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

1. AIM:

• Simulate flow through a full open throttle butterfly valve.
• 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 stationary non-slip wall constraint with Dirichlet temperature of 300K as well.
• Timestepping and Cycles: Simulation was run for about 16000 cycles with minimum time step of 1E-09 and max of 1second. 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 while monitoring good convergence and ensuring solution doesn't blow up.

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. We have about 50000 cells in the domain with all the refinements and embedding.

3. RESULTS

As seen in the plots below, the velocity through the medium is extremely high, near sonic in certain region of flows. As one can see, after 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. Upon the throttle, the flow is slowed down due to effect of wall shear. There is a small wake region behind the throttle pivot pin as well. The stagnation region is also observed near the front of the throttle plate where air is slowed down drastically from moving stream. 

The flow on the inner curvature near throttle body is accelerated due to constriction (although minor) or throttle plate. Infact, if we take a contour plot section on the different plane than the slice we can see the air accelerating all around the throttle plate section in the image as shown.

A similiar contour plot can be observed for pressure 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. There is also a low pressure region on the inner edge of curvature especially near the throttle plate region. This is due to throttle plate constriction which accelerates flow increasing velocity and decreasing pressure as well as the curvature effect. The curvature effect yields in flow being pushed outwards, infact 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, the curvature inner edge has much less pressure than curvature outer edge.

LINE PLOTS & DISCUSSIONS:

Pressure plots:

As seen here the Inlet boundary 'total pressure' condition of 150000 Pa is reflected in the plot along with outlet boundary condition of 100000 Pa of 'static pressure' which remains relatively constant throughout the sim. At the inlet, the 'total pressure' head actually gets converted into velocity which drives the flow throughout the domain which results in drop in 'static pressure' and increase in the velocity at the inlet. 

The same velocity when reaches the outlet region, it is further accelerated due to low static pressure boundary condition at the outlet. This accelerated velocity contributes to 'total pressure' at the outlet along with already dirichlet specified static pressure which leads to increase in outlet 'total pressure'. Comparing the inlet and outlet total pressures it seems there is a drop of 20KPa due to bend and throttle valve thickness constriction. Velocity plot below makes it all more clear.

For convergence we had monitored the mass flow rate plots which show a steady values after about 10000 cycles. 

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. The time step per cycle graph can be observed below, notice the fluctuations

Finally the transient convergence of the solver can be shown in detail with a video of pressure and velocity contour plot through the slice through throttle plate.