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Evaluation of Turbulence Models in SU2 CFD: A Comparative Analysis of Spalart Allmaras and Transitional SST for NACA 23012 airfoil

5th Annual SU2 Conference

Felipe Diogo Moura Silva and Luís Eduardo Bispo Gonçalves

Universidade Federal do Vale do São Francisco

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Motivation

To understand the flow behavior over the airfoil is crucial during airplane conceptual design.
Evaluation of the models accuracy are a imperative part of analysis.
Consider the accuracy and computational efficiency is essential.

To compare the application of two turbulence closure models in a bidimentional analysis.
Conduct a mesh independence analysis
Compare the results with experimental data.

Objectives

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Introduction

The experiment was conducted by Jacobs and Abbott in a variable-density wind-tunnel.
With this results, it was possible to compare with analysis outputs.

Figure 1: Variable-density wind tunnel

Source: Jacobs (1933)

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Boundary Conditions

O-type domain.
The bounds was defined as Far Field.
The airfoil was defined as as no-slip wall and isobaric surface.

40C

Figure 2: Fluid domain.

Source: Authors (2024)

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Freestream Conditions

Freestream Parameter	Values
Mach	0.23
Reynolds Number	3.5 * 10^6
Turbulence Intensity	0.01

The airfoil that analysis was performed is the NACA 23012.
The analysis was performed using SU2 CFD and covering the range of AoA 0º to 16º.

Source: Authors (2024)

Figure 3 NACA 23012

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Numerical Setup

Numerical setting	Type
Gradient Numerical Method	Green-Gauss
CFL Number	0.95
Linear Solver	FGMRES
Linear Preconditioner	LU-SGS
Multigrid Level	3
Convective Numerical Method for Flow	JST
Convective Numerical Method for Turbulence	Scalar Upwind
Slope Limiter for Turbulence	Venkatakrishnan

Tests to achieve the best configuration.
Both time integration are Euler Implicit.
CFL Number is adaptive.
Multigrid type: W-cycle

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Mesh Definition

The mesh was done using Gmsh.
Tests using structured mesh and unstructured for this case.
The calculated Y+ near the wall is 1.2 for fine mesh.
The ratio of 1.15 was used from the first to the 30th layer.

Fine mesh

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Mesh Independence

Type	Elements [x1000]	Y+
Coarse	33.5	5.0
Medium	42.1	3.0
Fine	53.4	1.2
Extrafine	79.4	0.8

Slightly difference of suction region.
The frictional impact in the airfoil leading edge.

Using Transitional SST

Cp @ 16º

Cf @ 0º

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Results: Detachment

Behavior for AoA = 16º with transitional SST.

Decay of friction coefficient.
Beginning of detachment.
𝛾-Reθt Formulation.

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Results: Aerodynamic coefficients

Aerodynamic coefficients comparison

A trivial variation of Cl for most of the range.
Evident drag variation for the fully turbulent model.

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Results: Aerodynamic coefficients

The SA lift curve slope difference.
Transitional SST minor drag error.

Percentual difference relative to experimental
	Cl @ 0º	Cd @ 0º	Cl @ 8º	Cd @ 8º	Cl @ 16º	Cd @ 16º
Transitional SST	32,25	5,15	5,70	8,08	6,07	11,06
Spalart-Allmaras	19,78	17,70	1,63	19,19	14,15	13,77

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Conclusions

The SU2 CFD shows high efficiency and versatility to compute a bidimensional airfoil analysis.
The mesh generation in Gmsh can be easily done using an script in any programming language.
The fully turbulent model Spalart-Allmaras turbulence model is accurate for lift calculation, however, not enough for drag for this case.
The transitional fluctuations were well captured by Transitional SST model.
The Transitional SST is more effective for accurate drag calculations..
The time per step under the same computational setup was very similar between both models.
A good setup ensure a good reliability for bidimentional analysis and results at medium-high reynolds.

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References

Jacobs, Eastman N., and Ira H. Abbom. The N.A.C.A VARIABLE-DENSITY WIND TUNNEL. NASA Technical Report Server, 1 Jan. 1933.
“Gmsh: A Three-Dimensional Finite Element Mesh Generator with Built-in Pre- and Post-Processing Facilities.” Gmsh.info, 2024, gmsh.info/#Download. Accessed 7 Sept. 2024.