G. Monni, M. De Salve, B. Panella
Politecnico di Torino, C.so Duca degli Abruzzi 24, 10129 Torino
grazia.monni@polito.it
HEFAT2014
10th International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics
14 – 16 July 2014
Orlando, Florida
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Context
Objective
Experimental Facility and Test Matrix
Venturi Flow Meter (VFM) Experimental Results
VFM Modeling
Two-Phase Flow Mass Flow Rates Estimation
Conclusions
HEFAT2014 14 – 16 July 2014 - Orlando, Florida
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
Experimental Facility for thermal-hydraulic simulation
of innovative small and medium size PWR  SPES3

Measurement of the mixture mass flow rate 
instruments and methodologies to evaluate different
two- phase flow parameters need to be developed

Typically a set of instruments (Spool Piece - SP) must be
installed: each instrument of the SP has to be sensitive to
the different properties of the flow (momentum,
velocity, density, void fraction, etc..)

Different number of instruments can be coupled in a SP
HEFAT2014 14 – 16 July 2014 - Orlando, Florida
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Analysis of the response of a Venturi Flow Meter (VFM)
in two-phase flow

To develop a methodology for the signals interpretation
and a “model of the instrument” for the phases mass
flow rate estimation

The SP is tested in a vertical test section for air-water
flow at very high void fraction

The model and the results are presented and discussed
HEFAT2014 14 – 16 July 2014 - Orlando, Florida
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Vertical Test section:
Di = 80 mm De = 90 mm
L≈4m
VFM placed at L/D~ 30 from the inlet
Test section equipped with pressure
transducers
thermocouple and
Quick- Closing Valves
HEFAT2014 14 – 16 July 2014 - Orlando, Florida
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1
Fluids:
◦ Demineralized water





◦ Air
0.99
Jg : 14 - 18 m/s
Jl : 0.0008 – 0.005 m/s
x : 0.78 – 0.96
0.98
α : 0.97 - 1
p : ≈ 1 bar
0.97
T : 20 – 25 °C
Jl =
0.99
0.98
0.97
Jl =
Jl = 0.0017 m/s
Jl =
Jl =
Jl = 0.0033 m/s
Jl =
Jl = 0.0039 m/s
Jl =
Jl = 0.0050 m/s
0.96
14
0.96
14
Jl = 0.0008 m/s
Jl = 0.0028 m/s


1


16
16
18
18
20
Jg [m/s]
20
Jg [m/s]
Very high void fraction corresponding
to annular and
mist-annular flow
HEFAT2014 14 – 16 July 2014 - Orlando, Florida
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Estimation of the fluid flow rate from the
pressure drop across a pipe restriction
This is perhaps the most commonly used flow
measurement technique in industrial
applications (low Δp, economic, no moving
part, etc…)
Characteristic parameters of the present tests
VFM (designed by Polito)
Type
D1
D2
β
Bi-Directional
80
40
0.5
Fluid
mm
mm
-
water
θconv.= θdiv.
21°
Lup-downstream
Ltot
628
340
mm
mm
HEFAT2014 14 – 16 July 2014 - Orlando, Florida
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
 2p
Q  C d A2 
4


1










0.5
CTP  Fa  Y
K
A2
4
1 

  Fa  Y


1.0
0.9
0.8
0.7
0.6
Cd
The air single-phase flow
discharge coefficient is
evaluated, based on the
experimental data
(Y and Fa ≈ 1)
0.5
0.4
C d a  Re b
Calibration parameters:
a=1.5054
b=-0.0510
0.3
0.2
0.1
0.0
0.E+00
2.E+04
4.E+04
6.E+04
8.E+04
1.E+05
Re
HEFAT2014 14 – 16 July 2014 - Orlando, Florida
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ΔpV
Δpirr
The two-phase flow pressure drop
and losses analyzed at different
superficial velocities of the two phases
 theoretical/experimental modeling
45
24
22
40
20
200.0017 m/s
Jl =
Jl =
180.0028 m/s
30
Jl =
160.0033 m/s
25
20
14
Jl =
140.0039 m/s
Jl = 0.0050 m/s
12
15
16
17
Jg [m/s]
18 10
8
14
pTP-irr [mbar]
220.0008 m/s
Jl =
35
pVirr [mbar]
pTP-V [mbar]
24
18
16
Jl = 0.0017 m/s
14
Jl = 0.0028 m/s
12
Jl = 0.0033 m/s
10
Jl = 0.0039 m/s
8
14
19
Jl = 0.0008 m/s
Jl = 0.0050 m/s
15
17
16
Jg [m/s]
18
16
17
18
19
Jg –
[m/s]
HEFAT2014 14
16 July 2014 - Orlando, Florida
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15
9
The measured ΔpV increases of about 10%, if compared to the
single-phase flow, the ΔpV –irr increases from about 20% to 100%
depending on the liquid flow rate
ΔpV –irr high sensitivity to the liquid flow rate
2
1.08
1.9
1.07
1.06
1.7
 pV-TP / pV-g
( p /Δp
p ))
(Δp
TP
g girrirr
TP
1.8
1.6
1.5
1.05
Jl = 0.0033 m/s
J = 0.0033 m/s
1.03
Jl = 0.0039 m/s
J = 0.0039 m/s
Jl = 0.0050 m/s
Jl = 0.0050 m/s
1.01
0.9
0.95
1
l
1.04
1.3
0.85
J = 0.0017 m/s
J = 0.0028 m/s
1.02
0.8
Jl = 0.0008 m/s
Jl = 0.0017 m/s
Jl = 0.0028 m/s
1.4
0.75
Jl = 0.0008 m/s
1
14
15
x
ΔpTP-irr = f(x,Jg,Jl)
17
16
Jg [m/s]
l
l
l
18
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10
VFM Experimental Results: Two-Phase (III)
45
 pV [mbar]
40
35
30
25
20
0.08
0.09
0.1
W t [kg/s]
0.11
0.12
0.13
11
VFM Experimental Results: Two-Phase (IV)
50
25
V: in-throat
Irr: in-out
20
pirr [mbar]
p [mbar]
40
30
10
20
10
0.08
15
0.09
0.1
0.11
W t [kg/s]
0.12
VFM pressure drop and VFM
irreversible pressure loss vs.
total mass flow rate
0.13
5
25
single-phase (air)
two-phase
30
35
 pV [mbar]
40
45
VFM irreversible pressure
loss vs. VFM pressure drop
12
pTP
 
pg
2
g
1.12
 2M
1.1
 2C
2
mod
 7.8    1
 2mod
1.08
2
g
 2exp
 1  x    g
2
 

x

  l
 
2
g
1.06
C
1.04
 
1.02
2
g
1
0
0.002
0.004
0.006
exp
M
0.008
 1  5 
2
0.01



0 .5
 1  C   2
A Two-Phase flow
Multiplier correlation has
been developed, based on
experimental data and
compared with classical
correlations.
The new correlation
predicts ΔpV with an
error lower than 5%
HEFAT2014 14 – 16 July 2014 - Orlando, Florida
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

pTP irr  k1   g J gk2  J l J g  3  k4
k
k1 = 0.2096 - k2 = 2 - k3 = 0.13 - k4= -2.9786
26
+5%
 pirr [mbar]
22
-5%
18
14
10
10
A new correlation has been
developed, based on
experimental data.
The proposed correlation
describes the irreversible
pressure loss change as a
function of the superficial
velocities of the two phases
and of the ratio between the
liquid and the gas superficial
velocities, highlighting the
effect of the dispersed phase.
The new correlation predicts
ΔpVirr with an error lower
than 5%
14
18
pirr [mbar]
22
26
HEFAT2014 14 – 16 July 2014 - Orlando, Florida
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Mass Flow Rate Estimation

The Model consists of a set
of equations able to derive
the mass flow rate of the
phases from the
instruments signals of:
◦ Venturi flow meter
◦ Pressure transducers
◦ Thermocouples
• An iterative approach is
used to estimate the flow
parameters of the two
phases
ΔpV
Δpirr
T, P
l   g
l   g
 1  x    g
2
 

x

  l




xguess
0 .5
pV TP  (7.8    1)  pV  g

pirr  k1   g J gk2  J l J g  3  k 4
k
WTP
HEFAT2014 14 – 16 July 2014 - Orlando, Florida
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Results
0.11
0.035
0.105
0.03
[kg/s]
0.095
-2%
0.09
-20%
0.02
0.015
-30%
0.01
0.085
0.08
0.08
+30%
0.025
+2%
l,est
0.1
+20%
W
W
g,est
[kg/s]
With the proposed approach the flow quality of the mixture can be evaluated
with an accuracy of 5% and the mass flow rate of air and water can be
estimated with a minimum accuracy of 2% and 30% respectively
0.005
0.09
0.1
W g,exp [kg/s]
0.11
0
0
0.01
0.02
W l,exp [kg/s]
0.03
The standard deviations are 1%, 10 % and 2 % for the air flow
rate, the liquid flow rate and the quality respectively
HEFAT2014 14 – 16 July 2014 - Orlando, Florida
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
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In the present research work, the experimental investigation
of a vertical upward annular two-phase flow by a Venturi
Flow Meter (VFM) has been performed.
The dependence of the pressure drops, evaluated between
the VFM inlet and throat sections and between the inlet and
outlet sections, on the characteristic flow parameters (flow
velocities, quality and void fraction) have been analyzed and
discussed.
Correlations describing the relation between velocities and
VFM pressure drops have been proposed for the two
pressure drops components. For both correlations the error
is lower than 5%.
HEFAT2014 14 – 16 July 2014 - Orlando, Florida
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
The analysis of the VFM irreversible pressure losses shows
that important information can be derived concerning the
effect of the liquid dispersed phase

The proposed correlation describes the irreversible
pressure loss change as a function of the flow rate of the
two-phases, highlighting the effect of the dispersed phase.

A model for the estimation of the mass flow rate of the two
phases from the instrument signals has been developed: it
allows the evaluation of the flow quality with an accuracy of
5% and the estimation of the mass flow rate of air and water
with an error of 1% and 10% respectively
HEFAT2014 14 – 16 July 2014 - Orlando, Florida
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HEFAT2014 14 – 16 July 2014 - Orlando, Florida
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