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Turbulence Generated by Fractal Trees

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Turbulence Generated by Fractal Trees Turbulence generated by Fractal Trees PIV Measurements and Comparison with numerical Data Master Thesis Submitted by: Marc Dreissigacker Date of Birth: September 26, 1990 Course: Physikalische Ingenieurwissenschaft First Supervisor: Prof. Dr. sc. techn. habil. Jörn Sesterhenn Second Supervisor: Dr.-Ing. Thomas Engels Date: May 12, 2017 Eidesstattliche Erklärung Hiermit erkläre ich, dass ich die vorliegende Arbeit selbstständig und eigen- händig sowie ohne unerlaubte fremde Hilfe und ausschließlich unter Ver- wendung der aufgeführten Quellen und Hilfsmittel angefertigt habe. Statutory Declaration I hereby declare that I have authored this thesis independently, that I have not used other than the declared sources / resources, and that I have explic- itly marked all material which has been quoted either literally or by content from the used sources. Berlin, Marc Dreissigacker CONTENTS Abstract xv 1 Introduction 17 2 Literature Review: Fractal Tree Turbulence 19 3 Fractal Trees 23 3.1 Design & Choice of Parameters . 24 3.1.1 First Approach in MATLAB . 25 3.1.2 Vortex Shedding Frequency and Branch Diameters . 28 3.1.3 Generation of 3D-STL-mask with FLUSI . 30 3.2 3D-printing and Assembly ..................... 33 3.2.1 Preparation in SOLIDWORKS . 33 3.2.2 Printing the H-tree ..................... 35 3.2.3 Printing the Pyramid- & Spherical Tree . 38 4 Experimental Setup & Validation 41 4.1 Windtunnnel ............................. 41 4.1.1 Blockage ........................... 43 4.2 PIV System .............................. 44 4.3 Analysis Software PIVLAB ..................... 46 4.4 Validation Cases ........................... 47 5 Experimental Results 55 5.1 Pyramid-tree ............................. 55 5.2 Large Branch of the spherical tree . 64 5.3 Small Branch of the spherical tree . 69 5.4 Small Branch of the Pyramid-tree . 73 5.5 Young Spruce Tree ......................... 77 5.6 Parts of a yew tree .......................... 79 6 Numerical Simulations 87 6.1 Spherical Tree - Simulation & Experiment . 88 6.2 Pyramid-tree - Simulation & Experiment . 111 7 Conclusion & Outlook 137 Appendices 141 Bibliography 147 iii LIST OF FIGURES 3.1.1 H-tree created in MATLAB ..................... 26 3.1.2 Pyramid-tree created in MATLAB . 26 3.1.3 Spherical tree created in MATLAB . 27 3.1.4 Evolution of the generation of the H-tree from J = 1 − 9 . 27 3.1.5 H-tree created with FLUSI ..................... 31 3.1.6 Pyramid-tree created with FLUSI . 31 3.1.7 Spherical tree created with FLUSI . 32 3.2.1 H-tree created with SOLIDWORKS . 33 3.2.2 Pyramid-tree created with SOLIDWORKS . 34 3.2.3 Spherical tree created with SOLIDWORKS . 34 3.2.4 From the 3D-model to the printed component . 36 3.2.5 Surface structure of a printed component . 36 3.2.6 The printed and assembled H-tree . 37 3.2.7 Densely packed building volumes . 38 3.2.8 The printed and assembled Pyramid-tree . 38 3.2.9 The printed and assembled Spherical tree . 39 3.2.10 The small trees for more detailed studies . 40 3.2.11 The small trees for more detailed studies . 40 4.1.1 Model of the windtunnel ...................... 42 4.1.2 The experimental setup ....................... 42 4.2.1 The principle of PIV, adapted from [28] . 44 4.4.1 Orientation of the planes for the validation case . 48 4.4.2 Velocity scatter-plots, empty wind-tunnel, with and without flow, different interrogation windows . 50 v 4.4.3 Velocity in the empty channel, no flow, 16 px, validation plane 1 51 4.4.4 Velocity in the empty channel, no flow, different interrogation windows, validation plane 2 .................... 52 4.4.5 Velocity magnitudes for the empty channel with flow, 16 px . 53 4.4.6 Histogram for the empty channel with flow, 16 px, validation plane 1 ................................ 53 4.4.7 Histogram for the empty channel with flow, 16 px, validation plane 2 ................................ 54 4.4.8 Turbulence intensities for the empty channel with flow, 16 px . 54 5.1.1 Overview of the PIV measurements for the Pyramid-tree, each plane shows the average velocity magnitude . 56 5.1.2 Detailed view in flow direction, tree opacity 30% . 56 5.1.3 Instantaneous velocity field at z = 14 cm . 57 5.1.4 Instantaneous velocity field at z = 24 cm . 58 5.1.5 Instantaneous velocity field at z = 29 cm . 59 5.1.6 Instantaneous velocity field at z = 34 cm . 60 5.1.7 Overview of the measured turbulence intensity for the Pyramid- tree .................................. 61 5.1.8 Turbulence intensity behind the Pyramid-tree . 62 5.1.9 Contours of Tu = 7.5, 10, 12.5, 15 % from the interpolated data 62 5.1.10 Areas of higher Tu behind distinct (clusters of) branches, Tu = 7.5, 10, 12.5, 15 % ......................... 63 5.1.11 Top view on the contour-plot, Tu = 7.5, 10, 12.5, 15 % . 63 5.2.1 Overview of the average velocity for the large spherical branch 64 5.2.2 Overview of the turbulence intensity for the large spherical branch ................................ 65 5.2.3 Locations of the selected planes . 65 5.2.4 The selected planes for a more detailed study of Tu . 66 5.2.5 Contourplot of Tu from interpolated dataset, Tu = 5, 10, 15, 20, 25 % .................................. 68 5.2.6 Visualization of high Tu behind the trunk and close to the tree 68 5.3.1 Overview of the average velocity for the small spherical tree . 69 5.3.2 Overview of the turbulence intensity for the small spherical tree 69 5.3.3 Three representations of the isosurfaces for Tu = 5, 10, 15, 20 % for the small spherical tree ..................... 70 5.3.4 View of Tu (note the low values numbers in the very middle) behind the trunk’s tip ........................ 71 5.3.5 Z-component of the time-averaged vorticity for the small spher- ical tree ................................ 72 5.4.1 Overview of the average velocity for the small Pyramid-tree . 73 5.4.2 Overview of the turbulence intensity for the small Pyramid-tree 74 5.4.3 Three representations of the iso-surfaces for Tu = 5, 10, 15m 20 % for t he small Pyramid-tree . 75 5.4.4 Z-component of the time-averaged vorticity for the small Pyramid- tree .................................. 76 5.5.1 The spruce tree for correlations with the printed models . 77 5.5.2 Overview of the average velocity magnitude for the spruce . 78 5.5.3 Overview of the turbulence intensity for the spruce . 78 5.6.1 The yew branch without (left) and with (right) flow, view from the top ................................ 79 ◦ 5.6.2 The yew branch bent by 30 , flow from the left . 80 5.6.3 The two yew branches, views from the side and top . 80 5.6.4 Overview of the average velocity magnitude for the single yew branch .............................. 81 5.6.5 Overview of the turbulence intensity for the single yew branch 82 5.6.6 Turbulence intensity for the single yew branch at z = 8.5 cm . 82 5.6.7 Turbulence intensity for the single yew branch at z = 8.5 cm, further downstream ......................... 83 5.6.8 Overview of the average velocity magnitude for the two branches 84 5.6.9 Overview of the turbulence intensity for the two branches . 84 5.6.10 Velocity magnitude for the two branches . 85 5.6.11 Turbulence Intensity for the two branches . 85 6.1.1 Location of the compared planes, side view . 88 6.1.2 Location of the compared planes, isometric view . 88 6.1.3 Comparison between the 2D- and 3D average velocity magni- tude, z = 25 cm ........................... 89 6.1.4 Comparison of two instantaneous velocity fields, z = 25 mm . 91 6.1.5 Comparison of the average velocity, z = 25 mm . 92 6.1.6 Comparison of Tu, z = 25 mm ................... 93 6.1.7 Comparison of the average vorticity (z-component), z = 25 mm 94 6.1.8 Comparison of two instantaneous velocity fields, z = 40 mm . 95 6.1.9 Comparison of the average velocity, z = 40 mm . 96 6.1.10 Comparison of Tu, z = 40 mm . 97 6.1.11 Comparison of the average vorticity (z-component), z = 40 mm 98 6.1.12 Comparison of two instantaneous velocity fields, z = 45 mm 99 6.1.13 Comparison of the average velocity, z = 45 mm . 100 6.1.14 Comparison of Tu, z = 45 mm . 101 6.1.15 Comparison of the average vorticity (z-component), z = 45 mm102 6.1.16 Comparison of two instantaneous velocity fields, z = 50 mm 103 6.1.17 Comparison of the average velocity, z = 50 mm . 104 6.1.18 Comparison of Tu, z = 50 mm . 105 6.1.19 Comparison of the average vorticity (z-component), z = 50 mm106 6.1.20 Comparison of two instantaneous velocity fields, z = 55 mm 107 6.1.21 Comparison of the average velocity, z = 55 mm . 108 6.1.22 Comparison of Tu, z = 55 mm . 109 6.1.23 Comparison of the average vorticity (z-component), z = 55 mm110 6.2.1 Location of the compared planes, side view . 111 6.2.2 Location of the compared planes, isometric view . 111 6.2.3 Comparison of two instantaneous velocity fields, z = 10 mm . 113 6.2.4 Comparison of the average velocity, z = 10 mm . 114 6.2.5 Comparison of Tu, z = 10 mm . 115 6.2.6 Comparison of the average vorticity (z-component), z = 10 mm 116 6.2.7 Comparison of two instantaneous velocity fields, z = 25 mm . 117 6.2.8 Comparison of the average velocity, z = 25 mm .
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