2D Cavitation simulation

Winkl Hoffer Nozzle

Objective

to simulate Winkl Hoffer nozzle and to investigate how cavitation will behaviour while pressure difference increases.

We have 3 cases: 30Bar, 70Bar and 100Bar pressure differences.

Theory

Cavitation is a phenomenon in which rapid change of pressure in liquid lead to the formation of small vapour-filled cavities, where pressure is relatively small.

When subjected to high pressure these vapour-filled cavities so called "Bubbles" or "Voids" collapse and generate shock waves which are strong close to the Bubble but rapidly weakens as it propagates from the bubble.

Cavitation occurs when the local static pressure is lower than the liquid vapour pressure, therefore as we know according to the Bernulli's equation of the energy conservation, static pressure is the lowest where the Kinetic energy is the highest, for instance on the suction side of the pump blades, However cavitation may also occur where velocity is low along with pressure, for example, in a pipe where flow immediately induces from a large cross-section to a narrow cross-section, where flow experiences large portion static pressure drop and velocity increase, we encounter circulation motion of fluid close to a sharp corners of a pipe, where velocity and pressure both become much lower than in the surrounding areas (shown in the Figure 1).

• Figure 1

While the local static pressure is lower than the liquid vapour pressure cavitation bubbles are growing (Shown in the Figure 2).

• Figure 2

When the cavitation bubbles are transported, as they reach the liquid vapour pressure, they stop growing (Shown in the Figure 3).

• Figure 3

When the local pressure exceeds the liquid vapour pressure, bubble starts to break down at it's weakest point (Shown in the Figure 4).

• Figure 4

When the bubble breaks down water (or other liquid) flows into the volume, which is occupied by the vapour, subsequently the bubble becomes toroid and the micro jet pierces into the remains of the bubbles (shown in the Figure 5).

• Figure 5

The micro jet hits the walls of the material where the liquid flows (Shown in the Figure 6).

• Figure 6

The micro jet collisions to the walls lead us to the micro cracks, which after some portion of time may cause severe damages to the material (Shown in the Figure 7).

• Figure 7

Case Set Up

We have 3 cases: 30Bar, 70Bar and 100Bar pressure differences between the inflow and the outflow. As a fluid we use a fuel C14H30.

We study the simulations in 2 dimensions.

• Geometry (isometric back-side view)

• Geometry (isometric front-side view)

• Boundary flagging

• Materials

We have 2 phase: liquid and gas of the fuel C14H30

• Run parameters

• Time parameters

• Boundary Conditions

The "Inflow" and the "Outflow"

The Walls ("Top and bottom walls" and "Throat")

The "Side wall A" and "Side wall B" are TWO_D (2 dimensional) boundary types.

• Turbulence model

• Volume of Fluid (VOF) model

• Mesh

Base grid size

AMR

Adaptive mesh refinement (AMR) is used to refine mesh dynamicly only within the areas where it's needed. we are using velocity and species AMR. while the second order derivative (which shown the curvature of a function) of the velocity exceeds 0.1m/s and second order derivative of mass fraction of C14H30 (SGS embed) is more than 0.0001, the mesh will be refined to capture complex flow structures.

Fix embedding

In the Embedding 3 you can see that the Cylinder is the area where the mesh will be refined within the whole geometry.

Mesh generation

Post Processing

• 30Bar pressure drop case

Mass flow

In the plot above it's clear that mass flow has been converged perfectly.

Velocity

As we see in the plot above velocity at the Outflow is approximately 4 times bigger than at the Inflow, This is due to hugh pressure difference which drives the fluid, Furthermore in the nozzle we encounter immidiate cross-section decrease, which also increases the velocity of the fluid. According to the energy conservation when we have static pressure drop, dynamic pressure (kinetic energy), therefore velocity should increase.

Velocity and Alpha (indicates void fraction) contour animation

when the pressure difference is 30Bar we see that there is almost no cavitation.

Mass flow at the Outflow

You can see than the profile of the mass flow at the outlet is not even, at the walls mass flow is significantly less than in the middle of the nozzle, it's due to channel fully developed flow (Poiseuille equation). In this case we see that fluctuation in mass flow is negligible.

• 70Bar pressure drop case

Mass flow

Velocity

Velocity and Alpha (indicates void fraction) contour animation

In the 70Bar pressure drop case, we encounter cavitations close to the sharp edges, In the areas where the Alpha equals to 1 there we have a gas phase and where the Alpha equals to 0, the fluid is in liquid phase.

Mass flow at the Outflow.

In the 70Bar pressure drop case we see that fluctuations of the mass flow has been increased due to increase in cavitation.

• 100Bar pressure drop case

Mass flow

In the 100Bar pressure drop case, it's clear that we have noticable fluctuations in the mass flow at the Outlet.

Velocity

All this fluctuations (instabilities) are caused due to severe cavitation.

Velocity and Alpha (indicates void fraction) contour animation

Mass flow at the Outflow.

In the 100Bar pressure drop case, mass flow fluctuations is the highest due to higer cavitation intension.

• Pressure difference VS Cavitation zone length

As we see as the pressure difference increases, cavitation zone increase exponentialy.

Conclusion

We successfully simulated all 3 cases. Learnt what cavitation means and how it occurs. Found out that when pressure difference increases cavitation increases as well. Furthermore saw that cavitation affects mass flow rate of the system.