Steady-state simulation of flow over a throttle body
Steady-state simulation of flow over a throttle body
The present project consists of a steady-state simulation of a throttle body using converge CFD software. The throttle body consists of a butterfly valve to let the fluid inside the throttle. The geometry of the throttle body and the valve are shown in figure 1.
Fig 1: throttle body and valve
The model imported from the design software is cleaned for simulation. Firstly, the simulation is carried for two different mesh conditions and analyzed with respect to the velocity profile at the outlet of the flow. Once the mesh is refined well, the simulation is carried out for different CFL no and checked for stability and analyzed with respect to mass flow rate. Since the flow is steady, the throttle valve is stationary.
Boundary conditions:
Inlet: Inflow pressure boundary condition: 0.15 Mpa
Outlet: Outflow pressure boundary condition: 0.1 Mpa
Throttle valve: Stationary wall
Elbow body: Wall
The difference in the pressure between the inlet and the outlet boundary condition drives the flow. Air is used as a fluid with O2 and N2 mass fraction being 0.23 and 0.77. The temperature is maintained at 300 K.
Meshing:
Meshing technique used by Converge studio is called as \"Cut cell cartesian method\" or \"Adaptive grid refinement\" method. This makes sure that the geometry details are not loosened even when the mesh is coarsened, which represents that even the base grid is coarse, the mesh can be refined automatically in the regions where its needed to capture the flow. In the software, this can be done using a technique called Fixed embedding. In the present problem, we need to make sure that there are more cells present near the throttle valve. This gives accurate results.
Fixed embedding:
Embedding refers to local mesh refinement. In our problem, the embedding is done to the throttle valve with the following conditions.
Embedded layers: 2
Mode: Permanent
Scale: 2 for coarse, 3 for fine mesh
Scaling refers to the multiplication factor the mesh. In our case, the base grid for the entire domain is 2e-3 in all x, y and z directions. For the throttle valve, after scaling, the mesh on valve boundary scales to 4e-3 for coarse mesh and 6e-3 for the fine mesh. Below figures represent the coarse and fine mesh near the throttle. The difference can be visualized easily.
Fig 2: Coarse mesh (Scale: 2)
Fig 3: Fine mesh (Scale:3)
The base mesh of 2mm for the entire body is shown below. In the figure, the mesh for the throttle valve is refined.
Fig 4: Base grid of 2mm
The total cells for coarse and fine mesh are represented below.
Sl.no Mesh Total cells
1. Coarse 16014
2. Fine 41454
Time parameters:
The simulation is run for 15000 steady cycles starting from zero. The simulation uses pressure based steady solver as the flow solver with the PISO algorithm. The initial/minimum time step is taken as 1e-09. This lower time step is taken because of the dynamic time stepping algorithm is done by converge software. Once the initial and boundary conditions are correct, the converge makes sure that the time-step value is updated for each time step as the flow progresses. This makes sure that at each time-step, the flow parameter values are accurate.
Three types of CFL conditions are used in Converge software being, convection CFL which is the basic CFL for all flow. Diffusion CFL which is known as Viscosity CFL since it uses viscosity as an added value, used for the flow with high viscous layers and Mach CFL which uses Mach no. In the present problem, only convection CFL is changed for different cases. The simulation is run for 0.5, 1.0 and 1.5 CFL cases with diffusion and Mach CFL being constant. The flow is then visualized by mass flow rate at inlet and outlet.
Result:
The simulation is run parallelly. The converge uses MPI programming to parallelize the solver, which means that the solver is equally distributed to given no of processors in the working computer. In the present problem, the solver is run with 4 processors which equally distributing the cell structure to each of the processors since the flow is steady.
Figure 5 represents the outlet velocity profile for different meshes.
Fig 5: Outlet velocity profile
Although the velocity is converged for both the cases, there is some slight difference during the flow. Since the domain is simple this velocity change is small. This change in values due to mesh effects majorly in the complex structures. Figure 6 represents the velocity flow over the domain and figure 7 represents the pressure variation on the throttle valve due to the velocity.
Fig 6: Velocity profile
Fig 7: Pressure profile on the throttle valve
From fig 7, we can observe that as the flow hits the valve, high pressure is created showing red in color, and less pressure on the opposite side of the flow. This represents that the flow physics is correct and can be continued with further analysis.
Mass flow rate:
The CFL condition is measured using velocity, space, and time-step giving the equation as:
CFL = u*dt/dx.
If the CFL value is too high, it leads to unstable results and if it is too low, it takes more computational time to evaluate the flow. Figure 8 and 9 represents the mass flow rate for outlet and inlet flow for different CFL numbers for fine mesh condition.
Fig 8: Outlet mass flow rate
Fig 9: Inlet mass flow rate
Firstly, we can observe that the mass flow rate satisfies the continuity equation in all the CFL cases. The variation in the mass flow rate can be easily observed in all the cases. For CFL 0.5, the mass flow rate takes more amount of cycles to converge than other two CFL conditions. This gives accurate results throughout the flow but with more computational time. The CFL with 1.5 value converges faster and might not capture the flow parameters at accurate at certain locations. For complex flow, this may lead to unstable results. The CFL with 1.0 gives ideal result in convergence and stability. Although, these variations are smaller, an ideal CFL value depends on the flow domain and flow characteristics.