Current Developments:

Multi-phase Sediment-liquid Georgios Fourtakas

Multi-phase Liquid-gas Athanasios Mokos

DEM-SPH coupling Ricardo Canelas

DualSPHysics User Workshop, 8-9 September 2015

3-D SPH Modelling of Sediment Scouring Induced by Rapid Flows

G. Fourtakas, B. D. Rogers, D. Laurence

School of Mechanical, Aerospace and Civil Engineering,

University of Manchester,

UK

DualSPHysics User Workshop, 8-9 September 2015

Outline of the presentation

o Motivation

o Eulerian schemes and multi-phase flows

o SPH methodology

o Multi-phase model

o Liquid - sediment model o Yield criteria

o Constitutive equations

o Sediment suspension

o GPU implementation

o Validation and applications

o Conclusions

Courtesy of the National Nuclear Laboratory, UK

Courtesy of the National Nuclear Laboratory, UK

Motivation

o Real life engineering problems o Underwater sand bed trenching o Local scour around structures o Suspension of hazardous materials

o UK Nuclear industry application o Industrial tank o Hazardous material o Sediment agitation o Submerged jets

o GPUs Why? o Complicated geometry o Complex industrial flows o Computational cost

Traditional CFD methods (Eulerian)

Grid based methods

o Mesh generation can be expensive o Mesh refinement in areas of interest (some knowledge a priori) o Not applicable to highly non-linear deformations, (or very expensive) o Multi-phase, free surfaces and phase-change flows

The SPH method

o Using the total derivative

the Lagrangian form of the Navier-Stokes equations is:

o Momentum equation (conservation of momentum)

o Continuity equation (conservation of mass)

o Tait’s equation of State (weakly compressible SPH (WCSPH))

o Plus other closure models

Navier Stokes equations in Lagrangian form and SPH formalism

d

dt=¶

¶t+ui ×Ñ

dr

dt+ rÑ×u = 0

dridt

= m j (ui -u j ) ×Ñj

N

å Wij

du

dt=

1

r

¶s

¶x+g g

u

ij

N

j ij

ij

ji Wm

dt

d

p = Br

r0

æ

èç

ö

ø÷

g

-1æ

è

çç

ö

ø

÷÷

Multi-phase model

o Liquid phase o Newtonian flow

o Sediment phase

o Yield criteria

o Surface yielding

o Sediment skeleton pressure

o Non-Newtonian flow

o Sediment shear layer at the interface

o Seepage forces

o Sediment resuspension

o Entrainment of soil grains by the liquid

Liquid – sediment model

o Weakly compressible SPH (WCSPH) o Tait’s equation of state to relate pressure to density

o δ-SPH – Density diffusion term

o Particle shifting – Particle re-ordering o Turbulence is modelled through a SPS model

o GPU implementation to DualSPHysics

Liquid phase

Multi-phase model

o Multi-phase implementation

since from

Liquid phase

o Newtonian constitutive equation o Single phase DualSPHysics

SPSP

dt

d

gu

x

u 21

SPSx

Wm

WPP

mdt

d

ij

ijijN

j

ijij

ij

j

ij

N

j ij

ij

ji

gx

u

u

22

du

dt=

1

r

¶s

¶x+g g

xx

u

11 P

dt

d

)( ii f

i

ijN

j ji

ji

ji

x

Wm

x

1

i

ijN

j

ij

j

j

ix

Wu

m

x

u

i

i

i

i

i

ii

x

u

x

u

x

u

3

1

2

1

Liquid phase

o δ-SPH o Diffusion term

where T

o The continuity equation

Dd-SPH =ddhCs0m j

r j

Tij ×j

N

å ÑWij

Tij = 2(r j - ri )xij

xij2

+ 0.1h2

iSPH

i

ijN

j

ji

j

j

ii D

x

Wuu

m

dt

d,)(

Liquid phase

o Shifting scheme [Lind et al. 2012, Skillen et al.

2013]

o Interior fluid domain

o Surface of the fluid

where

i

iii

x

CtuAhr

a

i

i

iii s

s

CtuAhr

N

j i

ij

j

ji

x

Wm

x

C

Sediment phase

o Treated as a semi-solid non-Newtonian fluid

o Non-Newtonian flow o Herschel-Bulkley-Papanastasiou Bingham constitutive model

o Entrained suspended sediment o Concentration based apparent viscosity based on a Newtonian formulation, Vand model

Multi-phase model

o Approximation of seepage forces on the surface o Darcy law

o Yield criterion Drucker-Prager o Below a critical level of sediment deformation sediment particles remain still o Above a critical level of sediment deformation follow the governing equations

Sediment phase

o Surface Yielding o Drucker-Prager (DP) yield criterion

o For an isotropic material

o Apply the yield criterion

o Yielding occurs when

skeletonPJ2

02 yJ

1y

2tan129

tan

2tan129

3

c

Constants

where c is the cohesion and φ angle of repose

Drucker-Prager (DP) yield surface in principal stress

space

Sediment phase

o Sediment skeleton pressure o For a fully saturated soil

o Terzaghi relationship

o or

o Pore water pressure

pwskeletontotal PPP

satswwtotal hhP '

1

0,

,,

sat

isatipw Bp

w

wswcB

0,0,2

pwtskeleton PPP

Sediment skeleton pressure

Sediment phase

o Sediment constitutive equation o Simple Bingham

o Herschel-Bulkley-Papanastasiou (HBP)

o Viscous – Plastic (m exponential growth)

o Shear thinning or thickening (n power law)

d

D

y

Bingh

mpap =t y

IID1- e

-m IIDéë

ùû+KD(n-1)/2

Dpapi 2

x

u

x

uD

2

1

Sediment phase

o Seepage force o Generalised Darcy law

o Suspension

Ss,ia =

m j

rir jjÎW ,Sat

N

å SijaWij

sw uuKS k

nK wr

SPH formalism

Vand equation

Concentration volume fraction of sediment

3.064

391

5.2

v

c

c

fluidsusp cev

v

N

hj j

j

N

hj j

j

ivm

m

c sat

2

2

,

(Soil properties)

Inflow

o Multi-phase issues o Branching

o Registers

o Arithmetic operations

o Larger data size

o Resolve o Memory operations

o Smaller kernels

o Combine similar operations

(See Mokos et al. 2015)

GPU implementation in DualSPHysics

GPU algorithm speed up curve (x58 compared to a single thread CPU)

Numerical results

Soil Dam break Bui et al., Langrangian method for large deformation and failure flows of geo-material, 2008

Sediment block collapse Lude et al., Axisymmetric collapses of granular columns, 2014

Numerical results

Case definition Erodible Dam break

Spinewine et al., Intense bed-load due to sudden dam break, 2013

Parameter Value Units

Liquid height 0.1 m

Sediment height 0.6 m

Density ratio 1.54

Porosity

Numerical cohesion

100 Pa

Sediment viscosity

500 Pa.sec

m (HBP) 100

n (HBP) 1.6

Runtime 1.5 sec

No. Particle 328 000

2-D Erodible dam break

Qualitative comparison of (a) experimental and (b) current numerical results and (c) comparison of liquid-sediment profiles of the experiments, numerical results

of Ulrich et al. and current model at t = 0.25 s.

2-D Erodible dam break

Qualitative comparison of (a) experimental and (b) current numerical results and (c) comparison of liquid-sediment profiles of the experiments, numerical results

of Ulrich et al. and current model at t = 0.50 s.

2-D Erodible dam break

Qualitative comparison of (a) experimental and (b) current numerical results and (c) comparison of liquid-sediment profiles of the experiments, numerical results

of Ulrich et al. and current model at t = 0.75 s.

2-D Erodible dam break

Qualitative comparison of (a) experimental and (b) current numerical results and (c) comparison of liquid-sediment profiles of the experiments, numerical results

of Ulrich et al. and current model at t = 1.00 s.

Case definition 3-D Erodible dam break

Soares-Frazão, S., et al., Dam-break flows over mobile beds., 2013

Numerical results

Parameter Value Units

Liquid height 0.47 m

Sediment height 0.085 m

Density ratio 2.63

Porosity 0.42

Numerical cohesion

100 Pa

Sediment viscosity

150 Pa.sec

m (HBP) 100

n (HBP) 1.8

Runtime 20 sec

No. Particle 4 million

o Sediment bed profile evolution video

3-D Erodible dam break

o Sediment bed profile at t = 20 s

3-D Erodible dam break

Bed profile at locations y1 Bed profile at locations y2

Bed profile at locations y3 Schematic of probes and

Profile locations

o Water level elevation video

3-D Erodible dam break

o Water level elevation from 0 to 20 s

3-D Erodible dam break

Water level at probe US1 Water level at probe US6

Schematic of probes and Profile locations

o A novel sediment model has been presented with improvements to the yielding, shear layer constitutive modelling and sediment resuspension

o Good speed up characteristics achieved by the multi-phase GPU implementation (x58)

o The 2-D and 3-D results where in good agreement with the experimental data especially for the 3-D case: o The sediment profile at different locations

o The water level elevation at the probe locations

o Future work

o Inclusion of more physics, Shield’s criterion

o Turbulence modelling (cheaper mixing length / RANS model)

o Subaqueous sediment flows e.g. sea bed slope failure

Conclusions

Thank you

Acknowledgments

o NNL: Brendan Perry, Steve Graham

o U-Man: Athanasios Mokos, Stephen Longshaw,

Steve Lind, Abouzied Nasar, Peter Stansby

o U-Vigo: Jose Dominguez, Alex Crespo, Anxo

Barreiro, Moncho Gomez-Gesteira

o U-Parma: Renato Vacondio

Websites

o http://www.dual.sphysics.org/

o https://wiki.manchester.ac.uk/sphysics

o http://www.mace.manchester.ac.uk/...sph

References

Bui, H.H., R. Fukagawa, K. Sako, and S. Ohno, Lagrangian meshfree particles method (SPH) for large deformation and failure flows of geomaterial using elastic–plastic soil constitutive model. International Journal for Numerical and Analytical Methods in Geomechanics, 2008. 32(12): p. 1537-1570. Crespo, A.C., J.M. Dominguez, A. Barreiro, M. Gomez-Gesteira, and B.D. Rogers, GPUs, a New Tool of Acceleration in CFD: Efficiency and Reliability on Smoothed Particle Hydrodynamics Methods. Plos One, 2011. 6(6) Lind, S.J., R. Xu, P.K. Stansby, and B.D. Rogers, Incompressible smoothed particle hydrodynamics for free-surface flows: A generalised diffusion-based algorithm for stability and validations for impulsive flows and propagating waves. Journal of Computational Physics, 2012. 231(4): p. 1499-1523. LUBE, G., H.E. HUPPERT, R.S.J. SPARKS, and M.A. HALLWORTH, Axisymmetric collapses of granular columns. Journal of Fluid Mechanics, 2004. 508: p. 175-199. Marrone, S., et al., δ-SPH model for simulating violent impact flows. Computer Methods in Applied Mechanics and Engineering, 2011. 200(13–16): p. 1526-1542. Skillen, A., S. Lind, P.K. Stansby, and B.D. Rogers, Incompressible smoothed particle hydrodynamics (SPH) with reduced temporal noise and generalised Fickian smoothing applied to body-water slam and efficient wave-body interaction. Computer Methods in Applied Mechanics and Engineering, 2013. 265: p. 163-173. Soares-Frazão, S., et al., Dam-break flows over mobile beds: experiments and benchmark tests for numerical models. Journal of Hydraulic Research, 2012. 50(4): p. 364-375. Mokos, A., Multi-phase Modelling of Violent Hydrodynamics Using Smoothed Particle Hydrodynamics (SPH) on Graphics Processing Units (GPUs), in School of Mech. Aero and Civil Eng. 2014, University of Manchester: Manchester. Ulrich, C., M. Leonardi, and T. Rung, Multi-physics SPH simulation of complex marine-engineering hydrodynamic problems. Ocean Engineering, 2013. 64(0): p. 109-121.