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Determination of the operation range of a vertical two-phase closed thermosyphon

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Abstract

A comprehensive model, proposed for a vertical two-phase closed thermosyphon (TPCT) by the present authors, is further developed by utilizing the criteria for dryout, flooding and boiling limits to investigate the effects of filling ratio on them together, while the available models can just consider one or two limits of them. A new concept named dryout ratio is proposed, which can be used for predicting dryout limit. The empirical correlation and the empirical value, provided by other researchers, are used for predicting flooding and boiling limit, respectively. The experiments with nitrogen as working fluid are performed, and compared with the calculations. The maximum filling ratio is introduced, beyond which the liquid could be carried to condenser and the heat transfer performance can be deteriorated. And then the closed operation range of a vertical TPCT is finally determined, which has not been reported before. The effects of operating pressure and geometries on the range are also analyzed.

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Abbreviations

A :

Area (m2)

C 1–C 7 :

Equation coefficients

C f :

Frictional coefficient

C o :

Distribution parameter

$$ C_{\text{o}} = 1.2 - 0.2\sqrt {{{\rho_{\text{v}} } \mathord{\left/ {\vphantom {{\rho_{\text{v}} } {\rho_{\text{l}} }}} \right. \kern-\nulldelimiterspace} {\rho_{\text{l}} }}} $$
c p :

Specific heat (J kg−1 K−1)

D :

Diameter (m)

Dr :

Dryout ratio

FR :

Filling ratio

g :

Gravitational acceleration (m s−2)

h :

Heat transfer coefficient (W m−2 K−1)

h fg :

Latent heat of vaporization (J kg−1)

J :

Superficial velocity (m s−1)

J * :

Dimensional superficial velocity

\( J_{k}^{*} = J_{k} \sqrt {{{\rho_{k} } \mathord{\left/ {\vphantom {{\rho_{k} } {\left( {\rho_{\text{l}} - \rho_{\text{v}} } \right)gD}}} \right. \kern-\nulldelimiterspace} {\left( {\rho_{\text{l}} - \rho_{\text{v}} } \right)gD}}} \quad (k{\text{ = l, v)}} \)

L :

Length (m)

M :

Mass (kg)

N f :

Dimensional parameter

p :

Pressure (MPa)

Q :

Heat transfer rate (W)

q :

Radial heat flux (W m−2)

Re :

Reynolds number

T :

Temperature (K)

u :

Flow velocity (m s−1)

V vj :

Vapor drift velocity (m s−1)

x :

Axial coordinate

y :

Radial coordinate

δ :

Liquid film thickness (m)

σ:

Surface tension (N m−1)

ρ:

Density (kg m−3)

α:

Void fraction

μ:

Dynamic viscosity (Pa s)

ν:

Kinematic viscosity (m2 s−1)

τ:

Shear stress (N m−2)

λ:

Thermal conductivity (W m−1 K−1)

Γ:

Mass flow rate per unit width (Kg m−1 s−1)

a:

Adiabatic section

c:

Condenser section

cr:

Critical value

e:

Evaporator section

ef:

Liquid film region in evaporator

f:

Friction force

i:

Interface of liquid and vapor

l:

Liquid

m:

Mass transfer

max:

Maximum

NB:

Nucleate boiling

NC:

Natural convection

p:

Liquid pool

s:

Saturation

v:

Vapor

w:

Wall

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Acknowledgments

The project is supported by National Funds for Distinguished Young Scientists of China under Contract No. 50825601 and by the Doctoral Foundation of Ministry of Education, China under contract No. 200803350034.

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Authors and Affiliations

  1. Institute of Refrigeration and Cryogenics, Zhejiang University, Hangzhou, 310027, People’s Republic of China

    B. Jiao, L. M. Qiu, Z. H. Gan & X. B. Zhang

  2. Rongcheng College, Harbin University of Science and Technology, Rongcheng, 264300, People’s Republic of China

    B. Jiao

Authors
  1. B. Jiao
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  2. L. M. Qiu
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  3. Z. H. Gan
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  4. X. B. Zhang
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Correspondence to L. M. Qiu.

Appendix

Appendix

The correlation provided by Gorbis et al. [11] for boiling limit is

$$ q_{\max } = A_{3}^{2} q_{\max ,\infty } \left( {0.4 + 0.012D\sqrt {\frac{{g(\rho_{\text{l}} - \rho_{\text{v}} )}}{\sigma }} } \right)^{2} $$
(22)
$$ q_{\max ,\infty } = 0.14h_{\text{fg}} \sqrt {\rho_{\text{v}} } \root{4} \of {{g\sigma (\rho_{\text{l}} - \rho_{\text{v}} )}} $$
(23)
$$ A_{3} = A_{4} (D/L_{\text{c}} )^{ - 0.44} (D/L_{\text{e}} )^{0.55} FR^{{A_{5} }} $$
(24)

where A 4 = 0.538, A 5 = 0.13 at FR ≤ 35%; A 4 = 3.54, A 5 = −0.37 at FR > 35%.

The correlation proposed by Bezrodnyi et al. [12] for boiling limit is

$$ Q_{\max } = A_{6} \frac{\pi }{4}D^{2} p_{\text{v}}^{0.22} L_{\text{e}}^{{A_{7} }} $$
(25)

Equation 25 can be applied for FR > 4.5%. The coefficients of A 6 and A 7 depend on the following rules: A 6 = 20.8 × 106, A 7 = 0 at L e ≥ 0.6 m and D ≥ 27 mm; A 6 = 16 × 106, A 7 = 0 at L e ≥ 0.6 m and D < 27 mm; A 6 = 24.4 × 106, A 7 = 0.33 at L e < 0.6 m.

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Jiao, B., Qiu, L.M., Gan, Z.H. et al. Determination of the operation range of a vertical two-phase closed thermosyphon. Heat Mass Transfer 48, 1043–1055 (2012). https://doi.org/10.1007/s00231-011-0954-x

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  • DOI: https://doi.org/10.1007/s00231-011-0954-x

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