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Heat transfer during film condensation inside horizontal tubes in stratified phase flow

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Abstract

In this paper, the experimental study of heat transfer during condensation of freons R22 and R407С in a plain smooth tube with 17 mm inner diameter was carried out at saturated condensing temperature 40 °C, while mass velocity ranged between 6 and 57 kg/(m2s) and vapour quality changed from 0.23 to 0.95. The unique measurements of circumferential heat fluxes and heat transfer coefficients were performed with the thick wall method during the stratified flow of the phases. The authors performed numerical simulation of heat transfer from condensing vapour to cooling water through the thick-walled cylindrical wall. The CFD model was validated by conducting the physical experiment, which indicated the results coincidence with an error from 7 to 20%. The obtained results allowed improving prediction of effective heat transfer coefficients for vapour condensation, which takes into account the influence of condensate flow in the bottom part of the tube on the heat transfer. This method generalizes with sufficient accuracy (error ± 30%) the experimental data on condensation of freons R22, R134a, R123, R125, R32, R410a, propane, isobutene, propylene, dimethyl ether, carbon dioxide and methane under the stratified flow conditions. Using this method for designing heat exchangers, which utilize such types of fluids, will increase the efficiency of thermal energy systems.

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Abbreviations

A l :

– tube area that is flooded with condensate, [m2]

A ld :

– dimensionless tube area that is flooded with condensate

A v :

– tube area that is occupied by vapour, [m2]

A vd :

– dimensionless tube area that is occupied by vapour

c p :

– liquid specific heat, [J/(kgK)]

d :

– inner diameter of the tube, [m]

e :

– deviation, [%]

f i :

– interfacial roughness 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 :

– heat transfer coefficient, [W/(m2K)]; enthalpy, [J/kg]

h l :

– liquid height, [m]

h ld :

– dimensionless liquid height

h lv :

– latent heat, [J/kg]

h v :

– heat transfer coefficient assuming total mass flowing as a vapour (\( =0.023{\operatorname{Re}}_v^{0.8}{\Pr}_v^{0.33}{k}_v/d \))

Ja l :

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

k :

– thermal conductivity, [W/(mK)]

K w :

– correction factor

l :

– length of the tube, [m]

ℒ :

– characteristic length, (\( ={\left[{\mu}_l^2/\left({\rho}_l^2g\right)\right]}^{1/3} \))

Nu:

– Nusselt number (=hd/λl)

p :

– pressure, [Pa]

P l :

– wetted perimeter, [m]

Pr:

– Prandtl number

p r :

– reduced pressure (=ps/pcr)

q :

– heat flux, [W/m2]

R v :

– thermal resistance of the vapour phase

Re f :

– film Reynolds number (=ql/(hvlμl))

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)

t :

– temperature, [°C]

u :

– axial velocity, [m/s]

x :

– vapour quality

X tt :

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

δ:

– thickness of the condensate film, [m]

ΔT :

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

ΔT g :

– temperature glide, [K]

Δh m :

– enthalpy of the mixture (=hl(1 − x) + hvx), [K]

ε :

– void fraction

θ :

– liquid level angle subtended from the bottom of the tube to the liquid level, [rad]

θ flood :

– angle of the tube flooding, [rad]

θ strat :

–stratified angle, [rad]

μ:

– dynamic viscosity, [Pa·s]

ν:

– kinematic viscosity, [m2/s]

ρ:

– density, [kg/m3]

σ:

– surface tension, [N/m]

aver :

– average

bot :

– bottom part of the tube

c :

– convective

calc :

– calculated

cr :

– critical

exp :

– experimental

f :

– film

flood :

– flooding

l :

– liquid

lo :

– corresponding to the entire flow as a liquid

m :

– mixture

s :

– saturated

st :

– steel

strat :

– stratified

top :

– top part of the tube

v :

– vapour

w :

– wall

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Authors and Affiliations

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

    Volodymyr Sereda, Volodymyr Rifert, Vadim Gorin, Oleksandr Baraniuk & Peter Barabash

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  1. Volodymyr Sereda
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  2. Volodymyr Rifert
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  4. Oleksandr Baraniuk
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Correspondence to Volodymyr Sereda.

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Sereda, V., Rifert, V., Gorin, V. et al. Heat transfer during film condensation inside horizontal tubes in stratified phase flow. Heat Mass Transfer 57, 251–267 (2021). https://doi.org/10.1007/s00231-020-02946-2

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