Spark-Ignited Port Fuel Injected Engine Simulation

Grid: A base grid of 4 mm with boundary embedding of scale 3 was used on the exhaust valve angle and intake valve angle boundaries that would help to provide a cell of 0.5 mm in the minimum lift region. Furthermore, two cylinder embeddings were created, one which would create a fine mesh near intake port-1 and cylinder head, the other cylinder embedding would create an even finer mesh in the combustion chamber. A grid scaling of -2 was selected to run the simulation on a low spec system. This completed the entire no-hydro case setup for the IC Engine. The simulation was run to see the mesh generation process and piston movement both of which can be seen below.

Full-Hydrodynamic Case Setup:This involves setting up the IC engine case so as to simulate the spray and combustion processed inside the engine. It involves setting up spray modelling where fuel parcels are introduced via injector nozzles which are then combusted through set-up of combustion modelling. To help ignite the fuel, source and sink modelling is done that would act as an energy source at the spark plug terminal. Finally the turbulence that occurs as a result of all these processes is setup through turbulence modelling. These four different modelling processes have been detailed below.

a.Spray Modelling: There are two types of spray modelling techniques that Converge uses: Gaseous and Liquid Sprays. Gaseous sprays are modelled using Eulerian solver which is the cell-centred solver. For Liquid sprays, Lagrangian Solver is used to model discrete parcels and the Eulerian solver to model continuous fluid domain. These lagrangian parcels need to be transferred to the eulerian or gas phase domain where heat, momentum and mass transfer is facilitated through source term in the species transport equations. The various links that Converge uses to get from Eulerian to Lagrangian and capture the physical processes is known as Sub-Grid Modelling.

A parcel represents a collection of identical fuel drops that have the same properties. Converge introduces these parcels into the domain of the injector which statistically represent the entire spray field. These spherical parcels need to capture the liquid sprays which they do by undergoing several physical processes:

• Primary Breakup: As soon as parcels are injected through the nozzle, it undergoes the first breakup which is known as Primary breakup.

• Secondary Breakup: These primary spray field undergoes a secondary breakup where the parcels become even smaller.

• Drop Drag: Parcels encounter turbulence which leads to the deformation of drops causing the vapourization to either become faster or slower.

• Evaporation: This further reduces the size of drops.

• Collision & Coalescence: The drops collide and breakup or they may coalesce to form larger drops.

• Turbulent Dispersion: It states how the fluctuating velocity in the gas phase affects the drop.

Spray Modelling Setup

1) Parcel Distribution- Converge assumes that injection is conical for solid cone sprays. The injector introduces parcels by either clustering them near cone center or distributing them evenly throughout the cone. By various imaging techniques it has been shown that gasoline is \'evenly distributed throughout cone\'.

2) Turbulent Dispersion- Amongst O\'Rourke, TKE Preserving Model and No Turbulent Dispersion, O\'Rourke was selected as it has been proven to work better for gasoline fuels.

3.1) Evaporation Model- It sets the rate at which the drop evaporates and the mass transfer rate gets added as a source terms in gas phase in species equation.

3.2) It is used to specify how converge simulates multi-component species. Source all base parcel species was selected where IC8H18 would be converted from liquid phase to gas phase.

3.3) Larger drops have a significant difference between the internal and external surface temperature of drops. This difference is ignored for drops of small size. Maximum radius for Ordinary Differential Equation droplet heating controls if the drop temperature is uniform or radially varying. Converge solves heat equation ODEs on the droplets by discretizing to create spherical Finite Volume Cells. Since it is time consuming, a maximum radius is specified where if the drop exceeds this value, Converge will assume a radially varying temperature and if the drop radius is small than the max value, a uniform temperature distribution will be assumed.

4) Spray Penetration: When an injector sprays the fuel, the liquid fuel on contact with the outer atmosphere vapourises. This vapourization depends on the ambient temperatures. The liquid fuel would only penetrate upto a certain length due to high temperatures inside the combustion chamber. This length is known an the Liquid Penetration Length. It is the distance that encompasses the calculated penetrated spray mass that is arrived at by multiplying the mass fraction by total liquid mass in the domain. LPL is not calculated along the spray axis of the nozzle but along the injector axis.

4.1) Just as how LPL is calculated, Converge calculates the Vapor Penetration Length (VPL) for each nozzle. The solver calculates fuel vapor mass fraction in each cell inside the spray cone. For each cell that meets the below two criterias, distance from center of nozzle to cell center of vapur mass is calculated.

• The fuel vapor mass fraction exceeds the user specified Fuel Vapor Mass Fraction.

• The cell size does not exceed the user specified Bin Size. A bin size of atleast twice the size of the cells in the spray cone must be present.

As an example, if there are 5 cells with the first 4 cells having fuel vapor mass fraction as 0.001 and the last cell having a value of 0.002. If the bin-size has been specified as 0.0015, then only the first 4 cells will be taken into account since they are within the range making the VPL as 4mm. However, if the 4th cell has 1e-5 amounts of fuel vapor mass fraction, then that will also not be taken into account leaving a VPL of 3mm instead.

5.1) Drop Collision options allows to select how the drops will interact with each other. No Collision means that the two parcels will never collide and will only pass by each other. There are two other models, O\'Rourke Numercial Algorithm and NTC Algorithm which dictate how the parcels will interact among themselves.

5.3) In a typical spray simulation, parcels can collide only with parcels in the same cell which can lead to grid sensitivity. By using an Adaptive Collision Mesh, this grid sensitivity can be reduced. It will also allow parcels to collide across grid cells.

5.4) When parcels enter through gas phase, they encounter drop-drag whose effects can be introduced in the simulation. If Spherical Drop Drag is selected, the drag co-eficient will be calculated assuming the drop is a perfect sphere. However, Dynamic Drop Drag Model is selected which calculated drag co-efficient by taking into account the influence of valocity and drag on drop shape.

5.6) Under Spray-Wall Interaction model, Wall Film was selected. This model takes a hybrid approach where the drop forms film on top of solid objects as well as encounters thermal breakup on hitting the wall.

6) After defining all the parameters for parcels, the next step was to add an injector and 4 nozzles through which the liquid fuel would be sprayed. Injector species which is IC8H18 with mass fraction of 1 was added. Rate-shape is defined that would tell when and for how long the injector sprays fuel. Converge takes the total mass of the fuel specified and total specified time. Using this data it injects the mass of fuel in that specified duration.

7) Injector Models: The constants under Kelvin-Helmholtz model control how the parcel will breakup. Stability equation or dispersion will tell how long it will take for the disturbance on a parcel to go unstable. Since this equation has been derived in a simple manner, putting these constants will help increase or decrease the time to breakup and also size of child droplets. When K-H model predicts the size of child droplets, it gets multiplied by model-size constant for further breakup.

8) Time/Temp/Mass/Size- Although injection does not continuously take place inside an IC engine, it can be lumped into Fuel Mass/cycle.

1. Fuel flow rate = 7.5e-4 Kg/second
2. Injection start time = -480.0
3. Injection duration = 191.2
4. Fuel temperature = 330K

The RPM of the engine (3000) is converted into Revolution per second (50) which is further converted into Degrees per second (18000). Using this Time/degree can be calculated (5.55E-5 sec/deg) using which the time for 720 degrees is calculated (0.04). Since fuel flow rate is known (7.5E-04), fuel mass per cycle(3E-5) is calculated by multiplying it with time for 720 degrees.

8.1) Injection pressure for gasoline engine is kept at a much lower value than diesel\'s injection pressure. This is because gasoline can be atomized easily. The injection pressure was roughly 5.48 bar.

9) Nozzle- Four nozzles were added inside the injector with the following parameters,

Nozzle diameter = 250 micro-meter

Circular injection radius = Nozzle radius

Spray cone angle = 10

Initially when the injector was created, it was placed on the spark plug by default. The following co-ordinates were used to modify the position of the injector and nozzle.

• Nozzle 0
  • center 0.0823357 0.00100001 0.07019
  • Align Vector -0.732501 0.210489 -0.647408
• Nozzle 1
  • center 0.0823357 -0.00099999 0.07019
  • Align Vector -0.732501 -0.210489 -0.647408
• Nozzle 2
  • center 0.0823357 -0.0004 0.07019
  • Align Vector -0.5 -0.2 -0.647408
• Nozzle 3
  • center 0.0823357 0.0003 0.07019
  • Align Vector -0.5 0.2 -0.647408

Combustion Modelling: Combustion facilitates the energy transfer inside an IC engine. Converge contains a detailed chemistry solver known as SAGE which is the most accurate and precise way to model combustion. The SAGE detailed chemistry solver uses local conditions to calculate reaction rates based on principles of chemical kinetics. This is used to determine phenomenon such as engine knock and emissions.

Converge computes the rate of change of species concentration/mass fraction for all the compound in the reaction mechanism file and then adds these as source terms in the species transport equations. The new species mass fraction is computed immediately prior to solving transport equation at every time step. The file is in CHEMKIN format and it is used to solve ODEs to find reaction rates. The reaction mechanism file contains detailed instructions of how reactions take place and also the values that will be used in the Arrhenius Reaction rate equation.

Combustion Modelling-Acceleration Options Since SAGE chemistry solver is 3 times slower than the transport equation solver, Converge provides a host of option to reduce the computational time.

1) Increase the Minimum Cell Temperature and Minimum Hydro-Carbon species mole fraction to reduce the number of cells in which combustion calculations are performed. If sufficied hydro-carbons are not present in the cell where combustion is supposed to take place, then the cell may not combust at all leading to erronerous results.

2) While simulating an engine, the start time for combustion should be when the spark plug ignites the air-fuel mixture or when the fuel is about to be injected. The end time should be when the exhaust valve is opening.

3) Limiting SAGE to specific Regions like combustion chamber of an engine and turning SAGE off in regions like intake or exhaust port.

4) Activating \'Use Multizone Model\' reduces the number of SAGE calculations by grouping cells into bins. These bins are created on the basis of two or more variables like equivalence ratio, temperature, pressure, reaction ratio. The average quantities are calculated and SAGE solver is invoked once per bin instead of once per cell. After solving the quantities, all cells are mapped in the bin.

5) In order for NOx emissions to not be affected by the binning, Conserve NOx during species remap must be checked to allow mapping based on N2 atoms and thus improve NOx predictions.

Source/Sink Modelling:To introduce spark plug, two energy sources need to be introduced. This energy is going to be sourced through the energy equation that is going to increase the temperature of species and in the species transport equation this temperature is going to be introduced. In the species transport eq, the source term will see the temperature change, that will affect chemical kinetics which is going to cause new products and subsequent heat release that will combe back to the species equation, produce more species, release more heat which will again show as an increase in the temperature of energy equation.

The start time of spark is just a few crank ange degrees before combustion occurs. The time is chosen to be a few degrees higher so that the solver is ready to solve the combustion process. Combustion ends when exhaust valve opens. On observing the exhaust lift profile the end crank angle of combustion comes out to be 130 degrees.

• Start of spark = -15 deg
• Spark duration = 10 deg
• Spark location = -0.003 0 0.0091
• Spark radius = 0.0005m

Reason behind two Spark Plug Source:

During the breakdown phase, more energy needs to be put in to conduct through the spark gap. Once achieved a little more energy is needed to keep the injector going. During breakdown 40mJ of energy is provided. So that is why two energy sources are introduced, one that would last 0.5° and provide 40mJ. The other would last for the remaining duration and provide 20mJ. Adding this much spark energy, it needs to be made sure that there is less numerical diffusion in those areas so that the energy when inputted stays long enough to combust the reactants. That is why fixed embedding is added.

Injector Embedding:Scale of 4 was chosen because it has been shown that when the cell is 0.25mm or less, the spray is grid independent. The nozzle length is 0.02m to provide a seed value for Temperature AMR. When the injection is about to start, cell size of 4mm will not let the calculation of 2nd order derivatives accurately. The initial refinement will allow to calculate the derivatives and then leave the rest of the calculation to Adaptive Mesh Refinement.

The image below is the Timing Map which gives a graphical representation of when and for how long different processes will occur inside the engine during the entire period.

SIMULATION RESULTS:

Parcel Simulation: The case was setup with Exhaust stroke beginning at first, followed by intake, compression and combustion. The cylinder has been marked with temperature contours and parcel with velocity.

Temperature Variation Inside Cylinder: This contour shows how temperature varies within the cylinder during the entire cycle. Meshes have also been displayed to show the effect of fixed embedding and Adaptive Mesh Refinement.

1) Compression Ratio: It is the ratio of the volume inside the cylinder when the piston is at the bottom dead center to the volume when the cylinder is at the top dead center. This can be obtained from graph by looking at the minimum and maximum volume inside the engine.

Maximum Volume displaced by Cylinder: 0.000574216 `m^3`

Minimum Volume displaced by Cylinder: 5.70298e-05 `m^3`

Compression Ratio: Max/Min= 10.0687:1

2) Combustion Efficiency: It is the ratio of total heat released during combustion to the total energy content of the fuel. Heat released is obtained from Integrated Heat Rate plot.

Combustion Efficiency ηc= `Total Heat Released/Total Energy Content of the Fuel`

From the integrated heat released plot, the total heat release is 1241.1 J.

The total heat content of the fuel = Amount of fuel x Calorific Value

Amount of fuel is = `3*10^-5`kg per cycle

Calorific Value of fuel = 44 MJ/K

Total heat content of the fuel = `(3*10^-5)*(44*10^6)` = 1320 J

Combustion Efficiency `eta_c=(1241.1/1320)*100=94.02%`

3) Power and Torque of Engine:

Work Done by the engine is extracted from \'engine performance calculator\' by importing thermo.out file for cylinder region.`

Work done came out to be 468.646 Nm.

Power= Work Done/Time Taken

• Conversion of RPM to Time per degree

RPM of engine= 3000

Revolutions/second= `3000/60=50`RPS

Degrees Per Second= `50*360=18000`

Time Per Degree= `60/(360*3000)=5.55*10^-5` sec/deg

Time for moving 240.2°= `5.55*10^-5*240.2=1333.11*10^-5=0.01333`sec/cycle

Power= `468.646/0.01333=35157.24`W

•Power=35.16 kW

•Torque Calculation:

`P`=`(2*pi*N*T)/60`

`T=(P*60)/(2*pi*N)`

`T=(35.16*60)/(2*3.14*3000)`

Torque of Engine=111.97 Nm

4) Emissions: The major pollutants emitted in the combustion of gasoline in an Internal Combustion engine are Hiroy-Soot, Carbon Monoxide and NOx. Exhaust after-treatment systems like catalytic converters are used to minimize the emission of these pollutants into the atmosphere.

Hiroy Soot: About 7.5E-08 kg of Hiroy Soot has been produced during the combustion process.

Carbon Monoxide:

This pollutant is mainly produced due to incomplete combustion which produces CO instead of CO2. 1.1E-05 kg of CO was produced. Among the three pollutants, CO was produced in the largest amount.

NOx: 1.3E-06 kg of nitric oxide was produced.

5) Liquid Spray Drops: This plot gives the number of active lagrangian parcels in the domain throughout the cycle. Parcels drop because of vapourization and combustion takes place. Zero parcels indicate no unburnt hydro-carbons. The parcels have been timed to be introduced during intake stroke which is shown as a surge in the number of parcels inside the combustion chamber from the plot below.

6) Significance of CA10, CA50, CA90

CA10- It is the crank angle at which 10% of the fuel has been burnt or the heat rate is 10% of cumulative HR. Its value is 6.83717°

CA50- It is the crank angle at which 50% of the fuel has been burnt or the heat rate is 50% of cumulative HR. Its value is 18.4623°.

CA90- It is the crank angle at which 90% of the fuel has been burnt or the heat rate is 90% of cumulative HR. Its value is 31.701°.

7) Necessity of Wall-Heat Transfer Model- In Computational Fluid Dynamics, Thermal wall function models are used to calculate wall temperature. The assumptions made in the model lead to the model underpredicting wall heat losses as compared to experimental measurements.

The assumptions made in thermal wall function model includes:

1: Flow is parallel to the chamber walls with negligible flow normal to the walls
2: Quasi-steady flow with negligible transients
3: Constant density and transport properties in the boundary layer
4: High Reynolds number flow, very thin laminar shear layer
5: Zero pressure gradients along the flow
6: No combustion and chemically inert mixture

None of the following assumptions can be met with engines. The flow is neither one dimensional nor steady. Assumption three is perfectly invalid, because of large thermal gradients within the boundary layer. Hence, we need non-equilibrium models to predict wall temperatures accurately. Some of the wall heat transfer models include Angleberger model, Werner Wengle model, etc.

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