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Study of divergence angle influence for sonic nozzle in non-equilibrium condensation

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Abstract

The condensation happens generally in a nozzle during expansion of compressed steam from convergent to the divergent part of the nozzle. The divergence angle is the angle measured from the throat of the nozzle to the outlet. In this paper, the outlet is kept constant and the throat diameter is varied. In turn, the divergence angle of the sonic nozzle is altered. The effect of divergence angle on condensation phenomena is investigated with wet steam in a sonic nozzle. For analyzing the wet steam properties, the non-equilibrium condensation model is used. This model is the classical nucleation theory coupled with the droplet growth rate equation. The base nozzle is designed with the throat diameter of 4.5 mm and other dimensions are calculated according to ASME nozzle formulas. Furthermore, the chosen divergence angles are 3°, 4.2°, and 6° for which the throat diameters are 4.5 mm, 3 mm, and 1.5 mm, respectively. As the divergence angle is gradually increased, the position of maximum Mach number of the flow moves upstream, the static temperature of the flow near the throat reaches the lower value, and the droplet nucleation rate is increased. The condensation shock gets gradually stronger with decreasing the divergence angle.

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Abbreviations

B, C :

Virial equation of state coefficients

C p :

Specific heat at constant pressure (J kg−1 K−1)

C v :

Specific heat at constant volume (J kg−1 K−1)

e :

Specific energy (J kg−1)

h lv :

Latent heat of condensation (J kg−1)

I :

Nucleation rate (m−3 s−1)

k B :

Boltzmann constant

K eff :

Effective thermal conductivity (W m−1 K−1)

M m :

Molecular mass (kg mol−1)

p :

Pressure (Pa)

q c :

Evaporation coefficient

\(\bar r\) :

Average radius of droplet (m)

r * :

Kelvin-Helmholtz critical droplet radius (m)

R :

Gas constant (J kg−1 K−1)

P1 :

Inlet pressure

P3 :

Outlet pressure

S :

Supersaturation ratio

t :

Time (s)

T :

Temperature (K)

T 0 :

Temperature of droplet (K)

T sat :

Saturation temperature (K)

v :

Velocity (m s−1)

α :

Divergence angle

β :

Liquid mass fraction

γ :

Specific heat ratio

Γ :

Liquid mass generation rate (kg m−3S−1)

δ x/h :

Length of condensation region (m)

η :

Number of droplets per unit volume (m−3)

θ :

Kantrowitz non-isothermal correction factor

ρ :

Density (kg m−3)

σ :

Liquid surface tension (N m−1)

τ :

Viscous shear stress tensor (Pa)

g :

Saturation phase

l :

Liquid phase

v :

Vapor phase

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Acknowledgments

This work was supported by a Research Grant of Andong National University.

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Authors and Affiliations

  1. Department of Mechanical Engineering, Andong National University, Andong, 36729, Korea

    Balasubramanian Dhandapani & Jang-Chang Lee

Authors
  1. Balasubramanian Dhandapani
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  2. Jang-Chang Lee
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Correspondence to Jang-Chang Lee.

Additional information

Jang-Chang Lee received his B.S. and M.S. degrees in Mechanical Engineering from Chung-Ang University, Korea, in 1989 and 1991, respectively. He then received his Ph.D. degree from R.P.I. in 2000. Dr. Lee is currently a Professor in Department of Mechanical Engineering at Andong National University in Andong, Korea. Dr. Lee’s research interests include Two-phase flows, Aerodynamics, Condensation, and Cavitation dynamics.

Balasubramanian Dhandapani received his B.Tech. degree in Mechatronics Engineering from SRM University, India in 2019. He completed his M.S. degree in Mechanical Engineering at Andong National University, Korea in Febrary 2022. His research interests include Two-phase flows, Non-equilibrium condensation, and Machine learning.

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Dhandapani, B., Lee, JC. Study of divergence angle influence for sonic nozzle in non-equilibrium condensation. J Mech Sci Technol 36, 2993–2999 (2022). https://doi.org/10.1007/s12206-022-0531-x

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  • DOI: https://doi.org/10.1007/s12206-022-0531-x

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