HP8
HEAT PROCESSES
Heat transfer phase
changes, evaporators
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
Rudolf Žitný, Ústav procesní a
diagram).techniky
Vacuum
zpracovatelské
ČVUT FScooling.
2010
HP8
HEAT transfer condensation
Dropwise
condensation
Film
condensation
Duchamp
HEAT transfer film condensation
HP8
Film condensation (Nusselt)
The following analysis holds only for laminar films (Re<1800). It is usually
sufficient, because majority of practical cases are laminar.
Transversal parabolic velocity profile and balance of forces
3u 2 y y 2
u( y)  (  2 )
2  
 g 
 2 3 g
m   u 
3
3 u
gravity

Viscous force at wall
Transversal linear temperature profile, heat and mass fluxes
dx
x

Tw
dm
Mass flow rate of
condensed steam
Ts=Tw+T
Thickness of film determines
the heat transfer coefficient
T
q ( x) 

T
 2 2 g
dm 
dx 
d
hGL

T
 2 3 g
dx 
d
hGL

 4 hGL  2 g 3
 ( x)  

4Tx
T
2g 4
x

hGL
4
Gravity acting in
the flow direction
increases 
HP8
HEAT transfer film condensation
Enthalpy balancing of a condenser requires mean value of heat transfer
hGL  2 g  3
1
 ( L)    ( x)dx  c 4
L0
4TL
L
The coefficient c is theoretically c=2/32=0.94 but experiments indicate that
the actual value should be about 20% higher, therefore c=1.13
The increased film
thickness
decreases heat
transfer

c  1.13 4 cos 
c=0.725
Inclined wall
Horizontal pipe
c
0.725
4
N
N-rows of
horizontal pipes
See also M.N.Ozisik: Heat transfer, a basic approach, McGraw Hill, 1985
HP8
HEAT transfer dropwise condensation
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.
=liquid-solid
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.
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
M. ABU-ORABI: Modeling of heat transfer in dropwise condensation. Int. J. Heat Mass Transfer. Vol. 41, No. 1, pp. 81-87, 1998
HP8
HEAT transfer dropwise condensation
H.M.Steinhagen: Smart surfaces for improved heat exchangers. Institute for Thermodynamics and thermal engineering,
University of Stuttgart (presentation)
HP8
HEAT transfer boiling
Pool boiling
Flow boiling
Tanguy
HP8
HEAT transfer pool boiling
Nukyama curve (q-TSAT) see A.Bejan, A.Kraus: Heat transfer handbook. Willey 2003
Boiling crisis
of the first kind
HP8
HEAT transfer pool boiling
Nucleate (pool) boiling Rohsenow (1952)
All parameters are
related to liquid L
1
Nu 
Re 2 / 3 Pr  m
C LS
Rohsenow W.M., Trans.ASME, Vol.74,pp.969-975 (1952)
Db
Nu 
,
L
uL - velocity of liquid surface
uL 
Re 
u L Db  L
L
,
q
hLG  L
Pr 
L
aL
.
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
Db 

g (  L  G )
Interpretation of Db follows from the equilibrium of surface
stress  and buoyancy forces
D  g (  L   G )
D 3
12
D
12
g( L  G )
HP8
HEAT transfer boiling onset
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)?
Balance of forces: overpressure – surface tension
Db2
4
( pb  p )
 Db  pb  p 
.
-surface tension
Db
4
pb corresponds to saturated
steam temperature at
Tw=TSAT+TSAT
Db diam. of a microcavity
on heat transfer surface
p corresponds to saturated
steam temperature TSAT
Pressure difference pb –p can be calculated from the temperature difference using
Clausius Clapeyron equation
pb  p dp
hLG
G hLG
TSAT

dT

(vG  vL )TSAT

TSAT
Substituting into the balance of forces gives the final result
Db 
4 TSAT
.
G hLG TSAT
HP8
HEAT transfer boiling crisis
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
qkrit  chLG  gG (  L  G ) .
1/4
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 H 2) 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 W g.
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 D b).
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.
HP8
HEAT transfer flow boiling
Flow boiling in vertical pipes is characterized by gradual changes of flow regime
and the vapor quality x increase along the pipe
x
Annular flow
(rising film)
Slug
flow
h  hL,SAT
hLG
,
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.
Vapor quality is related to the Martinelli’s
parameter (ratio of pressure drops
corresponding to liquid and vapor)
Nucleate boiling
(bubbles), e.g.
Rohsenow
correlation
0,5
0,1
(p / z ) L  1  x   G    L 
X

     .
(p / z )G  x    L   G 
0,9
Heat transfer by
forced convection
(e.g.Dittus Boelter)
Vapor quality and Martinelli’s parameter
are used in most correlations for
convective boiling heat transfer.
HP8
HEAT transfer flow boiling
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)
p
z
2
u
 m
Re
 1mu 2m  m
Exponent m=0.25 for
low Re (Blasius), m=0.2
for high Reynolds
numbers
therefore
1  x 2m m
m
m
 1Lm (
) L
0,5
1
(p / z ) L
L
 1  x  2  G    L  2
X


.





x
(p / z )G
G1m ( )2m Gm  x    L   G 
G
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 Chen
HP8
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
  b  c
S (ReTP ) 
 b  S FZ ,
 FZ
 TSAT 
 0, 00122 

 hLG G 
0,24
0,75 0,45 0,49 0,79
pSAT
c pL  L L
 0,5  L0,29
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)
 c  F DB .
 DB D
0,4
 0, 023Re0,8
L PrL ,
L
1,05  7 ,67  10 7 ReTP
1,0  1,67  10 5 ReTP
.
ReTP  F 1.25 Re L
F ( X )  0,62  2,152 X 0 ,754 .
Re L 
4M (1  x)
,
 D L
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
( p / z )L  1  x 
X


( p / z )G  x 
0 ,9
 G

 L



0 ,5
 L

 G
0 ,1

 .

HP8
HEAT transfer flow boiling
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 (1976) introduced correlations based upon boiling number Bo, convection
number Co (that replaces the Martinelli’s parameter) and Froude number Fr
q
Bo 
GhLG
G is the mass
flux, kg/m2s
1  x 0.8 G 0.5
Co  (
) ( )
x
L
G2
Fr  2
 L gD
Viscosity ratio (see
Martinelli’s parameter)
seems to be unimportant
Shah M.M.: A new correlation for heat transfer during boiling through pipes. ASHRAE Transactions,
Vol.82, Part.II, pp.66-86 (1976)
HP8
HEAT transfer flow boiling
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.
HP8
Evaporators
Hopper
HP8
Evaporators
Vapours
(brüden)
Saturated steam
Evaporation of water
(pool or flow boiling)
Condenstation
of saturated
steam
feed
concentrate
condensate
Minton P.E.: Handbook of evaporation technology. Noyes Publ., New Jersey, 1986
Evaporators
HP8
Nomenclature
mf
What to do with vapor:
D
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.
mf
It can be recompressed
(by mechanical or
thermo-compressor) and used for heating
W
mf
Overall mass
flow rate
Mass balances
m f  mc  W
mass flow rate of
dissolved solid
 f m f  c mc
=cc(Tc-T0)
Enthalpy balance
0  m f (h f  h f 0 )  mc (hc  hc 0 )  W (hv  hv 0 )  kS T 
 m f hf 0
mc
m f hdissolution
 mc hc 0
dissolution heat
 Whv 0
HP8
Evaporators
External heater
Natural circulation in short pipes
vacuum
vacuum
vacuum
POOL boiling prevails
Long residence times
condensate
Suppressed boiling
Vogelbusch
(flash
evaporation)
High velocity in HElow fouling steam
basket
steam
Robert’s
condensate
condensate
condensate
Climbed film
Falling film
Wiegand
Short residence times
Only for low viscosities
Kestner
Circulation
pump
Wiped film
Centrifugal
Centrifugal forces promote
dropwise condensation and
increase critical heat flux
Müller
Viscous
liquids
Centritherm
condensate
Very small T
Forced circulation
HP8
Evaporators
Multistage evaporators
Number of effects
1
2
3
4
5
(latent heat of vapor is used for the
next effect heating)
kg steam/kg of evaporated water
1,1
0,6
0,4
0,3
0,25
T1
T2
Counter current
Low viscosity feed flows to the
second stage at lower temperature
(advantageous from point of view
of heat transfer).
T1>T2 therefore p1>p2 and it is necessary to use a pump
T1
T2
Co current
High viscosity concentrate flows
to the second stage at lower
temperature (suitable for heat
sensitive products).
HP8
Evaporators
Number of effects is limited by range of temperatures (feed – condensate)
T1
>
T1
T2
>
T3
T3
T2
T1-T2 = THE + Tpch + Tp
Temperature difference on heat
transfer surface (rising film
>100C, falling film >40C)
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
Tpch
Sugar
0.5~3
NaCl
10
NaOH
16
HP8
Evaporators
Optimisation of a two effects evaporator
WI
WII
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
D,TS
TI
TII c – temperature and mass fraction of product
Tf,mf,f
kISI
TS – temperature of steam
TII
kIISII
What is to be calculated (9 variables):
D,W I,WII – mass flowrates of steam and vapours
m1,mc – mass flowrates of solution from the 1st and 2nd effect
mc,c
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
m1,1
Mass balances
Enthalpy balances
1st stage
m f  m1  WI
m f  f  m11
h f m f  k I S I (TS  TI )  h1m1  hIWI
D (hS  hcond )  k I S I (TS  TI )
2nd stage
m1  mc  WII
mcc  m11
h1m1  k II S II (TI  TII )  hc mc  hIIWII
WI (hI  hcond )  k II S II (TI  TII )
There exist only 8 equations for 9 parameters – one of them can be selected (for example boiling temperature in the first stage TI).
This degree of freedom can be used for optimisation (for minimisation of the heat transfer surface or consumption of steam).
HP8
Evaporators
Design of a two effect co-current evaporator can be implemented in Excel program
Specify
temperature of
steam and
feed
Select temperature
in the first effect TI
Select substance and
boiling point elevation
CALC starts
calculation
Heat transfer
surface will be
result
Evaporators MVR
HP8
MVR Mechanical Vapor Recompression
Root’s blower
A
C
D
Condensate
injection
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
BTU=1.054 kJ
psi=6.9 kPa
F=1.8C+32
Evaporators TVR
HP8
The most important
equation is the momentum
balance (mixing chamber)
TVR Thermal Vapor Recompression
2
m1u3   m1  m2  u4 .
1
5
Thermocompressor
Entrainment ratio fe (mass flowrate of entrained
vaports to the mass florate of motive steam) follows from the
momentum balance
fe 
h h
m2 u3
  1  1 3  1.
m1 u4
h5  h4
fe 
c p T1  T2 
c p T5  T2 
1 
T1
1
T2
1 
T5
1
T2
 p1 
 
 p2 
 p5 
 
 p2 
k 1
k
k 1
k
1
 1.
1
Power R.: Steam jet ejectors for the process industries. Mac Graw Hill, New York, 1994
u 4  2h5  h4 .
u3  2h1  h3 .
HP8
Evaporators TVR
Design diagram for TVR
Motive
steam
presure
Discharge
pressure
Suction
pressure
Power R.: Steam jet ejectors for the
process industries. Mac Graw Hill, New
York, 1994
HP8
Evaporators TVR
TVR Thermal Vapor Recompression
2
1
5
Thermocompressor
Previous analysis determined only the entrainment ratio fe  m2 / m1 . 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.
HP8
Evaporators TVR
Thermocompressor and Laval nozzle
Unknown 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
Ideal gas!
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
Mixing chamber
Motive
steam
du 2  2dh  2c p dT  2c p
Laval nozzle
Diffuser
v and dv is to be eliminated (expressed in terms of p)
v  v1 (
Suction
p1 1/
)
p
du 2  
Speed of sound
pdv  vdp
R
2c p
R
dv  v1 (
(v1 (
p1 1/ dp
)
p
p
p1 1/ dp
p
)
 v1 ( 1 )1/ dp)
p
p
p
By integration we obtain St.Venant Wanzel equation
p 1
u  2 p1v1
(1  ( ) )
 1
p1
2

HP8
Evaporators TVR
Mass flowrate is independent of axial coordinate
1
 p( z )  
m1  u ( z ) S ( z )  ( z )  S ( z ) 1 

 p1 
 1
2
 1










 p1   p( z )   
2
p
(
z
)
p
(
z
)

2
1 
p1 1 
   S ( z)
 
 .


  1 1   p1  
 1
 p1   p1  





Introducing dimension pressure P*=p(z)/p1 the throat geometrical constraint
(minimum cross section S) is
dS * d

dz dz
m1
2 p1 1  *
P
 1 
2
 2 * 2   1 *1  dP*
m1  P

P 


 dz  0.
 
 1
 1
*

2 p1 1  *2
*



P

P


P


1 



 2   1
*
Solution of this (algebraic) equation is
and corresponding mass flowrate
m1  S *
P 



1


S*
,
2
 1
 1


2 p1 1  2  1  2   1 
 2   1
*

 S  p1 1 
.




  1    1 
  1  
  1 


z
H2O molecule riding inside a Laval nozzle
HP8
7
6
5
S(z)
4
2
 1








2
p( z )
p( z )

.
S ( z )  m1 /
p1 1 

 p1   p1  
 1


S=1/(2*kappa/(kappa-1)*(A3^(2/kappa)-A3^((kappa+1)/kappa)))^0.5)
3
2
1
0
0.9
1
0.8
0.7
0.6
0.5
0.4
0.3
0.2
p(z)/p1
S*
z
0.1
0
HP8
H2O molecule riding inside a Laval nozzle
Slow, nice, eliptic ride, clear view
Approaching speed of sound, view is misty
Collision with different
pressure at outlet of Laval
nozzle (wrong design, of
course not by our students)
Speed of sound and still accelerating,
Molecule is blind, nothing is seen (only
the rear mirror view is clear)
S*
z
HP8
Evaporators St Venant Wanzel
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
p1
p
Evaporator chamber
operating at
underpressure
Mass flowrate through a gap
with cross section S at subsonic

flow  1
Leakage at sonic
flow (choking). Mass
flowrate is
independent of
vacuum level p.
p  2 


p1    1 
2
 1








2
p
p
m1  S
p1 1       .
 p1   p1  
 1


 2 
m1  S  p1 1 



1


 1
 1
.
HP8
Vacuum cooling LIQUIDS
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
M f c pf
dT f
dt
 mhLG
Condenser
Mass flow rate of
evaporated water
cooker
M. Dostal, K. Petera: Vacuum cooling of liquids: mathematical
model. Journal of Food Engineering 61 (2004) 533–539
Heating
jacket
Condensate
pump
Vacuum pump
There still exist controversial opinions
concerning interpretation of thermal and
mass transfer resistances at surface
conduction
Convection (n
is mass flux)
Area of liquid
surface
HP8
Vacuum cooling WATER
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.
HP8
Spray cooling WATER
Cooling ponds JETE
dT
3

[hLG ( wA  wA )   (T  TA )]
dt
r cp
HP8
Vacuum cooling MEAT
Relatively new vacuum cooling technology is applied also to porous solids, for
example meat.
The visualised cross-section of the cooked meat
L. Wang, D.-W. Sun / International Journal of
Refrigeration 25 (2002) 862–871
Mathematical modelling is usually based upon FK equation for heat transfer
Heat flux
Mass transport of vapour is expressed in terms of pressure P
Mass flux
Evaporation
rate
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
D.-W. Sun, L. Wang / Journal of Food Engineering 77 (2006) 379–385
HP8
Evaporators papers
Bosch
HP8
Evaporators papers
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.
Almost the same result can
be derived from the Weber
number limit
 u 2
We 
2

Nii S.et al: Membrane evaporators. Journal
of membrane science, 201 (2002), 149-159
HP8
Evaporators papers
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.
HP8
Evaporators papers
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.
HP8
Evaporators papers
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 961-968
The 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.
HP8
Evaporators papers
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
HP8
EXAM
Phase changes
Evaporators
Thermocompressors
What is important (at least for exam)
HP8
Nusselt correlation for film condensation
dx
x

T
w
dm
 4 hGL  2 g 3
 ( x)  

4Tx
Mass flow rate of
condensed
steam
Ts=Tw+T
Rohsenow correlation for pool boiling
1
Nu 
Re 2 / 3 Pr  m
C LS
Laplace constant Db is used as a characteristic
dimension in Nu and Re
Db 

g (  L  G )
HP8
What is important (at least for exam)
Vapours
(brüden)
Saturated steam
Evaporation of water
(pool or flow boiling).
Use Rohsenow or
Chen correlations
feed
Condensation of
saturated steam
(Nusselt correlation)
concentrate
Overall mass balance
m f  mc  W
Mass balance of solid
 f m f  c mc
condensate
Enthalpy balance 0  m f (h f  h f 0 )  mc (hc  hc 0 )  W (hv  hv 0 )  kS T  m f h f 0  mc hc 0  Whv 0
dilution heat
What is important (at least for exam)
HP8
Recompression of vapours by thermo-compressor (that is driven by Laval nozzle)
2
1
u 4  2h5  h4 .
5
Thermocompressor
u3  2h1  h3 .
Laval nozzle
Supersonic flow for pressure ratio
Mixing chamber
Motive
steam
Laval nozzle
Diffuser
Sucti
on
p3  2 


p1    1 
Mass flowrate is independent of outlet
pressure at supersonic flow
Speed of sound

 1
 0.53 for air
=0.58 for steam
 2 
m1  S  p1 1 

  1 
 1
 1
.