Modeling of deviation angle and performance losses in wet steam turbines using GMDH-type neural networks

Original Article
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Abstract

In the present study group method of data handling (GMDH) type of artificial neural networks are used to model deviation angle (θ), total pressure loss coefficient (ω), and performance loss coefficient (ξ) in wet steam turbines. These parameters are modeled with respect to four input variables, i.e., stagnation pressure (Pz), stagnation temperature (Tz), back pressure (Pb), and inflow angle (β). The required input and output data to train the neural networks has been taken from numerical simulations. An AUSM–Van Leer hybrid scheme is used to solve two-phase transonic steam flow numerically. Based on results of the paper, GMDH-type neural networks can successfully model and predict deviation angle, total pressure loss coefficient, and performance loss coefficient in wet steam turbines. Absolute fraction of variance (R2) and root-mean-squared error related to total pressure loss coefficient (ω) are equal to 0.992 and 0.002, respectively. Thus GMDH models have enough accuracy for turbomachinery applications.

Keywords

Deviation angle Performance losses Steam turbine Group method of data handling Artificial neural network 

List of symbols

af

Speed of sound (m/s)

C

Chord length (m)

Cp

Specific heat capacity at constant pressure (J/kg K)

et

Total internal energy per unit volume (J/m3)

Fk

Vector of convective flux in ξ direction

Gk

Vector of convective flux in η direction

H

Total enthalpy (J/kg)

hfg

Latent heat of evaporation (J/kg)

J

Jacobian of transformation

Jnuc

Nucleation rate [# droplets/(m3 s)]

kB

Boltzmann’s constant (=1.3807 × 10−23J/K)

M

Mach number

mv

Molecular weight of vapor (kg)

MAPE

Mean absolute percentage of error

N

Total number of droplets per unit mass of mixture

p

Pitch length (m)

P

Static pressure (Pa)

P0

Total pressure (Pa)

Pb

Back pressure (Pa)

Pz

Inlet stagnation pressure (Pa)

Q

Conservative vector

r

Droplet radius (m)

R2

Absolute fraction of variance

rc

Droplet critical radius (m)

Rv

Vapor constant (=461.4 J/kg.K)

RMSE

Root-mean-squared error

S

Source term

t

Time (s)

Tz

Inlet stagnation temperature (K)

u, v

Velocity components (m/s)

w

Weighting factor

x, y

Cartesian coordinates

β

Inflow direction

Δt

Time step (s)

ϕ

Dissipation coefficient

γ

Specific heat ratio of vapor (=1.327)

Γ

Stagger angle

ρ

Mixture density (kg/m3)

σ

Liquid surface tension (N/m)

θ

Deviation angle

ω

Pressure loss coefficient

χ

Wetness fraction

ξ

Performance loss coefficient

Subscripts

0

Stagnation condition

b

Back

e

Exit section

i

Inlet section

is

Isentropic state

l

Liquid

L

Left

R

Right

S

Saturation

v

Vapor

Superscripts

AUSM

Advection upstream splitting method

L

Left

n

Iteration number

R

Right

VL

Van Leer

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Copyright information

© The Natural Computing Applications Forum 2016

Authors and Affiliations

  1. 1.Faculty of EngineeringUniversity of ShahrezaShahrezaIran
  2. 2.Department of Mechanical Engineering, Faculty of EngineeringArak UniversityArakIran

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