FULL HYDRO case set up PFI


To simulate the full hydro setup of a Port Fuel Injected engine which uses Iso octane as the fuel.


When fuel injection takes place due to the interaction of the liquid with the surrounding air there is a drag force which causes disturbances in liquid length. These disturbances propagate and if they are large enough the spray breaks up i.e.Atomization. A liquid breaks into small parcels i.e. primary break up, and these parcels break up even further to tiny parcels i.e. secondary breakup. When spherical drops interact with ambient air their shapes get affected which results in fast or slow vaporization i.e. Drop Drag. Reduction in drop size is described with evaporation. All these properties which describe the behavior of fluid drops are explained by various physical models.

A liquid spray is made up of a bunch of parcels. i.e. Spherical structure with a lot of drops and together if we have a lot of parcels, in general, it represents our fuel spray. This type of modeling is called Lagrangian Modelling.

Our parcels i.e. Lagrangian Spray is made up of IsoOctane(IC8H18) which has the physical properties close to that of gasoline fuel. The physical properties of fuel in experiments must match with the parcel species used in the simulation. The list of participating species in the simulation is already provided with a reaction mechanism files. Parcels are a group of spray drops having the same geometry and same thermodynamic properties. A large number of parcels represent our entire spray field. The above diagram shows us how the parcels are represented.

Volume of Fraction

The VOF employed in the present study is based on a mathematical model composed of governing equations for the conservation of mass and momentum of a two-phase system, accredited. This system comprises two immiscible, compressible fluids and accounts for the surface tension between the two-phases. The VOF interface tracking method is a simple and flexible approach for the prediction of two-phase flows. A major limitation of this method is its limited ability to ensure boundedness of liquid volume fraction and preserve sharp interfaces without an interface reconstruction algorithm such as Piecewise Linear Interface Construction (PLIC).

It enables regional coupling of a Eulerian liquid-Eulerian gas (VOF) regime with a Eulerian gas-Lagrangian droplets (LPT) regime. The coupling is performed by interpolating field information between the liquid-gas mixture in the VOF simulation and the carrier phase (gas) in the LPT simulation. After receiving field information from the VOF simulation, the two-way
interaction of the carrier phase and droplets is handled in the LPT simulation. The effects of the droplet dynamics on the carrier phase is then reflected on the VOF simulation through the two-way field interpolation process. The overlapping region is where the transition from primary to secondary spray atomization occurs and it couples the VOF and LPT simulations with two identical overlapping grids. Figure 1 shows the position of this region in relation to the spray. The developing spray is divided into three stages, namely the primary breakup stage when an intact liquid core is present, the transition stage (dense region) at which the liquid core starts to disintegrate into large ligaments and finally the diluted phase in which small liquid structures form and are dispersed by the carrier phase. It should be mentioned that the right end of the coupling region should be placed far away from the maximum liquid penetration to avoid potential boundary effects and to prevent unconverted VOF droplets from escaping the domain.

Collision model
The collision of parcels is handled by a Stochastic Trajectory Collision (STC) model. Unlike the O‟Rourke collision model which initiates collision of two parcels when they occupy the same computational cell and their estimated probability of collision is higher than a threshold value, the STC model takes the trajectory of each participant into account. This model considers the onset of the collision between two parcels when their trajectories intersect, and the intersection point is reached at the same time within one Eulerian integration step.

Droplet Identification Procedure (DIP)
In this section, the development of a parallel droplet identification procedure is described. This procedure is designed to identify liquid structures that are smaller than 20% of their host cell‟s volume. In addition, it is determined that these liquid structures should be discretized by less than 5 mesh cells in order to minimize the effect of droplet eccentricity. Specifically, in the case that a small liquid structure satisfies the maximum volume criterion for VOF-LPT conversion and is spread over 5 or more mesh elements, it can have rather a high eccentricity. Extracting such a liquid ligament and representing it with a spherical droplet in the LPT simulation can be a significant source of error especially for sub-grid physics. Therefore, only liquid structures that satisfy the minimum volume requirement and are discretized by less than 5 elements are considered eligible candidates for  VOF-LPT conversion. Further, only identifying and extracting liquid structures occupying less than 5 mesh elements is computationally advantageous that such a process is not implemented on all large scale liquid structures which are dominant in the VOF simulation.

Geometry and Boundary Flagging

The geometry and the boundary flagging aspects have been explained in detail on the previous project. The geometry was imported in Converge using the STL file given and the surface preparation and boundary flagging were done. Once the No-Hydro simulation ran smoothly and after the results obtained from it were verified, the full hydro case setup was done.

Case Setup

A crank angle-based IC engine application was chosen to perform the simulation. The engine dimensions (bore, stroke and connecting rod length) was provided as inputs. The engine speed was chosen to be 3000 RPM.

The fuel chose was Iso Octane (iC8H18) and the spray parcel properties were taken from the data file of Iso Octane.

The transport parameters were set as default values. The reaction mechanism was set based on the data file for Isooctane combustion.

A full hydrodynamic solver is used in this case and the simulation was run for -520 Crank Angle Degree to 120 CAD with the initial time step being 1e-07 s and final time step being 0.0001s.

Boundary Conditions

The piston boundary was set at a temperature of 450 K and the motion type was set as translating. The piston speed is 3000 RPM (as mentioned earlier). The cylinder head and liner were also assumed to be at the same temperature as that of the piston and they were set as stationary wall boundaries with Law of Wall condition.

  1. Air was assumed to be the working fluid entering the intake port (inflow) at a temperature of 363K and at a pressure of 1 bar.
  2. The intake ports were assumed to be at a temperature of 425 K and they were set as stationary boundaries with Law of Wall condition.
  3. The intake valve boundaries were set at 480 K and they were set as translating wall boundaries. The intake valve lift input file was provided for specifying the valve lift at a given crank angle.
  4. The exhaust ports were assumed to be at a slightly higher temperature (500K) since the gas flowing out of the exhaust ports will have a higher temperature.
  5. Similarly, the exhaust valves were also set at higher temperatures (525 K) and were assumed to be translating boundaries with exhaust valve lift provided as input.
  6. The exhaust gas flowing out of the outflow boundary is assumed to be at a temperature of 800 K and the stoichiometric composition of each compound contained in the exhaust gas was calculated based on the combustion reaction for Iso-Octane and then the mole fraction was given as input.

Initial Conditions

The initial conditions can be assigned to the setup based on four regions:

  1. Cylinder
  2. Intake Port-1
  3. Intake Port-2
  4. Exhaust Port

Cylinder Initial Conditions: The initial cylinder pressure is set as 1.85731 bar and the temperature as 1360 K. The temperature is set high because the in-cylinder temperature at the end of the combustion process will be extremely high. The composition of species contained inside the cylinder was computed using the stoichiometric proportions of the combustion reaction.

Intake Port: In the intake port near the combustion chamber (Intake Port-1) air is assumed to be flowing in with the fuel being injected through the nozzle. Thus, the mass fractions of oxygen, nitrogen are assumed to be air’s composition and the amount of fuel injected is also given. The temperature is assumed to be slightly higher than atmospheric temperature -390K and pressure is 1 atm. In the intake port-2 which is closer to the inflow boundary, the temperature is 370K and pressure 1 atm. Mass fraction is that of airs.

Exhaust Port: The temperature is assumed to be 500 K and pressure 1 atm. The composition of the gas in the port is calculated by the stoichiometry of end products of combustion.

Events: The intake valve and exhaust valve opening and closing are controlled by an event. The valve lifts are provided as the input to control the opening and closing.

 Spray Modelling

The picture below depicts how CONVERGE CFD helps us to set up a spray model for our IC Engine geometry:

A Frossling spray model was used in this simulation to model the fuel spray. The parameters involved in the spray model was set to be the default values. The spray wall interaction model was chosen to be a wall-film one in the assumption that a film like a layer would get created if the spray comes in contact with the wall. A Kelvin-Helmholtz injector model was used to model fuel injection. The total mass injected was set as 3e-05 Kg and the rate shape value asset as below:

Four nozzles have been used in this simulation and their respective coordinates have been given as inputs. And the injection type is a solid-cone spray. An O’Rourke film splash was used.

  • For a Lagrangian model, our cone has a spread angle. The way in which the parcels are distributed in our case is through a solid cone having evenly distributed parcels. We have to set up the way in which our parcels are distributed like the picture given below:
  • Turbulent Dispersion is sort of turbulent fluctuations which is going to affect our droplet gas characteristics.
  • Our IsoOctane(IC8H18) liquid-phase fuel is converted to IC8H18 gaseous state.
  •  For our parcels, we are having a maximum value for the radius. If our drop radius is beyond this cut off value then the radius ODE is solved, else not.
  • Vapor penetration length is calculated by having a cell with vapor in which there is a minimum amount of vapor present in the cell characterized by a mass fraction as shown in the figure below:

  • The collision models are chosen based on experience and engine type on the model can be better suited than others. This comes by referring to journals or periodicals. Also for collision calculations, we use a mesh different from the original computational mesh. This improves collision calculations without mesh.
  • Dynamic drop models are based on drop distorts based on velocity, drag and compute drag coefficient (Cd). All these are mentioned in the picture below:

A wall film has additional spray parcels which can hit the wall and splash. When parcel hits the wall it may rebound or encounter thermal breakup these are studied by additional models mentioned in the setup picture below:

Combustion Model: A SAGE model was used to model the combustion process in this simulation. The start time was specified as -17 CAD and end time as 130 CAD. The SAGE model was assumed to be region independent for simplicity.

An RNG k-epsilon turbulence model with default parameters was used for turbulence modeling. The spark was modeled using a source model. The start of spark ignition is set as -15 CAD and the duration is 10 degree. The spark radius is set as 0.0005 m. The spark temperature is set as 50000 K.


The base grid was set around 1 mm since the target cell count was around 800000. AMR was used for the cylinder and intake ports to improve accuracy. Embedding level was set as 3 and subgrid criterion of 2.5 was used.

A cyclic embedding for the injector was used as embedding needs to be active only when the fuel is sprayed. The entire piston-cylinder arrangement was given an embedding at 2 levels in the scale of 1. The intake and exhaust valves were also provided with embedding.

If there is a gradient in temperature the temperature cells are refined. This is the basic principle of having AMR. When sparks are introduced at that distant we don't have good refinement so that these gradients are calculated accurately. Highly refined regions are created to last a few crank angles so that our temperature AMR is able to see a huge change in temperature gradient near the spark and then it vanishes. Having a coarse grid will have only low curvature values and no AMR. Having small cells will help us calculate turbulent length scales.

Performance Parameters


The compression in the cylinder has increased the pressure to the maximum value of 3.8 MPa. Because of the expansion phase, we can see the pressure decreasing rapidly. This can be seen in the graph below:

Mean Temperature

The mean temperature during the compression stage reaches the maximum possible value of 2500K as shown in the figure below:

Heat transfer in IC engines is a very vital phenomenon and it has a direct effect on the engine performance. In an SI engine, (like in this case) a spark ignites the compressed air-fuel mixture and a flame kernel propagates throughout the system. This flame kernel gets quenched near the wall and thus heat transfer occurs between the flame and the wall. Inside the cylinder due to turbulence, swirling and tumbling, the accuracy of measurement of critical parameters get affected. Hence due to the two reasons listed above a wall heat transfer model is used rather than CFD to predict wall temperature.

While solving thermodynamic equations we assume that the value of Gamma is constant but from the graph shown in the picture below, we can see that gamma value changes as a function of Crank Angles.

Mass and Volume

From the graph, we see that fuel is supplied to our engine in prescribed quantities. It reaches a maximum value of 1.4 micrograms and then starts vaporizing suddenly for the combustion to happen. We can also calculate the amount of fuel that is trapped in the engine as well which is one of the key aspects of its design.

The entire amount of chemical energy possessed by the fuel is not converted during the combustion process. Some amount of fuel goes unburnt and that chemical energy is not utilized. The extent to which complete combustion occurs is measured by combustion efficiency. The mass of fuel injected is given as 3*10^-5. The lower heating value of iso-octane is given as 44.6 MJ/kg. The mass trapped by the engine is found from the picture below. Mass trapped multiplied by the enthalpy of formation of the elements will give the heat released by combustion.

Based on the calculation the compression ratio of this engine was found out to be 10.07. It is an ideal compression ratio for a spark-ignition engine as not a lot of pressure is the need for combustion. For SI engines compression ratio is usually between 8-12. For CI engines the CR is between 12-20.


From the graph we can infer the following:

  • Hydrocarbons are absent as soon as the exhaust phase begins.
  • The presence of CO2 emissions is on a higher note. This can be reduced by making use of an exhaust after-treatment system.
  • Carbon Monoxide, Nox and SOOT are present in low quantities.

The engine cycle is assumed to be starting from the beginning of exhaust stroke. As the cylinder moves up pushing the exhaust gas out, the volume decreases and the pressure remains more or less constant at 1 bar. Similarly, when the intake stroke occurs the pressure is nearly atmospheric as atmospheric air is drawn into the cylinder. As the compression stroke occurs the volume reduces and pressure rises. The pressure reaches a peak at some point during the combustion process. This will be discussed in detail later. After the combustion, expansion occurs and the pressure drops.










Projects by Arun Gupta

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The End