Week-11 : Discretization of 3D intake manifold using GEM-3D

Discretization : The numerical solution of differential equations cannot produce a continuous distribution of the variables over the solution domain, thus the aim instead becomes to produce a set of discrete values at a number of nodes that cover the solution domain. There are three popular methods to discretize

1. FDM ( Finite Difference Method ) 2. FEM ( Finite Element Method ) 3. FVM ( Finite Volume Method ).

1. CASE STUDY (Varying discretizing length) ON CI ENGINE (single-cylinder) :

• The study is done on this single-cylinder diesel engine

Discretization Length:

• Approximate length of each sub-volume where solution quantities (pressure, temperature, mass fractions, etc.) are calculated.

Case setup :

Plots comparision :

1.

2.

3. Time elapsed

• We can clearly observe from above tables that there is variation in values i.e. error is found if discretizing length is more. This owes to inaccuruacy of solver assuming the flow and changes to be similar across varying lengths of intake pipe. Hence, discretizing is must when accuracy is required.
• Further, there is significant increase in time taken to perform simulation as discussed earlier ∆t ∝ ∆x, the discretized element length shouldn't be unnecessarily small as it increases the time step and shouldn't be of higher value to not capture the results accurately.

2. DISCRETIZATION OF INTAKE MANIFOLD

1. Import the STL file Plenum to GEM 3D to perform discretization.

2. To divide into components we have to first discrete them using separate by curves method. Below is the image depicting dividing into different parts where there is abrupt changes in area.

3. As the fluid enters and exits the pipe from intake and though the runners, openings are made then

4. We proceed next to distinguish intake runners of runners from plenum from the outlet by using a 3-points cutting plane. Care must be taken that the cutting plane doesn't cut off the plenum.

5. Now converting the intake-pipes(runner) into pipe of equal radius. i.e. Fig.1 to Fig. 2

Fig. 1 Fig. 2

ii. Also converting for outlet runners

Fig. 1 Fig. 2

6. For better transitional flow from manifold to runner we need to add orifice connection manually using Add Connection with a forward discharge coefficient of 0.95.

ii. Further define the extension i.e. outlet from runners

7. Further, more cuts are performed near the intake-manifold to obtain a proper discretized model

8. These shapes are converted into proper components and connections are added.

9. Then the pleunum is divided into components to easily identify the flow into runners.

10. Using Flow connection tool gaps are repaired so as to avoid uninterrupted fluid flow. Upon the selection of tool it previews where they are to be repaired.

11. Using the export-GT model discretize it with custom setting as shown an open in GT-ISE model. After properly arranging the circuits we get the final connection.