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

Aim:

To perform transient simulation of flow through an elbow pipe containing a moving throttle valve.

Objectives:

• Generating appropriate moving mesh for capturing the flow physics around the moving throttle valve by providing suitable boundary conditions, scaling for the mesh and embedded boudnary layers using CONVERGE Studio.
• Setup a case transient case for flow through elbow pipe with moving boudnary conditions for the throttle valve using CONVERGE Studio.
• Post Process the simulation results by generating line plots and contours for the primitive variables such as velocity and pressure using CONVERGE Studio and Paraview.

Theory:

The throttle valve operates by obstructing ("throttling') the fluid flow in a channel to control the flow rate. It is one the most common and easily implementable flow control devices used in industries where handling the fluid flow is of crucial importance. The device working principle is based on the position of the valve which can vary from providing virtually zero obstruction to completely chocking a pipe.

In the current study, we simulate flow through an elbow pipe containing a butterfly throttle valve. The mechanism which obstructes the flow in butterfly valve is a circular disk. Although the model is quite simplistic in design, it proves to be a useful model for understanding the effect of the closing mechanism (circular disk) on the flow. An interested reader is referred to the respective Wiki articles on Butterfly valve and other standard throttling devices for further details.

Geometry:

The geometry consists of an elbow pipe of diameter ~0.017m and arc length of the pipe as ~1m. The butterfly valve is modelled by a circular disk which is not connected to the pipe walls is approximately ~0.014m. After loading the STL file and repairing the geometry using CONVERGE Studio's inbuilt functions, we flag the boudaries and provide them with appropriate jargon used by CFD practitioners.

The appropriately boundary flagged geomtery's cut section view is as follows. The geometry clearly highlights the presence of the throattling valve (circular disk) inside the fluid domain (elbow pipe)

Case Setup:

The case setup for the current study is carried out using the CONVERGE Studio Case Setup GUI. The following settings have been chosen for the simulation in the respective subtree

• Application subtree:
  • Due to the relatively simple nature of the model, the Time based application was selected
• Materials subtree:
  • Predefined mixture of standard air with gas simulation default settings was used.
  • The global transport parameters were set to default values
  • The standard air consists of oxygen and nitrogen species which are assumed to be non-reacting mixtures.
• Simulation parameters subtree:
  • Fully compressible transient simulation with full hydrodynamic capacity is used for the simulation.
  • A steady state monitor was set for the velocity at the outlet to stop the simulation after 8 milliseconds, if a steady state is achieved. The sampling size for the monitor was chosen to be 0.5 milliseconds and the absolute tolerance was set `10^{-4}` as the convergence criteria
  • From steady state analysis, we concluded that the charactertistic length of the domain was 0.2 m and the average velocity at the outlet was 80 m/s, which gives the flow time as 2.5 milliseconds. For the current simulation, 10 milliseconds was chosen as the total run time and an adaptive time stepping scheme based on convective and diffusive number was chosen. The initial time step was chosen as 1 nanosecond and the minimum and the maximum time step for the simulation was chosen to be 1 nanosecond and 1 second respectively.
  • A standard density based PISO algorithm was chosen as the Navier-Stokes equation solver with default settings
• Boundary Conditions subtree:
  • Inlet: Pressure = Total pressure of 105000 Pa (1.05 bar), Velocity = Zero Normal Gradient, Temperature = Fixed value of 300K, Species = Standard Air, Turbulent kinetic energy and turbulent dissipation = default values
  • Outlet: Pressure = Static pressure of 100000 Pa (1 bar), Velocity = Zero Normal Gradient, Temperature = Backflow value of 300K, Species = Backflow value of Standard Air, Turbulent kinetic energy and turbulent dissipation = default values
  • Pipe Wall: Pressure = zero normal gradient, Velocity = Law of the Wall (stationary), Temperature = Law of the wall with wall temperature as 300K, Turbulent kinetic energy = zero normal gradient and Turbulent dissipation = Wall model
  • Throttle Body: Pressure = zero normal gradient, Velocity = Law of the Wall (Rotating about the throttle valve axis calculated by providing a rotation center and surface normal), Temperature = Law of the wall with wall temperature as 300K, Turbulent kinetic energy = zero normal gradient and Turbulent dissipation = Wall model
• Initial Conditions subtree:
  • Fluid domain is initialized by filling it standard Air with zero velcoity, temperature of 300K and pressure set at 1.05 bar.
• Physical Models subtree:
  
  • For the current simulation, Re-Normalized Group Reynolds Averaged Navier Stokes model with default settings is chosen
• Grid Control subtree:
  • The base grid settings for cell dimension is set to 0.002m in all directions.
  • A fixed embedding is provided on the throttle body which is permanent. The scale and the embedding layers is set to 3
  • The cut section of the mesh which includes the throttle device and a close up of the embedded layers is illustrated as follows

Simulation Results:

The animation of the velocity contour for the entire simulation: Animation link

The contours and the line plots generated using Paraview and Converge Studio are as follows

Velocity contour at time t = 0.5 milliseconds

Velocity contour at time t = 2.0 milliseconds

Velocity contour at time t = 4.0 milliseconds

Velocity contour at time t = 6.0 milliseconds

Velocity contour at time t = 8.0 milliseconds

Pressure contour at time t = 0.5 milliseconds

Pressure contour at time t = 2 milliseconds

Pressure contour at time t =4 milliseconds

Pressure contour at time t =6 milliseconds

Pressure contour at time t =8 milliseconds

Maximum, minimum and average pressure in the fluid domain

Mass flow rate at the inlet and outlet

Variation of total number of cells in the domain and number of cells assigned to 4 processors

The difference of sample mean of 0.1 milliseconds and current average of velocity and standard deviation of velocity at the outlet

From the above contours and line plots we can make the following obseravtions:

1. The average mass flow rate at the inlet and average mass flow rate at the outlet is equal for almost entire simulation time. From this, we can conclude that the results obtained are valid theoritically since they uphold the conservation principles
2. From the pressure and velocity contour and the cell count line plot, we can conclude that the throttle valve indeed rotate between the time interval of 0 to 2 milliseconds and 4 to 8 milliseconds and remain stationery for rest of the time
3. The minimum pressure curve in the pressure line plot and the pressure contour show us that there is significant pressure drop between the valve when it as 25 degrees angle which is along the trends of our expectation.
4. After 8 milliseconds, the valve is at the original position and from the steady state monitor, we can conclude that the pressure drops are minimal and the solution moves towards a steady state.

Conclusions:

From this project, we have noted how to setup a case and perform transient simulation with a moving geometry component. We have also used advanced post-processing in Paraview and CONVERGE Studio to interpret the simulation results so that we can verify and validate with theoritical results.