TWO-PHASE ANNULAR FLOW IN A VERTICALLY MOUNTED VENTURI FLOW METER

TWO-PHASE ANNULAR FLOW IN A VERTICALLY MOUNTED

VENTURI FLOW METER

G. Monni, M. De Salve, B. Panella Politecnico di Torino, C.so Duca degli Abruzzi 24, 10129 Torino grazia.monni@polito.it

HEFAT2014

10^th International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics 14 – 16 July 2014

Orlando, 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



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

HEFAT2014 14 – 16 July 2014 - Orlando, Florida 3

 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

Test Section

Vertical Test section:

D_i = 80 mm D_e = 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

HEFAT2014 14 – 16 July 2014 - Orlando, Florida 5

Experimental Matrix

14 16 18 20

0.96 0.97 0.98 0.99 1

J_g [m/s]



J_l = 0.0008 m/s J_l = 0.0017 m/s J_l = 0.0028 m/s J_l = 0.0033 m/s J_l = 0.0039 m/s J_l = 0.0050 m/s

14 16 18 20

0.96 0.97 0.98 0.99 1

J_g [m/s]



J_l = 0.0008 m/s J_l = 0.0017 m/s J_l = 0.0028 m/s J_l = 0.0033 m/s J_l = 0.0039 m/s J_l = 0.0050 m/s

Fluids:

◦ Demineralized water

◦ Air

 J_g : 14 - 18 m/s

 J_l : 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

Venturi Flow Meter (VFM)

Type Bi-Directional Fluid water

D₁ 80 mm ^θconv.= θ_div. 21°

D₂ 40 mm Lup-downstream 628 mm

β 0.5 - L_tot 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 Δ part, etc…)

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

HEFAT2014 14 – 16 July 2014 - Orlando, Florida 7





A C

Q _d  _a 



























 

5 . 0 2 4

1 2





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

experimental data (Y and F_a ≈ 1)

VFM Experimental Results: Single-Phase

4 2

1 F Y A K C^{TP a}

 



 

Calibration parameters:

a=1.5054 b=-0.0510

b

d a

C  Re

The two-phase flow pressure drop and losses analyzed at different superficial velocities of the two phases

 theoretical/experimental modeling

p

Δ _V Δp_irr

14 15 16 17 18 19

8 10 12 14 16 18 20 22 24

J_g [m/s]

p TP-irr [mbar]

J_l = 0.0008 m/s J_l = 0.0017 m/s Jl = 0.0028 m/s J_l = 0.0033 m/s J_l = 0.0039 m/s J_l = 0.0050 m/s

14 15 16 17 18 19

8 10 12 14 16 18 20 22 24

J_g [m/s]

p Virr [mbar]

J_l = 0.0008 m/s Jl = 0.0017 m/s J_l = 0.0028 m/s J_l = 0.0033 m/s Jl = 0.0039 m/s J_l = 0.0050 m/s

14 15 16 17 18 19

20 25 30 35 40 45

J_g [m/s]

p TP-V [mbar] _J

l = 0.0008 m/s Jl = 0.0017 m/s J_l = 0.0028 m/s J_l = 0.0033 m/s Jl = 0.0039 m/s J_l = 0.0050 m/s

VFM Experimental Results: Two-Phase (I)

HEFAT2014 14 – 16 July 2014 - Orlando, Florida 9

The measured pΔ _V increases of about 10%, if compared to the single-phase flow, the pΔ _{V –irr} increases from about 20% to 100%

depending on the liquid flow rate p

Δ _{V –irr} high sensitivity to the liquid flow rate

p

Δ = f(x,J ,J )

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 TP / Δp g) irr

14 15 16 17 18 19

1 1.01 1.02 1.03 1.04 1.05 1.06 1.07 1.08

J_g [m/s]

p V-TP /p V-g

J_l = 0.0008 m/s Jl = 0.0017 m/s Jl = 0.0028 m/s Jl = 0.0033 m/s J_l = 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 0.13

20 25 30 35 40 45

W_t [kg/s]

p V [mbar]

VFM Experimental Results: Two-Phase (IV)

0.08 0.09 0.1 0.11 0.12 0.13

10 20 30 40 50

W_t [kg/s]

p [mbar]

V: in-throat Irr: in-out

25 30 35 40 45

5 10 15 20 25

p_V [mbar]

p irr [mbar]

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 0.01 1

1.02 1.04 1.06 1.08 1.1 1.12

_exp

2 g

²_M

²_C

²_mod

²_exp

VFM Modeling: ΔpV

1 8

.

2 7

mod 





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 pV with an Δ

error lower than 5%

 

 

^

^

g TP

g p

p



 

2

HEFAT2014 14 – 16 July 2014 - Orlando, Florida 13

10 14 18 22 26

p irr [mbar]

+5%

-5%

VFM Modeling: ΔpV

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 pV

Δ _irr with an error lower than 5%

   

1 J ² J J ³ k

k

p_{TP irr}   _{g g}^k  _{l g} ^k 

 _ 

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

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

Δp_V

W_TP Δp_irr T, P

g l

g l













x_guess

g V TP

V p

p _     _

 (7.8  1)

   

1

2 J J 3 k

J k

p_irr   _{g g}^k  _{l g} ^k 

 

HEFAT2014 14 – 16 July 2014 - Orlando, Florida 15

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 0.03

0 0.005 0.01 0.015 0.02 0.025 0.03 0.035

W_l,exp [kg/s]

W l,est [kg/s]

+30%

-20%

+20%

-30%

0.08 0.09 0.1 0.11

0.08 0.085 0.09 0.095 0.1 0.105 0.11

W_g,exp [kg/s]

W g,est [kg/s]

-2%

+2%

Results

The standard deviations are 1%, 10 % and 2 % for the air flow

 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

HEFAT2014 14 – 16 July 2014 - Orlando, Florida 17

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

Thank you

for your kind attention

HEFAT2014 14 – 16 July 2014 - Orlando, Florida 19