Suppression of 3D flow instabilities in tightly packed tube bundles

Suppression of 3D flow instabilities in tightly packed tube bundles Nicholas Kevlahan kevlahan@mcmaster.ca Department of Mathematics & Statistics CSFD, June 13 15 2004 p.1/33

Collaborators CSFD, June 13 15 2004 p.2/33

Collaborators J. Wadsley (McMaster University, Canada) CSFD, June 13 15 2004 p.2/33

Collaborators J. Wadsley (McMaster University, Canada) J. Simon (École MatMéca, France) N. Tonnet (École MatMéca, France) CSFD, June 13 15 2004 p.2/33

Outline 1. Introduction CSFD, June 13 15 2004 p.3/33

Outline 1. Introduction 2. Goals CSFD, June 13 15 2004 p.3/33

Outline 1. Introduction 2. Goals 3. Problem formulation CSFD, June 13 15 2004 p.3/33

Outline 1. Introduction 2. Goals 3. Problem formulation 4. Numerical method CSFD, June 13 15 2004 p.3/33

Outline 1. Introduction 2. Goals 3. Problem formulation 4. Numerical method 5. Results CSFD, June 13 15 2004 p.3/33

Outline 1. Introduction 2. Goals 3. Problem formulation 4. Numerical method 5. Results 6. Conclusions CSFD, June 13 15 2004 p.3/33

Introduction Transition from 2D to 3D flow past an obstacle. CSFD, June 13 15 2004 p.4/33

Introduction Transition from 2D to 3D flow past an obstacle Well understood for flow past a single tube.. CSFD, June 13 15 2004 p.4/33

Introduction Transition from 2D to 3D flow past an obstacle Well understood for flow past a single tube. Not well understood for flow past a tightly packed tube bundle, e.g. spacing P/D = 1.5. CSFD, June 13 15 2004 p.4/33

Introduction (cont.) Transition from 2D to 3D flow past a single tube CSFD, June 13 15 2004 p.5/33

Introduction (cont.) Transition from 2D to 3D flow past a single tube Wake becomes 3D at Re 180 via formation of streamwise vortices with a spacing of about three cylinder diameters (mode A instability) CSFD, June 13 15 2004 p.5/33

Introduction (cont.) Transition from 2D to 3D flow past a single tube Wake becomes 3D at Re 180 via formation of streamwise vortices with a spacing of about three cylinder diameters (mode A instability) At Re 230 a second vortex mode appears (mode B instability), via the formation of irregular streamwise vortices with a spacing of one cylinder diameter (Williamson 1989) CSFD, June 13 15 2004 p.5/33

Introduction (cont.) Mode A instability at Re = 210 Mode B instability at Re = 250 (Thompson, Hourigan & Sheridan 1995) CSFD, June 13 15 2004 p.6/33

Introduction (cont.) As Reynolds number increases further, the wake becomes increasingly complicated until it is completely turbulent. CSFD, June 13 15 2004 p.7/33

Introduction (cont.) What about tightly packed tube bundles? Industrial heat exchanger CSFD, June 13 15 2004 p.8/33

Introduction (cont.) Transition from 2D to 3D flow past a tube bundle CSFD, June 13 15 2004 p.9/33

Introduction (cont.) Transition from 2D to 3D flow past a tube bundle Experiments appear to indicate that the flow and cylinder response remain roughly two-dimensional for Re 180 (Weaver 2001). CSFD, June 13 15 2004 p.9/33

Introduction (cont.) Transition from 2D to 3D flow past a tube bundle Experiments appear to indicate that the flow and cylinder response remain roughly two-dimensional for Re 180 (Weaver 2001). Price et al (1995) find that Strouhal frequency and rms drag do not change with Reynolds number for Re > 150. CSFD, June 13 15 2004 p.9/33

Introduction (cont.) Blevins (1985) demonstrated that acoustic forcing of an isolated cylinder at its Strouhal frequency is able to produce nearly perfect spanwise correlation of pressure for 20 000 Re 40 000. CSFD, June 13 15 2004 p.10/33

Introduction (cont.) Blevins (1985) demonstrated that acoustic forcing of an isolated cylinder at its Strouhal frequency is able to produce nearly perfect spanwise correlation of pressure for 20 000 Re 40 000. He conjectured that similar effects might be observed in tube bundles. CSFD, June 13 15 2004 p.10/33

Introduction (cont.) Blevins (1985) demonstrated that acoustic forcing of an isolated cylinder at its Strouhal frequency is able to produce nearly perfect spanwise correlation of pressure for 20 000 Re 40 000. He conjectured that similar effects might be observed in tube bundles. This confirmed earlier work by Toebes (1969) showing cylinder vibration of A/D 0.125 is required to enforce spanwise correlation. CSFD, June 13 15 2004 p.10/33

Goals 1. Determine which conditions (if any) allow flow to remain 2D for Re > 180. CSFD, June 13 15 2004 p.11/33

Goals 1. Determine which conditions (if any) allow flow to remain 2D for Re > 180. Is tight packing sufficient? CSFD, June 13 15 2004 p.11/33

Goals 1. Determine which conditions (if any) allow flow to remain 2D for Re > 180. Is tight packing sufficient? Is resonant tube motion effective in tube bundles? CSFD, June 13 15 2004 p.11/33

Goals 1. Determine which conditions (if any) allow flow to remain 2D for Re > 180. Is tight packing sufficient? Is resonant tube motion effective in tube bundles? Is tube motion amplitude large enough in tube bundles? CSFD, June 13 15 2004 p.11/33

Goals 1. Determine which conditions (if any) allow flow to remain 2D for Re > 180. Is tight packing sufficient? Is resonant tube motion effective in tube bundles? Is tube motion amplitude large enough in tube bundles? Does tube response remain 2D even if the flow is 3D? CSFD, June 13 15 2004 p.11/33

Goals (cont.) 2. Compare 2D and 3D flows at the same Reynolds number. CSFD, June 13 15 2004 p.12/33

Goals (cont.) 2. Compare 2D and 3D flows at the same Reynolds number. What are the differences between 2D and 3D flows? CSFD, June 13 15 2004 p.12/33

Goals (cont.) 2. Compare 2D and 3D flows at the same Reynolds number. What are the differences between 2D and 3D flows? What are the differences in tube response? CSFD, June 13 15 2004 p.12/33

Goals (cont.) 2. Compare 2D and 3D flows at the same Reynolds number. What are the differences between 2D and 3D flows? What are the differences in tube response? We consider flows at Re = 200 and Re = 1 000 in rotated square tube bundles with P/D = 1.5. CSFD, June 13 15 2004 p.12/33

Problem formulation D = 1 P = 1.5 U D = 1 L = 6 (Re=200) L = 1.5 (Re=1000) CSFD, June 13 15 2004 p.13/33

Problem formulation D = 1 P = 1.5 U D = 1 L = 6 (Re=200) L = 1.5 (Re=1000) Periodic boundary conditions. CSFD, June 13 15 2004 p.13/33

Problem formulation D = 1 P = 1.5 U D = 1 L = 6 (Re=200) L = 1.5 (Re=1000) Periodic boundary conditions. One tube in the periodic domain. CSFD, June 13 15 2004 p.13/33

Problem formulation D = 1 P = 1.5 U D = 1 L = 6 (Re=200) L = 1.5 (Re=1000) Periodic boundary conditions. One tube in the periodic domain. All tubes move in phase (extreme case). CSFD, June 13 15 2004 p.13/33

Problem formulation (cont). No-slip boundary conditions at tube surface Modelled by Brinkman penalization of Navier Stokes equations. u t + (u + U) u + P = ν u u = 0 CSFD, June 13 15 2004 p.14/33

Problem formulation (cont). No-slip boundary conditions at tube surface Modelled by Brinkman penalization of Navier Stokes equations. u t + (u + U) u + P = ν u 1 η χ(x, t)(u + U U o) u = 0 CSFD, June 13 15 2004 p.14/33

Problem formulation (cont.) where the solid is defined by { 1 if x solid, χ(x, t) = 0 otherwise. The upper bound on the global error of this penalization was shown to be (Angot et al. 1999) O(η 1/4 ). We observe an error of O(η). CSFD, June 13 15 2004 p.15/33

Problem formulation (cont.) Cylinder response modelled as a damped harmonic oscillator mẍ o (t) + bẋ o (t) + kx o = F (t), CSFD, June 13 15 2004 p.16/33

Problem formulation (cont.) Cylinder response modelled as a damped harmonic oscillator mẍ o (t) + bẋ o (t) + kx o = F (t), where the force F (t) is calculated from the penalization F (t) = 1 χ(x, t)(u + U U o ) dx. η CSFD, June 13 15 2004 p.16/33

Numerical method Combine two methods: CSFD, June 13 15 2004 p.17/33

Numerical method Combine two methods: 1. Pseudo-spectral method for calculating derivatives and nonlinear terms on the periodic spatial domain. CSFD, June 13 15 2004 p.17/33

Numerical method Combine two methods: 1. Pseudo-spectral method for calculating derivatives and nonlinear terms on the periodic spatial domain. 2. Krylov time scheme for adaptive, stiffly stable integration in time. CSFD, June 13 15 2004 p.17/33

Results Cases: Re resolution L m b k f 200 128 2 64 6.0 5 0 249 0.98 1 000 288 2 96 1.5 5 0 130 1.00 CSFD, June 13 15 2004 p.18/33

Results Cases: Re resolution L m b k f 200 128 2 64 6.0 5 0 249 0.98 1 000 288 2 96 1.5 5 0 130 1.00 Fixed and moving tube simulations are done for each case. CSFD, June 13 15 2004 p.18/33

Results Cases: Re resolution L m b k f 200 128 2 64 6.0 5 0 249 0.98 1 000 288 2 96 1.5 5 0 130 1.00 Fixed and moving tube simulations are done for each case. Moving tubes are tuned to match the Strouhal frequency. CSFD, June 13 15 2004 p.18/33

Results Cases: Re resolution L m b k f 200 128 2 64 6.0 5 0 249 0.98 1 000 288 2 96 1.5 5 0 130 1.00 Fixed and moving tube simulations are done for each case. Moving tubes are tuned to match the Strouhal frequency. 2D simulations are also done for each case. CSFD, June 13 15 2004 p.18/33

Re = 200 results Vorticity at t = 15 (a) Fixed cylinder, 3 components. (b) Fixed cylinder, spanwise vorticity. (c) Moving cylinder, spanwise vorticity. CSFD, June 13 15 2004 p.19/33

Re = 200 results (cont.) Lift 15 15 Fixed 10 5 (a) 10 5 (b) C L 0 C L 0 5 5 10 10 15 0 2 4 6 8 10 t 15 40 42 44 46 48 50 t Moving 50 (c) 50 (d) C L 0 C L 0 50 0 2 4 6 8 10 t 2D, blue 3D, red 50 40 42 44 46 48 50 t CSFD, June 13 15 2004 p.20/33

Re = 200 results (cont.) Drag Fixed Cd 15 10 5 (a) Cd 10 9 8 7 6 5 (b) 4 0 0 2 4 6 8 10 t 3 40 42 44 46 48 50 t Moving Cd 25 20 15 10 Cd 25 20 15 10 5 (c) 0 0 2 4 6 8 10 t 5 2D, blue 3D, red (d) 0 40 42 44 46 48 50 t CSFD, June 13 15 2004 p.21/33

Re = 200 results (cont.) Cylinder motion 0.3 0.2 (a) 0.1 A/D 0 2D, blue 3D, red 0.1 0.2 2 1 0 5 10 15 20 25 30 35 40 45 50 t (b) V o 0 1 2 0 5 10 15 20 25 30 35 40 45 50 t CSFD, June 13 15 2004 p.22/33

Re = 200 results (cont.) Strouhal frequencies Case Peak frequency 2D, fixed 1.32 3D, fixed 1.18 2D, moving 0.95 3D, moving 0.95 CSFD, June 13 15 2004 p.23/33

Re = 1 000 results Vorticity at t = 15 Fixed (a) (b) (c) Moving (d) (e) (f) Spanwise Streamwise Transverse CSFD, June 13 15 2004 p.24/33

Re = 1 000 results (cont.) Lift and drag 40 40 30 (a) 30 (b) 20 20 C D 10 C D 10 0 0 2D, blue 3D, red 10 20 10 0 5 10 15 20 (c) t 10 30 20 10 0 5 10 15 20 (d) t C L 0 C L 0 10 10 20 20 30 0 5 10 15 20 t Fixed 0 5 10 15 20 t Moving CSFD, June 13 15 2004 p.25/33

Re = 1 000 results (cont.) Cylinder motion 0.2 (a) A/D 0 0.2 2D, blue 3D, red 0 5 10 15 20 t 2 (b) V o 0 2 0 5 10 15 20 t CSFD, June 13 15 2004 p.26/33

Re = 1 000 results (cont.) Lift spectra 1 0.9 Fixed Moving 1 0.9 0.8 (a) 0.8 0.7 0.7 0.6 0.6 Energy 0.5 0.4 Energy 0.5 0.4 0.3 0.3 0.2 0.2 0.1 0.1 0 0 0.25 0.5 0.75 1 1.25 1.5 1.75 2 f Two-dimensional 0 0 0.5 1 1.5 2 f Three-dimensional CSFD, June 13 15 2004 p.27/33

Re = 1 000 results (cont.) Spectra of cylinder oscillation 1 0.9 Energy 0.8 0.7 0.6 0.5 0.4 2D, blue 3D, red 0.3 0.2 0.1 0 0.5 0.6 0.7 0.8 0.9 1 1.1 f CSFD, June 13 15 2004 p.28/33

Re = 1 000 results (cont.) Strouhal frequencies Case Peak frequency 2D, fixed 1.06 3D, fixed 0.95 2D, moving 0.75 3D, moving 0.88, 0.68 CSFD, June 13 15 2004 p.29/33

Conclusions Suppression of 3D flow instabilities CSFD, June 13 15 2004 p.30/33

Conclusions Suppression of 3D flow instabilities 1. At Re = 200 cylinder vibration suppresses 3D fluid instability (A/D = 0.23 > 0.125). CSFD, June 13 15 2004 p.30/33

Conclusions Suppression of 3D flow instabilities 1. At Re = 200 cylinder vibration suppresses 3D fluid instability (A/D = 0.23 > 0.125). 2. Tight packing alone does not suppress instability. CSFD, June 13 15 2004 p.30/33

Conclusions Suppression of 3D flow instabilities 1. At Re = 200 cylinder vibration suppresses 3D fluid instability (A/D = 0.23 > 0.125). 2. Tight packing alone does not suppress instability. 3. At Re = 1 000 cylinder vibration is insufficient (A/D 0.05 < 0.125) to suppress 3D fluid instability. CSFD, June 13 15 2004 p.30/33

Conclusions Suppression of 3D flow instabilities 1. At Re = 200 cylinder vibration suppresses 3D fluid instability (A/D = 0.23 > 0.125). 2. Tight packing alone does not suppress instability. 3. At Re = 1 000 cylinder vibration is insufficient (A/D 0.05 < 0.125) to suppress 3D fluid instability. However, the 2D and 3D Strouhal frequencies and cylinder response differ only slightly. CSFD, June 13 15 2004 p.30/33

Conclusions (cont.) Suppression of 3D flow instabilities (cont.) CSFD, June 13 15 2004 p.31/33

Conclusions (cont.) Suppression of 3D flow instabilities (cont.) 4. Moving cylinder has less effect at Re = 1 000 than at Re = 200. CSFD, June 13 15 2004 p.31/33

Conclusions (cont.) Suppression of 3D flow instabilities (cont.) 4. Moving cylinder has less effect at Re = 1 000 than at Re = 200. 5. Moving cylinder has less effect in 3D than in 2D. CSFD, June 13 15 2004 p.31/33

Conclusions (cont.) Effect of 3D vorticity compared with 2D flow CSFD, June 13 15 2004 p.32/33

Conclusions (cont.) Effect of 3D vorticity compared with 2D flow 1. Reduces lift amplitude by about three times. CSFD, June 13 15 2004 p.32/33

Conclusions (cont.) Effect of 3D vorticity compared with 2D flow 1. Reduces lift amplitude by about three times. 2. Reduces drag amplitude by about three times, and drag is always positive. CSFD, June 13 15 2004 p.32/33

Conclusions (cont.) Effect of 3D vorticity compared with 2D flow 1. Reduces lift amplitude by about three times. 2. Reduces drag amplitude by about three times, and drag is always positive. In fact, drag is roughly constant. CSFD, June 13 15 2004 p.32/33

Conclusions (cont.) Effect of 3D vorticity compared with 2D flow 1. Reduces lift amplitude by about three times. 2. Reduces drag amplitude by about three times, and drag is always positive. In fact, drag is roughly constant. 3. Reduces cylinder amplitude by about two times. CSFD, June 13 15 2004 p.32/33

Re = 10 4, t = 3.5, P/D = 1.5 CSFD, June 13 15 2004 p.33/33