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

OBEJCTIVE:

• To import the CAD model of engine in converge Software and check for errors.
• To set up the case with proper grid size, material and boundary conditions.
• To solve the case using suitable solver and convert the result for Paraview software.
• To import output files in Paraview and generate required contours and plots.
•  To setup the case and run the full hydrodynamic simulation of a PFI Engine.
• To find out the compression ratio of this PFI Engine.
• To calculate the combustion efficiency of this engine.
• To determine the torque and power of the engine using the engine performance calculator.

A heat engine is a device which transforms chemical energy of a fuel into thermal energy and uses it to produce work. Mainly, Heat engine is classified into two categories External combustion engine and internal combustion engine. when the products of combustion of air and fuel transfer heat to a second fluid which is the working fluid of the cycle, then engine is called external combustion engine and when the combustion of air and fuels take place inside the cylinder and are used as the direct motive force then engine is called as internal combustion engine.

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:

 Primary breakup

 Secondary breakup

 Drag drop

 Collision and coalescence

 Turbulent dispersion

 Evaporation     

*Below figure shows the spray and its physical models:

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.

 Secondary breakup: After primary breakup, the tiny parcels can further breakup into even smaller parcels. This phenomenon is called secondary breakup.

 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.

 Collision and coalescence: This phenomenon refers to the collision among the tiny parcels as well as merging of the tiny parcels after collision.

 Turbulent dispersion: The turbulent dispersion takes into account the of fluctuating velocity in the gas phase on the drop.

 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

The related connstants $D_o\text{and}{n}_o$ are set.

From the drop down menu, select the default $D_o\text{and}{n}_o$ 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

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:

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 $N{O}_x$  during species remap" is checked to allow mapping based on nitrogen atomsand thus improve $N{O}_x$emissions.

 

FULL HYDRO CASE SETUP:

Material:

In the Parcel simulation section, from the predefined liquids section select Iso-octane (IC8H18${}_{\mathrm{)}}$ and click on 

"Add selected". The fuel is selected as Iso-octane because the thermal properties of Iso-octane are similar to that of gasoline

 

In the species section under the parcel tab from the query available list option, Iso-octane (IC8H18) is added.

Simulation parameter:

under the run parameter section the simulation mode is selected as full hydrodynamic.

Simulation time parameter:

Physical modelling:

spray modelling, combustion modelling, source/sink modelling is checked.

In spray modelling:

iso octane is addef as the injected parcel species and its mass fraction is set as 1.0

in injection rate shape the profile option is selected and the rate shape file is selected and the profile is set as shown in image.

here the cyclic period :720 degrees

start of injection:-480.0 deg

duration of injection:191.2 deg

total injected mass:

The total injected mass per cycle is calculated as shown below:

fuel flow rate: 7.5*10^-4 kg/s

RPM:3000

now RPS will be 50

one revolution is equivalent to 360 degrees.

so degree per second will be 50*360=18000

time per degree will be 1/18000=5.5555*10^-5 s -deg^-1

now time per 720 degree is 5.5555*10^-5/720 =0.04 s - (720 deg)^-1

there fore fuel mass per cycle= fuel flow rate * time per 720 degrees (or 1 cycle of 4 stroke IC engine)

=0.04*7.5*10^-4

=3.00*10^-5

injector 0

injector 1

injector 2

injector 3

below image show the nozzle and injector:

now the spray modelling is completed from the tools in the injecor tab the properties of the spray such as pressure, temperature can be previewd. 

check the inputs provide and modify if required then click on calculate rate. and click on the plots icon.

now many quantities are plotted as a function of crank angle as it can be seen from the image below. select the injector pressure to see the plot between the injection pressure vs crank angle.

the peak pressure is observed at 5.4869 bar from the plot which is the feasible range for the gasoline engine.

The nozzle location can also be verified to do this validate nozzle location option is selected from tools option.

 

COMBUSTION MODELLING:

Under the models check the SAGE detailed chemistry solver.

SOURCE/SINK MODELLING:

TWO SOURCE :

base grid:

adaptive mesh refinement:

select all the region except for exaust region in the available region and transfer the selected region to the active regions.

FIXED EMBEDDING:

spherical embedding

larger spherical embedding

injector embedding

 

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 /2n

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= 0.004/2^1=0.002m.

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= 0.004/2^1=0.002m.

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.

 

Calculation of mass fraction of species which are present in combustion chamber and exhaust:

The combustion recation is assumed to be stoichiometric and the balanced reaction is shown:

C8H18 + 12.5(O2 + 3.76N2) = 8C02 + 9H2O +12.5 *3.76N2

The mass fraction are 

 

RESULTS:

From the above plot it can be observed that the air volume iinside the cylinder is maximum at the beginning at -520 degrees crank angle, which means that the piston is at the bottom dead centre. As the piston moves towards the top dead centre, the air compresses and as a result the air volume decreases. It reaches its minimum value at the top dead centre. At this point the compression stroke is complete and ignition takes place. Due to energy released after combustion, the piston is pushed towards the bottom dead centre and hence the volume of the air and other combustion gases increases. This is the power stroke. After this, the combustion flue gases are sent outside the cylinder through the exhaust, during which the piston moves from bottom dead centre to top dead centre, decreasing the air volume again. After this the air from the inlet valve is allowed in to the cylinder as the piston moves from top dead centre to bottom dead centre.

Compression ratio of this engine:

Compression ratio of an engine is given by the ratio of maximum air volume inside the cylinder to the minimum air volume inside the cylinder which is Vmax/ Vmin.

From the above plot between air volume inside the cylinder vs crank angles, the maximum and minimum volumes of the air can be obtained.

here there fore the compression ratio = Vmax/Vmin=5.742*10^-4  /  5.702*10^-5 =10.07

 

 Plot of Pressure of air and other gases inside the cylinder vs crank angle:

mean temperature plot:

mass flow rate:

 heat released:

Some performance parameters are calculated as follows.

 Compression ratio –

Volume measure from graph –

Maximum volume – 5.724e-4

Minimum volume – 5.7036e-5 

Compression ratio(C_r) = Maximum volume/ Minimum volume

C.R=5.724 *10^-4/5.7036*10^-5 = 10.036

 Combustion efficiency –

Lower calorific value of fuel (LCV) = 44 MJ/K

Fuel injected = 3e-5Kg

Potential energy of fuel = fuel injected*LCV =3.106-5 * 44*10^-6 = 13.2 J

Total heat released (Taken from integrated heat released graph) = 1241.11 J

Combustion efficiency = Total heat released / potential energy of fuel

Combustion efficiency =1241.11/13.2= 94.03%

The need of wall heat transfer model

It is known that heat transfer in engines affects engine efficiency and emission. An increase of heat transfer to the combustion chamber walls is lower the in-cylinder pressure and the average gas temperature and this reduces the work per cycle transferred to the piston. Thus, the magnitude of engine heat transfer is strongly dependent on engine efficiency. Since the engine heat transfer is important, the accurate predicted engine heat transfer results are needed. For it, wall heat transfer model is used. We chose O’Rouke and Amsden wall heat transfer model. If some one wants wall temperature without using wall heat transfer model, he have to solve additional equations and it is a time consuming process, so, to use wall heat transfer model is always beneficial.