EUROMECH 448, "Vortex dynamics and field interactions"

6th-10th September 2004, Paris, France

LAGRANGIAN VISUALIZATIONS and

EULERIAN DIAGNOSTICS of VORTEX BREAKDOWN

Naumov I.V., Okulov V.L., J. N. Sorensen*

Institute of Thermophysics SB RAS, 630090, Novosibirsk, Russia

*Technical University of Denmark, DK-2800 Kgs. Lyngby, Denmark

e-mail: naumov@itp.nsc.ru

Motivation

Objectives of current experiments:

• Most experimental observations of swirl flow generated by a rotating lid inside a closed cylindrical container are mainly restricted to visualizations of the evolution of breakdown bubbles (M.P. Escudier Exp. Fluids, 1984).

• Using Lagrangian visualizations particle paths displaying chaotic behavior were found at stationary vortex-breakdown bubbles (Sotiropoulos F. et al. J.Fluid Mech., 2002).

• Difficulties in comparison of chaotic Lagrangian visualizations (J.N. Sorensen Rep. AFM,1992) and Eulerian numerical calculation of regular flow with bubble oscillations.

Strategy:

• Work has focused on experimental investigation of the velocity field in a closed cylinder using two non-intrusive optical methods: determination of a velocity field by particle tracks (PIV) and a velocity pulsation by Laser Doppler Anemometry (LDA).

• Comparison of Lagrangian particle distribution with velocity maps of PIV.• LDA measurements allow to estimate a period of the flow oscillation to define the

averaging time interval for PIV measurements.• Simultaneous PIV and LDA measurements permit to show real flow structure with

changes in sizes and positions of the vortex breakdown zone for different times in the whole oscillation period.

Investigation of vortex breakdown in closed cylindrical container

ν

2

Re R⋅Ω=

Escudier diagram (Exps. Fluids. 1984)

•Cylinder (R=144 mm; H/R = 2) (submerged in a rectangular glass tank with tap water)

•Seeding particles: polyamide beads ~ 20 µm (density ~ 1.03 g/cm3)

•The working fluid: 83% water/glycerin mixture

Aspect ratio: h = H/R

H – height of cavityR – disk radiusΩ – angular velocityν – fluid viscosity

Disk rotation error < 0.1%.Gap ~ 0.3 mm.

Visualization in a cylindrical container for different ReSørensen J.N. DTU, Lyngby, Denmark (Rep. AFM 1992)

seeding particles were Rhodamine B ~ 50 µmH/R=2

2002 2103 2204 2301 2404 2505 2598

2707 2805 2896 3004 3500 4014 4996 5981 7007

PIV visualization

Comparison of visualization and numerical calculation for H/R = 2 and different Reynolds numbers

Unsteady regime with strong bubble oscillation (Re = 3500)

steady bubble flow (Re = 2043)

Sotiropoulos F. et al. J.Fluid Mech. 2002

Lagrangian chaotic visualizations

Eulerian visualizations by numerical simulation

t = 0 t = T/2

Experimental Techniques

2

13

4

5

67

Ω

CCD

PIV2100

10

BSA

9

8

LDAprobe

Argon Ion

laser

PIV:• Pulsed Nd:YAG laser(λ=532 nm, 100 mJ, 10 ns,10 Hz)• Light sheet - 1.4 mm• CCD camera:Kodak Mega Plus ES 1.0(1008×1018 pixel)• Size of calculation area: 32x32pixels with 25% overlapping• Dantec PIV 2100 processor

LDA:Dantec 2D Fiberflow LDA2 W Argon-Ion laserDiameter of gauge 112 mm(Focal length 500 mm, λ=514,5 nm)Probing field: 0.12×0.12×1.52 mm. Frequency shift 40 MhzBSA57N2 (Burst specter analyzer) signal processor

Investigation of velocity fluctuations by Laser Doppler Anemometer

0.291.120,023-0,38130735000

0.291.020,029-0,34112584500

0.290.880,023-0,31164444000

0.240.650,018-0,28174773500

0.230.520,01-0,24124713000

0.230.450,008-0,21111222600

ffluid/ΩdiskFfluid[Hz]

Vel-RMS [m/s]

Vel-Mean[m/s]

Vel-countRe

1 E - 0 0 3

2 E - 0 0 3

3 E - 0 0 3

4 E - 0 0 3

5 E - 0 0 3

6 E - 0 0 3

7 E - 0 0 3

8 E - 0 0 3

9 E - 0 0 3

1 E - 0 0 2

1 E - 0 0 2

0 , 2 0 0 , 4 0 0 , 6 0 0 , 8 0 1 , 0 0 1 , 2 0 1,40 1,60 1,80 2,00

Spectrum [BSA1 Vel] [x²/Hz]

Frequency [Hz]

Re = 3500 (unsteady flow)

Fluctuations of the breakdown area exhibit a clear periodic character

- 0 , 4 0 - 0 , 3 8 - 0 , 3 6 - 0 , 3 4 - 0 , 3 2 - 0 , 3 0 - 0 , 2 8

- 0 , 2 6 - 0 , 2 4 - 0 , 2 2 - 0 , 2 0 - 0 , 1 8 - 0 , 1 6

0 , 0 0 0 1 0 0 0 0 , 0 0 2 0 0 0 0 , 0 0 30000,00

BSA V (м/с)

T (мс)

Measurement point:x=R/2; h=3H/4

Calculation procedure of PIV velocity fields

• Velocity fields was measured for four moments of the oscillation period with a step divided by the quarter of period. The velocity field was obtained using statistical averaging of four PIV-samples of the flow got in corresponding moments of time with time lag t = 0, T, 2T, and 3T.

• Cross sections of instantaneous fluid tubes was calculated using the velocity fields measured by the PIV-method with divisible-periodic averaging according to LDA-measurements.

• There are cross sections of 25 instantaneous fluid tubes of constant flow rate Qi,which are presented with a uniform step for the cube root of the flow rate value:constlevel-i = min(Q) + [max(Q) - min(Q)] × (i / 25)3.

• The size of a calculation area was [3R/4; 3R/4] in horizontal and [H/8;7H/8] in vertical directions. It occupies 55 % of the cylinder cross section.

Vortex breakdownLagrangian and Eulerian visualizations of oscillating flows

(I.V. Naumov et al. Thermophysics and Aeromechanics, 2003)

Eulerian visualizations →by PIV and LDA

Eulerian visualizations →by numericalsimulation

t = 0 t = T/4 t = T/2 t = 3T/4

Lagrangian visualizations →

Re=3500, H/R=2

3/4R-3/4R

7H/8

H/8

Experimental investigation of three-dimensional instability in a rotating lid-cylinder flows

K=3

K=4

K=5

K=4

PIVLight sheet – 3 mm

located h/4

Mirror

Investigation of velocity fluctuations by LDA h=3.5 Re= 2000 - 5000, h= 2.5 - 3.5

K=5

Measurement points:

1. x=R/2; z=h/22. x=R/4; z=h/43. x=R/2; z=h/44. x=3R/4; z=h/4

K=4

K=3

K=0

K=1K=2

Experimental investigation of three-dimensional instability in a rotating lid-cylinder flows

h= 3.5 h= 3

Eulerian diagmostics by computation Perturbation of radial velocity

A.Yu. Gelfgat at al. J.Fluid Mech., 2001

z= h/4Re= 2132, ω= - 0.297 Re= 2839, ω= - 0.438

h= 3.5

-0.594 -0.504 -0.415 -0.325 -0.236 -0.147 -0.057 0.032 0.122 0.211 0.301 0.390 0.479 0.569 0.658 0.748

-1 . 0 5 6 -0 . 9 1 7 -0 . 7 7 8 -0 . 6 3 9 -0 . 5 0 0 -0 . 3 6 0 -0 . 2 2 1 -0 . 0 8 2 0 . 0 5 7 0 . 1 9 6 0 . 3 3 5 0 . 4 7 5 0 . 6 1 4 0 . 7 5 3 0 . 8 9 2 1 .-1.226 -1.019 -0.813 -0.607 -0.400 -0.194 0.013 0.219 0.425 0.632 0.838 1.044 1.251 1.457 1.664 1.870

Flow diagnostic by PIV + LDA

Vorticity K=5K=3 K=40

0 2 0 4 0 6 0 8 0 10 0 12 0 14 0 16 0 18 0 2 0 0 2 2 0 2 4 0 2 6 0 2 8 0mm0

2 0

4 0

6 0

8 0

10 0

12 0

14 0

16 0

18 0

2 0 0

2 2 0

mm

0 2 0 4 0 6 0 8 0 10 0 12 0 14 0 16 0 18 0 2 0 0 2 2 0 2 4 0 2 6 0 2 8 0mm0

2 0

4 0

6 0

8 0

10 0

12 0

14 0

16 0

18 0

2 0 0

2 2 0

mm

0 2 0 4 0 6 0 8 0 10 0 12 0 14 0 16 0 18 0 2 0 0 2 2 0 2 4 0 2 6 0 2 8 0mm0

2 0

4 0

6 0

8 0

10 0

12 0

14 0

16 0

18 0

2 0 0

2 2 0

mm

Velocity field’s(azimuthal+radial)

U(x,y) = U(x,y,t) – U (x,y)

Re= 2200, ω= 0.295 Re= 2800, ω= 0.443 Re= 4400, ω= 0.523

Conclusions

Transition from steady to unsteady flow regimes of axial pulsations of vortex breakdown bubbles are investigated. A strong distinction between chaotic Lagrangian visualization and Eulerian diagnostics were found.

Simultaneous PIV and LDA measurements permit to show flow structures with changes in size and position of the vortex breakdown zone for different times in the whole oscillation period. Besides, for the first time, the measurements allowed us to diagnose the flow structure as an intensive axial oscillations of the bubble-like area.

Perfect agreement between Eulerian calculation and experiments reveals the efficiency of the suggested diagnostics method for pulsating vortex flow.

The experimental investigation of the three-dimensional instability of axisymmetric flow gives a very good agreement between the experimental data and computations. It allows us to analyze the transition phenomenon in detail.

REFERENCES

• M.P. Escudier, Observation of the flow produced in cylindrical container by rotating endwall, Exp. Fluids, 1984, Vol. 2, P. 189 - 196.

• Sotiropoulos, F., Websrter, D.R & Lackey, T.C. Experiments on Lagrangiantransport in steady vortex-breakdown bubbles in a confined swirling flow. J. Fluid Mech. 2002, 466, 215-248.

• J.N. Sorensen, Visualization of rotating fluid flow in a closed cylinder, Lyngby[Denmark]: Department of Fluid Mech., 1992, Rep. AFM 92-06.

• W.Z. Shen, J.A. Michelsen, and J.N. Sоrensen, Improved rhie-chow interpolation for unsteady flow computations, AIAA J., 2001, Vol. 39, No.2, P. 2406 - 2409.

• R.J. Adrian, Particle imaging techniques for experimental fluid mechanics, Ann. Rev. Fluid Mech., 1991, Vol. 23, P. 261 - 304.

• T.S. Durrani and C.A. Greated, Laser Systems in Flow Measurement, Plenum Press, N. Y., 1977.

• J.N. Sorensen and E.A. Christensen, Direct numerical simulation of rotating fluid flow in a closed cylinder, Phys. Fluids, 1995, Vol. 7, No. 4, P. 764 - 778.

• I.V. Naumov, V.L. Okulov, K.E. Meyer, J.N. Sorensen and W.Z. Shen, LDA-PIV diagnostics and 3D simulation of oscillating swirl flow in a closed cylindrical container, Thermophysics and Aeromechanics, 2003, Vol. 10, No.2, P. 143-148.

• A. Yu. Gelgaft, P.Z. Bar-Yoseph and A.Solan. Three-dimensional instability of axisymmetric flow in a rotating lid-cylinder enclosure. J. Fluid Mech. 2001, 438, 363-377