MULTIPHASE HEAT TRANSFER

P M V Subbarao

Associate Professor

Mechanical Engineering Department

IIT Delhi

Rules for Design of Steam Generators………

)( satss TThq

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.

Multi Phase Heat Transfer in Flow Boiling

Single-Phase Liquid Heat Transfer• Under steady state one-dimensional conditions

the tube surface temperature is given by:

fwfluidwall TzTzT )()(

.

''

,)(

pf

ifluidfluid

Cm

PzqTzT

zh

qT fw

''

•Temperature excess

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

• and where

• q’’ is the heat flux,

• P is the heated perimeter,

• 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.

• Heat transfer in turbulent flow in a circular tube can be estimated by the well-known Dittus-Boelter equation.

3/18.0Re023.0 prk

hD

f

H

This relation is valid for heating in fully developed vertical

upflow in z/D > 50 and Re > 10,000.

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

hCm

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

•For any fluid

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,

Sequence of Events in Flow Boiling

Natural or forced convection heating of liquid

Onset of Nucleation Boiling at wall

Subcooled Boiling

Saturation Boiling

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.

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

F

D

h

k

CDxmh liquid

liquid

liquidpliquid

liquid

hc

4.0

,

8.0

1023.0

SpT

h

CkDxmh satsat

vfgl

ll

liquid

hNcB

lp 75.024.0

4.0

24.024.029.05.0

49.045.079.08.0

,100122.0

•http://wins.engr.wisc.edu/teaching/mpfBook/node31.html

Multi Phase Heat Transfer in Pool Boiling

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).

Boiling Curve

0C

W/m

2 .s

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.

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

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……

Role of SG in Rankine Cycle

Using Natural resources of energy.

Basic Geometry of A Furnace in A Large Steam Generator

Burner

Flame

Hot Exhaust gases

Furnace Exit

Heat Radiation & Convection

Structure of Furnace Wall

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.

• For high capacity Steam Generators, the steam generation per unit cross section is kept within the range.

• High pressure (>9.5 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.

Circulation Ratio

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

s

m

m

mcirk

•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.