Neural Computing and Applications

, Volume 28, Supplement 1, pp 489–501 | Cite as

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

  • Hamed Bagheri-Esfe
  • Hamed Safikhani
Original Article


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 (P z ), stagnation temperature (T z ), back pressure (P b), 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 (R 2 ) 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.


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

List of symbols


Speed of sound (m/s)


Chord length (m)


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


Total internal energy per unit volume (J/m3)


Vector of convective flux in ξ direction


Vector of convective flux in η direction


Total enthalpy (J/kg)


Latent heat of evaporation (J/kg)


Jacobian of transformation


Nucleation rate [# droplets/(m3 s)]


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


Mach number


Molecular weight of vapor (kg)


Mean absolute percentage of error


Total number of droplets per unit mass of mixture


Pitch length (m)


Static pressure (Pa)


Total pressure (Pa)


Back pressure (Pa)


Inlet stagnation pressure (Pa)


Conservative vector


Droplet radius (m)


Absolute fraction of variance


Droplet critical radius (m)


Vapor constant (=461.4 J/kg.K)


Root-mean-squared error


Source term


Time (s)


Inlet stagnation temperature (K)

u, v

Velocity components (m/s)


Weighting factor

x, y

Cartesian coordinates


Inflow direction


Time step (s)


Dissipation coefficient


Specific heat ratio of vapor (=1.327)


Stagger angle


Mixture density (kg/m3)


Liquid surface tension (N/m)


Deviation angle


Pressure loss coefficient


Wetness fraction


Performance loss coefficient



Stagnation condition




Exit section


Inlet section


Isentropic state













Advection upstream splitting method




Iteration number




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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