DES Simulation aroundNACA0012 Airfoil using

Unstructured Grid

Masafumi KurodaKazuhiro Nakahashi

Yu FukunishiDep’t. of Mechanical System and Design,

Tohoku University

Background

･Unsteady, complex flowfield is created at wing-tip･Sound is generated by shear layer shedding from bottom edge and vortices in wake

･ The computation around a single wing-tip flow using unstructured grid.

- To check the computational validity(preliminary test)

- For future extension (high lift devices)

The purpose of this research

Numerical Method ： Flow solver & Conditions

i. Mach # ： 0.2ii. Reynolds # ： 2.0 x 106

iii. Far boundary ： Uniform Flowiv. Wall boundary ： No slip conditionv. Time step ： UΔt=c/5000vi. Newton subiterations ： 3 times

i. Governing Eq. ： Compressible Navier-Stokes Eq.ii. Spatial Discritization ： Cell-Vertex, Finite Volume Methodiii. Numerical Flux Evaluation ： HLLEW Riemann Solveriv. Time Integration ： LU-SGS Implicit Method

TAS code, Tohoku univ. Aerodynamic Simulation code

Simulation conditions

Computational Grid

・NACA0012 with blunt tip (span length = 2.5c)

Grids in present study

・Grid 1 : isotropic grid・Grid 2 : stretched grid・Grid 3 : grid refinement

Grid 1 Grid 2 Grid 3

Computation using isotropic grid (Grid1)

・Grid is dense at wake, upper, side, and edge

Computational grid (Grid 1)

Result (Grid 1)

instantaneous at t=80000Δt ω=10

Iso-surface of vorticity magnitude

ω=5

instantaneous at t=120000Δt mean in 110000-120000Δt

Iso-surface of vorticity magnitude (ω=10)

・The unsteady fluctuations did not appear in Grid 1.

middle: x=0.067c at center linelower: x=0.067c, y=2.4946c

Pressure record for last 10000 time step

・Two vortices emerge from top and bottom edges.

y ×x

zvorticity magnitude x=0.2c

・Departing vortices are captured.・Strong shear layers exist but are dissipated

y ×x

zx=0.5c

・Shear layer is primary in sidewall region.・Two vortices merge over the upper surface

y ×x

zx=0.8c

・Vortices and shear layer merge.・They dissipate by numerical viscosity.

y ×x

zx=1.0c

Cp distributions at wing center line and 2.5% c inside

Vortex footprintx ◎ z

y

Pressure contour at upper surface

current resultexperiment

Comparison of U velocity at each section(0.5,0.7,0.95,1.1c)

Computation using stretched grid (Grid2)

Difficulties in using isotropic grid

･The flowfield is unique for rapid change in z-direction･Grid generation yields huge number of computational grids in vain, but it is too coarse in y-z plane

Streett et al

Computational grid (stretched 5 times streamwise)

Surface mesh Volume mesh

x=2.0c

x=1.0c

6,891,4376,778,675# of tetra10,498,18014,357,070# of edge

1,773,7472,758,260# of nodestretched gridisotropic grid

isotropic stretched

Result (Grid 2)

instantaneous at t=27000Δt

Iso-surface of vorticity magnitude (ω=5)

mean for 5000Δt

isotropic

stretched

Iso-surface of instantaneous vorticity magnitude at t=27000Δt(ω=10)

・The strength of secondary vortex is different.

y ×x

zisotropic

stretched

vorticity magnitude x=0.5c

・Merging of vortices is captured sharply.

y ×x

zisotropic

stretched

x=1.0c

・Vortex in wake is captured well.

y ×x

z

stretched

x=1.5c

isotropic stretched

Comparison of U velocity at each section (0.5,0.7,0.95,1.1c)

Computation using grid refinement (Grid3)

Difficulties in using equally sized grid

･Sharp shear layer is blurred completely

Grid is dense at high vorticity, strong shear layer

Refined grid

Method:・Equi-dividing.・8-way cut based on shortest edge (tetra).・Vorticity-based refinement.

before refinement after refinement

y ×x

z

0.0 40.0

・Sharp shear layer now emerges.・Strength of vortices is different.

vorticity magnitude x=0.5c

before refinement after refinement

y ×x

z

0.0 40.0

・Merging of vortices and shear layer are captured sharply.

x=0.8c

Comparison of Cp distributions (wing center line)

Comparison of Cp distributions (2.5% c inside)

before refinement after refinement

z ◎ x

y

0.975 1.0

Comparison of pressure contour(upper surface from x=0.2 to 0.4 c)

before refinement after refinement

y ×x

z

0.0 40.0

・Vortex is captured well. This supports the existence of lower pressure region.

vorticity magnitude x=0.3c

ascendingvortices vortices

at shear layer

Fluctuation of vorticity magnitude at t=32500Δt (ω=1)

middle: x=0.067c at center linelower: x=0.067c, y=2.4946c

fluctuation is too weak to be seen

Pressure record for last 10000Δt span

･Qualitative steady result is obtained.･Use of stretched computational grid yields favorable result.･Downstream grid resolution is important to capture shear layer correctly.･Shear layer instability could no be captured well possibly because of grid resolution.

Conclusion

0.96

Pressure distribution of bottom corner at x=0.5c surface

numericaldissipation