Transient state simulation of flow over a throttle body

Aim:

This particular project aims at obtaining a transient simulation of flow in an elbow-shaped channel through a throttle body that is fitted in it.

Governing Equations:

The simulation is run on the basis of the Navier Stokes equations. The NS equation consists of three momenta, one continuity, and one energy equation. The energy equation is solved only during the time where there is a heat transfer taking place. This is done so to reduce unnecessary computational time.

Objective:

The objective is to obtain a comparison between the flow of a fluid over throttle body when it is steady (not moving) and when the throttle body is dynamic. This project deals with the latter half of the comparison. The former half i.e the steady-state simulation was carried out in the previous project. The results obtained are later evaluated and conclusions will be drawn accordingly.

The workflow involves:

1. Creating a geometry of the backward flowing step model using the create function in the converge studio.
2. Flagging the boundaries starting from the flow into the model and the fluid exiting from it.
3. It is important to make sure that the throttle body is selected as a whole and submitted as a particular boundary.
4. The throttle body since is dynamic has to be given movement degree at a particular time.
5. Creating the required case setup and setting up parameters according to the requirements.
6. Transporting the input files and running the simulation
7. Convert the obtained 3D files into a corresponding viewable form.
8. Obtaining the contours and animation and drawing results from them using a 3D viewing platform such as ParaView.

The case setup:

The simulation was run with a base mesh size of 2mm. The boundary was first flagged into 4 different regions. The four different regions being the inlet, outlet, throttle body, and elbow wall as seen in Figure1. The regions have been indicated based on the colors. Once the boundary flagging is finished, the case setup is started, starting with time-based as the application type. Air is selected as a gas mixture. Global transport parameters were selected to be the default with the Prandtl number being 0.9 and Schmidt number being 0.78.

The solver was selected to be a transient solver since we will be needing the throttle body to be rotating. The simulation was run for 10ms with an initial time step of 1e-9seconds. The 10ms value was selected once after considering the approximate time required for the fluid to flow through the elbow. The x-axis was approximated to be 0.2m and the velocity according to the steady-state value from the previous was found to be 100m/s. So considering these values will yield a value of 2ms for the fluid to run through the body. Hence a 10ms window would result in the fluid running approximately 5 times.

v=100m/s

d=0.2m

t=dv

t=2ms

The throttle body here has to move for the simulation to be transient. The movement was fed into the setup in the boundary dock of the throttle body. The setup was as seen in Figure3. The rotating center was obtained by measuring the arc center of three points on the rotating axis of the throttle body. The movement of the throttle body was fed in using a separate excel file as seen in Figure4. The solution was obtained using the NS equation. The solver scheme was selected to be PISO. PISO stands for Pressure Implicit with Splitting of operator. All the boundaries were dropped under a single region. Turbulence modeling was run according to the RNG k-ε equation. Coming to setting the grid control, the base grid was set to 2mm. Fixed embedding was enabled to capture the very minute area that is present between the channel and the throttle body. For this particular project, the setup is as seen in Figure2 below. The output tab was selected to be same all default. Once the setup was completed, the files were exported to a particularly saved output folder.

Figure1. Screenshot involving boundary flagging window during a flow over throttle simulation

Figure2. Screenshot involving fixed embedding window during a flow over throttle simulation

Figure3. Screenshot involving throttle body boundary setup window during a flow over throttle simulation

Figure4. Screenshot involving time data setup window during a flow over throttle simulation

Results and Figures:

The base grid size was selected to be 2mm with a fixed embedding enabled having a scale of 1 with 2 layers. This helped the simulation to capture the small area present around the throttle body and the channel. The total cell count varies over a range from 7050 to 7400 cells as seen in FIgure3. This can be attributed to the transient behavior of the throttle body. The body starts rotating to 25 degrees starting at time 0. This can be observed as the total cell count reducing during that time, Now the throttle remains constant between 2ms to 4ms where the cell count remains constant. Once the throttle again starts reducing from 25 degrees to 0 degrees over a period of 4ms to 8ms, the cell count increases proportionally and reaches a stable value of 7400 from thereon. The closely packed cell grid is clearly visible in the sliced section view of Figure5 with smaller cell blocks present around the throttle body.

Figure5. The plot of number of cells during a backward-facing step simulation

Figure6. The plot showing surface with edges during an elbow flow simulation.

The velocity contour at end of the simulation was as obtained as Figure7. The flow shows that the velocity reaches a peak of 210 m/s at near the outlet starting from around 60m/s at the inlet. This final velocity is around 10m/s higher than the steady-state flow velocity. The flow forms a pattern such that the fluid is concentrated at the periphery of the tube. This can be attributed to the throttle body present at the center which is blocking the flow of the fluid. As a result, the fluid at the periphery experiences a velocity of 120 m/s. The fluid coming in direct contact with the throttle body at a speed of around 160m/s slows down considerably and flows around the throttle body. This is where the separation of fluid takes place. As a result, the velocity immediately after the throttle body is lower than the previous value. The fluid once after combining at the very end has the highest velocity of around 210m/s. The inlet average velocity wobbles and is highly inconsistent due to the transient flow. The velocity reaches a low of 80 m/s which can be attributed to the 25-degree closure of the throttle body during that time period blocking most of the flow. The outlet velocity increases to 150 m/s at around 1ms as seen in Figure8 but again like the inlet, never settles or converges.

Figure9 shows the velocity contour during the movement of the throttle body and seen, the flow has a low overall velocity with an average of around 90m/s. The velocity is lowest at the point of contact with the throttle body. The vector arrows show how the fluid tries to surpass the blocked path with most of the fluid flowing in the periphery of the tube.

Figure7. velocity contour plot during an elbow flow simulation.

Figure8. The plot of average velocity (m/s) of inlet and outlet during an elbow flow simulation.

Figure9. velocity contour plot during the throttle movement duration of an elbow flow simulation.

The pressure contour at end of the simulation was as obtained as Figure10. The inlet pressure was set to 1.5 bar and the outlet was set to 1bar. This difference in pressure was the driving force for the fluid. This 1.5 bar of high pressure is visible in the contour plot at the inlet which gradually reduces as the flow progresses and reaches 1.2 bar before coming in contact with the throttle body. The pressure after the throttle body is at 1.2bar. The pressure is still considerably high because of the low velocity in the region and also because of the separation of the fluid that takes place. The pressure value is at a minimum at the very end of the tube at around 1 bar and this is attributed to the high velocity experienced by the fluid at the exit. Figure11 shows that static inlet pressure reduces to 1.4bar and the outlet total pressure converges at 1.1bar at around 200 cycles from the start of the simulation.

Figure10. pressure contour plot during an elbow flow simulation.

Figure11. The plot of pressure (Pa) of inlet and outlet during an elbow flow simulation.

The mass flow rate plot as seen in Figure11 has a similar trend to that of the velocity and an inlet rate of 0.004kg/s before it converges and the outlet flow increases by the same amount at around 200 cycles from the start of the simulation.

Figure12. The plot of mass flow rate (kg/s) of inlet and outlet during an elbow flow simulation

Conclusion:

The elbow flow with a throttle body shows the flow of the fluid is physically sound meaning that the behavior of the flow was as expected. The base mesh was set to be 2mm along with the use of fixed embedding. As a result, the simulation time ran for a longer time. The flow clearly shows a drop in velocity during the throttle body movement. A 10m/s increase in velocity is observed at the outlet. The link for the youtube video would be https://youtu.be/HBjiMwRiIAA