MULTI DIMENSIONAL SIMULATION OF A PORT FUEL INJECTION ENGINE

OBJECTIVE:

                 To perform Boundary flagging and surface preparation in spark-ignited port fuel injected engine.

                 To setup and run No-hydrodynamic simulation.

                 After running the simulation using No-hydro solver, Full hydrodynamic simulation is perfomed in Spark Ignited PFI Engine.

INTRODUCTION:

                 A spark-ignition engine (SI engine) is an Internal Combustion Engine, generally a petrol engine, where the combustion process of the air-fuel mixture is ignited by a spark from a spark plug.The working cycle of both spark-ignition and compression-ignition engines may be either two stroke or four stroke.A four stroke spark-ignition engine is an otto cycle engine. It consists of following four strokes: suction or intake stroke, compression stroke, expansion or power stroke, exhaust stroke. Each stroke consists of 180 degree rotation of crankshaft rotation and hence a four-stroke cycle is completed through 720 degree of crank rotation. Thus for one complete cycle there is only one power stroke while the crankshaft turns by two or more revolutions.

                Port fuel injection (PFI), injects fuel into the intake ports just upstream of each cylinder's intake valve, rather than at a central point within an intake manifold.

Boundary Flagging:

                           From the given PFI geometry we have flagged the boundaries and it is grouped as regions. There are four regions namely Intake region_1, Intake region_2, Cylinder region, Exhaust region.

 

 NO-HYDRO SETUP:

                          Before running the full hydro setup, to clean the setup and to check the boundary flagging and initial conditions in No-hydro condition is easy and it is basically used for testing the setup.

                         IC Engine - Crank angle based is selected under application type.  

                                   In gas simulation therm.dat file and in reaction mechanism mech.dat files are imported.

                                   In Simulation parameter, under run parameter No-Hydrodynamic solver is  selected and in Simulation time parameter the starting time of the crank angle is -480 deg and the end time is 240 deg.

                                   In this simulation, exhaust valve will open first due to the starting time of -480 deg and this runs till 720 deg.                                                                    

STOICHIOMETRIC CALCULATION:

                                    When iso-octane reacts with air in the combustion chamber and produces a stoichiometric reaction in which carbon-di-oxide, water and nitrogen are the products. In Converge, Mass fraction of these values are given as inputs so it is calculated.

          `C_8H_18 + 12.5(O_2+3.76N_2) -> 8CO_2 + 9H_2O + (3.76*12.5) N_2`

         

REGIONS AND INITIALIZATION:

          Intake port_1 - IC8H18 - 0.025508

                                 O2 - 0.20157

                                 N2 - 0.77292

                                 Temperature - 390 K

                                 Pressure - 1 bar

          Intake port_2 -  Air

                                  Temperature - 370 K

                                  Pressure - 1 bar

         Cylinder region - Stoichiometric composition

                                  Pressure - 1.85731 bar

                                  Temperature - 1360K

         Exhaust region - Stoichiometric composition

                                  Pressure - 1.85731 bar

                                  Temperature - 1360K

BOUNDARY CONDITIONS:

                     

1. Piston - temperature - 450K; Wall motion type - Translating; Surface type - Moving - Piston motion
2. Liner temperature - 450K
3. Head temperature - 450K
4. Spark Plug temperature - 550K
5. Spark Plug electrode temperature - 600K
6. Exhaust ports temperature  - 500K
7. Exhaut outflow - Pressure - 1 bar;  temperature - 800k; species concentration - stoichiometric conditions
8. Exhaust valve top - temperature - 525K; Wall motion type - Translating; Surface type - Moving - exhaust_lift.in
9. Exhaust valve angle - temperature - 525K; Wall motion type - Translating; Surface type - Moving -exhaust_lift.in
10. Exhaust valve bottom - temeprature - 525K; Wall motion type - Translating; Surface type - Moving -exhaust_lift.in
11. Intake port_1 - temperature 425K;
12. Intake port_2 - temperature 425K;
13. Inflow - pressure - 1 bar total pressure; temperature - 363K; species - Air
14. Intake valve top - temperature - 480K; Wall motion type - Translating; Surface type - Moving - intake_lift.in
15. Intake valve angle - temperature - 480K; Wall motion type - Translating; Surface type - Moving - intake_lift.in
16. Intake valve bottom - temeprature - 480K; Wall motion type - Translating; Surface type - Moving -intake_lift.in

EVENTS:

          

     Events were created among combustion chamber, intake and exhaust ports. Disconnect traingles are created between the regions when there is no flow and also it regulate the flow between these regions during the piston movement.

DISCONNECT TRIANGLES:

     In an actual engine, periodically the port and the valve are in contact, which prevents the flow between these part of the engine.

    To control the flow while avoiding intersecting triangles, CONVERGE adds or removes virtual triangle (disconnect triangle) at user specified times(Events)

    There are two types of diconnect triangles. 

         1.SINGLE LOOP DISCONNECT TRIANGLE - At an edge that belongs to two boundaries that are in different regions.

          2.CONCENTRIC CIRCLE DISCONNECT TRIANGLE - From one set of edges to another. Each set of edges demarcates two different regions.

 When disconnect triangles are activated ( i.e, when the inter region flow is stopped) the disconnect triangles have a symmetry boundary condition.

 Disconnect triangles are two sided(i.e, fluid on both sides)

  In an IC Engine, CONVERGE uses concentric circle disconnect triangle to control the flow between cylinder and the port regions.

GRID CONTROL:

Base grid is 5mm and fixed embedding of scale 4 is used in both Inlet valve angle and Exhaust valve angle embedding to prevent cell pairing. Addition with two embedding, Big cylinder embedding is used with scale of 1 and cylinder radius of 0.05m which creates a finer mesh in the combustion chamber.

NO HYDRODYNAMIC IC ENGINE FLOW:

NO-HYDRO FLOW

                  From this flow we can clearly see the piston and valves movement. Thus the spray and combustion process can be setup and full hydrodynamic simulation can be done.

FULL HYDRO CASE SETUP:

                               In this case, the entire IC engine flow is simulated with the spray modelling and combustion process. In the spray modelling fuel parcles are sprayed through injector nozzles in the Intake port and combustion takes place in the combustion chamber. The fuel is ignited at the spark plug terminal by source/sink modelling which generates energy source to the terminal and the spark plug.

SPRAY MODELLING:

                               Converge can model both gaseous and liquid sprays. It includes state of art models for spray process including liquid atomization, drop breakup, collision and coalescence, turbulent disperion and drop evaporation.

                              For gaseous spray converge uses Eulerian solver, which set the species mass fractions and mass flow rate at the Inflow boundary.

                              For liquid spray converge uses Lagrangian solver to model discrete parcels and Eulerian solver to model continuous flow domain. Heat, momentum, mass transfer occur between the discrete and continuous phases through sorce terms in the transport equations.

                           

 

                               Parcel is a group of identical drops with same velocity, temperature and radius. It is collection of drops into domain at the injector.

                               Converge solves for radius, velocity etc on per parcel basis rather than per drop basis because the drops in parcel are identical.

                               Parcel undergo several physical process

                               

When fuel injection takes place due to surrounding air there willl be drag force and causes a distance. When the distance propogates and causes spray to breakup.

                              1. Primary breakup - when fuel injection takes place the liquid breaks up into tiny parcels, this is known as primary breakup.

                              2. Secondary breakup - These tiny parcels can go ahead and break further it is known as secondary breakup.

                              3. Drop drag - These spherical drops interact with ambient air and due to this their shapes may get affected which would result in faster or slower vapourisation that may result in drop drag.

                              4. Evaporation - The rate at which radius of the drop decreases is due to Evaporation.

                               5. Collision and coalescence - The drop may collide and it will reduce in size or the drop may coalesce to form larger drops.

                               6. Turbulent dispersion - It explains about how does the fluctuating velocity in the gas phase affects the drop.

 

SPRAY MODELLING SETUP:

                              

Parcel distribution - For solid cone sprays, Converge assumes the injection is conical. For gasoline engines, 'Parcels evenly throughout the cone' is better than the 'cluster parcel near cone centre'.

            

Turbulent dispersion - O'Rourke model is better in gasoline engine than the tke preserving model and No turbulent dispersion.

EVAPORATION MODEL - It defines the rate at which radius of drop shrinks and rate at which mass is being transferred. Frossling model is used here.

EVAPORATION SOURCE - "Source all base parcel species" is used which means, IC8H18 liquid fuel is converted into IC8H18 gaseous fuel. We are converting it into gas phase because gas phase chemistry are captured accurately with this species

                                          'Source specified species' evaporates according to specified species. 

                                          'Source all composite parcel species' is used when there is two species involved.                              

RADIUS ABOVE WHICH 1D HEAT DIFFUSION WILL BE SOLVED - It will control the drop temperature wheather it varies uniform or radially. Maximum value is maintained in order to maintain uniform temperature distribution. If the value is maximum Converge will automatically consider as Uniform distribution and if the value is minimum then it wil consider as radially varying temperature distribution.

LIQUID MASS FRACTION FOR CALCULATING SPRAY PENETRATION - When fuel injection takes place some of the fuel may vapourize if the ambient temperature is high. The fuel will penetrate into the combustion chamber upto certain length due to the high temperature in it. This length is known as Liquid Penetration Length. Converge calculates the penetrated spray mass by multiplying the mass fraction by total liquid mass in the domain. Liquid penetration length is not calculated based on the spray axis of the nozzle, it is calculated based on the injector axis. In this example, the mass fraction of the liquid fuel is 0.98 left side bar indicates the LPL.

 

BIN SIZE FOR CALCULATING VAPOR PENETRATION & FUEL VAPOR MASS FRACTION FOR CALCULATING VAPOR PENETRATION - Converge calculates vapor penetration length for each nozzle. The recommended bin size is to be twicethe size of cells in spray cone. Converge calculates the fuel vapor mass fraction in each cell inside the spray cone. It calculates the distance from the centre of nozzle to centre of cell. The fuel vapor mass fraction exceeds the user specified fuel vapor mass fraction.

USE COLLISION MESH - In a typical spray simulation, parcles can collide only with parcels in same cell which lead to grid sensitivity. Using collision mesh will lead parcel to collide across grid cells, this feature is independent of gas phase grid and used only for collision calculations.

DROP DRAG MODEL - Dynamic drag model is the advanced method because the drop coefficient calculation accounts for variation in the drop shape. This model invokes the TAB model to determine the drop distortion. This model is mostly preferred.

 

SPRAY WALL INTERACTION MODEL - Wall film is selected because the drop actions are calculated with a hybrid approach based on particle based quantities or film based quantities.

INJECTOR - After setting up the parcel, injector and four nozzles are created for liquid fuel to be sprayed. IC8H18 is the parcel species and mass fraction of 1.0. Rate shape tells us that how does the injector sprays the fuel. Converge takes the total mass of the fuel and the total specified time.

                  KH-RT model is used because they are preferrable for solid cones and LISA model is used for hollow cones. TAB model is a legacy model and mostly it is not used. 

                  The values in KH model control how does the parcel breakup. Stability equation or dispersion will tell how long it will take for the disturbance on the parcel to go unstable.

             

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 is 3000, by converting it into revolution per second we get 50, by further converting  into degree per second we get 1800. From this we can calculate time per degree, it is 5.55556E-05. Time per 720 degree is 0.04. Now, Fuel mass per cycle is calculated by multiplying fuel flow rate(7.50E-04) and Time per 720 degree(0.04). The obtained fuel mass per cycle is 3.0E-05.

NOZZLE:

              Four nozzles were created in the injector with these parameters

Nozzle diameter = 250 micro-meter

Circular injection radius = Nozzle radius

Spray cone angle = 10

• 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 in an engine. Converge contains a detailed chemistry solver and simplified combustion models. SAGE detailed chemistry solver is most predictive and accurate way to model combustion. It also accurately model ignition and laminar flame propagation. Simplified combustion models are generally less computationally expensive and predictive than SAGE. It may provide acceptable results for specific applications.

COMBUSTION TEMPERATURE CUTOFF & MINIMUM HC SPECIES MOLE FRACTION - Increase in the cell temperature and minimum hydrocarbon species mole fraction to reduce the number of cells to perform combustion. If enough hydrocarbons are not present in the cell incomplete combustion can take place.

START TIME & END TIME - The combustion starts certain angle before the spark begins and  the end time is when the exhaust valve opens.

TURBULENCE MODELLING:

                    Turbulence is the stste of chaotic and unstable fluid flow - opposite to laminar flow.

                    Largest turbulence length scales in IC engines ranges from 0.1 to 1mm.

                    During combustion, turbulence corrugates and stretches the flame surface area on which reactions occur causing faster burning due to increased flame surface and faster extinction due to overstretching of flame surface.

                    Re, quantifies turbulent level in a system. It is the ratio of inertial forces to viscous forces. The higher the Re, the more chaotic the turbulence. For flow to be turbulent, Re must be greater than critical value. For IC Engines, the flow is almost always turbulent.

  Turbulence modelling for IC Engine - In non-premixed(fuel spray) regions, combustion depends on the rate of fuel-air mixing. Turbulence increases the rate of mixing( although mixing would require cells of order 1e-6m). 

                                                       In premixed engine, the turbulence wrinkles the flame front, which enhances the burn rate. We must resolve the laminar flow thickness(order 1e-5m) to accurately model diffusion and predict the proper flame speed.

                                                       These length scale cannot be resolved with current IC engine simulation capabilities. Thus we need turbulence model.

    RANS - REYNOLDS AVERAGED NAVIER STROKES solves equations for an time averaged velocity field and magnitude of turbulent fluctuations.                   

                             

SOURCE/SINK MODELLING :

                                            Two energy sources are setup. The energy is developed in this through energy equations which will increase the temperature of the species and in species transport equation this temperature is applied. In the species transport equation, the source term will see the temperature change, that will affect the chemical kinetics which is going to cause new products and equal heat release that will come back to the species transport equation and produce more species, release more heat which will again show as an increase in temperature of energy equation.

     

 

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

REASON BEHIND TWO SPARK SOURCE:

 

      One energy source will provide 20mJ only for 0.5 degree and 10 degree 20mJ is provided by another energy source. This means that for first 0.5 degree 40mJ is provided. By giving this much energy we have to make sure that there is less numerical diffusion in those areas such that it can stay for long enough to combust the reactants. For this fixed embedding is used around the energy source. Two sphere shaped fixed embedding is used.

FIXED EMBEDDING:

  INJECTOR EMBEDDING -  Nozzle length of 0.02m is used along with scale of 4 is used because it has proved by Converge that when the cell size is 0.25 or less the spray is grid independent. When the injection is about to start with the cell size of 4mm it is not possible to calculate the 2nd order derivates accurately so AMR is used. 

ADAPTIVE MESH REFINEMENT:

                     AMR automatically increases the grid resolution based on curvatures(second derivatives) in the field variables. AMR can be permanent or activated at specific times. AMR is activated on region by region basis. AMR can be activated for velocity, temperature, void fraction, species, passives, y+( a dimensionless wall distance) on a boundary.

                    Here, velocity and temperature AMR is used.

TIMING MAP:

 

TEMPERATURE OF FULL HYDRODYNAMIC SOLVER:

Full hydro flow

TEMPERATURE FLOW OF THE CYLINDER REGION:

Temp flow of cylinder 

PRESSURE PLOT:

 

 Compression ratio of this engine:

                                     It is the ratio between the volume of the cylinder and combustion chamber when the piston is at bottom of its stroke and the volume of combustion chamber when the piston is at top of its stroke. 

                     From the graph, vt = 0.000574216 m3 , vc = 5.70298e-05 m3

                        Compression ratio = vt/vc 

           vt = Maximum cylinder volume, vc = clearance volume

                   Compression ratio = 10.0687:1          

 

 Why do we need a wall heat transfer model? Why can't we predict the wall temperature from the CFD simulation?

                                      CFD simulation only solves the momentum, energy and continuity equations for the species and predicts the thermodynamic values for regions and boundaries. 

                                     Wall heat transfer model is needed because it is used to find the wall temperature by performing conduction, convection and radiation.

                                     In a CFD simulation the wall temperature cannot be predicted from assumptions because the experimental outcomes differ from the assumptions made.   

                                     Non-equillibrium models are used to predict the wall temperature accurately.

                                    

Calculate the combustion efficiency of this engine:

                                      Combustion efficiency is the ratio of total heat released during combustion to the total energy content of the fuel.   

          Combustion Efficiency = Total heat released/ Total energy content of the fuel           

          Integrated_HR is Total heat released = 1241.1 J

          Total energy content of the fuel = Amount of fuel * Calorific fuel

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

          Calorific cycle = 44 MJ/K

          Total energy content of the fuel = 1320 J

           Combustion Efficiency = (1241.1/1320)*100

           Combustion Efficiency = 94.02%

 

By using the engine performance calculator, to determine the power and torque for this engine:

Work done by the engine is calculated from the engine performance calculator, by adding thermo.out file of cylinder region.

      Work done  = 468.646 Nm

      Duration = 240.199(deg)

      Power = Work done/ Time

      To convert time from degree to second,

      RPM of the Engine = 3000

      RPS = 3000/60 = 50

      Time per degree = 60/(360*3000) = 5.55*10^-5 sec/deg

      Time for 240.2 degree = (5.55*10^-5)* 240.2 = 0.01333 sec

      Power = 468.646/0.01333 = 35157.24 W

      Power = 35.16 kW

To Find Torque,

      Power(P) = (2*π*N*T)/60

        T = P * 60/(2*pi*N)

        T = 35.16*60/(2*3.14*3000)

        Torque, T = 111.97 Nm

 VOLUMETRIC EFFICIENCY - is defined as the ratio between the actual (measured) volume of intake air V_a [m³] drawn into the cylinder/engine and the theoretical volume of the engine/cylinder V_d [m³], during the intake engine cycle.

                         ηv=Va/Vd

   Displacement volume, Vd = 5.1693* 10^-4 m^3

  To calculate intake air Va, we consider ideal gas equation

   P*Va = m*R*T

   P = Pressure at initial condition in cylinder = 101325 Pa

   T = Temperature at initial condition in cylinder =  300 K

   R = Gas constant = 287

   m = Total mass  = 0.00053481613 kg

     Va  = 0.0004537 m^3

Thus, volumetric efficiency = 0.0004537 / 5.1693* 10^-4 

         Volumetric efficiency = 87.63%   

 

 Significance of ca10, ca50 and ca90:

  ca10(onset of combustion) -  The crank angle of 10% mass is burnt or the heat rate is 10% of cumulative Heat released. Its value is 6.83717 degree.

 ca50(combustion phasing) -  The crank angle of 50% mass is burnt or the heat rate is 50% of cumulative Heat released. Its value is 18.4623 degree. 

 ca90(Burn duration) -   The crank angle of 90% mass is burnt or the heat rate is 90% of cumulative Heat released. Its value is 31.701 degree.

 

EMISSION CHARACTERISTICS:

                            Undesirable EMISSIONS IN IC Engines are of major concern beause of their negative impact on air quality, human health, and global warming. Undesirable emissions include unburned hydrocarbons (HC), carbon monoxide (CO), nitrogen oxides (NOx), and particulate matter (PM).

                               

                                   Hydrocarbons are a class of burned or partially burned fuel, hydrocarbons are toxins. 3.2E-05 kg of HC has been produced during combustion.

                                    In the exhaust of IC Engines, NOx refers to a class of compounds called nitrogen oxides. 1.36E-06 kg of NOx has been produced during combustion.

                                   The highest CO emission occurs during engine start up (warm up) when the engine is run fuel rich to compensate for poor fuel evaporation. 1.5E-05 kg of CO has been produced duting combustion.

                                   Hiroy soot is mass of impure carbon particles resulting from the incomplete combustion of hydrocarbons. 7.5E-08 Kg of hiroy soot has been produced during combustion.

                                   A carbon footprint is historically defined as the total greenhouse gas (GHG) emissions. Burning 1 L of gasoline produces approximately 2.3 kg of CO2. 8.5E-05 kg of CO2 has been produced during combustion.