Validating dilute settling suspensions numerical data through MRI, UVP and EIT measurements

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Flow Measurement and Instrumentation

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Validating dilute settling suspensions numerical data through MRI, UVP and EIT measurements

R. Silva a,n, F.A.P. Garcia a, P.M. Faia b, Paul Krochak c, Daniel Söderberg d, Fredrik Lundell d,

M.G. Rasteiro a

a Chemical Engineering Department, Faculty of Sciences and Technology of the University of Coimbra, and CIEPQPF – Research Centre on Chemical Process and Forest Products, Polo 2, Pinhal de Marrocos, 3030-790 Coimbra, Portugal

b Electrical and Computers Engineering Department, Faculty of Sciences and Technology of the University of Coimbra and CEMUC – Centre of Mechanical Engineering, Polo 2, Pinhal de Marrocos, 3030-290 Coimbra, Portugal

c Innventia AB, SE-114 86, Stockholm, Sweden

d Wallenberg Wood Science Centre, Royal Institute of Technology, KTH Mekanics, SE 100 44 Stockholm, Sweden

a r t i c l e i n f o

Article history:

Received 23 August 2015 Received in revised form 22 April 2016

Accepted 4 June 2016

Available    online    6    June    2016               


Mixture model

Solid–liquid suspensions Magnetic resonance imaging Electrical impedance tomography Ultrasonic velocity profiling

a b s t r a c t

The measurement of fluid dynamic quantities are of great interest both for extending the range of va- lidity of current correlations to be used in equipment design and for verification of fundamental hy- drodynamic models. Studies where comparisons are made between imaging techniques serve to provide confidence on the validity of each technique for the study of multiphase flow systems. The advantage of cross-validation is that it can help establish the limitations of each technique and the necessary steps towards improvement. A small amount of comparative studies are found in the literature and none of them reports the study of settling particles suspension flow using simultaneously Ultrasonic Velocity Profiling (UVP), Magnetic Resonance Imaging (MRI) and Electrical Impedance Tomography (EIT), at least not to the best of the authors knowledge. In the present paper the authors report efforts made on the characterization of dilute suspensions of glass particles in turbulent flow, with increasing flow velocities and particles concentrations, in a pilot rig at a laboratorial scale, using both MRI, EIT and UVP: direct comparisons of EIT, MRI and UVP measurements acquired and mixture model numerical simulations are presented and the level of agreement explored.

& 2016 Elsevier Ltd. All rights reserved.

  1. IntroductionThe application of settling suspensions in industrial environ- ments has become widespread; however, as a result of their innate complexity there is no unified predictive numerical model or em- pirical correlation to predict the flow characteristics (pressure drop, flow regime, etc.) [1,2]. When working with settling suspensions a number of variables have to be accounted as flow patterns, transi- tion velocities, the flow behaviour in pipes of different geometries, and also particle concentration, particle shape, size, and size dis- tribution. Industries still rely on custom charts or data for their particular suspension flow, which is rather inefficient resulting in oversized dimensioning, low energy efficiency and even operation limitations/difficulties. The design and scale-up of equipment for multiphase flows are still predominantly based on empirical cor- relations validated over a limited range of operating conditions and physical properties. Application of more fundamental fluid dynamicn Corresponding author.E-mail address: (R. Silva). 0955-5986/& 2016 Elsevier Ltd. All rights reserved.numerical models awaits their experimental verification. Hence, measurement of fluid dynamic quantities such as phase velocities, phase holdups, bubble size etc. are of great interest both for ex- tending the range of validity of current correlations and for ver- ification of fundamental hydrodynamic models.Tomography offers a unique opportunity to reveal the com- plexities of the internal structure of an object without the need to invade it. Magnetic Resonance Imaging (MRI) is a high spatial re- solution tomographic technique with the ability to provide in- formation about the behaviour of protons present in a system, usually contained in the 1H nuclei of water. Amongst others, MRI is used to image motion of water expressed in the form of velocity profiles. The major limitations of MRI are the types of particles and the size of the system that can be studied, together with the size, weight and cost of the instrument. Only particles containing MR- sensitive nuclei, such as 1H, can be detected [3,4]. The maximum diameter of the system is bounded by the inner diameter of the coil in the magnet. Thus, MRI experiments are typically limited to laboratory-scale fluidised beds or small diameter pipes [5]. Insummary, the strength of MRI is in studying centimetre-scale systems at spatial resolutions of approximately 100 μm. ElectricalNomenclatureEIT Electrical Impedance Tomography ID Internal diameterMRI Magnetic Resonance Imaging UPV Ultrasound Pulse VelocimetryUVP Ultrasound Doppler Velocimetry Profiling∇ Mathematical gradient∇⋅ Mathematical divergenceδ First gradient pulse duration∆P Pressure dropε Turbulent dissipation rateη Normalized conductivityμm Mixture dynamic viscosityμc Dynamic viscosity of the continuous phase μd Dynamic viscosity of the dispersed phase ν Mixture kinematic viscosityνT Turbulent kinematic viscosityρm Mixture densityρc ; ρL Continuous phase densityρd; ρs Dispersed phase densityτGm Turbulent and viscous stressesσ Electrical conductivityσm Mixture electrical conductivity σ0 Reference electrical conductivity σw Water electrical conductivityσs0 Electrical conductivity for a known initial concentra- tion of solidsσT Particle Schmidt Numberϕap Apparent solids concentrationϕc Continuous phase volumetric fraction ϕ; ϕd Dispersed phase volumetric fraction ϕk Volumetric concentration of phase k ϕ0 Initial concentration of solidsϕ ( z) Calculated vertical particle distribution profileϕmax Maximum packing of solidsAσ Area under the normalized electrical conductivity curvecd Dispersed phase mass fractionCD Drag coefficientCε1 Closure coefficient for the k-ε turbulence model Cε2 Closure coefficient for the k-ε turbulence model σε Closure coefficient for the k-ε turbulence model σk Closure coefficient for the k-ε turbulence model Cμ Closure coefficient for the k-ε turbulence modeldp Particle diameterDmd Turbulent eddy diffusionDt Scalar diffusivity coefficientF Volume forcesg Gravitational accelerationIT Turbulence intensityk Turbulent kinetic energyL Characteristic length of the equipmentLT Turbulence length scalemdc Mass transfer ratio between phasespm Pressure of the mixturePk Turbulence production Rep Particle Reynolds Number Ti Turbulence intensityum mixture velocityumk Velocity of phase k in function of the center of the mass of the mixture.uT Transpose of the mixture velocityuc Continuous phase velocityud Dispersed phase velocityU V W Velocity in the x, y and z directions, respectively.Vk Volume of particley+ Wall lift-off in viscous unitsyp Distance from the wallImpedance Tomography (EIT) can be used to study much larger- scale systems and gives good quality qualitative images of gas– liquid–solid distributions [6]. The main advantages of EIT are its portability, simplicity of scale up, and relative low cost. Spatial resolution, however, is typically limited: this is due to both the reconstruction algorithms used (the nature of the reconstruction problem posed by EIT, which is ill conditioned and non-linear, makes the detection of small objects a challenge) and the number of unique measurements of conductivity obtainable, as derived from the current injection-voltage measurement system (very strongly dependent on the number of measuring electrodes) [7]. Furthermore, information concerning the absolute amount of so- lids suspended, cannot be accurately determined, since the images obtained represent not absolute values of the conductance/im- pedance, but the distribution of their variation. The measurement of instantaneous velocities in water flows has long been a chal- lenging issue. Due to their relatively low price and easy handling, Acoustic Doppler systems are widely used at present. Ultrasound systems, based on echography and Doppler Effect, allowed the development of equipment capable of measuring almost in- stantaneous velocity profiles [8,9]. Initially, the Ultrasonic Velocity Profiling (UVP) technique was limited to opaque fluids [10] and it was typically used to measure across pipe walls at small scale pressure [11]. An UVP probe emits an ultrasound beam that travels along the incident axis and, afterwards, receives the echo from the same beam after reflection by small particles present in the fluid. The UVP system measures the time delay of the echo to reach theprobe and the Doppler frequency shift. Knowing the speed of the sound in the fluid, the distance to and the velocity of the particle in the direction of the beam can be calculated. Although the UVP technique has been developed for 1D measurements, measure- ment of 2D velocity fields using UVP probes have been reported to give promising results [8,9].Detailed reviews on experimental tomographic techniques are given in the literature [1214] where comparisons are made be- tween imaging techniques which serve to provide confidence on the validity of each technique for the study of multiphase flow systems. The advantage of cross-validation is that it can help es- tablish each the limitations of each technique and the necessary steps towards improvement. Magnetic resonance imaging, ultra- sonic pulsed Doppler velocimetry, electrical impedance tomo- graphy, x-ray radiography and neutron radiography are shown to be capable of measuring the distribution of solids in suspensions [12], while only the velocity profiles are attained with magnetic resonance imaging and ultrasonic pulsed Doppler velocimetry. These reviews serve as a guide to identify suitable methods to meet specific measurement requirements through a broad analysis of the basic theory of each individual technique as well as their merits in acquiring velocity, size, shape and concentration mea- surements of particulate mixtures [13]. Additionally, they serve as a summary on the progress and developments in velocimetry techniques and flow imaging techniques [14]. However, the cross- validation between these techniques in each of the reviews is limited to two techniques at a time, either comparing velocity orconcentration profiles for the same case study. So, a small amount of comparative studies are found in the literature and none ofthem reports the study of settling particles suspension flow usingTable 1Solid–liquid suspensions experimental conditions for the performed tests.Q ⎡ l. s−1⎤U ⎣⎡ m. s−1⎤ Resimultaneously UVP, MRI and EIT, at least not to the best of the authors knowledge. In the following section, first, the experi-0.34 m ID Pipe⎣ ⎦ ⎦mental and numerical methods and models are introduced. The results are presented and discussed in the following order: (i) MRI, UVP and simulated velocity data from a pipe with 0.34 m inner diameter (ii) EIT particle concentration data from a pipe with0.50 m inner diameter and (iii) MRI, UVP and simulated velocity data from a pipe with 0.50 m inner diameter. The conclusions are summarised after the presentation and discussion of the data.
  2. Experimental setup and conditions

    dp50 [ mm]

    dp50 [ mm]

    0.15 ϕ ⎣⎡ v/v⎦⎤0.15 ϕ ⎡⎣ v/v⎤⎦0.005 1.0 1.10 366412.0 2.20 732810.01 1.0 1.10 366412.0 2.20 732810.03 1.0 1.10 366412.0 2.20 732810.005 1.0 1.10 366412.0 2.20 732810.01 1.0 1.10 366412.0 2.20 732810.03 1.0 1.10 366412.0 2.20 732810.50 m ID PipeIn this section the experimental conditions employed in the study of dilute solid-liquid suspensions flow are described. The tests were performed in the joint recirculatory pipe flow facility of KTH Royal Institute of Technology and Innventia AB in Stockholm, Sweden. Two different configurations were assembled to perform tests with two different internal pipe diameters, 0.34 and 0.50 m. The test sections of the flow loop for both configurations were built from cylindrical Perspexs piping possessing a total length of7.0 m which allowed the flow to be fully developed at the mea- suring sections. The schematics of the flow loop can be observed in Fig. 1.The solid-liquid suspensions were composed of Type S Sili-beadss spherical glass beads, provided by Sigmund Lindner GmbH, and tap water. The tests were performed some time (ap- proximately 10 min) after the pump had been started in order to ensure that the flow had stabilized. The spherical glass beads size, concentrations and flow rates employed are summarized in Table 1.
  3. Experimental tomographic techniques

    dp50 [ mm]

    0.5 ϕ ⎣⎡ v/v⎤⎦

    0.01 2.0 1.02 498314.0 2.04 996620.03 2.0 1.02 498314.0 2.04 996620.05 2.0 1.02 498314.0 2.04 99662In this study MRI, UVP and EIT tomographic techniques were employed in the study of dilute solid-liquid suspensions flow. The vertical and horizontal velocity profiles for both liquid and solids using the MRI and UVP, respectively, were attained with these ex- perimental techniques. Moreover, the EIT apparatus was used to obtain data regarding the distribution of particles in the pipe section.
    Fig. 2. Radiofrequency and magnetic pulse sequence used to obtain NMR velocity profile images for the flow of water in the pipe. Gsl is the slice selection gradient and Gfe is the frequency selection gradient. The slice selection gradient is used for flow encoding.
    Fig. 1. Schematics of the flow loops with 34 (Top) and 50 (Bottom) mm ID pipes.
    1. Magnetic Resonance Imaging (MRI)With this study, for the MRI flow characterization, a gradient- echo pulse sequence was used (see Fig. 2). A detailed description of this technique is found in the literature [15].The technique can be summarized as selective excitation of a streamwise slice of fluid and a 90° radiofrequency (RF) pulse rotating the magnetization orthogonally. A first phase-encoding gradient pulse is then applied for a duration, δ, giving each spin a spatially dependent phase offset. A 180° RF pulse is then applied rotating each spin iso- chromat (a microscopic group of spins, which resonate at the same frequency) through 180°. A second phase-encoding gradient pulseis applied at a time Δ after the first one to obtain a phase offset relative to the fluid displacement. A frequency position encode gradient is applied during readout.Throughout the experiments, the phase dispersion is sensitive to the mean and fluctuating velocities; therefore, the duration and separation times for the phase flow encoding gradients need to be adjusted manually. For the higher speed flow, i.e., for U=2.2 m.s-1 (see Table 1) profiles were averaged over 128 individual mea-surements and 64 measurements were averaged for lower flow rates. In all cases the slice was 10 mm long and the gain was on the order of 1000 dB. The MRI system consists of a 1 T permanent magnet connected to a Bruker NMR spectrometer. A 60 mm RF coil, calibrated to 43.5 MHz is used for transmission/reception. The entire system has been provided by Aspect Imagings and is con- trolled using NTNMRs software. Devoted measurement and data processing software was developed at the University of California Davis and further adapted in-house for post-processing [16].
    2. Ultrasonic Velocity Profiling (UVP)Ultrasonic Velocity Profiling (UVP), also designated Ultrasound Doppler Velocimetry Profiling (UVP), was utilized to measure the velocity of the particles. UVP fundamentals have been well docu- mented in the literature [8,9]. In the studies presented in this manuscript a 4 MHz transducer with a 5 mm active diameter element (maximum resolution of 0.37 mm) and a minimum measuring distance (near field) of 16.9 mm was used. After this minimum, the beam diverges with a half-angle of 2.2°. The pulse repetition frequency was 10.762 kHz with 128 spatial measure- ment channels. Data was acquired over 768 measurement cycles to obtain a velocity distribution profile and mean data was obtained by averaging over 64 profiles, providing a spatial and velocity re- solutions of 0.37 mm and 3.8 mm/s, respectively. The transducers were flush mounted to the inside pipe wall at a 70 degree angle to the flow and were in direct contact with the suspension (see Fig. 3).With this approach, the effects of attenuation and wall reflec- tions were reduced. The UVP hardware was provided by Met- Flows and the software, FlowVizs, was developed by SIK - The Swedish Institute for Food and Biotechnology in Gothenburg,Fig. 4. Block diagram of the EIT system employed in this study.Sweden [17,18].
    3. Electrical Impedance Tomography (EIT)The EIT system used in the studies depicted in this manuscript) has already been described in the literature [19,20]. The system is composed of function specific modules: signal generation and phase shifting occur on the same module, signal multiplication, demodulation and conditioning are done in another module and multiplexing is done in a third module. In EIT an electrical current is injected through a set of pair of electrodes placed in the boundary of the domain under study (see Fig. 4), thereby resulting an electrical field that is conditioned by the materials distribution within the domain.The resulting electrical potentials in the domain perimeter can be measured using the remaining electrodes, and those values are fed to a non-linear inverse algorithm to attain the previously un- known conductivity/resistivity distribution. The procedure is only complete when all electrodes are used for injection or projection, so the cycle has as many projections as the number of electrodes (see Fig. 5).For the depicted tests an EIT test section with 16 titanium electrodes was produced: each electrode has a diameter of 5 mm, which were previously optimized and equally spaced around the test section perimeter. In all the tests an excitation frequency of 10 kHz with 2 V peak-to-peak amplitude was used: adjacent in- jection and measuring protocols were used. For image re- construction, the open source software EIDORS [21], considering direct differential measured voltages and using a structured Mesh consisting of 2304 linear elements and 1201 nodes was used (in the reconstructed images the electrode corresponding to higher vertical position is electrode number 1). This software implements a non-linear back projection method using a regularization algo- rithm (Tikhonov”s regularization) [22]. To solve the forward pro- blem the Complete Electrode model (CEM) [23] was chosen: this model incorporates the shunt effect and the contact impedance in the electrode/domain interface.In the present study an in house built EIT apparatus was em- ployed to obtain vertical concentration profiles through normal- ized electrical conductivity measurements. The normalization is done using the reference measurements for tap water without particles, as described by Eq. (1)
      η= σ0−σm .σ0 (1)Fig. 3. General set-up for the UVP probe system.To accomplish the proposed endeavour two approaches were used to attain the vertical particle distributions: the first approach was based on the Maxwell Equation, which is one of the most widely used equations that correlates the electrical conductivity with particle concentration, and has shown great promise in de- position recognition [24] and depicting the asymmetry in swirling flows [25]. Since all particles involved in this study are non-
      Fig. 5. EIT injection and measurement protocols for the first (A) and second (B) projections. Adapted from [23].conducting settling particles, one of the approaches to achieve vertical particle distributions will be to directly use the Maxwell Equation (see Eq. 2)m w ⎜ ⎟.σ =σ ⎛  2 − 2ϕ0 ⎞dispersed phase (solid particles, liquid droplets, etc.) and a con- tinuous phase (liquid). It is translated by a momentum equation (Eq. (6)) and a continuity equation for the mixture (Eq.(7)). An additional term is included to describe the effect of thevelocity difference between the phases (Eq. (8)). Its application is⎝ 2+ϕ0 ⎠(2)conditioned by the following assumptions: each phase density isUsing the studies by Giguère et al. [26] as the basis, where the normalized electrical conductivity, η, is combined with Eq. (2), and through algebraic manipulation, Eq. (3) is obtained for the ap-constant, both phases share the same pressure field, and the ve- locity difference between phases is determined assuming that pressure, gravity and viscous drag are all balanced.parent solids concentration, ϕap:ρut+ρ ( u∙∇)u= − ∇p−∇∙( ( ρcd ( 1 − cd))uSLIP uSLIP )+∇∙τGm+ρg+F(6)ϕap=2 − 2( 1 + η)( σ0/σs0)) ,2 − ( ( 1 + η)( σ0/σs0 ))(3)⎡ρc −ρd ⎢∇∙( ϕd ( 1 − cd)uSLIP−Dmd∇ϕd )+⎣⎤mdc⎥+ρc ( ∇∙u)=0ρd ⎦(7)where the σ0/σs0 quantity is achieved using the known initial concentration of solids, ϕ0, as the initial condition in Eq. (2). Thisud−uc=ucd=uSLIP−  Dmd   ∇ϕd( 1 − cd)(8)assumes a homogenous particle distribution which is contrary to the observed experimental flow regimes.In order to avoid the homogeneous particle distribution and provide a more accurate description of the particle distribution, based on the normalized electrical conductivity profiles, the fol- lowing assumption was made where the initial concentration of solids is multiplied by the normalized electrical conductivity:m w ⎜ ⎟.σ =σ ⎛  2 − 2ηϕ0 ⎞The use of a turbulence model is justified by the values of the Reynolds Number (Re) in Table 1. Additionally to a turbulence closure, a model for the interphase forces, namely the drag force, is needed. Since the choice of a drag model is dependent on Particle Reynolds Number ( Rep) range it is necessary to have a good estimate of this value. Adding on the particle data in Table 1, the calculated Particle Stokes Number ( Stp) and Particle Reynolds Number as well as theTerminal Velocity c an be seen below in Table 2. Since Rep >1 and the solid-liquid suspensions are dilute, in all experimental cases, the⎝ 2+ηϕ0 ⎠(4)Schiller–Naumann correlation [31] was chosen for the drag forceWith Eq. (4) the new σ0/σs0 quantity is calculated and then used in Eq. (3) to calculate the apparent solids concentration.The second approach was to calculate the area under the nor-modelling. The highest Stp is 2.20 for the bigger particles in the 0.34 m ID pipe, while the remaining values are all close to one, thus validating the application of the mixture model in these studies [27,32,33].malized electrical conductivity curve, Aσ , and obtain the verticalparticle distribution according to Eq. (5),ϕ ( z)= ϕ0 η.Aσ(5)
        1. Drag correlationsThe velocity between phases, uslip, was obtained using the Schiller–Naumann [34] correlation for the calculation of the drag coefficient, CD:⎧  24 ( 1 + 0. 15 Re 0.687 ) Re <1000
  4. Numerical studies⎪ Re p p⎩CD=⎨ pThe numerical results presented in this manuscript were at- tained using the mixture model in the COMSOL Multiphysicss software. These numerical simulations were conducted by emu- lating the flow conditions depicted in Table 1 until mesh in- dependent results were attained. The mixture model is a single fluid Euler–Euler model [2730] in which the phases consist of a⎪ 0. 44Rep= dpρc  uSLIP   μ
      1. Turbulence closureRep>1000(9)(10)The High Reynolds k–ε turbulence model, in general, adds twoTable 2Particle data for the simulations of the solid-liquid suspensions flows.Particle Data 0.34 m ID Pipe 0.50 m ID Pipe
            1. InletAt the inlet the initial velocities were imposed in the direction perpendicular to the pipe section and the turbulence intensity and length scales are as depicted below. When conceiving a CFD si-

              dp50 [ mm]

              ρP ⎡⎣ kg. m−3⎤

              ⎦U ⎡⎣ m.s−1⎤0.15 0.5 0.52500 2500 25000.55 0.55 0.511.10 1.10 1.022.20 2.20 2.04mulation a user seldom has knowledge on the distributions for k and ε at the inlet. To circumvent this lack of information k and ε inlet values for internal flows can be estimated, taking the tur- bulence intensity scale and the turbulent length scale as a starting point, using the following expressions [38]:k= 3 ( uIT )2

              ϕ ⎡⎣ v/v⎤⎦

              0.005 0.005 0.010.01 0.01 0.030.03 0.03 0.052ε= 3 C 3/4 k3/22 μ LT(17)(18)

              Stp 0.05









              VT ⎡⎣ m.s−1⎤ 0.018



              Rep 2.65



              ⎦extra transport equations that are solved for two additional vari-
            2. Outlet and symmetry axisAdditionally, at the outlet the normal gradients of k and ε are fixed equal to zero, which corresponds to the Neumann (‘do- nothing’) boundary condition. In the finite element framework, these homogeneous boundary conditions imply that the surface integrals resulting from integration in the variational formulation vanish [39].∂k=0ables: the turbulent kinetic energy, k, and the dissipation rate of the turbulent kinetic energy, ε. The following equations define the High Reynolds k–ε Turbulence Model, which is incorporated in the∂n∂ε =0∂n(19)(20)mixture model [35].The Turbulent Eddy Viscosity is defined as:k2μT =ρCμ
              ,ε(11)Moreover, a pressure value has to be assigned at the outlet section which is typically fixed at zero; however, to avoid nu- merical instabilities that hinder numerical convergence a hydro- static pressure profile was assigned,the turbulent kinetic energy, k, being given by:ρ k +ρu⋅∇k=∇⋅⎛ ⎛ μ+ μT ⎞∇k⎞+P −ρε,p= − g ( s + D)( ρc ( 1 − ϕ0 )+ρd ϕ0 ).(21)∂twhere:⎛⎜ ⎜ ⎟ ⎟⎝ ⎝ σ⎠ ⎠T  2k2⎞  2(12)
            3. Near-wall treatment for turbulent flows
        The Law of the Wall or Wall Function was used as depicted in Eq. (22) for the near wall treatment of the flow [40,41] in the numerical studies using a High Reynolds Turbulence Closure,⎝Pk=μT ⎜ ∇u :(∇u+( ∇u) )− 3( ∇⋅u) ⎟−⎠3 ρk∇⋅u,(13)uτ=    u    .1 ln y+ +B(22)and finally the dissipation rate, ε, is obtained through: κ∂ε ⎛ ⎛ρ
        +ρu⋅∇ε=∇⋅⎜ ⎜ μ+⎞ ⎞ 2μT ε ε⎟∇ε⎟+Cε1
        ,The turbulence parameters κ and B values are 0.41 and 5.2, respectively [40].∂t ⎝ ⎝σε ⎠ ⎠ k k(14)where the closure coefficients ( Cε1¼ 1.44; Cε2 ¼ 1.92; Cμ ¼ 0.09;σk ¼ 1.0; σε ¼ 1.3) were obtained empirically [35].The turbulence modelling must also take into account the dispersed phase velocity. This is accomplished calculating the diffusion coefficient for the particle (Eq. (16)), which is a function of the turbulent particle Schmidt number [27]. The turbulent Schmidt number (σT ) is defined as the ratio between the turbulent kinematic viscosity and the scalar diffusivity coefficient [36], and it is related to the diffusion of the particles. A default value of 0.35 is present in most commercial codes and most authors accept this value [37]. Thus, σT and Dmd are:ν
  5. Results and discussionPrior to the solid–liquid suspensions experiments preliminary tests were performed with water under the experimental condi- tions depicted in Table 1, which allowed to verify if the MRI ap- paratus were suitably calibrated. The experimental 1D MRI velo-city profiles were compared with numerical results from CFD si- mulations using the High Reynolds k–ε turbulence model [35]. These preliminary tests demonstrated a good agreement between the experimental and calculated results, thus, validating the cor-rect calibration of the MRI apparatus.DσT=
    tDmd= μT   ρσT
      1. Boundary conditions
    1. 0.1–0.2 mm particles in 0.34 m ID pipeThe first tests were conducted with small spherical particles with size between 0.1–0.2 mm in the flow loop. As described in Table 1 the volumetric concentrations studied were 0.5, 1.0 and3.0% (v/v) for flow rates of 1.0 and 2.0 l.s−1. The numerical andAdditionally, the following boundary conditions were enforced on the numerical studies:experimental results, from both MRI and UVP, match quite well,
      Fig. 6. Experimental MRI, UVP and Simulated normalized horizontal (Top) and vertical (Bottom) velocity profiles for flow rates of 2.0 (Left) and 1.0 l.s−1 (Right) in a 34 mm ID pipe for a solids volumetric concentration of 0.5% (v/v) with 0.1–0.2 mm particles.with negligible deviations, as presented in Figs. 68.The UVP and MRI profiles, representing the velocities of the dispersed and continuous phases, respectively, are concordant with what was expected, since the Stokes Numbers for these particles is smaller than one, for all flow velocities tested (see Table 2), indicating that the particles follow the fluid streamlines for the three concentrations tested; in other words, the particle motion is tightly coupled with the motion of the fluid since there is very little slip between the phases.The simulated (mixturemodel) and experimental values did, however, match quite well again, for this particle concentration.
    2. 0.4–0.6 mm particles in 0.34 m ID pipeFollowing the tests with the 0.1–0.2 mm particles, similar testing was performed with bigger particles with a size range of 0.4–0.6 mm, and a mean particle diameter of 0.5 mm. The same solids volumetric fractions and flow rates used for the 0.1–0.2 mm
      Fig. 7. Experimental MRI, UVP and Simulated normalized horizontal (Top) and vertical (Bottom) velocity profiles for flow rates of 2.0 (Left) and 1.0 l.s−1 (Right) in a 34 mm ID pipe for a solids volumetric concentration of 1.0% (v/v) with 0.1–0.2 mm particles.
      Fig. 8. Experimental MRI, UVP and Simulated normalized horizontal (Top) and vertical (Bottom) velocity profiles for flow rates of 2.0 (Left) and 1.0 l.s−1 (Right) in a 34 mm ID pipe for a solids volumetric concentration of 3.0% (v/v) with 0.1–0.2 mm particles.particles testing were employed for these trials. With these bigger particles, it can be seen from Fig. 9 to 11that the numerical and MRI experimental velocity profiles present a good fit for all the concentrations tested. The UVP data, however, deserves some considerations as there are asymmetries, which should not occur for the horizontal profiles.This lack of symmetry, rather than depicting a physical phe-nomenon, can result from the accumulation of particles in the posterior probe [42,43], thus, causing an obstruction in the signalgeneration and acquisition for this probe (which is located in the right side of the flow direction as depicted in Fig. 3). Nevertheless, if the offset in the lower half of Figs. 1012 is disregarded, and only the upper half of the UVP velocity profiles is considered, then it becomes apparent that the velocity profiles approach the MRI and mixture model numerical profiles, except when we come close to the wall. For the larger velocities, with a Stokes Number of 2.20, it was assumed that the mixture model application was still valid and the velocity profiles seem to further validate the assumption. Also,
      Fig. 9. Experimental MRI, UVP and Simulated normalized horizontal (Top) and vertical (Bottom) velocity profiles for flow rates of 2.0 (Left) and 1.0 l.s−1 (Right) in a 34 mm ID pipe for a solids volumetric concentration of 0.5% (v/v) with 0.4–0.6 mm particles.
      Fig. 10. Experimental MRI, UVP and Simulated normalized horizontal (Top) and vertical (Bottom) velocity profiles for flow rates of 2.0 (Left) and 1.0 l.s−1 (Right) in a 34 mm ID pipe for a solids volumetric concentration of 1.0% (v/v) with 0.4–0.6 mm particles.for the higher concentrations and lower flow velocity, it is apparent some asymmetry in the MRI vertical profiles and in the simulated ones, in agreement with the non-homogeneous distribution of these larger particles in the pipe cross-section, in opposition to what happened for the smaller particles.
    3. 0.4–0.6 mm particles in 0.50 m ID pipeIn addition to the previous experiments it was also possible tostudy solid-liquid suspensions using a pipe with a bigger internal diameter. The larger particles, with a size range of 0.4–0.6 mm, were tested in this pipe. The experimental conditions were as depicted in Table 1. With the 0.50 m ID pipe it was also possible to acquire vertical normalized distributions of conductivity, using the EIT system, that were used to infer on the distribution of particles in the pipe section (see Eqs. to 5). For this technique to retrieve adequate images, the reference measurements were done without any particles in the flow rig. The reconstructed 2D images shown
      Fig. 11. Experimental MRI, UVP and Simulated normalized horizontal (Top) and vertical (Bottom) velocity profiles for flow rates of 2.0 (Left) and 1.0 l.s−1 (Right) in a 34 mm ID pipe for a solids volumetric concentration of 3.0% (v/v) with 0.4–0.6 mm particles.

      Flow rate (l.s-1)

      2 4




      Fig. 12. Reconstructed 2D images of the pipe cross-section using EIT normalized conductivity measurements for solid–liquid suspensions of 0.4–0.6 mm particles for 1.0 (Top), 3.0 (Middle) and 5.0% (v/v) (Bottom) solids volumetric concentration in a 50 mm ID Fig. 12 represent normalized conductivity measurements, η. The normalization is performed using Eq. (1). From Fig. 12 it is possible to observe the effect of particle concentration on the conductivity gradient. For 1.0 and 3.0% (v/v) particle concentration at 2l.s−1 the colour change towards blue in the bottom of the images indicates an increase in particle concentration along the bottom of the pipe. The regions with a more intense red colour represent the areas where there is little change in the electrical conductivity, thus, meaning; little or no particles are present. Also, the effect of the flow velocity increase in the turbulent dispersion of particles is obvious by comparison of the left and right columns, demon- strated by the shift in the colour profiles towards the top of the colourbar, i.e., indicating a lower normalized electricalconductivity difference between the mixture and the reference measurements.At 5.0% (v/v) particle concentration it would be expected that the lower part of the image would be of a similar blue colour as in the 3.0% (v/v) reconstructed images, but corresponding to an even greater blue area, denoting a higher particle concentration at the bottom, due to the effect of gravity. This is, however, not the case when the two bottom reconstructed images in Fig. 12 are in- spected in detail. The particles seem to be more fluidized as de- noted by wider white and yellow areas. This colour arrangement, particularly at the lower flow velocities, appears to indicate the presence of strong particle-particle interactions, due to increased particle concentration, which is augmented with an increase in the