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Abstract
In this paper a method developed earlier by the authors is applied to calculations of pressure drop and heat transfer coefficient for boiling flow and condensation flow with account of nonadiabatic effects for some recent data collected from the literature. The first effect, the modification of interface shear stresses in an annular flow pattern, is considered through incorporation of the so-called “blowing parameter.” The mechanism of modification of shear stresses at the vapor–liquid interface for such case is presented in detail in the paper. In the case of annular flow it contributes to thickening and thinning of the liquid film, which correspond to condensation and boiling, respectively. There is also another influence of the wall heat flux, where it is influencing the bubble nucleation in the case of the bubbly flow pattern. As a result, a modified general form of the two-phase flow multiplier, applicable both to boiling flow and condensation flow, is obtained, in which the nonadiabatic effects are clearly pronounced. The obtained model of the two-phase multiplier, incorporating the nonadiabatic effects, is additionally used in predictions of the heat transfer coefficient.
NOMENCLATURE
| Af | = | cross section area wetted by liquid film (m2) |
| Ac | = | cross section area of the core (m2) |
| B | = | blowing parameter (—) |
| Bo | = | Boiling number (—) |
| C | = | parameter in Lockhart–Martinelli correlation (—) |
| cf | = | friction factor (—) |
| Con | = | constraint number (—) |
| D | = | droplet deposition (kg/ms) |
| d | = | diameter (m) |
| E | = | droplet entrainment (kg/m-s) |
| ETP | = | energy dissipation without the bubbles (W/m3) |
| EPB | = | energy dissipation from the bubble generation (W/m3) |
| fi | = | interface friction coefficient (—) |
| G | = | mass flux (kg/m2-s) |
| g | = | acceleration due to gravity (m/s2) |
| hlv | = | latent heat of vaporization (kJ/kg) |
| l | = | channel length (m) |
| = | total mass flow rate (kg/s) | |
| = | liquid film mass flow rate (kg/s) | |
| = | liquid droplets mass flow rate (kg/s) | |
| = | vapor mass flow rate (kg/s) | |
| M | = | molecular weight (kg/mol) |
| P | = | wetted perimeter (m) |
| pv | = | vapor pressure (Pa) |
| pl | = | liquid pressure (Pa) |
| ΔpLO | = | pressure drop for liquid phase only (Pa) |
| ΔpTP | = | pressure drop in two-phase flow (Pa) |
| Δp0 | = | total pressure drop in single phase flow (Pa) |
| pkr | = | critical pressure (Pa) |
| Re | = | Reynolds number (—) |
| s | = | slip ratio (—) |
| ug | = | liquid-phase velocity (m/s) |
| uv | = | vapor-phase velocity (m/s) |
| u∗ | = | friction velocity m/s |
| wTP | = | two-phase velocity m/s |
| wLO | = | liquid film only velocity m/s |
| x | = | quality (-) |
Greek Symbols
| δ | = | liquid film thickness (m) |
| σ | = | surface tension (N/m) |
| ρ | = | density (kg/m3) |
| ξ | = | friction factor (—) |
| Φ2 | = | two-phase flow multiplier |
| Γlv | = | phase change rate (kg/m-s) |
| τ* | = | dimensionless shear stress (—) |
| ϑ0 | = | transverse velocity (m/s) |
| τw0 | = | wall shear stress in case where nonadiabatic effects are not considered |
| qw | = | wall heat flux (kJ/kg) |
| α | = | heat transfer coefficient (W/m2-K) |
| λ | = | thermal conductivity (W/m-K) |
Superscripts
| + | = | nondimensional |
| cb | = | convective boiling |
| f | = | forced flow |
| G | = | gas |
| h | = | hydraulic |
| kr | = | critical |
| L | = | liquid |
| LO | = | liquid only |
| PB | = | pool boiling |
| sat | = | saturation |
| TP | = | two-phase flow |
| TPB | = | two-phase boiling |
| TPK | = | two-phase condensation |
| v | = | saturated vapor |
Additional information
Notes on contributors
Dariusz Mikielewicz
Dariusz Mikielewicz has been a professor at the Gdansk University of Technology, Gdansk, Poland, since 1996. He received his M.Sc. degree from the Gdansk University of Technology (1990), Ph.D. degree from the University of Manchester (1994), and in 2002 he presented his habilitational dissertation at the Gdansk University of Technology. In the years 1994–1996 he worked as an engineer at the Berkeley Nuclear Laboratories, Nuclear Electric plc, Gloucestershire, UK. His research interest is in the field of modeling of two-phase flows during both boiling and condensation, efficient and precise jet and microjet cooling of hot surfaces, and recently heat recovery from low-temperature sources and renewable energy. He is currently working on enhanced heat transfer and condensation in heat exchangers, capillary effects in porous media, and microjet technology.
Rafał Andrzejczyk
Rafał Andrzejczyk is a lecturer at Gdansk University of Technology (GUT), Faculty of Mechanical Engineering, Gdansk, Poland. He received his Ph.D. from the GUT, Gdansk, Poland. He is currently working on enhanced heat transfer in heat exchangers for both the numerical and experimental aspects, and pool boiling and condensation on enhanced heat transfer surfaces.
Blanka Jakubowska
Blanka Jakubowska is a Ph.D. student at the Faculty of Mechanical Engineering of Gdansk University of Technology, under the supervision of Prof. Dariusz Mikielewicz. She received her M.Sc. degree in heat-flow technologies from the University of Technology in Gdansk, Poland. She is currently working on heat transfer during flow boiling and flow condensation in conventional channels and minichannels with the objective of investigating the effect of pressure on the heat transfer characteristics.
Jarosław Mikielewicz
Jarosław Mikielewicz has been the director of the Institute of Fluid-Flow Machinery of the Polish Academy of Sciences, Gdansk, Poland in the years 1998–2014. He completed his higher education studies and all the academic qualifications at the Faculty of Mechanical Engineering of the Gdansk University of Technology. He has been the head of the Institute of Fluid Flow Machinery Polish Academy of Sciences during 1998–2014, and is now retired. He is a full member of Polish Academy of Sciences and a member in a number of professional societies. He was awarded a distinction of Doctor Honoris Causa by Technical Universities of Cracow, Koszalin, and Bialystok, Poland. He has made numerous scientific research visits to U.S. and former Soviet Union institutions, His current main areas of research are single- and two-phase flow and heat transfer in conventional channels and microchannels, cooling systems for high heat flux sources, energy recovery systems, and renewable energy.