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Prediction of two-phase flow distribution in microchannel heat exchangers using artificial neural network
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Prediction of Two-phase Flow Distribution in Microchannel Heat Exchangers using Artificial Neural Network Niccolo Giannetti , Mark Anthony Redo , Sholahudin , Jongsoo Jeong , Seiichi Yamaguchi , Kiyoshi Saito , Hyunyoung Kim PII: DOI: Reference:
S0140-7007(19)30504-3 https://doi.org/10.1016/j.ijrefrig.2019.11.028 JIJR 4595
To appear in:
International Journal of Refrigeration
Received date: Revised date: Accepted date:
13 July 2019 17 October 2019 23 November 2019
Please cite this article as: Niccolo Giannetti , Mark Anthony Redo , Sholahudin , Jongsoo Jeong , Seiichi Yamaguchi , Kiyoshi Saito , Hyunyoung Kim , Prediction of Two-phase Flow Distribution in Microchannel Heat Exchangers using Artificial Neural Network, International Journal of Refrigeration (2019), doi: https://doi.org/10.1016/j.ijrefrig.2019.11.028
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Highlights
ANN is implemented for the prediction of two-phase refrigerant distribution; the possibility for substantially improved prediction accuracy is demonstrated; the optimized ANN model mostly achieves a ±5% deviation without overfitting; reverse ANN could define optimal values of design parameters to achieve a target take-offratio;
1
Prediction of Two-phase Flow Distribution in Microchannel Heat Exchangers using Artificial Neural Network
Niccolo Giannettia,b, Mark Anthony Redoc, Sholahudinc, Jongsoo Jeongc, Seiichi Yamaguchib,c, Kiyoshi Saitob,c, Hyunyoung Kimd
a
Waseda Institute for Advanced Study, Waseda University, 1-6-1 Nishiwaseda, Shinjuku-ku, Tokyo 169-8050, Japan
b
Interdisciplinary Institute for Thermal Energy Conversion Engineering and Mathematics, Waseda University, Tokyo, 169-8555, Japan
c
Department of Applied Mechanics and Aerospace Engineering, Waseda University, Tokyo 169-8555, Japan d
Samsung Research and Development Institute Japan, Osaka, 562-0036, Japan
ABSTRACT Due to the intrinsic complexity of two-phase flow distribution and the limited mathematical flexibility of conventional formulations of the
phenomenon,
previous
attempts
generally
fall
short
in
the
accuracy and applicability of their prediction. To address these issues,
this
flexibility.
study
focuses
Specifically,
on
methods
the
with
higher
construction
and
mathematical training
of
Artificial Neural Network (ANN) is presented for the identification of this complex phenomenon. The interaction of the numerous physical phenomena, occurring at different scales, is thus represented by the network
structure,
offering
a
formulation
capable
of
achieving
higher accuracy. Experimental data from a full-scale heat exchanger of
an
air-conditioning
system
operating 2
over
a
wide
range
of
conditions
are
used
to
train
and
test
the
ANN.
The
network
optimization with Bayesian regularization against experimental data leads to a structure featuring 4 inputs, 3 hidden layers, and 3 neurons for each layer, which demonstrates deviations on the single output mostly lower than ±10% and a correlation index higher than 98%, when the whole data set is used for training the ANN. The analysis of the network optimisation for different shares of data used for the network testing, shows higher training and testing accuracy as the number of training data increases, along with no apparent overfittig.
Keywords: Artificial Neural Network, two-phase flow, microchannel heat exchanger, flow distribution
Nomenclature A,B,C,D
Coefficients (-)
R
Resistance (Ω)
b
Bias coefficients
Re
Reynolds number (-)
Ca
Capillary number (-)
S
Entropy rate (W K-1)
D
Diameter (m)
T
Temperature (°C)
f
Transfer function
u
Input
Fr
Froude number (-)
U
Data uncertainty
G
Mass flux (kg m-2s-1)
V
Volume (m3)
g
Gravity (m s-2)
w
Weight coefficients
h
Specific enthalpy (J K-1)
x
Vapour quality (-)
H
Height (m)
y
Output
i
Current (A)
Greek symbols
ṁ
Mass flowrate (kg h-1)
β
Void fraction (-)
N
Number of branch tubes (-)
Geometrical parameter
p
Pressure (kPa)
ρ
Density (kg m-3)
P
Dissipated power (kW)
µ
Viscosity (Pa s)
Q
Heat transfer rate (kW)
σ
Surface tension (N m-1)
3
Г
j, k, n
Take-off ratio (-)
Subscripts
Indexes
l
Saturated liquid
m
Microchannel
1,2,3,4,5
Tube number
o
Outlet
e
Evaporation
p
Pre-heated
g
Entropy generation
s
Superheated
h
Header
v
Saturated vapour
i,j
Channel index
id
Ideal
Superscript
in
Inlet
a,b,c,d
exponents
1. INTRODUCTION
In the context of very demanding numerical targets in terms of carbon
dioxide
emissions
reduction
[1],
the
development
and
spreading of the heat pump technology was cited as one of the most promising elements to meet this objective. This technology includes vapour compression heat pumps [2], vapour sorption heat pumps [3-5], inverse Brayton heat pumps [6], chemical heat pumps [7], and combinations of these in cascade configurations [8-9], or
hybrid
systems
[10-12].
Heat
exchangers
are
the
main
components for ensuring efficient operation of these systems [1314]. The need for more efficient, smaller, and cheaper devices has
driven
the
development
of
microchannel
heat
exchangers
(MCHX). Miniaturization widens the application field ranging from small vehicles to aerospace systems [15]; it is also associated to higher heat transfer coefficients (resulting in thermal-energy savings,
smaller
systems,
and
less
refrigerant
charge
[16]),
along with higher pressure drop. Pressure drop can be reduced by implementing
multiple
parallel
channels
merging
in
a
common
header for flow distribution. However, during actual operation this component often encounter the occurrence of highly complex and
dynamic
properly
multiphase
accounted
for,
transport lead
to 4
phenomena, detrimental
which, effects
if
not
such
as
dryout of the transfer interfaces [17], poor phase separation or phase distribution. Flow maldistribution within the MCHX headers constitutes their
a
major
challenge
implementation
limiting
their
[18].
Kulkarni
potential
performance et
al.
and [19]
estimated a 20% degradation in the cooling capacity of a system employing MCHXs in relation to this type of flow maldistribution. Two-phase flow distributions within MCHX headers demonstrate complex characteristics under the influence of several parameters such as structural features, external force fields and/or heat transfer, operating conditions, and thermodynamic properties of the working fluid. Interactions between these parameters and the fluid
flow
induce
phase
mixing
and/or
separation,
along
with
momentum dissipations, thereby resulting in pressure drops. The relative
importance
of
these
dissipative
phenomena
is
then
influenced by variable operating conditions. Since an established formulation
for
these
phenomena
is
not
presently
available,
design and control methods of operative machineries has so far relied
on
empirical
rules
or
trial/error
procedures,
hence
leading to non-optimized operation. Interactions between multi-phase fluids and solid structures remain
a
computational
challenge
owing
to
moving
transfer
interfaces, time dependency and non-linearity [20]. The number of numerical
studies
related
to
the
accurate
treatment
of
such
interplays is still limited due to difficulties in modelling the phase interface [21] and defining an appropriate mesh size [22]. Therefore, calculations are computationally intensive and it is usually
impractical
to
establish
the
appropriate
set
of
information for defining the boundary conditions to be imposed and closing the problem. Li et al. (2018) [23] presents numerical results
of
gas–liquid
flow
characteristics
in
a
small
sized
reactor, stating that each calculation case, using coupled volume of fluid and Level Set method, required a computation time of approximately performed refrigerant
one
month.
computational distribution
Whereas, fluid
dynamics
within 5
Huang the
et (CFD)
common
al.
(2014)
[24]
simulations header
of
of a
microchannel
heat
fluid.
approach
This
analyses,
but
optimisation
exchanger is
by
considering
accordingly
cannot
be
procedures
or
suitable
effectively early
only for
used
predesign
single-phase
for
post-design iterative
simulations,
where
numerically lighter models, requiring fewer input parameters, are preferable.
On
needed
a
at
the
one
hand,
pre-design
simple
stage
when
analytical limited
equations
are
information
is
available; on the other hand, given the intrinsic complexity of these
phenomena,
necessary
to
advanced
achieve
the
mathematical target
formulations
prediction
become
accuracy.
As
a
consequence, most of the distribution correlations available in literature
are
establishing
based
on
their
the
Buckingham
analytical
Pi-theorem
formulation
for
[25–31],
conventionally, as the product of power laws of dimensionless groups summarizing the main influential parameters. For instance, Zou and Hrnjak [32] fitted their experimental data to such a kind of correlation dependent on vapour quality, dimensionless cross sectional
area,
and
vapour
Reynolds
number.
The
resulting
correlation exhibits deviations higher than ±40%. Redo et al. [25] designed and installed an experimental facility employing a large-sized MCHX, and performed experiments over a wider range of refrigerant mass flux. An empirical correlation was deduced. An improved ±25% deviation from experimental results was observed in the result prediction. This conventional type of formulation has been considered as a relatively “rigid” mathematical framework, which, hence, may fall short with regard to representing the target variable over a broad range of physical conditions and with sufficient accuracy. To address the issue of achieving an accurate prediction based on a limited amount of input information, in a previous work of the authors (Giannetti et al. 2019 [26]), a method for deriving an advanced mathematical form of the correlation equation has, therefore,
been
proposed.
The
analytical
formulation
of
the
steady state take-off ratio was obtained from Prigogine’s Theorem of
minimum
entropy
generation
6
[33-34]
by
considering
an
approximate representation based on the analogy between fluidflow networks and electric circuits. Alternatively, provided that a sufficient number of training data is available, Artificial neural network (ANN) method has the ability of mathematically reconstructing the interdependencies of complex phenomena while relying on a limited number of input parameters [35-37] with equivalent computational requirements of those necessary for calculating an analytical expression. In the last two decades, this method has been extensively applied to building
energy
optimisation
management
[40-41],
strategies
heat
exchanger
[38-39],
system
characterization
control [42-44],
and prediction of various phenomena [45-48]. Most recently, the advantage
of
ANN
over
conventional
methods
in
predicting
oscillatory heat transfer coefficient of one thermoacoustic heat exchanger was discussed by Rahman and Zhang (2018)[49]; Ricardo et
al.
(2016)[50]
used
this
method
to
characterize
the
convective heat transfer rate that occurs during the evaporation of a refrigerant flowing inside tubes of small diameter; Sablani et al. (2005) [51] proposed ANN to avoid the use of a timeconsuming, iterative procedures for the heat transfer coefficient for
a
solid/fluid
assembly
from
the
knowledge
of
the
inside
temperature; numerous other works presented several successful application
of
coefficients
ANN
[52-56].
for It
the has
estimation been
also
of
heat
recognised
transfer that
the
complex mathematical framework of an ANN model has the advantage of easily handling large number of data with high prediction accuracy,
thus
enabling
to
summarise
data
from
different
investigation to cover larger ranges and set of working fluids within one model [57]. Finally, ANN has been applied for flow pattern identification (e.g. [58]). However, the advantage of using this method for the prediction of two-phase refrigerant distribution has not been discussed in previous literature. By relying on this approach, this study focuses on a method with
higher
mathematical
flexibility,
presents
its
comparison
with conventional formulations, and suggests the possibility of a 7
new
advanced
common
representation
vertical
header
of
of a
flow
MCHX.
distribution In
this
within
respect,
it
the is
demonstrated that ANN provides a possibility for substantially improved
accuracy
Specifically, Artificial
for
an
equal
the
construction
Neural
Network
number
and
(ANN)
of
input
training is
of
parameters.
an
presented
optimized for
the
identification of this complex phenomenon. The interaction of the numerous physical phenomena, occurring at different scales, is thus represented by the network structure, offering a formulation capable of achieving higher accuracy.
2. System and experiments Experimental results reported by Redo et al. [25] obtained for a full-scale evaporating MCHX for an air-conditioning system are referred in this study to investigate the ability of different mathematical formulations to predict these results. Parameters representing the experimental range covered by this experiment are summarized in Table 1.
Table 1. Experimental conditions Inlet Total inlet flow rate ṁin -1
[kg·h ]
Inlet vapour saturation quality xin
temperature
[-]
Te
Tube protrusion depth [%]
[°C] 40, 50, 60, 80, 100, 150
0.1, 0.2
10
50
50, 100, 150, 200
0.1, 0.2
15
50
50, 100, 150
0.2
10
0
8
Figure
1
experimental
depicts
the
equipment
and
characterised.
The
schematic test
header
flow
section
comprises
diagram
where
20
flat
the
tubes
of
the
header
is
containing
microchannels branching out from the header. These are grouped together forming 5 measurement tubes (tube 1 to tube 5). Mass flow
rates
individually
exiting
from
measured
each
along
of
these
with
tubes
their
(ṁ1 to
ṁ5)
corresponding
were
vapour
qualities (x1 to x5).
rear header
test section RV51 RV
BV51 BV
front header
CV51 CV
ṁ5 tube tube5 ṁ 1 1
microchannels
xxx551
ṁ24 tube tube4 ṁ 2
xi x. i
ṁ3 tube3
. .
ṁ24 tube tube2 ṁ 4 T
T
vap. flow meter
condenser
F brine chiller
Tin
ṁ15 tube tube15 ṁ
P
control valve 2
Ts Ps
x1
xx15
Pin
Δp ṁin xin
vapor heater
Qs
T
T
bypass
Qp
subcooler
tank
Psub Tsub
T
F T
magnetic pump T
preheater
control liq. flow valve 1 meter
T
brine chiller
Figure 1. Schematic diagram of the experimental setup.
The instruments’ measurement ranges and accuracies are indicated in Table 2.
Table 2. Ranges and accuracies of instrumentation devices.
9
Instrument
Range
Pressure transmitter Differential pressure transmitter Platinum resistance thermometer sensor
Accuracy
0–3500 kPa
± 1.0% of full scale
0.75–100 kPa
± 0.1% of full scale
-200–500 ℃
±（0.3+0.005|t|）, t: measurement
Liquid Coriolis flowmeter
0–200 kg h-1
Vapor Coriolis flowmeter
0–60 kg h-1
Clamp on power meter
0–6 kW
± 0.2% ± (0.09[kg/h] / Q[kg h-1] ×100[%])of reading ± 0.1% ± (0.036[kg/h] / Q[kg h-1] × 100[%])of reading ± (0.6% of reading + 0.4% of range)
The fluid flow within an MCHX header such as the one depicted in Fig. 2a, enters from the bottom of the vertical header and is distributed between multiple horizontally oriented microchannels. When
referring
to
elementary
control
volumes,
these
can
be
represented as one-inlet–two-outlet junctions (inset to Fig. 2b within dotted box). At each junction, a portion of the inlet flow is withdrawn through the branch tube; the remaining fluid within the header passes
through
along
the
vertical
direction
towards
the
successive junction. The flow partition between branch tubes is governed by the interaction between structural parameters of the junction, fluid momentum, and thermo-physical properties of the working fluid.
10
tube 5 ṁ5
x5
tube 4 ṁ4
x4
tube 3 ṁ3
x3
tube 2 ṁ2
x4
ṁo,2
tube 1 ṁl
x1
ṁo,1
ṁo,5 ṁh,5 ṁo,4 ṁh,j+1
ṁh,4 ṁo,3 ṁh,3 ṁo,j ṁh,2 ṁin xin
ṁh,1
tube protrusion
ṁh,j
ṁin xin
(a)
(b)
Figure 2. (a) Actual fluid flow; (b) Fluid-flow representation within MCHX
The total circulating flowrate (ṁin) and the inlet vapor quality before the header (xin) were first experimentally adjusted to the target condition, at saturation temperatures of 10 °C or 15 °C. Individual pressure drop (Δpi) was measured for each of the five measurement
tubes
at
a
steady
state
condition,
and
the
average
reading from the pressure gauge was taken as a reference. These recorded
values
individual
were
flowrate
used
(ṁ1 to
as
a
ṁ5).
reference
Individual
when flow
measuring rates
are
the then
bypassed to the measurement section mainly consisted of a cartridge heater and vapor Coriolis flowmeter. While targeting corresponding pressure drops Δpi by adjusting the control valve 2 (Fig. 1), a vapour heater was used to superheat the flow entering the vapour Coriolis flow meter. Once a fairly stable condition was maintained, the individual vapour flowrate was directly measured for a time span of 15 minutes. As this experiment was carried out under adiabatic conditions of the test section the evaluation of the individual inlet quality (xi) relied on a set of measured quantities, and refrigerant
properties
taken
from
the
NIST
standard
reference
database of thermodynamic and transport properties of refrigerants 11
[26]. Specifically, once the steady operative saturation pressure and the bypassed refrigerant flowrate (ṁi) were known, the heat input at the vapour heater in the bypass channel (Qs) to reach the target superheated condition (Ts) from the inlet conditions at the front
header
(measured).
Equation
1
describes
the
calculation
procedure adopted to obtain this parameter.
xi The combined
mi hs hl Qs mi hv hl uncertainty uncertainties
Eq. 1
analysis of
the
of
the
collected
measurements,
data
which
gave
the
includes
the
theoretical uncertainty caused by sensor accuracy limitations and the uncertainty contribution due to experimental variability. An expanded uncertainty is subsequently calculated, providing a higher level of confidence with a coefficient value of 2. The range of the calculated uncertainties are presented in Table 3 [25].
Table 3. Combined expanded uncertainties. Total inlet flow rate Uṁin
Inlet vapour quality Uxin
[kg h-1]
0.16–0.24
[-]
0.009–0.012
Individual mass flow rate Uṁi
Individual vapour quality Uxi
Individual pressure drop UΔpi
[kg h-1]
[-]
[kPa]
0.05–0.80
0.02–0.14
0.10–0.47
This enables the calculation of the take-off ratio (Eq.3) as a derived quantity defined by eq. 2.
i
mi 1 xi i 1
Eq. 2
min 1 xin m j 1 x j j 1
i 2 2 U i U U min xin j 1 m j min xin 2
2
12
2
2
i 2 2 U m j U x j j 1 x j
Eq. 3
The
range
of
the
take-off
ratio
uncertainty
extends
over
values of i between 0.0056 and 0.1997, whereas the individual values are plotted as error bars in Figures 3 and 7.
3. Analysis of the mathematical framework 3.1 Dimensionless groups Despite the limited applicability and accuracy of conventional formulations for characterizing fluid-flow distributions within MCHX, empirical correlations built up as the multiplication of power laws of selected dimensionless groups have been developed in numerous extant studies. This is the case of the pioneering work of Watanabe et al. [59], who performed modelling of twophase
flow
distributions
within
MCHX,
thereby
resulting
in
a
correlation to determine the ratio of the fluid mass flow rate exiting the branch tube (ṁo,i) to that immediately upstream of the header (ṁh,i). This same ratio was subsequently adopted in the study performed by Byun & Kim [31] and Zou and Hrnjak [32], who named it as the take-off ratio i. This was considered the same to
be
related
to
the
vapour-phase
Reynolds
number.
Other
researches have similarly tried to relate the said ratio to other dimensionless numbers, which they deemed significant. Similarly, in this study, the same set of plausibly influent dimensionless parameters is considered in different mathematical formulations mostly
of
fluid
considered
the
flow
within
Reynolds
MCHXs.
number
Extant
(Re)
studies
evaluated
have at
a
location immediately upstream of the branch tube [25,30-32]. The liquid
take-off
related
to
the
ratio
for
Reynolds
an
number
evaporator (Rel)
in
application accordance
can with
be the
following expression (Eq. 4).
Rel
Gh,l ,i Dh
(4)
l
As the strong effect of gravitational forces was demonstrated in the occurrence of different flow-patterns, and liquid reach 13
[60]. The Froude number is hereby expressed as in Eq. (5) to represent the upwards liquid momentum against that of a liquid falling freely from height Hi in a saturated vapour environment [25]. Frl
G
2
h ,l ,i
(5)
l l v gH i
Small channels result in generation of axisymmetric or nonstratified flow patterns with low Reynolds numbers along with high
wall-shear
stresses
and
surface
tension
[61].
Chung
and
Kawaji [62] exclusively observed slug-flow patterns generated by the balance between effects of viscosity and surface tension. Therefore, the capillary number expressed as the ratio of surface tension to viscous forces (Eq. 3) is assumed to play an important role in describing fluid-flow distribution within MCHXs. The mass flux in Eq. (6) is estimated with reference to the hydraulic diameter of the microchannel flat tube.
Cal The
G 'h ,l ,i l
(6)
l void
fraction
(Eq.
7)
is
also
an
important
factor
reflecting the flow regime and directly associated to the slip ratio of the average velocity of each phase, hence, critical with regard to the occurrence of pressure drop.
Vv V
(7)
Although other groups were considered in [63], in this study, this
set
of
4
dimensionless
groups
is
used
in
3
different
mathematical formulations to compare their ability of predicting this phenomenon.
3.2 Conventional formulation
14
The first direct possibility comes from the adoption of a conventional formulation, as the multiplication of power laws of the above-stated parameters (Eq. 8).
l , j A Rel Frl (1 )c Cal a
b
d
(8)
The fitting to the data from Redo et al. [25] leads to Eq. (9), with a deviations mostly below ±30% and a correlation index higher than 83% (Figure 3).
1
+15
+30 +20
0.9
-15
0.8 -20
ṁo,l,i/ṁh,l,i
0.7 -30
0.6 0.5 0.4 0.3 0.2
R2 = 0.835
0.1 0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
A[(B*Relb+C*Frlc+D*(1-β)d)Calα + N-j+1]-1 Figure 3. Predicted versus actual data results obtained using a conventional formulation [26]
l , j 10410000Rel 1.11 Frl 0.475 (1 )1.18 Cal1.81
(9)
3.3 ANN identification At present, artificial intelligence (AI) is being used and studied in
various
fields,
and
there
is 15
no
exception
in
the
field
of
refrigeration and air conditioning. In fact, several major phenomena at
play
in
this
complexity.
are
Accordingly,
encapsulated prediction
field
within of
characterized mathematically
when
explored
simplified
these by
characterized
at
deviations.
reconstructing
the
the As
a
over
mathematical
phenomena
large
by
ANN
high
wide
degree
of
ranges
and
formulations,
the
pre-design has
the
interdependencies
stage
is
ability
of
of
complex
phenomena while relying on a limited number of input parameters, this opens up to possibilities of advanced identifications of such complex phenomena. The interaction of the numerous forces, within different scales, during flow distribution within the common header can
hence
be
accurately
represented
by
an
optimised
network
structure. Figure 4 represents a possible schematic structure of the ANN used in this research, for the purpose of which, the output is the take-off ratio. Here, as an example for evaluating the potential of this method in predicting the flow distribution phenomenon, the set
of
4
dimensionless
parameters,
used
in
presented above, is selected as the input layer.
16
the
formulations
Input layer
Hidden layer
Output layer
Re Fr
Ca
Figure 4. Simplified ANN configuration
The correlation between input and output for one hidden layer can be conceptually represented by Fig. 5. The product of input elements u(k) and weight w1 is fed to summing junctions and is summed with bias b1 then passes through the transfer function f1 to generate n. Subsequently, the output from hidden layer n is multiplied by the weight coefficient w2 and summed with b2, the transformed by the transfer function f2 to generate output y(k).
Fig. 5 Mathematical representation of ANN model 17
Network optimization When developing an ANN model, the input and output training data is first normalized in the range [-1, 1] to facilitate the training process
towards
convergence
[64].
The
network
configuration
is
optimized by varying number of hidden layers H and neurons. The increase of number of neurons in one and two hidden layer shows no significant effect on the accuracy. This is because the increase of number
of
weight
coefficients
cannot
improve
the
structural
flexibility of ANN. Meanwhile, the increase of number of hidden layers can make the network to be more flexible.
Fig. 6 ANN model optimization
The accuracy achieved by the network with three hidden layers fluctuates
widely.
Conversely,
when
the
network
is
not
rigid,
convergence becomes non-trivial during the training process because the optimisation passes through a higher order of the number of parameters
to
be
modulated.
possibility
of
attaining
Nonetheless,
better
accuracy.
this Figure
expands
the
6
the
shows
training results using 100% data. Based on this results, the highest accuracy can be achieved by three hidden layers and three neurons for each hidden layer. Table 4 summarises network structure and 18
training accuracy as the RMSE between predicted take-off ratio and experimental data, as well as the correlation index R2.
Table 4 Network structure and training accuracy Network structure
Training
Correlation
(I-H-H-H-O)
accuracy (RMSE)
index (R2)
4-3-3-3-1
0.043
0.9802
Figure 7 illustrates the prediction ability of this model and makes evidence for obviously higher accuracy when compared to the previously discussed formulations. Most of the take-off ratio values are estimated within a ±10% deviation and a correlation index higher than 98% is achieved.
1 +5% +10
0.9
+20 -5%
0.8
-10
ṁo,l,i/ṁh,l,i
0.7 -20
0.6 0.5 0.4 0.3
0.2
R2 = 0.980
0.1 0 0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
ANN(Re,Fr,Ca,) Figure 7. Predicted versus actual data results obtained using proposed method 19
Network testing accuracy To ensure that the ANN model is not experiencing overfitting, which would lead to possible large deviation when tested on a set of data not included in the training data, the values of the take-off ratio measured by Redo et al. [25] is divided into two shares: one intended for training and the other for testing. The ANN model is optimised while targeting the best training accuracy for
4
different
training
and
subdivisions
testing
data
of
(Table
the
experimental
5).
Prediction
results results
in are
summarized in Table 5 in terms of network structure, testing and training accuracy.
Table 5 Optimised network structure and training/testing accuracy 50% testing
20% testing
10% testing
1% testing
Network
(I-H-H-H-O)
(I-H-H-H-O)
(I-H-H-H-O)
(I-H-H-H-
structure
4-2-2-2-1
4-3-3-3-1
4-4-4-4-1
O)
(RMSE)
4-4-4-4-1
Testing
0.081
0.047
0.044
0.036
0.052
0.059
0.039
0.035
0.929
0.949
0.973
0.980
accuracy (RMSE) Training accuracy (RMSE) Correlation 2
index (R )
As illustrated in Figure 8, in general, the optimised ANN model exhibits better testing (red markers) accuracy when more data are used for training (blue markers).
20
1 0.9
+20
+10
+5 -5
0.8
-10
ṁo,l,i/ṁh,l,i
0.7 -20
0.6 0.5 0.4 0.3
0.2 0.1 0 0
0.1
0.2
0.3
0.4
0.5
a 1 +10
0.9
0.7
0.8
0.9
1
0.8
b
1
+5
+20
+10
0.9
-5
+5
+20 -5
0.8
-10
0.7
-10
0.7
ṁo,l,i/ṁh,l,i
-20
0.6 0.5 0.4
-20
0.6 0.5 0.4
0.3
0.3
0.2
0.2
0.1
0.1
0
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
ANN(Re,Fr,Ca,)
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
ANN(Re,Fr,Ca,)
c
d
1 0.9
+20
+10
+5 -5
0.8
-10
0.7
ṁo,l,i/ṁh,l,i
ṁo,l,i/ṁh,l,i
0.6
ANN(Re,Fr,Ca,)
-20
0.6 0.5 0.4 0.3 0.2 0.1 0 0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
ANN(Re,Fr,Ca,)
Figure 8. Testing results for different sets [(a) 50%/50%; (b) 80%/20%; (c) 90%/10%; (d) 99%/1%] of training/testing data
However, considering the uncertainty of the experimental data [25], the improvement between 90% and 99% training data is quite 21
irrelevant. Accordingly, the set of experimental data used for training should stay within this range to achieve high prediction accuracy while ensuring that no overfitting is occurring in this process. The implementation of this same method is easily attainable from
the
user
by
performing
the
ANN
training
with
Bayesian
regularization of the ANN toolbox of MATlab®, referring to the optimized setting presented in Table 4 and Table 5.
3.4. Results comparison Table
6
compares
formulations
the
presented
ability
above
of
to
the
predict
2
mathematical
two-phase
flow
distribution in microchannel heat exchangers. More complex and flexible mathematical formulations yield better accuracy.
Table 4 Comparison between different formulations [26]
Correlation
Conventional
This study
0.835
0.980
index (R2)
Although,
the
implementation
of
ANN
does
not
provide
an
interpretation for physical understanding of the phenomenon, and, being a black-box approach, applied to a limited set of training data
related
to
a
specific
experimental
structure,
it
is
recommended not to extrapolate the ANN results outside the range of training. This method can be further extended to wider ranges of operation, different working fluids, and header structures. Namely, data from different set-ups and extensive sets of results from computational fluid dynamics could be summarised in a single ANN model to provide a general prediction tool for two-phase flow distribution in microchannel heat exchangers. However, this could 22
worsen the correlation index for a given set of input parameters, whereas it could be advantageous to improve the accuracy of all the correlations available in literature by individually applying this method to different set of data from different header types.
3.5. Reverse ANN By relying on the identification of flow distribution obtained in the previous section (summarised in Table 4), it is possible to calculate the values of Reynolds, Froude and capillary numbers as design parameters for approaching ideally uniform distribution with a constrained value of the liquid fraction (1-). These values can be referenced for re-establishing geometrical features such
as
vertical
position
of
the
branching
tubes
Hi ,
cross
sectional area of the header Ah,i, and hydraulic diameter Di on a local basis for target rated conditions. Figure 9 illustrates the results of this calculation procedure (numerically reported in Table 7). For instance, referring to the value of the Reynolds number in figure 9a, it is advantageous to have a quickly flowing fluid at the bottom of the header, to avoid excessive fluid stagnation at this location. At the third vertical position, a higher value of Reynolds than the second branch is required and can be obtained by means of a locally narrower cross sectional area of the header. In the same circumstance of an operative inlet liquid fraction (1-=0.247), a higher Capillary number at the second vertical position can be represented by a narrower hydraulic diameter of the access to the tubes branching at this location. Similar observation can be reported for the cases in Figures 9b and 9c, where results make evidence for different distribution characteristics at different operative conditions. In the design process
of
the
vertical
header
all
these
conditions
can
be
accounted for when evaluating the distribution performance on a comprehensive
operative
range.
Furthermore,
in
the
favourable
circumstance of the utilization of local actuators which enable 23
dynamic adjustments of structural features in relation to the operative condition, ideal distribution could be approached in the whole system operation range, with obvious possibilities for advanced energy saving control strategies.
1 0.9
1-=0.247 1/5
Fr Rel*10-5
Caid, Frid, Reid*10-5
0.8
1/3
0.7
Ca
0.6 0.5 1/4
0.4
1/2
0.3 0.2 0.1
1
0 1
2
3
4
5
Branch tube position
1-=0.127 0.9
1/5
1/3
1
1/2
Caid, Frid, Reid*10-5
0.8
Fr Ca
0.7
1/4
0.6
0.9
Rel*10-5
0.5 0.4
0.3 0.2
Fr
1/3
Rel*10-5 Ca
0.7 0.6 0.5
1/4
0.4 0.3
1/2
0.2
0.1
1
2
3
4
1
0.1
1
0
(b)
1-=0.024 1/5
0.8
Caid, Frid, Reid*10-5
1
(a)
0
5
1
Branch tube position
2
3
4
5
Branch tube position
(c)
Figure 9. Values of Reynolds, Froude and Capillary numbers for approaching optimal take-off-ratio
However, the results from this design method are subject for verification, and it might be necessary to rely on a larger set of data to increase the level of confidence of the derivable design and operation strategies.
Table 7 Results from reverse ANN for approaching optimal take-offratio 24
Tube position
Target Achievable
1-
Cal
Rel
Frl
(constrained)
1
0.2000
0.2573
0.2470
0.0475
90525
0.0577
2
0.2500
0.2746
0.2470
0.0841
35412
0.0547
3
0.3333
0.3551
0.2470
0.0517
70046
0.0132
4
0.5000
0.5164
0.2470
0.0169
24934
0.0656
5
1
1
0.2470
"
"
"
1
0.2000
0.2573
0.1270
0.0413
90519
0.0504
2
0.2500
0.2746
0.1270
0.0223
56605
0.1240
3
0.3333
0.3551
0.1270
0.0260
87492
0.0114
4
0.5000
0.5164
0.1270
0.0029
79852
0.0046
5
1
1
0.1270
"
"
"
1
0.2000
0.2573
0.0240
0.0363
90527
0.0442
2
0.2500
0.2746
0.0240
0.1002
34172
0.0932
3
0.3333
0.3551
0.0240
0.0805
84136
0.0190
4
0.5000
0.5164
0.0240
0.0196
20829
0.0461
5
1
1
0.0240
"
"
"
5. Conclusions The development of an alternative method for predicting twophase flow distribution in microchannel heat exchangers, via use of an optimised ANN model has been presented. Additionally, the model
prediction
mathematical
ability
formulations
has of
been
the
compared
phenomenon
with from
other
previous
literature. When tested on the same set of experimental data, and with the same
set
of
dimensionless
numbers
as
input
parameters,
conventional power laws formulation, semi-theoretical variational formulation from Prigogine’s theorem, and ANN model demonstrate prediction
deviations
mostly
within 25
±30%,
±15%,
and
±10%,
respectively.
The
ANN
model
exhibits
the
highest
correlation
index (above 98%), followed by the variational formulation (above 94%); the conventional formulation, with a correlation index of 84%, is characterized by the lowest accuracy. When
the
values
of
the
take-off
ratio
are
divided
into
different shares for training and testing, it has been concluded that,
to
achieve
overfitting,
the
high
set
of
prediction
accuracy
experimental
data
while
used
avoiding
for
training
should stay within 90% and 99% of the total data set. In
this
possibility
respect, for
it
is
demonstrated
substantially
improved
that
ANN
accuracy
provides
for
an
a
equal
number of input parameters. In this respect, this investigation brings along the possibility of improving the accuracy of other correlations available in literature by applying ANN to different set of data. Besides providing the highest prediction accuracy among the mathematical formulations available at present, this method can be
further
working
extended
fluids,
and
to
wider
header
ranges
structures
of by
operation, including
different data
from
different set-ups and results from computational fluid dynamics in a single ANN model - targeting a general prediction tool for two-phase flow distribution in microchannel heat exchangers. Finally, the possibility of reversing this ANN to define the optimal values of design parameters to achieve the target value of
take-off-ratio
is
suggested
and
could
open
up
to
new
guidelines for optimised header designs and operation strategies. Declaration of interests The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
26
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Exchanger, Proceedings of the International Refrigeration and Air Conditioning Conference (2016), Paper 1719. [61] Kawahara, A., 2002. Investigation of two-phase flow pattern, void
fraction
and
pressure
drop
in
a
microchannel,
Int.
J.
Multiphase Flow, 28, pp. 1411–1435. [62] Chung, P.M., Kawaji, M., 2004. The effect of channel diameter on adiabatic two-phase flow characteristics in microchannels q, Int. J. Multiphase Flow, 30, pp. 735–761. [63] Zou, Y., Hrnjak, P.S., 2014, Comparison and Generalization of R410A and R134a Distribution in the Microchannel Heat Exchanger with the
Vertical
Header,
International
Refrigeration
and
Air
Conditioning Conference (2014). Paper 1364. [64] Jayalakshmi,
T.,
Santhakumaran,
A.
2011.
Statistical
Normalization and Back Propagation for Classification, International Journal of Computer Theory and Engineering, 3(1), pp. 1793-8201.
34
Prediction of Two-phase Flow Distribution in Microchannel Heat Exchangers using Artificial Neural Network Niccolo Giannetti , Mark Anthony Redo , Sholahudin , Jongsoo Jeong , Seiichi Yamaguchi , Kiyoshi Saito , Hyunyoung Kim PII: DOI: Reference:
S0140-7007(19)30504-3 https://doi.org/10.1016/j.ijrefrig.2019.11.028 JIJR 4595
To appear in:
International Journal of Refrigeration
Received date: Revised date: Accepted date:
13 July 2019 17 October 2019 23 November 2019
Please cite this article as: Niccolo Giannetti , Mark Anthony Redo , Sholahudin , Jongsoo Jeong , Seiichi Yamaguchi , Kiyoshi Saito , Hyunyoung Kim , Prediction of Two-phase Flow Distribution in Microchannel Heat Exchangers using Artificial Neural Network, International Journal of Refrigeration (2019), doi: https://doi.org/10.1016/j.ijrefrig.2019.11.028
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Highlights
ANN is implemented for the prediction of two-phase refrigerant distribution; the possibility for substantially improved prediction accuracy is demonstrated; the optimized ANN model mostly achieves a ±5% deviation without overfitting; reverse ANN could define optimal values of design parameters to achieve a target take-offratio;
1
Prediction of Two-phase Flow Distribution in Microchannel Heat Exchangers using Artificial Neural Network
Niccolo Giannettia,b, Mark Anthony Redoc, Sholahudinc, Jongsoo Jeongc, Seiichi Yamaguchib,c, Kiyoshi Saitob,c, Hyunyoung Kimd
a
Waseda Institute for Advanced Study, Waseda University, 1-6-1 Nishiwaseda, Shinjuku-ku, Tokyo 169-8050, Japan
b
Interdisciplinary Institute for Thermal Energy Conversion Engineering and Mathematics, Waseda University, Tokyo, 169-8555, Japan
c
Department of Applied Mechanics and Aerospace Engineering, Waseda University, Tokyo 169-8555, Japan d
Samsung Research and Development Institute Japan, Osaka, 562-0036, Japan
ABSTRACT Due to the intrinsic complexity of two-phase flow distribution and the limited mathematical flexibility of conventional formulations of the
phenomenon,
previous
attempts
generally
fall
short
in
the
accuracy and applicability of their prediction. To address these issues,
this
flexibility.
study
focuses
Specifically,
on
methods
the
with
higher
construction
and
mathematical training
of
Artificial Neural Network (ANN) is presented for the identification of this complex phenomenon. The interaction of the numerous physical phenomena, occurring at different scales, is thus represented by the network
structure,
offering
a
formulation
capable
of
achieving
higher accuracy. Experimental data from a full-scale heat exchanger of
an
air-conditioning
system
operating 2
over
a
wide
range
of
conditions
are
used
to
train
and
test
the
ANN.
The
network
optimization with Bayesian regularization against experimental data leads to a structure featuring 4 inputs, 3 hidden layers, and 3 neurons for each layer, which demonstrates deviations on the single output mostly lower than ±10% and a correlation index higher than 98%, when the whole data set is used for training the ANN. The analysis of the network optimisation for different shares of data used for the network testing, shows higher training and testing accuracy as the number of training data increases, along with no apparent overfittig.
Keywords: Artificial Neural Network, two-phase flow, microchannel heat exchanger, flow distribution
Nomenclature A,B,C,D
Coefficients (-)
R
Resistance (Ω)
b
Bias coefficients
Re
Reynolds number (-)
Ca
Capillary number (-)
S
Entropy rate (W K-1)
D
Diameter (m)
T
Temperature (°C)
f
Transfer function
u
Input
Fr
Froude number (-)
U
Data uncertainty
G
Mass flux (kg m-2s-1)
V
Volume (m3)
g
Gravity (m s-2)
w
Weight coefficients
h
Specific enthalpy (J K-1)
x
Vapour quality (-)
H
Height (m)
y
Output
i
Current (A)
Greek symbols
ṁ
Mass flowrate (kg h-1)
β
Void fraction (-)
N
Number of branch tubes (-)
Geometrical parameter
p
Pressure (kPa)
ρ
Density (kg m-3)
P
Dissipated power (kW)
µ
Viscosity (Pa s)
Q
Heat transfer rate (kW)
σ
Surface tension (N m-1)
3
Г
j, k, n
Take-off ratio (-)
Subscripts
Indexes
l
Saturated liquid
m
Microchannel
1,2,3,4,5
Tube number
o
Outlet
e
Evaporation
p
Pre-heated
g
Entropy generation
s
Superheated
h
Header
v
Saturated vapour
i,j
Channel index
id
Ideal
Superscript
in
Inlet
a,b,c,d
exponents
1. INTRODUCTION
In the context of very demanding numerical targets in terms of carbon
dioxide
emissions
reduction
[1],
the
development
and
spreading of the heat pump technology was cited as one of the most promising elements to meet this objective. This technology includes vapour compression heat pumps [2], vapour sorption heat pumps [3-5], inverse Brayton heat pumps [6], chemical heat pumps [7], and combinations of these in cascade configurations [8-9], or
hybrid
systems
[10-12].
Heat
exchangers
are
the
main
components for ensuring efficient operation of these systems [1314]. The need for more efficient, smaller, and cheaper devices has
driven
the
development
of
microchannel
heat
exchangers
(MCHX). Miniaturization widens the application field ranging from small vehicles to aerospace systems [15]; it is also associated to higher heat transfer coefficients (resulting in thermal-energy savings,
smaller
systems,
and
less
refrigerant
charge
[16]),
along with higher pressure drop. Pressure drop can be reduced by implementing
multiple
parallel
channels
merging
in
a
common
header for flow distribution. However, during actual operation this component often encounter the occurrence of highly complex and
dynamic
properly
multiphase
accounted
for,
transport lead
to 4
phenomena, detrimental
which, effects
if
not
such
as
dryout of the transfer interfaces [17], poor phase separation or phase distribution. Flow maldistribution within the MCHX headers constitutes their
a
major
challenge
implementation
limiting
their
[18].
Kulkarni
potential
performance et
al.
and [19]
estimated a 20% degradation in the cooling capacity of a system employing MCHXs in relation to this type of flow maldistribution. Two-phase flow distributions within MCHX headers demonstrate complex characteristics under the influence of several parameters such as structural features, external force fields and/or heat transfer, operating conditions, and thermodynamic properties of the working fluid. Interactions between these parameters and the fluid
flow
induce
phase
mixing
and/or
separation,
along
with
momentum dissipations, thereby resulting in pressure drops. The relative
importance
of
these
dissipative
phenomena
is
then
influenced by variable operating conditions. Since an established formulation
for
these
phenomena
is
not
presently
available,
design and control methods of operative machineries has so far relied
on
empirical
rules
or
trial/error
procedures,
hence
leading to non-optimized operation. Interactions between multi-phase fluids and solid structures remain
a
computational
challenge
owing
to
moving
transfer
interfaces, time dependency and non-linearity [20]. The number of numerical
studies
related
to
the
accurate
treatment
of
such
interplays is still limited due to difficulties in modelling the phase interface [21] and defining an appropriate mesh size [22]. Therefore, calculations are computationally intensive and it is usually
impractical
to
establish
the
appropriate
set
of
information for defining the boundary conditions to be imposed and closing the problem. Li et al. (2018) [23] presents numerical results
of
gas–liquid
flow
characteristics
in
a
small
sized
reactor, stating that each calculation case, using coupled volume of fluid and Level Set method, required a computation time of approximately performed refrigerant
one
month.
computational distribution
Whereas, fluid
dynamics
within 5
Huang the
et (CFD)
common
al.
(2014)
[24]
simulations header
of
of a
microchannel
heat
fluid.
approach
This
analyses,
but
optimisation
exchanger is
by
considering
accordingly
cannot
be
procedures
or
suitable
effectively early
only for
used
predesign
single-phase
for
post-design iterative
simulations,
where
numerically lighter models, requiring fewer input parameters, are preferable.
On
needed
a
at
the
one
hand,
pre-design
simple
stage
when
analytical limited
equations
are
information
is
available; on the other hand, given the intrinsic complexity of these
phenomena,
necessary
to
advanced
achieve
the
mathematical target
formulations
prediction
become
accuracy.
As
a
consequence, most of the distribution correlations available in literature
are
establishing
based
on
their
the
Buckingham
analytical
Pi-theorem
formulation
for
[25–31],
conventionally, as the product of power laws of dimensionless groups summarizing the main influential parameters. For instance, Zou and Hrnjak [32] fitted their experimental data to such a kind of correlation dependent on vapour quality, dimensionless cross sectional
area,
and
vapour
Reynolds
number.
The
resulting
correlation exhibits deviations higher than ±40%. Redo et al. [25] designed and installed an experimental facility employing a large-sized MCHX, and performed experiments over a wider range of refrigerant mass flux. An empirical correlation was deduced. An improved ±25% deviation from experimental results was observed in the result prediction. This conventional type of formulation has been considered as a relatively “rigid” mathematical framework, which, hence, may fall short with regard to representing the target variable over a broad range of physical conditions and with sufficient accuracy. To address the issue of achieving an accurate prediction based on a limited amount of input information, in a previous work of the authors (Giannetti et al. 2019 [26]), a method for deriving an advanced mathematical form of the correlation equation has, therefore,
been
proposed.
The
analytical
formulation
of
the
steady state take-off ratio was obtained from Prigogine’s Theorem of
minimum
entropy
generation
6
[33-34]
by
considering
an
approximate representation based on the analogy between fluidflow networks and electric circuits. Alternatively, provided that a sufficient number of training data is available, Artificial neural network (ANN) method has the ability of mathematically reconstructing the interdependencies of complex phenomena while relying on a limited number of input parameters [35-37] with equivalent computational requirements of those necessary for calculating an analytical expression. In the last two decades, this method has been extensively applied to building
energy
optimisation
management
[40-41],
strategies
heat
exchanger
[38-39],
system
characterization
control [42-44],
and prediction of various phenomena [45-48]. Most recently, the advantage
of
ANN
over
conventional
methods
in
predicting
oscillatory heat transfer coefficient of one thermoacoustic heat exchanger was discussed by Rahman and Zhang (2018)[49]; Ricardo et
al.
(2016)[50]
used
this
method
to
characterize
the
convective heat transfer rate that occurs during the evaporation of a refrigerant flowing inside tubes of small diameter; Sablani et al. (2005) [51] proposed ANN to avoid the use of a timeconsuming, iterative procedures for the heat transfer coefficient for
a
solid/fluid
assembly
from
the
knowledge
of
the
inside
temperature; numerous other works presented several successful application
of
coefficients
ANN
[52-56].
for It
the has
estimation been
also
of
heat
recognised
transfer that
the
complex mathematical framework of an ANN model has the advantage of easily handling large number of data with high prediction accuracy,
thus
enabling
to
summarise
data
from
different
investigation to cover larger ranges and set of working fluids within one model [57]. Finally, ANN has been applied for flow pattern identification (e.g. [58]). However, the advantage of using this method for the prediction of two-phase refrigerant distribution has not been discussed in previous literature. By relying on this approach, this study focuses on a method with
higher
mathematical
flexibility,
presents
its
comparison
with conventional formulations, and suggests the possibility of a 7
new
advanced
common
representation
vertical
header
of
of a
flow
MCHX.
distribution In
this
within
respect,
it
the is
demonstrated that ANN provides a possibility for substantially improved
accuracy
Specifically, Artificial
for
an
equal
the
construction
Neural
Network
number
and
(ANN)
of
input
training is
of
parameters.
an
presented
optimized for
the
identification of this complex phenomenon. The interaction of the numerous physical phenomena, occurring at different scales, is thus represented by the network structure, offering a formulation capable of achieving higher accuracy.
2. System and experiments Experimental results reported by Redo et al. [25] obtained for a full-scale evaporating MCHX for an air-conditioning system are referred in this study to investigate the ability of different mathematical formulations to predict these results. Parameters representing the experimental range covered by this experiment are summarized in Table 1.
Table 1. Experimental conditions Inlet Total inlet flow rate ṁin -1
[kg·h ]
Inlet vapour saturation quality xin
temperature
[-]
Te
Tube protrusion depth [%]
[°C] 40, 50, 60, 80, 100, 150
0.1, 0.2
10
50
50, 100, 150, 200
0.1, 0.2
15
50
50, 100, 150
0.2
10
0
8
Figure
1
experimental
depicts
the
equipment
and
characterised.
The
schematic test
header
flow
section
comprises
diagram
where
20
flat
the
tubes
of
the
header
is
containing
microchannels branching out from the header. These are grouped together forming 5 measurement tubes (tube 1 to tube 5). Mass flow
rates
individually
exiting
from
measured
each
along
of
these
with
tubes
their
(ṁ1 to
ṁ5)
corresponding
were
vapour
qualities (x1 to x5).
rear header
test section RV51 RV
BV51 BV
front header
CV51 CV
ṁ5 tube tube5 ṁ 1 1
microchannels
xxx551
ṁ24 tube tube4 ṁ 2
xi x. i
ṁ3 tube3
. .
ṁ24 tube tube2 ṁ 4 T
T
vap. flow meter
condenser
F brine chiller
Tin
ṁ15 tube tube15 ṁ
P
control valve 2
Ts Ps
x1
xx15
Pin
Δp ṁin xin
vapor heater
Qs
T
T
bypass
Qp
subcooler
tank
Psub Tsub
T
F T
magnetic pump T
preheater
control liq. flow valve 1 meter
T
brine chiller
Figure 1. Schematic diagram of the experimental setup.
The instruments’ measurement ranges and accuracies are indicated in Table 2.
Table 2. Ranges and accuracies of instrumentation devices.
9
Instrument
Range
Pressure transmitter Differential pressure transmitter Platinum resistance thermometer sensor
Accuracy
0–3500 kPa
± 1.0% of full scale
0.75–100 kPa
± 0.1% of full scale
-200–500 ℃
±（0.3+0.005|t|）, t: measurement
Liquid Coriolis flowmeter
0–200 kg h-1
Vapor Coriolis flowmeter
0–60 kg h-1
Clamp on power meter
0–6 kW
± 0.2% ± (0.09[kg/h] / Q[kg h-1] ×100[%])of reading ± 0.1% ± (0.036[kg/h] / Q[kg h-1] × 100[%])of reading ± (0.6% of reading + 0.4% of range)
The fluid flow within an MCHX header such as the one depicted in Fig. 2a, enters from the bottom of the vertical header and is distributed between multiple horizontally oriented microchannels. When
referring
to
elementary
control
volumes,
these
can
be
represented as one-inlet–two-outlet junctions (inset to Fig. 2b within dotted box). At each junction, a portion of the inlet flow is withdrawn through the branch tube; the remaining fluid within the header passes
through
along
the
vertical
direction
towards
the
successive junction. The flow partition between branch tubes is governed by the interaction between structural parameters of the junction, fluid momentum, and thermo-physical properties of the working fluid.
10
tube 5 ṁ5
x5
tube 4 ṁ4
x4
tube 3 ṁ3
x3
tube 2 ṁ2
x4
ṁo,2
tube 1 ṁl
x1
ṁo,1
ṁo,5 ṁh,5 ṁo,4 ṁh,j+1
ṁh,4 ṁo,3 ṁh,3 ṁo,j ṁh,2 ṁin xin
ṁh,1
tube protrusion
ṁh,j
ṁin xin
(a)
(b)
Figure 2. (a) Actual fluid flow; (b) Fluid-flow representation within MCHX
The total circulating flowrate (ṁin) and the inlet vapor quality before the header (xin) were first experimentally adjusted to the target condition, at saturation temperatures of 10 °C or 15 °C. Individual pressure drop (Δpi) was measured for each of the five measurement
tubes
at
a
steady
state
condition,
and
the
average
reading from the pressure gauge was taken as a reference. These recorded
values
individual
were
flowrate
used
(ṁ1 to
as
a
ṁ5).
reference
Individual
when flow
measuring rates
are
the then
bypassed to the measurement section mainly consisted of a cartridge heater and vapor Coriolis flowmeter. While targeting corresponding pressure drops Δpi by adjusting the control valve 2 (Fig. 1), a vapour heater was used to superheat the flow entering the vapour Coriolis flow meter. Once a fairly stable condition was maintained, the individual vapour flowrate was directly measured for a time span of 15 minutes. As this experiment was carried out under adiabatic conditions of the test section the evaluation of the individual inlet quality (xi) relied on a set of measured quantities, and refrigerant
properties
taken
from
the
NIST
standard
reference
database of thermodynamic and transport properties of refrigerants 11
[26]. Specifically, once the steady operative saturation pressure and the bypassed refrigerant flowrate (ṁi) were known, the heat input at the vapour heater in the bypass channel (Qs) to reach the target superheated condition (Ts) from the inlet conditions at the front
header
(measured).
Equation
1
describes
the
calculation
procedure adopted to obtain this parameter.
xi The combined
mi hs hl Qs mi hv hl uncertainty uncertainties
Eq. 1
analysis of
the
of
the
collected
measurements,
data
which
gave
the
includes
the
theoretical uncertainty caused by sensor accuracy limitations and the uncertainty contribution due to experimental variability. An expanded uncertainty is subsequently calculated, providing a higher level of confidence with a coefficient value of 2. The range of the calculated uncertainties are presented in Table 3 [25].
Table 3. Combined expanded uncertainties. Total inlet flow rate Uṁin
Inlet vapour quality Uxin
[kg h-1]
0.16–0.24
[-]
0.009–0.012
Individual mass flow rate Uṁi
Individual vapour quality Uxi
Individual pressure drop UΔpi
[kg h-1]
[-]
[kPa]
0.05–0.80
0.02–0.14
0.10–0.47
This enables the calculation of the take-off ratio (Eq.3) as a derived quantity defined by eq. 2.
i
mi 1 xi i 1
Eq. 2
min 1 xin m j 1 x j j 1
i 2 2 U i U U min xin j 1 m j min xin 2
2
12
2
2
i 2 2 U m j U x j j 1 x j
Eq. 3
The
range
of
the
take-off
ratio
uncertainty
extends
over
values of i between 0.0056 and 0.1997, whereas the individual values are plotted as error bars in Figures 3 and 7.
3. Analysis of the mathematical framework 3.1 Dimensionless groups Despite the limited applicability and accuracy of conventional formulations for characterizing fluid-flow distributions within MCHX, empirical correlations built up as the multiplication of power laws of selected dimensionless groups have been developed in numerous extant studies. This is the case of the pioneering work of Watanabe et al. [59], who performed modelling of twophase
flow
distributions
within
MCHX,
thereby
resulting
in
a
correlation to determine the ratio of the fluid mass flow rate exiting the branch tube (ṁo,i) to that immediately upstream of the header (ṁh,i). This same ratio was subsequently adopted in the study performed by Byun & Kim [31] and Zou and Hrnjak [32], who named it as the take-off ratio i. This was considered the same to
be
related
to
the
vapour-phase
Reynolds
number.
Other
researches have similarly tried to relate the said ratio to other dimensionless numbers, which they deemed significant. Similarly, in this study, the same set of plausibly influent dimensionless parameters is considered in different mathematical formulations mostly
of
fluid
considered
the
flow
within
Reynolds
MCHXs.
number
Extant
(Re)
studies
evaluated
have at
a
location immediately upstream of the branch tube [25,30-32]. The liquid
take-off
related
to
the
ratio
for
Reynolds
an
number
evaporator (Rel)
in
application accordance
can with
be the
following expression (Eq. 4).
Rel
Gh,l ,i Dh
(4)
l
As the strong effect of gravitational forces was demonstrated in the occurrence of different flow-patterns, and liquid reach 13
[60]. The Froude number is hereby expressed as in Eq. (5) to represent the upwards liquid momentum against that of a liquid falling freely from height Hi in a saturated vapour environment [25]. Frl
G
2
h ,l ,i
(5)
l l v gH i
Small channels result in generation of axisymmetric or nonstratified flow patterns with low Reynolds numbers along with high
wall-shear
stresses
and
surface
tension
[61].
Chung
and
Kawaji [62] exclusively observed slug-flow patterns generated by the balance between effects of viscosity and surface tension. Therefore, the capillary number expressed as the ratio of surface tension to viscous forces (Eq. 3) is assumed to play an important role in describing fluid-flow distribution within MCHXs. The mass flux in Eq. (6) is estimated with reference to the hydraulic diameter of the microchannel flat tube.
Cal The
G 'h ,l ,i l
(6)
l void
fraction
(Eq.
7)
is
also
an
important
factor
reflecting the flow regime and directly associated to the slip ratio of the average velocity of each phase, hence, critical with regard to the occurrence of pressure drop.
Vv V
(7)
Although other groups were considered in [63], in this study, this
set
of
4
dimensionless
groups
is
used
in
3
different
mathematical formulations to compare their ability of predicting this phenomenon.
3.2 Conventional formulation
14
The first direct possibility comes from the adoption of a conventional formulation, as the multiplication of power laws of the above-stated parameters (Eq. 8).
l , j A Rel Frl (1 )c Cal a
b
d
(8)
The fitting to the data from Redo et al. [25] leads to Eq. (9), with a deviations mostly below ±30% and a correlation index higher than 83% (Figure 3).
1
+15
+30 +20
0.9
-15
0.8 -20
ṁo,l,i/ṁh,l,i
0.7 -30
0.6 0.5 0.4 0.3 0.2
R2 = 0.835
0.1 0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
A[(B*Relb+C*Frlc+D*(1-β)d)Calα + N-j+1]-1 Figure 3. Predicted versus actual data results obtained using a conventional formulation [26]
l , j 10410000Rel 1.11 Frl 0.475 (1 )1.18 Cal1.81
(9)
3.3 ANN identification At present, artificial intelligence (AI) is being used and studied in
various
fields,
and
there
is 15
no
exception
in
the
field
of
refrigeration and air conditioning. In fact, several major phenomena at
play
in
this
complexity.
are
Accordingly,
encapsulated prediction
field
within of
characterized mathematically
when
explored
simplified
these by
characterized
at
deviations.
reconstructing
the
the As
a
over
mathematical
phenomena
large
by
ANN
high
wide
degree
of
ranges
and
formulations,
the
pre-design has
the
interdependencies
stage
is
ability
of
of
complex
phenomena while relying on a limited number of input parameters, this opens up to possibilities of advanced identifications of such complex phenomena. The interaction of the numerous forces, within different scales, during flow distribution within the common header can
hence
be
accurately
represented
by
an
optimised
network
structure. Figure 4 represents a possible schematic structure of the ANN used in this research, for the purpose of which, the output is the take-off ratio. Here, as an example for evaluating the potential of this method in predicting the flow distribution phenomenon, the set
of
4
dimensionless
parameters,
used
in
presented above, is selected as the input layer.
16
the
formulations
Input layer
Hidden layer
Output layer
Re Fr
Ca
Figure 4. Simplified ANN configuration
The correlation between input and output for one hidden layer can be conceptually represented by Fig. 5. The product of input elements u(k) and weight w1 is fed to summing junctions and is summed with bias b1 then passes through the transfer function f1 to generate n. Subsequently, the output from hidden layer n is multiplied by the weight coefficient w2 and summed with b2, the transformed by the transfer function f2 to generate output y(k).
Fig. 5 Mathematical representation of ANN model 17
Network optimization When developing an ANN model, the input and output training data is first normalized in the range [-1, 1] to facilitate the training process
towards
convergence
[64].
The
network
configuration
is
optimized by varying number of hidden layers H and neurons. The increase of number of neurons in one and two hidden layer shows no significant effect on the accuracy. This is because the increase of number
of
weight
coefficients
cannot
improve
the
structural
flexibility of ANN. Meanwhile, the increase of number of hidden layers can make the network to be more flexible.
Fig. 6 ANN model optimization
The accuracy achieved by the network with three hidden layers fluctuates
widely.
Conversely,
when
the
network
is
not
rigid,
convergence becomes non-trivial during the training process because the optimisation passes through a higher order of the number of parameters
to
be
modulated.
possibility
of
attaining
Nonetheless,
better
accuracy.
this Figure
expands
the
6
the
shows
training results using 100% data. Based on this results, the highest accuracy can be achieved by three hidden layers and three neurons for each hidden layer. Table 4 summarises network structure and 18
training accuracy as the RMSE between predicted take-off ratio and experimental data, as well as the correlation index R2.
Table 4 Network structure and training accuracy Network structure
Training
Correlation
(I-H-H-H-O)
accuracy (RMSE)
index (R2)
4-3-3-3-1
0.043
0.9802
Figure 7 illustrates the prediction ability of this model and makes evidence for obviously higher accuracy when compared to the previously discussed formulations. Most of the take-off ratio values are estimated within a ±10% deviation and a correlation index higher than 98% is achieved.
1 +5% +10
0.9
+20 -5%
0.8
-10
ṁo,l,i/ṁh,l,i
0.7 -20
0.6 0.5 0.4 0.3
0.2
R2 = 0.980
0.1 0 0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
ANN(Re,Fr,Ca,) Figure 7. Predicted versus actual data results obtained using proposed method 19
Network testing accuracy To ensure that the ANN model is not experiencing overfitting, which would lead to possible large deviation when tested on a set of data not included in the training data, the values of the take-off ratio measured by Redo et al. [25] is divided into two shares: one intended for training and the other for testing. The ANN model is optimised while targeting the best training accuracy for
4
different
training
and
subdivisions
testing
data
of
(Table
the
experimental
5).
Prediction
results results
in are
summarized in Table 5 in terms of network structure, testing and training accuracy.
Table 5 Optimised network structure and training/testing accuracy 50% testing
20% testing
10% testing
1% testing
Network
(I-H-H-H-O)
(I-H-H-H-O)
(I-H-H-H-O)
(I-H-H-H-
structure
4-2-2-2-1
4-3-3-3-1
4-4-4-4-1
O)
(RMSE)
4-4-4-4-1
Testing
0.081
0.047
0.044
0.036
0.052
0.059
0.039
0.035
0.929
0.949
0.973
0.980
accuracy (RMSE) Training accuracy (RMSE) Correlation 2
index (R )
As illustrated in Figure 8, in general, the optimised ANN model exhibits better testing (red markers) accuracy when more data are used for training (blue markers).
20
1 0.9
+20
+10
+5 -5
0.8
-10
ṁo,l,i/ṁh,l,i
0.7 -20
0.6 0.5 0.4 0.3
0.2 0.1 0 0
0.1
0.2
0.3
0.4
0.5
a 1 +10
0.9
0.7
0.8
0.9
1
0.8
b
1
+5
+20
+10
0.9
-5
+5
+20 -5
0.8
-10
0.7
-10
0.7
ṁo,l,i/ṁh,l,i
-20
0.6 0.5 0.4
-20
0.6 0.5 0.4
0.3
0.3
0.2
0.2
0.1
0.1
0
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
ANN(Re,Fr,Ca,)
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
ANN(Re,Fr,Ca,)
c
d
1 0.9
+20
+10
+5 -5
0.8
-10
0.7
ṁo,l,i/ṁh,l,i
ṁo,l,i/ṁh,l,i
0.6
ANN(Re,Fr,Ca,)
-20
0.6 0.5 0.4 0.3 0.2 0.1 0 0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
ANN(Re,Fr,Ca,)
Figure 8. Testing results for different sets [(a) 50%/50%; (b) 80%/20%; (c) 90%/10%; (d) 99%/1%] of training/testing data
However, considering the uncertainty of the experimental data [25], the improvement between 90% and 99% training data is quite 21
irrelevant. Accordingly, the set of experimental data used for training should stay within this range to achieve high prediction accuracy while ensuring that no overfitting is occurring in this process. The implementation of this same method is easily attainable from
the
user
by
performing
the
ANN
training
with
Bayesian
regularization of the ANN toolbox of MATlab®, referring to the optimized setting presented in Table 4 and Table 5.
3.4. Results comparison Table
6
compares
formulations
the
presented
ability
above
of
to
the
predict
2
mathematical
two-phase
flow
distribution in microchannel heat exchangers. More complex and flexible mathematical formulations yield better accuracy.
Table 4 Comparison between different formulations [26]
Correlation
Conventional
This study
0.835
0.980
index (R2)
Although,
the
implementation
of
ANN
does
not
provide
an
interpretation for physical understanding of the phenomenon, and, being a black-box approach, applied to a limited set of training data
related
to
a
specific
experimental
structure,
it
is
recommended not to extrapolate the ANN results outside the range of training. This method can be further extended to wider ranges of operation, different working fluids, and header structures. Namely, data from different set-ups and extensive sets of results from computational fluid dynamics could be summarised in a single ANN model to provide a general prediction tool for two-phase flow distribution in microchannel heat exchangers. However, this could 22
worsen the correlation index for a given set of input parameters, whereas it could be advantageous to improve the accuracy of all the correlations available in literature by individually applying this method to different set of data from different header types.
3.5. Reverse ANN By relying on the identification of flow distribution obtained in the previous section (summarised in Table 4), it is possible to calculate the values of Reynolds, Froude and capillary numbers as design parameters for approaching ideally uniform distribution with a constrained value of the liquid fraction (1-). These values can be referenced for re-establishing geometrical features such
as
vertical
position
of
the
branching
tubes
Hi ,
cross
sectional area of the header Ah,i, and hydraulic diameter Di on a local basis for target rated conditions. Figure 9 illustrates the results of this calculation procedure (numerically reported in Table 7). For instance, referring to the value of the Reynolds number in figure 9a, it is advantageous to have a quickly flowing fluid at the bottom of the header, to avoid excessive fluid stagnation at this location. At the third vertical position, a higher value of Reynolds than the second branch is required and can be obtained by means of a locally narrower cross sectional area of the header. In the same circumstance of an operative inlet liquid fraction (1-=0.247), a higher Capillary number at the second vertical position can be represented by a narrower hydraulic diameter of the access to the tubes branching at this location. Similar observation can be reported for the cases in Figures 9b and 9c, where results make evidence for different distribution characteristics at different operative conditions. In the design process
of
the
vertical
header
all
these
conditions
can
be
accounted for when evaluating the distribution performance on a comprehensive
operative
range.
Furthermore,
in
the
favourable
circumstance of the utilization of local actuators which enable 23
dynamic adjustments of structural features in relation to the operative condition, ideal distribution could be approached in the whole system operation range, with obvious possibilities for advanced energy saving control strategies.
1 0.9
1-=0.247 1/5
Fr Rel*10-5
Caid, Frid, Reid*10-5
0.8
1/3
0.7
Ca
0.6 0.5 1/4
0.4
1/2
0.3 0.2 0.1
1
0 1
2
3
4
5
Branch tube position
1-=0.127 0.9
1/5
1/3
1
1/2
Caid, Frid, Reid*10-5
0.8
Fr Ca
0.7
1/4
0.6
0.9
Rel*10-5
0.5 0.4
0.3 0.2
Fr
1/3
Rel*10-5 Ca
0.7 0.6 0.5
1/4
0.4 0.3
1/2
0.2
0.1
1
2
3
4
1
0.1
1
0
(b)
1-=0.024 1/5
0.8
Caid, Frid, Reid*10-5
1
(a)
0
5
1
Branch tube position
2
3
4
5
Branch tube position
(c)
Figure 9. Values of Reynolds, Froude and Capillary numbers for approaching optimal take-off-ratio
However, the results from this design method are subject for verification, and it might be necessary to rely on a larger set of data to increase the level of confidence of the derivable design and operation strategies.
Table 7 Results from reverse ANN for approaching optimal take-offratio 24
Tube position
Target Achievable
1-
Cal
Rel
Frl
(constrained)
1
0.2000
0.2573
0.2470
0.0475
90525
0.0577
2
0.2500
0.2746
0.2470
0.0841
35412
0.0547
3
0.3333
0.3551
0.2470
0.0517
70046
0.0132
4
0.5000
0.5164
0.2470
0.0169
24934
0.0656
5
1
1
0.2470
"
"
"
1
0.2000
0.2573
0.1270
0.0413
90519
0.0504
2
0.2500
0.2746
0.1270
0.0223
56605
0.1240
3
0.3333
0.3551
0.1270
0.0260
87492
0.0114
4
0.5000
0.5164
0.1270
0.0029
79852
0.0046
5
1
1
0.1270
"
"
"
1
0.2000
0.2573
0.0240
0.0363
90527
0.0442
2
0.2500
0.2746
0.0240
0.1002
34172
0.0932
3
0.3333
0.3551
0.0240
0.0805
84136
0.0190
4
0.5000
0.5164
0.0240
0.0196
20829
0.0461
5
1
1
0.0240
"
"
"
5. Conclusions The development of an alternative method for predicting twophase flow distribution in microchannel heat exchangers, via use of an optimised ANN model has been presented. Additionally, the model
prediction
mathematical
ability
formulations
has of
been
the
compared
phenomenon
with from
other
previous
literature. When tested on the same set of experimental data, and with the same
set
of
dimensionless
numbers
as
input
parameters,
conventional power laws formulation, semi-theoretical variational formulation from Prigogine’s theorem, and ANN model demonstrate prediction
deviations
mostly
within 25
±30%,
±15%,
and
±10%,
respectively.
The
ANN
model
exhibits
the
highest
correlation
index (above 98%), followed by the variational formulation (above 94%); the conventional formulation, with a correlation index of 84%, is characterized by the lowest accuracy. When
the
values
of
the
take-off
ratio
are
divided
into
different shares for training and testing, it has been concluded that,
to
achieve
overfitting,
the
high
set
of
prediction
accuracy
experimental
data
while
used
avoiding
for
training
should stay within 90% and 99% of the total data set. In
this
possibility
respect, for
it
is
demonstrated
substantially
improved
that
ANN
accuracy
provides
for
an
a
equal
number of input parameters. In this respect, this investigation brings along the possibility of improving the accuracy of other correlations available in literature by applying ANN to different set of data. Besides providing the highest prediction accuracy among the mathematical formulations available at present, this method can be
further
working
extended
fluids,
and
to
wider
header
ranges
structures
of by
operation, including
different data
from
different set-ups and results from computational fluid dynamics in a single ANN model - targeting a general prediction tool for two-phase flow distribution in microchannel heat exchangers. Finally, the possibility of reversing this ANN to define the optimal values of design parameters to achieve the target value of
take-off-ratio
is
suggested
and
could
open
up
to
new
guidelines for optimised header designs and operation strategies. Declaration of interests The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
26
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