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Simplified numerical study of evaporation processes inside vertical tubes

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Abstract

The paper presents a simplified numerical model of evaporation processes inside vertical tubes. In this model only the temperature fields in the fluid domain (the liquid or two-phase mixture) and solid domain (a tube wall) are determined. Therefore its performance and efficiency is high. The analytical formulas, which allow calculating the pressure drop and the distribution of heat transfer coefficient along the tube length, are used in this model. The energy equation for the fluid domain is solved with the Control Volume Method and for the solid domain with the Finite Element Method in order to determine the temperature field for the fluid and solid domains.

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Abbreviations

A :

area, m2

d i :

inner diameter of tube, m

f D :

Darcy-Waisbach friction coefficient, —

G :

mass velocity, kg/(m2 s)

g :

gravitational acceleration, m/s2

h :

heat transfer coefficient, W/(m2·K)

i :

specific enthalpy, J/kg

k :

thermal conductivity, W/(m K)

L :

tube length, m

N, M :

number of nodes in vertical and horizontal direction (solid domain), —

m :

mass flow rate, kg/s

p :

pressure, bar

p crit :

critical pressure, bar

p in :

inlet pressure, bar

p r :

reduced pressure p/p crit

Δp :

pressure drop, bar

q i :

heat flux density at the inner surface of tube wall, W/m2

q o :

heat flux density at the outer surface of tube wall, W/m2

q onb :

critical heat flux for the onset of nucleate boiling, W/m2

q 0 :

reference heat flux density, W/m2

r, z :

radial, and axial coordinates (cylindrical coordinate frame), m

r b :

critical nucleation radius, m

r i :

inner radius of tube, m

r o :

outer radius of tube, m

R p :

height of wall roughness, μm

T :

temperature, °C

T in :

inlet temperature, °C

T sat :

saturation temperature, °C

T ∞ :

bulk temperature, °C

X :

dryness fraction, —

X cr :

critical dryness fraction — X cr = 0.5, —

ɛ :

void fraction, —

µ:

dynamic viscosity, Pa·s

Φ2 Fr :

the multiplier of single phase (liquid) pressure drop used in two-phase Friedel model, —

ρ :

density, kg/m3

ρ H :

homogenous density of the two-phase mixture, kg/m3

σ :

surface tension, N/m

g :

vapor

l :

liquid

sp :

single-phase

tp :

two-phase

FrH :

Froude number (homogenous density model), —

Pr:

Prandtl number, —

Re:

Reynolds number —

WeH :

Weber number (homogenous density model),-

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Authors and Affiliations

  1. Faculty of Mechanical Engineering, Institute of Thermal Power Engineering, Cracow University of Technology, Al. Jana Pawła II 37, 31-864, Cracow, Poland

    Paweł Ocłoń, Marzena Nowak & Stanisław Łopata

Authors
  1. Paweł Ocłoń
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  2. Marzena Nowak
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  3. Stanisław Łopata
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Ocłoń, P., Nowak, M. & Łopata, S. Simplified numerical study of evaporation processes inside vertical tubes. J. Therm. Sci. 23, 177–186 (2014). https://doi.org/10.1007/s11630-014-0693-7

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  • DOI: https://doi.org/10.1007/s11630-014-0693-7

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