In an engine, fuel flow follows a complex path as it flows from the tank to the combustion chamber. When the fuel flows through chambers the area suddenly changes, resulting in increased or decreased pressure.

In this project, we will be focusing on how fuel flow induces cavitation when it enters the combustion chamber through a Winkl-Hoffer nozzle. In this context, cavitation refers to the formation of gaseous bubbles in the fuel as some of the fuel vaporizes when it flows through sudden-pressure areas.

When the fuel exits the fuel chamber and enters the throat of the nozzle, there is a sudden drop in the static pressure. This is because there is an abrupt change in the flow area. When the flow area suddenly decreases, it creates a zone of low pressure or separation zone which is basically vacuum.

Cavitation occurs when the static pressure drops below the vapor pressure of the liquid due to the formation of a vacuum. When this happens, the boiling point of the fuel also reduces. Hence the fuel will essentially start boiling and begin vaporizing into gas. Cavitation affects the fuel flow rate which can further affect the combustion and emission performance. Therefore, the study of cavitation is very important in automotive applications

In HVAC or Turbomachinery world, it is important to study cavitation in rotating devices. For example, in a centrifugal pump, the impeller rotates at a very high speed due to which a low-pressure zone is formed.  When the fluid in this low-pressure zone, it vaporizes to create gas bubbles that hits the component and cause erosion on the impeller. This results in decreased life of the component.

Therefore, the study of cavitation is extremely important and CFD is the tool to study this complex process.


To simulate fuel injection computationally in a Winkl – Hoffer Nozzle and study the cavitation happening through it.

Software used: CONVERGE STUDIO

In CONVERGE, cavitation is studied by using the Volume of Fluid (VOF) approach.


Cavitation is a multi-phase flow problem as it has both liquid phase and gas phase and in order to run such a simulation, the VOF methodology will be adopted.

In CONVERGE CFD, the transition from a liquid phase to gas phase is described by the following rate law,


Case setup for 2D Cavitating Nozzle in CONVERGE STUDIO:

The following image displays the case setup for 2D Cavitating Nozzle in Converge Studio:

Case setup for 2D Cavitating Nozzle

Fuel used: Tetradecane (C14H30)

Properties of both gaseous and liquid tetradecane is enabled as liquid tetradecane (lC14H30) will be vaporized into gaseous tetradecane (C14H30)

  • Liquid Tetradecane (IC14H30)
  • Gas Tetradecane (C14H30)

The process was simulated ran for 2 milliseconds (i.e. 0.002 seconds) which is typically the duration of injection.

Case Setup:

Boundary Conditions:

  • Pressure at Inlet = 100 bars
  • Pressure at outlet = 30 bars

There is a pressure drop of 70 bars between the inlet and outlet pressure. This pressure will result in increased velocities. In such simulations where the velocity values are high, we need to pay special attention to the velocity based CFL number which is also called a convection based CFL number.

Since the geometry is symmetrical about the Z-axis it is better to have a 2D simulation, as the flow along the Z-axis is not going to change.

  • Turbulence model: RNG K-ξ
    • Since cavitation is an effect of pressure and not shear, we will be choosing the RNG K- ξ turbulence model.
  • VOF model: Basic VOF
    • The Basic VOF solver will solve one transport equation for the liquid phase and one transport equation for the gas phase. It will automatically take into account, the calculations that must be performed due to the interface between the liquid and the gas.
  • Grid Control:
    • Base grid
      • dx = 4m
      • dy = 4 m
      • dz = 4 m
    • Adaptive Mesh Refinement (AMR):
      • When the cavitation takes place there will be gas-phase specie and liquid phase specie and to track the curvature of gas-phase species in the entire domain, we are enabling AMR.
      • Wherever curvature exceeds value 1e-4, the mesh will be refined.
      • Here AMR for velocity and species is enabled as shown below,


Post-processing results:

Velocity contour of the Winkl-Hofer nozzle

We can see above from the velocity contour that the velocity reaches a maximum at the throat. This is because when the fuel enters the throat, the sudden contraction of the area causes the pressure levels to drop critically.

Also, there is a small region in the throat where the velocity is low. This is shown in the image below:

When the fuel exits the fuel chamber and enters the throat of the nozzle, the layer of fuel flowing along the walls get separated and flow towards the center of the throat. This will cause a vacuum to form in that region which denotes low static pressure. When the static pressure in that region drops below the vapor pressure of the liquid ( which is C14H30), cavitation occurs as some of the fuel cavitates to a gaseous phase. This can be visualized in 2 ways by looking at the contours of a void fraction (⍺) as shown below,

Contours of void fraction

If  = 0, it denotes that we are dealing with liquid phase.

If  = 1, it denotes that we are dealing with gas phase.

During cavitation when both liquid and gas co-exist, the void fraction levels (⍺) will be between 0 and 1.

In the contour above, we can see that the void fraction levels are zero (denoted by dark blue contour) for most of the mechanism. But in a small area near the sharp corner, the void fraction level is 1 (denoted by red contour). And in the area lying sandwiched between the two contours, the void fraction levels are intermediate of 0 and 1. This denotes cavitation in that region.

Important line plots:



The plot of mass flow rate at inlet and outlet confirms that mass is conserved. Also, we can see that the mass flow rate fluctuates at the outlet which is expected because of cavitation.


The reason for studying the cavitation is that physical systems like fuel injectors undergo cavitation frequently. When we consider diesel injectors, the injecting pressure is rather high which increases pressure drop as well and this can result in cavitation. Although cavitation is not necessarily bad, it does affect the life-time of the part, but more importantly, it affects the fuel flow rate.

As we can see in the snapshot below, the mass flow rate of fuel is fluctuating excessively:

These fluctuations in the mass flow rate can affect the system performance.

Any fluctuations in the fuel flow can affect the combustion characteristics. Therefore, the study of cavitation is important when studying automobile and engines.


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