1. Design of Port Injection Systems for SI Engines
P M V Subbarao
Professor
Mechanical Engineering Department
Methods & Means to Control Premixed Combustion…..

2. Port Fuel Injection System

3. Physical Models for Spray Characterization
Entropy of a group of droplets:
where S is the information entropy, the name used when the information concept is applied to problems in physics and engineering.
In this equation K is a constant and Pi is the probability of the occurrence of a certain result, in terms of number fraction.
Maximum feasible entropy corresponding to physical conditions will decide the droplet distribution.

4. Physical Constraints
The following physical and mathematical constraints must be obeyed:
The sum of all probabilities must be unity:
(ii) the mass flow of sprayed liquid must be equal to the
mass of all droplets produced per unit time:
where n is the total number of droplets produced per unit
time and mL is the liquid mass flux.

5. Simplified Engineering fuel Evaporation model
The comprehensive fuel spray model predicts individual motions of liquid fuel droplets and evaporation of each droplet.
It also includes a more detailed treatment of in-cylinder evaporation.
In a simplified engineering model a representative diameter for the entire group is defined to compute evaporation rate.
Equivalent diameter of same number of uniformly sized droplets having
same total surface area.

6. Sauter Mean Diameter Introducing the definition of SMD:
where dnozz is the nozzle diameter,
μf , μg are the fuel and gas dynamic viscosity, respectively,
Re the Reynolds number and
We the Weber number.

7. Fuel Droplet Dynamics : Prediction of Trajectory

8. Details of Heat and Mass Transfer across Droplet

9. Evaporation Process

10. Droplet dynamics
During the spray penetration, there is a drag force exerted on the droplets from the surrounding gases, which tends to decrease the relative velocity between the drop and the gas flow.
From the Newton's Second Law, the equation is:
Where d is the droplet diameter, ug and uf are the velocities of the gas flow and the liquid fuel droplet, respectively.
And the drag coefficient CD is given as:

11. Droplet evaporation The droplet evaporation rate is given by
where d is the droplet diameter, DAB the gas diffusivity, Sh* the non-dimensional Sherwood number, and Bm the mass transfer number.
The mass transfer number BM is equal to:

12. The heat flux available for heating up the droplet is:
where the ambient temperature, T∞ and ξ the correction factor to account for the effect of evaporation on heat transfer.
The gas phase temperature is evaluated from the one-third rule

13. Port Fuel Injection System : Spray Wall Impingement

14. Control of Wall Wetting in Port Injection

15. Geometrical Features of Fuel Spray

16. Model to Design a Spray

17. Wall Wetting in Valve Regime

18. Droplet Impingement Process

19. Droplet Impingement on Film

20. Film Height And Surface Angle Distribution

21. Simulated Experiments

22. Variation of Volume Fluxes

23. Spray Wall Impingement
In an engine system, a liquid fuel spray may impinge on the solid walls, either on the smooth sidewalls in ducts, manifolds and cylinders.
A Model is needed to find the impingement site with the given fuel spray cone angle and impingement incidence angle.
This model estimates the nominal area covered by the spray cone angle from the duct geometry.
For each impingement site, the impingement probability and the passing-by probability then are assumed to be proportional to the spray covered wall area and the downstream flow cross-sectional area.

24. Regimes of Wall Impingement
The droplets in the cylinder can be discharged to the exhaust duct, when the exhaust valve opens.
It is assumed that the droplets are uniformly distributed within the cylinder.
There exists a wide range of spray wall impingement regimes, which have been identified as, Adhesion, Rebound, Spread and Splash.
The outcomes of impingement depend on the incoming droplet conditions: droplet velocity, size and temperature, incidence angle, wall temperature, surface roughness, wall film thickness
and fluid properties, such as viscosity and surface tension.

25. Film Dynamics
There are two different forces exerted on a fuel wall film.
On the gas side, the gas flow tends to drive the film moving along the same direction.
On the wall side, the viscous friction tends to resist the film movement.
The force balance on the film gives the equation for the film motion:

26. τg and τw are the driving force on the gas side, the viscous stress on the wall side.
τimp the momentum source per unit film area due to the impingement.

27. Deposited Film Mass Fraction