Heat transfer phase changes, evaporators Rudolf Žitný, Ústav procesní a zpracovatelské techniky ČVUT FS 2010 HEAT PROCESSES HP8 Heat transfer at phase.

Heat transfer phase changes, evaporators

Rudolf Žitný, Ústav procesní a zpracovatelské techniky ČVUT FS 2010

HEAT PROCESSESHP8

Heat transfer at phase changes (boiling and condensation). Evaporation and evaporators. Powerpoint presentation of evaporators (falling, climbing film, multiple effects, vapour recompression). Mass and enthalpy balances. Boiling point temperature and its elevation. Design of thermal vapour recompression (Laval nozzle and Ts diagram). Vacuum cooling.

HEAT transfer condensationHP8

Dropwise condensation

Film condensation

Duchamp

HEAT transfer film condensationHP8

Film condensation (Nusselt)

2 2

( ) GL

T T gq x dm dx d

h

2

2

3 2( ) ( )

2

u y yu y

3 u

g

gravity Viscous force at wall

Transversal parabolic velocity profile and balance of forces

Transversal linear temperature profile, heat and mass fluxes

2 3

3

gm u

2 3 24

4GL GL

T g T gdx d x

h h

Thickness of film determines the heat transfer coefficient

2 3

4( )4GLh g

xTx

Tw

Ts=Tw+T

x

dx

dmMass flow rate of condensed steam

Gravity acting in the flow direction

increases

The following analysis holds only for laminar films (Re<1800). It is usually sufficient, because majority of practical cases are laminar.

HEAT transfer film condensationHP8

41.13 cosc

2 3

4

0

1( ) ( )

4

LGLh g

L x dx cL TL

Enthalpy balancing of a condenser requires mean value of heat transfer

The coefficient c is theoretically c=2/32=0.94 but experiments indicate that the actual value should be about 20% higher, therefore c=1.13

c=0.725

Horizontal pipe4

0.725c

N

Inclined wall N-rows of horizontal pipes

See also M.N.Ozisik: Heat transfer, a basic approach, McGraw Hill, 1985

The increased film thickness

decreases heat transfer

HEAT transfer dropwise condensationHP8

Kakac S.: Boilers, evaporators, and condensers, Wiley 1991

D.W. Tanner, C.J. Potter, D. Pope, D. West: Heat transfer in dropwise condensation—Part I The effects of heat flux, steam velocity and non-condensable gas concentration International Journal of Heat and Mass Transfer, Volume 8, Issue 3, March 1965, Pages 419-420, IN5, 421-426

=liquid-solid

Dropwise condensation (Schmidt) yields much higher heat

transfer coefficients than the film condensation, however special smooth or hydrophobic coatings (large contact angle and very low surface energy of wall) of heat transfer surfaces must be provided.

Gold plated surface

Schmidt, E., Schurig, W. and Sellschop, W., Versuche uber die kondensation von wasserdampf und film und tropfenform. Tech. Mech. Thermodynamiks, Berlin,1930, 1, 53-63.

M. ABU-ORABI: Modeling of heat transfer in dropwise condensation. Int. J. Heat Mass Transfer. Vol. 41, No. 1, pp. 81-87, 1998

HEAT transfer dropwise condensationHP8

H.M.Steinhagen: Smart surfaces for improved heat exchangers. Institute for Thermodynamics and thermal engineering, University of Stuttgart (presentation)

HEAT transfer boilingHP8

Pool boiling

Flow boiling

Tanguy

HEAT transfer pool boilingHP8

Nukyama curve (q-TSAT) see A.Bejan, A.Kraus: Heat transfer handbook. Willey 2003

Boiling crisis of the first kind

HEAT transfer pool boilingHP8

m

LSCNu PrRe

1 3/2

,D

NuL

b

,Du

ReL

LbL

.a

PrL

L

Nucleate (pool) boiling Rohsenow (1952)

Exponent m is 0,7 for all liquids with the exception of water (m=0). The coefficient CLS depends upon the combination surface-liquid (tables see Özisik (1985)) and for

the most common combination steel-water CLS=0,013.

Db is the Laplace constant characterizing diameter of bubble ( )bL G

Dg

)(

12

12)(

3

GLGL g

DD

gD

All parameters are related to liquid L

uL - velocity of liquid surface

LLG L

qu

h

Interpretation of Db follows from the equilibrium of surface stress and buoyancy forces

Rohsenow W.M., Trans.ASME, Vol.74,pp.969-975 (1952)

HEAT transfer boiling onsetHP8

.D

ppDD

)pp(b

bbb

b

4

4

2

Pressure difference pb –p can be calculated from the temperature difference using

Clausius Clapeyron equation

( )b LG G LG

SAT G L SAT SAT

p p h hdp

T dT v v T T

Substituting into the balance of forces gives the final result4

.SATb

G LG SAT

TD

h T

The nucleate boiling (bubble boiling) regime is optimal for boilers or evaporators. How to specify its onset (or the level of superheating necessary for bubble formation on the heat transfer surface)?

pb corresponds to saturated steam temperature at

Tw=TSAT+TSATp corresponds to saturated

steam temperature TSAT

-surface tensionDb diam. of a microcavity on heat transfer surface

Balance of forces: overpressure – surface tension

HEAT transfer boiling crisisHP8

Bubble flow regime ends at such a high intensity of evaporation that a more or less continuous layer of vapor is formed and creates a thermal barrier between the heat transfer surface and liquid. Critical heat flux

1/4( ) .krit LG G L Gq c h g

Theoretical solution Zuber (1958) predicts coefficient c=0,131 , experimental data suggest little bit greater value c=0,18 , Rohsenow (1973). The relation for critical heat flux shows that the boiling crisis can be delayed by increasing pressure (and therefore density G) or by acceleration pressing liquid layer towards the heat transfer surface

(this is utilised in centrifugal evaporators).

Theoretical prediction of boiling crisis is based upon stability analysis of a liquid layer (thickness H2) sitting above the light layer of vapor (H1). A small disturbance of initially planar interface increases area of interface (and therefore potential energy of surface tension W ) but at the same time decreases gravitational potential energy Wg. At the stability limit (neutral stability) the differential of the total potential energy is zero, This condition determines wavelength of disturbance causing disruption of continuous layer, and location of steam jets breaking through the liquid layer (it can be shown that the distance of these parallel jets is a multiple of the Laplace constant Db). Following stability analysis of these steam jets, based upon variation of potential energy of surface tension and kinetic energy, yields the previous expression for the critical heat flux.

HEAT transfer flow boilingHP8

Flow boiling in vertical pipes is characterized by gradual changes of flow regime and the vapor quality x increase along the pipe

, ,L SAT

LG

h hx

h

Enthalpy of liquid at saturation

temperature

Vapor quality x<0 means subcooled liquid, vapor quality x=0 liquid at the beginning of evaporation, x=1 state when all liquid is evaporated and x>1 superheated steam.

Heat transfer by forced convection (e.g.Dittus Boelter)

Nucleate boiling (bubbles), e.g.

Rohsenow correlation

Slug flow

Annular flow (rising film)

Vapor quality is related to the Martinelli’s parameter (ratio of pressure drops corresponding to liquid and vapor)

0,10,50,9( / ) 1

.( / )

GL L

G L G

p z xX

p z x

Vapor quality and Martinelli’s parameter are used in most correlations for convective boiling heat transfer.

HEAT transfer flow boilingHP8

The previous slide introduced two basic characteristics of two phase liquid- vapor flows: vapor quality x and the Martinelli’s parameter X. Their relationship follows from the following reasoning:

Gradient of pressure dp/dz for one phase flow is proportional to (see dArcy Weisbach equation)

21 2

Rem m m

m

p uu

z

Exponent m=0.25 for low Re (Blasius), m=0.2

for high Reynolds numbers

therefore1 2

0,51 22

1 2

1( )

( / ) 1.

( / ) ( )

m m m mmL L

GL L L

m m mG L GG G

G

xp z x

Xxp z x

and you can see that the corresponding exponent of Reynolds number in the correlation for pressure drop is m=0.2. It is obvious that the Martinelli’s parameter is a decreasing function of vapor quality (its value is infinity for liquid).

HEAT transfer flow boiling ChenHP8

Chen (1966) calculates the flow boiling heat transfer coefficient as the weighted sum of nucleate boiling b and the convective heat transfer in liquid film c

cb

,S FZb

.F DBc

0,24 0,75 0,45 0,49 0,79

0,5 0,290,00122 .SAT pL L LSAT

FZLG G L

p cT

h

0,8 0,4 4 (1 )0,023Re Pr , Re ,DB

L L LL L

D M x

D

TP

TPTP

Re,,

Re,,)(ReS

5

7

1067101

10677051

.X,,)X(F ,75401522620

1.25Re ReTP LF

.x

x

)z/p(

)z/p(X

,

G

L

,

L

G,

G

L

1050901

Forster Zuber correlation for nucleate boiling (Chen’s concept was later modified by different correlations for nucleate regime, for example by Rohsenow correlation for pool boiling)

Dittus Boelter correlation for convective heat transfer

Chen J.C.: A correlation for boiling heat transfer to saturated fluids in convective flows. Industrial and Engineering Chemistry, Process design and development, Vol.5, no.3, (1966), pp.322-329

HEAT transfer flow boilingHP8

Chen’s method is probably the most frequently used, but it seems that his correlation overpredicts the effect of nucleation and many modifications were therefore suggested. These modifications replace the Forster Zuber pool boiling correlation by Rohsenow’s correlation and the suppression factor S and the convective enhancement factor F were correlated with other system variables

Kandlikar S.G.: A general correlation for saturated two phase flow boiling heat transfer inside horizontal and vertical tubes. Journal of Heat Transfer, Vol.112, pp.219-228 (1990)

Bennett D.L., Chen J.C.: Forced convective boiling in vertical tubes for saturated pure components and binary mixtures. AIChE J., Vol.26, pp.454-461 (1980)

Shah M.M.: A new correlation for heat transfer during boiling through pipes. ASHRAE Transactions, Vol.82, Part.II, pp.66-86 (1976)

Shah (1976) introduced correlations based upon boiling number Bo, convection number Co (that replaces the Martinelli’s parameter) and Froude number Fr

LG

qBo

G h

0.8 0.51

( ) ( )G

L

xCo

x

G is the mass flux, kg/m2s

Viscosity ratio (see Martinelli’s parameter)

seems to be unimportant

2

2

L

GFr

gD

HEAT transfer flow boilingHP8

Heat transfer correlations for the film condensation (Nusselt) and the flow boiling (Chen) are used in the following Excel program designed for modeling of a climbed film evaporator (Kestner).

Procedure:

Tube is divided to short sections z. At each section (starting from bottom, feed input) are calculated: heat transfer coefficient at outer surface, heat flux, wall temperature, enthalpy change h, steam quality x, Martinelli’s parameter, and heat transfer coefficient using Chen’s method. Temperature dependence of all thermophysical properties is considered.

EvaporatorsHP8

Hopper

EvaporatorsHP8

Condenstation of saturated

steam

Evaporation of water (pool or flow boiling)

feed

concentrate

condensate

Saturated steam

Vapours (brüden)

Minton P.E.: Handbook of evaporation technology. Noyes Publ., New Jersey, 1986

fm

HP8

f cm m W fm

Nomenclature

What to do with vapor: 1. It can be condensed in a direct (spray), shell

and tube or plate condensers

2. It can be used for heating the following evaporator unit (multiple effects evaporators)

3. It can be recompressed (by mechanical or thermo-compressor) and used for heating

fm

W

D

cm

f f c cm m

0 0 0

0 0 0

0 ( ) ( ) ( )

f f f c c c v v

f f c c v

m h h m h h W h h kS T

m h m h Wh

f dissolutionm h

Mass balances

Enthalpy balance

dissolution heat

Overall mass flow rate

mass flow rate of dissolved solid

=cc(Tc-T0)

Evaporators

HP8

Natural circulation in short pipes

Climbed film

Robert’s basket Vogelbusch

Kestner

Wiegand Müller

Centritherm

condensate condensatecondensate

condensate

vacuumvacuumvacuum

steam

steam

Circulation pump

condensate

Wiped filmFalling film Centrifugal

POOL boiling prevails Long residence times

Suppressed boiling (flash evaporation) High velocity in HE-low fouling

Short residence times Only for low viscosities Viscous

liquids

Centrifugal forces promote dropwise condensation and increase critical heat flux

External heater Forced circulation

Very small T

Evaporators

HP8

Multistage evaporators (latent heat of vapor is used for the next effect heating)

T1 T2

T1 T2

Counter currentLow viscosity feed flows to the

second stage at lower temperature (advantageous from point of view

of heat transfer).

Co currentHigh viscosity concentrate flows

to the second stage at lower temperature (suitable for heat

sensitive products).

T1>T2 therefore p1>p2 and it is necessary to use a pump

Number of effects 1 2 3 4 5

kg steam/kg of evaporated water 1,1 0,6 0,4 0,3 0,25

Evaporators

HP8

Number of effects is limited by range of temperatures (feed – condensate)

T1-T2 = THE + Tpch + Tp

T1 T2 T3

T1 > T2 > T3

Temperature drop corresponding to pressure

drop (frictional losses). Usually small ~ 10C

Physico chemical elevation of boiling point temperature (solution boils at

elevated temperature). Can be large, depends on concentration

Temperature difference on heat transfer surface (rising film >100C, falling film >40C)

Tpch

Sugar 0.5~3

NaCl 10

NaOH 16

Evaporators

HP8

TI TII

Tf,mf,f

m1,1

mc,c

WI WII

D,TS

kISI kIISII

What is given (it is assumed that the temperature TII is determined by condenser and is the same as the temperature of boiling solution in the second effect and the temperature of product):

Tf mf f – temperature, mass flowrate, mass fraction of feed

TII c – temperature and mass fraction of product

TS – temperature of steam

What is to be calculated (9 variables):

D,WI,WII – mass flowrates of steam and vapours

m1,mc – mass flowrates of solution from the 1st and 2nd effect

1- mass fraction of solution after 1st stage

TI –temperature of boiling solution in the 1st effect

kISI, kIISII- heat transfer surfaces in both effects

1 1 1

1 1 1

f I f f

c II c c

m m W m m

m m W m m

1 1

1 1

( ) ( ) ( )

( ) ( ) ( )

f f I I S I I I S cond I I S I

II II I II c c II II I I cond II II I II

h m k S T T h m h W D h h k S T T

h m k S T T h m h W W h h k S T T

Mass balances Enthalpy balances

1st stage

2nd stage

There exist only 8 equations for 9 parameters – one of them can be selected (for example boiling temperature in the first stage T I).

This degree of freedom can be used for optimisation (for minimisation of the heat transfer surface or consumption of steam).

Optimisation of a two effects evaporator

Evaporators

HP8

Design of a two effect co-current evaporator can be implemented in Excel program

Select substance and boiling point elevation

Specify temperature of

steam and feed

CALC starts calculation

Heat transfer surface will be

result

Select temperature in the first effect TI

Evaporators

Evaporators MVRHP8

MVR Mechanical Vapor Recompression

AC

D

Root’s blower

Condensate injection

F=1.8C+32

BTU=1.054 kJpsi=6.9 kPa

It would not be a good idea to use superheated steam for

heating, because will be too small. Saturated steam and condensation is achieved by

water injection

Evaporators TVRHP8

TVR Thermal Vapor Recompression

1

5

2

Thermocompressor

.hhu 454 2

.hhu 313 2

1 3 1 2 4.m u m m u

3 1 32

1 4 5 4

1 1.e

u h hmf

m u h h

1

11

1 2 221

55 25

22

11

1 1 1.1

1

k

k

pe k

p k

pTc T T pT

fTc T T

pT

p

The most important equation is the momentum balance (mixing chamber)

Entrainment ratio fe (mass flowrate of entrained

vaports to the mass florate of motive steam) follows from the momentum balance

Power R.: Steam jet ejectors for the process industries. Mac Graw Hill, New York, 1994

Evaporators TVRHP8

Power R.: Steam jet ejectors for the process industries. Mac Graw Hill, New York, 1994

Design diagram for TVR

Motive steam presure

Suction pressure

Discharge pressure

Previous analysis determined only the entrainment ratio . To complete the TVR design it is necessary to calculate the mass flowrate of motive steam through the Laval nozzle (given inlet pressure). Laval nozzle is characterised by converging and diverging section and the mass flowrate depends only upon the cross section of throat (the smallest cross section S*) where the speed of sound is achieved.

To determine the flow rate m1 as a function of S* and the inlet pressure p1 it is necessary to solve the complete velocity and pressure profiles along the Laval nozzle.

Evaporators TVRHP8

TVR Thermal Vapor Recompression

1

5

2

Thermocompressor

2 1/ef m m

Evaporators TVRHP8

Mixing chamber

Laval nozzle

Diffuser

Speed of sound

Motive steam

Suction

Thermocompressor and Laval nozzleUnknown profiles along the Laval nozzle: p(x), v(x)-or density, T(x), u(x)-velocity, and h(x), together 5 unknowns

Available equations:

pv=RT - state equation

pv=p1v1 - isoentropic flow (without friction)

dh=-du2/2 - Bernoulli equation

dh=cpdT

By selecting any of the parameters, for example the pressure p, it is possible to calculate all other variables, for example the velocity u

2 2 2 2p p

pdv vdpdu dh c dT c

R

v and dv is to be eliminated (expressed in terms of p)

1/ 1/1 11 1( ) ( )

p p dpv v dv v

p p p

2 1/ 1/1 11 1

2( ( ) ( ) )pc p pdp

du v v dpR p p p

By integration we obtain St.Venant Wanzel equation

12

1 11

2 (1 ( ) )1

pu p v

p

Ideal gas!

Evaporators TVRHP8

Mass flowrate is independent of axial coordinate1 1 2 1

11 1 1 1

1 1 1 1 1

( ) ( ) 2 ( ) ( )( ) ( ) ( ) ( ) 2 1 ( ) .

1 1

pp z p z p z p zm u z S z z S z S z p

p p p p

2 1 ** *

1*1

2 12 1 * ** * 1 11 1

2 1

0.22

11

dPm P P

dzmdS d

dz dz pp P PP P

Introducing dimension pressure P*=p(z)/p1 the throat geometrical constraint (minimum cross section S) is

,P* 1

1

2

2 1 1

1 1 1* *1 1

1 1 1

2 2 2 2.

1 1 1 1

pm S S p

zS*

Solution of this (algebraic) equation is and corresponding mass flowrate

H2O molecule riding inside a Laval nozzleHP8

zS*

0

1

2

3

4

5

6

7

00.10.20.30.40.50.60.70.80.91

p(z)/p1

S(z

)

S=1/(2*kappa/(kappa-1)*(A3 (̂2/kappa)-A3 (̂(kappa+1)/kappa)))^0.5)2 1

1 1 11 1

2 ( ) ( )( ) / .

1

p z p zS z m p

p p

H2O molecule riding inside a Laval nozzleHP8

zS*

Slow, nice, eliptic ride, clear view

Approaching speed of sound, view is misty

Speed of sound and still accelerating, Molecule is blind, nothing is seen (only the rear mirror view is clear)

Collision with different pressure at outlet of Laval nozzle (wrong design, of course not by our students)

Mass flowrate through a gap with cross section S at subsonic

flow

Evaporators St Venant WanzelHP8

St Venant Wanzel equation is quite useful and not only for the Laval’s nozzle design. It is applied for example for estimation of an evaporator or a condenser leakage

2 1

1 1 11 1

2.

1

p pm S p

p p

1

1

2

1

p

p

1

1

1 1 1

2.

1m S p

p

p1

Evaporator chamber operating at underpressure

Leakage at sonic flow (choking). Mass

flowrate is independent of vacuum level p.

Vacuum cooling LIQUIDSHP8

Evaporation is also used for rapid cooling of food materials. Material containing water (liquid solutions, but also porous solids like flowers, vegetables, meat) can be cooled down by evaporation of water at a decreased pressure. Assuming uniform temperature Tf(t) of the cooled material the enthalpy balance can be written as

Foam separator

Condenser

Vacuum pump

cooker

Condensatepump

Heatingjacket

ff pf LG

dTM c m h

dt

Mass flow rate of evaporated water

M. Dostal, K. Petera: Vacuum cooling of liquids: mathematical model. Journal of Food Engineering 61 (2004) 533–539

conduction Convection (n is mass flux)

Area of liquid surface

There still exist controversial opinions concerning interpretation of thermal and mass transfer resistances at surface

Vacuum cooling WATERHP8

Technical realization is similar to vacuum evaporators, only without heating of evaporated liquid. Jet pumps (steam ejectors) are usually used.

Example: GEA Wiegand GmbH, 2-stage steam jet cooling plant of compact design, cooling 44 m3/hr of water from 30 to 10 °C.

Spray cooling WATERHP8

Cooling ponds JETE

3[ ( ) ( )]LG wA wA A

p

dTh T T

dt r c

Vacuum cooling MEATHP8

Relatively new vacuum cooling technology is applied also to porous solids, for example meat.

The visualised cross-section of the cooked meatL. Wang, D.-W. Sun / International Journal of Refrigeration 25 (2002) 862–871

Mathematical modelling is usually based upon FK equation for heat transfer

Mass transport of vapour is expressed in terms of pressure P Heat flux

D.-W. Sun, L. Wang / Journal of Food Engineering 77 (2006) 379–385

There exists doubt about this approach. It was objected that this model doesn’t recognize moving front between the boiling and diffusive regions. T.X. Jin, L. Xu / Energy Conversion and Management 47 (2006) 1830–1842

Mass flux Evaporation rate

Evaporators papersHP8

Bosch

Evaporators papersHP8

K.R. Morison, Q.A.G. Worth, N.P. O’dea Minimum Wetting and Distribution Rates in Falling Film Evaporators Food and Bioproducts Processing, Volume 84, Issue 4, December 2006, Pages 302-310

Falling film evaporators are used extensively in the food industry for their ability to process heat sensitive liquids. A coherent liquid film is required to maintain heat transfer efficiency and minimize fouling. It is likely that most evaporator fouling occurs after film breakdown as the substance within the evaporator dries out. The minimum flow rate required to maintain a film is known as the minimum wetting rate which is defined as the minimum mass flow rate per unit circumference. In this work, minimum wetting rates were determined in a 1 m long, 48 mm internal diameter, vertical, stainless steel tube. Water and aqueous solutions of glycerol, alcohol and calcium chloride were used. These substances were chosen so as to give a wide range of properties such as viscosity (0.5–39 mPa s), density (950–1410 kg m-3), surface tension (35–90 mN m-1) and contact angle (64–980). In a separate set of experiments, the minimum flow rate required to distribute liquid and completely wet the top of industrial evaporator tubes was measured using a range of sucrose solutions. The tube wetting results obtained fitted a dimensionless power law relationship well. Surface tension and contact angle had a strong influence on the wetting rate but viscosity and density were found to have very little effect. The minimum flow rates for distribution were found to nearly always exceed the minimum wetting rates showing that more attention needs to be given to distributor design.

Nii S.et al: Membrane evaporators. Journal of membrane science, 201 (2002), 149-159

Almost the same result can be derived from the Weber

number limit2

2u

We

Evaporators papersHP8

Susumu Nii, R. Selwyn Jebson, E. L. Cussler Membrane evaporators Journal of Membrane Science, Volume 201, Issues 1-2, 31 May 2002, Pages 149-159

We have built and tested a flat-sheet membrane evaporator for removing water from dilute feed streams likemilk and orange juice. The energy for the water’s evaporation comes from steam channels next to the feed channels, so that the operation differs sharply from other forms of “membrane distillation”. The membrane evaporator retains flavors effectively. Because it has an overall vapor phase mass transfer coefficient of about 1 cm/s, it is only 68% efficient: only about 0.68 kg water is evaporated per kg steam condensed. This efficiency should be over 95% for a membrane which is 10 times more permeable.

Evaporators papersHP8

S. Sharma, G.P. Rangaiah, K.S. Cheah Multi-objective optimization using MS Excel with an application to design of a falling-film evaporator system Food and Bioproducts Processing, Available online 9 February 2011

An Excel-based MOO (EMOO) program is developed based on the elitist non-dominated sorting genetic algorithm (NSGA-II) and tested on benchmark problems. It is then applied for MOO of design of a falling-film evaporator system, consisting of a pre-heater, evaporator, vapor condenser and steam jet ejector, for milk concentration. The EMOO program gave well-distributed Pareto-optimal solutions for the MOO problems tested. Design equations and results for two bi-objective optimization problems are presented and discussed.

Evaporators papersHP8

Tarif Ali Adib, Bertrand Heyd, Jean Vasseur: Experimental results and modeling of boiling heat transfer coefficients in falling film evaporator usable for evaporator design Chemical Engineering and Processing: Process Intensification, Volume 48, Issue 4, April 2009, Pages 961-968The aim of this paper is to describe the variation laws of the boiling heat transfer coefficient (h) versus the main process parameters, using a pilot scale falling film evaporator as found in many food industries. Sugar solutions at different concentrations are used as a model of Newtonian liquid food. The studied parameters affecting boiling heat transfer coefficient (h) in the falling film evaporator are: the dry matter concentration XDM (or Brix for sugar solution), the evaporating temperature (L) or pressure (P) taking into account the boiling point elevation (BPE), the heat flux or the temperature difference between the heated surface and boiling liquid temperature () and the specific mass flow rate per unit of perimeter length ( ). The nature of heated surface is kept constant (stainless steel) and the effect of the emitted vapor velocity is not taken into account in our study. The variations of h with or , are given for pure water and sugar solutions at different concentrations (10%, 30%, 50% and 70%), and interpreted in relation with the two boiling regimes (non-nucleate and nucleate). The transition between non-nucleate regime and nucleate regime has also been visually observed. The critical specific mass flow ( cri) for water and sugar solution at dry matter concentration 50% has been studied.

Variation of h as a function of temperature difference at P = 1010mbar and = 0.56 kg s−1 m−1 for pure water and sugar solution X = 10%, 30%, 50% and 70% DM.

Evaporators papersHP8

Xianchang Li, Ting Wang, Benjamin Day: Numerical analysis of the performance of a thermal ejector in a steam evaporator Applied Thermal Engineering, Volume 30, Issues 17-18, December 2010, Pages 2708-2717

Ejectors have been widely used in many applications such as water desalination, steam turbine, refrigeration systems, and chemical plants. The advantage of an ejector system lies in its extremely reliable operation due to the complete absence of moving parts. However, the performance depends on a number of factors, among which the flow channel configuration/arrangement is critical. To improve the performance of an existing thermal compressor in a steam evaporator, a comprehensive study was conducted in this paper with a main focus on the sensitivity of performance to the geometric arrangement. Numerical simulation was employed to investigate the thermal-flow behavior. The performance is measured by the entrainment ratio, i.e., the secondary (suction) flow rate from a vapor plenum over the primary steam jet flow. It is observed that any downstream resistance will seriously impede the suction flow rate. In addition, the entrainment ratio is sensitive to the location of the jet exit, and there is an optimum location where the primary flow should be issued. A well-contoured diffuser can increase the entrainment ratio significantly. However, the size of suction opening to the plenum is less important, and a contoured annular passage to guide the entrained flow shows little effect on the overall performance. Based on the numerical results the steam entrainment rate of the best case in the confinement of the current study is approximately 430% of the jet flow rate, while some cases with mediocre design can only produce an entrainment of 24% of the primary jet flow.

Fluent

HP8

EXAMHP8

Phase changes

Evaporators

Thermocompressors

What is important (at least for exam)HP8

T

w Ts=Tw+T

xdx

dm

Mass flow rate of condensed steam

2 3

4( )4GLh g

xTx

Nusselt correlation for film condensation

m

LSCNu PrRe

1 3/2

( )bL G

Dg

Rohsenow correlation for pool boiling

Laplace constant Db is used as a characteristic dimension in Nu and Re

What is important (at least for exam)HP8

Condensation of saturated steam

(Nusselt correlation)

Evaporation of water (pool or flow boiling).

Use Rohsenow or Chen correlations

feed

concentrate

condensate

Saturated steam

Vapours (brüden)

f cm m W

f f c cm m

0 0 0 0 0 0

dilution heat

0 ( ) ( ) ( )f f f c c c v v f f c c vm h h m h h W h h kS T m h m h Wh

Overall mass balance

Mass balance of solid

Enthalpy balance

What is important (at least for exam)HP8

.hhu 454 2

.hhu 313 2

1

5

2

Thermocompressor

Recompression of vapours by thermo-compressor (that is driven by Laval nozzle)

Laval nozzle

Mixing chamber

Laval nozzle

Diffuser

Speed of sound

Motive steam

Suction

1

1

1 1 1

2.

1m S p

13

1

0.53 for air=0.58 for steam

2

1

p

p

Supersonic flow for pressure ratio

Mass flowrate is independent of outlet pressure at supersonic flow