Week 10: Project 1 - FULL HYDRO case set up (PFI)

OBJECTIVES

1. Set up Spray modeling - Injector & Nozzles + Source modelling of the spark ignition.
2. Full Hydrodynamic Case-setup - Combustion modeling, Grid Control parameters, AMR + Fixed Embedding.
3. Combustion of the stochiometric species, Species mass fraction.
4. Plot and evaluate emissions characteristics(Nox, soot, CO, CO₂) , in cylinder pressure, volume(Comustion chamber region) and Compression ratio.
5. Plot PV diagram to calculate power and work done.
6. Plot Heat Release Rate and evaluate combustion efficiency
7. Post process to get Temperature animation and spray discrete parcels animation.

Introduction

This project deals with full hydrodynamic simulation using Combustion modelling and Spray modelling of the PFI engine  using SAGE (chemical kinetics solver). The objectives are discussed above. The emissions such as Nox & Soot produced during combustion are plotted . Performance parameters of the engine such as power, combustion efficiency, attained in the combustion chamber are evaluated. The project is started with theoretical explanation of Spray modelling process, combustion modeling , theoretical explanation of SAGE solver in Converge .

SI8-PFI  Geometry(Completely prepared from the Part 1 of the project) .The only difference visually from part 1 is the nozzle and  AMR along with Fixed embedding case setup ( addition is Source Fixed Embedding,Injector Fixed Embedding from Part 1).

 

Modelling theories in Converge with their case setup

Case-setup of FULL-HYDRO setup is explained, the spray modeling, source modeling, and additional parameters.

The boundary flagging & regions is already explained in PART1.

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 kno

wn as Sub-Grid Modelling. Lagrangian specification of the flow field is a way of looking at fluid motion where the observer follows an individual fluid parcel as it moves through space and time. Plotting the position of an individual parcel through time gives the pathline of the parcel. Heat, momentum & mass transfer occur between the discrete and continous phases via source terms in transport equations.

A parcel represents a collection of identical fuel drops that has the same properties. These parcels are introduced 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.

Below shown is the injector from which spray parcels are injected.

 Evaporation Model: The spray evaporation that takes place needs to be considered and for that converge uses certain standard pre-created models such as Frossling, Chiang, or with boiling. In this project, the Frossling model is used and it does not need to provide the particular equations as Converge takes care of it. Converge asks for evaporation source to simulate multi-component vaporization. The source used in this project is "Source all base parcel species" which denotes multi-component liquid species evaporate into the base species. As the evaporation source is specified, the maximum radius of ODE droplet heating needs to be specified as well, its basically a temperature discretization parameter which will control if drop temperature is uniform or radially varying. If the drop radius exceeds maximum value the converge assumes a radially varying temperature or else uniform temperature distribution is assumed.

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.

Spray Penetration and Distribution: Converge writes the liquid and vapor penetration lengths at each output interval, it calculates vapor penetration length for each nozzle. For each cell that meets the criteria that fuel vapor mass fraction exceeds the user-specified value or cell size does not exceed user-specified bin size, converge calculates the center of the nozzle to the center of the cell. The parcel distribution is done in two ways where the parcels are either distributed evenly throughout the cone or clustered near the center of the cone. Depending upon the requirement either distribution can be selected, for this project, even distribution is selected.

 

Penetration length

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.

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.

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.

Collision/Coalescence & Drop Drag: 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.If in a spray simulation parcels collide with parcels only in the same cell, it can lead to grid sensitivity, which is why converge has an adaptive collision mesh to reduce the grid sensitivity, Once collision mesh is checked, the parcels can collide across grid cells, requiring no additional mesh or any other setup. In this project, it is done using a standard NTC collision model & dynamic drop drag calculates the drag coefficient to account for variation in drop shape as shown in spray breakup. In the figure shown below, it is observed that parcels with collision mesh look more reasonable & natural, Othe drop options are spherical drop drag & No drop drag.

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.

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.

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. 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.

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.

Once the spray breakup, & Parcel modeling is done, Injector and nozzles need to be specified, their locations, model, radius and such. One injector can have multiple nozzles and for this project there are 4 nozzles in one injector, This is done as per the engine manufacturer's requirement based on the amount of fuels and speed at which the fuel has to be sprayed inside the chamber. The injector has a profile rate_shape.in where its rate vs crank is determined is is shown below.

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.

Fuel Mass Calculation: We need to input the total mass of fuel injected per cycle in kg.

RPM is converted to RPS (rotations per second) which is further converted to DPS (degrees per second).

From DPS we can determine the time taken for 720 deg and the mass flow in kg can be obtained.

3000 RPM = 3000/60 RPS = 50 RPS 50 RPS = 50*360 DPS = 18000 DPS

Time taken for rotation by one degree is 1/18000.

Time per degree = 1/18000 DPS = 5.55e-5 s.

Time for 720 degrees = 5.55e-5 * 720 = 0.04s

So, the total mass of fuel injected per cycle is 7.5e-4 (kg/s)* 0.04 s= 3e-5 kg

 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.

Inclusion of injector

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

Nozzle diameter = 0.00025m

Circular injection radius = Nozzle radius = 0.000125 m cone 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 chemical kinetics solver ,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. It requires a CHEMKIN-formatted input fils to solve the reaction rate ODEs. The ODE solver used is called as CVODE solver. SAGE couples with transport solver via source terms in the species transport equations. A chemical reaction mechanism is a set of elementary reactions that describe an overall chemical reaction. The combustion of different fuels can be modeled. SAGE calculates the reaction rates for each elementary reaction while the CFD solver solves the transport equations. Given an accurate mechanism, SAGE (in addition to AMR) can be used for modeling many combustion regimes (ignitions, premixed, mixing-controlled). One can use SAGE to model either constant volume or constant pressure combustion in a combustion chamber/reactor.

 

Using analytical jacobian to pass an analytically calculated jacobian to the solver. SAGE also reduces time by using multizone modeling where it groups cells into bins for which options are provided in Converge

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 will take place , then the cell may not combust at all leading to errors in 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. . Using start time and end time to limit SAGE to a specific time interval and can limit SAGE operation to a specific region.

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

 4) Using analytical jacobian to pass an analytically calculated jacobian to the solver. SAGE also reduces time by using multizone modeling where it groups cells into bins for which options are provided in Converge. 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, one needs to conserve NOx during species remap which should be checked to allow mapping based on N2 atoms and thus improve NOx predictions.

Source Modeling: Two sources are created at the same location at different times and with different intensities but others with same settings to obtain realistic ignition in the combustion chamber.

The start time of spark is just a few crank angle 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 analysing 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.

From the above sjnap, it is clear that two sources are superimposed between -15 to -14.5 deg i.e., during this duration 0.04J of energy is released due to spark ignition and for the rest of the duration i.e., -14.5 to -5 , 0.02J of energy is released due to the aftereffect of spark.

Boundary conditions are already discussed in Part 1.

Regions, Events and Importance of Ring Triangle

Each regions are assigned their own boundary conditions and are coupled with events as in this case (a cyclic & permanent events) .Also other boundary like spray modelling, combustion modelling and parcel simuilation as discussed above with setup are  created in this project. The regions are created to assign boundaries to a specific region and also to merge multiple boundaries together. Converge provides specifc valve events which reads the valve profile and automatically create disconnect triangles in the regions to block the flow path when valve is closed.

Importance of Ring Triangle:

Ring triangles are required to be created, as it is important to flag it to both the exhaust port and  intake port. They connect the valve top to the Exhaust & intake ports in all cylinders according to their position.

If the ring triangles are not set, then the respective valve tops would appear so as shown in the picture. The no ring triangle valve is the ring joined with the valve instead of the intake port and the ring triangle merged with intake port is created just like the picture above.

This is how no-ring Triangle in the cylindrical portion of the 4 valves  appears, and during the valve movements, intake valves are moved down. When they are moves down, they pull the surface of the exhaust region in a conical way instead of straight down. So without the inclusion of ring triangle when the valves moves down, the intake port region at the top of the valve is pulled down in aconical way distorting the shape which can make the conical shape portion also interact with the fuel spray which should not be the case which can give erroneous results.

Intake valve pulled down.

Grid control:

 Apart from the fixed embedding used in Part-1 further refinements are added to the Grid control.

Adaptive Mesh Refinement: Adaptive mesh refinement is a method of adapting and enhancing the grid dynamically depending upon the variation in the second-order variation of parameters. When solutions are calculated numerically, they are often limited to pre-determined quantified grids as in the Cartesian plane which constitute the computational grid, or 'mesh'.

Velocity SGS It is permanent with an embedding level of 3 for SGS of 1 m/s. Temperature SGS is cyclic with an embedding level of 3 for SGS of 2.5K after the fuel is injected into the cylinder. Time period of the combustion is the period from the spark ignition to exaust valve opening period

The formula used is as below:

Velocity-SGS

Temperature-SGS

Fixed Embedding: Apart from the fixed embedding used in Part 1 further embedding is added near the spark plug and injectors. Two level of embedding is done, one for the initial spark & another a little bigger with smaller scale of refinement to capture the initial combustion phase

Source-Fixed Embedding

Embedding- source

We can see the refinement with embedding done near exhaust value from the below figure.

Injector-Fixed embedding

 

Total Cells:

This is where we can observe how the mesh first decreased then increased. It shows how the cells are adapted according to the combustion activities and effectiveness of AMR and fixed embedding.

Cell count segregated among multiple cores.

Timing Map: The timing map is like a pathway that lays out all simulation timing details into something like process charts which displays which process is activated at a particular time. It is a handy tool to verify the activities in one place.

Post Processing Results and Discussions

In-Cylinder Pressure: The cylinder pressure contains different values at different strokes of the cylinder, max of which is seen in the combustion/Expansion stroke. This stroke is where the spark plug ignites the air-fuel mixture, creating very high pressure. This is where the engine power is generated. The peak pressure is 3.884 MPa.

Volume & Compression Ratio:

The volume vs crank angle graph plotted in the cylinder region is as shown below.

 

PV plot:The SI engine follows a typical otto cycle as can be observed from this pv plot, but the one from the simulation is an Actual
cycle PV diagram & not theoretical. However the 4 stroke processes can be understood from the ideal cycle. The Pv diagrams
were invented to improve the efficiency of engines originally

Engine Performance Calculator:

Work done  = 468.646 Nm.
 Power = Work/Time
Where, Time is the combustion duration -241 deg
RPM - 3000
RPS - 50
DPS - 50*360 = 18000
Combustion duration in seconds =`241/18000=0.01334`
Power = Work/Time = 468.646/0.01334 = 35130 W.
Torque (T) = 

Heat release rate & combustion efficiency: Heat release & Integrated heat release is plotted as shown below. It gives the amount of heat i.e., total amount of heat released from combustion process. From the total heat release in the combustion chamber, the combustion efficiency of the engine can be determined.

Combustion efficiency is defined as the ratio of total heat energy released by the burning of fuel to the total energy content of fuel mass in a cycle.

Mass of fuel injected = 3e-5 kg

Calorific value of fuel = 44e6 J/kg

Integrated heat released = 1.250 kJ

Combustion Efficiency = Integrated Heat released / Total heat energy content of fuel.

 Mean Temperature:

 This is the mean temperature inside the cylinder region. The max value reached is 2483.55 K. This data can be used to check highest cylinder temperature & utilize in liner & engine design parameters & thermal analysis.

Temperature Animation :This animation is post processed in Paraview shows the ignition time frame. The spark occuring and temperature shooting up as the combustion begins is captured..

 

Emissions:

The major cause of emissions is due to rich/lean mixtures or unburnt hydrocarbons. The emissions of concern are unburnt hydrocarbons (HC), oxides of carbon, nitrogen & sulfur and soot particles. The emissions are produced in the combustion region which is then released from the exhaust port.

Hiroy soot:

As soon as the combustion process starts Soot starts to accumulate in small quantity then shoots up when the pressure is highest then gets dissolved slightly till it reaches approx 2.5e-8 kg. These are generated in the fuel rich zones within cylinder during combustion & come out as exhaust smoke.

Comparisons of different emissions:

Spray Parcels:

Spray parcels are injected from nozzle to intake port and then to the cylinder region with the aid of the intake valve. When the spray parcels are reached into the cylinder region half of the parcels are atomized as can be seen from the figures below. Few of the parcels get trapped in the intake port before all the parcels reach the cylinder region and it was taken care by giving the appropriate initial conditions in that region.

Spray Parcels Velocity Animation: The inlet parcels in the velocity animation can be seen as they inject with high velocity . The velocity reduces when it strikes the inlet valve and then then force their way through the valve opening in a turbulent way into the combustion chamber and few of the parcels are trapped in the intake port. These parcels upon reaching the cylinder region get vaporized and combusted in the later stages and then disappears gradually.

Spray parcels with velocity streamline animation:

 

Neccessity of wall heat transfer models:

Simulated results accuracy is important to predict engine performance and hence create an efficient SI engines. Modeling of heat transfer and wall temperature is a critical and a necessary task of any engine thermodynamic model. In addition to the fluid domain, engine design needs to consider the materials of the engine. Additionally, one need to perform the CHT or thermal analysis of the engine model wherein the temperatures of the solid domains need to be predicted accurately. Wall heat transfer modeling consists of solid domain(Y+) in addition to the fluid domain there are lots of parameters to calculate There is a difference in temperature of the wall and the fluid domain which is in contact with the solid.This difference is created by wall material's thermal resistance, heat transfer coefficient, thickness, overall heat flux. In order to predict the wall temperatures, we need to use well-defined wall heat transfer models to obtain accurate results.

Significance of CA10, CA50 and CA90:

CA refers to the crank angle and the number suffixed to it represents the percentage of fuel burnt. For Eg. CA50 means crank angle at which 50% of combustion (fuel burnt) takes place. In general, CA10 represents the onset of combustion, CA50 represents combustion phasing and CA10-90 represents the burn duration.

Conclusion:

1. Spark - ignition and diesel engines are major source of air pollution & it is extremely important to keep developing methods, refining engines, creating strategies and proper analysis of parameters to build an efficient SI and diesel engine to perform complete combustion in order to reduce pollution.
2. It is critical to perform the simulation of injected spray parcels, i.e parcel modelling as well as combustion modelling in an accurate manner by assigning proper values so that it would direct the entire simulation to get accurate results.

    3. Grid control parameters like Fixed embedding and AMR with SGS are excellent case setups in converge and it should be assigned proper values as mesh that enhances the accuracy of post processed results and is a critical setup to reduce over all simulation time with advanced refinement in sensitive areas and coarse mesh in some areas which are not a matter of concern ain accordance with the results