Transport and deposition behaviour of model slurries in closed pipe flow Hugh Patrick Rice Submitted in accordance with the requirements for the degree of Doctor of Philosophy University of Leeds School of Process, Environmental and Materials Engineering Institute of Particle Science and Engineering April 2013 Intellectual property and publication statements The candidate confirms that the work submitted is his own and that appropriate credit has been given where reference has been made to the work of others. This copy has been supplied on the understanding that it is copyright material and that no quotation from the thesis may be published without proper acknowledgement. © 2013 The University of Leeds and Hugh Patrick Rice. The right of Hugh Patrick Rice to be identified as the author of this work has been asserted by him in accordance with the Copyright, Designs and Patents Act 1988. Abstract Suspensions of solid particles are ubiquitous in nature and industry. From sub- aqueous and aeolian dunes and ripples to plug flow in the minerals engineering industry, the complexity of the fluid dynamics and interparticle interactions in multiphase flow is such that specific applications require specific solutions. The behaviour of suspensions of solid particles in a water carrier fluid in closed pipe flow is investigated over a range of flow regimes, from fully suspended, homogeneous flows to settled beds, using four particle species. The suspensions are intended to be simple analogues of more complex slurries that are encountered in the nuclear industry, the disposal and transport of which represent an ongoing challenge. An off-the-shelf ultrasonic signal processing unit, with two ultrasonic transducers operating at 2 and 4 MHz, is used as both a Doppler velocimeter and an acoustic backscatter system. The results of a range of distinct measurements are presented. The effect of suspended particles of several types at several volume fractions on the first- and second-order flow statistics is described. The dependence of two critical velocities that delineate the homogeneous, heterogeneous and moving-bed flow regimes on the flow and particle properties is described, and the results are compared to two correlations of critical transport velocity in the literature. A model was developed to measure the scattering and attenuation properties of arbitrary solid particles in suspensions, and the measured values are incorporated into an inversion method in order to construct particle concentration profiles in pipe flow. Lastly, the behaviour of stable and time-dependent bedforms, which have been studied in natural and rectangular channels extensively, is investigated in closed pipe flow, and phase diagrams of bedform types are presented and compared with a similar diagram in the literature. A full set of particle characterisation results is also presented in terms of size, density, shape and packing fraction, and the effect of the particle properties on the results is discussed in detail. i Table of contents 1 Background and introduction ............................................................................................... 1 1.1 Characteristics of UK nuclear industry radioactive waste ................................. 1 1.2 Objectives and overview of thesis ................................................................................ 5 2 Literature review ........................................................................................................................ 8 2.1 Physical processes in insonified suspensions of particles.................................. 8 2.1.2 Regimes and dependences of scattering and absorption ........................ 11 2.2 Fluid mechanics of multiphase pipe flow ............................................................... 14 2.2.1 Coordinates, velocity and stress fields in turbulent pipe flow .............. 14 2.2.2 Mean and turbulent velocities and Reynolds stresses ............................. 18 2.2.3 Turbulent scales ...................................................................................................... 23 2.2.4 Basic multiphase flow parameters ................................................................... 26 2.2.5 Influence of suspended particles on multiphase flow .............................. 26 2.2.6 Slurries and high-concentration flows ........................................................... 31 2.2.7 Models and correlations of slurries and concentrated suspensions .. 33 2.3 Summary and identification of opportunities ...................................................... 36 3 Experimental method ............................................................................................................ 38 3.1 Review and selection of measurement methods................................................. 38 3.2 Specification of flow loop and ultrasonic measurement system .................. 43 3.2.1 Main flow loop ......................................................................................................... 43 3.2.2 Basic operation of UVP-DUO ultrasonic measurement system ............. 48 3.3 Data processing method ............................................................................................... 55 3.4 Choice of coordinate system and notation: reiteration .................................... 57 3.5 Selection and characterisation of particle species.............................................. 58 3.5.1 Particle sizing ........................................................................................................... 60 3.5.2 Particle density measurement ........................................................................... 62 ii 3.5.3 Packing fraction measurement .......................................................................... 62 3.5.4 Determination of particle shape ....................................................................... 63 3.5.5 Summary of particle characterisation studies ............................................. 65 3.6 Calibration and data validation .................................................................................. 67 3.6.1 Influence of suspended particles on sound speed ..................................... 67 3.6.2 Consideration of flow parameters and instrumental resolution ......... 70 3.6.3 Probe position calibration ................................................................................... 72 3.6.4 Flow rate calibration ............................................................................................. 76 3.6.5 Statistical analysis and filtering of experimental data ............................. 79 3.6.6 Validation of single-phase data: inner variables and law of wall ......... 83 3.7 Bed and shear layer thickness measurement ....................................................... 89 4 First- and second-order turbulence statistics and critical velocities in turbulent pipe flow ........................................................................................................................... 94 4.1 Experimental method .................................................................................................... 94 4.1.1 Decomposing velocity and stress components ........................................... 95 4.1.2 Critical flow velocity 1, Uc1 (homogeneous transition velocity) ........... 96 4.1.3 Critical flow velocity 2, Uc2 (limit deposition velocity) ............................ 97 4.2 Results and discussion ................................................................................................ 100 4.2.1 Homogeneous suspensions at low volume fractions .............................. 101 4.2.2 Homo- and heterogeneous suspensions at moderate volume fractions 107 4.2.3 Settling suspensions at low volume fractions ........................................... 111 4.2.4 Heterogeneous and settling suspensions at high volume fractions .. 115 4.2.5 Summary: trends in first- and second-order flow statistics ................ 121 4.2.6 Critical flow velocity 1, Uc1 (homogeneous transition velocity) ......... 124 4.2.7 Critical flow velocity 2, Uc2 (limit deposition velocity) .......................... 127 4.3 Summary and conclusions ......................................................................................... 133 iii 5 Concentration gradients in suspensions in closed pipe flow ............................... 135 5.1 Literature review: Thorne et al. model of backscatter strength ................. 135 5.2 Homogeneous case: determination of backscatter and attenuation coefficients of arbitrary suspensions ................................................................................. 138 5.2.1 Derivation ................................................................................................................ 139 5.2.2 Testing for homogeneity in stirred mixing vessel ................................... 141 5.2.3 Measurements and results: attenuation constant, ξh .............................. 143 5.2.4 Measurements and results: combined backscatter and system constant, Kh .............................................................................................................................. 149 5.2.5 Discussion and summary: measured backscatter and attenuation coefficients ............................................................................................................................... 154 5.3 Heterogeneous case: measurement of the particle concentration profile using the dual-frequency inversion