Project Transient simulation of flow over a throttle body

• Case setup : CONVERGE CFD STUDIO
• Commanad editor : Cygwin
• Post-processor : Paraview

GOVERNING EQUATIONS FOR THE FLOW THROUGH GEOMETRY (NAVIER-STOKES EQUATION)

The flow through the geometry is governed by three physical rules.

1. Conservation of mass.

   ∂(ρu)/∂x = 0​

2. Newtons second law,

   F = ma ​

3. Conservation of energy.

   h1+ (u1^2)/2= h2+ (u2^2)/2​

The air traveling past the throttle plate is assumed to be an ideal gas, i.e. the ideal gas law can be utilized p = ρRT

THE CASE SETUP

• The case setup was done using the converge software. The geometry was imported to the converge and the was cleaned to check if there were any voids or gap in it.
• The diagnosis was done and all the errors were solved
• Boundary flagging was done and the geometry was divided into 4 different regions, namely inlet, outlet, elbow wall and the throttle-body.
• Boundary fencing technique was made used to group or flag the boundaries into different regions.
• The body has an inlet pressure of 150k Pa and an outlet pressure of 100k Pa.
• And further in the case setup the condtions such as law of wall were selected.
• A desired mesh of 2mm was assigned in all three dimensions of the body, ie,,, in other words around 5000 cells or elements were created in the body along each of their length in the respective axis (dx, dy, dz)
• The simulation that we are intrested here is a transient-state simulation where we are intrested only in the results that vary w.r.t. time and how the solution converges with time.
• Turbulence model – RNG K-Ɛ

The Simulation parameters

• The simulation was ran for a maximum time step of 1sec, starting with a initial time interval of 1e-9 and the minimum time interval of 1e-9.
• The calculation is done in such a way that, for every 1 ms the 3d output file is dumped and since the simulation is ran for 10 ms, around 10, 3d output files are dumped into the output files.
• For writing the text output file, ie,,,,, the points in the graphs to see the behavior of the flow, for every 1e-9 s a text output is printed.

CALCULATION

The length of the throttle is approximately 0.2m. And from the transient flow simulation the average velocity in the body is about 100 m/s

Therefore time taken for the flow to flow through the body once is

                                  t= d/v  

                                  	t = 0.2/100

ie,,, t = 0.002 s or 2 ms

say that we want to make flow to flow 5 times through the body

therefore it takes 10 ms to flow 5 times through the body.

Hence, the simulation starts at 0 s and ends at 0.01 s.

ROTATING-CONDITIONS (THROTTLE BODY)

• Wall-motion type : Rotating
• Surface Movement : Moving

How should the throttle rotate??

To give the input for the throttle, ie,,, how the throttle rotates about it’s axis of rotation, arc normal is calculated and rotation centre is chosen about it’s axis of rotation.

An input file is chosen on how the throttle should rotate for every milli sec.

Post Processing the 3d output files

• So when all the 3d output files are getting dumped into the output files by the cygwin, it is important to convert it into format that the paraview can understand like .case format or .vtm format using cygwin.
• Once the post processed files are ready paraview can read those files and the desired contour of the different parameters can be obtained and the animation can be done.

Surface mesh with edges

• The given geometry has been discritized into finite number of elements or cells inorder to visualize the behaviour of the flow through each and every element.
• If the meshing is done properly then it will resutl in the non-linear or too much deviation in the solution and the solution will not converge to the exact solution.
• Since the geometry is not too complicated the meshing is done in converge itself. There are about 35000 cells or elements created in the given geometric model.
• Around 2 layer of fixed embedding is added around the region of throttle body

Because,

1) To make sure the mesh around it is generated quite uniformly, like atleast to have some cells around the throttle, as the throttle needs to rotate the clearence between the elbow (wall) and the throttle is very less.

2) To capture the data even more precisely around the throttle body by adding the fixed embedding layer.

How do we know the size of the cells in layer of fixed embedding??

Well the answer to this question is quite easy.

Converge uses a optisturct mesh refinement and the size of the element or grid-size is given by

                      	grid size=(base_grid)/2^(embed level) 

Since our base grid is 0.002m or 2 mm and embed-level is 2

Therefore,

                        	Grid-size = 0.002/2^2 
                             Grid-size = 0.0005 m or 0.5mm

Thus the least cell size or element size we’ll be having is 0.5 mm or 0.0005 m during the simulation.

PLOTS OF PRESSURE, VELOCITY, CELL-COUNT AND MASS-FLOW RATE

• PRESSURE

The variation of the pressure is as shown in the plot. For a flow to occur there should be a pressure diffrence developed. Hence an inlet pressure of 150k Pa and an oultet pressure of 100k Pa is provided and it is this pressure diffrence the makes the flow to happen.

A higher pressure is experienced when the flow stream meets the valve surfaces.

When the flow starts to accelerate the pressure is low initally and starts increasing as the flow starts accelerating. The increasein pressure is observed till the flow reaches the throttle presesnt inside the body. Once the flow reaches the throttle high fluctuation of pressure is observed if the throttle body is rotating, else the pressure increases linearly and once it reaches the outlet of the body, the flow pressure decreases as at the exit the flow accelerates ie,,,it’s velocity increases, as pressure decreases. After some time the flow reaches thr steady state comdition and pressure remains almost a constant value.

• TOTAL CELL-COUNT

The total cell count is a constant value throughout the simulation and it mainly depends on the mesh size that we have given during the time of setting up the case.

As shown in the above fig, there are four different ranks shown. Each rank corresponds to a number of processors used during running the simulation. Since the simulation is ran for 4 processors (to reduce the computational time involved and to lower the loads on only 1 processor), hence there are 4 rank indicated. The main intention of creatin the cells or elements is to visualize the flow through each cells and what is causing the flow to vary in that particular region of the cells created.

There are about 40000 cells created here for running the simulation

VELOCITY

Due to the pressure difference at the inlet and the outlet the flow starts with zero velocity initially and starts accelerating. Once the flow starts accelerating it’s velocity increases gradually and reaches the maximum value at the exit of the throttle body.

The variation in the velocity of the flow in the above plot is due to it’s interaction with the throttle body as the flow encounters it. Once the flow encounters the throttle body as the body is exposed to a fluid flow stream it’s velocity decreases, because some amount of area of throttle body is exposed to the fluid flow which decelerates the flow.

A Maximum velocity of 165 m/s is achieved in this simulation at the throttle body outlet

Once the flow reaches the staedy state condition the flowhas a constant velocity of 150 m/s

• MASS-FLOW RATE

Mass-flow rate involves the terms like density, area and velocity of the flow. It is the quantity of fluid flowing through the given geometry in unit time interval in kg/s.

At the inlet the fluid is just accelerating the velocity of the flow will be lesser and hence the mass-flow rate will also be lesser. As the fluid moves towards the outlet the flow accelerated and it’s velocity increases thereby increasing the flow rate of the fluid passing through the cycles. At the throttle the mass-flow rate decreases and after certain amount of time the flow attains a steady state and the mass-flow rate is almost a constant value.

A VIEW OF STREAM LINES THROUGH THE THROTTLE BODY

Stream lines are the imaginary lines drawn tangentially to the direction of the velocity vector at every point in a flow. Stream lines helps us to determine the behaviour of the

flow in a given geometry. In the above figure the stream lines are introduced to the geometry and the variation of pressure and velocity is observed

1.) The flow is highly chaotic once the throttle starts to rotate

2.) The velocity starts to increase linearly from the inlet

3.) Once the flow reaches the throttle body the velocity of the flow and the pressure increases, because as the throttle rotates it exposes

more and more area to the region of the flow thereby causing the flow to increase it's pressure

The above figure clearly shows how chaotic (high velocity and high pressure zones) once the flow reaches the throttle and as it starts rotating.

PS : Dear respected sir/madam I’ve a problem with my YouTube account. So I’m attatching the .zip files of animations created here