[PPT] - Modification of Turbulent Flow using Distributed Suction Maurizio PowerPoint Presentation

SLIDE 1

✬ ✫ ✩ ✪

Modification of Turbulent Flow using Distributed Suction

Maurizio Quadrioa, J. Maciej Floryanb & Paolo Luchinic

a Dip. Ingegneria Aerospaziale Politecnico di Milano,

maurizio.quadrio@polimi.it

b Dept. Mechanical and Materials Eng. University of Western Ontario, c Dip. Ingegneria Meccanica Universit`

a di Salerno

M.Quadrio, M. Floryan & P .Luchini 5th EFMC, Toulouse (FR), August 24-28, 2003 1

SLIDE 2

Introduction

✬ ✫ ✩ ✪

INTRODUCTION

Use of wall-normal blowing/suction is very effective for turbulence control. Sumitani & Kasagi, AIAA J. 1995: constant blowing (suction) is known to affect significantly the friction drag and the heat transfer. Choi et al. JFM 1994: use of time- and space-dependent blowing/suction (difficult to implement in practice!) is known to allow 25% turbulence drag reduction. Jim´ enez et al JFM 2001: active/passive porous walls, increase in drag.

M.Quadrio, M. Floryan & P .Luchini 5th EFMC, Toulouse (FR), August 24-28, 2003 2

SLIDE 3

Introduction

✬ ✫ ✩ ✪

MOTIVATION I

Study the effect of a steady, longitudinal distribution of suction at the wall, with low amplitude and zero net mass flux. λs = 2π/αs A Tool: DNS of the turbulent plane channel flow. v(x, y = ±h, z, t) = A sin (αsx)

M.Quadrio, M. Floryan & P .Luchini 5th EFMC, Toulouse (FR), August 24-28, 2003 3

SLIDE 4

Introduction

✬ ✫ ✩ ✪

MOTIVATION II

Schoppa & Hussain, PoF 1998: large-scale streamwise vortices are known to produce a signifcant drag reduction. In laminar regime, Floryan JFM 2003 has shown that sinusoidal suction creates such vortices. Result from stability analysis with mean turbulent profile as base flow:

M.Quadrio, M. Floryan & P .Luchini 5th EFMC, Toulouse (FR), August 24-28, 2003 4

SLIDE 5

Introduction

✬ ✫ ✩ ✪ Re = 3300, A = 0.004Uc

0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

0.5

1 1.5 2 2.5 3 3.5 4 4.5 5

M.Quadrio, M. Floryan & P

.Luchini 5th EFMC, Toulouse (FR), August 24-28, 2003 5

SLIDE 6

Introduction

✬ ✫ ✩ ✪

MOTIVATION III

Floryan JFM 2003: the laminar case is qualitatively analogous to the flow over a wavy wall. Many papers exist on turbulent flow over wavy walls. It is currently believed that the wavelength of the wavyness by itself does not play any role, von R¨

hr, JFM 2003.

The same is assumed by Jim´ enez et al (suction). Does the wavelength matter?

M.Quadrio, M. Floryan & P .Luchini 5th EFMC, Toulouse (FR), August 24-28, 2003 6

SLIDE 7

Numerical issues

✬ ✫ ✩ ✪

THE NUMERICAL METHOD

Our solver of the incompressible Navier–Stokes equations has:

➜ II-order equation for the normal vorticity and IV-order equation for the normal velocity, without pressure ➜ Fourier discretization in the homogeneous directions ➜ Fourth-order compact finite-differences over a 5-point unevenly spaced computational molecule in the wall-normal direction ➜ Three-substeps Runge–Kutta partially implicit time advancement ➜ Parallel execution on both shared-memory and distributed-memory computers

M.Quadrio, M. Floryan & P .Luchini 5th EFMC, Toulouse (FR), August 24-28, 2003 7

SLIDE 8

Numerical issues

✬ ✫ ✩ ✪

PARAMETERS OF THE SIMULATIONS

Computational parameters: the same as Kim, Moin & Moser in JFM, 1987 (longer integration time). 8 · 106 d.o.f. Plane turbulent channel flow at Reτ = 180.

Periodic-box dimensions: Ly = 2h

Lx = 4πh Lz = 2πh

Spatial discretization: Nx = 193

Nz = 129 Ny = 161

Spatial resolution: ∆x+ = 11.7

∆y+ = 0.8 to 4.5 ∆z+ = 7.0

Temporal resolution: ∆t+ ≈ 0.15
Total integration time: T ≈ 600h/Uc

Calculations run on Itanium II machines of the SHARCNET Computing Center at the University of Western Ontario. Approx. 40 cases plus some accuracy checks.

➀ The effect is proportional to A at fixed αs. The threshold of minimum A depends on αs. ➁ A better parameter could be the product Aλs (flow rate) ➂ Suction wavelength does matter! ➃ When λs → ∞ the limit of uniform blowing + uniform suction is

recovered. Agreement with λ+

s ≈ 4000 from Jim`

enez, and with results from Sumitani & Kasagi.

Is the flow over a wavy wall really independent on the wavelength

f the corrugation? Probably not...

M.Quadrio, M. Floryan & P .Luchini 5th EFMC, Toulouse (FR), August 24-28, 2003 11

SLIDE 12

Results

✬ ✫ ✩ ✪

UNEXPECTED RESULT: SMALL DRAG REDUCTION αs h % Cf

4 6 8 10

4
3
2
1

1 2 3 4

A=0.03 UP

10 20 30 40 10

8

10

7

10

6

10

5

10

4

10

3

10

2

ref αh=1 αh=5

M.Quadrio, M. Floryan & P .Luchini 5th EFMC, Toulouse (FR), August 24-28, 2003 16

SLIDE 17

Turbulence statistics

✬ ✫ ✩ ✪

STREAMWISE DIRECTION IS NOT-HOMOGENOUS!

y/h U/UP

0.1 0.2 0.3 0.4 0.1 0.2 0.3 0.4 0.5 0.6 0.7 λ=0 λ=1/4 λ=1/2 λ=3/4 mean

αh=1

M.Quadrio, M. Floryan & P .Luchini 5th EFMC, Toulouse (FR), August 24-28, 2003 17

SLIDE 18

Turbulence statistics

✬ ✫ ✩ ✪

VERTICAL MEAN VELOCITY AND STREAMLINES

x/h y/h

0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 0.1 0.2 0.3 0.4

αh=1

x/h y/h

0.5 1 0.1 0.2 0.3 0.4

αh=5

M.Quadrio, M. Floryan & P .Luchini 5th EFMC, Toulouse (FR), August 24-28, 2003 18

SLIDE 19

Turbulence statistics

✬ ✫ ✩ ✪

TRANSVERSAL CORRELATIONS, u AT y+ ≈ 10

x/h ∆z

0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 0.5 1 1.5 2

αh=5

x/h ∆z

0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 0.5 1 1.5 2

αh=1

M.Quadrio, M. Floryan & P .Luchini 5th EFMC, Toulouse (FR), August 24-28, 2003 19

SLIDE 20

Turbulence statistics

✬ ✫ ✩ ✪

STREAMWISE FRICTION

x/h z/h

5

5

2

2

αh=5

x/h z/h

5

5

2

2

αh=2

M.Quadrio, M. Floryan & P .Luchini 5th EFMC, Toulouse (FR), August 24-28, 2003 20

SLIDE 21

✬ ✫ ✩ ✪

CONCLUSIONS

Suction wavelength λs plays a fundamental role. Dramatic drag increase at wavelenghts λ+

s > 350, towards the

asymptotic value of uniform blowing and uniform suction. Usual turbulence structure (elongated low-speed streaks) disappear. Small drag reduction below the threshold λ+

s = 350. Critical

wavelength is related to the typical size of near-wall turbulent structures. No evidence of large-scale vortices. Basic flow structure is a pair of large-scale spanwise rolls.

M.Quadrio, M. Floryan & P .Luchini 5th EFMC, Toulouse (FR), August 24-28, 2003 21