Available online at ScienceDirect. Procedia Engineering 102 (2015 )

Transcription

1 Available online at ScienceDirect Procedia Engineering 10 (015 ) The 7th World Congress on Particle Technology (WCPT7) Quadrant and conditional analyses of non-sherical article segregation in a turbulent channel flow Derrick O. Njobuenwu*, Michael Fairweather Institute of Particle Science and Engineering, School of Process, Environmental and Materials Engineering,University of Leeds, Leeds LS 9JT, UK Abstract Turbulent flows transorting articles of different sizes and shaes can be found in many natural and industrial systems. In understanding such flows, it is imortant to identify the mechanisms resonsible for the disersion, segregation and deosition on solid surfaces of articles with different shaes, and of secific interest here how such articles interact with near-wall coherent turbulent structures (outward motion, ejection, inward motion and swee). Results from large eddy simulation couled with Lagrangian article tracking are used together with conditional statistics (robability density function and scatter lots) in quadrants to study the distribution of fluid, article and sli velocity fluctuations. The results, though challenging to analyse, give insight into the values of the quadrants and how these distributions reveal the mechanisms resonsible for article segregation in the near-wall region The Authors. Published by Elsevier by Elsevier Ltd. This Ltd. is an oen access article under the CC BY-NC-ND license (htt://creativecommons.org/licenses/by-nc-nd/4.0/). Selection and eer-review under resonsibility of Chinese Society of Particuology, Institute of Process Engineering, Chinese Selection Academy and of eer-review Sciences (CAS). under resonsibility of Chinese Society of Particuology, Institute of Process Engineering, Chinese Academy of Sciences (CAS) Keywords: Large eddy simulation; turbulence; non-sherical articles; article segregation; swee-ejection event 1. Introduction Understanding and characterising the mechanisms that control the disersion and segregation of inertial nonsherical articles in a turbulent boundary layer has imortant imlications for many natural and industrial systems, such as solid deosition in marine flows and the deosition of corrosion roduct in the form of CRUD (corrosion * Corresonding author. Tel.: ; fax: address: d.o.njobuenwu@leeds.ac.uk The Authors. Published by Elsevier Ltd. This is an oen access article under the CC BY-NC-ND license (htt://creativecommons.org/licenses/by-nc-nd/4.0/). Selection and eer-review under resonsibility of Chinese Society of Particuology, Institute of Process Engineering, Chinese Academy of Sciences (CAS) doi: /j.roeng

2 14 Derrick O. Njobuenwu and Michael Fairweather / Procedia Engineering 10 ( 015 ) residual unidentified deosit) on the outside of the fuel ins in nuclear reactors. Turbulent article transfer mechanisms in roximity to a solid wall are characterised by comlex interactions between turbulence structures and the disersed hase. Coherent structures (outward motion, ejection, inward motion and swee) bring articles towards and away from the wall and favour article segregation in the viscous region, giving rise to non-uniform article distribution rofiles, which eak close to the wall [1]. When articles segregate in secific flow regions, the effect of the disersed hase on turbulence is no longer negligible since the local article volume fraction changes. This leads to ockets of high concentrations of articles where the one-way couling assumtion between the articles and the fluid is no longer valid. This study relies on a recise understanding of the dynamics of articles in a turbulent flow field obtained using large eddy simulation. The translational dynamics of articles is well described by the convection of the articles centroid in the flow domain. For non-sherical articles, the orientational dynamics must also be considered in order to cature the comlete motion of the articles []. Jeffery [3] derived an aroximate uation of motion for the orientational dynamics of non-sherical articles in the absence of inertia. Jeffery s solution redicts that elongated axisymmetric articles mostly align with the flow direction, but eriodically raidly turn through two-right angles. With much ast (e.g. [4-6]), resent (e.g. [7-9]) and future research based on Jeffery s uations, it is necessary to study how accounting for article orientation alters the interaction with turbulent coherent structures and article segregation in the near-wall region. Fluid, article and sli velocities are the dynamic arameters used in this work to demonstrate that article-turbulence interaction is a function of article shae, inertia and location along the wallnormal axis of a turbulent channel flow. Sli velocity is defined here as the difference in velocity between the fluid and a article. Statistical analyses of sli velocity have reviously aeared in the literature, but only for sherical [10] and rolate [7] articles. The instantaneous and statistical values of the sli velocity fluctuations, together with those of the fluid and the article, are used herein to characterise articles traed in ejection-swee events and articles segregated in near-wall fluid streaks.. Mathematical models.1. Large eddy simulation The conservation uations for mass and momentum are decomosed into resolved (large-scale) and unresolved (sub-grid scale) fields using a to-hat filter as this fits naturally into the finite-volume formulation used for solution. The filtered forms of these uations for the resolved scales are given by: j u x ui ui u j 1 t x x x j j 0, (1) i j ij ij, where ij sij and ij uiu j uiu j reresent the kinematic viscous stress and the sub-grid scale (SGS) stress tensors, resectively. The unknown SGS stress term ruired to close these uations was modelled using a dynamic aroach [11] which reresents the SGS stress as the roduct of a SGS viscosity and the resolved art of the strain tensor, and is based on the ossibility of allowing different values of the Smagorinsky constant at different filter levels. Test filtering was erformed in all sace directions, with no averaging of the comuted model arameter field. The comutations were carried out with the BOFFIN large eddy simulation (LES) code [9, 1]. The code imlements an imlicit finite-volume incomressible flow solver using Cartesian co-ordinates and a co-located variable storage arrangement. Time advancement is erformed using an imlicit Gear method for all transort terms with variable time ste, and the overall rocedure is second-order accurate in sace and time. For the convection terms an energy conserving discretization scheme is used and matrix re-conditioned conjugate gradient methods are emloyed to solve the uations for ressure and velocity. ()

3 Derrick O. Njobuenwu and Michael Fairweather / Procedia Engineering 10 ( 015 ) Kinematics and dynamics of a non-sherical article The dynamics of an anisotroic article at time t t is fully determined by four non-scalar quantities: the osition of its centre of mass, its orientation, and its translational and rotational velocities. Each of these hysical quantities changes as a function of time and can be easily reresented as a three-comonent vector, together with orientation, giving a total of thirteen variables. There are two frames of reference: the inertial (or Eulerian) coordinate system, x [ x, y, z], which is a fixed frame of reference, and the article coordinate system, x [ x, y, z], which is a frame of reference with its origin at the article centre of mass and its axis being the rincial axis. The transformation between the inertial frame and the article frame is exressed as x Ax [13]. The transformation matrix A [ a ij ] can be exressed in terms of either Euler angles (,, ) or quaternions q ( q1, q, q3, q0) [13]. The Euler angles reresent the direction cosines of the article axes in the inertial frame, as shown in Figure 1. The orientational matrix A in terms of the quaternion q, subject to the constraint that the sum of the individual comonents is unity, is given by: 1 ( q q3 ) ( q1q q3q0 ) ( q1q3 qq0) A ( qq1 q3q0 ) 1 ( q3 q1 ) ( qq3 q1q0 ), (3) ( q3q1 qq0) ( q3q q1q0 ) 1 ( q1 q ) where the individual quaternions are obtained from the Euler angles [14]. Fig. 1. Schematic of co-ordinate system and orientational angles of a article with resect to article major axis z (left), and distance between centres of ressure (CP) and of mass (CM) of article, x c, and incidence angle between (u-u ) and article major axis z, α i (right). The forces, F, and torques, T, acting on a article may change the momenta of a article as exressed in Eq. (4): x 1 P m q 1 qq x ( t) P, (4) F L T where x is the osition of its centre of mass, q is the quaternion describing its orientation, P is the linear momentum, L is the angular momentum, m is the mass of the body, and ω q indicates a quaternion with scalar art 0 and a vector art with angular velocity ω. Note a boldfaced letter denotes a vector, and a dotted letter denotes a time derivative. For heavy articles (ρ /ρ 1) the deterministic art taken from the Maxey and Riley formulation for the force was limited to the drag force, F D, while the effect of other forces were neglected for the sake of imroving fundamental

4 16 Derrick O. Njobuenwu and Michael Fairweather / Procedia Engineering 10 ( 015 ) understanding of fluid-article interaction with a manageable arameter range. With the above simlifications, the drag force resulting from article orientation is given, according to [14], as: 1 FD ADC D u u ( u u ), (5) where u ( u, v, w) and u ( u, v, w) are the fluid velocity vector at the article centre of mass and the article velocity vector resectively and A D is the article area normal to the direction of the drag force. The rojected area A D can be exressed as a function of the article incidence angle, α i, between the article sli velocity, ( u u ), and the article rincial axis, z (see Figure 1) as [14]: A D 1 4b a cos i sin i, (6) a where A D a for a sherical article with The drag coefficient C D has been measured for a wide range of article shaes, but is not generally available in terms of a functional relationshi with the Reynolds number, and the orientation and geometric arameters of the article. One way to deal with this roblem is by using the shericity factor, S, and the volume uivalent diameter, d, as geometric arameters and introducing orientation deendency in drag correlations using the effective area normal to the direction of the drag force. Here, following a review of available drag coefficient correlations [15], the Ganser [16] drag coefficient exression is used for C D in Eq. (5), as given by: C K D ReK1K, (7) Re K K /( Re K ) 1 1K where C D and Re u v d / are based on the ual volume shere diameter, d, K1 f1( dn, d, S) and K f( S) are the Stokes and Newton shae factors that model the article shericity and orientation, 1/ dn ( 4A D / ) is the ual-rojected area circle diameter, and S is the article shericity, defined as the ratio of the surface area of a shere having the same volume as the article to the actual surface area of the non-sherical article. A stochastic Markov model is adoted to reresent the influence of the unresolved fluid velocity fluctuations exerienced by a stochastic article over a time, d t [1]. Adding the deterministic art, the drag term, F D, and the stochastic (SGS disersion) art together gives: du ( FD )dt ( C0k sgs / ) dw, (8) where the last term in Eq. (8) models the SGS article disersion [1]; k sgs is the unresolved kinetic energy of the fluid, C 0 is a model constant, d Wt reresents the increment of the Wiener rocess and t is a sub-grid timescale which affects the rate of interaction between the article and turbulence dynamics. The rate of change with time of the rincial comonents of the angular velocity ω ( x, y, z) is given by the Euler uation rotation as: t t da Ia Ta ( Ib Ic) bc, (9) dt where ( i, j, k) ( x, y, z), ( y, z, x) and ( z, x, y) are the rincial comonents of the torque, Ti TH TR, with the moment of inertia, I i, and the angular velocity, i. The rincial moments of inertia of a sheroid are Ix x I yy ( 1) a 15 and I z z a The net torque T [ Tx, Ty, Tz ] acting on the article is the sum of the hydrodynamic torque, T H, caused by the non-coincident centres of mass and of ressure, and the torque due to the resistance on a relatively rotating body, T R, which always acts to attenuate the relative sin. T H and T R are given in the article frame of reference as [14, 17]:

5 Derrick O. Njobuenwu and Michael Fairweather / Procedia Engineering 10 ( 015 ) TH A[( xcz) ( FD )], (10) where T H will change its sign, such that TH TH when cos i 0. The term x c is a semi-emirical exression roosed in [14] that defines the offset between the centres of mass and ressure. T R can be directly derived by integration of the friction, caused by rotation, over the article length, L. T R for sheroidal articles within Stokes conditions is known [3] and has also been exanded to other shaes and to higher Reynolds numbers, with the local 1 relative sin given as ( Aω f ω), and with ω f u accounting for the undisturbed fluid vorticity at the oint occuied by the article s centre of mass [14, 17]. The resulting torque is thus exressed as: L / T C A [( Aω ω) l] dl, (11) R 0 D f where the sign ( ) of T R is selected as the sign of ( Aω f ω), and l is the distance from the centre of rotation (see Figure 1). The time evolution of the quaternion is used to udate the orientation of the articles and is comuted as: q 0 qo q1 q q3 0 q 1 1 q1 q0 q3 q x q. (1) q q q3 q0 q1 y q 3 q3 q q1 q0 z D f Lastly, it should be noted that there is couling between the translational and rotational motion. In Eq. (10), the torque due to the non-coincident centres of mass and of ressure, T H, is a function of the hydrodynamic force in the inertial frame which is transformed to the article frame by the transformation matrix A. For each time or integration ste, the transformation matrix is obtained from the new quaternions, and these quaternions are subsuently used to obtain new values of α i, A D, d n, C D, F D and T R. This is also the case for the torque due to the resistance on a relatively rotating body, T, which is a function of A D and C D. R (a) (b) (c) Fig.. Quadrant analysis of bursting rocess: (a) u w Reynolds stress in u w sace, (b) in w w sace, and (c) in w sace. 3. Quadrant decomosition of velocity and sli velocity fluctuations The bursting rocess consists of four categories of event; these categories are defined by the quadrant of the event as shown in Fig.. This categorisation is common for the fluid Reynolds stress between the streamwise ( w ) and wall-normal ( u ) velocity fluctuations [18] and this aroach will be adoted for the fluid-article interactions, i.e. the sli velocity fluctuation, u. The fluid, article and sli velocity are largely deendent on the osition within the boundary layer between the two arallel walls. Following Reynolds decomosition, the instantaneous fluid, article and sli velocity vectors are decomosed into a mean art,, and a fluctuating art,, given as: w

6 18 Derrick O. Njobuenwu and Michael Fairweather / Procedia Engineering 10 ( 015 ) u u u u u u u u u The instantaneous fluid and article velocity vectors are decomosed as resectively. Note the arameters are both time- and saced- averaged. (13) u u u and u u u, As show in Figure (a), a Q1 event ( u 0 and w 0 ) corresonds to an outward motion of high-seed fluid away from the wall. A Q event ( u 0 and w 0 ) describes an ejection of low-seed fluid into the high-seed stream. A Q3 event ( u 0 and w 0 ) reresents an inward motion of low-seed fluid towards the wall, while an event with ( u 0 and w 0 ) falls into Q4 and describes the inrush of high-seed fluid into a low-seed region, also known as a swee. 4. Numerical Simulations The turbulent channel flow into which articles were injected was reresented using a comutational domain (h hπ 4hπ) that was discretized with ( ) nodes, where the (x y z) axes are in the wall normal, sanwise and streamwise directions, resectively. The Reynolds numbers Re τ ( = hu τ /ν) and Re b ( = hu b /ν) were 300 and 4910 based on the shear velocity, u τ, and the bulk velocity, u b, with the channel half height h, kinematic viscosity ν = m s -1 and density ρ = 1.3 kg m -3. The shear velocity is defined as u τ = (τ w /ρ) 1/, where τ w is the mean shear stress at the wall. The mesh sacing was uniform in the y and z directions and non-uniform in the x direction. Periodic boundary conditions were used in the streamwise and sanwise directions, while no-sli boundary conditions were imosed at the walls. In the streamwise direction the mass flow was fixed, such that the driving ressure gradient which corresonds to the average wall shear stress for the comutational domain at a given time had to vary. A dynamic time-ste was chosen to ensure that Courant numbers were always less than 0.3. The solution was assumed to be statistically stationary when the driving ressure gradient was quasi-eriodic in time. To avoid laminarisation of the flow, an initial simulation at high Reynolds number was carried out and the resulting solution used to initialize flow at Re τ 300. Variables are reorted in wall units, with suerscrit +, by normalizing them by u τ, and ν. A Lagrangian article tracking code couled with the LES code was develoed [], an extension of the work reorted in [14] for ellisoidal articles, and that of [9] for articles in a shear flow, to calculate article trajectory, rotation and orientation in the flow field. The code interolates fluid velocities at Eulerian grid nodes onto the article osition by means of trilinear interolation, and integrates the uations of article motion forward in time by means of a 4 th order Runge-Kutta scheme. The articles are assumed to be ointwise, rigid and the shae is a function of the asect ratio, c / a, where a and c corresond to the article semi-minor and semi-major axis lengths. Periodic boundary conditions are imosed on articles in both streamwise and sanwise directions. The article wall boundary condition is straightforward for sherical and comlex for non-sherical articles. Sherical articles are assumed to have contacted the wall when the distance from their centre of mass to the wall is less than the article radius. However, for the ellisoidal articles, three article-wall collision scenarios could occur [5]. First, if the distance of the article centroid from the boundary surface is less than the semi-minor axis, a, it has contacted the wall. Second, if this relative osition is greater than the semi-major axis, c, the ellisoid is in susension. Third, when the distance between the article centroid and the wall is within the range of the a and c axes, whether the ellisoid is in contact with the wall or not deends on its orientation relative to the wall. The article initial conditions are such that at the beginning of the simulation, articles are distributed randomly over the comutational domain and their initial velocity and sin is set ual to that of the fluid at the article osition, while their initial orientation was obtain from randomly samled Euler angles. The article size (inertia) was measured using the uivalent volume diameter, d, and a non-dimensional relaxation time,. The uivalent volume diameter, d,

7 Derrick O. Njobuenwu and Michael Fairweather / Procedia Engineering 10 ( 015 ) is defined as the diameter of the shere with the same volume of the ellisoidal article, Sd /18, where d d u /. 1/ 3 d a and 5. Results and discussion The LES results from a channel flow with Re τ = 300 are first validated against DNS results [19] in Fig. 3(a) for the Reynolds normal stress terms ( u ms, v and ms w ) in the wall-normal, sanwise and streamwise directions. There ms is good agreement between the LES and DNS results which gives confidence in the resent two-hase comutations. By using quadrant analysis analogous to Fig. (a), Fig. 3(b) shows how each quadrant s events contribute to the distribution of the shear stress term u w as a function of the non-dimensional wall-normal location, x. Note, the exact exression for the Reynolds stress is ( uw). The first (Q1) and third (Q3) quadrants contribute to the negative Reynolds shear stress while the second (Q) and fourth (Q4) quadrants show ositive turbulence roduction. The intensity of swee events dominates at x, while that of ejection events is greatest away from the wall, at x. These results are consistent with other findings reorted in the literature [18, 0], where it has been show that the magnitude of the turbulent velocity fluctuations in the three directions eaks in the buffer region ( 5 x 30 ), with the region being dominated by strong Q and Q4 events. Fig. 3. (a) Reynolds normal stresses (linear-linear scale, squares DNS, circles LES), and (b) Reynolds shear stress <u w > from each quadrant (log-linear scale) normalised by the friction velocity, for the single-hase flow. Next, results based on the robability density function (PDF) of the fluctuating velocities at the article osition are resented. Two hundred thousand articles with density 1000 kg m -3 and three shaes based on asect ratio, reresenting a disk ( 0.1), a shere ( 1) and a needle ( 10) following the Loth [1] classification, were tracked in the flow to analyse the shae and orientation effect on article segregation. Note, the three shaed articles have an ual uivalent volume diameter d but different shericity due to their different asect ratios. A great deal of results were generated from this study, although only the results for non-dimensional article resonse time based on an uivalent volume diameter 5 are reorted in this aer. Other statistical analyses for the full range of arameters studied ( Re,, x ) will be rovided in the future. τ, Instantaneous scatter lots of the non-dimensional streamwise sli velocity fluctuation ( w ) versus the nondimensional fluid streamwise fluctuating velocity, ( w ), are shown in Fig. 4, and versus the non-dimensional article streamwise fluctuating velocity, ( w ), in Fig. 5, where results for the disk, shere and needle articles are given. Note that the suerscrit ( + ) has been omitted from the figures and subsuent text for simlicity. The statistical analyses resented in Fig. 4 and Fig. 5 were obtained from conditional averaging rather than averaging over discrete Eulerian grid oints. Four hundred samles at intervals of 100 time stes at buffer region wall-normal ositions, 7 x 9, and subjected to the quadrant analyses based on Fig. (b) and (c), resectively, are

8 130 Derrick O. Njobuenwu and Michael Fairweather / Procedia Engineering 10 ( 015 ) considered. The ercentage figures given in Fig. 4 and Fig. 5 are the time-averaged ercentage values of the quadrant distributions. Similarly, the time-averaged ercentage values of the quadrant distributions are also shown in Table 1 for the same analysis alied in the wall-normal direction, u. The asymmetric distributions in the ( w, w )- and ( w, w )-lanes show non-homogeneity in the article segregation in the near-wall region. The maximum ositive sli velocity ( w ) was obtained when w 0 in Fig. 4 and when w 0 in Fig. 5. Similarly, the maximum negative sli velocity ( w ) was obtained when w 0 in Fig. 4 and when w 0 in Fig. 5. Interestingly, in both figures, and in the results of Table 1, there is a common trend. For events with alternating sign between w and w or w (i.e. Q and Q4), the Q (ejection) events are more fruent than the Q4 events at this samling location, 7 x 9. Note that the Q4 events ( w 0, w 0 ) of Fig. 4 reresent highly intermittent article-to-fluid motions in high-seed fluid streaks. Similarly, for events with the same sign between w and w or w (i.e. Q1 and Q3), the Q3 (inward interaction) events are more fruent than the Q1 events at the same samling location. This tread will change when the statistics are samled at other boundary layer locations, esecially away from the near-wall region, as well as for different article inertia. (a) (b) (c) Fig. 4. Scatter lots of the fluid streamwise velocity fluctuation, w, and streamwise sli velocity fluctuation, w, for a) a disk ( = 0.1), (b) a shere ( = 1.0) and (c) a needle ( = 10), all with uivalent relaxation time 5 and conditionally samled article wall normal ositions x 7 9. For comarison uroses, a ercent value corresonding to the number of articles in each quadrant is rovided. (a) (b) (c) Fig. 5. Scatter lots of the article streamwise velocity fluctuation, w, and the streamwise sli velocity fluctuation, w, for (a) a disk ( = 0.1), (b) a shere ( = 1.0) and (c) a needle ( = 10), all with uivalent relaxation time 5 and conditionally samled article wall normal ositions x 7 9. For comarison uroses, a ercent value corresonding to the number of articles in each quadrant is rovided. In Fig. 4, showing the ( w, w )-lane, the summation of Q and Q3 events, reresenting events with a negative streamwise fluid velocity fluctuation w 0, accounts for u to 70% of the reorted events. This trend holds for all three shaes of article. This means that, regardless of the article shae, articles with finite inertia tend to referentially concentrate in low-seed streaks that dominate the near-wall regions. Furthermore, the fractions of the number of events in each of the four quadrants is similar for articles with asect ratios In contrast, for the distributions in Fig. 5 that shows the ( w, w )-lane, the fractions of the number of events in each of the four

9 Derrick O. Njobuenwu and Michael Fairweather / Procedia Engineering 10 ( 015 ) quadrants are similar for articles with asect ratios In Fig. 5, the summation of Q and Q4 events dominates and totals to aroximately 70% of the overall events. Particles with a tendency to referentially concentrate in low-seed streaks are therefore likely to encounter the wall and, if the energy barrier is overcome, to deosit on the wall surface. A similar analysis can be erformed in terms of the correlation of the wall-normal sli velocity fluctuation with the wall-normal fluid velocity fluctuation ( u, u ), and the wall-normal sli velocity fluctuation with the article wall-normal velocity fluctuation ( u, u ), as resented in Table 1. Lastly, Figure 6 shows the robability density function of the non-dimensional streamwise fluid velocity fluctuations, PDF( w ), samled again in the buffer region, at 7 x 9, and conditionally samled for articles with ositive ( w 0 ) and negative ( w 0 ) streamwise sli velocity fluctuation values. This figure is intended to give more insight into the role of article sli velocity fluctuations in article segregation behaviour in the nearwall region of a turbulent channel flow. The shae of the distributions are similar for the three shaes of article with 5. Hence, for the range of article asect ratios considered, the satial distribution of the articles conditionally samled at 7 x 9 is skewed, with all three article shaes having eaks in the PDF( w ) at w 0. This is the region where the local fluid velocity is lower than the mean fluid velocity at the article osition. The eak of the PDF( w ) of articles with w 0 is also larger than that for w 0, suggesting that a larger number of articles lag the local fluid motion, and that their disersion is strongly deended on the drag force. Table 1. Percent article counts for each ( u, u ) quadrant (left) and ( u, u ) quadrant (right). ( u, u ) Quadrant ( u, u ) Quadrant λ Q Q1 Q Q % 7.% 31.0% 14.6% % 8.4% 30.8% 19.3% % 4.6% 41.5% 13.% Q3 Q4 Q3 Q % 6.0% 37.9% 16.5% % 0.5% 36.8% 13.1% % 1.8% 7.4% 17.9% PDF(w' ) (w' > 0) (w' < 0) PDF(w') (a) (b) (c) (w' > 0) (w' < 0) PDF(w') (w' > 0) (w' < 0) w' w' w' Fig. 6. Effect of article asect ratio on conditioned PDF(w ) for articles with streamwise w 0 and w 0 for a) disk ( = 0.1), (b) shere ( = 1.0) and (c) needle ( = 10). 6. Conclusions In this aer, article segregation has been studied using large eddy simulation, Lagrangian article tracking and a conditional statistical analyses of article and fluid velocity fields in a turbulent channel flow with shear Reynolds number Re 300. One-way couling was adoted and only the drag force and the contribution from the τ

10 13 Derrick O. Njobuenwu and Michael Fairweather / Procedia Engineering 10 ( 015 ) unresolved sub-grid scale of the velocity fluctuations on article acceleration was accounted for. Particles with asect ratios of 0. 1, 1.0 and 10, reresenting a disk, a shere and a needle, were simulated. The three shaed articles had an ual uivalent volume diameter and non-dimensional article relaxation time, 5. The article interaction with near-wall turbulent coherent structures (outward motion, ejection, inward motion and swee) was analysed by using conditional statistics (robability density function and scatter lots) in quadrants to study the distribution of the fluid, article and sli velocity fluctuations. The results showed that, regardless of their shae, all the articles tend to referentially concentrate in low-seed streaks within the near-wall region. Acknowledgements The authors wish to thank the Engineering and Physical Sciences Research Council for their financial suort of the work reorted in this aer under EPSRC Grant EP/I003010/1, Comutational Modelling for Advanced Nuclear Power Plants. References [1] C. Marchioli, A. Soldati, Mechanisms for article transfer and segregation in a turbulent boundary layer, J. Fluid Mech. 468 (00) [] D.O. Njobuenwu, M. Fairweather, Non-sherical article translation and orientation in wall-bounded turbulence, in: T.E. Simos, G. Psihoyios, C. Tsitouras (Eds.) 11 th International Conference on Numerical Analysis and Alied Mathematics 013 (ICNAAM-013), AIP Conference Proceedings, Rhodes, Greece, 013, [3] G.B. Jeffery, The motion of ellisoidal articles immersed in a viscous fluid, P. Roy. Soc. Lond. A Mat. 10 (19) [4] F.P. Bretherton, The motion of rigid articles in a shear flow at low Reynolds number, J. Fluid Mech. 14 (196) [5] F.-G. Fan, G. Ahmadi, A sublayer model for wall deosition of ellisoidal articles in turbulent streams, J. Aerosol Sci. 6 (1995) [6] H. Zhang, G. Ahmadi, F.-G. Fan, J.B. McLaughlin, Ellisoidal articles transort and deosition in turbulent channel flows, Int. J. Multihas. Flow 7 (001) [7] P.H. Mortensen, H.I. Andersson, J.J.J. Gillissen, B.J. Boersma, Dynamics of rolate ellisoidal articles in a turbulent channel flow, Phys. Fluids 0 (008) [8] C. Marchioli, M. Fantoni, A. Soldati, Orientation, distribution, and deosition of elongated, inertial fibers in turbulent channel flow, Phys. Fluids (010) [9] D.O. Njobuenwu, M. Fairweather, Effect of shae on inertial article dynamics in a channel flow, Flow Turbul. Combust 9 (014) [10] L.H. Zhao, C. Marchioli, H.I. Andersson, Stokes number effects on article sli velocity in wall-bounded turbulence and imlications for disersion models, Phys. Fluids 4 (01) [11] U. Piomelli, J. Liu, Large-eddy simulation of rotating channel flows using a localized dynamic model, Phys. Fluids 7 (1995) [1] M. Bini, W.P. Jones, Large-eddy simulation of article-laden turbulent flows, J. Fluid Mech. 614 (008) [13] H. Goldstein, Classical Mechanics, nd ed., Addison-Wesley, Reading, MA, [14] C. Yin, L. Rosendahl, S. Knudsen Kær, H. Sørensen, Modelling the motion of cylindrical articles in a nonuniform flow, Chem. Eng. Sci. 58 (003) [15] R.P. Chhabra, L. Agarwal, N.K. Sinha, Drag on non-sherical articles: an evaluation of available methods, Powder Technol. 101 (1999) [16] G.H. Ganser, A rational aroach to drag rediction of sherical and nonsherical articles, Powder Technol. 77 (1993) [17] C. Yin, L. Rosendahl, S. K. Kær, T. J. Condra, Use of numerical modeling in design for co-firing biomass in wall-fired burners, Chem. Eng. Sci. 59 (004) [18] J. Kim, P. Moin, R. Moser, Turbulence statistics in fully develoed channel flow at low Reynolds number, J. Fluid Mech. 177 (1987) [19] C. Marchioli, A. Soldati, Reynolds number scaling of article referential concentration in turbulent channel flow, in: J.M.L.M. Palma, A.S. Loes (Eds.) Advances in Turbulence XI, Sringer Berlin Heidelberg, 007, [0] J. Huang, Y. Murai, F. Yamamoto, Quadrant analysis of bubble induced velocity fluctuations in a transitional boundary layer, J. Hydrodyn. Ser. B 1 (009) [1] E. Loth, Drag of non-sherical solid articles of regular and irregular shae, Powder Technol. 18 (008)