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Full scale simulation of port fuel injected engine (SI8-PFI) starting from geometry cleanup to setting up different physical phenomena using CONVERGE CFD

SURFACE PREPARATION: CONVERGE CFD utilizes geometry provided in the ".stl" format, which contains a triangulated surfaces that make up the body. The geometry of the PFI engine is provided with certain geometrical errors. Some of the errors are and the methodology to correct them are listed below: 1. Intersections This…

Shrey Shah
updated on 29 Apr 2020

SURFACE PREPARATION:

CONVERGE CFD utilizes geometry provided in the ".stl" format, which contains a triangulated surfaces that make up the body.

The geometry of the PFI engine is provided with certain geometrical errors. Some of the errors are and the methodology to correct them are listed below:

1. Intersections

This problem occurs, as the name suggests, when one triangle passes through another in the imported geometry.

This problem can be resolved by moving the intersecting triangles (translation/rotation). This is done after boundary flagging (discussed later), so that only the intersecting triangles can be selected and moved. After proper boundary flagging and translation of the triangles along the normal axis, we get the following geometry without any intersecting triangles.

2. Nonmanifold Problems

Nonmanifold problems occur when an edge is shared by more than two triangles. This usually occurs in case of duplicate or wrongly created triangles.

This problem is resolved by deleting the conflicting triangles, then filling the empty area through triangle patching.

3. Open Edges

This problem arises when there are holes in the surface geometry.

This is easily resolved by creating/patching new triangles in the holes.

4. Overlapping Triangles

This problem arises when there are overlapping triangles in the geometry. This problem is not easily visible, but the Diagnosis tool of CONVERGE Studio can effectively identify overlapping triangles in the geometry.

This issue can be easily fixed by deleting one set of overlapping triangles.

5. Normal Orientation

CONVERGE Studio requires that the normals for all the triangles be pointed inwards (towards the fluid domain). The Diagnosis tool can identify Normal Orientation issues by considering the directions of normals of the neighboring triangles, since they need to be pointed in the same direction.

CONVERGE Studio provides the tool which can invert the normals of all the connected triangles propagating from one location.

After all the surface issues are resolved, the Diagnosis tool is run again to check whether there are any remaining errors.

BOUNDARY FLAGGING:

Boundary flagging is an important aspect of running CFD simulations. Proper boundary flagging is essential to apply realistic boundary conditions and assign them to proper regions in the computational domain. The boundary flagging is performed based on the guidelines provided by CONVERGE CFD to model a proper crank-angle based IC Engine simulation in the software.

1. Piston, Liner and Head

2. Spark Plug and Spark Plug Electrode

3. Intake and Exhaust Ports

4. Inflow and Outflow

5. Intake and Exhaust Valves

The valves are divided into three parts based on the guidelines provided by CONVERGE CFD:

(a) Valve Bottom - This is the part of the valve that is considered inside the Cylinder region.

(b) Valve Angle - This is the part of the valve which connects the Cylinder region to the Intake/Exhaust regions. This flagging is extremely essential to generate "disconnect" triangles during the simulation based on the valve lift profile.

SETTING UP THE FLOW PHYSICS:

Once the boundary flagging is done properly, we proceed to the Case Setup. This is a Crank Angle-based IC Engine simulation. In addition to the momentum transport, we will also be considering spray modeling and combustion modeling. The fuel that is going to be injected is iC8H18, which premixes with air before entering the cylinder. The simulation is run as a full hydrodynamic transient simulaition starting from a crank angle of $- 520^{0}$ $-520^0$ to $120^{0}$ $120^0$ .

1. Engine Parameters

Bore: $0.086$ $0.086$ $m$ $m$

Stroke: $0.09$ $0.09$ $m$ $m$

Connecting Rod Length: $0.18$ $0.18$ $m$ $m$

RPM: $3000$ $3000$

2. Regions and Initialization

(A) Region 0 - Cylinder:

Pressure: $1.85731$ $1.85731$ $b a r$ $ba r$

Temperature: $1360$ $1360$ $K$ $K$

Species Mass Fractions: Assuming stoichiometric combustion products

Reaction: $C_{8} H_{18} + 12.5 (O_{2} + 3.76 N_{2}) \to 8 C O_{2} + 9 H_{2} O + (3.76 \times 12.5 N_{2})$ $C_8H_{18} + 12.5(O_2 + 3.76N_2) rarr 8CO_2 + 9H_2O + (3.76times12.5 N_2)$

(B) Region 1 - Intake-1 (Closer to combustion chamber)

Pressure: $1$ $1$ $b a r$ $ba r$

Temperature: $390$ $390$ $K$ $K$

Species Mass Fractions:

$i C_{8} H_{18} : 0.025508$ $iC_8H_18: 0.025508$

$O_{2} : 0.20157$ $O_2: 0.20157$

$N_{2} : 0.77292$ $N_2: 0.77292$

(C) Region 2 - Intake-2 (Away from combustion chamber)

Pressure: $1$ $1$ $b a r$ $ba r$

Temperature: $370$ $370$ $K$ $K$

Species: Air

(D) Region 3 - Exhaust

Pressure: $1.85731$ $1.85731$ $b a r$ $ba r$

Temperature: $1360$ $1360$ $K$ $K$

Species Mass Fractions: Assuming stoichiometric combustion products (See Region 0)

3. Boundary Conditions

(A) Piston

Boundary Type: Wall

Wall Motion Type: Translating $\to$ $rarr$ Piston Motion

Wall Temperature: $450$ $450$ $K$ $K$

Region: Cylinder

(B) Liner and Cylinder Head

Boundary Type: Wall

Wall Motion Type: Stationary

Wall Temperature: $450$ $450$ $K$ $K$

Region: Cylinder

(C) Spark Plug

Boundary Type: Wall

Wall Motion Type: Stationary

Wall Temperature: $550$ $550$ $K$ $K$

Region: Cylinder

(D) Spark Plug Electrode

Boundary Type: Wall

Wall Motion Type: Stationary

Wall Temperature: $600$ $600$ $K$ $K$

Region: Cylinder

(E) Intake Ports 1 & 2

Boundary Type: Wall

Wall Motion Type: Stationary

Wall Temperature: $425$ $425$ $K$ $K$

Region: Intake-1 and Intake-2 respectively

(F) Exhaust Port

Boundary Type: Wall

Wall Motion Type: Stationary

Wall Temperature: $500$ $500$ $K$ $K$

Region: Exhaust

(G) Inflow

Boundary Type: Inflow

Pressure: $1$ $1$ $b a r$ $ba r$

Temperature: $363$ $363$ $K$ $K$

Species: Air

Region: Intake-2

(H) Outflow

Boundary Type: Outflow

Pressure: $1$ $1$ $b a r$ $ba r$

Backflow Temperature: $800$ $800$ $K$ $K$

Species: Stoichiometric composition (See Region 0)

Region: Exhaust

(I) Intake Valve Angle and Top

Boundary Type: Wall

Wall Motion Type: Translating $\to$ $rarr$ intake_lift.in

Wall Temperature: $480$ $480$ $K$ $K$

Region: Intake-1

(J) Intake Valve Bottom

Boundary Type: Wall

Wall Motion Type: Translating $\to$ $rarr$ intake_lift.in

Wall Temperature: $480$ $480$ $K$ $K$

Region: Cylinder

(K) Exhaust Valve Angle and Top

Boundary Type: Wall

Wall Motion Type: Translating $\to$ $rarr$ exhaust_lift.in

Wall Temperature: $525$ $525$ $K$ $K$

Region: Exhaust

(L) Exhaust Valve Bottom

Boundary Type: Wall

Wall Motion Type: Translating $\to$ $rarr$ exhaust_lift.in

Wall Temperature: $525$ $525$ $K$ $K$

Region: Cylinder

4. Spray Modeling

(A) Injection Parameters

Fuel flow rate: $7.5 \times 10^{- 4}$ $7.5times 10^{-4}$ $k g / s$ $kg"/"s$

Based on the cyclic period of $720^{0}$ $720^0$ with a $3000$ $3000$ $r p m$ $rp m$ piston, total mass of fuel: $3 \times 10^{- 5}$ $3 times 10^{-5}$ $k g$ $kg$ $= 30$ $= 30$ $m g$ $mg$

Injection start time: $- 480^{0}$ $-480^0$

Injection duration: ${191.2}^{0}$ $191.2^0$

Fuel Species: IC8H18

Fuel temperature: $330$ $330$ $K$ $K$

(B) Nozzle Positions

Nozzle Diameter: $250$ $250$ $μ m$ $mu m$

Circular Injection Radius: $125$ $125$ $μ m$ $mu m$

For Nozzle 0,

Center: $[0.0823357, 0.00100001, 0.07019]$ $[0.0823357, 0.00100001, 0.07019]$
Align Vector: ${- 0.732501, 0.210489, - 0.647408}$ ${-0.732501, 0.210489, -0.647408}$

For Nozzle 1,

Center: $[0.0823357, - 0.00099999, 0.07019]$ $[0.0823357, -0.00099999, 0.07019]$
Align Vector: ${- 0.732501, - 0.210489, - 0.647408}$ ${-0.732501, -0.210489, -0.647408}$

For Nozzle 2,

Center: $[0.0823357, - 0.0004, 0.07019]$ $[0.0823357, -0.0004, 0.07019]$
Align Vector: ${- 0.5, - 0.2, - 0.647408}$ ${-0.5, -0.2, -0.647408}$

For Nozzle 3,

Center: $[0.0823357, 0.0003, 0.07019]$ $[0.0823357, 0.0003, 0.07019]$
Align Vector: ${- 0.5, 0.2, - 0.647408}$ ${ -0.5, 0.2, -0.647408}$

The nozzle positions and directions are shown below:

5. Source/Sink Modeling

(A) Spark Ignition Parameters

Start of spark: $- 15^{0}$ $-15^0$

Duration of spark: $10^{0}$ $10^0$

Spark location: $[- 0.003, 0, 0.00915]$ $[-0.003, 0, 0.00915]$

Spark Radius: $0.0005$ $0.0005$ $m$ $m$

(B) Energy Source for Spark

Source Shape: Sphere

Source Mode: Cyclic

Period: $720^{0}$ $720^0$

For Source 0,

Energy: $0.02$ $0.02$ $J$ $J$
Start Time: $- 15^{0}$ $-15^0$
End Time: $- {14.5}^{0}$ $-14.5^0$

For Source 1,

Energy: $0.02$ $0.02$ $J$ $J$
Start Time: $- 15^{0}$ $-15^0$
End Time: $- 5^{0}$ $-5^0$

The above breakdown of the energy source ensures $0.04$ $0.04$ $J$ $J$ of energy for the first ${0.5}^{0}$ $0.5^0$ of the spark and $0.02$ $0.02$ $J$ $J$ of energy for the rest of the spark duration.

6. Combustion Modeling

Fuel Species: IC8H18

Temporal Type: Cyclic

Start Time: $- 17^{0}$ $-17^0$

End Time: $130^{0}$ $130^0$

Combustion Model: SAGE

7. Grid Control

(A) Base Grid

Base Gird Size: $0.004$ $0.004$ $m = 4$ $m = 4$ $m m$ $mm$ in all directions

(B) Fixed Embedding

For Intake and Exhaust Valve Angles (Permanent),

Scale: $3$ $3$
Embed Layers: $2$ $2$

For Cylinder (Permanent),

Scale: $2$ $2$
Cylinder Centers: $[0, 0, - 0.2]$ $[0,0,-0.2]$ to $[0, 0, 0.1]$ $[0,0,0.1]$
Cylinder Radius: $0.06$ $0.06$ $m$ $m$

For Spark Plug (Bigger Sphere - Cyclic),

Scale: $4$ $4$
Start Time: $- 16^{0}$ $-16^0$
End Time: $0^{0}$ $0^0$
Center: $[- 0.003, 0, 0.00915]$ $[-0.003, 0, 0.00915]$
Radius: $0.003$ $0.003$ $m$ $m$

For Spark Plug (Smaller Sphere - Cyclic),

Scale: $5$ $5$
Start Time: $- 16^{0}$ $-16^0$
End Time: $0^{0}$ $0^0$
Center: $[- 0.003, 0, 0.00915]$ $[-0.003, 0, 0.00915]$
Radius: $0.001$ $0.001$ $m$ $m$

For Injector (Cyclic),

Scale: $4$ $4$
Start Time: $- 485^{0}$ $-485^0$
End Time: $- 265^{0}$ $-265^0$
Radius 1: $0.002$ $0.002$ $m$ $m$
Radius 2: $0.004$ $0.004$ $m$ $m$
Length: $0.015$ $0.015$ $m$ $m$

(C) Adaptive Mesh Refinement (AMR)

Regions: Cylinder and Intake-1 (Closer to the combustion chamber)

For Velocity,

Max. Embed Level: $3$ $3$
Sub-grid Criterion: $1$ $1$ $m / s$ $m"/"s$
Timing Control: Permanent

For Temperature,

Max. Embed Level: $3$ $3$
Sub-grid Criterion: $2.5$ $2.5$ $K$ $K$
Timing Control: Cyclic
Start: $- 17^{0}$ $-17^0$
End: $131^{0}$ $131^0$
Period: $720^{0}$ $720^0$

RESULTS AND DISCUSSIONS:

1. Valve and Piston Motions

2. Injected Spray Particles

3. Temperature Distribution in Combustion Chamber

4. Pressure

5. Fuel and Product Mass Fractions

6. Calculating Compression Ratio

The plot for the volume of the cylinder region throughout the simulation is shown below:

The compression ratio of the engine can be calculated from the above plot as:

Max. Volume (Crest): $0.0005742195$ $0.0005742195$ $m^{3}$ $m^3$
Min. Volume (Trough): $0.0000570294$ $0.0000570294$ $m^{3}$ $m^3$
Compression Ratio $=$ $=$ Crest/Trough $= 10.07$ $= 10.07$

7. Need for Wall Heat Transfer Model

The entire SI8-PFI engine simulation takes a long time to run since it includes a number of physical phenomena interacting with each other - fluid flow, turbulence, injection, spark ignition, combustion, wall motions etc. Also, for the simulation only the fluid domain is modeled and the outer walls of the cylinder or the intake and exhaust ports (solid domains with thickness) are not modeled. If the solid domains are also modeled, the simulation time would increase considerably. Due to the complex physical interactions happening inside the regions and the absence of physical properties for the walls, it is not ideal to calculate the wall temperatures based on CFD alone. Hence, wall heat transfer models are used to predict the wall temperatures which is influenced by the turbulent mixing, reaction mechanisms, flame kernel hitting the walls etc.

8. Calculating Combustion Efficiency of the Engine

The heat release rate and the integrated heat release (total heat released) are plotted below:

Based on the total heat released in the combustion chamber, the efficiency of the engine can be calculated as:

Total Mass of Fuel: $30$ $30$ $m g = 3 \times 10^{- 5}$ $mg = 3times10^{-5}$ $k g$ $kg$
Lower Heating Value (LHV) of Fuel: $44$ $44$ $M J / k g$ $MJ"/"kg$
Total Heat Released (from the plot): $1241.1646$ $1241.1646$ $J$ $J$
Efficiency of the engine: Total Heat Released/Total Energy Content of the Fuel $= \frac{H R_{tot}}{m \times L H V} = \frac{1241.1646}{3 \times 10^{- 5} \times 44 \times 10^{6}} = 0.9403$ $= {HR_{text{tot}}}/{m times LHV} = {1241.1646}/{3 times 10^{-5} times 44 times 10^6} = 0.9403$
Combustion Efficiency: $94.03 %$ $94.03%$

9. Calculating Power and Torque

The engine performance calculator provided by CONVERGE CFD is used to calculate various output parameters:

From the performance calculator, work done $= 468.646$ $= 468.646$ $N - m$ $N-m$ .

The power can be calculated as "Work/Time", where "Time" is the time of the combustion $= {240.199}^{0}$ $= 240.199^0$ .

Revolutions per minute $= 3000$ $= 3000$
Revolutions per second $= 3000 / 60 = 50$ $= 3000"/"60 = 50$
Degrees per second $= 50 \times 360 = 18000$ $= 50times 360 = 18000$
Time of combustion $= \frac{{240.199}^{0}}{18000^{0} / s} = 0.0133$ $= {240.199^0}/{18000 ^0"/"s} = 0.0133$ $s$ $s$
Power: $P =$ $P =$ Work/Time $= 468.646 / 0.0133 = 35236.54$ $= 468.646"/"0.0133 = 35236.54$ $W$ $W$

Power is also defined in terms of Torque ( $T$ $T$ ) as:

$P = \frac{2 π N T}{60}$ $P = {2 pi N T}/{60}$
$T = \frac{60 P}{2 π N} = \frac{60 \times 35236.54}{2 \times π \times 3000} = 112.16$ $T = {60P}/{2 pi N} = {60 times 35236.54}/{2 times pi times 3000} = 112.16$ $N - m$ $N-m$

10. Significance of CA10, CA50, CA90

CA10, CA50 and CA90 represent the crank angles at which 10%, 50% and 90% of the combustion is completed. CA10 is generally considered as the starting point of combustion and CA90 is considered as the end point of the combustion. CA50 is the mid point of the combustion which denotes the point of maximum heat release rate from the combustion.