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Semi-mechanistic model for the interfacial velocity of gravity-driven laminar wavy film flow and its validation using infrared particle tracing velocimetry

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Abstract

Interfacial velocity is an important parameter in the modeling of momentum transfer for prediction of heat- and mass-transfer during film-wise condensation. In this study, the interfacial velocity is modeled using an empirical power-law velocity profile with the assumption that the interfacial shear stress is negligible compared with the wall shear stress. A non-intrusive infrared particle tracking velocimetry (IR-PTV) measurement technique is used to validate a newly proposed semi-mechanistic model for the interfacial velocity of a gravity-driven laminar wavy film flow. The proposed model predicts measured interfacial velocities reasonably well and could serve as a closure relation in estimating the film-wise condensation heat transfer coefficient.

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Abbreviations

d c :

Particles diameter (m)

I camera :

Thermal radiation received by the camera (Wm-2sr-1)

I l :

Thermal radiation emitted by the liquid (Wm-2sr-1)

I bg :

Thermal radiation emitted by the background (Wm-2sr-1)

k 1, k 2 :

Constants in uncertainty relation

Ka :

Kapitza number

\( \dot{m} \) :

Mass flow rate (kg/s)

R :

Reflectivity or Radius (m)

Re:

Film flow Reynolds number

Rel, inc :

Reynolds number of film at the inception of waviness

RE :

Relative error

St :

Stokes number

u :

Fluid velocity (m/s)

u δ :

Film velocity at the interface (m/s)

u K :

Film velocity at the crest of the interfacial wave (m/s)

\( \overline{V} \) :

Average velocity (m/s)

y :

Cross stream distance (m)

δ :

Film thickness (m)

ε :

Emissivity of water, or surface roughness

Γ :

Film flow rate per unit width (kg/m-s)

μ l :

Dynamic viscosity of water (N.s/m2)

v l :

Kinematic viscosity of water (m2/s)

θ :

Inclination angle to horizontal

ρ c :

Density of particles (kg/m3)

ρ l :

Water density (kg/m3)

σ :

Surface tension (N/m)

τ :

Relaxation time (s)

τ w :

Wall shear stress (kg/m-s2)

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Acknowledgements

This work was supported by the Korea Institute of Energy Technology Evaluation and Planning (KETEP) and the Ministry of Trade, Industry & Energy (MOTIE) of the Republic of Korea (No. 20152020105710). This work was also supported by the National Research Foundation of Korea (NRF) grant funded by the Korean government (MSIP) (No. 2018M2B2A9065841).

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Authors and Affiliations

  1. Department of nuclear engineering, Kyung Hee University, 1732, Deogyeong-daero, Giheung-gu, Yongin-si, Gyeonggi-do, South Korea

    Muritala Alade Amidu & Hyungdae Kim

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  1. Muritala Alade Amidu
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  2. Hyungdae Kim
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Correspondence to Hyungdae Kim.

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Highlights

• Semi-mechanistic model for the interfacial velocity of falling laminar wavy film.

• Non-intrusive IR-PTV technique for the measurement of interfacial velocity.

• Validation of model against experimental data.

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Amidu, M.A., Kim, H. Semi-mechanistic model for the interfacial velocity of gravity-driven laminar wavy film flow and its validation using infrared particle tracing velocimetry. Heat Mass Transfer 55, 1535–1544 (2019). https://doi.org/10.1007/s00231-018-2523-z

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  • DOI: https://doi.org/10.1007/s00231-018-2523-z

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