone indicated as 'Cut plot 1 Maximum' and in the 'velocity view', we can see the blue region on the surface of the cylinder exposed to the fluid flow which is denoted as the 'cut plot minimum'. These two regions indicate that the point where static pressure is maximum and velocity is minimum. Hence as we know that the point where velocity is minimum (near to zero) and static pressure is maximum is known as stagnation point.
iv. Separation Point and wake Region:- In the 'velocity view' we can see that the point is shown in red zone name as 'cut plot 1 maximum' is a point from where the separation of the fluid stream (or) boundary layer initiated. This is caused due to the boundary layer thickness affected by the pressure gradient also, separation takes place due to adverse (or) positive pressure gradient i.e when
dp/dx> 0 and
dv/dy<0
As we saw in the velocity view the flow separates from the surface and creating a highly turbulent region behind the cylinder called the wake.
Note:- The separation point is different for different cases. also may have a different point of maximum and minimum velocities.