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Investigation of the effect of water droplet injection on condensation flow of different nozzles geometry

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Abstract

In the present study, the effect of droplet injection of Moore A (MA), and De Laval nozzles (De) on the condensation shock, has been modeled and compared. The Eulerian–Eulerian method has been used in two-dimensional, compressible, viscous, and turbulent using the k−ω SST turbulence model to simulate the condensation flow field numerically. Four different nozzle inlet injection modes are evaluated; droplet injection in all cases caused a weaker condensation shock in the MA nozzle and could eliminate the De nozzle's shock. Also, the Mach number has increased by 2 and 5% at the output of the MA and De nozzles. The droplet spraying does not affect MA nozzle's wetness fraction, but it is reduced by about 30% at the De nozzle output. In general, the results showed that spray droplets at the inlet depend on geometry to improve aerodynamic and thermodynamic parameters.

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Abbreviations

A :

Area (m2)

\(C_{{\text{p}}}\) :

Specific heat capacity, (J/kg K–1)

\(B1,B2\) :

Virial coefficients

d :

Droplet diameter (m)

\(E\) :

Total energy (J kg−1)

\(H_{0}\) :

Throat height (m)

\(J\) :

Nucleation rate (m−3 s−1)

\(K_{{\text{b}}}\) :

Boltzmann's constant

\(L\) :

Latent heat (J kg−1)

\(P\) :

Pressure (Pa)

\(P_{0}\) :

Inlet total pressure (Pa)

\(P_{{\text{s}}} (T_{{\text{v}}} )\) :

Saturation pressure at TG (Pa)

\(q_{{\text{c}}}\) :

Condensation coefficient

\(r\) :

Droplet radius (m)

\(r^{*}\) :

Critical radius of droplets (m)

\(R\) :

Gas constant (J/kg K–1)

\(T_{{\text{v}}} ,{ }T_{{\text{l}}}\) :

Vapor and liquid temperature (K)

\(T_{0}\) :

Inlet total temperature (K)

\(T_{{\text{s}}} (P)\) :

Saturation temperature at P

\(t\) :

Time (s)

\(\omega\) :

Wetness fraction

\(\mu\) :

Dynamic viscosity (Pa s)

\(\gamma\) :

Specific heat ratio

\(\phi\) :

Non-isothermal correction coefficient

\(\rho_{{\text{v}}} , \rho_{{\text{l}}}\) :

Vapor and liquid density (kg/m3)

\(\sigma_{r}\) :

Liquid surface tension (N/m)

\({\text{v, l}}\) :

Vapor, liquid

\({\text{s}}\) :

Saturation

\({*}\) :

Critical condition

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Authors and Affiliations

  1. Department of Mechanical Engineering, Center of Computational Energy, Hakim Sabzevari University, Sabzevar, Iran

    Esmail Lakzian, Shima Yazdani, Reza Mobini, Mohammad Hosein Moghimi-Esfand Abadi, Ali Ramezani, Mojtaba Yahyazadeh & Mohsen Rashedi Tabar

  2. Peoples’ Friendship University of Russia (RUDN University), 6 Miklukho‑Maklaya Street, Moscow, Russian Federation, 117198

    Esmail Lakzian

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  1. Esmail Lakzian
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Lakzian, E., Yazdani, S., Mobini, R. et al. Investigation of the effect of water droplet injection on condensation flow of different nozzles geometry. Eur. Phys. J. Plus 137, 613 (2022). https://doi.org/10.1140/epjp/s13360-022-02812-6

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