Emission characterization on a CAT3410 engine- Project 2
AIM:
To run simulations for Open-w and Omega pistons and characterise the emissions like soot, NOX and UHC.
To Create cut-plane animations showing Pressure, temperature, Soot, Nox and UHC and compare them between the omega and the open-w pistons.
To compare the indicated mean effective pressure (IMEP) and Power values graphically.
INTODUCTION AND THEORY:
The CAT3410 engine is a commercial engine manufactered by Caterpillar company. It is used instead of desiel engine. The difference between the desiel engine and a CAT3410 engine is the injection of fuel. In case of diesel engine the fuel is injected directly into the combustion chamber before mixing it with the air. It mixes with the air inside the combustion chamber.
Spray modelling:
Spraying of the fuel inside the cylinder from the intake port to the cylinder is done every cycle during the operation of a PFI Engine. This phenomenon can be simulated accurately by using suitable equations but the drawback is that the simulation is too large to fit it as a step in simulating the PFI engine. So, approximate methods to calculate the spray motion and its relevant parameters has been made and these are the Spray models.
The spray models that converge uses are:
For gaseous spray: Eulerian solver
For liquid spray: Lagrangian solver to model to model discrete models and Eulerian solver to model the continuous fluid domain.
Liquid spray is made up of parcels and a parcel is a collection of identical drops.The parcel entirely represents statistically the entire spray field. This type of spray modelling is called Lagrangian spray modelling or discrete phase modelling.
The information needs to be tranferred from Eulerian gas phase to the lagrangian phase and this is done by using aditional models. For example, the heat, momentum and mass transfer occur between the discrete and continuous phases through source terms in the transport equations.
Converge solves radius, velocity etc per-parcel basis.
Parcels undergo several physical processes. They are:
1) Primary breakup
2) Secondary breakup
3) Drag drop
4) Collision and coalescence
5) Turbulent dispersion
6) Evaporation
Below figure shows the spray and its physical models:
1) Primary breakup: When the fuel injection takes place, due to the interaction of liquid with the surrounding air, there is going to be a drag force which causes disturbances in the length of the liquid spray. If the disturbances ar elarge enough then at some parts of the spray, the spray breaks into tiny parcels. This phenomenon of the spray breaking up into tiny parcels is called Primary breakup.
2) Secondary breakup: After primary breakup, the tiny parcels can further breakup into even smaller parcels. This phenomenon is called secondary breakup.
3) Drop drag: The drops as they interact with the ambient air their shaes get affected which would result in a faster or slower vaporisation. This is called as drop drag.
4) Collision and coalescence: This phenomenon refers to the collision among the tiny parcels as well as merging of the tiny parcels after collision.
5) Turbulent dispersion: The turbulent dispersion takes into account the of fluctuating velocity in the gas phase on the drop.
6) Evaporation: This phenomenon refers to the reduction in size of the tiny parcels due to the conversion of liquid into vapour.
Spray modelling in converge:
General:
Parcel distribution:
There are two options in the drop down list:
i) Cluster parcels near cone center.
ii) Distribute parcels evenly throughout the cone.
The suitable option is selected according to the requirement.
Evaporation model:
To calculate the drop radius rate of change, there are two models available as options in converge.
a) Frossling model
b) Chiang model
Evaporation source:
There are three options.
i) Source specified species: All the specified parcels are evaporated to specified species.
ii) Source all composite parcel species: If composites are defined, then the multi-component liquid species evaporate into composite species.
If composites are not defined, then the multi-component species evaporate into base species.
iii) Source all base parcel species: The multi-component species evaporate into base species whether or composites are defined or not.
Maximum radius for ODE droplet heating:
This parameter controls the uniformity of drop temperature.
For drops having larger radius, the temperature inside the drop and the temperature outside the drop is different.
If the drop radius is more than the maximum value then Converge will assume a radially varying temperature distribution.
If the drop radius is less than the maximum value then converge will assume a unifor temperature distribution.
Spray penetration:
Converge writes the liquid and vapour penetration lengths at each specified output interval in the penetration tab.
For the liquid penetration length the liquid fuel mass fraction is provided.
The liquid penetration length is the distance encompassing the calculated penetrated spray mass.
The penetrated spray mass is calculated by multiplying the mass fraction by the total liquid mass in the domain.
Liquid penetration length is not calculated along the spray axis of the nozzle but along the injector axis.
Vapour penetration length is calculated as follows:
1) The fuel vapour mass fraction in each cell inside the spray cone is calculated.
2) For each cell that meets the following two conditions, the distanc efrom the centre of the nozzle to the centre of the cell is calculated.
The two conditions are:
a) The fuel vapour mass fraction exceeds the user specified value of fuel vapour mass fraction.
b) The cell size does not exceed the user specified Bin size. The recommended bin size is atleast twice the number of cells in the spray cone.
The vapour penetration length is the maximum distance calculated in the second step.
Mass diffusivity constants:
D is the mass diffusivity of liquid vapour in air
`rho_(gas)D = 1.293D_o(T_(gas)/273)^(n_0-1)`
The related connstants `D_o and n_o` are set.
From the drop down menu, select the default `D_o and n_o` values for common fuels.
Collision/Coalescence:
Options for drop collisions:
i) No collision
ii) O'Rourke numerical algorithm
iii) NTC numerical algorithm
Based upon the type of engine, one option can work better than the other.
Collision/Coalescence outcome options:
i) O'Rourke collision outcomes
ii) Post collision outcomes.
Collision mesh:
In a typical spray simulation, parcels can collide with parcels only in the same cell, which can lead to grid sensitivity.
Converge has an adaptive collisioin mesh option to reduce grid sensitivity.
If the collision mesh option is checked, the parcels can collide across grid cells.
This feature is independent of the gas phase grid and used only for collision calculations.
Drop drag:
There are several options for drop drag.
i) No drop drag
ii) Spherical drop drag: The drag co-efficient calculation assumes the drops are perfect spheres.
iii) Dynamic drag model: Th edrag co-efficient calculations accounts for variations in the drop shape.
This model invokes the TAB model to determine the drop distortion.
Drop/wall interaction:
There are several drop/wall interaction models.
i) Rebound/slide: Drops can either rebound or slide after impingement.
ii) Wall film: Drop actions are calculated based on particle based quantities or film based quantities.
iii) Vanish: Drops vanish after hitting a WALL boundary.
Combustion Modelling:
Combustion process provides energy for the engine.
Converge provides varieties of ways to simulate the combustion whic takes place in an IC engine. There is a detailed approach called detailed chemistry solver (SAGE) and there are some combustion models with some approximations.
The only problem with the detailed chemistry approach is that it is very slow.
SAGE model:
SAGE detailed chemistry solver uses local conditions to calculate reaction rates based on principles of chemical kinetics.
It solves detailed chemical kinetics during combustion and determines kinetically limited phenomena such as engine knock and emissions.
The rate of change of species concentration are calculated using the Arrhenius rate law equation.
It reads a chemical reaction mechanism in CHEMKIN format and solves ODEs to find the reaction rates.
It couples with the transport solver through source terms in the species transport equations.
It parallelizes independent of the flow solver.
Each time step the chemistry solver calculates the new species mass fractions immediately prior to solving the transport equations.
The change in the species mass fractions is treated as a source
`(del(barrhoY_m))/(delt) + (del(barrhou_jY_m))/(delx_j) = del/(delx_j)(barrhoD_t(delY_m)/(delx_j)) + omega_m`
Where `omega_m` is the source term.
The system of ordinary reactions is is solved using CVODES (general ODE solver).
The elementary reactions in the mech.dat are in Arrhenius format.
The forward reaction rate is given by:
`k_(f) = A_r*T^b* e^(-E_r/(R_ut))`
Where `A_r` is the pre-exponential factor
b is the temperature exponent
`E_r` is the activation energy
R is the universal gas constant
The reverse reaction rate can be user- specified or calculated from the equilibrium constant which is determined from properties in therm.dat.
SAGE model in converge:
Although this method is a time consuming, converge provides the following options to speed up this method.
i) Increase the minimum cell temperature and minimum Hydro carbon species mole fraction to reduce the number of cells in which the combustion calculations are performed.
ii) Use start time and stop time to limit SAGE to specific time intervals.
iii) Limit SAGE to specific regions.
iv) Set the resolve option to "Only resolve if temperature changes by specified value".
a) To maintain solution accuracy the re-solve temperature less than or equal to 2k is recommended.
v) Check "analytical jacobian" to pass an analytically calculated jacobian to the solver.
a) This option is recommende for reactions in arrhenius form.
vi) The Multizone models reduces the number of SAGE calculations by
a)grouping cells into bins.
Bins are created based on two or more variables such as equivalence ratio, temperature, pressure,reaction ratio and cube root of the mass fractions of the specified species.
b) calculating average quantities
c) Invoking the SAGE solver once per bin instead of once per cell.
d) Mapping th esolved quantities to all cells in the bin.
vii) "Conserve `NO_x` during species remap" is checked to allow mapping based on nitrogen atomsand thus improve `NO_x` emissions.
Mesh refinement due to fixed embedding and Adaptive mesh refinement:
Fixed embedding: Fixed embedding is a type of grid control technique used in converge. This technique refines the mesh size at a particular selected cells of a boundary or a region or a particular part of the geometry for which the simulation is done. This refinement can last upto a specific time during the simulation or it can also be present throughout the simulation. The amount of refinement can be regulated by using the Scale of embedding.
If embedding scale is 'n' then the refined cell size = `("base grid")/2^n`
So, for the spherical embedding the scale is set to 5and the base grid size is 0.004 m.
Therefore, the refined cell size = `0.004/2^5` = 0.000125m.
The duration for the above embedding is from -16 degrees to 7 degrees.
For the large sphere, the embedding scale is 3, therefore the refined cell size = `0.004/2^3`= 0.0005m
The duration for the above embedding is from -16 degrees to 7 degrees.
For the Injector embedding, the embedding scale is 4, therefore the refined cell size = `0.004/2^4`=0.00025m
The duration for the above embeding is from -482 degrees to -286 degrees.
Adaptive mesh refinement: Adaptive mesh refinement is a type of grid control technique used in converge. This technique uses a criterion called sub-grid scale to refine the cells. If a quantity is fluctuating from large values to very small values and the range of fluctuation is high, then it will be very difficult to capture exactly all the data during the simulation as the change in the quantity under study is high. In this case, adaptive mesh refinement can be used. If the difference in the quantity between the two adjacent cells is more than a specified value called sub-grid scale criterion, then these cells get refined. So, unlike fixed embedding whose duration of occurance is fixed by the user, the adaptive mesh refinement adapts itself to when and where the sub-grid scale criterion is met. Thus, this technique is highly useful when the time and place of refinement of the cells is complex and does not follow a simple pattern.
For example, the quantity which varies a lot during the simulation is considered as temperature.
If in between any two sub-grids there exists a temperature difference that exceeds the value of sub grid scale temperature difference, the Adaptive mesh refinnement applies to those sub-grid cells and the cells get refined into more finer cells. This uneven, dynamic distribution of cells which changes according to the detailness of a particular quantity under study and at the particular time of requirement during the simulation is called Adaptive mesh refinement.
In Adaptive mesh refinement, the finest cells can be calculated as:
Finest cells = `("Base Grid size")/(2^("maximum embedding level"))`
In this PFI engine, in the velocity AMR,
The sub-grid scale criterion is 1.0 m/s.
So, if the veocity difference between the two adjacent cells is more than 1.0 m/s, those cells get refined as follows:
Refined cells = `("Base Grid size")/(2^("embedding level"))` = `0.004/2^1` = 0.002 m.
If those adjacent cells' velocity difference is still greater than 1.0 m/s then they get refined by one more embed level, and the refined cells have a size of 0.001m.
And if the velocity difference is still greater than 1.0 m/s, the cells get refined again by one embed level which gives the refined cells with a size of 0.0005m.
As the maximum embedding level is set as 3 for velocity AMR, the smallest cell size that can be obtained is 0.0005m.
Similarly, for temperature AMR,
The sub-grid scale criterion is 2.5k.
So, if the temperature difference between the two adjacent cells is more than 2.5k, those cells get refined as follows:
Refined cells = `("Base Grid size")/(2^("embedding level"))` = `0.004/2^1` = 0.002 m.
If those adjacent cells' temperature difference is still greater than 1.0 m/s then they get refined by one more embed level, and the refined cells have a size of 0.001m.
And if the temperature difference is still greater than 1.0 m/s, the cells get refined again by one embed scale which gives the refined cells with a size of 0.0005m.
As the maximum embedding level is set as 3 for temperature AMR, the smallest cell size that can be obtained is 0.0005m.
Importance of Regions and Events:
Regions in converge are a group of boundaries. These can be used to provide different initial conditions to different parts of a geometry. Events in converge studio, are used to connect or disconnect two regions. Events can be very helpful in simulating some cases where we it is requried to break some part of the geometry at a particular time such as breaking a diaphragm in a shock tube. Also, in some cases it may be required to connect the valve in the inlet port of a PFI engine at a particular time and disconnect them when not required.
GEOMETRY:
Below is the geometry showing a closed Liner and piston. This does not have any valves or inlet and outlet ports. This type of an engine geometry is used to study the power and expansion strokes and time can be saved by not including the valves and ports. The geometry is again reduced to a sector, and then by running the simulation on the sector geometry we can calculate the results for the 360 degree piston geometry.
The above geometry is called as open w piston.
To create an engine sector surface, first the profiles are extracted from the surface.dat by clicking on the option "Extract profiles from surface.dat".
Dimensions to make the surface are as follows:
Bore: 0.13716 m
Stroke: 0.1651 m
Connecting rod: 0.263 m
Use bowl profile is checked and an item is selected for automatic adjustment as squash height and the compression ratio is entered as 17.5.
The bowl profile is added which was obtained earlier by extracting the profiles from surface.dat.
Now, the make surface option is clecked to obtain the piston profile.
The sector surface for the open w piston is shown below. As it can be seen that the boundaries are also flagged automatically when the sector surface is created.
Similarly the piston surface geometry is obtained for omega piston as shown in the image below.
Below is the sector surface of the omega piston.
CASE SETUP:
1) Application type:
The appliction type is seected as 'Crank angle-based IC Engine'
Under the Crank angle-based IC Engine, the following are set.
Cylinder bore: 0.13716 m
Stroke: 0.1651 m
Connecting rod length: 0.263 m
Crank offset: 0.0 m
References are set as:
Piston surface ID: Piston
Liner ID: cylinder_wall
Head ID: cylinder_head
Materials:
In the materials section "Gas simulation", "Parcel simulation" and "Reactio mechanism" are checked.
i) Gas simulation:
In gas simulation the gas thermodynamic data(therm.dat) is clicked and it is validated as shown in the below image.
ii) Parcel simulation:
In the Parcel simulation section, from the predefined liquids section select Diesel2 and click on "Add selected".
iii) Species:
In the species section, under parcels tab, add Diesel2
Under the Internal passive tab, add HIROY_SOOT and NOX.
iv) Reaction mechanism:
Click on check properties and then validate.
3) Simulation parameters:
i) Run parameters:
In run parameters, the solver type is selected as Transient and the simulation mode is selected as hydrodynamic solver.
ii) Simulation time parameters:
Under the simulation time parameters the conditions are set as following:
1) start time = -147.0 degrees
2) End time = 135.0 degrees
3) Initial time step = 5e-7 s
4) Minimum time step = 1e-8 s
5) Maximum time step = 2.5e-5 s
6) Maximum convetion cfl limit = 1.0
For Solver parameters, set Navier-stokes solver scheme to PISO.
4) Regions:
Now, regions are set up as shown in the images below.
4) Boundary conditions:
i) Piston:
For piston set the following condoitions:
Boundary type: WALL
Velocity boundary condition:
Wall motion type: Translating
Surface movement: MOVING
Wall Treatment- select 'Law of the wall' from the drop down box and select piston motion.
Temperature boundary condition-
Select 'Law of the wall' from the drop down box. Select the Piston motion
Temperature value- 553.0 k
Turbulent Kinetic energy boundary Condition-
Zero normal gradient (NE)
ii) Front face:
For front face set the following condoitions:
Boundary type: PERIODIC
Periodic type: Stationary
Periodic shape: Rotational
Angle: 60 degrees.
iii) Back boundary:
Periodic type: Matched biundary
MAtching boundary: Front_face
iv) Cylinder wall:
For cylinder wall set the following condoitions:
Boundary type: WALL
Velocity boundary condition:
Wall motion type: stationary
Surface movement: FIXED
Wall Treatment- select 'Law of the wall' from the drop down box
Temperature boundary condition-
Select 'Law of the wall' from the drop down box.
Temperature value- 433.0 k
Turbulent Kinetic energy boundary Condition-
Zero normal gradient (NE)
v) Cylinder head:
For Cylinder head set the following condoitions:
Boundary type: WALL
Velocity boundary condition:
Wall motion type: Stationary
Surface movement: FIXED
Wall Treatment- select 'Law of the wall' from the drop down box
Temperature boundary condition-
Select 'Law of the wall' from the drop down box.
Temperature value- 523.0 k
Turbulent Kinetic energy boundary Condition-
Zero normal gradient (NE)
5) Physical Models:
In the physical models, Spray modelling, combustion modelling is checked.
i) Spray modelling:
Under the spray modelling section, the general tab is selected and the following settings are done.
Parcel distribution: "Cluster parcels near cone center" is selected from the drop down box.
Turbulence dispersion: "O'Rourke model" is selected from the drop down box.
Under the Drop evaporation tab,
Evaporation source: "0-Source specified species" is selected from the drop down box.
Temperature discritization is checked.
Radius above which 1D heat equation will be solved is set as 1000.0 m and remaining settings are set as default.
In the models tab, select the Kelvin-Helmholtz model (KH) and Rayleigh-Taylor model (RT) and Discharge co-efficient model. Set the discharge co-efficient value as 0.7.
Under the Time/Temperature/TKe/Eps/Mass/Size tab, in the Main section, set the following:
Injection temporal type: "CYCLIC" is selected from the drop down box.
Cyclic period: 720 degrees.
Start of injection: -480.0 degrees
Duration of injection: 191.2 degrees
Total injected mass:
The total injected mass per cycle is 2.70167e-05
Under the nozzles tab set the following:
Add one nozzle.
Select the nozzle and click on edit to edit the nozzle.
In the general tab, set the following:
Nozzle diameter: 0.000259m
Circular injection radius: 0.0001295m
Spray cone angle: 9.0 deg.
ii) Combustion modelling:
Under the Models,
Check the SAGE detailed chemistry solver.
iii) Turbulence modelling:
For turbulence modelling select the following:
Turbulence model: RNG k-epsilon
Remaining parameters are set as default.
7) GRID CONTROL:
Check Adaptve mesh refinement and fixed embedding.
i) In the adaptive mesh refinement section, add one AMR group.
Select the In_cylinder_region in the available region and transfer it to the active regions.
Check velocity and set the following under the velocity tab:
Embed type: Sub-grid Scale (SGS)
Maximum embedding level: 2
Sub-grid criterion: 2.0.
Timing control type: Permanent.
Use AMR when parcel count exceeds: 50.
Check temperature and set the following under the temperature tab:
Embed type: Sub-grid Scale (SGS)
Maximum embedding level: 2
Sub-grid criterion: 5.0.
Timing control type: SEQUENTIAL is selected from the drop down list.
Start: -12.0
End: 180.0
Maximum cells are set as 2000000
ii) In the Fixed embedding section add three embeddings.
For Embedding 1 set following:
Entity: NOZZLE
Mode: SEQUENTIAL
Scale: 2
Start: -12.0
End time: 15.0 degrees
Injector ID: Injector_0
Nozzle ID: Nozzle_0@Injector_0
Radius 1: 0.001 m
Radius 2: 0.003m
Length: 0.01 m
The settings of embedding 2 are as follows:
Entity type: BOUNDARY
Boundary ID: Piston
Mode: SEQUENTIAL
Scale: 1
Embed Layers: 1
Start time: -20.0 degrees.
End time: 180.0 degrees.
The settings of embedding 3 are as follows:
Entity type: BOUNDARY
Boundary ID: cylinder_head
Mode: SEQUENTIAL
Scale: 1
Embed Layers: 1
Start time: -20.0 degrees.
End time: 180.0 degrees.
8) Output/Post-processing:
i) Post variable selection: This is set as default as this is a No hydro simulation.
RESULTS AND DISCUSSION:
1) Plot of Pressure vs crank angle for Open w and Omega piston is shown below:
In the above plot it can be observed that the pressure inside the cylinder for both type of engines is the same initially. But the peak pressure in case of open w piston is reached earlier than that of omega piston and the value of peak pressure for open w piston is higher than that of the omega piston. As having higher peak pressure might help in better ignition as it may help to increase temperature inside the cylinder for better ignition. For this, the temperature plot has to be referred to clarify this.
2) Plot of mean temperature vs crank angles for both the piston is shown below:
In the above plot it can be observed that the mean temperature in case of omega piston is higher than that of the open w piston. The lower temperature in case of the open w piston is good becasuse it lowers NOx emissions as the NOx are emitted more at higher temperatures. But as it has been observed in the pressure plot that the open w piston has higher peak pressure than omega piston. This is not resulting in the higher mean temperature for the open w piston. So, from this it it may be inferred that there might be some unburnt fuel in case of the open w piston. To confirm this, the fuel quantity plot vs crank angle has to be observed.
3) Plot of n-heptane (gaseous fuel) vs crank angle for both the pistons is shown below:
From the above plot it can be observed that the amount of gaseous fuel is higher in case of omega piston which means that the vapour fuel is burning lately after the ignition which also explains the low increase in temperature in case of open w piston.
4) Plot of Heat Release Rate (HRR) vs crank angle for both the pistons is shown below:
In the above plot it can be observed that in case of omega piston the heat release rate is higher. This explains the higher temperature in case of omega piston. The sharp spikes in the above plot are due to noise in the data and can be ignored.
5) Plot of Integrated Heat Release (IHR) vs crank angle for both the pistons is shown below:
In the above plot, it can be observed that the Integrated heat release for both the pistons at each crank angle is shown. This plot is obtained by integrating the heat release rate vs the crank angle plot with respect to crank angle. In the above plot it can be observed that the IHR is higher during the combustion. But it can be observed that the IHR at the end of the simulation is not same for both pistons. This means that the amount of energy which was input as fuel is not obtained completely at the end of the cycle in case of open w piston and there is a difference of about 63 joules per cycle. This difference indicates that there is some unburnt fuel left inside the cylinder in case of open w piston which is also increases carbon dioxide emissions.
Mass of gaseous fuel (C7H16) corresponding to 63 joules of energy:
Heat of vaporisation of heptane = 318 kJ/kg
Therefore the amount of heptane corresponding to 63 joules of energy = `63/(318*10^3)`kg = 1.9811e^-4`kg
This amount of fuel is left unburnt in one cycle.
So, for 1600 cycles, the amount of unburnt fuel = 1600 x 1.9811e-4 = 316.9 grams or 0.3169 kg.
Also, the energy expenditure gap between the two pistons = 0.3169 x 318000 = 100.8 KJ
6) The plot of amount of NOx emissions vs the crank angles is shown below:
In the above plot it can be observed that the amount of NOx emissions in case of open w piston are less when compared to that of omega piston. This is because there is less increase in the mean temperature for open w piston.
7) The amount of Hiroy_soot vs the crank angles is shown below:
It is the amount of soot emitted which is obtained by using the hiroyasu model. In the above plot it can be observed that the hiroy soot emissions in case of the open w piston is higher when compared to that of omega piston.
8) The amount of Carbon monoxide vs crank angles is shown below:
In the above plot it can be observed that the amount of carbon monoxide emitted in case of open w piston is lower when compared to that of omega piston.
9) The amount of hydro carbons vs crank angles is shown below:
In the above it can be observed that the amount of unburnt hydro carbons in case of open omega piston is higher because some amount of fuel is left out without being burnt completely.
Work done and many other important perfrmance parameters obtained from the engine performance calculator for open w piston are as follows:
For open w Piston:
Work done by the engine: 3028.53 N-m
Indicated mean effective pressure (IMEP): 3.856 MPa
Peak firing pressure: 11.5373 MPa
Heat release rate peak: 217.947 J/deg
Caculation of power of engine:
RPM of engine: 1600
Time (in seconds) per degree = `60/(1600*360)' = 1.04166e-4 s/deg
Time taken for moving 270.156 deg = `270.156/(1.04166*10^-4)`= 0.02814125 s
Work done by the engine for 270.156 degrees of crank rotation = 3028.53 J
Power of the engine = `3028.53/0.02814125`= 107,618.886 W = 107.618 kW
If the frictional losses are neglected then, Brake power = Indicated power.
Calculation of Torque of engine:
Power, P= `(2*pi*n*T)/60`
Therefore, Torque, T = `30*P/(pi*n)`
= `(30*107618.86)/(pi.1600)``N-m`
= 642.301 N-m.
For omega Piston:
Work done by the engine: 3409.28 N-m
Indicated mean effective pressure (IMEP): 4.34083 MPa
Peak firing pressure: 11.2583 MPa
Heat release rate peak: 329.543 J/deg
Caculation of power of engine:
RPM of engine: 1600
Time (in seconds) per degree = `60/(1600*360)' = 1.04166e-4 s/deg
Time taken for moving 270.156 deg = `270.156/(1.04166*10^-4)`= 0.02814125 s
Work done by the engine for 270.156 degrees of crank rotation = 3409.28 J
Power of the engine = `3409.28/0.02814125`= 121148.847 W = 121.148 kW`
If the frictional losses are neglected then, Brake power = Indicated power.
Calculation of Torque of engine:
Power, P= `(2*pi*n*T)/60`
Therefore, Torque, T = `30*P/(pi*n)`
= `(30*121148.847)/(pi.1600)``N-m`
= 723.0523 N-m.
Comparision of results between open w piston and omega piston:
Work done- Omega piston has higher work done than open w piston. work done in case of open w is 3028.53 J and in case of omega piston is 3409.28 J. Omega piston is better in this case.
Power of the engine: The power in case of Omega piston is higher than that of open w piston. In case of open w iston it is 101.618 kW and for omega piston it is 121.148 kW . Omega piston is better in this case.
Torque: Omega piston has higher torque between the two pistons. In case of open w piston the topque is 642.301 N-m and in case of omega piston it is 723.0523 N-m. Omega piston is better in this case.
Emissions:
NOx: Open w piston has lower NOx emisssions than that of the omega piston. Open w piston is better in this case.
CO: Open w piston has lower CO formation than that of the omega piston. Open w piston is better in this case.
Hiroy soot: Omega piston has lesser amount of hiroy soot than that of the open w piston. Omega piston is better in this case.
HC: Unburnt hydrocarbons in case of omega piston is lower than that of the open w piston. Omega piston is better in this case.
Integrated heat release: In case of open w piston the fuel is not completely converted into energy. Some amount of fuel is left unburnt. The energy difference between the two pistons is 63 J per cycle and for 1600 cycles it is 100.8 KJ. In this case Omega piston is better.
So, Omega piston is better than open w piston in the follwing cases:
work done, power of the engine, torque, hiroy soot, unburnt hydrocarbons.
Omega piston only lags behind open w piston in the cases of NOx emissions and CO emissions.
So, in terms of performance, Omega piston is a better choice. But if the NOx and CO emissions is much preferred over the performance then Open w piston may be a better option.
Animations:
Omega piston:
Link for mesh motion animation is given below:
Link for temperature animation is given below:
Link for pressure animation is given below:
Open W piston:
Link for mesh motion animation is given below:
Conclusion:
Simulations for Open-w and Omega pistons were run and the emissions like soot, NOX and UHC were compared between them.
Cut-plane animations for mesh motion, pressure and temperature have been created and compared between open w and omega pistons.
Work done, power of the engine and torque values have been calculated and compared between open w and omega pistons.
It has been found that in terms of performance, Omega piston is a better choice. But if the NOx and CO emissions is much preferred over the performance then Open w piston may be a better option.