TWO-PHASE ANNULAR FLOW IN A VERTICALLY MOUNTED

VENTURI FLOW METERG. Monni, M. De Salve, B. Panella

Politecnico di Torino, C.so Duca degli Abruzzi 24, 10129 Torinograzia.monni@polito.it

HEFAT201410th International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics14 – 16 July 2014Orlando, Florida

Context Objective Experimental Facility and Test Matrix Venturi Flow Meter (VFM) Experimental Results VFM Modeling Two-Phase Flow Mass Flow Rates Estimation Conclusions

Outline

2HEFAT2014 14 – 16 July 2014 - Orlando, Florida

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

Context

3HEFAT2014 14 – 16 July 2014 - Orlando, Florida

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

Objectives

4HEFAT2014 14 – 16 July 2014 - Orlando, Florida

Test Section

Vertical Test section:

Di = 80 mm De = 90 mm

L ≈ 4 m

VFM placed at L/D~ 30 from the inlet

Test section equipped with pressure transducers

thermocouple and

Quick- Closing Valves

5HEFAT2014 14 – 16 July 2014 - Orlando, Florida

Experimental Matrix

14 16 18 200.96

0.97

0.98

0.99

1

Jg [m/s]

Jl = 0.0008 m/s

Jl = 0.0017 m/s

Jl = 0.0028 m/s

Jl = 0.0033 m/s

Jl = 0.0039 m/s

Jl = 0.0050 m/s

14 16 18 200.96

0.97

0.98

0.99

1

Jg [m/s]

Jl = 0.0008 m/s

Jl = 0.0017 m/s

Jl = 0.0028 m/s

Jl = 0.0033 m/s

Jl = 0.0039 m/s

Jl = 0.0050 m/s

Fluids:

◦ Demineralized water

◦ Air Jg : 14 - 18 m/s Jl : 0.0008 – 0.005 m/s x : 0.78 – 0.96 α : 0.97 - 1 p : ≈ 1 bar T : 20 – 25 °C

Very high void fraction corresponding to annular and mist-annular flow

6HEFAT2014 14 – 16 July 2014 - Orlando, Florida

Venturi Flow Meter (VFM)

Type Bi-Directional Fluid water

D1 80 mm θconv.= θdiv. 21°

D2 40 mm Lup-downstream 628 mm

β 0.5 - Ltot 340 mm

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 p, economic, no moving Δpart, etc…)

Characteristic parameters of the present tests VFM (designed by Polito)

7HEFAT2014 14 – 16 July 2014 - Orlando, Florida

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0.E+00 2.E+04 4.E+04 6.E+04 8.E+04 1.E+05

Cd

Re

YFp

ACQ ad

5.0

421

2

The air single-phase flow discharge coefficient is evaluated, based on the

experimental data (Y and Fa ≈ 1)

VFM Experimental Results: Single-Phase

241A

YFCK aTP

Calibration parameters: a=1.5054 b=-0.0510

bd aC Re

8HEFAT2014 14 – 16 July 2014 - Orlando, Florida

The two-phase flow pressure drop and losses analyzed at different

superficial velocities of the two phases theoretical/experimental modeling

ΔpV Δpirr

14 15 16 17 18 198

10

12

14

16

18

20

22

24

Jg [m/s]

p TP

-irr [

mba

r]

Jl = 0.0008 m/s

Jl = 0.0017 m/s

Jl = 0.0028 m/s

Jl = 0.0033 m/s

Jl = 0.0039 m/s

Jl = 0.0050 m/s

14 15 16 17 18 198

10

12

14

16

18

20

22

24

Jg [m/s]

p V

irr [

mbar]

Jl = 0.0008 m/s

Jl = 0.0017 m/s

Jl = 0.0028 m/s

Jl = 0.0033 m/s

Jl = 0.0039 m/s

Jl = 0.0050 m/s

14 15 16 17 18 1920

25

30

35

40

45

Jg [m/s]

p TP

-V [

mba

r]

Jl = 0.0008 m/s

Jl = 0.0017 m/s

Jl = 0.0028 m/s

Jl = 0.0033 m/s

Jl = 0.0039 m/s

Jl = 0.0050 m/s

VFM Experimental Results: Two-Phase (I)

9HEFAT2014 14 – 16 July 2014 - Orlando, Florida

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 rateΔpV –irr high sensitivity to the liquid flow rate

ΔpTP-irr = f(x,Jg,Jl)10HEFAT2014 14 – 16 July 2014 - Orlando, Florida

0.75 0.8 0.85 0.9 0.95 1

1.3

1.4

1.5

1.6

1.7

1.8

1.9

2

x

(p TP

p g) irr

Jl = 0.0008 m/s

Jl = 0.0017 m/s

Jl = 0.0028 m/s

Jl = 0.0033 m/s

Jl = 0.0039 m/s

Jl = 0.0050 m/s

(Δp T

P /

Δp g

) irr

14 15 16 17 18 191

1.01

1.02

1.03

1.04

1.05

1.06

1.07

1.08

Jg [m/s]

p V

-TP /

p V

-g

Jl = 0.0008 m/s

Jl = 0.0017 m/s

Jl = 0.0028 m/s

Jl = 0.0033 m/s

Jl = 0.0039 m/s

Jl = 0.0050 m/s

VFM Experimental Results: Two-Phase (II)

11

VFM Experimental Results: Two-Phase (III)

0.08 0.09 0.1 0.11 0.12 0.1320

25

30

35

40

45

Wt [kg/s]

p V

[m

bar]

12

VFM Experimental Results: Two-Phase (IV)

0.08 0.09 0.1 0.11 0.12 0.1310

20

30

40

50

Wt [kg/s]

p

[mba

r]

V: in-throat

Irr: in-out

25 30 35 40 455

10

15

20

25

pV

[mbar]

p irr

[m

bar]

single-phase (air)

two-phase

VFM pressure drop and VFM irreversible pressure loss vs. total mass flow rate

VFM irreversible pressure loss vs. VFM pressure drop

0 0.002 0.004 0.006 0.008 0.011

1.02

1.04

1.06

1.08

1.1

1.12

exp

2 g

2M

2C

2mod

2exp

VFM Modeling: ΔpV

18.72mod

5.0

2 1

l

g

x

x

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%

22 1 CC

g

22 51 M

g

g

TPg p

p

2

13HEFAT2014 14 – 16 July 2014 - Orlando, Florida

10 14 18 22 2610

14

18

22

26

pirr

[mbar]

p irr

[m

bar]

+5%

-5%

VFM Modeling: ΔpVirr

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%

4132 kJJJkp k

glkggirrTP

k1 = 0.2096 - k2 = 2 - k3 = 0.13 - k4= -2.9786

14HEFAT2014 14 – 16 July 2014 - Orlando, Florida

5.0

2 1

l

g

x

x

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

WTP

T, PΔpirr

gl

gl

xguess

gVTPV pp )18.7(

4132 kJJJkp k

glkggirr

15HEFAT2014 14 – 16 July 2014 - Orlando, Florida

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 0.01 0.02 0.030

0.005

0.01

0.015

0.02

0.025

0.03

0.035

Wl,exp

[kg/s]

Wl,e

st [

kg/s

]

+30%

-20%

+20%

-30%

0.08 0.09 0.1 0.110.08

0.085

0.09

0.095

0.1

0.105

0.11

Wg,exp

[kg/s]

Wg,

est [

kg/s

]

-2%

+2%

Results

The standard deviations are 1%, 10 % and 2 % for the air flow rate, the liquid flow rate and the quality respectively

16HEFAT2014 14 – 16 July 2014 - Orlando, Florida

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%.

Conclusions

17HEFAT2014 14 – 16 July 2014 - Orlando, Florida

Conclusions 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

18HEFAT2014 14 – 16 July 2014 - Orlando, Florida

Thank you for your kind attention

19HEFAT2014 14 – 16 July 2014 - Orlando, Florida