Comparative analysis of two piston bowl profiles in diesel engine using Converge CFD   (Converge CFD, Skill Lync, Very Hard)

Aim:

To compare the performance of 2 piston bowl profiles (Open W and Omega) using CFD.

 

Introduction:

Internal combustion engines have been used for transportation and other purposes from a long time now. Still, the designing process of these engines continues. New designs with more efficiency and power are made. Sometimes, few design parameters need to be checked by experimentation only. This involves huge cost of manufacturing a single IC engine. In order to solve this problem, a simulation of engine with different parameters is done and required results are obtained. This gives a huge saving in time and money.

The simulation of IC engine is very complex as it contains several moving parts which need to be simulated with correct timings and solution also needs to be accurate enough to compensate for experimental data. This simulation takes a long time to simulate. So to reduce simulation time, a closed cycle analysis is done. This means that the simulation is done only for compression and power stroke. The regions are initialized with appropriate initial conditions. To further reduce the computational requirement, a sector or a part of engine is only simulated. The sector angle depends on number of injectors and nozzles. In this project, a closed cycle analysis of engine sector is done for 2 piston bowl profiles (Open W and Omega). From this simulation, the performance of engine is calculated and various emissions are observed, which would help to justify which bowl profile is better for what kind of use.

Some theory concepts:

Spray modelling:

In a real world IC engine, the fuel is sprayed in the combustion chamber or near intake valves. This fuel spray can be completely simulated using CFD multiphase simulations, but doing so in a IC engine simulation would result in simulation running for very long. This can be prevented if we statistically model the same effect of the spray instead of actually simulating it. This approximating process of fuel sprays is called Spray modelling. Before understanding how the modelling takes place, we must know how an actual spray flow occurs. Any fuel spray undergoes a mechanism which has following processes:

1) Primary Breakup: Splitting of drop from main stream

2) Secondary Breakup: Splitting of primary drop into multiple drops

3) Drop Drag: Drag caused by air on the moving drop.

4) Collision and coalescence: Collision of two or more drops and formation of new drop.

5) Turbulent dispersion: Transport of mass, heat, or momentum within a system due to random and chaotic time dependent motions

6) Evaporation: Evaporation of small liquid drops into vapour

The sequence of processes is fairly easy to understand. The main stream breaks into multiple drops by primary and secondary breakups. New drops are formed due to coalescence. The evaporation reduces the drops and dispersion spreads the drops into region. While modelling the spray, each process is represented mathematically by using some pre-established models. These create the effect of spray without actually simulating the spray.

To calculate the spray in a simulation, CONVERGE introduces drop parcels into the domain at the injector location at a user-specified rate. Parcels represent a group of identical drops (i.e., same radius, velocity, temperature, etc.) and are used to statistically represent the entire spray field.

Evaporation: The evaporation is simulated using Frossling or Chiang model. They are responsible for flagging a parcel drop as evaporated or not. They consider the size of drop and its evaporation properties to make decisions for drops.

Penetration: The fuel spray penetration is also recorded in the software. It calculates this based on how long did the fuel travel as liquid. The cell upto which the 0.95*(mass of liquid fuel sprayed) is seen is called the liquid penetration length.

Collision: The software contains two models: O'Rourke model and NTC model. These models simulates the collision using a collision grid. Using a collision grid creates accurate particle movement data.

Drop Drag: This is simulated using Spherical drop drag model or Dynamic drop drag model. The Spherical model calculates the drag coefficient based on assuming the shape of drop as sphere, while the dynamic model accounts for variations in drop shape. It uses TAB model to determine the drop distortion.

Drop wall interaction: When a drop parcel would collide with wall, it could rebound back, escape or remain on wall, creating a film. This effects are modelled using: O'Rourke model or Kuhnke model.

[Each of the models decribed above are standard models. The values of variable used for simulation are directly taken depending what software recommends. So many values or expressions stated in this report might not have a logical reason mentioned along]

CONVERGE offers two categories of liquid injection mechanisms: injectors and nozzles. An injector is a group of nozzles that have some of the same characteristics. Each injector can have any number of nozzles, each with its own hole size, cone angle, position, and orientation.

Injector models: The models used are 'Kelvin-Helmholtz model' and 'Rayleigh-Taylor model'. These models look after the primary and secondary breakup of parcel drops. The calculations are based on 'Kelvin-Helmholtz instability theory' and 'Rayleigh-Taylor instability theory'. These theories are used for surface tension instabilities of drop, which lead to fluid breakup.

 

Combustion Modelling:

The combustion is modelled by using its reaction mechanism. There are multiple species and intermediate reactions which govern the combustion process. The reaction mechanism of real life combustion is very large and simulating it directly would take a long time. So, the combustion is solved only for those reactions and species whose presence has an effect on the combustion results. This is called a reduced mechanism file. These all processes of reducing mechanism and solving them is done by various solvers present in the software: SAGE, CTC/ Shell, G-Equation, CEQ, FGM ,etc. In this report, SAGE solver is used, so details of SAGE are only given.

SAGE: Its a detailed chemistry solver which uses local conditions to calculate the reaction rates based on principles of Chemical kinetics. It calculates the heat release, which is used as source term in fluid flow energy equations. The species are modelled using chemical kinetics ODEs and the values are used in species transport equations. The Solver used to solve the ODEs is CVODES.

Acceleration technique: The SAGE solver is a detailed chemistry solver, meaning that it would calculate values based on full mechanism instead of reducing it. This takes a lot of time if the calculations are done for every cell in the mesh. So, to increase the speed of solving, the solver is run using a multizone model. All the cells where combustion is going to be solved for, are grouped into bins. The bins are created based on the temperature and equivalence ratio of fuel and air. All the cells having same temperature and equivalence ratio will have same combustion results. So, the SAGE solver is solved once for each bin and accordingly the flow and species data is remapped to the cells. This increases the speed tremendously. The bins can also be created based on multiple variables like pressure, reaction ratio, etc.

 

Source modelling:

The spark plug releases energy at the point when combustion starts. This energy release can be modelled using Source modelling. The specified energy is included in the source term of flow energy equations.

 

Regions and events:

The flow volume in the computational domain can be divided in multiple regions. This division can be done based on boundaries associated with region, based on initial conditions, etc. The flow between these regions can be allowed or restricted based on our need. This is where the concept of events is used. The events look after the timing when two regions will be connected or disconnected. When the regions the connected they act like a single region. When disconnected, the events function creates an interface wall which restricts the flow between regions. This interface is virtually created is not to be created by user.

 

Fixed Embedding:

Depending on the flow taking place, we may require that the flow at some region is more accurate and at some region is more approximate. This can be done by varying the mesh element sizes in the region. The embedding option in Converge CFD does this work of creating finer mesh at mentioned location. The refinement is based on scale and number of embed layers. If the base mesh created has cubic elements of size 'E' mm then the scale of 'n' means the elements in refinement region will be of size `E/2^n` mm. This means that if base mesh has elements of size 4 mm then elements of scale 1, 2, 3, 4, 5 will have elements of size 2, 1, 0.5, 0.25, 0.125 mm respectively. With each element scale there is 8 times increase in total cell count. This happens because the elements are divided in size by 2 in all directions (X, Y, Z).

 

Adaptive Mesh Refinement:

The fixed embedding setting is preferred when the refinement is needed in the complete region or complete boundary area. When the refinement is to be done based on the solution of flow equations, the refinement technique is called AMR. The AMR monitors the solution and based on the curvature (second degree of rate of change) of a variable, the mesh is refined. There are two methods to use AMR: Sub-grid scale method and Value based method. In the value based method, the value of solution is specified. If the value is more/less than specified, the mesh is refined. The Sub-grid method works in following way:

For a scalar, the sub-grid field is defined as the difference between the actual field and the resolved field or

`phi' = phi - bar phi`

This sub-grid can also be represented as an infinite series, but since its not possible to evaluate the entire series, only the first term in the series is used to approximate the scale of the subgrid.

 

A cell is embedded if the absolute value of the sub-grid field is above a user-specified value. Conversely, a cell is released (i.e., the embedding is removed) if the absolute value of the subgrid is below 1/5th of the user-specified value. That means if the user specifies a value of 2.5, the mesh program would calculate sub-grid of the cell, based on the term shown above and if it is larger than 2.5, cell will be refined.

 

Case Setup:

 

A sector of 60 deg of engine volume is used for geometry. The following piston bowl profiles are imported along with geometric details of cylinder to create this engine sector.

Case Setup:

1) Physical Parameters:

Cylinder bore: 0.13716 m

Stroke length: 0.1651 m

Connecting rod Length: 0.263 m

Crank Speed: 1600 rpm

Compression ratio: 17.5

2) Solver Settings:

Solver: Compressible, density based PISO solver.

Start Crank Angle: -147 deg

End Crank Angle: 135 Deg

Initial Time step: 5e-7 sec

Minimum Time step: 1e-8 sec

Maximum time step: 2.5e-5 sec

Max Convection CFL: 1

Max Diffusion CFL: 2 

Max Mach CFL: 50

3) Initial and Boundary conditions and Regions:

The table shows the boundary conditions in a proper format. Since this is a close cycle analysis, there are no inlets and outlets. The initial temperatures of the wall are set based on what is expected inside an engine. The moving piston has temperature of 553 K which is higher than cylinder wall (433 K). This is because cylinder wall will be cooled by fins or coolants but piston will have to transfer heat to engine oil and liner. The cylinder head (523 K) is also cooled by some cooling mechanism. The front and back walls have periodic boundary condition. The 60 deg rotation is used because this engine is assumed to have injector with 6 nozzles, so 360/6 is 60 deg. The region initial temperature is because of initial heating of gases due to previous cycle. The region initial species are based on intake air species configuration.

4) Mesh:

A base mesh was created with element size of 1.4 mm and following embedding and AMR settings were applied to refine the mesh as required.

The piston and cylinder head had small elements because near the TDC position the combustion chamber would be largely surrounded by them. The nozzle embedding is done inorder to accurately capture the parcels, their evaporation and combustion. This would also be needed for proper flame capturing and emission calculations, since high temperatures lead to NOx.

AMR was used inorder to refine the mesh based on temperature and velocity gradients. The theory explains the use of each parameter used here.

 

Here we can see nozzle, its embedding and injector.

5) Spray Modelling:

The Spray parameters are explained in theory section. The appropriate reasons have been mentioned in the sides in red boxes.

 

6) Combustion Modelling:

The combustion parameters are also explained in theory section.

 

7) Timing Map: 

 

Results:

1) Mesh:

The figure above shows the refinement of cells caused by both, embeddings and AMRs. The cell count rise can be seen in figure below. A sudden rise is seen as the spray injection started. Omega case had more cells because there was more volume compared to open W case. The video shows the creation and refinement of mesh in mooving condition. It is clipped inorder to show only important time steps.

2) Pressure:

The pressure plot shows that the Omega case had faster and higher rise in pressure than open W case. This was because of faster burning of fuel after it is injected. This will be more evident in further plots.

 

3) Temperature:

The Maximum temperature reached in both cases is nearly equal. This is because the maximum temperature is function of Pressure and fuel equivalence ratio. At the point where the combustion begins, the pressure and equivalence ratio conditions for both the cases are nearly same. Hence, the maximum temperatures, near 0 deg, were nearly equal for both the cases. The maximum temperature at the end of power stroke was less in omega case than in open W case. The reason is mentioned below next figure.

As it can be seen from this figure that, the mean temperature is higher in omega case by 300K. This higher mean temperature is due to faster burning of fuel. A change in mean temperature is seen near the ending of stroke. This change is due to formation of NOx at higher temperature and oxidation of soot. These two processes take away the heat from gases. This two processes are not very powerful in open W case and hence there wasn't any big change in mean temperature.

The volume rendering shows the temperature values. The flame structure is clearly different in both cases. There is a big swirl or eddy in the omega case, which is responsible for faster burning of fuel.

These are images of slice taken at diameter or through centre of engine sector. The eddy is clearly visible in these slices. The maximum part of fuel in open W case burns near the cylinder wall. The centre region remains cool for sometime. In omega case, the piston bowl create two flames, one in big centre region and second in the region near cylinder wall. Since, the incoming fuel gets chance to split in two regions and burn simultaneously, it burns faster. This leads to higher temperatures and pressures. This high temperature is responsible for NOx creation and soot oxidation.

The videos below show the animation of temperature volume rendering and isosurface. These are useful for understanding the flame propagation.

 

4) Heat Release Rate:

The heat released from the combustion can be seen from the plots below. The faster burning in case of Omega is reason of the higher heat release rate. The IHR plot shows the total heat released till an instant. The slope of Omega case curve is higher, which means faster burning. The open W case curve does reach a final value near to the omega case but it is slow.

 

5) Spray results:

The plot below shows the number of parcels in the chamber that are in drop phase. The open W case curve has lower peack because when the spray enters the chamber it travels for some distance and then it forms a film on the piston surface. The fuel film eventually burns out by evaporation but it reduces the number of parcels in drop phase. In omega case, the parcels get enough time to evaporate and thus they burn out faster and we can see less drop parcels after -2 deg crank angle.

The spray penetration length shows the distance till which the spray parcels remain drop. In this plot we can see the distance of the last cell from injection point. The last cell is the cell till which there is 97% of mass fraction of the fuel available at that instant.

The penetration length is higher in omega case because the parcels can reach farther before converting to vapour or film. The graph beyond 0 deg crank angle is of little use because the length shown there represents the parcel in drop form which went the farthest. It might be only 1 or even a few parcels which reach that length. The fact which can be inferred from this is that in omega case even a single particle can't travel more. It gets combusted in short length. It may be because of the swirl or eddy formed in the chamber, which would keep parcel from going too far.

 

The images above show the formation of film in open W case and evaporation of parcels in omega case.

 

6) Unburned hydrocarbon emissions:

For open W case, the fuel didn't get burned as it was injected till 9 deg crank. It kept on collecting and after a point it reduced. In omega case the fuel was burned immediately after it was injected. There was no accumulation. This is the reason why there is small, constant horizontal slope from 0 to 7 deg crank angle. At the end of the power stroke, the omega case had less UHC emissions. The reason behind this is the formation of fuel film which restricts the fuel evaporation.

The following images and video show the fuel mass fractions. The fuel in open w case burns near the cylinder wall, thus keeping the temperatures cool in centre region. In omega case, the fuel vapour is divided in two parts which increases mean temperature and leads to faster combustion.

 

7) CO and CO2 Emissions:

Since the combustion is faster in omega case, we can see a faster rise in its weight compared to open W case. As there are more unburned hydrocarbons in open w case, the carbon dioxide emission is low and carbon monoxide emission is higher. The difference in the final values is very less in both cases for both emissions.

 

8) NOx emissions:

A big difference in NOx emissions is seen in both cases. The omega case has higher NOx emissions compared to open w case. This is because NOx formation happens at higher temperatures. The Omega case generates higher mean temperature than open W case due to its ability to make fuel burn faster. In images and video given below, we can see formation of NOx. If we compare these animation with temperature animation, we can see that NOx was formed in region from where the flame front has passed and region is at higher mean temperature (1800 to 2200 K). In open W case, such regions are low in proportion compared to total volume. Hence, it produces less NOx. Whereas in Omega case, such regions are in larger proportion compared to total volume. Hence, it would produce more NOx.

 

9) Soot emissions:

In the plot shown above, the mass of soot calculated using Hiroyasu model is shown. It shows how much of the soot is formed and oxidised for both cases. The curves with circle markers belong to Omega case. If we look at the soot formation curves, it can be said that omega case formed more soot than open W. But the total soot emissions at stroke end are less in omega case than open W. This happens because the soot formed in the chamber gets oxidised at higher temperature. The Omega case oxidises more soot, which reduces soot emissions at the end. In open W case, some part of soot remains to be oxidised and hence we get a higher soot emission level compared to omega case. In the images and video shown below, the oxidation of soot is seen. The regions in which soot is seen to be formed, later show reduction in mass fraction.

 

10) Combustion Efficiency:

The image shows how open W case waste 1.483e-6 kgs of fuel per cycle.

 

11) Compression ratio:

The compression ratio was less than 17.5, which was the required valve. This happened due to time gap in writing text output files. The time gap was 0.1 deg, so there will be some error in maximum and minimum values.

 

12) Power and Torque calculations:

Due to faster combustion, omega case piston generates more torque than open w case. The CA 10, 50, 90 represent the stages of combustion where 10, 50, 90% of total fuel mass is combusted respectively. The CA 90 values of both cases show that the fuel burned at nearly twice the rate in omega case than open w case.

 

Conclusion:

The Open W and Omega type piston bowl profiles are compared by using CFD analysis. The following image shows the features of both profiles.

Hence, it can be said that Omega type piston bowl is better than Open W type Piston bowl. The only problem with Omega type piston bowl is that it has higher NOx emissions. This design can be further improved by changing injection angle and changing the profile. A new model of Omega type piston is Chamfered Omega type piston where the profile is chamfered at the pointed edge near cylinder wall. Also, the injection angle is adjusted such that the spray vapourizes and the chamfer divides the vapours in two approximately equal parts, thus creating two eddies. The image given below shows this piston analysis.

Image credits: https://dieselnet.com/tech/engine_combustion.php