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Drag on Object Moving Through Foam Chinwha Chung Iowa State University Iowa State University Capstones, Theses and Retrospective Theses and Dissertations Dissertations 1991 Drag on object moving through foam Chinwha Chung Iowa State University Follow this and additional works at: https://lib.dr.iastate.edu/rtd Part of the Mechanical Engineering Commons Recommended Citation Chung, Chinwha, "Drag on object moving through foam " (1991). Retrospective Theses and Dissertations. 9606. https://lib.dr.iastate.edu/rtd/9606 This Dissertation is brought to you for free and open access by the Iowa State University Capstones, Theses and Dissertations at Iowa State University Digital Repository. It has been accepted for inclusion in Retrospective Theses and Dissertations by an authorized administrator of Iowa State University Digital Repository. For more information, please contact [email protected]. INFORMATION TO USERS This manuscript has been reproduced from the microfilm master. UMI films the text directly from the original or copy submitted. Thus, some thesis and dissertation copies are in typewriter face, while others may be from any type of computer printer. The quality of this reproduction is dependent upon the quality of the copy submitted. Broken or indistinct print, colored or poor quality illustrations and photographs, print bleedthrough, substandard margins, and improper alignment can adversely affect reproduction. In the unlikely event that the author did not send UMI a complete manuscript and there are missing pages, these will be noted. Also, if unauthorized copyright material had to be removed, a note will indicate the deletion. Oversize materials (e.g., maps, drawings, charts) are reproduced by sectioning the original, beginning at the upper left-hand corner and continuing from left to right in equal sections with small overlaps. Each original is also photographed in one exposure and is included in reduced form at the back of the book. Photographs included in the original manuscript have been reproduced xerographically in this copy. Higher quality 6" x 9" black and white photographic prints are available for any photographs or illustrations appearing in this copy for an additional charge. Contact UMI directly to order. University Microfilms International A Bell & Howell Information Company 300 North Zeeb Road, Ann Arbor, Ml 48106-1346 USA 313/761-4700 800/521-0600 Order Number 9207240 Drag on object moving through foam Chung, Chinwha, Ph.D. Iowa State University, 1991 UMI 300N.ZeebRd. Ann Aibor, MI 48106 Drag on object moving through foam by Chinwha Chung A Dissertation Submitted to the Graduate Faculty in Partial Fulfillment of the Requirements for the Degree of DOCTOR OF PHILOSOPHY Department: Aerospace Engineering and Engineering Mechanics Major: Engineering Mechanics Approved: Members of the Committee: Signature was redacted for privacy. In Charge of Major Work Signature was redacted for privacy. Signature was redacted for privacy. For the Major Department Signature was redacted for privacy. For the Graduate College Iowa State University Ames, Iowa 1991 Copyright © Chinwha Chung, 1991. All rights reserved. ii TABLE OF CONTENTS ACKNOWLEDGEMENTS xii CHAPTER 1. INTRODUCTION 1 CHAPTER 2. LITERATURE REVIEW 8 2.1. Dilute Gas Bubble Suspensions 9 2.2. Foam Structure 11 2.3. Slip at the Wall 11 2.4. Yield Stress and Viscosity Function 22 CHAPTER 3. EXPERIMENTAL APPARATUS 30 3.1. Experimental Set-up 30 3.1.1. Test section 32 3.1.2. Foam velocity control 32 3.1.3. Drag force measurement 34 3.1.4. Recording data 37 3.2. Foam Property Measurement Devices 38 3.2.1. Drainage rate measurement device 39 3.2.2. Quality (gas fraction) measurement device 39 3.2.3. Viscosity measurement devices 41 3.2.4. Surface tension measurement device 41 iii 3.3. Specimens 42 3.3.1. Smooth surface models 42 3.3.2. Rough surface models 42 CHAPTER 4. PROCEDURES 47 4.1. Preparation of the Soap-water Solution 47 4.2. Preparation of the Steady-state Foam Flow 47 4.3. Foam Property Measurement 48 4.3.1 Drainage rate measurement 48 4.3.2. Foam quality measurement 48 4.3.3. Liquid viscosity measurement 49 4.3.4. Surface tension measurement -50 4.4. Drag Force Measurement on Specimens 50 4.5. Investigating Wall Effect 51 4.6. Storing Experimental Data 51 4.7. Effective Viscosity Measurement on Dispersed Gas Bubble Suspensions 53 CHAPTER 5. THEORY 54 5.1. Highly Concentrated Emulsions 54 5.2. Flow Past a Sphere in a Bingham Plastic 56 5.3. Wall Effect 63 CHAPTER 6. RESULTS 67 6.1. Smooth Surfaced Models 68 6.1.1. General observations 68 6.1.2. Shape dependency 102 6.2. Drainage Rate 106 iv 6.3. Wall Effect 115 6.4. Comparison with Existing Foam Theory 120 6.5. Rough Surfaces '. 123 6.6. Dispersed Gas Bubble Suspensions 131 CHAPTER 7. CONCLUSION 139 Summary 139 Recommendations 143 BIBLIOGRAPHY 146 APPENDIX A. EXPERIMENTAL DATA 150 V LIST OF TABLES Table 3.1: Smooth surface models 43 Table 5.1: Solution parameters for selected values of Yg. From Beris et al. [1] 58 Table 6.1: The foam used for smooth specimen tests 68 Table 6.2: Constants for the curve fit equation for foam /Z? = SCFA . 88 Table 6.3: Constants for the curve fit equation for foam ID = SCFB . 89 Table 6.4: Constants for the curve fit equation for foam ID — SCFC . 89 Table 6.5: Constants for the curve fit equation for foam ID = SCFD . 90 Table 6.6: Constants for the curve fit equation for foam ID = SCFE . 90 Table 6.7: Constants for the curve equation for foam ID = SCFF ... 91 Table 6.8: Constants for the curve equation for foam ID = SCFG ... 91 Table 6.9: The drag force on different sizes of spheres and the drag force ratios for foam ID — SCFC and SCFD 93 Table 6.10: The wall shear stress on flat plates for foam ID — SCFF and SCFG at foam velocity U = 0.3 mfsec. (plate length, I, is in mm, Fjy is in iV, and r is in N/m'^) 105 vi Table 6.11: The apparent viscosity ratio for different expansion ratios. The viscosity and surface tension of a liquid phase are 210.6 Cst and 0.0627 lY/m 134 Table A.l: Raw drag-velocity data for smooth surfaced models 150 Table A.2: Experimental data for wall effect for 38.1 mm diameter sphere. (fi = 2.8yA0-^Ns/m^, (j) = 0.8) 164 Table A.3: Experimental data for rough surfaced 38.1 mm diameter sphere. (// = 7.1 XlO"-'^(f> = 0.8) 165 Table A.4: Experimental data for rough surfaced 101.6 mm-long flat plate. (/i = 7.1 <6 = 0.8) 166 Table A..5: Experimental data for dilute gas bubble suspensions. (/« = 210.6 X IQ-^NsIm'^) 167 vii LIST OF FIGURES Figure 1.1: Open cell foam: (a) Two-dimensional structure representation (b) Micrograph of a sample 2 Figure 1.2: Closed cell foam: (a) Two-dimensional structure representa­ tion (b) Micrograph of a sample 3 Figure 2.1: Two-dimensional representation of the Plateau border .... 12 Figure 2.2: The conceptual two-dimensional foam flow model 14 Figure 2.3: Variation of wall slip velocity for 2.75 in. diameter smooth pipe. From Wenzel et al. [45] 16 Figure 2.4: Variation of pressure loss with average velocity. From Wenzel et al. [45] 17 Figure 2.5: Liquid film thickness at the wall vs. visually measured wall bubble velocity for particle-free foam flowing through acrylic pipe of 4.44 cm i.d. From Lemlich [41] 20 Figure 2.6: Variation of yield stress with bubble diameter. From Wenzel [45] 24 Figure 3.1: Schematic diagram of experimental set-up 31 Figure 3.2: Schematic representation of test section 33 viii Figure 3.3: (a) Sketch of dual cantilever beam force transducer (b) The illustration of installation of model to the transducer slot . 35 Figure 3.4: Open cylinder device for measuring foam drainage rate ... 40 Figure 3..5: A photograph of the smooth surfaced models for this study . 44 Figure 3.6: A photograph of samples of 38.1 mm dia. rough surfaced sphere. Roughness for left is 44-74 //m, and right is 420-589 ftm 46 Figure 4.1: A photograph of a sample output on x-y plotter 52 Figure 5.1: Plastic and solid regions for the flow surrounding a solid sphere falling in a Bingham plastic material. From Beris et al. [1] . 57 Figure 5.2: Dependence of the Stokes drag coefficient on the yield-stress parameter Yg. From Beris et al. [1] 59 Figure 5.3: Dimensionless drag-velocity curve for Bingham material as dimensionless velocity approaches zero 62 Figure 5.4: Direction of rotation of a free falling spheres 65 Figure 6.1: Drag force on smooth spheres for foam ID — S CFA 69 Figure 6.2: Drag force on disks for foam ID = SCFA 70 Figure 6.3: Drag force on ellipsoids for foam ID — SCFA 71 Figure 6.4: Drag force on spheres for foam ID = SCFB 72 Figure 6.5: Drag force on disks for foam ID = SCFB 73 Figure 6.6: Drag force on ellipsoids for foam ID = SCFB 74 Figure 6.7: Drag force on spheres for foam ID = SCFC 75 Figure 6.8: Drag force on disks for foam ID = SCFC 76 IX Figure 6.9: Drag force on ellipsoids for foam ID = SCFC 77 Figure 6.10: Drag force on spheres for foam ID = SCFD 78 Figure 6.11: Drag force on disks for foam ID = SCFD 79 Figure 6.12: Drag force on ellipsoids for foam ID = SCFD 80 Figure 6.13: Drag force on spheres for foam ID = SCFE 81 Figure 6.14: Drag force on disks for foam ID = SCFE 82 Figure 6.1-5: Drag force on ellipsoids for foam ID = SCFE 83 Figure 6.16: Drag force on spheres for foam ID = SCFF 84 Figure 6.17: Drag force on flat plates for foam ID = SCFF 8.5 Figure 6.18: Drag force on smooth spheres for foam ID = SCFG 86 Figure 6.19: Drag force on flat plates for foam ID = SCFG 87 Figure 6.20: Drag force as a function of sphere diameter on foam ID = SCFC 94 Figure 6.21: Drag force as a function of sphere diameter on foam ID = SCFD 95 Figure 6.22: Relationship for drag force-viscosity-quality for 38.1 mm sphere at foam velocity 0.3 m/sec 97 Figure 6.23: Relationship for drag force-quality for 38.1 mm diameter sphere at foam velocity 0.3 m/sec.
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