Week 4: Project - Transient simulation of flow over a throttle body

1. AIM:

• Simulate flow through a moving butterfly throttle valve.
• Study the transient response of the system.
• Post process in Paraview.

2. GEOMETRY, BOUNDARY CONDITIONS AND INITIALIZATION:

• Geometry is a 3D butterfly throttle valve with pipe diameter of approx 17mm. 
• Inlet Boundary conditions: 150000 Pa of Dirichlet pressure with a fairly low turbulence intensity of 1e-06 and length scale of same value. Zero normal gradient for velocity was employed along with 300K dirichlet temperature.
• Outlet Boundary conditions: 100000 Pa of Dirichlet pressure with backflow allowed with a fairly low turbulence intensity of 1e-06 and length scale of same value. Zero normal gradient for velocity was employed along with 300K dirichlet temperature.
• Wall: The pipe walls were given a non-slip wall constraint with Dirichlet temperature of 300K.
• Throttle plate: It was given a rotating non-slip wall constraint with Dirichlet temperature of 300K as well. The plate was moved to an angle of 60 degrees between 3 to 6ms as seen in the graph.
• Timestepping and Cycles: Simulation was run for 0.01s as the end time with minimum time step of 1E-09 and max of 1 second. The convection, diffusion and mach CFLs were kept at standard values of 1, 2 and 50 respectively as per the default values.  The solution was continously monitored and CFL values were appropriately changed to accelerate the convergence rate.

REGION INITIALIZATION:

Agood initial guess for a region will help the solver to converge on the solution much faster than a very bad initial guess, the region thus was initialized with 125000 Pa pressure and 300K of air in the domain.

Mesh was configured for base size of 0.002 in all three directions. Fixed Embedding was used on throttle plate as a boundary with scale 3 and 2 layers to refine the mesh nearby. Also a sphere of influence or embedding was created with center of throttle body as its center and radius of 10mm to refine the throttle plate near region and resolve the flow better.

Since we have a moving boundary, at every time step the cartesian mesh is regenerated to account for the next boundary location. We took a very fine timestep for a smoother simulation and fine temporal resolution of results. The cell count and valve motion along with mesh can be seen in detail below. Notice how cell count in continously changing as the valve is moving around and reaches a steady value again after 6ms when the valve remains at 60 degrees.

3. RESULTS

As seen in the plots below, the velocity through the medium is extremely high, near sonic in certain region of flows. Initially, the flow fully develops and reaches steady state; there is a minor wake region behind the throttle plate as the air is at very high velocity and is unable to follow even such a thin geometry. At exactly 3ms the motion of throttle starts and the throttle starts constricting the flow of the fluid. The motion continues till 6ms where you can see a huge wake region is the flow beside the throttleplate is massively separated. Plots below depict both flow at 0 degree and 60 degree for ready comparision.

Notice that due to curvature of pipe, there is a centrifugal force which acts on the flow especially with high velocities. This leads to shift of poiseuille velocity profile to the outside of the curvature as seen in the plots. That is one more reason why the wake region formed is also having larger area at the outside. This creates huge drag on the throttle plate and eddy formations which leads to energy loss of flow. This energy loss is gone into driving the eddys and shearing off each fluid layers and development of turbulence. (This is kind of parasitic loss of flow due to turbulence). 

I can also be observed for pressure when valve is fully open where there is a high pressure at the front of the plate due to stagnation and there is a low pressure wake region at the separated area behind the plate as the flow isn't able to follow the surface exactly. As the angle increases the wake gets stronger and stronger, eventually creating a region of very low pressure behind the throttle plate.

The curvature effect yields in flow being pushed outwards as discussed above, the entire poiseuille velocity profile is shifted towards outside which leads to lower pressure on inner edges of the curvature than outer edge. This can be seen at the front of throttle plate as well, especially when valve is closed at 60 degree, the curvature inner edge has much less pressure than curvature outer edge.

LINE PLOTS & DISCUSSIONS:

Mass flow rate plots:

As seen, the initial values are definately zero at both boundaries and as the simulation begins the flow actually starts through domain and information starts communicating through the cells. As the flow reaches the outlet, its mass flow rate increases an reaches an almost steady value by 2ms shown by almost zero slope of curve near there. 

This is corroborated by the velocity plot. Although initially zero, the velocity at inlet increases drastically at both the boundaries. The pressure plots also tell the same story, at the inlet static pressure drops drastically as the portion of total pressure is used to drive the flow velocity and hence the velocity increases, the same velocity is actually leading to increased total pressure at the outlet as it gets added to existing static pressure condition of 100000 Pa.

Regardless, the pressure plots corroborate a steady state the later part of simulation from 6ms to 10ms. 

The CFL which mostly limited the solution were Dt_mach and Dt_U. The convection CFL was increased upto value of 5 during simulation from 1 and was changed in between frequently. The time step per cycle graph can be observed below, notice the fluctuations when the valve moves around. As the mesh is regenerated, CFLs are computed and a limit on time step is changed for every iteration as the solution converges or diverges, this is the beauty of converge's automatic time step.

Finally the transient  detail with a video of pressure and velocity contour plot through the slice through throttle plate and wake region besides it.