Flow Analysis around a Dimpled Cylinder Using Detached...

Hyoung-Chol KIM, Dep’t of Aerospace Engineering, Tohoku Univ., Japan

Hyoung-Chol KIM, Kazuhiro NAKAHASHI, Hyoung-Jin KIM

Dept. of Aerospace Eng., Tohoku Univ.

Masaya TSUNODASRI Research and Development LTD.

Takuma KATOInst. of Fluid Science, Tohoku University

Symposium on Hybrid RANSSymposium on Hybrid RANS--LES MethodsLES Methods

Rica City Hotel, Stockholm, 14Rica City Hotel, Stockholm, 14--15 July, 15 July, 2005 2005

Flow Analysis around a Dimpled Cylinder Using Detached-Eddy Simulation


I. BackgroundII. ObjectivesIII. Numerical MethodIV. ResultsV. Conclusions

Contents


Computational Fluid Dynamics (CFD) can be applied to the complicated flow fields.

However, analysis of complicated flow fields with massive separation such as blunt body problems at high Reynolds number is still challenging.

One of the reasons is difficulty in adequate consideration of turbulence effects.

To deal with these problems, recently, Detached-Eddy Simulation (DES) based on Spalart-Allmaras one equation turbulence model is proposed by Spalart et al.

Background : DES


Flow around a sphere has a very complicated and interesting physics.

A golf ball flies at about M=0.2 and the Reynolds Number of 105, but the drag coefficient is about half of the smooth sphere.

Background : Gold ball

0

0.2

0.4

0.6

0.8

1

1.2

104 105 106 107

smooth cylinder (Wieselsberg)smooth sphere (Achenbach, 1974)golf ball (Bearman and Harvey, 1976)

CD

Re


Dimples on the golf ball surface play an important role to trigger the boundary layer transition and reduce the drag.

However, the mechanism of the boundary layer transition by dimples has not been fully understood and the design of the dimples around a golf ball still highly depends on the experiences and experiments.

The CFD application to the golf ball is still challenging, but is becoming a powerful tool to investigate the effect of the geometry of dimples to the flows and the drag reduction.

Background : Gold ball


ObjectivesMain objective is to understand the effectiveness of the dimple shape on the turbulent flow around a dimpled sphere.

As a first step, flows around dimpled cylinders rather than dimpled spheres are simulated for simplicity and reduced computational cost.

This talk mainly focuses on the effectiveness of the DES for simulations of dimpled cylinders.

<top view><3-D view>On the cylinder surface, there are three lines of dimples, each line having thirty dimples in the circumferential direction.


Numerical Method ： Flow solver & Conditions

i. Ma. Number ： 0.17ii. Re. Number ： 1.65 x 105

iii. Far boundary ： Uniform Flowiv. Wall boundary ： No slip conditionv. Side boundary ： Symmetryvi. Time step ： UΔt=D/500vii. Newton subiterations ： 4 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)

Flow conditions (shot off)


Assumption of fully turbulent boundary layer

Numerical Method ： Turbulence models

Applied turbulence models

i. Without turbulence model (LAMINAR)

ii. Goldberg-Ramakrishnan one equation model (G-R)

iii. Spalart-Allmaras one equation model (S-A)

iv. Detached-Eddy Simulation based on S-A model (DES)


Hybrid volume grid information1) nodes : 1,045,9512) edges : 4,695,5763) tetrahedra : 1,132,5894) prisms : 1,620,8685) pyramids : 8,817

Grid density in the boundary layer region is increased by prismatic grid layer. (# of prism layers = 30, minimum spacing = 2.2 x 10-5)

Outer boundary is located at 50D from the cylinder surface (D is the cylinder diameter).

Numerical Method ： Grid


Result ： Separation regions (time averaged)

(U_velocity contours )

LAMINAR

G-R

S-A

DES

LAMINAR S-A

G-R DES

In turbulent flows, separation regions move downward resulting in drag reduction.


Result ： Vorticity magnitude contours (time averaged)

LAMINAR S-A

G-R DES

The difference with the high vorticity magnitude regions in the wake.

LAMINAR S-A

G-R DES


S-A

DES

LAMINAR

G-R

Result ： Vorticity magnitude contours (time averaged)

The vortices take place at dimple edges.


Result ： Vorticity magnitude contours (instantaneous, CL=0)

LAMINAR

G-R

S-A

DES

The difference in vortex structure at wake.


LAMINAR S-A

G-R DES

Result ： Velocity vectors (time averaged)

LAMINAR S-A

G-R DES

Secondary vortex


-5

-4

-3

-2

-1

0

1

2

0 30 60 90 120 150 180

LAMINARG-RExperiment

degree

C P

Result ： Section CP distributions (I)

y=0 section

-5

-4

-3

-2

-1

0

1

2

0 30 60 90 120 150 180

S-ADESExperiment

degree

CP

dimple geometry dimple geometry

Experiments : Institute of Fluid Science, Tohoku Univ. Japan (2004).In the front of the cylinder, CP distributions show good agreement with numerical and experimental results.

Peaky CP occurs between dimples


Result ： Section CP distributions (II)

y=0.4 section

-3

-2

-1

0

1

2

0 30 60 90 120 150 180

S-ADESExperiment

degree

C P

-3

-2

-1

0

1

2

0 30 60 90 120 150 180

LAMINARG-RExperiment

degree

CP


-600

-300

0

300

600

900

1200

0 30 60 90 120 150 180

LAMINARG-R

degree

(du/dy)y=surface

Result ： Velocity gradients distributions (I)

y=0 section

dimple geometry dimple geometry

At between dimples, the velocity gradients have a sudden peak, due to the dimpled surface geometry. This corresponds to the lower peak of CP.

-600

-300

0

300

600

900

1200

0 30 60 90 120 150 180

S-ADES

degree

(du/dy)y=surfac

e

Separation point Separation point

85.0°DES96.4°S-A97.0°G-R

73.0°LAMISeparation point (y=0 section)


-100

0

100

200

300

400

500

0 30 60 90 120 150 180

LAMINARG-R

degree

(du/dy)

y=surface

Result ： Velocity gradients distributions (II)

y=0.4 section

-100

0

100

200

300

400

500

0 30 60 90 120 150 180

S-ADES

degree

(du/dy)y=surfac

e

Separation pointSeparation point

In the smooth region of the dimpled cylinder, the separation takes place around 106°from the foremost stagnation point.

106.1°DES105.4°S-A106.1°G-R83.7°LAMI

Separation point (y=0.4 section)


0.6

0.8

1

1.2

1.4

1.6

1.8

2

40 50 60 70 80 90 100 110 120

LAMINARG-R

tU/D

C D

0.6

0.8

1

1.2

1.4

1.6

1.8

2

40 50 60 70 80 90 100 110 120

S-ADES

tU/D

C D

RESULT ： CD history

0.903DES0.763S-A0.942G-R1.298LAMI

Time averaged CD

In only S-A model, the CD history shows the periodic oscillation manner.


Result ： Comparisons of CD

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

104 105 106 107

cd-comparison

smooth cylinder (Wieselsberg)smooth sphere (Achenbach, 1974)golf ball (Bearman and Harvey, 1976)LAMINARG-RS-ADES

Re

C D

0.7

0.8

0.9

1

1.1

1.2

1.3

1.4

1.5

2 104 4 104 6 104 8 104 105

Experiment (Tohoku Univ.)LAMINARG-RS-ADES

Re

C D

At this flow conditions and grid, S-A model predicted the most accurate CDwith experimental results


Conclusions

i. Turbulence effects around a dimpled cylinder using DES were numerically simulated.

ii. For the comparison with DES, G-R and S-A one equation turbulence models and without turbulence model were applied.

iii. The results plotted with the time averaged vorticity magnitude and velocity vectors showed the difference in the high vorticity regions in the wake of cylinder.

iv. The time averaged section CP and velocity gradients distributions show the sudden peaks, due to the dimpled surface geometry.

v. For drag comparisons, S-A model predicted the most accurate results with experimental data.


Thank you for your attention.

Flow Analysis around a Dimpled Cylinder Using Detached...

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