FOUR-WAY COUPLED SIMULATIONS OF TURBULENT

FOUR-WAY COUPLED SIMULATIONS OF TURBULENT FLOWS WITH NON-SPHERICAL PARTICLES Berend van Wachem Thermofluids Division, Department of Mechanical Engineering Imperial College London Exhibition Road, London, SW7 2AZ, United Kingdom b.van-wachem@imperial.ac.uk Training School Behaviour of Non-Spherical Particles in Flows COST FP1005

OUTLINE 1 PARTICLES IN TURBULENCE Equations of motion Forces on non-spherical particles 2 CASE 1: CHANNEL FLOW WITH Re τ = 150 Effect of St Effect of shape 3 CASE 2: CHANNEL FLOW WITH Re τ 1, 000 Rough wall modelling Effect of gravity Effect of shape and orientation 4 CONCLUSIONS Berend van Wachem (Imperial College) Four-way coupled simulations May, 2015 2 / 33

PARTICLES IN TURBULENCE Particles affect turbulent flow and are affected by turbulent flow. So-far almost all computational studies in gas-solid flow assume spherical particles. In many flows, this is not an valid assumption. There is little data on non-spherical particles. Objective: How do non-spherical particles behave in and affect turbulent channel flow? Berend van Wachem (Imperial College) Four-way coupled simulations May, 2015 3 / 33

EQUATIONS OF MOTION FOR PARTICLES MOMENTUM EQUATION m p Dv p Dt N w = F d + F l + m p g V p P f + F pp + F pw +... N p ANGULAR MOMENTUM EQUATION I ij p dω P dt N p N w = T aero T rot + T pp + T pw Berend van Wachem (Imperial College) Four-way coupled simulations May, 2015 4 / 33

ALGORITHM SUMMARY For each body in the simulation, 1 Determine the mass and mass middle point. 2 Determine the inertia tensor in body-space. 3 Define a unit Quaternion. For each time-step for each body, 1 Determine the effect of collisions and fluid (force + torque). 2 Determine the effect of rotation, Q. 3 Integrate the state-vector and move the body accordingly. Zhao & van Wachem (2013). A novel Quaternion integration approach for describing the behaviour of non-spherical particles. Acta Mechanica, 224 Berend van Wachem (Imperial College) Four-way coupled simulations May, 2015 5 / 33

Berend Zastawny vanet Wachem al. (2012) (Imperial Int. J. Multiphase College) Flows 39, Four-way pp 227 coupled simulations May, 2015 6 / 33 FLUID FORCES AND TORQUES ON A PARTICLE DRAG FORCE LIFT FORCE F d = C D (...) 1 2 ρ π g 4 d p 2 (ṽ f v p ) 2 F l = C L (...) 1 2 ρ π g 4 d p 2 (ṽ f v p ) 2 AERODYNAMIC TORQUE ROTATIONAL TORQUE T aero = C T (...) 1 2 ρ π g 8 d p 3 (ṽ f v p ) 2 T rot = C R (...) ρ 2 ( ) 5 dp ω p ω p 2

zo u y z x y o xo world space ( ) ϕ = arctan uo,sh u o,ln u o y o body space z o xo F o, x = 1 2 ρ A eq C D (ϕ, Re) u o u o,x + F L sinϕ sign( u o,x ) F o, y = 1 2 ρ A eq C D (ϕ, Re) u o u o,y + F L cosϕ F o, z = 1 2 ρ A eq C D (ϕ, Re) u o u o,z + F L cosϕ u o,y u 2 o,y + u 2 o,z u o,z u 2 o,y + u 2 o,z Zastawny et al. (2012) Int. J. Multiphase Flows 39, pp 227 Berend van Wachem (Imperial College) Four-way coupled simulations May, 2015 7 / 33

COLLISION DYNAMICS FOR NON-SPHERICAL contacts can be found through spheres : Hertzian contact model: F n (t) = K n (t)δ 3 2 n (t)n(t) F t (t) = min(µf n (t), K t (t)δ t (t)) In doing this, we assume the deformation plane is circular! Zhao & van Wachem, B. G. M. (2013). Direct numerical simulation of ellipsoidal particles in turbulent channel flow. Acta Mechanica, 224 Berend van Wachem (Imperial College) Four-way coupled simulations May, 2015 8 / 33

CASE 1 In Case 1, we consider the DNS of the Marchioli et al channel flow We look at the effect of various shapes of particles. This means including effect of fluid on particles, particles on fluid and including particle-particle collisions. In this case we perform real DNS of the fluid: resolution sub-kolmogorov scale. Marchioli, C., et al. (2008). Int J of Multiphase Flow, 34(9), 879-93. Berend van Wachem (Imperial College) Four-way coupled simulations May, 2015 9 / 33

SIMULATION SET-UP Dimensions: 2πh 4πh 2h Re τ = 150 Flow driven by fixed pressure drop (source term) to sustain channel flow: the wall shear stress is always the same. Discretisation in domain of 169 171 169 cells. flow Marchioli, C., et al. (2008). Int J of Multiphase Flow, 34(9), 879-93. Berend van Wachem (Imperial College) Four-way coupled simulations May, 2015 10 / 33

GOVERNING EQUATIONS NAVIER-STOKES u f i t + u f j u f i x i = 0 u f i x j = 1 ρ f p x i +ν f 2 u f i x 2 j +δp i +Π i Berend van Wachem (Imperial College) Four-way coupled simulations May, 2015 11 / 33

EQUATIONS GOVERNING TURBULENT CHANNEL FLOW SHEAR STRESS τ(y) = ρ f ν f du 1 dx 2 ρ f u f 1 uf 2 = τ 0 = const Re τ = u τh ν u τ = τ0 ρ f DRIVING PRESSURE DROP δp 1 = ρ fν f 2 Re 2 τ h 3 Berend van Wachem (Imperial College) Four-way coupled simulations May, 2015 12 / 33

CHANNEL FLOW: TURBULENCE KINETIC ENERGY TURBULENCE KINETIC ENERGY WITH PARTICLES ( ) d 1 dy 2 < u f y u f i u i f >+ < u y f p > ρ f ν f d 2 (k +< u f y >) = dy PRODUCTION OF TKE DISSIPATION OF TKE P ε ε p P = < u f x u f y > Uf x y ε = 2ν f < S ij S ij > PARTICLE DISSIPATION RATE ε p =< Π i u f i > Berend van Wachem (Imperial College) Four-way coupled simulations May, 2015 13 / 33

CHANNEL FLOW WITH PARTICLES 20 20 15 15 U f+ 1 10 5 0 0 20 40 60 80 100 120 140 y + Fluid mean velocity Clear fluid Fluid with spheres St = 5 Fluid with spheres St = 30 Fluid with ellipsoids St = 5 and λ = 3 Fluid with ellipsoids St = 30 and λ = 3 Fluid with ellipsoids St = 5 and λ = 5 Fluid with ellipsoids St = 30 and λ = 5 U p+ 1 10 5 0 0 20 40 60 80 100 120 140 y + Particle mean velocity Clear fluid Spheres with St = 5 Spheres with St = 30 Ellipsoids with St = 5 and λ = 3 Ellipsoids with St = 30 and λ = 3 Ellipsoids with St = 5 and λ = 5 Ellipsoids with St = 30 and λ = 5 The wall shear stress is exactly the same for all plots. Different centerline values imply drag reduction. The viscosity is exactly the same also. Collapse at low y + implies no change in viscosity. Berend van Wachem (Imperial College) Four-way coupled simulations May, 2015 14 / 33

CHANNEL FLOW WITH PARTICLES: PRODUCTION AND DISSIPATION P + 0.25 0.20 0.15 0.10 0.05 Clear fluid Fluid with spheres St = 5 Fluid with spheres St = 30 Fluid with ellipsoids St = 5 and λ = 3 Fluid with ellipsoids St = 30 and λ = 3 Fluid with ellipsoids St = 5 and λ = 5 Fluid with ellipsoids St = 30 and λ = 5 0.00 0 20 40 60 80 100 120 140 y + Fluid TKE production ε + 0.00 0.05 0.10 0.15 Clear fluid Fluid with spheres St = 5 Fluid with spheres St = 30 Fluid with ellipsoids St = 5 and λ = 3 Fluid with ellipsoids St = 30 and λ = 3 Fluid with ellipsoids St = 5 and λ = 5 Fluid with ellipsoids St = 30 and λ = 5 0.20 0 20 40 60 80 100 120 140 y + Fluid TKE direct dissipation The particles decrease the fluid production and dissipation. The magnitude of dissipation decreases faster than production when adding ellipsoids. Berend van Wachem (Imperial College) Four-way coupled simulations May, 2015 15 / 33

CHANNEL FLOW WITH PARTICLES: PRODUCTION AND DISSIPATION 0.00 0.000000 0.05 0.000001 ε + 0.10 0.15 Clear fluid Fluid with spheres St = 5 Fluid with spheres St = 30 Fluid with ellipsoids St = 5 and λ = 3 Fluid with ellipsoids St = 30 and λ = 3 Fluid with ellipsoids St = 5 and λ = 5 Fluid with ellipsoids St = 30 and λ = 5 0.20 0 20 40 60 80 100 120 140 y + Fluid TKE direct dissipation ε + p 0.000002 0.000003 0.000004 0.000005 Fluid with spheres St = 5 Fluid with spheres St = 30 Fluid with ellipsoids St = 5 and λ = 3 Fluid with ellipsoids St = 30 and λ = 3 Fluid with ellipsoids St = 5 and λ = 5 Fluid with ellipsoids St = 30 and λ = 5 0 20 40 60 80 100 120 140 y + Dissipation caused by particles The particles decrease the fluid dissipation. The magnitude of dissipation decreases faster than production when adding ellipsoids. The dissipation caused directly by particles is negligible. Berend van Wachem (Imperial College) Four-way coupled simulations May, 2015 16 / 33

CHANNEL FLOW WITH PARTICLES Z X Y Streamwise fluid velocity (horizontal planes) and wall-normal velocity (vertical planes) of the flow in the channel The flow shows sweeps slowly moving towards or near the wall. The flow shows ejections quickly moving away from the wall. Berend van Wachem (Imperial College) Four-way coupled simulations May, 2015 17 / 33

CHANNEL FLOW WITH PARTICLES FIGURE : Fluid velocity with particles of St = 5 in stream-wise direction at y + = 8 FIGURE : Fluid velocity with ellipsoids of St = 30 in stream-wise direction at y + = 8 Particles affect sweeps and ejections in near-wall region. Berend van Wachem (Imperial College) Four-way coupled simulations May, 2015 18 / 33

SLIP VELOCITY OF PARTICLES WITH FLUID (U f+ U p+ 1 1 ) 0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 Spheres with St = 5 Spheres with St = 30 Ellipsoids with St = 5 and λ = 3 Ellipsoids with St = 30 and λ = 3 Ellipsoids with St = 5 and λ = 5 Ellipsoids with St = 30 and λ = 5 0 20 40 60 80 100 120 140 y + (U f+ U p+ 2 2 ) 0.20 0.15 0.10 0.05 0.00 0.05 0.10 0.15 0.20 Spheres with St = 5 Spheres with St = 30 Ellipsoids with St = 5 and λ = 3 Ellipsoids with St = 30 and λ = 3 Ellipsoids with St = 5 and λ = 5 Ellipsoids with St = 30 and λ = 5 0 20 40 60 80 100 120 140 y + FIGURE : Fluid-particle slip velocity in streamwise direction FIGURE : Fluid-particle slip velocity in wall-normal direction Berend van Wachem (Imperial College) Four-way coupled simulations May, 2015 19 / 33

CASE 1: PARTICLES IN TURBULENT CHANNEL FLOW Effect of dilute solutions not due to viscosity changes. Main effect is to change turbulence structures near wall by suppressing ejections. Continuity (of flow) implies both sweeps and ejections affected. But no continuity for particles - so clustering until collisions and bouncing from wall dominate other effects. High inertia ellipsoids pretty much ignore flow, but do affect the flow. Berend van Wachem (Imperial College) Four-way coupled simulations May, 2015 20 / 33

CASE 2: SIMULATION DOMAIN D d p m Re D < U > St 35 mm 200 µm 1.0 42, 000 19.7 m/s 52 Exp. data: Kussin and Sommerfeld (2002), Int J Heat and Fluid Flow, 23, pp 647 Berend van Wachem (Imperial College) Four-way coupled simulations May, 2015 21 / 33

ROUGH WALL MODELLING ' n n n n n hard-sphere model soft-sphere model Including the shadow-effect : particles do not see walls with v p n γ 0. v p n Berend van Wachem (Imperial College) Four-way coupled simulations May, 2015 22 / 33

ROUGH WALL MODELLING Spherical particles Spheres colliding with a rough wall Ellipoids colliding with a rough wall the effect of rough walls is different for non-spherical particles. Ellipsoids Berend van Wachem (Imperial College) Four-way coupled simulations May, 2015 23 / 33

SNAPSHOTS OF RESULTS Berend van Wachem (Imperial College) Four-way coupled simulations May, 2015 24 / 33

FLUID BEHAVIOUR FOR SPHERICAL PARTICLES Effect of wall roughness 1.0 1.0 0.8 0.8 y/h 0.6 0.4 Single phase experiment Experiment with particles Single Phase Simulation Hard Sphere rough walls Hard Sphere smooth walls y/h 0.6 0.4 Single phase experiment Experiment with particles Single Phase Simulation Hard Sphere rough walls Hard Sphere smooth walls 0.2 0.2 0.0 10 12 14 16 18 20 22 24 Uf 0.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 uf,rms 1.0 0.8 0.6 Single phase experiment Experiment with particles Single Phase Simulation Hard Sphere rough walls Hard Sphere smooth walls y/h 0.4 0.2 0.0 0.8 0.6 0.4 0.2 0.0 0.2 0.4 0.6 0.8 uf,rmsvf,rms Exp. data: Kussin and Sommerfeld (2002), Int J Heat and Fluid Flow, 23, pp 647 Results: Mallouppas and van Wachem (2013), Int J. Multiphase Flow, 54, pp 65 Berend van Wachem (Imperial College) Four-way coupled simulations May, 2015 25 / 33

SPHERICAL PARTICLES with part-part collisions and wall rough. with part-part coll but NO wall rough. NO no part-part collisions but with wall rough. part-part collisions and NO wall rough. Berend van Wachem (Imperial College) Four-way coupled simulations May, 2015 26 / 33

SPHERICAL PARTICLES Comparison of hard and soft-sphere models 1.0 Experiment with particles 1.0 Experiment with particles Hard Spheres rough walls Hard Spheres rough walls 0.8 Soft Spheres rough walls 0.8 Soft Spheres rough walls Hard Spheres smooth walls Hard Spheres smooth walls 0.6 Soft Spheres smooth walls 0.6 Soft Spheres smooth walls y/h y/h 0.4 0.4 0.2 0.2 0.0 16 18 20 22 24 Up 0.0 0.5 1.0 1.5 2.0 2.5 3.0 cn/cn,av 1.0 Experiment with particles Experiment with particles ψ = 0.70 rough walls Hard Spheres with collisions 0.8 ψ = 0.70 smooth walls 0.8 Hard Spheres without collisions ψ = 0.5 rough walls 0.6 ψ = 0.5 smooth walls 0.6 y/h y/h 0.4 0.4 0.2 0.2 0.0 16 18 20 22 24 Up 0.0 Effect of collision parameters 0.8 0.9 1.0 1.1 1.2 1.3 1.4 cn/cn,av Exp. data: Kussin and Sommerfeld (2002), Int J Heat and Fluid Flow, 23, pp 647; Results: Mallouppas and van Wachem (2013), Int J. Multiphase Flow, 54, pp 65 Berend van Wachem (Imperial College) Four-way coupled simulations May, 2015 27 / 33

NON-SPHERICAL PARTICLES y/h 0.8 0.6 0.4 Experiment rough walls Spheres rough walls Spheres smooth walls Discs rough walls Discs smooth walls Ellipsoids 1 rough walls Ellipsoids 1 smooth walls Ellipsoids 2 rough walls Ellipsoids 2 smooth walls Fibers rough walls Fibers smooth walls 0.2 0.0 0 1 2 3 4 5 6 c n /c n,avg Concentration of particles vs channel height Van Wachem, Zastawny, Zhao, Mallouppas, G. (2015). Modelling of gas-solid turbulent channel flow with non-spherical particles with large Stokes numbers. International Journal of Multiphase Flow, 68, 80-92. Berend van Wachem (Imperial College) Four-way coupled simulations May, 2015 28 / 33

NON-SPHERICAL PARTICLES 1.0 0.8 0.6 Experiment Spheres Discs Ellipsoids 1 Ellipsoids 2 Fibers y/h 0.4 0.2 0.0 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 c n /c n,avg concentration of particles vs channel height, rough walls only. Berend van Wachem (Imperial College) Four-way coupled simulations May, 2015 29 / 33

NON-SPHERICAL PARTICLES y/h 1.0 0.8 0.6 0.4 0.2 Experiment Particles Experiment Fluid Spheres Particles Spheres Fluid Discs Particles Discs Fluid Ellipsoids 1 Particles Ellipsoids 1 Fluid Ellipsoids 2 Particles Ellipsoids 2 Fluid Fibers Particles Fibers Fluid 0.0 0.8 0.9 1.0 1.1 1.2 1.3 u p /u bulk and u f /u bulk average particle and fluid velocities. Berend van Wachem (Imperial College) Four-way coupled simulations May, 2015 30 / 33

NON-SPHERICAL PARTICLES y/h 1.0 0.8 0.6 0.4 Discs rough walls Discs smooth walls Ellipsoids 1 rough walls Ellipsoids 1 smooth walls Ellipsoids 2 rough walls Ellipsoids 2 smooth walls Fibers rough walls Fibers smooth walls 0.2 0.0 55 60 65 70 75 80 85 90 φ Angle of particles vs channel height Berend van Wachem (Imperial College) Four-way coupled simulations May, 2015 31 / 33

NON-SPHERICAL PARTICLES RMS of angle of particles vs channel height Berend van Wachem (Imperial College) Four-way coupled simulations May, 2015 32 / 33

CASE 2: CONCLUSIONS Results for single-phase and spheres in line with experimental data. Comparison of soft-sphere and hard-sphere model. Strong effect of wall roughness predicted, in line with exp observations Wall roughness has different effect for spheres as for non-spherical particles. Non-spherical particles try to locally maximize their drag. Reason? Berend van Wachem (Imperial College) Four-way coupled simulations May, 2015 33 / 33