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Numerical study of transport phenomena in particle suspensions
KTH, School of Engineering Sciences (SCI), Mechanics.ORCID iD: 0000-0003-4328-7921
2019 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Suspensions of solid particles in a viscous liquid are of scientific and technological interest in a wide range of applications. Sediment transport in estuaries, blood flow in the human body, pyroclastic flows from volcanos and pulp fibers in papermaking are among the examples. Often, these particulate flows also include heat transfer among the two phases or the fluid might exhibit a viscoelastic behavior. Predicting these flows and the heat transfer within requires a vast knowledge of how particles are distributed across the domain, how particles affect the flow field and finally how they affect the global behavior of the suspension. The aim of this work is therefore to improve the physical understanding of these flows, including the effect of physical and mechanical properties of the particles and the domain that bounds them.To this purpose, particle-resolved direct numerical simulations (PR-DNS) of spherical/non-spherical particles in different flow regimes and geometries are performed, using an efficient/accurate numerical tool that is developed within this work. The code is based on the Immersed Boundary Method (IBM) for the fluid-solid interactions with lubrication, friction and collision models for the close range particle-particle (particle-wall) interactions, also able to resolve for heat transfer equation in both Newtonian and non-Newtonian fluids.

Several conclusions are drawn from this study, revealing the importance of the particle's shape and inertia on the global behavior of a suspension, e.g. spheroidal particles tend to cluster while sedimenting. This phenomenon is observed here for both particles with high inertia, sedimenting in a quiescent fluid and inertialess particles (point-like tracer prolates) settling in homogeneous isotropic turbulence. The mechanisms for clustering is indeed different between these two situations, however, it is the shape of the particles that governs these mechanisms, as clustering is not observed for spherical particles. Another striking finding of this work is drag reduction in particulate turbulent channel flow with disk-like spheroidal particles. Again this drag reduction is absent for spherical particles, which instead increase the drag with respect to single-phase turbulence. In particular, we show that inertia at the particle scale induces a non-linear increase of the heat transfer as a function of the volume fraction, unlike the case at vanishing inertia where heat transfer increases linearly within the suspension.

Place, publisher, year, edition, pages
KTH Royal Institute of Technology, 2019. , p. 63
Series
TRITA-MEK, ISSN 0348-467X ; 2019:03
National Category
Fluid Mechanics and Acoustics
Research subject
Engineering Mechanics
Identifiers
URN: urn:nbn:se:kth:diva-240126ISBN: 978-91-7873-065-0 (print)OAI: oai:DiVA.org:kth-240126DiVA, id: diva2:1270229
Public defence
2019-01-25, H1, Teknikringen 33, våningsplan 5, H-huset, KTH Campus, Stockholm, 10:30 (English)
Opponent
Supervisors
Funder
EU, European Research Council, ERC-2013-CoG-616186, TRITOSAvailable from: 2018-12-13 Created: 2018-12-12 Last updated: 2018-12-13Bibliographically approved
List of papers
1. Sedimentation of inertia-less prolate spheroids in homogenous isotropic turbulence with application to non-motile phytoplankton
Open this publication in new window or tab >>Sedimentation of inertia-less prolate spheroids in homogenous isotropic turbulence with application to non-motile phytoplankton
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2017 (English)In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 831, p. 655-674Article in journal (Refereed) Published
Abstract [en]

Phytoplankton are the foundation of aquatic food webs. Through photosynthesis, phytoplankton draw down $CO_2$ at magnitudes equivalent to forests and other terrestrial plants and convert it to organic material that is then consumed by other organisms of phytoplankton in higher trophic levels. Mechanisms that affect local concentrations and velocities are of primary significance to many encounter-based processes in the plankton including prey-predator interactions, fertilization and aggregate formation. We report results from simulations of sinking phytoplankton, considered as elongated spheroids, in homogenous isotropic turbulence to answer the question of whether trajectories and velocities of sinking phytoplankton are altered by turbulence. We show in particular that settling spheroids with physical characteristics similar to those of diatoms weakly cluster and preferentially sample regions of down-welling flow, corresponding to an increase of the mean settling speed with respect to the mean settling speed in quiescent fluid.  We explain how different parameters can affect the settling speed and what underlying mechanisms might be involved.  Interestingly, we observe that the increase in the aspect ratio of the prolate spheroids can affect the clustering and the average settling speed of particles by two mechanisms: first is the effect of aspect ratio on the rotation rate of the particles, which saturates faster than the second mechanism of increasing drag anisotropy.   

National Category
Fluid Mechanics and Acoustics
Identifiers
urn:nbn:se:kth:diva-204164 (URN)10.1017/jfm.2017.670 (DOI)000412936100010 ()2-s2.0-85031907204 (Scopus ID)
Note

QC 20170328

Available from: 2017-03-23 Created: 2017-03-23 Last updated: 2018-12-12Bibliographically approved
2. Numerical study of the sedimentation of spheroidal particles
Open this publication in new window or tab >>Numerical study of the sedimentation of spheroidal particles
2016 (English)In: International Journal of Multiphase Flow, ISSN 0301-9322, E-ISSN 1879-3533, Vol. 87, p. 16-34Article in journal (Refereed) Published
Abstract [en]

The gravity-driven motion of-rigid particles in a viscous fluid is relevant in many natural and industrial processes, yet this has mainly been investigated for spherical particles. We therefore consider the sedimentation of non-spherical (spheroidal) isolated and particle pairs in a viscous fluid via numerical simulations using the Immersed Boundary Method. The simulations performed here show that the critical Galileo number for the onset of secondary motions decreases as the spheroid aspect ratio departs from 1. Above this critical threshold, oblate particles perform a zigzagging motion whereas prolate particles rotate around, the vertical axis while having their broad side facing the falling direction. Instabilities of the vortices in the wake follow when farther increasing the Galileo number. We also study the drafting kissing-tumbling associated with the settling of particle pairs. We find that the interaction time increases significantly for non-spherical particles and, more interestingly, spheroidal particles are attracted from larger lateral displacements. This has important implications for the estimation of collision kernels and can result its increasing clustering in suspensions of sedimenting spheroids.

Keywords
Non-spherical particles, Sedimentation, Particle pair interactions, Drafting-kissing-tumbling, Numerical modelling
National Category
Applied Mechanics
Identifiers
urn:nbn:se:kth:diva-196969 (URN)10.1016/j.ijmultiphaseflow.2016.08.005 (DOI)000386645300003 ()2-s2.0-84985916725 (Scopus ID)
Note

QC 20161213

Available from: 2016-12-13 Created: 2016-11-28 Last updated: 2018-12-12Bibliographically approved
3. Clustering and increased settling speed of oblate particles at finite Reynolds number
Open this publication in new window or tab >>Clustering and increased settling speed of oblate particles at finite Reynolds number
2018 (English)In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 848, p. 696-721Article in journal (Refereed) Published
Abstract [en]

We study the settling of rigid oblates in a quiescent fluid using interface-resolved direct numerical simulations. In particular, an immersed boundary method is used to account for the dispersed solid phase together with lubrication correction and collision models to account for short-range particle-particle interactions. We consider semi-dilute suspensions of oblate particles with aspect ratio AR = 1/3 and solid volume fractions (Phi = 0.5-10%. The solid-to-fluid density ratio R = 1.02 and the Galileo number (i.e. the ratio between buoyancy and viscous forces) based on the diameter of a sphere with equivalent volume Ga = 60. With this choice of parameters, an isolated oblate falls vertically with a steady wake with its broad side perpendicular to the gravity direction. At this Ga, the mean settling speed of spheres is a decreasing function of the volume Phi and is always smaller than the terminal velocity of the isolated particle, V-t. On the contrary, in dilute suspensions of oblate particles (with Phi <= 1 %), the mean settling speed is approximately 33 % larger than V-t. At higher concentrations, the mean settling speed decreases becoming smaller than the terminal velocity V-t between (Phi = 5 % and 10%. The increase of the mean settling speed is due to the formation of particle clusters that for Phi = 0.5-1 % appear as columnar-like structures. From the pair distribution function we observe that it is most probable to find particle pairs almost vertically aligned. However, the pair distribution function is non-negligible all around the reference particle indicating that there is a substantial amount of clustering at radial distances between 2 and 6c (with c the polar radius of the oblate). Above Phi = 5 %, the hindrance becomes the dominant effect, and the mean settling speed decreases below V-t. As the particle concentration increases, the mean particle orientation changes and the mean pitch angle (the angle between the particle axis of symmetry and gravity) increases from 23 degrees to 47 degrees . Finally, we increase Ga from 60 to 140 for the case with (Phi = 0.5 % and find that the mean settling speed (normalized by V-t) decreases by less than 1 % with respect to Ga = 60. However, the fluctuations of the settling speed around the mean are reduced and the probability of finding vertically aligned particle pairs increases.

Place, publisher, year, edition, pages
Cambridge University Press, 2018
Keywords
multiphase and particle-laden flows, particle/fluid flow, suspensions
National Category
Other Engineering and Technologies
Identifiers
urn:nbn:se:kth:diva-232594 (URN)10.1017/jfm.2018.370 (DOI)000438342800001 ()2-s2.0-85048603916 (Scopus ID)
Funder
EU, European Research Council, ERC-2013-CoG-616186Swedish Research CouncilSwedish e‐Science Research Center
Note

QC 20180731

Available from: 2018-07-31 Created: 2018-07-31 Last updated: 2018-12-12Bibliographically approved
4. Inertial migration of spherical and oblate particles in straight ducts
Open this publication in new window or tab >>Inertial migration of spherical and oblate particles in straight ducts
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(English)In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645Article in journal (Refereed) Accepted
Abstract [en]

We study numerically the inertial migration of a single rigid sphere and an oblate spheroid in straight square and rectangular ducts. A highly accurate interface-resolved numerical algorithm is employed to analyse the entire migration dynamics of the oblate particle and compare it with that of the sphere. Similarly to the inertial focusing of spheres, the oblate particle reaches one of the four face-centred equilibrium positions, however they are vertically aligned with the axis of symmetry in the spanwise direction. In addition, the lateral trajectories of spheres and oblates collapse into an equilibrium manifold before ending at the equilibrium positions, with the equilibrium manifold tangential to lines of constant background shear for both sphere and oblate particles. The differences between the migration of the oblate and sphere are also presented, in particular the oblate may focus on the diagonal symmetry line of the duct cross-section, close to one of the corners, if its diameter is larger than a certain threshold. Moreover, we show that the final orientation and rotation of the oblate exhibit a chaotic behaviour for Reynolds numbers beyond a critical value. Finally, we document that the lateral motion of the oblate particle is less uniform than that of the spherical particle due to its evident tumbling motion throughout the migration. In a square duct, the strong tumbling motion of the oblate in the first stage of the migration results in a lower lateral velocity and consequently longer focusing length with respect to that of the spherical particle. The opposite is true in a rectangular duct where the higher lateral velocity of the oblate in the second stage of the migration, with negligible tumbling, gives rise to shorter focusing lengths.These results can help the design of microfluidic systems for bio-applications.

National Category
Fluid Mechanics and Acoustics
Identifiers
urn:nbn:se:kth:diva-204162 (URN)10.1017/jfm.2017.189 (DOI)000405373500005 ()2-s2.0-85018317724 (Scopus ID)
Note

QC 20170328

Available from: 2017-03-23 Created: 2017-03-23 Last updated: 2019-02-28Bibliographically approved
5. Drag reduction in turbulent channel flow laden with finite-size oblate spheroids
Open this publication in new window or tab >>Drag reduction in turbulent channel flow laden with finite-size oblate spheroids
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2017 (English)In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 816, p. 43-70Article in journal (Refereed) Published
Abstract [en]

We study suspensions of oblate rigid particles in a viscous fluid for different values of the particle volume fractions.Direct numerical simulations have been performed using a direct-forcing immersed boundary method to account for the dispersed phase, combined with a soft-sphere collision model and lubrication corrections for short-range particle-particle and particle-wall interactions. With respect to the single phase flow, we show that in flows laden with oblate spheroids the drag is reduced and the turbulent fluctuations attenuated.In particular, the turbulence activity decreases to lower values than those obtained by only accounting for the effective suspension viscosity.To explain the observed drag reduction we consider the particle dynamics and the interactions of the particles with the turbulent velocity field and show that the particle wall layer, previously observed and found to be responsible for the increased dissipation in suspensions of spheres, disappears in the case of oblate particles.These rotate significantly slower than spheres near the wall and tend to stay with their major axes parallel to the wall, which leads to a decrease of the Reynolds stresses and turbulence production and so to the overall drag reduction.

National Category
Fluid Mechanics and Acoustics
Identifiers
urn:nbn:se:kth:diva-204160 (URN)2-s2.0-85014045322 (Scopus ID)
Note

QC 20170328

Available from: 2017-03-23 Created: 2017-03-23 Last updated: 2018-12-12Bibliographically approved
6. Turbulence modulation in channel flow of finite-size spheroidal particles
Open this publication in new window or tab >>Turbulence modulation in channel flow of finite-size spheroidal particles
2018 (English)In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 859, p. 887-901Article in journal (Refereed) Published
Abstract [en]

Finite-size particles modulate wall-bounded turbulence, leading, for the case of spherical particles, to increased drag also owing to the formation of a particle wall layer. Here, we study the effect of particle shape on the turbulence in suspensions of spheroidal particles at volume fraction phi = 10 % and show how the near-wall particle dynamics deeply changes with the particle aspect ratio and how this affects the global suspension behaviour. Direct numerical simulations are performed using a direct-forcing immersed boundary method to account for the dispersed phase, combined with a soft-sphere collision model and lubrication corrections for short-range particle-particle and particle-wall interactions. The turbulence reduces with the aspect ratio of oblate particles, leading to drag reduction with respect to the single-phase flow for particles with aspect ratio AR <= 1/3, when the significant reduction in Reynolds shear stress is more than the compensation by the additional stresses, induced by the solid phase. Oblate particles are found to avoid the region close to the wall, travelling parallel to it with small angular velocities, while preferentially sampling high-speed fluid in the wall region. Prolate particles also tend to orient parallel to the wall and avoid its vicinity. Their reluctance to rotate around the spanwise axis reduces the wall-normal velocity fluctuation of the flow and therefore the turbulence Reynolds stress, similar to oblates; however, they undergo rotations in wall-parallel planes which increase the additional solid stresses due to their relatively larger angular velocities compared to the oblates. These larger additional stresses compensate for the reduction in turbulence activity and lead to a wall drag similar to that of single-phase flows. Spheres on the other hand, form a layer close to the wall with large angular velocities in the spanwise direction, which increases the turbulence activity in addition to exerting the largest solid stresses on the suspension, in comparison to the other studied shapes. Spherical particles therefore increase the wall drag with respect to the single-phase flow.

Place, publisher, year, edition, pages
CAMBRIDGE UNIV PRESS, 2018
Keywords
drag reduction, multiphase flow, particle/fluid flow
National Category
Mechanical Engineering
Identifiers
urn:nbn:se:kth:diva-239992 (URN)10.1017/jfm.2018.854 (DOI)000451288500005 ()2-s2.0-85057399152 (Scopus ID)
Note

QC 20181211

Available from: 2018-12-11 Created: 2018-12-11 Last updated: 2018-12-12Bibliographically approved
7. Computational modeling of multiphase viscoelastic and elastoviscoplastic flows
Open this publication in new window or tab >>Computational modeling of multiphase viscoelastic and elastoviscoplastic flows
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2018 (English)In: International Journal for Numerical Methods in Fluids, ISSN 0271-2091, E-ISSN 1097-0363, p. 521-543Article in journal (Refereed) Published
Place, publisher, year, edition, pages
Wiley-VCH Verlagsgesellschaft, 2018
National Category
Fluid Mechanics and Acoustics
Identifiers
urn:nbn:se:kth:diva-240127 (URN)10.1002/fld.4678 (DOI)000450028200001 ()2-s2.0-85052317831 (Scopus ID)
Funder
Swedish Research Council, VR 2014-5001Swedish Research Council, VR2017-4809Swedish Research Council, VR2013-5789
Note

QC 20181214

Available from: 2018-12-12 Created: 2018-12-12 Last updated: 2018-12-14Bibliographically approved
8. Turbulent duct flow with polymers
Open this publication in new window or tab >>Turbulent duct flow with polymers
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2019 (English)In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 859, p. 1057-1083Article in journal (Refereed) Published
Abstract [en]

We have performed direct numerical simulation of the turbulent flow of a polymer solution in a square duct, with the FENE-P model used to simulate the presence of polymers. First, a simulation at a fixed moderate Reynolds number is performed and its results compared with those of a Newtonian fluid to understand the mechanism of drag reduction and how the secondary motion, typical of the turbulent flow in non-axisymmetric ducts, is affected by polymer additives. Our study shows that the Prandtl's secondary flow is modified by the polymers: the circulation of the streamwise main vortices increases and the location of the maximum vorticity moves towards the centre of the duct. In-plane fluctuations are reduced while the streamwise ones are enhanced in the centre of the duct and dumped in the corners due to a substantial modification of the quasi-streamwise vortices and the associated near-wall low- and high-speed streaks; these grow in size and depart from the walls, their streamwise coherence increasing. Finally, we investigated the effect of the parameters defining the viscoelastic behaviour of the flow and found that the Weissenberg number strongly influences the flow, with the cross-stream vortical structures growing in size and the in-plane velocity fluctuations reducing for increasing flow elasticity.We have performed direct numerical simulation of the turbulent flow of a polymer solution in a square duct, with the FENE-P model used to simulate the presence of polymers. First, a simulation at a fixed moderate Reynolds number is performed and its results compared with those of a Newtonian fluid to understand the mechanism of drag reduction and how the secondary motion, typical of the turbulent flow in non-axisymmetric ducts, is affected by polymer additives. Our study shows that the Prandtl's secondary flow is modified by the polymers: the circulation of the streamwise main vortices increases and the location of the maximum vorticity moves towards the centre of the duct. In-plane fluctuations are reduced while the streamwise ones are enhanced in the centre of the duct and dumped in the corners due to a substantial modification of the quasi-streamwise vortices and the associated near-wall low- and high-speed streaks; these grow in size and depart from the walls, their streamwise coherence increasing. Finally, we investigated the effect of the parameters defining the viscoelastic behaviour of the flow and found that the Weissenberg number strongly influences the flow, with the cross-stream vortical structures growing in size and the in-plane velocity fluctuations reducing for increasing flow elasticity.

Place, publisher, year, edition, pages
Cambridge University Press, 2019
National Category
Fluid Mechanics and Acoustics
Identifiers
urn:nbn:se:kth:diva-240129 (URN)10.1017/jfm.2018.858 (DOI)000451519800001 ()2-s2.0-85057589811 (Scopus ID)
Funder
Swedish Research Council, 2014-5001EU, European Research Council, ERC-2013-CoG-616186Swedish e‐Science Research Center
Note

QC 20181213

Available from: 2018-12-12 Created: 2018-12-12 Last updated: 2018-12-13Bibliographically approved
9. The effect of elastic walls on suspension flow
Open this publication in new window or tab >>The effect of elastic walls on suspension flow
2018 (English)In: Physical Review Letters, ISSN 0031-9007, E-ISSN 1079-7114Article in journal (Other academic) Submitted
National Category
Fluid Mechanics and Acoustics
Identifiers
urn:nbn:se:kth:diva-240132 (URN)
Note

QC 20181213

Available from: 2018-12-12 Created: 2018-12-12 Last updated: 2018-12-13Bibliographically approved
10. Turbulent  flow of finite-size spherical particles with viscous hyper-elastic walls
Open this publication in new window or tab >>Turbulent  flow of finite-size spherical particles with viscous hyper-elastic walls
2018 (English)In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645Article in journal (Other academic) Submitted
National Category
Fluid Mechanics and Acoustics
Identifiers
urn:nbn:se:kth:diva-240131 (URN)
Note

QC 20181213

Available from: 2018-12-12 Created: 2018-12-12 Last updated: 2018-12-13Bibliographically approved
11. Heat transfer in laminar Couette flow laden with rigid spherical particles
Open this publication in new window or tab >>Heat transfer in laminar Couette flow laden with rigid spherical particles
2018 (English)In: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 834, p. 308-334Article in journal (Refereed) Published
Abstract [en]

We study heat transfer in plane Couette flow laden with rigid spherical particles by means of direct numerical simulations. In the simulations we use a direct-forcing immersed boundary method to account for the dispersed phase together with a volume-of-fluid approach to solve the temperature field inside and outside the particles. We focus on the variation of the heat transfer with the particle Reynolds number, total volume fraction (number of particles) and the ratio between the particle and fluid thermal diffusivity, quantified in terms of an effective suspension diffusivity. We show that, when inertia at the particle scale is negligible, the heat transfer increases with respect to the unladen case following an empirical correlation recently proposed in the literature. In addition, an average composite diffusivity can be used to approximate the effective diffusivity of the suspension in the inertialess regime when varying the molecular diffusion in the two phases. At finite particle inertia, however, the heat transfer increase is significantly larger, smoothly saturating at higher volume fractions. By phase-ensemble-averaging we identify the different mechanisms contributing to the total heat transfer and show that the increase of the effective conductivity observed at finite inertia is due to the increase of the transport associated with fluid and particle velocity. We also show that the contribution of the heat conduction in the solid phase to the total wall-normal heat flux reduces when increasing the particle Reynolds number, so that particles of low thermal diffusivity weakly alter the total heat flux in the suspension at finite particle Reynolds numbers. On the other hand, a higher particle thermal diffusivity significantly increases the total heat transfer.

Place, publisher, year, edition, pages
Cambridge University Press, 2018
Keywords
multiphase and particle-laden flows, multiphase flow, particle/fluid flows
National Category
Fluid Mechanics and Acoustics
Identifiers
urn:nbn:se:kth:diva-204163 (URN)10.1017/jfm.2017.709 (DOI)000415855500013 ()2-s2.0-85034576917 (Scopus ID)
Funder
Swedish e‐Science Research Center
Note

QC 20171207

Available from: 2017-03-23 Created: 2017-03-23 Last updated: 2018-12-12Bibliographically approved
12. Numerical study of heat transfer in laminar and turbulent pipe flow with finite-size spherical particles
Open this publication in new window or tab >>Numerical study of heat transfer in laminar and turbulent pipe flow with finite-size spherical particles
2018 (English)In: International Journal of Heat and Fluid Flow, ISSN 0142-727X, E-ISSN 1879-2278, Vol. 71, p. 189-199Article in journal (Refereed) Published
Abstract [en]

Controlling heat and mass transfer in particulate suspensions has many applications in fuel combustion, food industry, pollution control and life science. We perform direct numerical simulations (DNS) to study the heat transfer within a suspension of neutrally buoyant, finite-size spherical particles in laminar and turbulent pipe flows, using the immersed boundary method (IBM) to account for the solid fluid interactions and a volume of fluid (VoF) method to resolve the temperature equation both inside and outside the particles. Particle volume fractions up to 40% are simulated for different pipe to particle diameter ratios. We show that a considerable heat transfer enhancement (up to 330%) can be achieved in the laminar regime by adding spherical particles. The heat transfer is observed to increase significantly as the pipe to particle diameter ratio decreases for the parameter range considered here. Larger particles are found to have a greater impact on the heat transfer enhancement than on the wall-drag increase. In the turbulent regime, however, only a transient increase in the heat transfer is observed and the process decelerates in time below the values in single-phase flows as high volume fractions of particles laminarize the core region of the pipe. A heat transfer enhancement, measured with respect to the single phase flow, is only achieved at volume fractions as low as 5% in a turbulent flow.

Place, publisher, year, edition, pages
Elsevier, 2018
Keywords
Finite-size particles, Heat transfer, Particulate flows, Pipe flows
National Category
Energy Engineering
Identifiers
urn:nbn:se:kth:diva-227551 (URN)10.1016/j.ijheatfluidflow.2018.04.002 (DOI)000435428900016 ()2-s2.0-85045214851 (Scopus ID)
Funder
Swedish e‐Science Research Center
Note

QC 20180517

Available from: 2018-05-17 Created: 2018-05-17 Last updated: 2018-12-12Bibliographically approved

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