BOILING HEAT TRANSFER

P M V Subbarao

Associate Professor

Mechanical Engineering Department

IIT Delhi

A Means to induct Bountifulness to a Fluid……. A Basic means of Power Generation……A science which made Einstein Very Happy!!!

James Watt : A Statue !!!

• Mrs. Campbell, Watt's cousin and constant companion, recounts, in her memoranda, written in 1798:

• Sitting one evening with his aunt, Mrs. Muirhead, at the teatable, she said:

• "James Watt, I never saw such an idle boy; take a book or employ yourself usefully;

• for the last hour you have not spoken one word, • but taken off the lid of that kettle and put it on again, • holding now a cup and now a silver spoon over the steam,

watching how it rises from the spout, • and catching and connecting the drops of hot water it falls into. • Are you not ashamed of spending your time in this way? "

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Natural Convection in A Pool of Saturated Liquid

Tsat

Onset of Convection Tsurface

Further Behavior of Saturated Liquid

Increasin

g T

Natural Convection

Onset of Boiling

Isolated Bubble Regime

High Overshoots !!!

Wall Superheat (T=Ts – Tsat)

Heat Flux

Overshoot

A BA: Onset of Natural convection

B: Onset of Nucleate Boiling

Boiling

• In a steam power plant convective heat transfer is used to remove heat from a heat transfer surface.

• The  liquid  used  for  cooling  is  usually  in  a  compressed  state,  (that   is,  a  subcooled  fluid)  at pressures higher than the normal saturation pressure for  the given temperature.

• Under certain conditions some type of boiling can take place.

• It is  an important  process  in nuclear  field  when  discussing convection heat transfer.

• More  than  one  type  of  boiling  can  take  place  within  a  

nuclear facility.

Nuclear Power Plant

Steam Boiler

Classification of Boiling

• Microscopic classification or Boiling Science basis:

• Nucleated Boiling

• Bulk Boiling

• Film Boiling

• Macroscopic Classification or Boiling Technology basis:

• Flow Boiling

• Pool Boiling

Nucleate Boiling

• The most common type of local boiling encountered in nuclear facilities is nucleate boiling.

• In nucleate boiling, steam bubbles form at the heat transfer surface and then break away and are carried into the main stream of the fluid.  

• Such movement enhances heat transfer because the heat generated at the surface is carried directly into the fluid stream.   

• In the main fluid stream, the bubbles collapse because the bulk temperature of the fluid is not as high as the heat transfer surface  temperature  where  the  bubbles  were  created.   

• This  heat  transfer  process  is  sometimes desirable  because  the  energy  created  at  the  heat  transfer  surface  is  quickly  and  efficiently "carried" away.

Bulk Boiling

• As  system  temperature  increases  or  system  pressure drops,  the  bulk  fluid  can  reach  saturation conditions.  

• At this point, the bubbles entering the coolant channel will not collapse.  

• The bubbles will tend to join together and form bigger steam bubbles.  

• This phenomenon is referred to as bulk boiling.

• Bulk  boiling  can  provide  adequate  heat  transfer  provided  that  the  steam  bubbles  are carried  away  from  the  heat  transfer  surface  and  the  

surface  is  continually  wetted  with  liquid water.   

• When this cannot occur film boiling results.

Film Boiling

• As the temperature continues to increase, more bubbles are formed  than  can  be  efficiently  carried  away.   

• The  bubbles  grow  and  group  together,  covering small  areas  of  the  heat  transfer  surface  with  a  film  of  steam.    

• This  is  known  as  partial  film boiling.    

• Steam  has  a  lower  convective  heat  transfer  coefficient  than  water.   • The  steam patches on the heat transfer surface act to insulate the surface. • As  the  area  of  the  heat  transfer  surface  covered  with  steam  increases,  the

 temperature  of  thesurface  increases  dramatically,  while  the  heat  flux  from   the  surface  decreases.   

• This  unstable situation continues until the affected surface is covered by a stable blanket of steam.   

• The condition after the stable steam blanket has formed is referred to as film boiling.

Boiling Curve

0C

W/m

2 .s

• Four regions are represented in Figure.   • The first and second regions show that as heat flux increases,

the temperature difference (surface to fluid) does not change very much.

• Better heat transfer occurs during nucleate boiling than during natural convection.  

• As the heat flux increases, the  bubbles  become  numerous   enough  that  partial  film  boiling  (part  of  the  surface  beingblanketed  with  bubbles)  occurs.    

• This  region  is  characterized  by  an  increase  in  temperature difference and a decrease in heat flux.   

• The increase in temperature difference thus causes total film boiling, in which steam completely blankets the heat transfer surface. 

Departure from Nucleate Boiling and Critical Heat Flux

• In practice, if the heat flux is increased, the transition from nucleate boiling to film boiling occurs suddenly, and the temperature difference increases rapidly, as shown by the dashed line in the figure.    

• The  point  of  transition  from  nucleate  boiling  to  film  

boiling  is  called  the  point  of departure from nucleate boiling, commonly written as DNB.  

• The heat flux associated with DNB is  commonly  called  the  critical  heat  flux  (CHF).    

• In  many  applications,  CHF  is  an  important parameter.  

• For example, in a reactor, if the critical heat flux is exceeded and DNB occurs at any location

• in  the  core,  the  temperature  difference  required  to  transfer  the  heat  being  produced  from  the surface  of  the  fuel  rod  to  the  reactor  coolant  increases  greatly.    

• If,  as  could  be  the  case,  the temperature increase causes the fuel rod to exceed its design limits, a failure will occur.

• The amount of heat transfer by convection can only be determined after the local heat transfer coefficient  is  determined.   

• Such  determination  must  be  based  on  available  experimental  data.

• After experimental data has been correlated by dimensional analysis, it is a general practice to write   an   equation   for   the   curve   that   has   been   drawn   through   the   data   and   to   compare experimental results with those obtained by analytical means.  

Flow Boiling• Flow boiling occurs when all the

phases are in bulk flow together in a channel; e.g., vapor and liquid flow in a pipe.

• The multiphase flow may be classified as adiabatic or diabatic, i.e., without or with heat addition at the channel wall.

• An example of adiabatic flow would be oil/gas flow in a pipeline, or air/water flow.

• In these cases the flow patterns would change as the inlet mass flow rates of the gas or liquid are altered or as the velocity and void distributions develop along the channel.

Adiabatic Flow Through A Pipe

Diabatic Flow Through A Pipe

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Diabatic Boiling Along A Furnace Wall Tube

Burner

Flame

Hot Exhaust gases

Furnace Exit

Heat Radiation & Convection

Natural Circulation Steam Generator

Natural Circulation Nuclear Reactor

Forced Circulation Steam Generator

Forced Circulation Nuclear Reactor

Once Through Steam Generator

Once-through tangential fired Max. continuous rating: 520 kg/sMax.Steam temperature outlet: 540°CLive steam pressure outlet: 18,3 MPa

Super Critical Nuclear Reactor

Slip in Multi-Phase flow

• For example in a riser tube of a steam generator the vapor rises faster than the liquid due to buoyancy effects.

• One may term this velocity inequality as "slip" between the vapor and the liquid.

• The ratio of these velocities is called the "slip ratio".

• A better description of the phenomena is to consider it as a relative velocity difference between the phases, Vg - Vl .

• Flow boiling heat transfer can occur under two different boundary conditions, either a specified wall heat flux or a specified wall temperature.

• The former case is an idealized example of a boiler tube in a fossil fuel boiler and the latter case is an idealized example of a riser tube in a nuclear steam generator.

Multi Phase Heat Transfer

• One of the many applications 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.

• In this section we focus on the methodology to estimate the wall temperature or the wall heat flux depending on the appropriate boundary condition.

• We focus on describing the regions of heat transfer, locating the onset of nucleate boiling and finally estimating the wall condition.

Single-Phase Liquid Heat Transfer

• Figure shows an idealized form of the flow patterns and the variation of the surface and liquid temperatures in the regions designated by A, B, and C for the case of a uniform wall heat flux.

• Under steady state one-dimensional conditions the tube surface temperature in region A (convective heat transfer to single-phase liquid), is given by:

fwfluidwall TzTzT )()(

.

,

''

,)(

fluidp

ifluidfluid

GAC

PzqTzT

h

qT fw

''

• and where

• q’’ is the heat flux,

• P is the heated perimeter,

• G is the mass velocity,

• A is the flow area and is the liquid specific heat.

• Also Tfw 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.

• The liquid in the channel may be in laminar or turbulent flow, in either case the laws governing the heat transfer are well established; for example, 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 > 50 and Re > 10,000.

•For the case of a given constant wall temperature, the temperature difference will

decrease, as well as the heat flux.

•From an energy balance this is represented by a logarithmic decrease in the

temperature difference.

3/18.0Re023.0 prk

hD

f

H

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

hGAC

PZqTT

pf

ONBfiONBwall

1'',

ONBsatONBwall TTT ,

Now that we have a relation between TONB 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 TONB.

Using this approach, Bergles and Rohsenow (1964) obtained an equation for the wall superheat required for the onset of subcooled boiling.

fisatpf

ONBONB TT

hGAC

PZqT

1''

Their equation is valid for water only, given by

0234.0158.1

''

463.01082

558.0 pp

qTT ONBSATW

gfgf

SATONBSATW hk

TqTT

''8

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.

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

The superheat temperature, is then found by using the

universal temperature profile relation.

Now using the local energy balance one can relate the local bulk temperature, TfB, to the superheat temperature difference,

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.

• We once again want to be able to find the wall condition for this situation; e.g., wall temperature for a given heat flux.

• One should note that 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 W/m2 K have been reported.

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:

NCBcTP hhh

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, T, was first done by Nukiyama (1934).

Onset of Nucleate Boiling

• Vapor may form from 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.

gfgf

SATONBSATW hk

TqTT

''8

•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.

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.

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

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 (> 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