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Performance of a combined three-hole conductivity probe for void fraction and velocity measurement in air–water flows

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Abstract

The development of a three-hole pressure probe with back-flushing combined with a conductivity probe, used for measuring simultaneously the magnitude and direction of the velocity vector in complex air–water flows, is described in this paper. The air–water flows envisaged in the current work are typically those occurring around the rotors of impulse hydraulic turbines (like the Pelton and Cross-Flow turbines), where the flow direction is not known prior to the data acquisition. The calibration of both the conductivity and three-hole pressure components of the combined probe in a rig built for the purpose, where the probe was placed in a position similar to that adopted for the flow measurements, will be reported. After concluding the calibration procedure, the probe was utilized in the outside region of a Cross-Flow turbine rotor. The experimental results obtained in the present study illustrate the satisfactory performance of the combined probe, and are encouraging toward its use for characterizing the velocity field of other complex air–water flows.

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Abbreviations

A ex :

Nozzle exit area (m2)

C air :

Air concentration or void fraction

C pr :

Air concentration indicated by conductivity probe

H :

Head applied to turbine (m)

K i :

Coefficient relative to the ith pressure taping

\( \dot{m}_{\text{air}} \) :

Air mass flow rate (kg/s)

p air :

Air gauge pressure (Pa)

p dyn :

Jet dynamic pressure (Pa)

p i :

Pressure at the ith pressure taping (Pa)

p mix :

Mixture gauge pressure (Pa)

p n :

Pressure at standard conditions (p n = 101,325 Pa)

p s :

Static pressure (Pa)

Q air :

Air volume flow rate (m3/s)

Q n :

Air volume flow rate at standard conditions (T n = 273.15 K and p n = 101325 Pa) (m3/s)

Q tot :

Total volume flow rate of mixture (m3/s)

Q w :

Water volume flow rate (m3/s)

r ex :

Nozzle exit radius (m)

R :

Ideal gas constant [R = 287 J/(kg K)]

t air :

Air temperature (°C)

t mix :

Mixture temperature (°C)

T n :

Temperature at standard conditions (T n = 273.15 K)

U :

Rotor tip velocity (m/s)

U/V0:

Blade-jet velocity ratio

V :

Local velocity (m/s)

V j :

Velocity of calibrating jet (m/s)

V 0 :

Jet velocity given as: \( V_{0} = \sqrt {2gH} \left( {{{\text{m}} \mathord{\left/ {\vphantom {{\text{m}} {\text{s}}}} \right. \kern-\nulldelimiterspace} {\text{s}}}} \right) \)

V/V0:

Non-dimensional absolute velocity (m/s)

α :

Absolute velocity angle (degrees)

β :

Relative velocity angle (degrees)

γ :

Probe rotation angle (degrees)

θ :

Rotor peripheral angle (degrees)

ρ air :

Air density (kg/m3)

ρ air,mix :

Air density in the air–water jet (kg/m3)

ρ mix :

Mixture density (kg/m3)

ρ w :

Water density (kg/m3)

air:

Relative to the air part of the mixture

dyn:

Dynamic

ex:

Exit

i :

General pressure taping

j:

Jet

mix:

Relative to the air–water mixture

n:

Standard

pr:

Probe

s:

Static

tot:

Total

w:

Water

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Acknowledgments

The authors gratefully acknowledge the financial support granted by Fundação para a Ciência e Tecnologia (project PTDC/ECM/73867/2006), as well as the assistance given by the Hydraulic Investigations and Laboratory Services Group of the U.S. Bureau of Reclamation, the IDMEC, the IST-UTL and the EST Setúbal-IPS.

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Authors and Affiliations

  1. Department of Mechanical Engineering, IDMEC, Instituto Superior Técnico, Technical University of Lisbon, Lisbon, Portugal

    João Eduardo Borges

  2. Department of Mechanical Engineering, EST Setúbal, Polytechnic Institute of Setúbal, Setúbal, Portugal

    Nuno H. C. Pereira

  3. Department of Civil Engineering and Architecture, Instituto Superior Técnico, Technical University of Lisbon, Lisbon, Portugal

    Jorge Matos

  4. U.S. Bureau of Reclamation, Denver, CO, 80225, USA

    Kathleen H. Frizell

Authors
  1. João Eduardo Borges
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  2. Nuno H. C. Pereira
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  3. Jorge Matos
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  4. Kathleen H. Frizell
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Correspondence to João Eduardo Borges.

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Borges, J.E., Pereira, N.H.C., Matos, J. et al. Performance of a combined three-hole conductivity probe for void fraction and velocity measurement in air–water flows. Exp Fluids 48, 17–31 (2010). https://doi.org/10.1007/s00348-009-0699-1

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