Break of a water jet

prepared by : Stéphanie Roy & Alban Depoutre


 

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Let us consider a falling down water jet. If the jet is thin enough, it will break into drops after a short time. You can do the experiment in your bathroom by opening the faucet so that to obtain a laminar thin water jet.

We tried to simulate the drop formation with a numerical code called Fluent. According to the litterature, this is an axisymmetric situation ; that is why we used a 2D grid.

Physical problem

The following table is a summary of almost all the tests we did.

Before reading it, you must know that the fluid is flewing from the bottom to the top of the grid and that there is no gravity in our tests.
 

case Grid Description of the flow Results Comments
#0
  • 3-D 
  • Not uniform
  • Not cartesian
No description
No results
  • This grid is just a test, it is not a physical case. We wanted to precise it but...
    • Grid too ambitious
    • Too many cells
    • Not enough memory
  • Difficulties appear to obtain compatible cells in the interface
  • No simulation
#1
  • 2-D 50*120 cells
  • Cartesian-symetric
  • Uniform in the water jet
  • Non uniform anywhere else
  • Water jet in air
  • Unsteady and viscous model
  • VOF method
  • Time step : 0.001 s


    • Initial condition :

    • Water jet with a 1 mm radius and a 30 cm length at 0.1 m/s
    • 15 cm wide air inlet at 0.001 m/s
    Boundary conditions :
    • Velocity inlet for water / air
    • Symmetry on the water jet axis and on the other lateral face
    • Outflow for water / air
    No results
    • Reversed flows appear
    • Calculation do not converge after the second time step
    #2
  • Water jet in air
  • Unsteady and viscous model
  • VOF method
  • Time step : 0.001 s


    • Initial condition :

    • Water jet with a 5 mm radius and a 10 cm length at 0.1 m/s
    • 5cm wide air inlet at 0.001 m/s
    Boundary conditions :
    • Velocity inlet for water / air
    • Symetry on the water jet axis and on the other lateral face
    • Pressure outlet for water / air
    		 No Results
    • We drew this grid in order to know if the failure of the convergence was due to the shape of the grid (huge ratio length / width in the previous grid)
    • Reversed flows appear
    • Calculation do not converge after the second time step
    #3
    Same grid as case #2
    • Water-jet in engine-oil
    • Same conditions as case #2 
    Results after 0.126 s :

    Pressure & phase 
    • The goal of this case is to know if the results are better if we use two fluids having the same density range.
    • We did not continue calculation because the grid was not thin enough within the water and was too thin far from the jet.
    #4
    Same grid as case #1
    • Water jet in engine-oil
    • Same conditions as case #1
    Results after 3 s :

    Pressure & phase
    • A kind of drop but there is no break even after three seconds.
    • The pressure is uniform. Nothing in the pressure repartition can make us forecast a break.
    #5
  • 2-D 40*100 cells
  • Cartesian-symetric
  • Uniform in the water jet
  • Not uniform elsewhere
    		•
  • Water jet in engine-oil
  • Unsteady and viscous model
  • VOF method
  • Time step : 0.001 s


    • Iintial cindition :

    • Water jet with 2 mm radius and 10 cm lengh at 0.1 m/s
    • 5 cm wide engine-oil inlet at 0.001 m/s
    Boundary conditions :
    • Velocity inlet for water / engine-oil
    • Symetry on the water jet axis and on the other lateral face
    • Pressure outlet for water / engine-oil
    Results after 5 s :

    Pressure & phase
    • Same comments as the previous case
    #6
    Same grid as case #5
    		 We have decreased the viscosity of the water-liquid to 1E-10 kg/m-s (initialy equal to 1.003 E-3) with the same conditions as case #5.
    Results after 0.8 s :

    Pressure & phase
    • The goal of this case is to try an unviscid calculation with a viscous model because we could not use the unviscid model.
    • The results are not really convincing
    #7
    Same grid as case #5
  • We have decreased the viscosity of the engine-oil to 1E-5 kg/m-s (initaily equal to 1.06 kg/m-s)
  • We have decreased the viscosity of the water-liquid to 1E-5 kg/m-s 
  • We have patched the initial water-jet with an alternating static pressure in order to try to disturb the flow.
  • The other conditions are the same as case #5.
    		•
    Results after 0.5 s :

    Pressure & phase
    • The results are completely strange.
    • No use to go further.
    #8 Same grid as case #5
    • Water-jet in air
    • The conditions are the same as case #5 with a time step equal to 0.0001s
    		 Results after 3 s

    Pressure & phase
    • Test with a smaller time step
    • The calculation converge 
    • The pressure repartition make us think that drops will appear.
    • After 3 s, we still have no interesting results

    Conclusion

    In none of the case we saw the drops appear.

    The last case left us hopeful because of the good pressure repartition, but the phase did not show any drops even after a long time calculation. We should have tried a smaller time step (for instance 1E-5s). However this kind of calculation takes a long time, i.e. several days, and the work stations are rebooted every night.

    Another explanation may be that Fluent is not a specialised free interface code, and it is difficult to process such a situation.