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 2 Ω ⋅ R = Re ν Aspect ratio: h = H/R H – height of cavity R – disk radius Ω – angular velocity ν – fluid viscosity Disk rotation error < 0.1%. Gap ~ 0.3 mm. • 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/cm 3 ) Escudier diagram •The working fluid: 83% water/glycerin mixture (Exps. Fluids. 1984 )
Visualization in a cylindrical container for different Re Sørensen J.N. DTU, Lyngby, Denmark (Rep. AFM 1992 ) H/R=2 seeding particles were Rhodamine B ~ 50 µm 2002 2103 2204 2301 2404 2505 2598 2707 2805 2896 3004 3500 4014 4996 5981 7007
Comparison of visualization and numerical calculation for H/R = 2 and different Reynolds numbers Eulerian visualizations by numerical simulation steady bubble flow (Re = 2043) t = 0 t = T /2 Lagrangian chaotic visualizations PIV visualization Unsteady regime Sotiropoulos F. et al. J.Fluid Mech. 2002 with strong bubble oscillation (Re = 3500)
Experimental Techniques 8 PIV: 3 1 4 laser Argon Ion • Pulsed Nd:YAG laser ( λ =532 nm, 100 mJ, 10 ns,10 Hz) • Light sheet - 1.4 mm 2 • CCD camera: Kodak Mega Plus ES 1.0 5 Ω (1008 × 1018 pixel) 9 LDA CCD probe • Size of calculation area: 32x32 pixels with 25% overlapping • Dantec PIV 2100 processor 7 10 6 PIV BSA LDA: 2100 Dantec 2D Fiberflow LDA 2 W Argon-Ion laser Diameter of gauge 112 mm (Focal length 500 mm, λ =514,5 nm) Probing field: 0.12×0.12×1.52 mm. Frequency shift 40 Mhz BSA57N2 (Burst specter analyzer) signal processor
Investigation of velocity fluctuations by Laser Doppler Anemometer f fluid/ Ω disk Re Vel-count Vel-Mean Vel-RMS F fluid [m/s] [m/s] [Hz] 2600 11122 -0,21 0,008 0.45 0.23 3000 12471 -0,24 0,01 0.52 0.23 3500 17477 -0,28 0,018 0.65 0.24 4000 16444 -0,31 0,023 0.88 0.29 4500 11258 -0,34 0,029 1.02 0.29 5000 13073 -0,38 0,023 1.12 0.29 BSA V ( м / с ) - 0 , 1 6 - 0 , 1 8 - 0 , 2 0 - 0 , 2 2 - 0 , 2 4 - 0 , 2 6 - 0 , 2 8 - 0 , 3 0 - 0 , 3 2 - 0 , 3 4 - 0 , 3 6 - 0 , 3 8 - 0 , 4 0 0 , 0 0 0 1 0 0 0 0 , 0 0 2 0 0 0 0 , 0 0 30000,00 Re = 3500 Spectrum [BSA1 Vel] [x²/Hz] T ( мс ) 1 E - 0 0 2 (unsteady flow) 1 E - 0 0 2 9 E - 0 0 3 8 E - 0 0 3 7 E - 0 0 3 6 E - 0 0 3 5 E - 0 0 3 4 E - 0 0 3 Measurement point: 3 E - 0 0 3 2 E - 0 0 3 1 E - 0 0 3 x=R/2; h=3H/4 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 Frequency [Hz] Fluctuations of the breakdown area exhibit a clear periodic character
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 , 2 T , and 3 T . • 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 Q i , • which are presented with a uniform step for the cube root of the flow rate value: const level -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 breakdown Lagrangian and Eulerian visualizations of oscillating flows ( I.V. Naumov et al. Thermophysics and Aeromechanics , 2003) Re=3500, H/R=2 Lagrangian visualizations → t = 0 t = T /4 t = T /2 t = 3 T /4 Eulerian visualizations → by PIV and LDA 7H/8 Eulerian visualizations → by numerical simulation H/8 -3/4R 3/4R
Experimental investigation of three-dimensional instability in a rotating lid-cylinder flows K=5 PIV Light sheet – 3 mm K=4 located h/4 K=4 Mirror K=3 Investigation of velocity fluctuations by LDA h=3.5 Re= 2000 - 5000, h= 2.5 - 3.5 K=5 K=4 Measurement points: K=3 1. x=R/2; z=h/2 K=0 2. x=R/4; z=h/4 3. x=R/2; z=h/4 K=1 4. x=3R/4; z=h/4 K=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/4 Re= 2132, ω = - 0.297 Re= 2839, ω = - 0.438 h= 3.5 Flow diagnostic by PIV + LDA K=3 K=4 K=5 Vorticity -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 -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 . 0 -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 mm mm mm 2 2 0 2 2 0 2 2 0 2 0 0 2 0 0 2 0 0 18 0 18 0 18 0 16 0 16 0 16 0 14 0 14 0 14 0 Velocity field’s 12 0 12 0 12 0 10 0 10 0 10 0 (azimuthal+radial) 8 0 8 0 8 0 6 0 6 0 6 0 4 0 4 0 4 0 U(x,y) = U(x,y,t) – U (x,y) 2 0 2 0 2 0 0 0 0 0 2 0 4 0 6 0 8 0 10 0 12 0 14 0 16 0 18 0 2 0 0 2 20 2 4 0 2 6 0 mm 2 8 0 0 2 0 4 0 6 0 8 0 10 0 12 0 14 0 16 0 18 0 2 0 0 2 20 2 4 0 2 6 0 mm 2 8 0 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 mm 2 8 0 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.
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