Gasoline PFI engine simulation using Converge CFD   (Converge CFD, Skill Lync, Very Hard)

Aim:

To setup a full hydro simulation for case of gasoline engine (PFI) using Converge 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 take a long time to simulate. So, if there is any error in setting up the mesh motion accurately, the error would be noticed after a long time. To overcome this a no hydro simulation is used. In such simulations, only the mesh and geometry motion is simulated and flow equations and other modelling equations are not solved. This reduces the time required to find errors in mesh setup. Once a no hydro simulation is complete, the full hydro simulation is processed which gives us the final results.

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:

The geometry used for this setup had some errors like surface intersections and holes. These were cleared by manually correcting them one by one. After this, a clean geometry with named boundaries was obtained.

The intake and exhaust valves have three differently named walls. This done inorder to assign walls to proper regions and also the connection of two regions is depended on this naming. The valve bottom walls are walls of cylinder region. In order to restrict the flow during the closed position of valves, the cylinder and manifold regions need to be physically separated. In real world, the seals in valve seats prevent the flow between these regions but this can't be done during simulations because the geometry would intersect and cause error in simulation. To overcome this, the software creates a virtual interface wall between regions which are to be disconnected. The valve angles are the walls whose boundary edges will be used when the software would create the virtual interface.

The valves will move along their stem axis. When this happens, the valve bottom, angle and stem move together and intersection errors are cleared but, the surface to which stem is joined with, also moves. This is prevented by using ring triangles when the stem moves, the ring triangles stretch along the stem axis. Thus preventing the deformation of top surface.

Case Setup:

1) Physical Parameters:

Cylinder bore: 0.086 m

Stroke length: 0.090 m

Connecting rod Length: 0.180 m

Crank Speed: 3000 rpm

2) Solver Settings:

Solver: Compressible, density based PISO solver.

Start Crank Angle: -520 deg

End Crank Angle: 120 Deg

Initial Time step: 1e-7 sec

Minimum Time step: 1e-8 sec

Maximum time step: 0.0001 sec

Max Convection CFL: 1

Max Diffusion CFL: 2 

Max Mach CFL: 50

3) Initial and Boundary conditions and Regions:

This table gives the details in a very concise manner. The colours represent regions and their corresponding boundaries. The temperatures of the walls are based on what levels of temperatures are normally seen in a gasoline engine. The intake walls are cool compared to cylinder. The exhaust is hot than cylinder. The spark plug temperatures are the higher than cylinder. The backflow temperature at outflow is higher considering that the temperature of hot gases that escape from cylinder and get collected in exhaust systems. The species in intake manifold are expected to have fuel vapour species in some amount. The cylinder and exhaust manifold have products of combustion since the initial stroke with which the simulation is programmed to start with is exhaust stroke. The species concentration is calculated based on stoichiometric combustion products.

The Intake and exhaust valves are controlled using a file which contains the data of their motion. The motion profiles are:

4) Mesh Settings:

A base mesh of element size 4 mm is used for all regions. The mesh refinement is done using following embeddings:

The embedding is created along the valve angles inorder to capture accurate flow rate between regions. The big cylinder is embedding used to create refined elements in cylinder and some part of intake and exhaust stroke. The small and large sphere embedding is done so that the temperature AMR would accurately capture the temperature rise and the combustion solver would also start the combustion.

5) Events:

The events control the connection between regions.

When the flow has to be restricted, the events function creates virtual interface surface which blocks the flow from going between regions.

6) Spray modelling:

Level 5 boxes are the reasons of the settings chosen.

 

7) Combustion Modelling:

 

8) Source modelling (For spark plug):

9) Timing Map:

The map shows time and sequence of various embedding and valve motions. The exhaust lift looks like it went out of simulation but since the simulation is cyclic (720 Deg period), any thing that goes beyond the end time is treated as placed at starting of simulation with period as 720 Deg.

 

Results:

1) Mesh:

The mesh can be seen in the video:

 

2) Volume (in cylinder region):

The volume curve shows when exactly does each stroke begins. The volume is less when piston is at TDC and it is more when piston is at BDC.

The Compression ratio of engine is ratio of Total volume of cylinder to clearance volume of cylinder. The maximum volume is 0.0005742 m^3 and minimum volume is 0.000057029 m^3. This gives us the compression ratio of 10.0688.

 

3) Pressure (in cylinder region):

The peak pressure is 39 Bar at a point during expansion or power stroke.

 

4) Mean temperature (in Cylinder region):

The mean temperature is maximum at the point when the integrated heat release is close to its max value, i.e. the entire heat energy is released. It is also the point where there is maximum pressure in cylinder.

5) Spray Injection plots:

The parcels increased as injection started. The parcels started collecting in films on cylinder wall when the intake valves were open. This is because when the intake valves were fully open, the fuel spray was directly hitting the cylinder wall.

The total mass injected was 3e-5 kg. It was as specified in the spray modelling conditions. The mass flow rate can also be seen varying due to the changing injection velocities.

The trapezoidal rate shape was obtained because of the rate shape setting used for injection.

 

6) Fuel Mass fraction:

7) Species mass:

The soot emissions were also calculated but they were in range of 1e-8 Kg, so they are not shown here. The Hydrocarbon mass increases during injection and it drops suddenly when maximum of the fuel is burned. There is some amount of unburned fuel left.

 

8) Combustion Efficiency:

`eta_c = (IHR)/(m xx LCV_(fuel))`

IHR = 1240.22 J (from the plot of Integrated heat release)

LCV for iso octane = 44 MJ/Kg

m = 3 x 10^(-5) Kg

`eta_c = (1240.22)/(3xx10^(-5) xx 44 xx 10^6) = 93.9566 %`

 

9) Engine Performance:

The results of engine performance are calculated from tool of Converge CFD. It gave the following output:

Gross Work = 468.646 Nm

Duration used to calculate Gross work: 240.199 Degrees

IMEP = 896428 Pa

CA 10 = 6.83717 deg

CA 50 = 18.4623 deg

CA 90 = 31.701 deg

 

The calculator tool uses P.dV to calculate gross work. Since, the data is available only till 120 deg after combustion, the P.dV calculation is done using data from -120 to 120 deg.

`"Time for 240 deg" = 240.199 xx (60)/(360 xx RPM) = 240.199 xx (60)/(360 xx 3000) = 0.01334 sec`

`Power = ("Work")/(Time) =(468.646)/(0.01334) = 35130.8846 W`

 `Power = (2piNT)/60`

 `"Torque = " (60P)/(2piN) =(60xx35130.8846)/(2pixx3000) = 111.825 Nm`

 CA 10, 50, 90 represents the crank angle at which the amount of burned fuel reaches 10, 50, 90 percent of its maximum value for the cycle respectively.

 

Answer to a question asked:

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

A. In real life, some part of the heat due to combustion is released from the cylinder walls. This heat transfer takes place due to all modes of heat transfer. When more than one heat transfer modes are considered in the simulation with solid bodies, the simulation is called a conjugate heat transfer simulation. Simulating the IC engine flow along with CHT simulation would increase computation time. So, instead of simulating the heat transfer through walls, it is modelled (approximated) using different models like O'Rourke model. In this simulation, O'Rourke model is used as wall heat transfer model. We can't predict wall temperature from CFD simulation without using these models, because the wall heat transfer is only captured by a model or CHT simulation and not CFD simulation.

 

Conclusion:

The theoretical aspects of IC engine simulation are studied. The full hydro simulation is setup in Converge CFD software and results are presented.