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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.