On the bubble departure diameter and release frequency based on numerical simulation

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On the bubble departure diameter and release
frequency based on numerical simulation

• Gábor Házi, Attila Márkus

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Outline

• Motivation
• The lattice Boltzmann method
• Simulation results
• Bubble departure diameter
• Bubble release frequency
• Conclusion
• Future plans (proposed work)

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Motivation

• Two key parameters for nucleate boiling heat
  transfer
• bubble departure diameter
• bubble release frequency
• Standard force balance results are still
  challenged by some novel heat transfer model

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The lattice Boltzmann method (1)

• LBM is our numerical vehicle to study bubble
  dynamics
• Lattice BGK model pseudopotential extension
  (interaction between particle distribution
  functions to model attractive and repulsive
  forces ? non-ideal gas)
• The pseudopotential determines the equation of
  state and its parameters control the surface
  tension
• Energy equation is coupled in macroscopic level
• Wall-fluid interaction is taken into account by
  interaction potentials between the fluid and
  wall, parameter of the interaction potential
  controls the wettability of the wall
• All details in Házi G., Márkus A., On the bubble
  departure diameter and release frequency based on
  numerical simulations, Int. J. Heat and Mass Tr.
  accepted for publication

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Binodal and surface tension

• For this study special form of the
  pseudopotential has been used to achieve proper
  Maxwell construction (derived by analitical
  methods)

Binodal (coexistence curve)
Surface tension
(in lattice units)
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Wettability
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Study of evaporation

• Heated plate at the bottom and constant
  temperature in the domain
• Periodic domain in the horizontal direction
• Pressure boundary at the top of the domain
• Higher heat flux at the center of the plate, to
  mimic higher surface area of a cavity (I turn
  back to this issue later on !) ? to initiate
  boiling

Study of domain size effect
2. ábra Az érzékenységi paraméterek aránya
szuperkritikus nyomáson (ld. szöveg).
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Phases of bubble detachment

• no specific models at the micro and macro regions

microconvection

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Bubble departure diameter

• effect of variable gravity forces

• effect of variable wettability

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Bubble release frequency

• at 7000, 12000, 17000, 22000, 27000, 32000
  simulation steps

after the 1st cycle, periodic

1st cycle

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Effect of static contact angle

• The growing and departure process do not change
  qualitatively but they take place in another
  timescale. Larger contact angle means larger
  attractive force between the fluid and the wall.
  Larger force increases the residence time of the
  liquid layer adjacent the wall. Phase transition
  speeds up with overheating, so the net effect of
  larger surface tension can be faster growing up
  of bubbles. Larger attractive force also supports
  the rewetting of the dry spot, which can further
  speed up the bubble cycles.

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Detachment in horizontal background flow

Development of upstream and downstream contact
angles
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Effect of horizontal flow on departure diameter
Exponential function of the horizontal velocity
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Conclusion

• LBM can be a useful numerical tool to study
  evaporation and bubble dynamics
• simulation results support standard force
  balance correlations both for detachment diameter
  and release frequency
• wettability has an effect on release frequency
  but it does not influences on the departure
  diameter (contradicts some earlier simulation
  results obtained by pure macroscopic models)

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Future plans proposal (1)

• Comparison of various nucleation probability
  theories to get the best result for a given
  problem
• determine the cavitation probability vs. extent
  of overheating.
• Simple equation of state for water and
  corresponding interaction potentials
• van der Waals like EOS and corresponding pseudo
  interactionpotential has already been developed
  for water,
• further optimalization of the parameters could
  reduce the error of the binodal, which is
  currently below 20 in a wide range of
  temperatures
• Simulation of heterogeneous boiling in background
  turbulent flow
• detachment of bubbles is usually simulated by
  assuming turbulent velocity profile in the
  so-called microregion
• in our approach the background flow can be
  produced in a coupled domain (plane channel flow)
  and can be introduced into the boiling region (it
  has already been developed)
• Interactions between turbulence and the
  detachment process could be studied

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Future plans proposal (2)

• Simulation of bubble interactions during
  detachment considering packed nucleation sites
• using our approach, interactions between bubbles
  can be taken into account in a straightforward
  manner
• various aspects of such kind of interactions
  (effect on departure diameter, release frequency,
  sequence of events etc. could be studied in
  stagnant, slowly moving and turbulent fluids
• Simulation of boiling in rod bundle subchannels
• (NURESIM activity)
• with a focus on the detachment process