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A predictive model based on a 3-D computational approach for film cooling effectiveness over a flat plate using GMDH-type neural networks

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Abstract

A 3-D numerical solution is implemented for investigating incompressible turbulent flow and thermal fields of film cooling through a single row of inclined cylindrical holes over a flat plate model. The effects of parameters of interest on the film cooling performance have been simulated. The group method of data handling (GMDH)-type neural networks successfully employed for modeling and presenting a correlation for area-weighted average adiabatic film cooling effectiveness.

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Abbreviations

A :

Surface area

\(C_{\mu }\) :

The turbulence model constant

\(C_{2\varepsilon }\) :

The turbulence model constant

\(C_{1\varepsilon }\) :

The turbulence model constant

D :

Diameter of injection hole

DR :

Density ratio

I :

Momentum flux ratio

k :

Turbulence kinetic energy

L :

Length of injection hole

M :

Blowing ratio

PE :

Prediction error

Pr :

Prandtl number

Re :

Reynolds number

T :

Temperature

TE :

Training error

u :

Velocity

V :

Velocity

VR :

Velocity ratio

x :

Coordinate: streamwise (axial) direction

y :

Coordinate: vertical direction

\(y^{ + }\) :

Law of the wall coordinate

z :

Coordinate: lateral (spanwise) direction

\(\alpha\) :

Injection angle of hole

\(\delta_{ij}\) :

Kronecker delta

\(\varepsilon\) :

Turbulence dissipation rate

\(\eta\) :

Adiabatic film-cooling effectiveness

\(\mu\) :

Dynamic viscosity

v :

Kinematic viscosity

ρ :

Density

\(\sigma_{k}\) :

Prandtl number for turbulence kinetic energy

\(\sigma_{\varepsilon }\) :

Prandtl number for turbulence dissipation rate

\(\tau\) :

Shear stresses

aw :

Adiabatic wall

c :

Coolant

cl :

Centerline

m :

Main flow

i, j :

1,2 denote x–y space coordinate

t :

Turbulent

l :

Lateral direction

−:

Average value

′:

Fluctuating component

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Acknowledgments

The authors would like to thank Dr. Ali Jamali in the mechanical engineering department at the University of Guilan for his very valuable discussions in modeling using GMDH-type neural networks.

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Authors and Affiliations

  1. Mechanical Engineering Department, Faculty of Engineering, University of Guilan, 3756, Rasht, Iran

    M. Naghashnejad, N. Amanifard & H. M. Deylami

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  1. M. Naghashnejad
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  2. N. Amanifard
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  3. H. M. Deylami
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Correspondence to N. Amanifard.

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Naghashnejad, M., Amanifard, N. & Deylami, H.M. A predictive model based on a 3-D computational approach for film cooling effectiveness over a flat plate using GMDH-type neural networks. Heat Mass Transfer 50, 139–149 (2014). https://doi.org/10.1007/s00231-013-1239-3

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  • DOI: https://doi.org/10.1007/s00231-013-1239-3

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