Dispersed multiphase flows: From Stokes suspensions to turbulence

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1 Dispersed multiphase flows: From Stokes suspensions to turbulence Kyongmin Yeo EARTH SCIENCES DIVISION August 14, 2012 Thanks to: Martin R. Maxey (Brown University)

2 Overview Dispersed multiphase flows DISPERSED MULTIPHASE FLOWS Kyongmin Yeo LAWRENCE BERKELEY NATIONAL LAB 2 / 35

3 Overview Range of scales Reynolds number: ratio of viscous timescale to inertial timescale Re b = ρul µ Cloud: Re b O(10 5 ) O(10 6 ) Human respiratory system: Re b O(10 1 ) O(10 3 ) Blood flow: Re b O(10 3 ) O(10 2 ) Microfluidic devices: Re b O(10 3 ) O(1) DISPERSED MULTIPHASE FLOWS Kyongmin Yeo LAWRENCE BERKELEY NATIONAL LAB 3 / 35

4 Overview Range of scales Reynolds number: ratio of viscous timescale to inertial timescale Re b = ρul µ Re p = ρa2 γ µ Cloud: Re b O(10 5 ) O(10 6 ) a O(1) O(10 2 )µm, Re p O(10 1 ) O(10). Human respiratory system: Re b O(10 1 ) O(10 3 ) a O(10)µm, Re p O(10 2 ) O(1). Blood flow: Re b O(10 3 ) O(10 2 ) a O(1)µm, Microfluidic devices: Re p O(10 4 ) O(1). Re b O(10 3 ) O(1) a O(1)µm, Re p O(10 4 ) O(10 1 ). Stokes layer thickness: l St 1/Re p Particle-scale dynamics in Stokes regime, while bulk flow can be Stokes to Turbulent flow. DISPERSED MULTIPHASE FLOWS Kyongmin Yeo LAWRENCE BERKELEY NATIONAL LAB 3 / 35

Overview Examples of phase changes in dispersed flows

of concentrated suspensions Dilute turbulent dispersed

5 Overview Examples of phase changes in dispersed flows Sea-atmosphere interaction Sediment transport Ouriemi et al. (2009) Barenblatt (2009) Solid boundary Boundary layer of concentrated suspensions Dilute turbulent dispersed flows Tripathi & Acrivos (1999) DISPERSED MULTIPHASE FLOWS Kyongmin Yeo LAWRENCE BERKELEY NATIONAL LAB 4 / 35

6 Overview Outline 1 Overview 2 Dilute to semi-dilute suspension flows Finite-size effect Particle-pair hydrodynamics 3 Concentrated suspension flows Stokes suspensions Finite Re p suspensions 4 Conclusions DISPERSED MULTIPHASE FLOWS Kyongmin Yeo LAWRENCE BERKELEY NATIONAL LAB 5 / 35

7 Dilute to semi-dilute suspension flows Finite-size effect Review of Lagrangian point-particle model 1 Equation of motion for a spherical particle in unsteady flow (Maxey & Riley 1983): dv Du m p = (m p m f )g + m f dt Dt m { f d V u 1 } 2 dt 10 a2 2 u { t } 6πaµ Q + a Q =V ( a2 2 ) u 0 dq dτ [πν(t τ)] 1/2 dτ 1 Balachandar & Eaton ARFM (2010) DISPERSED MULTIPHASE FLOWS Kyongmin Yeo LAWRENCE BERKELEY NATIONAL LAB 6 / 35

8 Dilute to semi-dilute suspension flows Finite-size effect Review of Lagrangian point-particle model 1 Equation of motion for a spherical particle in unsteady flow (Maxey & Riley 1983): m p dv dt = (m p m f )g 6πaµ(V u) = F Phase-coupling through drag force F; { } u ρ f + (u )u = σ F, σ ij = pδ ij + 2µ f e ij t Understimates turbulent attenuation, particularly for a η. Unresolved local distortion of flow field around the particles. 1 Balachandar & Eaton ARFM (2010) DISPERSED MULTIPHASE FLOWS Kyongmin Yeo LAWRENCE BERKELEY NATIONAL LAB 6 / 35

9 Dilute to semi-dilute suspension flows Finite-size effect Review of Lagrangian point-particle model 1 Equation of motion for a spherical particle in unsteady flow (Maxey & Riley 1983): m p dv dt = (m p m f )g 6πaµ(V u) = F Phase-coupling through drag force F; { } u ρ f + (u )u = σ F, σ ij = pδ ij + 2µ f e ij t Understimates turbulent attenuation, particularly for a η. Unresolved local distortion of flow field around the particles. Bulk deviatoric stress in a suspension of force-free particles (Batchelor 1970) Σ ij = 2µ E ij 1 V ρ f u iu jdv + 1 µ(u in j + u jn i)da V Ω i e.g. In the dilute limit: Phase-coupling in stress tensor. 1 Balachandar & Eaton ARFM (2010) i Ω i µ(u i n j + u j n i )da = 20 3 πµa3 e ij 1 V = 5 2 φµe ij DISPERSED MULTIPHASE FLOWS Kyongmin Yeo LAWRENCE BERKELEY NATIONAL LAB 6 / 35

10 Dilute to semi-dilute suspension flows Finite-size effect Force-coupling method 2 Based on truncated regularized multipole expansion ( ) ui u i ρ f + u j = σij + [ F i M(r) + {T ij + S ] n ij} D(r), t x j x j x j n r = x Y. F: gravitational acceleration + inertia force F = F ext + (m F m p) dv dt T ij = 1 2 ɛ ijkt k : body torque + inerital torque T = T ext + (I F I p) dω dt S ij : surface traction e ij D dx = 0 Particle motion: V = u(x) M(r)d 3 x, Ω = 1 2 ω(x) D(r)d 3 x. 2 Lomholt & Maxey JCP (2002) DISPERSED MULTIPHASE FLOWS Kyongmin Yeo LAWRENCE BERKELEY NATIONAL LAB 7 / 35

11 Dilute to semi-dilute suspension flows Finite-size effect Force-coupling method 2 Based on truncated regularized multipole expansion ( ) ui u i ρ f + u j = σij + [ F i M(r) + {T ij + S ] n ij} D(r), t x j x j x j n r = x Y. F: gravitational acceleration + inertia force F = F ext + (m F m p) dv dt T ij = 1 2 ɛ ijkt k : body torque + inerital torque T = T ext + (I F I p) dω dt S ij : surface traction e ij D dx = 0 Particle motion: V = u(x) M(r)d 3 x, Ω = 1 2 ω(x) D(r)d 3 x. Mixture stress: σ m ij = σ ij + S ij D Mean shear stress in a homogeneous flow τ ij = ρ f u iu j + 2µ f e ij + φ S ij = ρ f u iu j + 2µ eff e ij ( S ij e ij ) c.f. Stokes-Einstein estimate: µ eff = µ( φ) 2 Lomholt & Maxey JCP (2002) DISPERSED MULTIPHASE FLOWS Kyongmin Yeo LAWRENCE BERKELEY NATIONAL LAB 7 / 35

12 Dilute to semi-dilute suspension flows Finite-size effect Dissipation spectra in isotropic turbulence Direct numerical simulation of forced isotropic turbulence 3 φ Re λ u ɛ a/η a/λ St l St K N N St l = τ p/(u 2 /ɛ), St K = τ p/τ K, k d = π/a Spectral redistribution of dissipation rate Significant suspension viscosity effect 3 Yeo et al. IJMF (2010) ten Cate et al. (2004) DISPERSED MULTIPHASE FLOWS Kyongmin Yeo LAWRENCE BERKELEY NATIONAL LAB 8 / 35

13 Dilute to semi-dilute suspension flows Finite-size effect Spectral energy transfer by particle phase Energy budget 0 = E in(k) + T(k) D(k) + H(k) { } Dipole energy transfer function: H(k) = F eij S ij D DISPERSED MULTIPHASE FLOWS Kyongmin Yeo LAWRENCE BERKELEY NATIONAL LAB 9 / 35

14 Dilute to semi-dilute suspension flows Finite-size effect Spectral energy transfer by particle phase Energy budget 0 = E in(k) + T(k) D(k) + H(k) = E in(k) + T(k) D(k) + H(k) { } Dipole energy transfer function: H(k) = F eij S ij D = 2µ add k 2 E(k) + H(k) Modified dissipation-rate spectra: D(k) = 2(µ + µ add )k 2 E(k) = 2µ eff k 2 E(k) Blue line 2µ add k 2 E(k), H(k) = H(k) [ 2µ add k 2 E(k)] µ eff = µ( φ) for larger particle, µ eff = µ( φ) for smaller particle. Turbulence enhancement at smaller scales Dipole energy transfer has a long-range effect DISPERSED MULTIPHASE FLOWS Kyongmin Yeo LAWRENCE BERKELEY NATIONAL LAB 9 / 35

15 Dilute to semi-dilute suspension flows Finite-size effect Kinetic Energy spectra in isotropic turbulence Turbulence enhance at small scales DISPERSED MULTIPHASE FLOWS Kyongmin Yeo LAWRENCE BERKELEY NATIONAL LAB 10 / 35

Dilute to semi-dilute suspension flows Particle-pair hydrodynamics Preferential concentration of inertial particles Low inertia approximation: 0 < St 1 (Maxey 1987a,b) St dv dt = (u(y, t) V) + W V(t)

16 Dilute to semi-dilute suspension flows Particle-pair hydrodynamics Preferential concentration of inertial particles Low inertia approximation: 0 < St 1 (Maxey 1987a,b) St dv dt = (u(y, t) V) + W V(t) = v(y, t) = (u(y, t) + W) St v = 1 St (e : e ω : ω) 4 ( ) u + (u + W) u t Effective particle velocity field v(x, t) is compressible. Convergence where e 2 > ω 2 Wang & Maxey (1993) Salazar et al. (2008) Need to consider particle-pair hydrodynamic interactions. DISPERSED MULTIPHASE FLOWS Kyongmin Yeo LAWRENCE BERKELEY NATIONAL LAB 11 / 35

17 Dilute to semi-dilute suspension flows Particle-pair hydrodynamics Particle-pair interaction For a gap aɛ < l St a/re p : Viscous time scale Inertial time scale Quasi-Stokes problem Rapid damping of inertial acceleration Coupling between particle motions Fundamental modes of Stokes flow Particle moving relative to flow u D (r) a r V Particle in a shear flow u D (r) a3 r 2 e DISPERSED MULTIPHASE FLOWS Kyongmin Yeo LAWRENCE BERKELEY NATIONAL LAB 12 / 35

18 Dilute to semi-dilute suspension flows Particle-pair hydrodynamics Particle-pair interaction For a gap aɛ < l St a/re p : Viscous time scale Inertial time scale Quasi-Stokes problem Rapid damping of inertial acceleration Coupling between particle motions Fundamental modes of Stokes flow Particle moving relative to flow u D (r) a r V Particle in a shear flow u D (r) a3 r 2 e hydbrid method: Ayala et al. (2007) St dv dt = V (u + u D ) W DISPERSED MULTIPHASE FLOWS Kyongmin Yeo LAWRENCE BERKELEY NATIONAL LAB 12 / 35

Dilute to semi-dilute suspension flows Particle-pair hydrodynamics Particle-pair interaction For a gap aɛ < l St a/re p : Viscous time scale Inertial time scale Quasi-Stokes problem Rapid damping of

19 Dilute to semi-dilute suspension flows Particle-pair hydrodynamics Particle-pair interaction For a gap aɛ < l St a/re p : Viscous time scale Inertial time scale Quasi-Stokes problem Rapid damping of inertial acceleration Coupling between particle motions Fundamental modes of Stokes flow Particle moving relative to flow u D (r) a r V Particle in a shear flow u D (r) a3 r 2 e Particle Stress S = S + S 10 + S hydbrid method: Ayala et al. (2007) St dv dt = V (u + u D ) W DISPERSED MULTIPHASE FLOWS Kyongmin Yeo LAWRENCE BERKELEY NATIONAL LAB 12 / 35

Dilute to semi-dilute suspension flows Particle-pair hydrodynamics Near-field interaction Near-field hydrodynamic interaction Particle Stress: S ij 1 ɛ Non-hydrodynamic short-range

20 Dilute to semi-dilute suspension flows Particle-pair hydrodynamics Near-field interaction Near-field hydrodynamic interaction Particle Stress: S ij 1 ɛ Non-hydrodynamic short-range interaction Particle roughness element Polymer coating Electrostatic repulsion Smart & Leighton (1988) DISPERSED MULTIPHASE FLOWS Kyongmin Yeo LAWRENCE BERKELEY NATIONAL LAB 13 / 35

Dilute to semi-dilute suspension flows Particle-pair hydrodynamics Effects of non-hydrodynamic interaction Potential force model: F P = f (ɛ)d (e.g.

21 Dilute to semi-dilute suspension flows Particle-pair hydrodynamics Effects of non-hydrodynamic interaction Potential force model: F P = f (ɛ)d (e.g. Lennard-Jones potential, electrostatic repulsion) Abbas et al. (2006) Particle Stress Equal & opposite repulsive force dipole force in the far-field Mean shear stress in a homogeneous flow τ ij = ρ f u iu j + 2µ f e ij + φ S ij n R F P Particles in a close proximity: S ij (1/ɛ)µe ij, R F P 2µe ij A particle doublet generates far-field dipolar flow additional stress. Dissipation rate can be largely affected by RDF. DISPERSED MULTIPHASE FLOWS Kyongmin Yeo LAWRENCE BERKELEY NATIONAL LAB 14 / 35

22 Dilute to semi-dilute suspension flows Particle-pair hydrodynamics Comments so far Due to the separation of lengthscales, Stokesian dynamics may play a role in modeling dispersed multiphase flow Particle stress, or suspension viscosity, has a significant effect in turbulence modulation for a > η Particle stresslet as well as potential force dipole have a long-range effect and may interact with flow at a scale larger than the particle size. For a better prediction, a dispersed model needs to consider stress coupling between fluid and particle phases. DISPERSED MULTIPHASE FLOWS Kyongmin Yeo LAWRENCE BERKELEY NATIONAL LAB 15 / 35

23 Stokes suspensions Background: Concentrated suspensions Concentrated Suspensions; average separation distance is smaller than the particle size 4 (φ > 0.2) Nature: B layers of density currents/ocean spray, Debris flow, Landslide Engineering: Micro-bubble/emulsion DR, CHE products, medical diagnostic device multiscale physics: Long-range multi-body O(10)a Lubrication interactions O(10 3 )a No general theory Challenging both in experiments and numerical simulations Non-Newtonian Rheology 4 Stickel & Powell ARFM 2005 DISPERSED MULTIPHASE FLOWS Kyongmin Yeo LAWRENCE BERKELEY NATIONAL LAB 16 / 35

24 Stokes suspensions Lubrication-Corrected FCM 5 Multiscale computation of hydodynamic interaction Far-field multibody interaction: Standard FCM Near-field interaction: Pairwise-additivity of Lubrication interaction (Brady & Bossis 1988) Resistance relation for a particle pair F 1 A 11 A 12 B 11 B 12 G 11 G 12 V 1 V (Y 1 ) F 2 T 1 = µ A 12 A 11 B 12 B 11 G 12 G 11 V 2 V (Y 2 ) Ω 1 Ω (Y 1 ) (B 11 ) T (B 12 ) T C 11 C 12 H 11 H 12 Ω 2 Ω (Y 2 ). T 2 (B 12 ) T (B 11 ) T C 12 C 11 H 12 H 11 E E R = R Exact R FCM : R 0 for the gap between particle ɛ > 0.6. A coupled system of far-field and near-field interactions is solved by using a PCG. Almost the same computational cost with the standard FCM, O(N p log N p) using a Fourier spectral method. 5 Yeo & Maxey JCP (2010) DISPERSED MULTIPHASE FLOWS Kyongmin Yeo LAWRENCE BERKELEY NATIONAL LAB 17 / 35

25 Stokes suspensions Characteristics of Concentrated Suspensions High-frequency viscosity Monte Carlo procedure: Ensemble average of 1000 random configuration µ /µ FCM-MD FCM-LUB Ladd (1990) K&D (1959) Einstein B & G (1972) φ DISPERSED MULTIPHASE FLOWS Kyongmin Yeo LAWRENCE BERKELEY NATIONAL LAB 18 / 35

26 Stokes suspensions Characteristics of Concentrated Suspensions Stokes-flow theory: Instantaneity Reversible Newtonian rheology DISPERSED MULTIPHASE FLOWS Kyongmin Yeo LAWRENCE BERKELEY NATIONAL LAB 19 / 35

Stokes suspensions Characteristics of Concentrated Suspensions Stokes-flow theory: Instantaneity Reversible Newtonian rheology Irreversible transition Experimental Observation: History effect

27 Stokes suspensions Characteristics of Concentrated Suspensions Stokes-flow theory: Instantaneity Reversible Newtonian rheology Irreversible transition Experimental Observation: History effect Irreversibility & Chaos Non-Newtonian rheology Particle migration Yeo & Maxey PRE (2010ab) Yeo & Maxey JFM (2011) DISPERSED MULTIPHASE FLOWS Kyongmin Yeo LAWRENCE BERKELEY NATIONAL LAB 19 / 35

Sierou & Brady (2002) Shear-induced diffusion Normal stress difference N 1 = σ 11

28 Stokes suspensions Non-hydrodynamic effects Non-hydrodynamic interaction breaks fore-after symmetry! Sierou & Brady (2002) Shear-induced diffusion Normal stress difference N 1 = σ 11 σ 22, N 2 = σ 22 σ 33 Sierou & Brady (2004) Zarraga et al. (2002) DISPERSED MULTIPHASE FLOWS Kyongmin Yeo LAWRENCE BERKELEY NATIONAL LAB 20 / 35

29 Stokes suspensions Inhomogeneous suspensions Suspensions in pressure-driven flow (a) 0.6 φ = 0.3 (a) 1.5 φ = 0.30 φ A V /u c (b) φ A φ = 0.4 y/a (b) V /u c φ = 0.40 y/a y/a Migration of particles: contradictory to Stokes theory Shear-induced migration by Leighton & Acrivos (1987) y/a DISPERSED MULTIPHASE FLOWS Kyongmin Yeo LAWRENCE BERKELEY NATIONAL LAB 21 / 35

30 Stokes suspensions Inhomogeneous suspensions Suspensions in pressure-driven flow (a) 0.6 φ = 0.3 (a) 1.5 φ = 0.30 φ A V /u c (b) φ A φ = 0.4 y/a (b) V /u c φ = 0.40 y/a y/a Migration of particles: contradictory to Stokes theory Shear-induced migration by Leighton & Acrivos (1987) High shear rate: more frequent collisions y/a Low shear rate: less frequent collisions DISPERSED MULTIPHASE FLOWS Kyongmin Yeo LAWRENCE BERKELEY NATIONAL LAB 21 / 35

31 Stokes suspensions Inhomogeneous suspensions Suspensions in pressure-driven flow (a) 0.6 φ = 0.3 (a) 1.5 φ = 0.30 φ A V /u c (b) φ A φ = 0.4 y/a (b) V /u c φ = 0.40 y/a y/a Migration of particles: contradictory to Stokes theory Shear-induced migration by Leighton & Acrivos (1987) High shear rate: more frequent collisions j γ Low shear rate: less frequent collisions DISPERSED MULTIPHASE FLOWS Kyongmin Yeo LAWRENCE BERKELEY NATIONAL LAB 21 / 35 y/a

32 Stokes suspensions Particle flux model Shear-induced migration is a phenomenological model and unreliable for general use. Stress-induced migration model: based on a phase-averaged momentum conservation 6 Morris & Boulay JOR (1999) DISPERSED MULTIPHASE FLOWS Kyongmin Yeo LAWRENCE BERKELEY NATIONAL LAB 22 / 35

33 Stokes suspensions Particle flux model Shear-induced migration is a phenomenological model and unreliable for general use. Stress-induced migration model: based on a phase-averaged momentum conservation Particle-phase momentum conservation: 6 χ pσ σ χ p = 0, χ p(x): particle-phase indicator function Local homogeneity assumption: χ pσ Σ P, σ χ p nf H, n = φ 3/4πa 3 Hydrodynamic drag model: F H = 6πµa(V u)/f (φ), Particle flux: j = φ(v u) = 2a2 f (φ) 9µ ΣP j ΣP 22 y u: mixture velocity Stress modeling: Local rheology assumption ) 2.5φm p(φ) µ eff (φ) 0 i.e. µ eff (φ) = (1 φφm Σ P = µ f γ µ eff (φ) λ 1p(φ) 0 ( ) 2 ( ) λ p(φ) = K φ 2p(φ) φ m 1 φ φ m 6 Morris & Boulay JOR (1999) DISPERSED MULTIPHASE FLOWS Kyongmin Yeo LAWRENCE BERKELEY NATIONAL LAB 22 / 35

34 Stokes suspensions Comparison with simulations Yeo & Maxey JFM (2011) Suspension model overestimates particle migration. DISPERSED MULTIPHASE FLOWS Kyongmin Yeo LAWRENCE BERKELEY NATIONAL LAB 23 / 35

35 Stokes suspensions Particle normal stresses Normal stresses, Σ P ii, scaled by the mean pressure gradient f D and channel height h. φ = 0.2 Σ P 11 = Σ P 22 = Σ P 33 = φ = 0.3 φ = 0.4 ΣP 22 y 0 consistent with the model DISPERSED MULTIPHASE FLOWS Kyongmin Yeo LAWRENCE BERKELEY NATIONAL LAB 24 / 35

Stokes suspensions Particle Shear Stress (a) χσ P 12 1 0.5 0 σ 12 tot = 1 - y/h Total Shear Stress: σ 12 = χ pσ 12 + χ f σ 12 ( = 1 y ) f D h. h (b) µ eff 20 15 10 5 0 0.2 0.4 0.6 0.

36 Stokes suspensions Particle Shear Stress (a) χσ P σ 12 tot = 1 - y/h Total Shear Stress: σ 12 = χ pσ 12 + χ f σ 12 ( = 1 y ) f D h. h (b) µ eff y/h Krieger & Dougherty Eilers φ L Effective Viscosity: µ eff µ 0 = σ12 χ f σ 12 = 1 + χ pσ 12 (1 y/h)f D h χ pσ 12. Local Rheology assumption is valid. Suspension microstructure changes near the center. Significant non-local effects in the channel center. DISPERSED MULTIPHASE FLOWS Kyongmin Yeo LAWRENCE BERKELEY NATIONAL LAB 25 / 35

37 Stokes suspensions Time & Length scales of concentrated suspension Melrose & Ball (2004) Hysteresis Stokes theory: fixed timescale ( γ) & lengthscale (a) Concentrated suspensions: Formation of hydro-cluster introduces time & lengthscales Lengthscales µ r H y = 10 H y = 20 C4Lb C4Lc C4H µ K & D (1959) Eilers φ Narumi et al. JOR (2002) Yeo & Maxey JFM (2010), Europhys. Lett. (2010) DISPERSED MULTIPHASE FLOWS Kyongmin Yeo LAWRENCE BERKELEY NATIONAL LAB 26 / 35

38 Finite Re p suspensions Suspensions in uniform shear flow: Re p > 0 Stokes suspensions: theoretical study, relevant to microfluidic devices, CHE products Mechanical/Natural flow systems of interest: 0 < Re p What is the effect of finite inertia on dynamics of concentrated suspensions? Particle-pair interaction revisited. Stokes flows Re p = 1 Re p > 0 introduces irreversibility to flow, beyond that due to contact forces At Re p > 0, particle-pair interaction is sufficient to generate diffusive motion DISPERSED MULTIPHASE FLOWS Kyongmin Yeo LAWRENCE BERKELEY NATIONAL LAB 27 / 35

39 Finite Re p suspensions Effective viscosity Effective shear viscosity Particle shear stress v.s. Re p Finite-Re p suspension is shear-thickening. stronger shear, higher viscosity DISPERSED MULTIPHASE FLOWS Kyongmin Yeo LAWRENCE BERKELEY NATIONAL LAB 28 / 35

40 Finite Re p suspensions Velocity fluctuations and PDFs 7 φ = 0.2 φ = 0.4 V a γ vs Re p V = V 2 σ 2 Kinetic Energy of the particle phase decreases at higher Re p Flatness increases slightly with Re p 7 Yeo & Maxey POF in review DISPERSED MULTIPHASE FLOWS Kyongmin Yeo LAWRENCE BERKELEY NATIONAL LAB 29 / 35

41 Finite Re p suspensions Cross-flow diffusion Diffusivity (D ii = V 2 i ρ(τ)dτ) φ = 0.2, φ = 0.3, φ = 0.4 Diffusivity is an increasing function of Re p, while the velocity fluctuation decreases at higher Re p. DISPERSED MULTIPHASE FLOWS Kyongmin Yeo LAWRENCE BERKELEY NATIONAL LAB 30 / 35

42 Finite Re p suspensions Cross-flow diffusion Diffusivity (D ii = V 2 i ρ(τ)dτ) Mean-square displacement φ = 0.2, φ = 0.3, φ = 0.4 φ = 0.2 Diffusivity is an increasing function of Re p, while the velocity fluctuation decreases at higher Re p. At higher Re p, the reduced intermediate region results in the increase in D ii. DISPERSED MULTIPHASE FLOWS Kyongmin Yeo LAWRENCE BERKELEY NATIONAL LAB 30 / 35

43 Finite Re p suspensions Lagrangian auto-correlation Decreased negative loop longer correlation larger T L increase in D ii Longer-time tail (τ > 3 γt) collapes onto one curve. DISPERSED MULTIPHASE FLOWS Kyongmin Yeo LAWRENCE BERKELEY NATIONAL LAB 31 / 35

Finite Re p suspensions Pair-distribution function in the plane of shear: g(r, θ, 0) Principal Axis Earlier detachment reduces the negative correlation.

44 Finite Re p suspensions Pair-distribution function in the plane of shear: g(r, θ, 0) Principal Axis Earlier detachment reduces the negative correlation. Increase inertia increase in the wake region Far-field PDF is less sensitive to inertia. DISPERSED MULTIPHASE FLOWS Kyongmin Yeo LAWRENCE BERKELEY NATIONAL LAB 32 / 35

4 Detachment point moves towards upstream Increased contributions from the

45 Finite Re p suspensions Near-contact pair distribution function Near contact PDF PDF weighted by S 12 φ = 0.2 φ = 0.3 φ = 0.4 Detachment point moves towards upstream Increased contributions from the compressible pricipal axis events (θ/π = 0.75) DISPERSED MULTIPHASE FLOWS Kyongmin Yeo LAWRENCE BERKELEY NATIONAL LAB 33 / 35

46 Finite Re p suspensions Intermittency of particle shear stress S 12 = hydrodynamic + potential force = S12 H 1 2 r F P S 12 = S12 S12 σ S Exponential decay at low Re p Algebraic decay at higher Re p DISPERSED MULTIPHASE FLOWS Kyongmin Yeo LAWRENCE BERKELEY NATIONAL LAB 34 / 35

47 Conclusions Summary Dispersed multiphase flow is a good example of multiscale physics. For a better understanding we need to gather information scattered across disciplines from microhydrodynamics to turbulent flows. Phase-coupling in stress tensor has a significant effect on turbulence modulation. For a better estimate of the stress coupling, not only stress re-distribution around an isolated particle, but also particle-pair dynamics needs to be accurately resolved. To develop a self-consistent multiscale model, there is a need to incorporate well established results of dense suspensions in CHE into the study of multiphase flow in the boundary layer. Dense finite-inertia suspension flow is a grey area, which is not well understood. DISPERSED MULTIPHASE FLOWS Kyongmin Yeo LAWRENCE BERKELEY NATIONAL LAB 35 / 35

Effects of Forcing Scheme on the Flow and the Relative Motion of Inertial Particles in DNS of Isotropic Turbulence

Effects of Forcing Scheme on the Flow and the Relative Motion of Inertial Particles in DNS of Isotropic Turbulence Rohit Dhariwal and Vijaya Rani PI: Sarma L. Rani Department of Mechanical and Aerospace