Simulation of a PFI Engine In Converge: Part-2
OBJECTIVE:
The aim of this project is to simulate the four strokes of a Port Fuel Injection (PFI) Engine. This is the part-2 of the PFI Engine simulation. This part covers the entire case set-up needed for the successful simulation of the PFI Engine in Converge CFD.
THEORY:
1) PFI BASED ENGINE
Port Fuel Injection is a one of the most widely used Fuel Injection system. The main design of PFI is that, the fuel is directly injected into the intake ports of the engine right before the cylinder.
Since the fuel is injected right before the cylinder, most of the fuel will be drawn into the cylinder causing less collection/stagnation of fuel in the manifold. One other advantage of this type of injection is that, the intake manifolds is not necessary to be made of metal as intake will mostly contain air at atmospheric pressure. This can reduce the weight and overall cost of the engine as well.
2) CONVERGE CFD
Converge CFD is a complete CFD package that was initially designed for simulating engines. Now, it has emerged as one of the top software for simulation of a wide range of CFD applications. Some of the prominent features include automatic mesh generation, fully coupled chemistry solver and some Advanced physical models.
3) Concept of Regions and Events in Converge:
In Converge, a 'Region' is a collection of boundaries used to delineate different areas in a geometry. Events are a feature that engages and disengages the two boundaries. To prevent the flow during disengagement of the regions, the solver creates temporary obstruction (triangles) between them. This temporary obstruction is called disconnect triangles. There are two types of disconnect triangles: Single Loop and Concentric. Engines use Concentric disconnects triangles.
In running of an engine, when the intake takes place, the flow must be allowed from the Intake manifold to the cylinder and at the same time the cylinder must be sealed at the exhaust ports. The disconnect triangles are created by the solver on the go to get the job done.
4) Concept of Adaptive Mesh Refinement (AMR) in Converge:
AMR inputs a parameter semi grid scale (SGS) which refines the mesh size when the curvature of the selected parameter goes beyond the set value. SGS can be applied on any of the flow parameters such as velocity, pressure or temperature. The formula for refinement is `(base grid)/2^(embed l evel)`
5) Concept of Parcels in Converge:
Converge introduces a parcel which is a collection of fuel drops onto the domain at Injector. Each parcel has identical drops in terms of radius, velocity and temperature. Rather than solving equations on droplets, Converge solves the ODE’s on parcels which tremendously reduces the simulation time. Parcels undergo the following physical processes during combustion:
- Primary Breakup
- Secondary Breakup
- Drop drag
- Collision/ Coalescence
- Turbulent Dispersion
- Evaporation
The spray when comes in contact with the air, due to drag, disturbances traverse through it and breaks up the spray into parcels. This is the start of atomization of fuel. This is the primary break-up. When these tiny droplets interact with ambient air, their shapes may change resulting in larger/smaller rate of vaporisation. This is called drop drag. Velocity fluctuations in gas phase may affect the drop. This is turbulence dispersion.
Capturing all these processes is called sub-grid modelling.
6) Spray Modelling:
Converge uses Lagrangian solver for liquid sprays and Eulerian solver for gaseous sprays. The Lagrangian spray is made up of a bunch of parcels. For usual cases, we assume solid cone sprays and the distribution in the cones can be selected. Usually the option of even distribution is selected.
The evaporation models give information about the rate of change of the diameter of the parcel. Converge uses two models for the same – Frossling model and Chaing Model. There is also an option to select the multi-component vapour model. We can specify into what species a certain parcel which contains a particular initial species evaporates into. This is because, that particular species in the gas phase may capture the physical properties very well.
The spray penetration length is the distance that encompasses the calculated spray mass. The spray penetration is calculated along the Injector axis. To determine whether a cell is vapour / liquid, there is an entry called fuel vapour mass fraction for calculating vapour penetration. If the mass fraction exceeds this value, then it is considered as vapour cell. Also a bin size is specified where this calculation takes place. Bin size must be at least twice the size of cells in spray cone.
In collisions, the separate collision mesh is used to have a lesser grid sensitivity. Standard collision models are available for the calculations of collisions.
In drop drag, there are options of No drag, spherical drag and dynamic drag. In spherical drag, drag coefficient calculation assumes drops are perfect spheres. The dynamic drop drag calculates the variation in drop shapes according to ambience. It is highly recommended to use dynamic model.
Converge includes several drop/wall interactions. They include rebound/slide, wall film, vanish models. Wall film model in particular has a sub selection of wall film model. O’ Rourke wall film model calculates splash criteria based on Weber number, film thickness and viscosity. The Kuhnke model has outcomes of rebounds, splash and thermal breakup.
7) SAGE Combustion Models:
Converge contains a detailed chemistry solver as well as simplified solvers. The SAGE is a detailed chemistry solver that accurately models ignition and laminar flame propagation. SAGE solved detailed chemical kinetics during combustion and determines kinetically limited phenomena such as engine knock and emissions. SAGE reads the mech.dat file and solves chemistry ODE (formed from rate of reactions based on Arrhenius Rate Law) to calculate the rate of change of species which can be applied to the species transport equation in the source term. The Species transport equation is solved with the help of CVODES (external ODE solver).
SAGE ODE system is usually huge and is solved between only in particular times. Converge includes accelerating options for SAGE. In order for combustion to take place, a cell must have right amount of Hydrocarbon in it. This is represented by Minimum HC species mole fraction which is set by user. SAGE can also be limited to regions. Resolving the chemistry in a particular cell is limited to 2K to speed up the solving.
One other feature present is the Adaptive/ Multizone model. It groups many cells into bins based on temperature and stoichiometric ratio (default) and solved the combustion equations on the bins rather than the cells. This improves the simulation time largely.
SETTING UP THE FULL-HYDRO SIMULATION/ PRE-PROCESSING:
1) APPLICATION TYPE:
Firstly the type of simulation is selected from the ‘Application type’ under case-setup. After the selection of Crank Angle based Engine option, it is necessary to input the geometric characteristics of the engine such as Bore diameter, Connecting Rod length and RPM. Other parameters are as per the default values.
2) MATERIALS:
Selection of the materials used in the simulation is the second step. Iso-Octane (iC8H18) is used as the parcel specie. Iso-Octane has similar chemical and knock properties to gasoline and hence considered as fuel. Atmospheric air is considered as the gas specie. Parameters such as Turbulent Prandtl number and Turbulent Schmidt number as kept as default values.
According to the above selections, the required mech.dat and therm.dat files are loaded / selected. Under species tab, iC8H18 is selected as the parcel unit. Under reaction mechanism tab in order to check whether all properties are loaded along with the thermodynamic data, the ‘check properties’ button is clicked. If setup is successful, a ‘No Error’ indication will be displayed (top-right).
3) SIMULATION PARAMETERS:
Under run parameters, the transient solver is selected and temporal settings are set to ‘crank angle based engine simulation’. The simulation is run in ‘Full Hydrodynamic’ mode. The time parameters are set as shown in the image below. The simulation is run from a crank angle of -520 to +120 degrees. The cyclic interval through which the cycle repeats is 720 degrees. Ideally, simulation can be run for one full cycle but the interval of 640 degrees will capture all the required information. Other values are set as per defaults.
4) INITIAL CONDITIONS AND EVENTS:
A total of four regions are set-up. It includes the Cylinder region, the Intake region 1 which is close to the cylinder, Intake region 2 which is away from the cylinder and the Exhaust region. The initial conditions of the problem are set according to the regions. They are listed below:
a) INITIAL CONDITIONS:
b) EVENTS:
Events describe the times when regions are connected/ disconnected. There are three important events that happen during the running of an engine.
- The event of the action of the inflow valves during which the air-fuel mixture enters the cylinder region from the Intake region 1.
- The event of the action of the exhaust valves during which the burnt gases leave the cylinder region from the cylinder region.
- The event of the opening of the Inlet manifold 1 and Inlet manifold 2 for flow of air.
The images events show about the cyclic events of the valves as described in the points 1 and 2 following by the permanent event of the opening in the Inlet manifold. During these events, the solver automatically creates / removes disconnect triangles to allow / disallow flow between the regions.
7) BOUNDARY:
The following is the entire flagging of boundaries and the respective regions assigned for the PFI geometry. The boundary conditions are listed below as well. The cylinder and the exhaust regions contain species at stoichiometric condition. It is necessary to calculate the mass fraction of each species. The calculation is shown below.
CALCULATION OF STOICHIOMETRIC MASS FRACTION OF SPECIES AT THE CYLINDER:
BOUNDARY CONDITIONS:
L.O.W stands for Law of Wall Boundary Condition. Also, motion is defined for Valves and Piston. For piston motion, Converge provides a checkbox called ‘Piston motion’ which has to be checked. For the Inlet valve, a file containing the detailed valve motion is loaded. The same is done for the exhaust valve as well. The profiles for the inlet and exhaust valve are shown:
The lift of the Inlet valve is ~300 degree crank angle and is full open ~460 degree and closes at ~600 degree. The lift of the Exhaust valve is ~100 degree crank angle and is full open ~250 degree and closes at ~400 degree.
8) PHYSICAL MODELS:
a) SPRAY MODELLING:
For liquid sprays, Converge uses a Legrangian Solver. Converge introduces a parcel, which is a collection of fuel drops that are identical (same radius, velocity and temperature).
The parcel distribution is assumed to be even throughout the Spray Cone. The turbulent dispersion model is assumed to be of O’Rourke’s Model. The evaporation model is checked which calculates the rate of change in the shape of parcel. The model used for the same is Frossling Model.
The droplet is assumed to be small. If the droplet size is bigger, it is possible to discretize the spherical drops and solve the heat equation at every radius of drop to obtain accurate results. But this slows down the simulation speed and is advisable only if solution is accuracy oriented. Hence, the threshold radius after which the discretization will be done is given as 1000m and hence it will never take place.
Collision Model used is NTC Collision Model with post collision outcomes. Also a separate collision mesh is used for higher accuracy and lower grid sensitivity. The Dynamic drop drag model is recommended to calculate the varying shape of the parcel when the drop interacts with ambient air.
The spray wall interaction selected is Wall-Film and the film splash model selected is O’Rourke and the default values are used wherever necessary.
The next input required is the Injection parameters. A new injector is assigned under the Injector tab and ‘edit’ is clicked to open up the Injector Configuration. Under parcel species iC8H18 is selected with a mass fraction of 1. The Injection rate shape must be provided here. The rate shape is provided as a file as the graphical plot of the entry is shown below (bottom left). At 0 and at 3, the injection rate is 0. At 1 and 2, the rate is 1. Converge will take the total injection time and split it according to the number of instances provided. Here we have 0,1,2,3 i.e. 4 instances. Hence the injection time will be divided into 4 intervals. During the intervals of rate of 1, the injector will spray the fuel and vice versa. The Injection time parameters have to be applied. It is shown below (bottom right):
The Injection is a cyclic process and the same is mentioned. The start of the injection and Injection duration is entered as per given value. The Injection temperature is set as 330K. The total injection mass is actually the mass of fuel consumed per cycle. It is calculated as shown below:
Under the Injection models, the following settings are made. Usually the Kelvin-Helmholtz and Rayleigh-taylor model is used for solid cone sprays (both diesel and gasoline fuels). LISA is used for hollow cone spray and TAB is a legacy model and not used much. The coefficients are loaded based on Gasoline PFI Injection recommendations.
After setting up the Injecting parameters, the location of nozzle (which is present in the injector) has to be set. Under the nozzle tab, the geometric information as well as the location has to be specified. The injection spray type is assumed to be Solid Cone and the Cone angle is assumed to be 10 degrees.
The nozzle geometry is entered as per the given data. A total of 4 nozzles are considered for injection. The coordinates of the same are given below:
After setting up the nozzles, the injector is set up. To validate the inputs, under the injector tab, there is a “tools” button. It contains tools such as ‘Validate nozzle locations, Check Parcel Species and Spray Rate Preview’. The first two commands can be clicked; In case of errors pop-ups of the same will be displayed. The injection pressure is an important criterion which determines the Spray penetration. We have not entered the spray pressure anywhere. Instead Converge automatically calculates it from first principles with the data available. The last tool- ‘Spray Rate Preview’ gives details such as Injection Pressure, Velocity and mass and plots it as well. The plot is shown below along with the obtained values:
Inj dur_inject = 191.2 (CA)
Inj dur_inject = 10.6222 (ms)
Peak Injection Pressure = 5.48269 (bar)
Peak Injection Velocity Old = 32.5264 (m/s)
Peak Injection Velocity New = 32.5264 (m/s)With this, the Spray Model has been set up completely.
b) COMBUSTION MODELLING:
In this project, the SAGE Combustion Model is used. The SAGE solver is a detailed chemistry solver that uses the local conditions to calculate the reaction rates based on chemical kinetics. The minimum cell temperature and minimum HC specie mole fraction needs to be specified as only under favourable conditions does combustion start. The start time and end time of combustion needs to be specified (-17 crank angle deg to 130 deg). The regions of combustion can be specified as well.
SAGE Solver is around 3 times slower than transport equation. Hence to speed up the solver, the solver is resolved for chemistry only when the change in temperature goes beyond a particular set value. The option of Adaptive zoning is selected where combustion is solved based on bins rather than cells. Also the chemistry is solved only if the change in temperaure is more than 200K. These factors speed up the combustional simulation. The combustion ODE are solver with an external ODE solver package called CVODE’s. With this the Combustion model setup is complete.
c) TURBULENCE MODELLING:
Next, the turbulence model has to be set up. The standard model of ‘RNG k-ε’ is used. The recommended values are set for the RANS constants. The near wall treatment is set to ‘Standard Wall Function’. The wall heat transfer model is set to ‘O’Rourke and Amsden’.
d) SOURCE AND SINK MODELLING:
The final physical model to be set up is that of the spark plug. The spark will be sourced via the energy equation. This spark will increase the energy of the species. The source term in the species transport equation, which is responsible for combustion, will take in this change in temperature of species and accordingly calculate the new chemical kinetics and heat release. This will, in turn, affect the energy equation, which increases the temperature. A typical plot of spark vs time is as shown below (bottom left). There are three regions. Initially the voltage is very high for a very small amount of time. This is the breakdown region. It is followed by the Arc and the Glow regions where the energy subsequently decreases. An energy of (20 + 20) mJ is released for the first 0.5 angle duration of and subsequently for the remaining 9.5 angle duration, energy of 20mJ are released.
9) GRID CONTROL:
The base grid is set as 4mm (default value). Additionally, an AMR as well as Fixed Embedding is set for higher accuracy of the solution.
a) AMR
A permanent AMR with a max embedding level of 3 is given for velocity in the regions of Cylinder region, Intake region 1 and Intake region 2. A cyclic AMR with max embedding of 3 is given for temperature in the regions of cylinder, Intake 1, Intake 2. The temperature AMR is for the refinement of the cells during combustion. Hence it must start a few crank angles before spark and end at the end of combustion. The end of the combustion is said to occur when the exhaust valve starts to lift. From the exhaust valve profile, it is around 130 degrees.
b) FIXED EMBEDDING:
The intake valve angle and exhaust valve angle are given permanent embedding with an embedding scale of 3. A permanent embedding of scale 1 is given to the in the purple region (shown in the image) and a permanent embedding scale of 2 is given to the white region. This is done to for cell refinement in the cylinder and Valve areas.
Even though temperature AMR is specified, at the instant when spark is produced, there is no refinement. If the rapid rise in temperature gradient during spark is not detected due to coarse mesh, then temperature AMR might not get activated as well. Hence this initial refinement of cells is needed to provide a better seed value for the temperature AMR calculation. A cyclic embedding is applied to a small spherical shaped region at the sparkplug shown in the image (bottom left). A cyclic embedding is given to the sparkplug and sparkplug terminal with an embed scale of 5. Another spherical-cyclic embedding of a bigger radius with an embed scale of 3 is applied at the same area to prevent any form of diffusion of parameters due to the sudden increase in temperature. The start time of spark embed must start a few crank angles before the spark and can end 1 or 2 degrees after spark time. The timing is set from -16 deg to 7 deg.
Finally, a cyclic-fixed embedding is added at the region of the injector (top right). Converge provides option of ‘Injector Embedding’. The embed geometry is a cylinder with different radii with embed scale set to 4 as spray becomes grid independent with a mesh size of around 0.25mm or less. There have been several papers published by CONVERGE on the same. The cyclic timing of the injector embedding is a few crank angles after the start of injection and ends a few crank angles before the stop of injection. The timing of embedding is given from -482 deg to -286 deg.
With this the entire case setup has been initialized. Now the Input files can be exported to Converge Run and can be solved.
10) TIMING MAP
The timing map gives the entire map of the processes, events and embedding with respect to the time. Below is the map from which, we can get to know the sequence of operations that will happen throughout the entire simulation. After setting up all parameters, the Input files are impoted to a folder and Converge solver is used to solve the case.
POST-PROCESSING:
After running the case, a set of text.out files and post.out files are genarated. The text.out files are loaded in the line plotting module of Converge and various plots (shown below) are obtained. The post.out files are post processed using Converge post processor and converted into Paraview VTK Inline Binary format (.vtm). These are then read by another post processing package, Paraview, to obtain the 3D output.
RESULTS:
1) MESH (generated in Paraview)
Meshes are generated according to base grid of 0.004m in all directions. From the timing map, it can be inferred that throughout the simulation time, the cylinder and a part of the manifolds has 1mm cells, the Intake and Exhaust Valves have 0.5mm cells. According to the AMR and cyclic-fixed embedding, the mesh gets refined during the run time as shown in the timing map. Some images of the base mesh are shown below.
2) ENGINE CHARACTERISTIC PLOTS:
The plots below are obtained in the cylinder region. The following are the volume averaged thermodynamic data for the entire domain.
- Pressure vs Crank Angle
INFERENCE:
Initially the simulation starts with exhaust stroke followed by the Intake stroke. During these strokes, the pressure does not increase much and is represented by the flat part of the curve. During the compression stoke and just before the spark, the peak pressure is attained and is about 3.8 MPa.
Pressure vs CA diagram is used for the calculation of Power and Torque of the Engine.
- Mean Temperature vs Crank Angle
INFERENCE:
During compression stroke the max temperature is attained and the same is about 2480K. The peaks at the initial stage of the curve represent the temperature of the exhaust gases after combustion.
The temperature distribution and the peak temperature is used for the Thermal analysis of the Engine.
- Volume vs Crank Angle
INFERENCE:
The volume swept during each stroke is plotted in the graph. The max volume divided by the minimum gives the compression ratio of the engine.
- Mass vs Crank Angle
INFERENCE:
The mass of the air fuel mixture in the cylinder region is plotted. It latter part (or) the flat part of the curve represents the trapped mass present inside the cylinder. The simulation gives the designers ideas of how much of mass of the combusted particles remain in cylinder so that the cylinder design can be modified.
- Heat release rate vs Crank Angle
INFERENCE:
The heat release rate gives the max value of heat released per crank angle. Here it is around 50J/time where time here is crank angle.
- Integrated Heat release rate vs Crank Angle
INFERENCE:
The Integrated heat release tells about the max heat that can be obtained from combustion alone. The max value is measured to be around 1241J. It is used to calculate the combustion efficiency of the Engine
The plots below are obtained in the cylinder region from the spray outputs. The following are the volume averaged spray data for the entire domain.
- No of Spray Parcels vs Crank Angle
INFERENCE:
The number of spray parcels increase during the inlet stroke and after compression and spark due to the high temperature and pressure, the parcels vaporize showing the decrease in the number of parcels.
The plot below is obtained in the exhaust region from the spray outputs. The following are the volume averaged spray data for the entire domain.
- Mass of fuel vs Crank Angle
INFERENCE:
The mass of fuel at the exhaust region signifies the trapped mass of the un-burnt fuel particles. This gives an insight to the designers to optimize the design. In this case, the trapped mass of fuel at the exhaust is found to be around 9.2e-4 grams.
The plot below is obtained in the cylinder region from the emission outputs. The following are the volume averaged spray data for the entire domain.
- Hiroy Soot vs Crank Angle
INFERENCE:
The plot represents the max hiroy soot produced during the combustion process. It is around 7.63e-8 kg
- NOx Emissions vs Crank Angle
INFERENCE:
The max amount of NOx produced is around 1.37e-6 during the combustion cycle.
- CO Emissions vs Crank Angle
INFERENCE:
The max amount of CO produced is around 1.1e-5 during the combustion cycle.
There is one other useful feature in CONVERGE. Under the Line Plotting Module of converge, in the tools section, there is a tool called ‘Engine Performance Calculator’. The engine.in file and the thermo.out file of the cylinder region have to be loaded in order for it to calculate important engine parameters. Once these files are loaded, the calculate button is clicked to obtain the results. From the above tab, the following parameters have been calculated.
# !CONVERGE_STUDIO=3.0
1 Cycle (no) 1.000000e+00
2 CA_From (deg) -1.200900e+02
3 CA_To (deg) 1.201100e+02
4 Duration (deg) 2.401990e+02
5 Gross_Work (N*m) 4.686460e+02
6 IMEP_(Gross) (Pa) 8.964280e+05
7 CA10 (deg) 6.837170e+00
8 CA50 (deg) 1.846230e+01
9 CA90 (deg) 3.170100e+01
10 PFP (MPa) 3.888840e+00
11 PFP_CA (deg) 2.397000e+01
12 HRR_peak (MPa) 5.935620e+01
13 HRR_peak_CA (deg) 1.884470e+01
These simulation of emissions and performance characteristics help in the calibration of the spark timing, valve timing or modification in design to compute a trade-off between the engine performance and the emission.
ANIMATIONS:
Animation of full hydro simulation
Animation of Change in temperature during spark:
Animation of Fuel Injection:
POST SIMULATION QUESTIONS:
1. What is the compression ratio of this engine?
The compression ratio is calculated from the volume vs crank angle plot. Under closed valve conditions, the ratio of maximum volume and the minimum volume gives the compression ratio. In this case, both the valves are closed between ~210 degees and 0. The volume at the same angles are considered for Compression ratio calc.
Comp Ratio = `(max volume)/(min volume)`= `0.000574/(5.754e-5)` = 9.9912
2. Why do we need a wall heat transfer model? Why can't we predict the wall temperature from the CFD simulation?
The temperature is calculated from the Energy equation of the N-S equations. In incompressible flows, usually the energy equation is decoupled from the momentum equations and can be solved backward with the velocity field kept frozen. Wall quantities (temperature and heat flux) are very sensitive to the modeling of near-wall turbulence. And when this backward trend of solving the energy equations is done, there is a high chance of ending up with less accurate values.
In addition, some multiphysics problems such as Modelling Natural Convection and Conjugate Heat Transfer (CHT) introduces a coupling between velocity and temperature field. To maintain accuracy, during the coupling of the equations, additional modelling is introduced for the solution of thermal equation. This adds additional approximations and errors parameters but computes the solution accurately.
3. Calculate the combustion efficiency of this engine?
Combustion efficiency is given by (Max IHR / Total energy of fuel)
Total energy of fuel = mass of fuel * LHV;
Max IHR = 1241J (obtained from IHR vs crank angle plot)
LHV of iC8H18 is 44.78 MJ/kg
Mass of fuel input in the intake stroke = 3e-5 kg (From input data)
`implies` Total energy of fuel = 3e-5 * 44.78e6 = 1343.4J
Hence, Combustion efficiency = 1241/1343.4 = 0.9237 = 92.37%
4. Use the engine performance calculator, to determine the power and torque for this engine.
Power(P) = (2*π*N*T)/60
From the Engine performance calculator, Work done = 468.646 Nm
CA Duration is 240.12 degrees.
Now RPM =N= 3000 `implies RPS = 50`
`implies DPS = 18000`
`implies` Time per degree is 5.55e-5
`implies` Time for Combustion in seconds is 240.12*5.55e-5 = 0.013333s
`implies` P = WD/time = 464.646/0.013333 = 35148.45 W
Now, T = (P*60 )/(2*pi*N)`
`implies T =` 111.8771 Nm
5. What is the significance of CA10, CA50 and CA90?
CA10, CA50 and CA90 represent the Crank angle at which cumulative there is a heat release equivalent to 10% combustion, 50% combustion and 90% combustion respectively. CA10 is commonly referred as onset of Combustion. CA50 is referred as phasing of Combustion and CA90 is referred as Duration of combustion.
The thermal and combustion efficiency of different fuels are calculated based on these values. They are also used to predict the burning rates of fuels which plays an important role in the flame calculations.
CONCLUSION:
The full hydro simulation of PFI based Engine was succesfully simulated in Converge CFD. The Power of the engine was estimated to be 35.14kW. A Torque of 111.87 Nm, Combustion efficiency of 92.37% and a Compression ratio of 9.99 were obtained. Also an insight into the amount of emissions produced by the engine was given.