Simulation and validation of turbulent gas flow in a cyclone using Caelus
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Transcript of Simulation and validation of turbulent gas flow in a cyclone using Caelus
Simulation and validation of turbulent gas flow in a cyclone using Caelus
Dr Darrin W StephensDr Chris SideroffProf. Aleksandar Jemcov
Introduction
• Cyclones play a dominant role in industrial separation of dilute particles from gas flow.
• High swirl and very large curvature of streamlines presents a modelling challenge.
• Paper’s main objective:• investigate the effect turbulence model selection has on
the predicted mean flow behaviour within a gas cyclone. • Numerical simulation results were compared against experimental data of Witt et al. (1999).
©Applied CCM. Eleventh International Conference on Computational Fluid Dynamics in the Minerals and Process Industries 20152
Turbulence models
• Three classes of turbulence models investigated• Two equation – offer a good compromise between
numerical effort and computational accuracy. • Reynolds stress - applicable for the flows where the
eddy-viscosity assumption is no longer.• LES - expected to be more accurate, particularly in
complex flows where the assumptions inherent to RANS models rarely exist.
©Applied CCM. Eleventh International Conference on Computational Fluid Dynamics in the Minerals and Process Industries 20153
Turbulence models cont’d
• Two equation models (k-ω SST):
• Standard: ;• Spalart and Shur Curvature Correction:
• Hellsten curvature correction
©Applied CCM. Eleventh International Conference on Computational Fluid Dynamics in the Minerals and Process Industries 20154
( )( ) ( )* *min ,10t j j j k t j r kk u k k f P k kν σ ν β ω β ω∂ + ∂ = ∂ + ∂ + −
( )( ) ( )( ) 2
*
24 1
min ,10
2 1 .
t j j j t j r k
j j
u f P kk
F F kφ
ω ω
ωω
ωω ω ν σ ν ω α β ωσ
β ω ωω
∂ + ∂ = ∂ + ∂ +
− + − ∂ ∂
( ) max min ,1.25 ,0.0r scale rotationf C f=
( ) ( )*
11 3 2 1*
21 1 tan1rotation r r r r
rf c c c r cr
− = + − − +
41
1 RC i
FC R
=+
1rf = 4 1F =
1mag magi
mag mag
R
= −
Ω ΩS S
Turbulence models cont’d
• Reynolds stress model:
• Launder Reece Rodi (LRR) pressure strain correlation:
• Omega equation:
©Applied CCM. Eleventh International Conference on Computational Fluid Dynamics in the Minerals and Process Industries 20155
*
*23
tt ij k k ij ik k j jk k i ij k k ij
ij
DR u R R u R u R
k
ννβ
β ωδ
∂ + ∂ = − ∂ − ∂ + Π + ∂ + ∂
−
( )*
1 3 5
423
ij ij ij ik jk jk ik
ik jk jk ik kl kl ij
C a C kS C k a a
C k a S a S a S
ε
δ
Π = − + + Ω + Ω + + −
( )( ) 2
2t j j j t j kku Rkω ω ωωω ω ν σ ν ω α β ω∂ + ∂ = ∂ + ∂ + −
23
ijij ij
Ra
kδ= −
Turbulence Models cont’d
• LES sub-grid scale (SGS) models • Unknown stress determined from • Smagorinsky (1963) – an algebraic model for the SGS
viscosity• Model parameter Cs is a constant
• Coherent structure (Kobayashi, 2005) – extends Smagorinsky model using a variable Cs.
;
©Applied CCM. Eleventh International Conference on Computational Fluid Dynamics in the Minerals and Process Industries 20156
2 2SGS s magCν = ∆ S
2ij SGS ijSτ ν= −
( )32 2 1s CSM CS CSC C F F= −
( )2i j j i
CS
i j
u uF
u
−∂ ∂=
∂1
22CSMC =
Case Study
• Gas cyclone geometry• Outer diameter 0.39 m• Half-angle of 20°• Bottom outflow is closed for all
simulations.• Tangential rectangular inlet.
• Grid - 606,264 hexahedral cells• Uniform inlet velocity of 21.5 m/s.• Neumann condition applied to all flow quantities at the vortex finder outlet.
©Applied CCM. Eleventh International Conference on Computational Fluid Dynamics in the Minerals and Process Industries 20157
Numerical Method
• Transient Solver• SLIM algorithm• Caelus v5.04 library.
• Discretization• Time - 2nd order backward scheme• Gradients - Green-Gauss method.• Advection - 2nd order linear upwind multidimensional
linear scheme with Barth-Jespersen limiter.• Courant number - 5 all but RSM (0.5).• Time averaged for 1000 residence times.
©Applied CCM. Eleventh International Conference on Computational Fluid Dynamics in the Minerals and Process Industries 20158
Results
©Applied CCM. Eleventh International Conference on Computational Fluid Dynamics in the Minerals and Process Industries 20159
ABCDEF
Tangential Vertical
Results cont’d
©Applied CCM. Eleventh International Conference on Computational Fluid Dynamics in the Minerals and Process Industries 201510
ABCDEF
Tangential Vertical
Results cont’d
©Applied CCM. Eleventh International Conference on Computational Fluid Dynamics in the Minerals and Process Industries 201511
ABCDEF
Tangential Vertical
Results cont’d
• Non-dimensionalised pressure loss coefficient
• Computational cost• 60 Intel Xeon E5-2620v3 cores per simulation
©Applied CCM. Eleventh International Conference on Computational Fluid Dynamics in the Minerals and Process Industries 201512
Model CPU time (hour) per 1s flow timeSST 1.01
SST-CC 1.14SST-HELL 1.05
SMAG 1.18CS 1.48
RSM-LRR 10.90
EXP SST SST-CC SST-HELL SMAG CS RSM-LRR6.80 10.2 6.02 8.77 6.19 6.56 6.09ξ21
2
in out
in
p p
uξ
′ ′−=
Conclusion
• Turbulent flow inside cyclone simulated with different turbulence models.
• Turbulence models tested:• k-ω SST, k-ω SST-CC, k-ω SST-HELL,• Smagorinsky and Coherent structure LES, • LRR Reynolds Stress.
• Simulations were performed with a transient solver using version 5.04 of the Caelus library.
©Applied CCM. Eleventh International Conference on Computational Fluid Dynamics in the Minerals and Process Industries 201513
Conclusion
• Comparison with experimental results of Witt et al. (1999).
• Not suitable for cyclone modelling:• Standard k-ω SST model• Hellsten curvature correction
• Most accurate - Coherent structure LES.• Least accurate - Standard k-ω SST model.• Most expensive - LRR Reynolds Stress model.
©Applied CCM. Eleventh International Conference on Computational Fluid Dynamics in the Minerals and Process Industries 201514
Thank you
Applied CCMDr Darrin StephensPrincipal Research Engineer
Phone: 03 8376 6962Email: [email protected]: www.appliedccm.com.au
©Applied CCM. Eleventh International Conference on Computational Fluid Dynamics in the Minerals and Process Industries 2015
Questions
15
What is Caelus?
• Caelus was forked from OpenFOAM• Free and open: www.caelus-cml.com• Support multiple platforms (Windows, Linux, Mac)• Easy installation/compilation• Documentation and validation cases• Improved algorithmic robustness on non-”perfect” meshes
• Multidimensional interpolation• Deferred corrections
• Improved accuracy on non-”perfect” meshes• New compressible solvers• New turbulence models – VLES, Coherent structure, etc• Python wrapping, tools and utilities
©Applied CCM. Eleventh International Conference on Computational Fluid Dynamics in the Minerals and Process Industries 201516
About Applied CCM
• Specialise in the application, support and development of OpenFOAM.
• People• Darrin Stephens, Aleks Jemcov and Chris Sideroff
• Locations• Australia, USA and Canada
• Engage with customers as their Technology partner
©Applied CCM. Eleventh International Conference on Computational Fluid Dynamics in the Minerals and Process Industries 201517