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Optimization volumetric heating in condensing steam flow by a novel method

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Abstract

In the last stages of steam turbines, the formation of liquid droplets causes losses and reduces turbine efficiency. One of the major problems of wet steam flow is the presence of the liquid phase, which volumetric heating reduces the wetness. One of the disadvantages of adding volumetric heating is increasing entropy generation and cost. Considering that three important parameters, including entropy losses, economic cost, and wetness play, an important role in the turbine blade flow. Reducing wetness can be accompanied by increasing heat and, on the other hand, adding heat leads to increasing cost and entropy. Therefore, as a first, a novel entropy, economic, and wetness (EEW) method is introduced to achieve optimal volumetric heating. Numerical simulation of the turbulent steam flow, SST k–ω model is used. Results are validated with experimental and numerical previous studies for two different geometries. It was also found that when the volumetric heating is optimal, these three parameters in EEW method have the lowest value. Moreover, EEW method is recommended for future research, and it is more optimized compared to the other types of methods. Therefore, corrosion and shock condensation can be decreased by using EEW method.

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Abbreviations

C l :

Specific heat of liquid (J kg−1 K−1)

C V :

Vapor isochoric specific heat (J kg−1 K−1)

E :

Total energy (J)

K b :

Boltzmann’s constant

K t :

Thermal conductivity (W m−1 K−1)

m r :

Liquid mass (kg)

M m :

Molecular mass (kg mol−1)

P :

Pressure (Pa)

q c :

Condensation coefficient

r :

Droplet radius (m)

s :

Specific entropy (J kg−1 K−1)

S :

Entropy

t :

Time (s)

u :

Velocity components (m s−1)

V :

Volume (m3)

Q :

Volumetric heating (W m−3)

W :

Wetness fraction

x, y, z :

Cartesian direction (m)

Γ :

Mass generation rate (kg m−3 s−1)

η :

Number of liquid droplets (1 m−3)

θ :

Non-isothermal correction coefficient

ξ :

Loss coefficient

ρ :

Density (kg m−3)

ϱ :

Mean rate-of-strain tensor

σ :

Liquid surface tension (N m−1)

τ :

Viscous stress tensor (Pa)

l:

Liquid

v:

Vapor

d:

Droplet

lv:

Liquid–vapor

n, m:

Number of control points

s:

Saturation

f:

Fuel

g:

Gas

t:

Turbulent

*:

Critical condition

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Authors and Affiliations

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

    Reza Hosseini & Esmail Lakzian

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  1. Reza Hosseini
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  2. Esmail Lakzian
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Correspondence to Esmail Lakzian.

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Hosseini, R., Lakzian, E. Optimization volumetric heating in condensing steam flow by a novel method. J Therm Anal Calorim 140, 2421–2433 (2020). https://doi.org/10.1007/s10973-019-09001-1

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