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Optimization of NACA 4412 augmented with a gurney flap by using grey relational analysis

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Abstract

The gurney flap which has increased the lift coefficient at the trailing edge is used to improve the aerodynamic performance of the airfoil. In this study, the effect of the aerodynamic performance of baseline augmented with various dimensions of gurney flap (GF) structures was optimized by Taguchi method-based grey relational analysis (GRA) unlike previous works. Based on Taguchi's L16 orthogonal array method, the designs of the experiments were employed to optimize four control factors that were position (Δx), angle (α), thickness (Δt), and length (ΔL) of the GF on the airfoils. In aerodynamic studies based on GRA method, optimum parameters for α, ΔL, Δt, and Δx of GF were obtained as 75°, 1.5%c, 2%c, and 0%c. The degree of effect in aerodynamic performance was investigated by analysis of variance (ANOVA). The results show that the effect order of these four control factors was obtained as Δx > Δh > Δt > α which means that while Δx parameter with 37.62% has the strongest effect on the lift coefficient (CL) and drag coefficient (CD), α parameter with 3.06% has the lowest effect. The use of the GF model, which has the most optimal parameter, increased the efficiency (high CL; low CD) by 35.62% compared to the baseline in terms of GRA. In addition, empirical equations of the CL and CD on the airfoils were derived by regression analysis (RA). The values attained from empirical and numerical results (confirmation test) were highly compatible with each other.

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Abbreviations

∆h :

Length of Gurney Flap

∆t :

Thickness of Gurney Flap

∆x :

Position of Gurney Flap

A:

Projection area of Airfoil

ANOVA:

Analysis of Variance

AOA:

Angle of Attack

c :

Chord Length

C D :

Drag Coefficient

CFD:

Computational Fluid Dynamics

C L :

Lift Coefficient

C P :

Critical Coefficient

Cμu :

Pressure Coefficient

Dof, νA :

Degrees of Freedom

F D :

Drag Force

F L :

Lift Force

GRA:

Grey Relational Grade

GRG:

Grey Relational Analysis

GF:

Gurney Flap

MS:

Mean Sum of Squares

n :

The Number of Observations

OA:

Orthogonal Array

P :

Static Pressure

RA:

Regression Analysis

Re:

Reynolds Number

R 2 :

The Percentage of Variation in the Response

S/N:

Signal-to-Noise

SS, SSA :

Sequential Sum of Squares

SST :

Total Sequential Sum of Squares

TKE:

Turbulence Kinetic Energy

TI:

Turbulence intensities

u :

Friction Velocity at The Nearest Wall

v :

The Friction Velocity of The Fluid

V :

Velocity

VAWT:

Vertical axis wind turbine

V e :

Variance Error

x, y, z :

Cartesian Coordinates

y + :

Normalized Wall-Normal Coordinate

y :

The Observed Data

α :

Angle of Gurney Flap

ρ :

Density

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Authors and Affiliations

  1. Technical Sciences Vocational School, Gazi University, 06500, Ankara, Türkiye

    Ramazan Çakıroğlu

  2. Department of Energy Systems Engineering, Elbistan Engineering Faculty, Kahramanmaraş Istiklal University, Kahramanmaraş, Türkiye

    H. Erdi Tanürün

  3. Department of Energy Systems Engineering, Faculty of Technology, Gazi University, 06500, Ankara, Türkiye

    H. Erdi Tanürün, Adem Acır, Furkan Üçgül & Sena Olkun

Authors
  1. Ramazan Çakıroğlu
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  2. H. Erdi Tanürün
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Correspondence to Ramazan Çakıroğlu.

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Çakıroğlu, R., Tanürün, H.E., Acır, A. et al. Optimization of NACA 4412 augmented with a gurney flap by using grey relational analysis. J Braz. Soc. Mech. Sci. Eng. 45, 167 (2023). https://doi.org/10.1007/s40430-023-04089-x

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