1. Space Distribution of Spray Injected Fluid
Peng Ye

2. Introduction
In a DI diesel engine, fuel is directly injected into the chamber.
Two phases: fuel and air
Assumed physical properties
Assess model's applicability

3. Governing Equation Navier-Stokes Convection and diffusion
ρ denotes the density, t denotes the time, u denote the velocity, P is the pressure, µ is the dynamic viscosity, F is the body force δts is the time-scaling coefficient, D is the diffusion coefficient, c is the concentration and R is the reaction rate.
From left to right of the Navier-Stokes: unsteady acceleration, convective acceleration, pressure gradient, viscosity force and body force.
Convection and diffusion

4. Level Set Method
Fuel: c=1; Air c=0

5. Stabilization Approach
Usually when Peclet number or Reynolds number is larger than 2, oscillation would occur.
Isotropic diffusion: to add an artificial coefficient.
The new Peclet number:

6. Modeling

7. Result

8. Applicability The assumptions for Navier-Stokes equation are:
Conservation of mass, momentum and energy.
Newton's second law holds.
The fluid is a newtonian fluid. The viscosity can be considered as constant and the fluid is isotropic and incompressible.
The supplementary equation describes a continuous fluid.
The 3rd assumption does not hold for complex Reynolds properties.

9. Reynolds number
Reynolds number could be used to indicate the applicability of this model.
This case: Re=1.414

10. Reynolds number up limit
Density: Re=2.1
Pressure: Re=3.38
Viscosity: Re=16.6
Not exactly the same, but not vary much. Density has the highest sensibility.
Pressure
Viscosity

11. Conclusion
The coupling of Navier-Stokes and convection and diffusion could solve injected fluid problem, but it requires low Peclet and Reynolds number.