Subject:Investigating the effects of numerical discretization and t b l   d li    th     f fl   l ti  turbulence modeling on the accuracy of flow solution 

around NACA0012 airfoil using OpenFOAM

Authors:Authors:Farshad Rezaei Ehsan Roohi Mahmood Pasandideh Frad

Ferdowsi University of Mashhad, Mashhad, Iran

Presented by:Farshad Rezaei

Contents:Contents:

IntroductionIntroduction

Grid IndependencyGrid Independency

Results and DiscussionResults and Discussion

ConclusionsConclusions

I t d tiIntroduction

Incompressible Flow around NACA0012Incompressible Flow around NACA0012

Using OpenFOAMUsing OpenFOAM

simpleFoam Solver: A Pressure-Based SolversimpleFoam Solver: A Pressure-Based Solver

SIMPLE Algorithm: The Semi-Implicit Method of Linked Equations

Turbulence Models:

Spallart-Allmaras: An one equation model

Turbulence Models:

K-ω SST: Two-equation eddy-viscosity model

Grid IndependencyGrid Independency

Grid Independency:Grid Independency:

Mesh Name Number of Thickness of Error%

Lift Coefficient for different Meshes AoA=10

Computational DomainCLmesh points around airfoil

first B.L cell (mm)

Computational DomainCL

Mesh-1 450 0.6 1.0834 1.204

Mesh-2 592 0.6 1.0897 0.631

Mesh-3 738 0.6 1.0916 0.458

Mesh

Results and DiscussionResults and DiscussionDiscretization Schemes of the Momentum Equations

leastSquares Improve the         CL 2 01%q p

Pressure Gradient: fourth Improve the

2.01%

CLfourth Improve the

I t l ti f l it f th ll t t ll’ f

CL

2.1%

Interpolation of velocity from the cell center to cell’s face: Linear,cubic-Correction,midpoint,linear-Upwind and CL C D

are exactly Limited-Linear-V, vanLeer-V, gamma-V, SFCDV the same

Results and DiscussionResults and DiscussionConvective term: for an Incompressible flow

)( UUdiv )( Udiv

QUICK

),( UUdiv ),( Udiv

QUICK Linear compared to linear-Upwind SFCD SFCD

The most accurate result was obtained by using linearS h f i d b 0 35%CScheme for improved by 0.35%),( UUdiv CL

Th t t ltUsing fourth order discretization scheme for presuure gradient term

The most accurate results:p g

Using linear scheme for diverjence term ),( UU

variation vs. angle of attack  from the current numerical work to thin airfoil theoryCL

Results and Discussion

Investigating the effect of Reynolds number:

CL vs. angle of attack for different Reynolds number compared to Thin Airfoil TheoryL g y p y

By increasing the Reynolds number,       increasers and become closer to Thin Airfoil Theory

CL

Wall Pressure CoefficientWall Pressure Coefficient

AOA=0 AOA=10

AOA=15

Wall‐Skin friction Coefficient using K‐ turbulence modelWall Skin friction Coefficient using K turbulence model

AOA=0 AOA=10

AOA=15

Drag Coefficientg

Drag Coefficient vs. Lift Coefficient

ConclusionConclusionUsing fourth order discretization scheme for presuure gradient

termterm.

U i li h f di j )(dUsing linear scheme for diverjence term .),( UUdiv

By increasing the Reynolds number increasers and become closer to Thin Airfoil Theory.

CL

K-SST model provides more accurate results for and compared to p pthe spalart-Allamras one.

Thanks For Your AttentionThanks For Your Attention