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Pressure Drop and Forced Convective Heat Transfer in Porous Media

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Pressure Drop and Forced Convective Heat Transfer in Porous Media Pressure Drop and Forced Convective Heat Transfer in Porous Media Ahmed Faraj Abuserwal Supervisor: Dr Robert Woolley Co-Supervisor: Professor Shuisheng He Dissertation Submitted to the Department of Mechanical Engineering, University of Sheffield in partial fulfilment of the requirements for the Degree of Doctor of Philosophy May 2017 Acknowledgments First and foremost, I would like to express my gratitude to my supervisor and tutor, Dr Robert Woolley, for his expert guidance which has been invaluable. The continual encouragement I have received from him has allowed me to persevere even when difficulties arose. His excellent comments and suggestions have improved my research capabilities and supported my efforts to publish a number of papers, including this dissertation. I owe a similar debt of gratitude to a lab technician, Mr Malcolm Nettleship, for his continuous support in the lab. His willingness to share his time, experience and knowledge for the construction the test rigs has been a tremendous help. Without this support, I frankly could not have achieved the aims and objectives of this thesis. In addition, acknowledgment and gratitude for Dr Russell Goodall is due for his enormous level of support and encouragement in giving me permission to use equipment and the required materials to produce the metal sponges. During various meetings, his comments and suggestions were invaluable to the success of my work and publications. Furthermore, I would like to offer thanks to Dr. Farzad Barari and Dr. Erardo Elizondo Luna for their support and help, and a special thank you to Mr. Wameedh Al-Tameemi, who supported me by sharing his instruments. I would also like to extend my thanks to my colleagues in the lab; Mr. Basim A Al-Bakri, Mr. Ahmed Al- Rubaiy and Mr. Abdulaziz Gheit. Finally, it is impossible to express with words the love and appreciation I have for my wife for the support she has given me to achieve my dreams and targets. Her patience and encouragement were the source my success. Without her taking on family responsibilities during my studies, I would not have been able to complete my thesis. I dedicate this work to my late and dear parents who were the source of tenderness, love and encouragement throughout my life. This work is also dedicated to my delicate and precious daughter, Arwa, to the rest of my children; Faraj, Abdalmohiemen and Abdalmalek and to my darling wife. i Abstract Metal foams, a new class of porous material with highly permeable structure and higher porosity (>0.60) compared with classical porous granular beds, are a viable solution to enlarge the thermal exchange area and provide a high heat capacity and high specific area. These metal foams are available in a number of solid materials with different porosities and pore size. There is a current lack of understanding regarding metal foam microstructure parameters’ effects on hydraulic and thermal parameters. This is a barrier to the design and implementation of various industrial applications. The current study aims to discover the effects of the pore shape and morphological parameters in terms of pore size and porosity at relatively low ranges of porosity (0.57-0.77) on fluid flow and conductive and convective thermal transport phenomena. Sixty nine aluminium metal sponges were produced with a replication manufacturing technique (porosities 0.57-0.77, pore diameters 0.7-2.4 mm) with different irregular and spherical pore shape. The porosity was controlled by infiltration pressure and the pore size by preform salt diameter. Two test rigs were designed and built to measure pressure drop at low and high flow rates. The frontal air velocity varied from 0.01 m/s to 8 m/s and the permeability based Reynolds number changed between 0.003 and 80. The four flow regimes; Pre-Darcy, Darcy, Forchheimer and Turbulent were identified in all samples. The transition points between the flow regimes were found to change gradually with the porosity and pore diameter. The permeability was measured in the Darcy flow regime while inertia and drag coefficients were measured in the Forchheimer regime. The pressure drop increased with frontal fluid velocity in linear and quadratic typical relations at low and high flow rates, respectively, and with decreases in both porosity and pore size. The permeability increased with both porosity and pore size whilst inertia and drag coefficients decreased. The permeability normalised with pore diameter and correlated well with porosity. The irregular pore shape samples induced lower pressure and inertia coefficient and higher permeability more than those with ii spherical pore shape. Permeability based friction factor was also expressed as function of permeability based Reynolds numbers and was found to tend towards inertia coefficient at turbulent regime. The comparative steady state technique was used to measure the effective thermal conductivity (ETC). The ETC was found to decrease with increase of porosity, and no measurable influence of pore size and shape was observed. ETC was normalised by solid phase material thermal conductivity and correlated well with porosity for a broad range of porosity from 0.5 to 1.0. The convective heat transport phenomenon was also studied experimentally using the single blow transient technique and a purpose built test rig. The outlet fluid temperature was modelled and matched with the recorded experimental history. The direct matching and maximum gradient approaches were used to obtain the number of transfer units (NTUm) by using an iterative approach. The convective and volumetric heat transfer coefficients were also determined over the range of permeability based Reynolds numbers between 10 and 80. The NTUm decreased with Reynolds number whilst the convective and volumetric heat transfer coefficients and Nusselt number increased. The thermal performance in terms of the above parameters increased with a decrease of both pore size and porosity. The thermal performance of irregular pore shape samples is lower than that of the spherical pore shape samples. In order to improve the thermal performance, three samples with different pore diameter were sliced and examined. The thermal performance in terms of NTUm and volumetric heat transfer coefficient were found to increase by 34% and 38%, respectively. The increase in both these parameters was more significant at lower Reynolds numbers. This is because the thermal conductivity effect reduced with an increase of flow rate. The manufacturing defects were tracked using the image processing technique for scanned surfaces samples. Missing or damaged cells, inclusions and closed cells defects were identified in some studied samples. The effect of these imperfections resulted in scattering of the experimental results. iii Table of Contents Acknowledgment…………………………………………………………………………………… i Abstract ………………………………………………………………………………………………… ii Table of Contents …………………………………………………………………………………. iv List of Figures ……………………………………………………………………………………….. viii List of Tables ………………………………………………………………………………………… xvi Nomenclature ………………………………………………………………………………………. xviii Chapter 1 ……………………………………………………………………………………………… 1 1. Introduction …………………………………………………………………………………………. 1 1.1 Background ………………………………………………………………………………………….. 1 1.2 Thermal regenerator ……………………………………………………………………………. 2 1.3 Aims and Motivation ……………………………………………………………………………. 4 1.4 Organization …………………………………………………………………………………………. 7 1.5 Publications ………………………………………………………………………………………….. 7 Chapter 2 ……………………………………………………………………………………………… 9 2. Literature review ………………………………………………………………………………….. 9 2.1 Fluid flow through porous media …………………………………………………………. 10 2.1.1 Fluid flow in granular beds ……………………………………………………………………. 10 2.1.2 Fluid flow in metal foams ……………………………………………………………………… 17 2.2 Effective thermal conductivity of metal foams ……………………………………… 27 2.3 Convective heat transfer in porous media ……………………………………………. 32 Chapter 3 ……………………………………………………………………………………………… 41 3. Experimental methods and processing techniques…….…..…………………….. 41 3.1 Steady state pressure drop measurements.………………………………………….. 41 3.1.1 Pressure drop analysis and hydrodynamics parameters determination…. 41 3.1.2 Friction factor ………………………………………………………………………………………. 42 3.1.3 Pressure drop experimental setup ……………………………………………………….. 43 3.2 Porous materials effective thermal conductivity measurements ….………. 47 3.2.1 ETC Experimental Apparatus ………………………………………………………………… 48 3.2.2 Effective thermal conductivity determination ………………………………………. 52 iv 3.3 Convective heat transfer in porous media ……………………………………………. 56 3.3.1 Introduction …………………………………………………………………………………………. 56 3.3.2 Convective heat transfer characteristics measurements ………………………. 56 3.3.2.1 Steady State Technique ………………………………………………………………………… 57 3.3.2.2 Transient Technique …………………………………………………………………………….. 58 3.3.3 Single Blow Technique Models and Assumptions …………………………………. 59 3.3.4 Single blow technique model development ………………………………………….. 60 3.3.5 Governing equations of single blow technique model ………………………….. 61 3.3.5.1 Energy balance equations …………………………………………………………………….. 61 3.3.5.2 Numerical solution ……………………………………………………………………………….. 66 3.3.6 Evaluation methods ……………………………………………………………………………… 69 3.3.7 Experimental apparatuses and data reduction ……………………………………… 71 3.3.7.1 Experimental setup ………………………………………………………………………………. 71 3.3.7.2 Experimental data reduction ………………………………………………………………… 73 3.3.8 Smoothing and fitting data …………………………………………………………………… 74 3.3.9 Fluid temperature prediction and matching
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