Week 4.2: Project - Transient simulation of flow over a throttle body

Transient simulation of flow over a throttle body

Objective:

• Perform a Transient simulation of flow over a throttle body and post-process the results.

Throttle Body:

• The throttle body is a flow controlling valve used in IC engines to control the intake air and in process industries in the form of a butterfly valve. In IC engines it is placed to either increase or decrease the power and in process industries, it is used for the transportation of fluid or gases at desired rates.
• The basic principle lies behind achieving desired flow rate by rotating the plate at an optimum angle. 0 deg and 180 deg corresponds to zero and max flow rate respectively.
• They can be operated using either mechanical or electrical actuators.

Fig. (a). Throttle Valve

Geometry:

• Figure (b) shows a throttle plate located at the bend parallel to the pipe cross-section when viewed from the front. This indicated that it is positioned at 180 deg. (fully open, max. flow rate)

Fig (b). Geometry of simplified throttle body

• Fig (c). shows the triangulated geometry in converge solver and its dimensions along 3 axes.
• 

Fig (c). Triangulated Geometry

Case Setup:

Fluid Regime: Air

Simulation Type: Transient (energy equations are not solved as the temperature is not a subject of interest in this particular study)

Solver: Pressure-Implicit with Splitting of Operators (PISO), Density-based. (Generally used for high-speed flows but here it is used as its solution is more robust with respect to this solver)

Turbulence Model: RANS RNG k-ε

Simulation time parameters:

• The end time is set to 0.01s. This is achieved using the characteristic length of the geometry and the inlet velocity data obtained from steady-state simulation.

The average velocity is 130 m/s and the characteristic length is approximately 0.2m. So flow through time is given by length/velocity, which corresponds to 0.0015s. This gives the time required for a molecule to exit through the outlet. In order to capture the behavior correctly an end, time is chosen to be ten times of flow through time (i.e., 0.01s).

• The initial time step is set to 1e-09s while the final time step is 1s
• Max. convection and diffusion CFL limits are set to 1.0 and 2.0 respectively. This ensures that the flow is solved without any instability.

Setup Ref. Simulation time parameters

Boundary conditions:

Inlet: Pressure inlet-150000 Pa

Outlet: Pressure outlet-100000 Pa

Throttle Plate: Moving wall, Rotating motion

The above profile shows that the throttle body rotates up to 25 deg at 0.004s and returns back to its original state at 0.008s.

Elbow Pipe: Wall

Initial conditions: 101325 Pa

Grid generation:

• Grid size is set to 0.002m across all directions x,y, and z. The estimated number of cells is 5094 without any AMR or embedding.
• A permanently fixed embedding of scale 3 and embed layers 2 is set around the throttle body in order to capture the physics near the walls of the throttle body while in motion.

Setup Ref. Fixed embedding

Grid generated with Fixed embedding

Fig (d). Cross-sectional view of Meshed body (Left), Fixed embedding near throttle body (Right)

The above image is a mesh cross-section of the pipe with a throttle body. It is clear that the fixed embedding is performed near the throttle body as the mesh is finer around the throttle body.

Fixed embedding refines the base grid as follows : cell_size = base_size/ (2^embedding scale). So, for example, if the base grid is 0.002m, after refinement with an embedding scale of 2, cell sizes are now 0.00025m in the fixed embedding volume in layer 1 and then reduces to 0.00003125m in layer 2.

Results:

The above motion of the throttle is obtained using the discussed case setup. All the plots extracted from it are explained below.

Mass flow rate:

Inference: The above plot shows that the mass is conserved. The flow rate is initially zero and then there is a gradual rise of flow rate between 0.001 and 0.002 secs. From 0.002s onwards till 0.0045s, the flow rate into the inlet and from the outlet decreases as the throttle body starts and ends to rotate. This causes obstruction to the flow thereby reducing the mass flow rate.

Velocity: (Click here)

Inference: Mass flow rate is directly related to velocity. This is evident here when the above plot/contour is compared with the previous plot. As the flow rate decreases between 0.001 and 0.004s, velocity also decreases. And once the throttle starts returning to its original position, velocity starts to regain.

Pressure: (Click here)

Inference: In the total pressure plot (left), pressure at the inlet almost remains constant as defined in the boundary condition but pressure at the outlet fluctuates abruptly. Between 0.001s and 0.002s, the pressure increases drastically. In this time frame, velocity decreases as the throttle body start to obstruct the flow. The pressure plot (right) shows the pressure experienced by the movement of a particle from inlet to outlet. Initially, the pressure drops, then the pressure increases as the throttle body starts to abrupt the flow, and then the pressure starts to decrease further as the throttle body returns to its original position.

Cell count:

Inference: Total number of cells throughout the simulation changes with respect to time. When the valve is opened to its maximum angle assigned, the total number of cells crosses 40000. This is obvious due to the reason that when the throttle wall rotates, the fixed embedding level applied tries to capture the flow near the boundary more precisely which leads to an increase in cell count.

References:

[1] https://www.learncax.com/knowledge-base/webinar/an-insight-into-meshing-for-cfd-simulations

[2]https://www.cfd-online.com/Forums/converge/214761-time-step-embedding-scale.html