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Heat transfer during film condensation inside plain tubes. Review of experimental research

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Abstract

This paper provides a comprehensive review of the published experimental researches on condensation heat transfer inside plain tubes. The existing methods of the research on heat transfer and hydrodynamics have been analyzed and their disadvantages are substantiated (shown). There are considered more than 40 empirical and semi-empirical methods and correlations for prediction of heat transfer coefficients in various heat exchangers, particularly in the evaporative systems of thermal desalinating plants, air conditioning systems, safety systems of reactors, heaters of power plants and condensers of cooling equipment. The given correlations are compared with the experimental data of various authors obtained in the case of condensation of diverse substances in different flow regimes. The correlations are evaluated with the experimental data of different authors for different fluids and flow conditions. According to the comparison performed, the correlations suggested by Thome and others (2003), Cavallini and others (2006), Shah (2015) and Rifert and others (2018) are recommended to be used for the most accurate prediction of heat transfer coefficients in case of condensation of various refrigerants, which in recent years are becoming widespread in power economy (fluid FC-72, methane, carbone dioxide, organic fluids R245fa, Novec®649, HFE-7000, steam, etc.).

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Abbreviations

Bo i :

Boiling number (\( =\frac{Q}{W\left({h}_{v, in}-{h}_{v, out}\right)} \)).

C f :

friction coefficient.

c p :

liquid specific heat, [J/(kgK)].

d :

inner diameter of the tube, [m].

f :

friction factor.

Fr l :

liquid Froude number (\( =\frac{{\left[G\left(1-x\right)\right]}^2}{\rho_l^2 gd} \)).

G :

mass velocity, [kg/(m2s)].

g :

gravitational acceleration, [m/s2].

Ga :

Galileo number (\( ={\rho}_l\left({\rho}_l-{\rho}_v\right){gd}^3/{\mu}_l^2 \)).

h v,in :

specific enthalpy of saturated vapour refrigerant at inlet of the tube, [J/kg].

h v,out :

specific enthalpy of saturated vapour refrigerant at outlet of the tube, [J/kg].

Ja l :

liquid Jakob number (\( ={\rho}_l\left({\rho}_l-{\rho}_v\right){gd}^3/{\mu}_l^2 \)).

J g :

dimensionless vapour velocity. (=xG/[gdρv(ρl − ρv)]0.5)

l :

length of the tube, [m].

Nu :

Nusselt number (=αd/λl).

Nu f :

film Nusselt number, (\( =\alpha /{\lambda}_l{\left({v}_l^2/g\right)}^{1/3} \)).

p :

pressure, Pa.

p cr :

critical pressure, Pa.

Pr:

Prandtl number.

p r :

reduced pressure (=ps/pcr).

Q :

total rate of heat rejected by refrigerant, [W].

q :

heat flux, [W∙m−2].

q z :

average along the length of the tube heat flux, [W∙m−2].

r :

heat of vaporization, [J∙kg−1].

Re f :

film Reynolds number (=ql/(rμl)).

Re l :

liquid Reynolds number (=G(1 − x)d/μl).

Re lo :

Reynolds number assuming total mass flowing as a vapour (=Gd/μl).

Re v :

vapour Reynolds number (=Gxd/μv).

Re vo :

Reynolds number assuming total mass flowing as a vapour (=Gd/μv).

Su v :

vapour Suratman nubmer (\( ={\rho}_v\sigma d/{\mu}_v^2 \)).

t :

temperature, [°C].

u :

axial velocity, [m/s].

W :

mass flow rate, [kg/s].

We :

Weber number, (=G2d/(ρσ)).

x :

vapour quality.

X tt :

Martinelli parameter (=(μl/μv)0.1(ρv/ρl)0.5[(1 − x)/x]0.9)

y :

radial distance from the wall, [m].

z :

axial coordinate, [m].

α :

heat transfer coefficient, [W/(m2K)].

α aver :

average along the length of the tube heat transfer coefficient, [W/(m2K)].

δ :

thickness of the condensate film, [m].

ΔP/Δz :

pressure drop, [Pa/m].

(ΔP/Δz)a :

acceleration pressure drop, [Pa/m].

(ΔP/Δz)f :

frictional pressure drop, [Pa/m].

ΔT :

temperature difference (=ts-tw), [K].

Δx :

changes in vapour quality.

ε :

void fraction.

θ :

liquid level angle subtended from the top of the tube to the liquid level, [rad].

λ :

thermal conductivity, [W/(mK)].

μ :

dynamic viscosity, [Pa·s].

ν :

kinematic viscosity, [m2 s−1].

ρ :

density, [kg/m3].

σ:

surface tension, [N/m].

τw :

shear stress, [Pa].

τg :

gravity force, [Pa].

φ:

angular coordinate, [°].

ϕ 2 :

two-phase multiplier.

Φ2 :

parameter that takes into account influence of two-phase flow on shear stress.

Φq :

parameter that takes into account surface suction at the interphase.

aver :

average.

b :

bottom.

c :

convective.

eq :

equivalent.

f :

film.

in :

inlet of the tube.

l :

liquid.

lo :

corresponding to the entire flow as a liquid.

m :

momentum.

out :

outlet of the tube.

s :

saturated.

t :

top.

tp :

two-phase.

v :

vapour.

vo :

corresponding to the entire flow as a vapour.

w :

wall.

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  1. Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”, National Technical University, Politehnichna 6, Kyiv, 03056, Ukraine

    Volodymyr Rifert, Volodymyr Sereda, Vadim Gorin, Peter Barabash & Andrii Solomakha

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  1. Volodymyr Rifert
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  2. Volodymyr Sereda
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Rifert, V., Sereda, V., Gorin, V. et al. Heat transfer during film condensation inside plain tubes. Review of experimental research. Heat Mass Transfer 56, 691–713 (2020). https://doi.org/10.1007/s00231-019-02744-5

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