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An experimental study of refrigerant expansion inside coiled adiabatic capillary tubes and development of a general correlation

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Abstract

This article provides experimental results on the expansion of a refrigerant inside adiabatic helically coiled capillary tubes. The experimental data were obtained in capillary tubes of 0.787, 0.914 and 1.041 mm internal diameter, 2 and 3 m length, 83 mm coil diameter, mass flow rates between 2.7 and 14.3 kg/h, R134a as refrigerant fluid, and inlet subcooling between 6 and 47 °C. The uncertainties of the results for mass flow rate were below 4.5%. Ten prediction methods from the literature were compared with the experimental data, and the best prediction achieved 11.9% mean absolute error. A novel, general and simple dimensionless correlation for coiled and straight adiabatic capillary tubes based on a regression with an extended database containing eleven different refrigerant fluids is proposed. The correlation predicted the extended database with 5.7% mean absolute error and can be applied for subcooled, two-phase or supercritical inlet conditions.

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Abbreviations

c p :

Specific heat (J/kg K)

\(c_{{{\text{p}},{\text{l}},P_{{{\text{in}}}} }}\) :

Saturated liquid specific heat based on the inlet pressure (J/kg K)

\(c_{{{\text{p}},{\text{l}},T_{{{\text{in}}}} }}\) :

Saturated liquid specific heat based on the inlet temperature (J/kg K)

D c :

Internal diameter of capillary tube (m)

D c ,e :

External diameter of capillary tube (m)

D coil :

Coil diameter (m)

F coil :

Coiling factor (–)

h lv :

Enthalpy of vaporization (J/kg)

\(h_{{{\text{lv}},P_{{{\text{in}}}} }}\) :

Enthalpy of vaporization based on inlet pressure (J/kg)

\(h_{{{\text{lv}},T_{{{\text{in}}}} }}\) :

Enthalpy of vaporization based on inlet temperature (J/kg)

L :

Tube length (m)

L c :

Capillary tube length (m)

L coil :

Coil length (m)

\(\dot{m}_{{\text{c}}}\) :

Capillary mass flow rate (kg/s)

\(\dot{m}_{\exp }\) :

Experimental capillary mass flow rate (kg/s)

\(\dot{m}_{{{\text{pred}}}}\) :

Predicted capillary mass flow rate (kg/s)

MRAE:

Mean relative absolute error (%)

n :

Number of coil turns

P :

Pressure (Pa)

p coil :

Coil pitch (m)

P cond :

Condensation pressure (Pa)

P crit :

Critical pressure (Pa)

P evap :

Evaporation pressure (Pa)

P in :

Pressure on inlet of capillary tube (Pa)

P sat :

Saturation pressure (Pa)

\(P_{{{\text{sat}},T_{{{\text{in}}}} }}\) :

Saturation pressure calculated at inlet temperature (Pa)

q :

Refrigeration capacity (W)

T :

Temperature (°C)

T crit :

Critical temperature (K)

T in :

Temperature on inlet of capillary tube (°C)

T sat :

Saturation temperature (°C)

v :

Specific volume (m3/kg)

\(v_{{{\text{l}},P_{{{\text{in}}}} }}\) :

Liquid specific volume under saturated condition based on inlet pressure (m3/kg)

\(v_{{{\text{l}},T_{{{\text{in}}}} }}\) :

Liquid specific volume under saturated condition based on inlet temperature (m3/kg)

x :

Vapor quality (-)

x in :

Inlet vapor quality (-)

λ % :

Percentage of data predicted within a percentage level of MRAE (%)

μ in :

Liquid viscosity at inlet state of capillary tube (Pa.s)

μ l :

Liquid viscosity under saturated condition (Pa.s)

\(\mu_{{{\text{l}},P_{{{\text{in}}}} }}\) :

Vapor viscosity under saturated condition based on inlet pressure (Pa s)

\(\mu_{{{\text{l}},T_{{{\text{in}}}} }}\) :

Liquid viscosity under saturated condition based on inlet temperature (Pa s)

μ v :

Vapor viscosity under saturated condition (Pa s)

π :

Dimensionless group (–)

π a :

Dimensionless group independently indexed by author (–)

ρ in :

Liquid density at inlet state of a capillary tube (kg/m3)

ρ l :

Liquid density under saturated condition (kg/m3)

\(\rho_{{{\text{l}},P_{{{\text{in}}}} }}\) :

Liquid density under saturated condition based on inlet pressure (kg/m3)

\(\rho_{{{\text{l}},T_{{{\text{in}}}} }}\) :

Liquid density under saturated condition based on inlet temperature (kg/m3)

ρ v :

Vapor density (kg/m3)

ΔT sub :

Degree of subcooling, ΔTsub = Tsat − Tin (°C)

σ :

Surface tension (N/m)

\(\sigma_{{P_{{{\text{in}}}} }}\) :

Surface tension based on inlet pressure (N/m)

\(\sigma_{{T_{{{\text{in}}}} }}\) :

Surface tension based on inlet temperature (N/m)

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Acknowledgements

The authors acknowledge CAPES (Coordination for the Improvement of Higher Education Personnel, Finance Code 001), CNPq (National Council for Scientific and Technological Development, process 304972/2017-7) and FAPESP (São Paulo Research Foundation, 2011/01372-3), for funding researches that have contributed to this study.

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Authors and Affiliations

  1. Heat Transfer Research Group, Department of Mechanical Engineering, São Carlos School of Engineering, University of São Paulo, Av. Trabalhador São Carlense, 400, São Carlos, SP, Brazil

    Gérson Koiti Kurosawa Shimizu, Alex Roger Almeida Colmanetti, Álvaro Roberto Gardenghi, Luben Cabezas-Gómez & Cristiano Bigonha Tibiriçá

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  1. Gérson Koiti Kurosawa Shimizu
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  2. Alex Roger Almeida Colmanetti
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  3. Álvaro Roberto Gardenghi
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  4. Luben Cabezas-Gómez
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  5. Cristiano Bigonha Tibiriçá
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Correspondence to Cristiano Bigonha Tibiriçá.

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Shimizu, G.K.K., Colmanetti, A.R.A., Gardenghi, Á.R. et al. An experimental study of refrigerant expansion inside coiled adiabatic capillary tubes and development of a general correlation. J Braz. Soc. Mech. Sci. Eng. 43, 71 (2021). https://doi.org/10.1007/s40430-020-02762-z

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