Visualizing 2D Transient Flow Simulation Through an Elbow Duct Holding a Variable Throttle Plate Using Converge CFD & Post-processing It In ParaView

Aim:- The work is focused on simulating fluid flow using transient solver through an elbow channel duct containing a variable throttle plate. Newtonian fluid, the air is considered as the working fluid for this project. The pre-designed geometry will be exported as an STL file & modified using the various geometric editing tools available in Converge Studio. We will be also making use of boundary flagging techniques for assigning each side of the geometry to a particular boundary & these boundaries will later be assigned to a volumetric region. Next, we set up the simulation parameters using a transient based solver. Once the setup is complete, we export these inputs files generated by Converge CFD & run it using CYGWIN to generate 3D post output files. These 3D output files are first converted into either Paraview vtk inline binary format or EnSite format for Paraview to read & generate the flow field simulation. Through this simulation project, we will be able to observe flow separation near the throttle & elbow wall region by using ‘boundary embedding’. Alongside we will be visualizing the flow behavior as the throttle disk changes its angle of rotation inside the elbow duct. We will also be visualizing the pressure field & velocity flow contour throughout the elbow at various time steps to capture the physics accurately.

                                                                                                                          Fig 1:- Elbow duct with throttle disc geometry

Objective                                                                                                                                                                                                                                                                                              

The purpose of the study was to investigate the flow behavior through an elbow channel duct and visualize velocity & pressure difference around the static throttle plate by using the boundary mesh embedding technique in Converge studio. We then compare the results for the normal meshing technique with mesh embedding. Generate velocity & pressure contours mesh near the throttle plate where fluid flow separation can be observed. Plot graphs for velocity, pressure, mass flow rate at different sections of the geometry, and total cell count for all both two base mesh sizes.

Note:- While solving a CFD simulation it\'s required for us to assign a start time & an end time. This time range can then be divided into multiple time steps depending on our requirements. We use a Transient flow solver to analyze in detail each & every time step & solve the Navier stokes equation very accurately. However, the drawback being, it\'s an extremely time-consuming process when compared to a Steady-state solver simulation.

GOVERNING EQUATIONS                                                                                                                                                                                                                                                                       

 The solution for a CFD simulation is obtained by solving the Navier-Stokes (NS) equations. The NS equations comprise of 5 equations, namely the continuity, momentum (3 equations), and energy equations. The continuity and momentum equations are solved for all flow problems with the energy equation being optional and can be used only when heat transfer is taking place to save computation time. For our purpose, we will be assuming that there is no heat transfer and that the temperature is constant, leaving us with 4 equations now, the continuity, and 3 momentum equations, one for each axis direction. 

 An important property of Converge is that any geometry created or exported is assumed to be made of triangles. In boundary flagging, we group these triangles to a particular ‘Boundary’ & assign these boundaries to a ‘Volumetric region’. Defining these boundary conditions is a fundamental step in any CFD simulation as this helps solve the NS equations. Converge creates and exports ‘input’ file of these complex governing equations which are then solved by CYGWIN for running the simulation.

                                                                                                                             1. Creating the Geometry                                                                                                                                    

We start by importing an STL file of the elbow duct containing the static disc or plate. Since the geometry was created in solid works, the dimensions of the geometry are expressed in millimeters or ‘mm’ but the Converge software package uses S.I unit systems i.e. ‘meters’ & thereby assumes that the geometry imported is in meters as shown in Fig 1.1. To fix this we use the geometry editing tools available in converge, we ‘Transform’ the entire geometry by a uniform scale factor of 0.001 as shown in Fig 1.2. Since the thickness of the elbow doesn’t influence us we can delete the top surface wall of the elbow & also the edges near the inlet & Outlet port as shown in Fig 1.3 & Fig 1.4.  Once done, if we run a diagnostic test, we will get several errors in the form of ‘Open edges’ as shown in Fig 1.5. To resolve this error, we use the ‘boundary fence’ method to cover both the ends of the elbow which will be our Inlet & Outlet port of the duct as shown in Fig 1.6. Having modified the geometry, a second diagnostic test is conducted to check for any anomaly like intersection errors, nonmanifold problems, open edges, etc within the geometry contour. If no errors, which is denoted by “green checks”, then we proceed to check for the orientations of the “Normal’s” in the geometry.                                                                                                                                                                                                                                                                     

                                                                                  Fig 1.1:- Original Geometric Dimensions

                                                                                                                                              Fig 1.2:- Transformed Geometric dimensions

                                          Fig 1.3:- Deleting the top surface of the elbow wall 

                                            Fig 1.4:- Deleting the inlet & outlet edges

                                                                                Fig 1.5:- 'Open edge' error   

                       Fig 1.6:- Covering the inlet & outlet section of geometry to fix 'open edge' error

 Every geometry will have a normal vector which is perpendicular to the geometry, for this problem we use the “Normal Toggle” option to check for the direction of the normal. If the normals are pointing outside of the geometry, then it’s essential to transform these normals to point inside the geometry, where the fluid flow will occur as shown in Fig 1.7.

                                                                                         Fig 1.7:- Normal's pointing inside where the fluid flow will occur 

 In Converge, all the surface information is stored in the form of 3 entities vertices, edges & triangles. Therefore, any geometry created or exported from other CAD software (like in our case) into converge is converted into triangles & that is the fundamental entity in Converge, where every part of the geometry is assumed to be a triangle. The process of grouping these triangles into boundaries is known as boundary flagging. Each boundary is assigned with a distinct ID as shown in Fig 1.8. For our geometry, we have 4 distinct surfaces Inlet, Outlet, Elbow Wall & Throttle Plate.

                                                                                                                  Fig 1.8:- Boundary Flagging 

                                                                                                                                  2. Case Setup                                                                                                                                                                                                                                                                                                               

Having edited the geometry, the next stage of the process is to set up the simulation parameters. This step involves specifying certain properties to capture the physics of the problem perfectly, such as materials used, simulation time parameters, solver parameters, initial & boundary conditions to solve the Navier Stokes equation which are PDE’s, defining body forces, type of fluid flow, species involved & grid size of the mesh.

We start setting up the time-based general flow simulation by first defining the Materials involved in the simulation. Since we are simulation fluid (air) flow inside a channel we choose ‘gas simulation’ and our choice of fluid for this project is ‘air’, hence we choose that as our pre-defined mixture. For gas simulation parameters we will be using the Redlich-Kwong equation of state with a critical temperature of 133K & critical pressure of 3770000pa. For global transport parameters, we use the default values of ‘turbulent Prandtl number’ and ‘Schmidt number’ which is 0.90 & 0.78 respectively. Since the fluid flow is air our ‘species’ will be a mixture of Oxygen (O2) & Nitrogen (N2) with a chemical composition of 23% & 77% respectively.

The next parameter for our case setup is the Simulation Parameters, which include the ‘run parameters’, ‘simulation time parameters’ & the ‘solver parameters’. For the elbow duct with throttle flow problem, we will be running a transient flow solver at \'Full Hydro\' & \'No Hydro\' simulation mode. When we run the simulation in \'Full Hydro\' we solve the complex NS equations whereas when we run the simulation in \'No Hydro\' we don\'t expect to solve the NS equations we just visualize the mesh generation around the moving part. In addition to this, we will have to calculate the End time of the simulation manually. To do so we start by using the \'geometry bounding box\' to measure the length of the elbow duct then we check for the avg flow velocity near the inlet using Converge line plot feature, then we divide the length of geometry by average velocity. For this particular case, our length of the geometry is (0.2) & average velocity is (100), upon dividing we get (0.002) which is the Flow Throat Time which defines the time taken for the flow to go through the pipe once. We then multiply the flow throat time with the number of time steps we wish to perform. Since we wish to perform the simulation for 5-time steps we get an end time of (0.002)*(5)=10 milliseconds or 0.01 sec. Therefore for simulation time parameters, we will be running the simulation with an initial & minimum time step as (1e-06) & an end time of 0.01 sec.

As earlier, after designing the geometry, we grouped the triangles and assigned them to a particular boundary ID. Similarly, in Boundary Condition, we group the 4 boundaries & assign each of them to a volumetric region. To do so we add a volumetric region from Initial Conditions & Events & assign the volumetric region (Region 0) to each of the boundaries. These volumetric regions are required to set up the initial conditions for solving PDE\'s. Initial conditions are assigned at the volume whereas boundary conditions are given at boundaries. The Inlet & Outlet boundaries are inflow & outflow boundaries respectively. Elbow wall boundary is stationary walls with fixed surface movement following the ‘Law Of Wall’ & a temperature boundary condition of 300k which is also following the ‘Law Of Wall’. The throttle is a rotating wall & we need to specify the angle of rotation around an axis. We do so by using the \'Arc Normal\' feature from the editing tolls & calculate the arc center & arc normally by selecting any 3 vertices from the cylinder of the throttle which will be the rotation axis of the throttle. 

At the inlet boundary of the geometry, we defined a total pressure of  150000 Pa & a temperature of 300K with Air being the species. At the outlet boundary of the geometry, we defined a total pressure of 100000 pa & temperature of 300K with Air being the species if backflow occurs.

The final parameter that we need to setup is defining the Mesh that is the Base grid size. We will also be creating a fixed boundary embedding along the elbow wall & the throttle surface of the geometry as this helps in refining particular areas in the domain. For this particular challenge we will be using a mesh grid size dx = 2.0e-3m, dy = 2.0e-3m, dz = 2.0e-3m.

                                                                                                                                  4. Post Processing                                                                                                                                           

The function of Converge studio is to set up the simulation & then create several input files that are then exported to a particular folder. To run these input files we use CYGWIN, a command-line interface that reads these inputs files & solves the complex PDEs of governing equation to generate several output files. These output files are then post-converted into 3D output files which are readable files for ParaView. Since we are performing a transient flow simulation, we will be solving the NS equations at every time step, thereby it requires more time to convert the input files into post out files as compared to steady-state simulation. 

                                                                                                                            5. Results                                                                                                                                                                 

 A. Mesh With Embedding

B. Total Cells Generated

C. Pressure Contour When Throttle Disk Rotates at a 50 Degree angle inside the Cross-Section Of The Elbow Duct

D. Pressure Contour When Throttle Disk Returns To Its Original Position at 0 degree

E. Velocity Contour When Throttle Disk Rotates at a 50 Degree angle inside the Cross-Section Of The Elbow Duct

F. Velocity Contour When Throttle Disk Returns To Its Original Position at 0 degree

G. Plot Over Line For Pressure Throttle When Disk Rotates at a 50 Degree angle inside the Cross-Section Of The Elbow Duct

H. Plot Over Line For Velocity when Throttle Disk Rotates at a 50 Degree angle inside the Cross-Section Of The Elbow Duct

 I. Plot Over Line For Pressure When Throttle Disk Returns To Its Original Position at 0 degree

  J. Plot Over Line For Velocity When Throttle Disk Returns To Its Original Position at 0 degree

K. Mass Flow Rate at Inlet & Outlet

                                                                                                                                           Conclusion                                                                                                                                              

We observe that the number of mesh generated for this particular case is varying from a range of ~35000 to ~40000. This is caused due to the fact that our throttle is in motion & the mesh grid embedding is adjusting accordingly. There is an increase in the number of cells when the throttle rotates to an angle & decreases when the throttle returns back to its original position after rotation. We observe a few layers of finer mesh near the elbow wall boundary & the throttle, this was a result of using \"Boundary Embedding\" in case setup. From pressure magnitude contour, plot over line for pressure & GLYPH scale, we observe that fluid (air) enters the medium at high pressure & becomes steady near the elbow curve but as it hits the walls of the throttle we observe a sudden increase in pressure, on the side of the inlet this is caused due to the throttle rotation obstructing the path of the fluid & a region of low pressure is created on the opposite side of the throttle. This low-pressure region is caused due to fluid flow separation. This flow separation is accompanied by lower static pressure. From plot over line of pressure, we can also observe the pressure variation once the throttle body completes the rotation & then rotates back to its original position. During this period the high-pressure region was the small gap between the throttle body & elbow wall. It\'s primitive that the fluid enters the domain at high pressure & due to the throttle obstructing the crosssection of the elbow the fluid keeps settling down on one side of the duct at very high pressure while the other side is the low-pressure region. This low-pressure region starts to fill with the fluid at high pressure as the throttle starts to rotate back to its original position. Once, the throttle is set to 0-degree fluid flows over the throttle body & the pressure magnitude decreases steadily & exits the duct at low-pressure. In the case of velocity, air enters the duct at low velocity but as it encounters the throttle plate the velocity decreases as it hits the walls of the throttle but some amount of fluid escaping from the edges meets at the opposite side at high velocity. This is the region of maximum velocity when the throttle is set to a 50-degree angle. We can observe that the velocity contour magnitude increases as the throttle stops obstructing the fluid path. Hence, once the throttle is set to 0 degrees the velocity rises & escapes the domain at high speed. To conclude we observe an increase in pressure & decrease in velocity when fluid encounters the throttle plate at an angle of 50 degrees while a pressure drop & a rise in fluid velocity is observed after flow separation i.e when the throttle was set back to 0 degrees.