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An investigation of finding the best arrangement of hot steam injection holes in the 3D steam turbine blade cascade

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Abstract

Steam turbines play a critical role in power generation systems. Therefore, increasing the efficiency of steam turbines is highly desirable, especially in LP stages. One of the suggested techniques to reduce wetness losses in LP stages is the hot steam injection. In the first section of the present study, the effect of 3D turbine blade span length on wet steam flow parameters is investigated. Then, the performance of various arrangements of hot steam injection holes (single slot, in-line no. 1, in-line no. 2, staggered no. 1, and staggered no. 2) is evaluated and compared. The results demonstrated that the in-line no. 1 arrangement is the best design for hot steam injection. In this arrangement, the wetness and condensation loss are reduced by 79% and 44%, respectively, and the kinetic energy loss is less than the other arrangements. However, the kinetic energy is still about 28% lower than in the no-injection case. Ultimately, excessive kinetic energy reduction due to hot steam injection is prevented by decreasing the injection pressure. As the injection pressure is reduced from 160 to 100 kPa, the kinetic energy, wetness, and condensation loss are reduced by 9%, 40%, and 17%, respectively, compared to the no-injection case.

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Abbreviations

A :

Area (m2)

B :

Second virial coefficient (m3 kg−1)

C :

Third virial coefficient (m6 kg−2)

C p :

Heat capacity at constant pressure (J kg−1 K−1)

C v :

Heat capacity at constant volume (J kg−1 K−1)

E :

Total energy (J)

EC:

Economic cost ($ h−1)

H r :

HSI ratio (–)

h :

Static enthalpy (J kg−1)

h lv :

Specific enthalpy of evaporation (J kg−1)

I :

Nucleation rate (no. of droplets/m3 s)

K :

Kinetic energy (kg m2 s−3)

K r :

Kinetic energy ratio (–)

k :

Turbulent kinetic energy (m2 s−2)

k B :

Boltzmann constant (–)

L r :

Condensation loss ratio (–)

l :

Length of the nozzle’s divergent section (m)

M m :

Specific molecular mass of water (kg mol−1)

P :

Pressure (Pa)

Pr:

Prandtl number

q c :

Condensation coefficient (–)

r :

Radius (m)

R :

Gas constant (J kg−1 K−1)

S :

Super saturation ratio (–)

t :

Time (s)

T :

Temperature (K)

u :

Flow velocity (m s−1)

V :

Average volume (m3)

W r :

Wetness ratio (–)

\(\mathrm{HSI}\) :

Hot steam injection

β :

Liquid mass fraction (–)

γ :

The ratio of specific heat capacities (–)

Γ :

Mass production rate due to condensation (kg m−3 s−1)

δ ij :

Kronecker delta function

ε :

Turbulent kinetic energy dissipation rate (m2 s3)

η :

Number of droplets per unit volume (m−3)

θ :

Non-isothermal correction factor (–)

μ :

Viscosity (Pa s)

ρ :

Mixture density (kg m−3)

σ :

Liquid surface tension (N m−1)

τ :

Viscous shear stress tensor (Pa)

d :

Droplet

eff:

Effective

exit:

Exit surface

i, j :

Tensor notation

I :

Injection case

in:

Inlet

l :

Liquid phase

lv :

Liquid–vapor

M :

Main case (no injection)

out:

Outlet

sat:

Saturation

t :

Turbulence

v :

Vapor phase

0:

Stagnation

\(^{\overline{\,}}\) :

Average

\(^{\widetilde{\, }}\) :

Time averaged

\(^{\acute{\, }}\) :

Fluctuation

*:

Critical condition

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Authors and Affiliations

  1. Department of Mechanical Engineering, Ferdowsi University of Mashhad, Mashhad, Iran

    Amir Kafaei

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

    Esmail Lakzian

  3. Department of Mechanical and Aeronautical Engineering, Clarkson University, Potsdam, NY, 13699-5725, USA

    Goodarz Ahmadi

  4. Department of Power Engineering and Turbomachinery, Silesian University of Technology (SUT), 44-100, Gliwice, Poland

    Sławomir Dykas

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  1. Amir Kafaei
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  2. Esmail Lakzian
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  4. Sławomir Dykas
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Correspondence to Esmail Lakzian.

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Kafaei, A., Lakzian, E., Ahmadi, G. et al. An investigation of finding the best arrangement of hot steam injection holes in the 3D steam turbine blade cascade. J Therm Anal Calorim 147, 10595–10612 (2022). https://doi.org/10.1007/s10973-022-11242-6

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