HEFAT2014 10 International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics

HEFAT2014 10 International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics
HEFAT2014
10th International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics
14 – 16 July 2014
Orlando, Florida
EXPERIMENTAL ANALYSIS OF THE RATE OF ABSORPTION OF STEAM BUBBLES
IN LITHIUM BROMIDE SOLUTION FOR USE IN AN ABSORPTION HEAT
TRANSFORMER
Donnellan P.a*, Byrne E.a, Lee W.b, Cronin K.a
*Author for correspondence
a
Department of Process and Chemical Engineering, University College Cork, Ireland
b
MACSI, Department of Mathematics and Statistics, University of Limerick, Ireland
E-mail: [email protected]
ABSTRACT
An experimental investigation is conducted into the
absorption of steam bubbles in a concentrated lithium bromide
solution. The aim of the work is to determine whether such
bubble absorption may be advantageously utilised within the
absorber column section of an absorption heat transformer
system. A glass bubble column is constructed and a high speed
camera is used to track the collapse of steam bubbles at
different temperatures and solution concentrations. A simple
ordinary differential equation model is developed which is
capable of explaining 96% of the observed experimental
variance. Very high mass transfer coefficients of ~0.012m/s are
observed which indicates that this method of absorption may
have significant advantages over alternative methods
previously examined.
a well-established technology, it has several key drawbacks in
comparison to the direct absorption of steam vapour bubbles in
the solution by means of a bubble column, such as a much
lower contact surface area per unit vapour and lower heat and
mass transfer coefficients.
It has been demonstrated that conventional vertical falling
film absorbers, in which the LiBr-H2O solution is flowing
vertically downwards and absorbing water vapour on the
outside of tubes containing a coolant, can achieve mass transfer
coefficients of ~3.15x10-5m/s [5]. The performance of the
absorber may be increased dramatically by utilising a spray
absorber instead. In spray absorbers, the solution is atomized in
a nozzle before being sprayed into a vessel filled with water
vapour, and mass transfer coefficients of ~6x10 -5m/s have been
reported for such units [6]. The mass transfer coefficient may
be increased even further to approximately 2x10 -4m/s if the
solution is not atomized, but instead falls through the water
vapour as a liquid film, primarily due to the increased liquid
mixing achieved by the falling film [7]. This design may then
be further improved by allowing the liquid film to enter the
absorber in a conical shape, leading to mass transfer
coefficients of up to 7x10-4m/s [8].
The most successful heat and mass transfer coefficients
reported to date for absorbers have been achieved by bubble
absorbers. In a bubble absorber, the vapour is simply bubbled
into the bottom of a bubble column containing the desired
absorbent. It has been demonstrated using numerical
simulations that the absorption of NH3 vapour into a NH3-H2O
solution may achieve mass transfer coefficients of ~1.15x10 3
m/s and heat transfer coefficients of ~16000W/(m2K) [9]. It
has also been shown in a direct comparison that a bubble
column allows more effective absorption of NH3 into NH3-H2O
solution compared to a conventional vertical falling film
absorber [10].
INTRODUCTION
Minimising energy wastage remains a very important issue
in the process and chemical industries. In this context, there is
an opportunity for the investigation of a range of suitable
alternative technologies which allow for the more efficient and
sustainable use of energy. Absorption heat transformers are one
such system. They are closed cycle thermodynamic units which
are capable of upgrading the temperature of waste heat energy
so that it may be recycled within a plant, thus dramatically
reducing primary energy requirements [1].
The principle of operation of certain absorption heat
transformers is the absorption of low temperature steam into a
lithium bromide solution at a higher temperature. It is this
absorption which actually increases the temperature of the
waste heat energy [2]. Currently, the vast majority of reports in
the literature achieve this absorption through the use of
horizontal or vertical falling film absorbers [3, 4]. While this is
1647
From the above literature review, it can be seen that bubble
absorbers have significant advantages over conventional falling
film units. However to the authors’ best knowledge no bubble
absorber operating with LiBr-H2O solution has yet been tested,
even though this is the most commonly utilised working fluid
in absorption heat transformers [11]. Thus this study attempts
to experimentally monitor the absorption of a single steam
bubble in a concentrated LiBr-H2O solution. A simple model is
also be developed which allows for the prediction of bubble
behaviour during the absorption process.
Subscripts
abs
absorption
B
Buoyancy
b
bubble
D
Drag
H2O
i
L
LiBr
v
vm
NOMENCLATURE
A
EXPERIMENTAL SET UP
The experimental bubble column consists of a 1m high,
10cm wide glass cylinder, bolted on to a stainless steel base
plate. The cylinder is filled with approximately 32cm of
aqueous lithium bromide, and the solution is maintained at a
constant temperature by circulating it through a temperature
controlled oil bath at a flowrate of 29mL/s. The oil bath is
operated in on-off mode, controlled by a Honeywell UDC 3000
PID controller, and the solution is pumped from the oil bath
back into the cylinder by means of a Watson Marlow 505S
peristaltic pump.
Measurement of some solution properties is made difficult
due to the high temperature and concentration of the LiBr-H2O
solution. The concentration of Lithium Bromide in solution is
often measured using a refractometer [4], however no reference
data relating the solution's refractive index to lithium bromide
concentration at temperatures of interest in this research
(~140˚C) could be located. Thus the buoyancy force exerted by
the solution on a copper bob of known mass and volume is
measured by suspending the copper mass in the solution
contained within the oil bath from a mass balance (Precisa 3610
CD-FR) (positioned directly above the oil bath).
Simultaneously the temperature of the oil bath is being
recorded by means of a thermocouple connected to the
temperature logging software being used (Pico Log R5). By
using equation 1 and the measured temperature, the mass
fraction of lithium bromide salt in the solution may be found
using the LiBr-H2O solution density correlation reported by
[12].
Surface Area (m2)
2
Aprojected
C
Vertically projected bubble area (m )
Water concentration (mol/m3)
CD
Drag coefficient
cp
D
Specific heat capacity (W/(kg.K))
Pipe Diameter (m)
Dab
dt
F
g
H
h
Mass diffusivity of water in LiBr-H2O solution (m2/s)
Time interval between frames in high speed video (1/500 seconds)
Force (N)
Acceleration due to gravity (m/s2)
Enthalpy (J)
Specific enthalpy (J/kg)
hpw
k
m
n
P
P*
Pv
Q
R
T
t
Partial specific enthalpy of water in LiBr-H2O solution (J/kg)
Thermal conductivity (W/(m.K))
Mass (kg)
Moles
Pressure (Pa)
Vapour pressure (Pa)
Partial pressure (Pa)
Rate of enthalpy flow (W)
Radius (m)
Temperature (K)
Time (s)
t50
u
v
V
x
y
Time for the modelled bubble's volume to reduce by 50% (s)
Liquid velocity (m/s)
Velocity (m/s)
Volume (m3)
Lithium Bromide mass fraction (kg/kg)
Volume fraction in the vapour phase (m3/m3)
 L TL , x L  
Dimensionless Numbers
Re
Reynolds Number = ρLvbD/µL
Pr
Prandtl Number = cpLµL/kL
Sc
Pe
Schmidt Number = µL/ρLD
Peclet Number = RePr
Pem
Mass transfer Peclet Number = ReSc
Greek Symbols
α
Liquid side heat transfer coefficient (W/(m2K))
αtherm
β
ρ
µ
Liquid thermal diffusivity = k/(cpρ) (m2/s)
Liquid side mass transfer coefficient (m/s)
Density (kg/m3)
Dynamic Viscosity (Ns/m2)
τ
σ
Dimensionless Time parameter (t/t50)
Surface Tension (N/m)
Water
Bubble-Liquid interface
Bulk Liquid
Lithium Bromide
Vapour
Virtual Mass (or added mass)
1648
FB
gVCopperMass
(1)
Table 1 - All of the concentrations and temperatures used in the
experiment
Concentration (%w/w)
46
51
56
Temperature (˚C)
111
119
122
121
126
132
131
136
141
Saturated steam for the experiment was produced in a
53x25cm stainless steel cylindrical steam generator. The steam
generated travels by insulated flexible tubing to the top of the
cylinder. Condensed steam is prevented from entering the
bubble column by making all steam flow through a steam trap,
and the flowrate of steam entering the cylinder is controlled by
means of a needle valve following this steam trap. Following
the needle valve, the steam entering the bubble column is
connected to a 2.15mm diameter stainless steel pipe (secured to
the inside of the cylinder) through which it flows to the bottom
of the cylinder. This pipe has a 180 degree bend at its
submerged end, and thus acts as a sparger through which the
steam bubbles are formed.
Upon start-up, a certain mass of air is contained within the
steam generator. Therefore initially the needle valve controlling
vapour flow into the bubble column is closed completely in
order to ensure that as much air is removed from the system as
feasible.
Two experimental runs were conducted for each
concentration and temperature setting at different flowrates,
with each experimental run lasting ten minutes. The bubbles
were recorded using an AOS X-Motion high speed camera
operating with a shutter speed of 500 frames per second. In
order to ensure high visibility of the bubbles for the recordings,
the bubble point of entry was illuminated using two Dedolight
150W Tungsten Aspherics spotlights and a Luxform 500W
Halogen spotlight. The reflection of light off the bubble caused
by these three spotlights ensures that there was sufficient
contrast between the bubble and its surrounding fluid. Three
recordings were taken during each experimental run at evenly
spaced intervals.
Each recording was then analysed using the ProAnalyst
Contour Tracking software package (Xcitex Inc.). This
software was used to determine both the perimeter and
projected area of each analysed bubble (in pixels). From each
recording, three bubbles were selected at random (one from the
beginning, one from the middle and one from the end of the
recording) for analysis in order to ensure that representative
results were obtained.
In order to determine the bubble's volume from the obtained
perimeter and projected area, bubble sphericity is assumed.
Thus using equation 2 an equivalent hydraulic diameter can be
calculated which leads to a definition for the equivalent volume
of the bubble given by equation 3.
Figure 1 - Schematic of the experimental bubble column
developed and used during this study
The temperature profile within the bubble column is
measured by means of 7 type T thermocouples located at
regular intervals along its length. These thermocouples which
have an accuracy of ±0.8˚C are then connected to the
temperature logging software. Upon start-up, the temperature
within the bubble column is lower than in the oil bath. Thus the
solution is allowed to circulate until no further changes in
temperature are measured by any of the thermocouples (to
within experimental accuracy of the thermocouples). At this
point the system is assumed to have reached steady state.
A full factorial analysis involving three concentrations and
temperatures was conducted. Three mass fractions (of lithium
bromide salt) were selected. At each concentration, three
different temperatures were then analysed. As the pressure of
the system is to remain atmospheric, the temperatures selected
for each concentration are limited by the saturation temperature
of the solution. Thus for each concentration, temperatures were
selected so that one is ~3.5˚C, one is ~10˚C, and one is ~15˚C
below the saturation temperature for the solution. The resulting
temperatures and concentrations used in the experiment are
outlined in Table 1. In order to reference the different
parameter settings succinctly, the concentrations and
temperatures are named using levels as may be read from Table
1. Concentration levels run in ascending order from top to
bottom and temperature levels in ascending order from left to
right in Table 1. For example, Concentration 1-Temperature 2
means that this experimental run utilises a concentration of
46%(w/w) and a temperature of 119˚C.
D expt :
1649
4A
P
(2)
Vexpt :
32
3
 A
 P 
Thus the enthalpy balance across the vapour bubble is given
by equation 7.
3
(3)
H b mv

hv Tb , Pb   h pw Tb , PL , xi    L Ab Tb  TL  (7)
t
t

All perimeter and projected area readings are recorded in
pixels. The bubble is produced by the gas sparger, and thus
these are (at least initially) located in the same plane relative to
the camera. Therefore the width of the sparger is measured
using a micrometer and compared to its width in pixels as
recorded by the high speed camera. This allows for a
conversion between pixels and length to be established which
takes into consideration all refractive obstacles encountered by
the light. This conversion ratio is measured for every single
bubble analysed, as small movements of the camera or its
refocusing may otherwise cause discrepancies.
Analogously to the heat transfer scenario, mass transfer
across the bubble interface may be represented by equation 8.
This equation examines the flow of water (not lithium
bromide), and thus the term C corresponds to the concentration
of water. However, as this study measures the mass fraction of
lithium bromide experimentally (instead of water
concentration), equation 8 is converted to equation 9 consisting
of salt mass fraction terms.
MATHEMATICAL MODELLING
In the model, the bubble itself is being defined as the
control volume of interest. The temperature of the bulk liquid in
the system varies slightly over the length of the cylinder, but is
shown to change negligibly with respect to time over the course
of any one experimental run. The spatial distribution of
temperature occurs gradually over the entire liquid height,
however the vapour bubbles are found to absorb within the first
few millimetres of contact liquid. Thus the temperature of the
liquid is assumed to remain constant with respect to time at the
average temperature as reported by the two closest
thermocouples (on average within ~0.17% of each other).
Tv
r
  L Ab Ti  TL 
(4)
(5)
mv
hv Tb , Pb   h pw Tb , PL , xi 
t


(9)
d 2 Rb 3  dRb  4 L dRb
2 (10)
 

 
2
2  dt 
Rb dt
 L Rb
dt
2
 Rb
Although this equation is derived based upon the
assumption of a stationary spherical bubble, it is being used in
this study, as it represents the limiting rate of bubble collapse
(if heat and mass transfer were believed to occur extremely
rapidly) and also approximates the relationship between the
internal pressure of the vapour and the rate of change of its
diameter.
Currently, three independent equations (equations 7, 9 and
10) have been derived, however four unknowns exist (Tb, xi, Pb
and Rb). Thus one further equation is required to provide
closure. Saturation at the absorption interface is assumed to
achieve this. As negligible pressure drop along the bubble’s
radial direction is also being assumed, the vapour pressure at
the bubble interface must equal the pressure of the bubble (Pb).
As a slight residue of air exists in the bubble, this should be
accounted for in the vapour pressure model. The bubble is
assumed to be saturated with water vapour, and thus we can
estimate the partial pressure of water within the vapour
(equation 11). The water-air mixture is treated as an ideal
mixture, and thus Dalton's law is used to find the total pressure
from the vapour volumetric fraction of water (equation 12).
The heat of absorption is defined using a method similar to
[13], utilising the partial specific enthalpy of water in the LiBrH2O solution (equation 6).
Q abs 
mv
   L Ab 1  xi  i  1  x L  L 
t
L
int erface
H b
  L Ab Tb  TL 
t
(8)
PB t   PL t 
Upon examination of the experimental data, it is observed
that significant motion is occurring in the bubble which will
result in a high degree of turbulence within the vapour phase
and hence mixing. Due to this mixing and also the small
diameter of the bubbles (~≤7mm), it was decided to simplify
equation 4 further by assuming a uniform temperature within
the bubble. Thus it is postulated that the interface temperature
is very rapidly advected throughout the bubble, and therefore
(Ti ≈ Tb). Hence equation 4 may be reduced to equation 5.
Q abs 
nv
   L Ab Ci  C L 
t
The effect of water inertia upon the collapse of the steam
bubble is defined by the Rayleigh-Plesset equation shown in
equation 10.
Absorption Rate
Heat energy transfer in the liquid phase is assumed to occur
by convection, and thus the overall energy balance at the site of
absorption may be represented by equation 4.
Q abs  k v Ab

*
Tb , xi 
PHv2O  PLiBr
 1
Pb  
 yH O
 2
(6)
1650
 *

 PLiBr Tb , xi    1

 yH O

 2
(11)
 v
 PH O
 2

(12)
seconds of the absorption process. It may be seen that the
majority of the absorption has been completed after 0.06
seconds in both Figures 2 and 3, while in Figure 4 the diameter
has on average reduced by more than half its initial value at this
point. In these three figures, the experimentally observed
diameters from all of the experimental runs (at the particular
temperature and concentration) are plotted against time.
Absorption is found to be especially rapid at temperature level
1, while even at level 3 (~3.5˚C below the saturation
temperature of the fluid) absorption occurs much more rapidly
than has been previously achieved in any of the absorber
studies cited in the introduction. The rapid absorptions depicted
in Figures 2 to 4 represent a mass transfer coefficient of
~0.012m/s, which is therefore superior to the previous results
outlined in the introduction by several orders of magnitude.
Therefore equations 7, 9, 10 and 12 represent a set of
interdependent, non-linear differential equations which
characterise the absorption of a steam bubble in a LiBr-H2O
solution. These differential equations contain both liquid side
heat and mass transfer coefficients (α and β respectively).
These coefficients are calculated from the bubbles' Nusselt and
Sherwood numbers using equations 13 and 14.
Nu 
D
k
D
Sh 
Dab
(13)
(14)
The correlations used to predict these Nusselt and
Sherwood numbers are discussed as part of the Results section.
It should be noted however that almost all of the sources from
which the heat and mass transfer coefficient correlations are
obtained define either a Nusselt or Sherwood number
correlation, but not both. Thus the heat and mass transfer
analogy is being implemented in this study, on the basis of
analogous behaviour between heat and mass transfer.
Bubble Hydrodynamic Modelling
A simple model consisting of basic forces to describe the
bubble vertical displacement versus time is developed. The
forces included are buoyancy, weight, drag and added mass (or
virtual mass). As the bulk solution is assumed to be quiescent
in this model, the lift force is excluded in this section. The drag,
weight and buoyancy forces are defined in equations 15 to 17.
1
FD    L vb2 C D Aprojected
2
Fw    vVb g
FB   LVb g
(15)
Figure 2 - Experimentally observed diameter versus time at
concentration 3-temperature 1
(16)
(17)
As the surrounding fluid is assumed to be in a steady,
isotropic state, the term Du/Dt = 0, and thus the virtual mass
force expression used in this model may be simplified to
equation 19.
Fvm  
L 
V 
v
Vb
v b 

2  t
t 
(18)
The final hydrodynamic model is given by equation 20.
mb
dvb
 FD  Fw  FB  Fvm
dt
(19)
Figure 3 - Experimentally observed diameter versus time at
concentration 3-temperature 2
RESULTS AND DISCUSSION
Experimental Results
The experimental results obtained highlight the speed at
which the absorption of bubbles takes place. Unlike the
simulation results reported by Merrill [9], the bubble diameter
is not found to remain almost constant during the first 0.06
1651
Bubbles entering the LiBr-H2O solution are initially
spherical but then begin to oscillate after a very short period of
time. This spherical phase is however so short (~0.01 seconds)
that it is approximated as being part of the oscillating regime in
the model. In order to utilise the equations 21 and 22, two
parameters, namely the frequency of oscillation (f) and the
amplitude of the area oscillation (ε), need to be fixed. Clift [15]
states that generally ε ≈ 0.3, and thus this value is used in this
study, while the value of f is approximated at 500Hz based
upon the examination of recorded data. The relationship
between the oscillating bubble model and observed
experimental data is displayed in Figure 6.
Figure 4 - Experimentally observed diameter versus time at
concentration 3-temperature 3
Modelling Results
The set of non-linear differential equations developed in this
paper describing the time dependent collapse of the steam
bubble is dependent upon the inclusion of heat and mass
transfer coefficients (α and β respectively). It is found that
judicious selection of these parameters is of pivotal importance.
From the experimental data, it is apparent that the bubbles are
not perfectly spherical, and thus spherical correlations such as
those developed by Azbel [14] dramatically underestimate the
rate of absorption.
From analysis of the recorded data, it appears that the
bubble collapse occurs in two distinct regimes or phases
(apparent in Figure 2). In the first of these phases, the rate of
absorption appears to be occurring relatively slowly, while the
second phase shows a distinctly faster rate of collapse. The
reason for this appears to be the onset of bubble shape
deformation and bubble oscillation as illustrated in Figure 5.
Thus in order to model these bubbles, Nusselt and Sherwood
correlations are required which include such oscillations in
their derivation.
Figure 6 - Percentage reduction in bubble volume with respect
to dimensionless time as predicted by the model and
experimentally observed at concentration 3 and temperature 3
The model’s goodness of fit it demonstrated in Figure 7. A
slight over prediction of the absorption rate may be observed
during the initial (spherical) phase of the bubble’s residence
time. However as reasoned previously, the time period over
which this phase exists is so short that such over prediction has
negligible effect upon the model’s overall accuracy. Although a
degree of scatter exists in the data (this is to be expected due to
the inherent variability between different bubbles), the model
achieves a coefficient of determination (R2) of 0.96, indicating
that it is capable of describing 96% of the observed
experimental variance.
Figure 5 - Example of the oscillating nature of the bubble
The fresh surface model proposed by Clift [15] is used, in
an attempt to include the effect of bubble oscillation in the
simulation. As previously outlined, the heat and mass transfer
analogy is used to convert the given Sherwood number
equation to an equivalent Nusselt number correlation (equations
21 and 22).
D2 f
1  0.687
Dab
Sh 
2
Nu 
2
D2 f

 therm

1  0.687
(20)
(21)
1652
[3]
[4]
[5]
Figure 7 - Illustration of the goodness of fit between the model
and the experimental data
CONCLUSION
An experimental analysis has been conducted, investigating
the absorption of vapour bubbles in a concentrated lithium
bromide (LiBr-H2O) solution for use in the absorber of a heat
transformer. An experimental bubble column is constructed and
a high speed camera is used to track the collapse of the bubble.
A model consisting of a set of nonlinear differential equations
has been developed which is capable of describing this bubble
collapse. It is determined that the Nusselt and Sherwood
number correlations are highly significant factors in relating the
model to observed data. A good fit is obtained with a fresh
surface oscillating bubble model, capable of explaining 96% of
all the experimentally observed variance. Mass transfer
coefficients of 0.012m/s, represent a large increase upon values
previously reported for other absorption methods, indicating
that bubble absorption may be a highly efficient method of
reducing the required size of this unit operation, and hence
increasing the attractiveness of heat transformers.
[6]
[7]
[8]
ACKNOWLEDGEMENTS
[9]
Philip Donnellan would like to acknowledge the receipt of
funding for this project from the Embark Initiative issued by
the Irish Research Council. William Lee would also like to
acknowledge the receipt of funding from the MACSI grant
issued by Science Foundation Ireland (12/IA/1683).
[10]
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[11]
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1653
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