Abstract
An algorithm for calculating heat exchange in the course of evaporation and boiling of a film that showers a bundle of finned tubes is described and a comparison of calculated and experimental data is performed. The calculated parameters are in quite satisfactory agreement with the experimental data.
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Funding
This work was performed at the Kutateladze Institute of Thermophysics, Siberian Branch, Russian Academy of Sciences, with financial support from a program of the Fundamental Scientific Research of State Academies of Sciences for 2013–2020 (topic III.18.2.3. AAAA–17117030310025–3).
NOTATION
\(b = \left[ {1 + 10{{{\left( {\frac{{{{{\rho }}_{V}}}}{{{{{\rho }}_{L}} - {{{\rho }}_{V}}}}} \right)}}^{{{2 \mathord{\left/ {\vphantom {2 3}} \right. \kern-0em} 3}}}}} \right]\) | dimensionless complex |
| heat capacity of liquid and wall, J/(kg K) |
\(D\) | diameter of tube or rod, m |
\(\bar {D} = {D \mathord{\left/ {\vphantom {D {{{l}_{\sigma }}}}} \right. \kern-0em} {{{l}_{\sigma }}}}\) | dimensionless tube diameter; |
\(G\) | showering density, kg/(m s) or m3/(m s) |
H | liquid height in the interfinal zone, m |
h | fin height, m |
\(\bar {h}\) | dimensionless height |
\({{K}_{t}} = \frac{{{{{\left( {{\text{r}}{{{\rho }}_{V}}} \right)}}^{2}}{{l}_{\sigma }}}}{{{{C}_{P}}{{T}_{S}}{{{\rho }}_{L}}{\sigma }}}\) | thermal similarity criterion |
L | length, m |
\({{l}_{\sigma }} = \sqrt {{{\sigma } \mathord{\left/ {\vphantom {{\sigma } {g\left( {{{{\rho }}_{L}} - {{{\rho }}_{V}}} \right)}}} \right. \kern-0em} {g\left( {{{{\rho }}_{L}} - {{{\rho }}_{V}}} \right)}}} ;\)\({{l}_{\nu }} = {{\left( {{{{{{\nu }}^{2}}} \mathord{\left/ {\vphantom {{{{{\nu }}^{2}}} g}} \right. \kern-0em} g}} \right)}^{{{1 \mathord{\left/ {\vphantom {1 3}} \right. \kern-0em} 3}}}}\) | capillary and visco-gravitational constant, m |
\(q\) | specific heat flux, W/m2 |
\({{R}_{Z}}\) | roughness height on the cooled wall, µm |
\(\overline {{{R}_{Z}}} = {{{{R}_{Z}}} \mathord{\left/ {\vphantom {{{{R}_{Z}}} {{{l}_{\nu }}}}} \right. \kern-0em} {{{l}_{\nu }}}}\) | dimensionless roughness |
\(r\) | latent heat of vaporization, J/kg |
\({{T}_{S}}\) | saturation temperature, K |
\({{t}_{S}}\) | saturation temperature, °C |
\(y\) | coordinate, m |
\({{{\alpha }}_{0}},\)\({{{\alpha }}_{d}},\)\({\bar {\alpha }}\) | boiling heat transfer coefficients in the initial part of the thermal boundary layer under evaporation; average value according to (6), W/(m2 K) |
\({\delta },\)\({{{\delta }}_{0}}\) | film thickness and residual film thickness, m |
\({\bar {\delta }}\) = \({{\delta } \mathord{\left/ {\vphantom {{\delta } {{{l}_{{v}}}}}} \right. \kern-0em} {{{l}_{{v}}}}}\) | dimensionless film thickness, m |
\({\lambda },\)\({{{\lambda }}_{W}}\) | thermal conductivity of the liquid and cooled wall, W/(m2 K) |
\(\frac{{{\lambda }C{\rho }}}{{{{{\lambda }}_{W}}{{C}_{W}}{{{\rho }}_{W}}}}\) | ratio between the physical properties of the liquid and the physical properties of the cooled wall |
\({\mu }{\text{,}}\)\({{{\mu }}_{{\text{T}}}}\) | dynamic and turbulent viscosity, Pa s |
ν | kinematic viscosity, m2/s |
\({{{\rho }}_{L}},\)\({{{\rho }}_{V}},\)\({{{\rho }}_{W}}\) | density of liquid, vapor and cooled wall, kg/m3 |
\({\text{Ga}}\) = \(\frac{{g{{D}^{3}}}}{{{{{\nu }}^{2}}}}\) | Galileo criterion |
\({\rm N}{\text{u}}_{0}^{ * }\) = \({{{{\alpha }_{0}}{{l}_{\sigma }}} \mathord{\left/ {\vphantom {{{{\alpha }_{0}}{{l}_{\sigma }}} \lambda }} \right. \kern-0em} \lambda },\)\({\rm N}{\text{u*}}\) = \({{\alpha {{l}_{\nu }}} \mathord{\left/ {\vphantom {{\alpha {{l}_{\nu }}} \lambda }} \right. \kern-0em} \lambda }\) | Nusselt numbers constructed according to the capillary and the visco-gravitational constant |
\(\Pr = \frac{\nu }{a}\) | Prandtl number |
\(\operatorname{Re} = {G \mathord{\left/ {\vphantom {G {2\mu }}} \right. \kern-0em} {2\mu }}\) | Reynolds number of a film for a bundle of horizontal tubes |
\({\text{R}}{{{\text{e}}}_{ * }}\) = \(\frac{{q{{l}_{\sigma }}}}{{r\rho \nu }}\) | Reynolds number according to vaporization rate |
SUBSCRIPTS AND SUPERSCRIPTS
0 | boiling |
d | initial part |
L | liquid |
S | saturation |
T | turbulent |
V | vapor |
W | wall |
σ | film |
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Translated by O. Polyakov
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Gogonin, I.I. Heat Exchange under the Evaporation and Boiling of a Film Showering a Bundle of Horizontal Finned Tubes. Theor Found Chem Eng 54, 641–646 (2020). https://doi.org/10.1134/S0040579520030033
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DOI: https://doi.org/10.1134/S0040579520030033