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Research Papers: Multiphase Flows

Study of a Cavitating Venturi Tube by Lumped Parameters

[+] Author and Article Information
Samuel Cruz

Facultad de Ingeniería,
Universidad Nacional Autónoma de México,
Circuito Escolar s/n,
Ciudad Universitaria,
Delegación Coyoacán,
CDMX 04510, México
e-mail: samisam98@hotmail.com

Francisco A. Godínez

Instituto de Ingeniería,
Universidad Nacional Autónoma de México,
Circuito Escolar s/n,
Ciudad Universitaria,
Delegación Coyoacán,
CDMX 04510, México;
Polo Universitario de Tecnología
Avanzada Universidad Nacional Autónoma
de México Vía de la Innovación,
No. 410, Autopista Monterrey-Aeropuerto
km. 10 PIIT,
Apodaca C.P. 66629, Nuevo León, México
e-mail: fgodinezr@gmail.com

Margarita Navarrete

Instituto de Ingeniería,
Universidad Nacional Autónoma de México,
Circuito Escolar s/n, Ciudad Universitaria,
Delegación Coyoacán CDMX 04510, México
e-mail: mnm@pumas.iingen.unam.mx

1Corresponding author.

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received April 5, 2018; final manuscript received December 19, 2018; published online January 30, 2019. Assoc. Editor: Bart van Esch.

J. Fluids Eng 141(7), 071304 (Jan 30, 2019) (9 pages) Paper No: FE-18-1244; doi: 10.1115/1.4042375 History: Received April 05, 2018; Revised December 19, 2018

The hydrodynamic cavitation in a Venturi tube is studied both theoretically and experimentally. A lumped parameter model was developed to describe the accumulation and dissipation of energy in the biphasic flow as a function of the bubble population characteristics (mean volume, standard deviation, and void fraction). Resistance, capacitance, inductance, and frequency lumped-parameters were identified applying the fluid conservation equations (mass and momentum) along with electrical/hydraulic analogies. Experiments with 1,2-propanediol were carried out in a hydraulic circuit composed of valves, a pump, and a Venturi nozzle. The acoustic noise generated (at different cavitation regimes) by the passage of the fluid through the tube was acquired with a piezoelectric sensor. After processing the experimental signals, the system frequency at each operation condition was determined. Plausible estimations of the void fraction were obtained at different experimental frequencies by evaluating a theoretical expression of the frequency lumped-parameter. This semi-empirical technique might be a low-cost alternative when the void fraction of a flow needs to be determined and tomography devices are not available.

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Figures

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Fig. 1

Schematic representation of the Venturi-tube

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Fig. 2

Schematic representation of the experimental setup

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Fig. 3

Resistance parameter behavior (Eqs. (9) and (16), f=0.91,ϑ=0.25), for a homogeneous (solid line, β=0) and a heterogeneous (dashed line, β=1.5) bubble population in the inlet and outlet of the constriction zone as a function of their pressure drop, as well as the void fraction with VB between 4.2×10−24m3 and 4.2×10−6m3 and the Reynolds number. The solid symbols are the maximum resistance values and show the respective value of VB. It should be noted that bubble populations with homogeneous volumes or with small mean volumes VB≈10 nm3 show major opposition to flowing by the geometric changes in the Venturi profile.

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Fig. 4

Capacitance parameter behavior (Eq. (23)) of a homogeneous (solid line, β=0) and a heterogeneous (dashed line, β=1.5) flow regimen in the inlet and outlet of the constriction zone as a function of the pressure drop, and void fraction with VB between 4.2×10−24m3 and 4.2×10−6m3. The solid symbols are the maximum capacitance values and show the respective value of VB. It is observed that bubble populations with homogeneous volumes or with major mean volumes 20nm3>VB<35nm3 tend to store more energy than bubble populations with small mean volumes.

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Fig. 5

Frequency behavior of a homogeneous (solid line, β = 0) and a heterogeneous (dashed line, β = 1.5) flow regimen as a function of the pressure drop, mean volume of the population, and void fraction. Where the solid symbols are the minimum values of the function.

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Fig. 6

Frequency spectra of the Venturi tube with and without 1,2 propanediol. The separation between the main frequencies indicates the range (0–35 ks-1) where ω is most likely to be found.

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Fig. 7

Frequencies spectrum analysis of some signals acquired on the constriction zone at different cavitation numbers σ of the constriction zone. The shift of ω (solid symbols) to lower values is due to the increment of α.

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Fig. 8

Comparison between the theoretical (lines) and experimental data (points) of ω as a function of ΔP for α from 0.001 to 0.15. Each point shows its respective cavitation number σ. The top picture shows the case when α≈0. The bottom picture shows the case when the constrict zone is filled with of thesingle gas phase (α≈0.15). Data are averages of three experiments.

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Fig. 9

Frequency and pressure drop changes as a function of the cavitation number σ. Data are averages of three experiments.

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Fig. 10

Frequency changes as a function of the Venturi length for different values of α

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Fig. 11

A cycle of the dynamic behavior of the biphasic flow in the divergent zone with σ=0.36. A video was taken at 49,008 fps, and the shutter speed was 5.16 μs.

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