MULTIPHASE HEAT TRANSFER

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MULTIPHASE HEAT TRANSFER

• P M V Subbarao
• Associate Professor
• Mechanical Engineering Department
• IIT Delhi

Rules for Design of Steam Generators
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Multi Phase Convection Heat Transfer

• One of the many Objectives of multiphase
  heat-transfer is
• to be able to predict the temperature of the wall
  of a boiling surface for a given heat flux or
• the variation of wall heat flux for a known wall
  temperature distribution.
• The main focus on the methodology to estimate the
  wall temperature or the wall heat flux depending
  on the appropriate boundary condition.
• Focus is on describing the regions of heat
  transfer, locating the onset of nucleate boiling
  and finally estimating the wall condition.

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Multi Phase Heat Transfer in Flow Boiling
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Single-Phase Liquid Heat Transfer

• Under steady state one-dimensional conditions the
  tube surface temperature is given by

z

• Variation of Fluid Temperature along z for
  uniform wall heat flux

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• and where
• q is the heat flux,
• P is the heated perimeter,
• A is the flow area and is the liquid specific
  heat.
• Also DTfw is the temperature difference between
  the wall surface and the mean bulk liquid
  temperature at a given length z from the tube
  inlet,
• h is the heat transfer coefficient to
  single-phase liquid under forced convection.
• Heat transfer in turbulent flow in a circular
  tube can be estimated by the well-known
  Dittus-Boelter equation.

This relation is valid for heating in fully
developed vertical upflow in z/D gt 50 and Re gt
10,000.
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The Onset of Nucleate Boiling

• If the wall temperature rises sufficiently above
  the local saturation temperature pre-existing
  vapor in wall sites can nucleate and grow.
• This temperature, TONB, marks the onset of
  nucleate boiling for this flow boiling situation.
  
• From the standpoint of an energy balance this
  occurs at a particular axial location along the
  tube length, ZONB.
• Once again for a uniform flux condition,

We can arrange this energy balance to emphasize
the necessary superheat above saturation for the
onset of nucleate boiling
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Now that we have a relation between DTONB and
ZONB we must provide a stability model for the
onset of nucleate boiling. one can formulate a
model based on the metastable condition of the
vapor nuclei ready to grow into the world. There
are a number of correlation models for this
stability line of DTONB. Using this approach,
Bergles and Rohsenow (1964) obtained an equation
for the wall superheat required for the onset of
subcooled boiling.
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Their equation is valid for water only, given by

• For any fluid

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Subcooled Boiling

• The onset of nucleate boiling indicates the
  location where the vapor can first exist in a
  stable state on the heater surface without
  condensing or vapor collapse.
• As more energy is input into the liquid (i.e.,
  downstream axially) these vapor bubbles can grow
  and eventually detach from the heater surface and
  enter the liquid.
• Onset of nucleate boiling occurs at an axial
  location before the bulk liquid is saturated.
• Likewise the point where the vapor bubbles could
  detach from the heater surface would also occur
  at an axial location before the bulk liquid is
  saturated.
• Now this axial length over which boiling occurs
  when the bulk liquid is subcooled is called the
  "subcooled boiling" length.
• This region may be large or small in actual size
  depending on the fluid properties, mass flow
  rate, pressures and heat flux.
• It is a region of inherent nonequilibrium where
  the flowing mass quality and vapor void fraction
  are non-zero and positive even though the
  thermodynamic equilibrium quality and volume
  fraction would be zero since the bulk
  temperature is below saturation.

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The first objective is to determine the amount of
superheat necessary to allow vapor bubble
departure and then the axial location where this
would occur. A force balance to estimate the
degree of superheat necessary for bubble
departure.
this conceptual model the bubble radius rB, is
assumed to be proportional to the distance to the
tip of the vapor bubble,YB , away from the heated
wall. One can then calculate this distance
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The superheat temperature, is then found by
using the universal temperature profile relation.
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Now using the local energy balance one can relate
the local bulk temperature, TfB, to the superheat
temperature difference,
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Sequence of Events in Flow Boiling
Natural or forced convection heating of liquid
Onset of Nucleation Boiling at wall
Subcooled Boiling
Saturation Boiling
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Saturated Boiling and the Two-PhaseForced
Convection Region

• Once the bulk of the fluid has heated up to its
  saturation temperature, the boiling regime enters
  saturated nucleate boiling and eventually
  two-phase forced convection.
• Objective is to find the wall condition for this
  situation e.g., wall temperature for a given
  heat flux.
• The heat transfer coefficient is so large that
  the temperature difference between the wall and
  the bulk fluid is small allowing for large errors
  in the prediction, without serious consequences.
• The saturated nucleate boiling and two-phase
  forced convection regions may be associated with
  an annular flow pattern.
• Heat is transferred by conduction or convection
  through the liquid film and vapor and is
  generated continuously at the liquid film/vapor
  core interface as well as possibly at the heat
  surface.
• Extremely high heat transfer coefficients are
  possible in this region values can be so high as
  to make accurate assessment difficult.
• Typical figures for water of up to 200 kW/m2 K
  have been reported.

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Following the suggestion of Martinelli, many
workers have correlated their experimental
results for heat transfer rates in the two-phase
forced convection region in the form
The convection heat transfer coefficient is
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• http//wins.engr.wisc.edu/teaching/mpfBook/node31.
  html

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Multi Phase Heat Transfer in Pool Boiling
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POOL BOILING

• Pool boiling is the process in which the heating
  surface is submerged in a large body of stagnant
  liquid.
• The relative motion of the vapor produced and the
  surrounding liquid near the heating surface is
  due
• primarily to the buoyancy effect of the vapor.
  Nevertheless, the body of the liquid as a whole
  is essentially at rest.
• Though the study on the boiling process can be
  traced back to as early as the eighteen century,
  the extensive study on the effect of the very
  large difference in the temperature of the
  heating surface and the liquid, DT, was first
  done by Nukiyama (1934).

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Boiling Curve
W/m2.s
0C
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Onset of Nucleate Boiling

• Vapor may form a liquid
• (a) at a vapor-liquid interface away from
  surfaces,
• (b) in the bulk of the liquid due to density
  fluctuations, or
• (c) at a solid surface with pre-existing vapor or
  gas pockets.
• In each situation one can observe the departure
  from a stable or a metastable state of
  equilibrium.
• The first physical situation can occur at a
  planar interface when the liquid temperature is
  fractionally increased above the saturation
  temperature of the vapor at the vapor pressure in
  the gas or vapor region.
• Thus, the liquid "evaporates" into the vapor
  because its temperature is maintained at a
  temperature minimally higher than its vapor
  "saturation" temperature at the vapor system
  pressure.
• Evaporation is the term commonly used to describe
  such a situation which can also be described on a
  microscopic level as the imbalance between
  molecular fluxes at these two distinctly
  different temperatures.

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• To find the particular heat flux and superheat
  pair natural convection mode of heat transfer
  that would exist prior to boiling is considered.

• For water at atmospheric pressure this model
  predicts an "onset of nucleate boiling" for a
  superheat less than 10C, with a cavity size of
  about 50 microns.
• In practice the superheat may be as high as 100C
  for very smooth, clean metallic surfaces.

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Pool Boiling Critical Heat Flux

• Critical heat flux (CHF) in pool boiling is an
  interesting phenomenon.
• If one controls the input heat flux, there comes
  a point where as the heat flux is increased
  further the heater surface temperature undergoes
  a drastic increase.
• This increase originally was not well understood.
• Kutateladze (1951) offered the analogy that this
  large abrupt temperature increase was caused by a
  change in the surface geometry of the two phases.
  
• In fact, Kutateladze first empirically correlated
  this phenomenon as analogous to a gas blowing up
  through a heated porous plate cooled by water
  above it.
• At a certain gas volumetric flow rate (or
  superficial velocity, ) the liquid ceases to
  contact the heated surface and the gas forms a
  continuous barrier.

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• where the constant, Co, is found to be in the
  range of 0.12 to 0.18.

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Film Boiling and the Minimum FilmBoiling Point

• Once the critical heat flux is exceeded the
  heater surface is blanketed by a continuous vapor
  film i.e., film boiling.
• Under this condition one must find the heat
  transfer resistance of this vapor film as well as
  consider the additional effect of radiation heat
  transfer at very high heater surface temperatures
  through this vapor film (gt 10000 C).
• Bromley (1950) used the approach first developed
  by Nusselt for film condensation to predict the
  film boiling heat transfer coefficient for a
  horizontal tube

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FLOW BOILING Design of Water Wall SYStem

• P M V Subbarao
• Associate Professor
• Mechanical Engineering Department
• IIT Delhi

Best means to Generate High Pressure steam
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Role of SG in Rankine Cycle
Using Natural resources of energy.
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Basic Geometry of A Furnace in A Large Steam
Generator
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Furnace Exit
Hot Exhaust gases
Heat Radiation Convection
Flame
Burner
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Structure of Furnace Wall

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Water Wall Arrangement

• Reliability of circulation of steam-water
  mixture.
• Grouping of water wall tubes.
• Each group will have tubes of similar geometry
  heating conditions.
• The ratio of flow area of down-comer to flow are
  of riser is an important factor, RA.
• It is a measure of resistance to flow.

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• For high capacity Steam Generators, the steam
  generation per unit cross section is kept within
  the range.
• High pressure (gt9.5 Mpa) use a distributed
  down-comer system.
• The water velocity in the down-comer is chosen
  with care.
• For controlled circulation or assisted
  circulation it is necessary to install throttling
  orifices at the entrance of riser tubes.
• The riser tubes are divided into several groups
  to reduce variation in heat absorption levels
  among them.

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Circulation Ratio

• The circulation ratio is defined as the ratio of
  mixture passing through the riser and the steam
  generated in it.

• The circulation rate of a circuit is not known in
  advance.
• The calculations are carried out with a number of
  assumed values of mixture flow rate.
• The corresponding resistance in riser and down
  comer and motive head are calculated.
• The flow rate at steady state is calculated.

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