Week 10: Project 1 - FULL HYDRO case set up (PFI)

Aim: Project 1 - FULL HYDRO case set up (PFI)

Objective:

1. What is the compression ratio of this engine?

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

3. Calculate the combustion efficiency of this engine

4. Use the engine performance calculator, to determine the power and torque for this engine.

Introduction

Fuel injection is the introduction of fuel in the internal combustion engine most commonly automotive engines by the means of an injector. Port fuel injections long ago replaced carburetors in cars because of their efficiency and lower maintenance requirements.

The fuel injector is installed in the intake manifold and they are cheap in production and do not have to withstand high pressure from the combustion chamber. The fuel injector injects the fuel into the combustion chamber through the intake valve owing to which the intake valve always remains and there is no carbon deposit in the intake valve. The major disadvantage with respect to the other injection system is that it lacks efficiency (better fuel economy) with respect to the other fuel delivery system.

Case setup

The PFI engine model is loaded into the Converge-CFD environment and errors in the geometry were resolved.

Simulation Run Parameters

The transient solver is selected which captures the combustion as time progresses. The Full hydrodynamic simulation mode is selected and the rest are default settings.

Simulation time parameters

The start time is set as -520 degrees and the end time is set as 120 degrees and the rest settings are kept as default.

The Navier Stokes Solver scheme is PISO and the solver type is density-based.

Species

The Converge-CFD expects us to tell the participating species, therefore under the Parcel tab, `IC_8H_18` is chosen.

Spray modeling

The Converge can model both liquid and gaseous sprays and it has a model through which it captures how the spray is taking place inside the combustion chamber through liquid atomization, drop breakup, collision, coalescence, turbulent dispersion, and drop evaporation. The usage of models illustrates the fact that it is completely impossible to simulate the spray by solving the equation.

The liquid sprays are made up of a bunch of parcels, which is a spherical structure that contains a lot of drops, and together it constitutes a fuel spray. This modeling is termed Langrangian modeling or DPM, the information travels from the gas phase (Eulerian phase) to the liquid phase (Langrangian phase). The heat, momentum, mass transfer occur between the two mediums and they are taken into account by adding suitable source terms in the transport equation. The Converge introduces parcels into the Injector domain, these parcels are made of tiny droplets which are having the same physical properties(radius, velocity, temperature, etc). The Converge solves the equation on a per parcel basis rather than on a drop basis (since drops are identical).

Sub Grid Modeling 

Once the parcel is injected into the domain the big parcel droplet breaks into the tiny droplets which are known as a Primary Breakup. These droplets are again broken into more tiny droplets which are known as a Secondary Breakup. When these droplets react with the ambient air their shape gets affected which is known as Drop Drag. After the Drop Drag, the size of the droplets gets reduced further by Evaporation. The fluctuating velocity in the gas phase is governed by the Turbulent Dissipation.

Setting up of Spray Modeling

The Spray Modeling can be set up by following these steps Case setup>Physical Models>Spray modeling. For setting up of Parcels Case Setup>Materials>Species>Parcel and select `IC_8H_18`. For setting up of Parcel Distribution the Converge assumes that the injection is conical, Distribute parcels evenly throughout the cone is selected. For setting up of Evaporation model the Converge expects us to tell that at what rate the radius of the droplet is decreasing, and the rate at which the mass is being transferred, the liquid droplet vaporizes and there is an additional gas mass that needs to be added as the source term in the species equation. The Converge provides two models for evaporation that is Frossling and Chiang models. The Frossling model is selected. The maximum radius of the ODE droplet has been set up by Converge as 1000m which is being divided into the number of spheres which is 15. If the radius of the droplet exceeds the maximum radius then Converge will assume radially varying temperature distribution. If the drop radius does not exceed the maximum radius, Converge will assume uniform temperature distribution.

The Penetration tells us that how much the liquid has penetrated in the combustion chamber from the injector which depends on the ambient temperature in the combustion chamber. If the ambient temperature is 800K, or more the liquid vaporizes into the gas phase, so after some time the steady-state is achieved and there is no further penetration. It is quite possible to achieve the penetration length using the three parameters, "Liquid fuel mass fraction for calculating spray penetration" for example if we calculate the mass fraction from where the fuel is injected and we reach the point which is 95% of the mass fraction of the fuel then the value is termed as Liquid fuel mass fraction for calculating spray penetration. "Bin size for calculating vapor penetration", "Fuel vapor mass fraction for calculating vapor penetration". In order to calculate the VPL, the cell is chosen which should contain the minimum amount of vapor in terms of the mass fraction which is 1e-3 anything less than that should be considered that the cell has no vapor. The value of the Bin size is selected in such as way that the cell size is two times smaller than the Bin size especially in the location of the spray.

Mass diffusivity can be expressed mathematically by 

`rho_(gas)**D=1.293D_0(frac{T_(gas)}{273})^(n_0-1)`

`D_0` `&``n_0` values can be selected from the drop-down menu provided by the Converge.

In the Collision model, we have three types of algorithm which is No collision, O'Rourke collision, NTC collision. Based upon the engine and user experience the type of model is selected. Similarly in the collision outcomes, there are two types of outcomes which are O'Rourke collision outcomes, Post-collision outcomes which can be selected on the basis of the engine and user experience. The collision mesh is an important option that is selected. When we are going to perform a collision calculation we need another mesh apart from the computational mesh. This feature is independent of the gas phase grid and is used for performing collision calculations and improves the accuracy further.

Drop drag model: When the parcel is entering through the gas phase it encounters air resistance. In the spherical drop drag model, the drag coefficient calculation assumes that the shape of the parcel is spherical. The dynamic drop drag model accounts for the variation of the shape of the parcel based on the velocity and the drag. It invokes the TAB model to determine the drop distortion.

In the Spray wall interaction model, the Converge provides three options which are Rebound/Slide, Vanish, Wall film. The Wall film model is recommended. The O'Rourke model is selected as the Film splash model.

Injector setup

In Spray modeling, the Injector is selected and then the injector is added. The Edit option is selected from the same dialogue box. The Parcel species is chosen as `IC_8H_18` with a mass fraction of 1. A trapezoidal profile injection rate shape is provided which is shown below

The Kelvin-Helmholtz model(KH) and Rayleigh-Taylor model are selected for the solid cone sprays. The discharge coefficient model is selected and the discharge coefficient value is 0.8.

Time/Temp/Tke/Eps/Mass/Size

Nozzles

The cartesian type nozzle location and orientation are selected. Four nozzles are added inside the intake port region before the intake valve.

Nozzle diameter = 250 micro-meter

Circular injection radius = Nozzle radius

Spray cone angle = 10

• Nozzle 0
  • center 0.0823357 0.00100001 0.07019
  • Align Vector -0.732501 0.210489 -0.647408
• Nozzle 1
  • center 0.0823357 -0.00099999 0.07019
  • Align Vector -0.732501 -0.210489 -0.647408
• Nozzle 2
  • center 0.0823357 -0.0004 0.07019
  • Align Vector -0.5 -0.2 -0.647408
• Nozzle 3
  • center 0.0823357 0.0003 0.07019
  • Align Vector -0.5 0.2 -0.647408

Spray rate graph

CA

Mass Injection (kg)

Injection velocity old (m/sec)

Injection velocity new (m/sec)

Injection pressure (bar)

 

Combustion modeling

There are several simplified models which converge uses to simulate the combustion process in an Engine, which are SAGE detailed chemistry solver and Simplified combustion models. The SAGE model is the most predictive and accurate way to model ignition and laminar flame propagation. The Simplified model is less predictive and computationally less expensive than SAGE and is applicable for specific applications. The SAGE solver utilizes the values of equivalence ratio, temperature, and pressure to solve the reaction rates based on the chemical kinetics. The Converge calculates the rate of change of species concentration for all the species from the mech.dat files. The Converge uses the species transport equation to solve ODE. The rate of change of species terms is added as the source term in the species transport equation and computes how the species mass fraction changes during the combustion.

The equation is summed as 

`frac{delbarrhotildeY_m}{delt}+frac{delbarrhotildeu_jtildeY_m}{delx_j}=frac{del}{delx_j}(barrhoD_tfrac{delbarY_m}{delx_j})+tildeomega_m`

`frac{delbarrhotildeY_m}{delt}+frac{delbarrhotildeu_jtildeY_m}{delx_j}` is the generic species transport equation, it dictates how the species which are the part of the computational domain is conserved.

`tildeomega_m` is the source term which is calculated by chemistry solver which is solved by CVODES (ODE solver)

SAGE solver setup

Start time: In an IC engine simulation the start time denotes when the combustion will start, i,e, when the spark will ignite or when the fuel is going to be injected.

End time: In an IC engine simulation the end time denotes that when the exhaust valve will open.

The SAGE can be turned off in certain regions or not. For example, in simulating an IC Engine it does not make sense to make the SAGE turned on in the intake port and the exhaust port. The SAGE should be turned on inside the cylinder region where the chemical reaction takes place.

 

 

Minimum species HC mole fraction: In order to have the combustion started we need to have the right temperature, pressure, and most importantly there is a requirement for the correct combination of fuel and air mixture. If we have an HC-based fuel, in order to have the combustion started we should have the minimum amount of hydrocarbon present in the computational mesh. If the mass fraction of HC in a cell is less than 1e-08 then combustion will not take place.

SAGE acceleration options: The SAGE solver is very slow, it is three times slower than the transport equation (momentum, turbulence, and species), and solving for a refined mesh becomes very tedious. There are few things that can be done to speed up the SAGE solver. The Re-solve temperature value is set to 2K only if the temperature in the cell exceeds 2K the SAGE solver is executed. The Analytical Jacobian solver is selected.

The other technique employed by the Converge to accelerate the SAGE solver is using the Multizone model. The new computational mesh is created with `phi` and `T` space with `phi` be equivalence ratio and T be temperature. A bin is created which contains a computational mesh and the chemistry for the bin is solved and not for the individual cells which speeds up the calculation because the number of bins is substantially lower than the number of cells. Conserve NOx is selected.

Simplified Combustion Modeling

It is characterized into non-premixed turbulent combustion models and premixed turbulent combustion models. Non-premixed turbulent combustion model is used for simulating diesel engines, for example, CTC, Shell Ignition, Chemical Equilibrium the recent model is ECFM3Z Premixed combustion models are used where the fuel is injected and it takes a lot of time to vaporize, for example, G-Equation is very common in this case.

Source/Sink modeling 

In order to set up the spark plug, we are going to introduce the energy equation that will act as the spark plug. This energy source is going to heat the source term in the species transport equation which is going to affect the chemical kinetics and is going to cause the formation of products with the release in energy. This energy is again going to heat up the source term in the species transport equation resulting in product formation.

Setup

Source-1

Source-2

Boundary condition

The boundary selection and their parameters are tabulated as under

 

 

 

Species information at the Outflow boundary

Combustion of iso-octane will yield carbon dioxide, water, and nitrogen at the outlet.

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

The combustion is stoichiometric which means if we place the right amount of fuel corresponding to that the right amount of end products are obtained.

Regions and initialization

The regions with parameters are tabulated below. The one major significance of creating regions is that we can speed up the SAGE solver. The SAGE solver can be turned off in the intake port and the exhaust port region because the combustion is not taking place whereas in the cylinder region the SAGE solver is turned on.

Events

Events are created between the regions to regulate the flow between them. As the Events are activated between the regions the Converge creates a disconnect triangle between them. Please note that these triangles are virtual triangles and should not be created by the user. Events can be cyclic, sequential, and permanent.

Cyclic 

Permanent

 

 

Ring Triangle

They are created to make sure that only the valves are moved and the manifolds are not deformed.

Base grid 

The base grid of 4e-3 m was used for simulation

Fixed embedding

Intake valve angle: The boundary embedding is added to the intake valve angle with a scale of 3 and 1 layer which means we have an embedding of 0.5mm cells in the intake valve angle region. The same goes by the formula which is `frac{0.004}{2^3}`.

Exhaust valve angle: The boundary embedding is added to the exhaust valve angle with a scale of 3 and 1 layers which means we have an embedding of 0.5mm cells in the intake valve angle region. The same goes by the formula which is `frac{0.004}{2^3}`.

In addition to that, the embedding for the spark is also set up because when the energy is sourced into the spark plug then the combustion can propagate, and the cell size inside the combustion chamber needs to be 1mm.

Big cylinder embedding: A cylinder embedding is added which covers the region of the entire cylinder and the intake port with the scale of 1 which means we are getting an embedd of 2mm cells.

Small cylinder embedding: The small cylinder embedding has an embedd scale of 2, which means we are going to cover the combustion chamber.

 

 Spherical embedding

Additional refinement is added to the energy sources at the spark plug so that the energy stays there long enough for the combustion process to avoid numerical diffusion. Sphere type embedd is selected in that region.

Large sphere embedding

 

Injector embedding 

 

Adaptive Mesh Refinement and SGS

Adaptive mesh refinement is a technique that is used to refine the grids automatically based on fluctuating and moving conditions such as temperature or velocity. The feature is used to refine the grid in the flow region of interest such as flame propagation or high velocity without slowing down the simulation with a globally refined grid. There are two types of AMR, mainly sub-grid scale-based and value-based.  The AMR type and criteria are chosen in such a way that the embedding is added where the flow field is most unresolved.

AMR Group-1 is velocity type AMR in which SGS is 1 m/sec. AMR Group-2 is temperature type AMR in which SGS is 2.5K. For the cell whose value is greater than the SGS criterion then AMR is going to refine the mesh in that region. 

AMR Group-1

AMR Group-2

 

Valve profiles

Exhaust valve profile

The exhaust valve opens at around 130 crank angles and closes at around 430 crank angles.

 Intake valve profile

The intake valve opens at around 309 crank angles and closes at around 619.50 crank angles.

 

 Results

Mesh

The line plot is opened in Converge-CFD software and thermo_region0.out is selected because it contains the thermodynamic data file related to the combustion chamber.

Compression Ratio: The compression ratio can be calculated with the help of the below graph

Pressure

 

 

In this graph, it can be seen that the volume of air is maximum at -520 degree crank angle which indicates that the piston is at the bottom dead center. As the piston moves forward the air inside the combustion chamber compresses and at this time the combustion starts, the air volume decreases at the top dead center. Once the energy is released after the combustion the piston again moves to BDC and the volume of air increases which indicates that the intake valve is open to increase the volume of air. At TDC the exhaust valve is open which releases the product of combustion.

The Compression ratio is given by : `frac{V_max}{V_min}`

`V_max=0.00056259868`

 `V_min=5.7029438E-05`

Therefore, the Compression ratio of this Engine is 9.865

Trapped mass(kg)

 

 The above plot indicates whether there is unburnt fuel left inside the cylinder. For an efficient engine, the trapped mass should be minimum.

Heat release rate(J/time)

The heat release rate is constant as the combustion occurs, as the combustion process releases heat energy the heat release rate increases and reaches a maximum value and, as the combustion ends the heat release rate also decreases.

Integrated heat release(J)

The heat release rate is integrated over time and the resulting quantity is integrated which indicates the amount of heat released during combustion. The above parameter is used to calculate the combustion efficiency of the engine. From the above graph, the heat released after the combustion is `1241.1646J`.

Combustion efficiency of the engine

Calorific value of gasoline=43.4MJ/kg

Mass of gasoline injected=`3.00**10^-5kg`

The energy content of gasoline = `43.4**3.00**10^-5**10^6``=1302J`

Combustion efficiency=[heat released due to combustion]/[energy content of gasoline]*100%

Combustion efficiency`=frac{1241.1646}{1302}**100%`

Combustion efficiency`=95.32%`

Liquid spray drops

The above graph indicates that when the fuel is not injected then the mass of iso-octane is zero. When the fuel is injected then the mass of iso-octane increases rapidly and, then decreases due to evaporation and vaporization. When the combustion is complete then the mass of iso-octane is zero which means it gets completely burnt.

Emissions

Hiroy soot: The soot is obtained by using Hiroy model. The mass of soot obtained is  `2.5303679E-08Kg`

NOx: The NOx emission is about `1.2864612E-06Kg`

HC: The amount of HC produced is `1.440608E-08 Kg`

CO: The amount of CO produced is `7.1112219E-06Kg`

CO2: The amount of CO2 produced is `8.5066703E-05Kg`

Work done and various other important parameters obtained from the Converge are as follows

Work done by the engine=468.65 N-m

Indicated mean effective pressure=0.8964MPa

RPM=3000

Number of revolution in 1 cycle = 2

Cycles per minute = 1500

Cycles per second = 25

Work done by the engine per cycle = 468.65 J

Power of the engine = Work done by the engine per cycle * Cycles per second

Power of the engine = 11.716 kW

If the frictional losses are negligible then the Brake power=Indicated power

Power P = `frac{2**pi**n**T}{60}`

Therefore Torque T= `30**frac{P}{pi**n}`

Torque T=`30**frac{11.716**10^3}{pi**3000}`

Torque T= 37.294 N-m

Significance of ca10, ca50 and ca90

Ca10 indicates the crank angle at which 10 % of the combustion is completed.

Ca50 indicates the crank angle at which 50 % of the combustion is completed.

Ca90 indicates the crank angle at which 90 % of the combustion is completed.

Wall heat transfer model for IC engine

The measure of heat transfer in an IC Engine is a challenging task considering the different heat transfer mechanisms ( conduction, convection, and radiation) and the rapid and unsteady changes that take place inside the cylinder. Due to the complexity involved in a mathematical solution, there is a need to adopt suitable modeling.

CFD can accurately predict the heat transfer within the engine, but the boundary condition set up for the engine wall is the temperature boundary condition which is assumed constant throughout the process. It will affect the combustion process leading to inaccurate results.

PFI Engine animation

Temperature

Pressure

Conclusion

• The full hydro setup for PFI engine animation was performed successfully using Converge-CFD software and, CYGWIN command prompt terminal.
• The setting up of the injection source was done successfully at the intake port.
• The combustion, spray, and source/sink modeling was set up successfully.
• The Engine performance parameters were calculated and it was observed that the compression ratio was found out to be 9.865, combustion efficiency was found out to be 95.32%, the power of the engine was found out to be 11.716KW, and the torque was found out to be 37.294 N-m.