Suppression of 3D flow instabilities in tightly packed tube bundles
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1 Suppression of 3D flow instabilities in tightly packed tube bundles Nicholas Kevlahan Department of Mathematics & Statistics CSFD, June p.1/33
2 Collaborators CSFD, June p.2/33
3 Collaborators J. Wadsley (McMaster University, Canada) CSFD, June p.2/33
4 Collaborators J. Wadsley (McMaster University, Canada) J. Simon (École MatMéca, France) N. Tonnet (École MatMéca, France) CSFD, June p.2/33
5 Outline 1. Introduction CSFD, June p.3/33
6 Outline 1. Introduction 2. Goals CSFD, June p.3/33
7 Outline 1. Introduction 2. Goals 3. Problem formulation CSFD, June p.3/33
8 Outline 1. Introduction 2. Goals 3. Problem formulation 4. Numerical method CSFD, June p.3/33
9 Outline 1. Introduction 2. Goals 3. Problem formulation 4. Numerical method 5. Results CSFD, June p.3/33
10 Outline 1. Introduction 2. Goals 3. Problem formulation 4. Numerical method 5. Results 6. Conclusions CSFD, June p.3/33
11 Introduction Transition from 2D to 3D flow past an obstacle. CSFD, June p.4/33
12 Introduction Transition from 2D to 3D flow past an obstacle Well understood for flow past a single tube.. CSFD, June p.4/33
13 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 p.4/33
14 Introduction (cont.) Transition from 2D to 3D flow past a single tube CSFD, June p.5/33
15 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 p.5/33
16 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 p.5/33
17 Introduction (cont.) Mode A instability at Re = 210 Mode B instability at Re = 250 (Thompson, Hourigan & Sheridan 1995) CSFD, June p.6/33
18 Introduction (cont.) As Reynolds number increases further, the wake becomes increasingly complicated until it is completely turbulent. CSFD, June p.7/33
19 Introduction (cont.) What about tightly packed tube bundles? Industrial heat exchanger CSFD, June p.8/33
20 Introduction (cont.) Transition from 2D to 3D flow past a tube bundle CSFD, June p.9/33
21 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 p.9/33
22 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 p.9/33
23 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 Re CSFD, June p.10/33
24 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 Re He conjectured that similar effects might be observed in tube bundles. CSFD, June p.10/33
25 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 Re He conjectured that similar effects might be observed in tube bundles. This confirmed earlier work by Toebes (1969) showing cylinder vibration of A/D is required to enforce spanwise correlation. CSFD, June p.10/33
26 Goals 1. Determine which conditions (if any) allow flow to remain 2D for Re > 180. CSFD, June p.11/33
27 Goals 1. Determine which conditions (if any) allow flow to remain 2D for Re > 180. Is tight packing sufficient? CSFD, June p.11/33
28 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 p.11/33
29 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 p.11/33
30 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 p.11/33
31 Goals (cont.) 2. Compare 2D and 3D flows at the same Reynolds number. CSFD, June p.12/33
32 Goals (cont.) 2. Compare 2D and 3D flows at the same Reynolds number. What are the differences between 2D and 3D flows? CSFD, June p.12/33
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 p.12/33
34 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 = in rotated square tube bundles with P/D = 1.5. CSFD, June p.12/33
35 Problem formulation D = 1 P = 1.5 U D = 1 L = 6 (Re=200) L = 1.5 (Re=1000) CSFD, June p.13/33
36 Problem formulation D = 1 P = 1.5 U D = 1 L = 6 (Re=200) L = 1.5 (Re=1000) Periodic boundary conditions. CSFD, June p.13/33
37 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 p.13/33
38 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 p.13/33
39 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 p.14/33
40 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 p.14/33
41 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 p.15/33
42 Problem formulation (cont.) Cylinder response modelled as a damped harmonic oscillator mẍ o (t) + bẋ o (t) + kx o = F (t), CSFD, June p.16/33
43 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 p.16/33
44 Numerical method Combine two methods: CSFD, June p.17/33
45 Numerical method Combine two methods: 1. Pseudo-spectral method for calculating derivatives and nonlinear terms on the periodic spatial domain. CSFD, June p.17/33
46 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 p.17/33
47 Results Cases: Re resolution L m b k f CSFD, June p.18/33
48 Results Cases: Re resolution L m b k f Fixed and moving tube simulations are done for each case. CSFD, June p.18/33
49 Results Cases: Re resolution L m b k f Fixed and moving tube simulations are done for each case. Moving tubes are tuned to match the Strouhal frequency. CSFD, June p.18/33
50 Results Cases: Re resolution L m b k f 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 p.18/33
51 Re = 200 results Vorticity at t = 15 (a) Fixed cylinder, 3 components. (b) Fixed cylinder, spanwise vorticity. (c) Moving cylinder, spanwise vorticity. CSFD, June p.19/33
52 Re = 200 results (cont.) Lift Fixed 10 5 (a) 10 5 (b) C L 0 C L t t Moving 50 (c) 50 (d) C L 0 C L t 2D, blue 3D, red t CSFD, June p.20/33
53 Re = 200 results (cont.) Drag Fixed Cd (a) Cd (b) t t Moving Cd Cd (c) t 5 2D, blue 3D, red (d) t CSFD, June p.21/33
54 Re = 200 results (cont.) Cylinder motion (a) 0.1 A/D 0 2D, blue 3D, red t (b) V o t CSFD, June p.22/33
55 Re = 200 results (cont.) Strouhal frequencies Case Peak frequency 2D, fixed D, fixed D, moving D, moving 0.95 CSFD, June p.23/33
56 Re = results Vorticity at t = 15 Fixed (a) (b) (c) Moving (d) (e) (f) Spanwise Streamwise Transverse CSFD, June p.24/33
57 Re = results (cont.) Lift and drag (a) 30 (b) C D 10 C D D, blue 3D, red (c) t (d) t C L 0 C L t Fixed t Moving CSFD, June p.25/33
58 Re = results (cont.) Cylinder motion 0.2 (a) A/D D, blue 3D, red t 2 (b) V o t CSFD, June p.26/33
59 Re = results (cont.) Lift spectra Fixed Moving (a) Energy Energy f Two-dimensional f Three-dimensional CSFD, June p.27/33
60 Re = results (cont.) Spectra of cylinder oscillation Energy D, blue 3D, red f CSFD, June p.28/33
61 Re = results (cont.) Strouhal frequencies Case Peak frequency 2D, fixed D, fixed D, moving D, moving 0.88, 0.68 CSFD, June p.29/33
62 Conclusions Suppression of 3D flow instabilities CSFD, June p.30/33
63 Conclusions Suppression of 3D flow instabilities 1. At Re = 200 cylinder vibration suppresses 3D fluid instability (A/D = 0.23 > 0.125). CSFD, June p.30/33
64 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 p.30/33
65 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 = cylinder vibration is insufficient (A/D 0.05 < 0.125) to suppress 3D fluid instability. CSFD, June p.30/33
66 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 = 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 p.30/33
67 Conclusions (cont.) Suppression of 3D flow instabilities (cont.) CSFD, June p.31/33
68 Conclusions (cont.) Suppression of 3D flow instabilities (cont.) 4. Moving cylinder has less effect at Re = than at Re = 200. CSFD, June p.31/33
69 Conclusions (cont.) Suppression of 3D flow instabilities (cont.) 4. Moving cylinder has less effect at Re = than at Re = Moving cylinder has less effect in 3D than in 2D. CSFD, June p.31/33
70 Conclusions (cont.) Effect of 3D vorticity compared with 2D flow CSFD, June p.32/33
71 Conclusions (cont.) Effect of 3D vorticity compared with 2D flow 1. Reduces lift amplitude by about three times. CSFD, June p.32/33
72 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 p.32/33
73 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 p.32/33
74 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 p.32/33
75 Re = 10 4, t = 3.5, P/D = 1.5 CSFD, June p.33/33
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