fhp, poiseuille flow lbm, karman vortex streetmaq/zajecia/cfd2015/exam/... · karman vortex street...
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FHP, Poiseuilleflow
LBM, Karmanvortex street
Beata Kowal
Outline
FHP
Poiseuille flow
Simulation results
Lattice BoltzmannmethodThe Boltzmann Equation
BGK
Reflection
Karman vortexstreet
Simulation results
Frequancy ofvortex structures
FHP, Poiseuille flowLBM, Karman vortex street
Beata Kowal
FHP, Poiseuilleflow
LBM, Karmanvortex street
Beata Kowal
Outline
FHP
Poiseuille flow
Simulation results
Lattice BoltzmannmethodThe Boltzmann Equation
BGK
Reflection
Karman vortexstreet
Simulation results
Frequancy ofvortex structures
Outline
FHP
Poiseuille flow
Simulation results
Lattice Boltzmann method
Karman vortex street
Simulation results
Frequency of vortex structures
FHP, Poiseuilleflow
LBM, Karmanvortex street
Beata Kowal
Outline
FHP
Poiseuille flow
Simulation results
Lattice BoltzmannmethodThe Boltzmann Equation
BGK
Reflection
Karman vortexstreet
Simulation results
Frequancy ofvortex structures
FHP
The FHP model of fluid flow is a cellular automaton inwhich particles move in triangular grid.Two- and threebody collision rules (FHP1):
Reflections: bounce back and specular
FHP, Poiseuilleflow
LBM, Karmanvortex street
Beata Kowal
Outline
FHP
Poiseuille flow
Simulation results
Lattice BoltzmannmethodThe Boltzmann Equation
BGK
Reflection
Karman vortexstreet
Simulation results
Frequancy ofvortex structures
FHP
FHP 2Stationary particles
FHP 3
FHP, Poiseuilleflow
LBM, Karmanvortex street
Beata Kowal
Outline
FHP
Poiseuille flow
Simulation results
Lattice BoltzmannmethodThe Boltzmann Equation
BGK
Reflection
Karman vortexstreet
Simulation results
Frequancy ofvortex structures
Poiseuille flow
The initial velocity of the fluid is directed along axis X. Aftersome time the velocity of the fluid has parabolic profile.
FHP, Poiseuilleflow
LBM, Karmanvortex street
Beata Kowal
Outline
FHP
Poiseuille flow
Simulation results
Lattice BoltzmannmethodThe Boltzmann Equation
BGK
Reflection
Karman vortexstreet
Simulation results
Frequancy ofvortex structures
Program
FHP, Poiseuilleflow
LBM, Karmanvortex street
Beata Kowal
Outline
FHP
Poiseuille flow
Simulation results
Lattice BoltzmannmethodThe Boltzmann Equation
BGK
Reflection
Karman vortexstreet
Simulation results
Frequancy ofvortex structures
Simulation results
FHP 1
FHP, Poiseuilleflow
LBM, Karmanvortex street
Beata Kowal
Outline
FHP
Poiseuille flow
Simulation results
Lattice BoltzmannmethodThe Boltzmann Equation
BGK
Reflection
Karman vortexstreet
Simulation results
Frequancy ofvortex structures
Simulation results
FHP 2
FHP, Poiseuilleflow
LBM, Karmanvortex street
Beata Kowal
Outline
FHP
Poiseuille flow
Simulation results
Lattice BoltzmannmethodThe Boltzmann Equation
BGK
Reflection
Karman vortexstreet
Simulation results
Frequancy ofvortex structures
Simulation results
FHP 3
FHP, Poiseuilleflow
LBM, Karmanvortex street
Beata Kowal
Outline
FHP
Poiseuille flow
Simulation results
Lattice BoltzmannmethodThe Boltzmann Equation
BGK
Reflection
Karman vortexstreet
Simulation results
Frequancy ofvortex structures
Lattice Boltzmann method
Lattice Boltzmann methods is a class of computational fluiddynamics methods for fluid simulation.
Instead of solving the Navier–Stokes equations, we solve thediscrete Boltzmann equation.
FHP, Poiseuilleflow
LBM, Karmanvortex street
Beata Kowal
Outline
FHP
Poiseuille flow
Simulation results
Lattice BoltzmannmethodThe Boltzmann Equation
BGK
Reflection
Karman vortexstreet
Simulation results
Frequancy ofvortex structures
Lattice Boltzmann method
f (x,u, t) - distribution function
dN = f (x,u, t)d3xd3u - number of particles in finite elementof momentum/position space
The Boltzmann Equation
(∂t + u∇)f (x,u, t) = (∂t f )coll
FHP, Poiseuilleflow
LBM, Karmanvortex street
Beata Kowal
Outline
FHP
Poiseuille flow
Simulation results
Lattice BoltzmannmethodThe Boltzmann Equation
BGK
Reflection
Karman vortexstreet
Simulation results
Frequancy ofvortex structures
Lattice Boltzmann method
Bhatnagar-Gross-Krook (BGK) collision model.
BGK collision operator:
(∂t f )coll =1τ
(f eq − f )
FHP, Poiseuilleflow
LBM, Karmanvortex street
Beata Kowal
Outline
FHP
Poiseuille flow
Simulation results
Lattice BoltzmannmethodThe Boltzmann Equation
BGK
Reflection
Karman vortexstreet
Simulation results
Frequancy ofvortex structures
Lattice Boltzmann method
f eqi is the discrete, equilibrium distribution function.
f eq = ρ2πRT exp
(− (e−u)2
2RT
)f eqi = ρwi exp
(3eiuc2 − 3u2
2c2
)≈ ρwi
(1 + 3eiu
c2 − 3u2
2c2 + 9(eiu)2
2c4
)weights wi :w0,w1,w2,w3 = 1/9w4,w5,w6,w7 = 1/36w8 = 4/9
FHP, Poiseuilleflow
LBM, Karmanvortex street
Beata Kowal
Outline
FHP
Poiseuille flow
Simulation results
Lattice BoltzmannmethodThe Boltzmann Equation
BGK
Reflection
Karman vortexstreet
Simulation results
Frequancy ofvortex structures
Lattice Boltzmann method
elementary vectors of on a two-dimensional rectangular grid.ei :e0 = (1, 0) e1 = (0, 1) e2 = (−1, 0) e3 = (0,−1)e4 = (1, 1) e5 = (−1, 1) e6 = (−1,−1) e7 = (1,−1)e8 = (0, 0)
FHP, Poiseuilleflow
LBM, Karmanvortex street
Beata Kowal
Outline
FHP
Poiseuille flow
Simulation results
Lattice BoltzmannmethodThe Boltzmann Equation
BGK
Reflection
Karman vortexstreet
Simulation results
Frequancy ofvortex structures
Lattice Boltzmann method
The collision and transition step are defined:
collision step
fi (x , t + δt) = fi (x , t) +1τ
(f eqi − fi )
transition step
fi (x + eiδt, t + δt) = fi (x , t + δt)
i - directions of momentum.
FHP, Poiseuilleflow
LBM, Karmanvortex street
Beata Kowal
Outline
FHP
Poiseuille flow
Simulation results
Lattice BoltzmannmethodThe Boltzmann Equation
BGK
Reflection
Karman vortexstreet
Simulation results
Frequancy ofvortex structures
Lattice Boltzmann method
ReflectionBorder is located halfway between vertices.
Fluid directed toward the border isn’t translated but it’sreflected in the opposite direction.
FHP, Poiseuilleflow
LBM, Karmanvortex street
Beata Kowal
Outline
FHP
Poiseuille flow
Simulation results
Lattice BoltzmannmethodThe Boltzmann Equation
BGK
Reflection
Karman vortexstreet
Simulation results
Frequancy ofvortex structures
Karman vortex street
Karman vortex street in the Greenland Sea (NASA image by Jeff Schmaltz,
http://earthobservatory.nasa.gov/NaturalHazards/view.php?id=77654)
FHP, Poiseuilleflow
LBM, Karmanvortex street
Beata Kowal
Outline
FHP
Poiseuille flow
Simulation results
Lattice BoltzmannmethodThe Boltzmann Equation
BGK
Reflection
Karman vortexstreet
Simulation results
Frequancy ofvortex structures
Karman vortex street
Karman vortex street is a repeating pattern of vorticescaused by the separation of flow of a fluid by obstacles.
Vortex structures are seen in a case of sufficiently high valueof Reynolds number.
Re =Vdν
ν = 13
(τ − 1
2
)- viscosity
d - diameter of the cylinderV - flow velocity.
FHP, Poiseuilleflow
LBM, Karmanvortex street
Beata Kowal
Outline
FHP
Poiseuille flow
Simulation results
Lattice BoltzmannmethodThe Boltzmann Equation
BGK
Reflection
Karman vortexstreet
Simulation results
Frequancy ofvortex structures
Simulation results
FHP, Poiseuilleflow
LBM, Karmanvortex street
Beata Kowal
Outline
FHP
Poiseuille flow
Simulation results
Lattice BoltzmannmethodThe Boltzmann Equation
BGK
Reflection
Karman vortexstreet
Simulation results
Frequancy ofvortex structures
Simulation results
Grid 150x50, 10’000 steps, velocity visualisation, τ = 0.551000 steps
2000 steps
3000 steps
4000 steps
5000 steps
FHP, Poiseuilleflow
LBM, Karmanvortex street
Beata Kowal
Outline
FHP
Poiseuille flow
Simulation results
Lattice BoltzmannmethodThe Boltzmann Equation
BGK
Reflection
Karman vortexstreet
Simulation results
Frequancy ofvortex structures
Simulation results
Grid 150x50, 10’000 steps, velocity visualisationτ = 0.6 ν = 0.033 Re = 50
τ = 0.57 ν = 0.023 Re = 70
τ = 0.56 ν = 0.02 Re = 80
FHP, Poiseuilleflow
LBM, Karmanvortex street
Beata Kowal
Outline
FHP
Poiseuille flow
Simulation results
Lattice BoltzmannmethodThe Boltzmann Equation
BGK
Reflection
Karman vortexstreet
Simulation results
Frequancy ofvortex structures
Simulation results
Grid 150x50, 10’000 steps, velocity visualisationτ = 0.55 ν = 0.017 Re = 100
τ = 0.53 ν = 0.01 Re = 160
τ = 0.52 ν = 0.0067 Re = 240
FHP, Poiseuilleflow
LBM, Karmanvortex street
Beata Kowal
Outline
FHP
Poiseuille flow
Simulation results
Lattice BoltzmannmethodThe Boltzmann Equation
BGK
Reflection
Karman vortexstreet
Simulation results
Frequancy ofvortex structures
Simulation results
Grid 150x50, 10’000 steps, density visualisationτ = 0.6 ν = 0.033
τ = 0.57 ν = 0.023 Re = 70
τ = 0.56 ν = 0.02 Re = 80
FHP, Poiseuilleflow
LBM, Karmanvortex street
Beata Kowal
Outline
FHP
Poiseuille flow
Simulation results
Lattice BoltzmannmethodThe Boltzmann Equation
BGK
Reflection
Karman vortexstreet
Simulation results
Frequancy ofvortex structures
Simulation results
Grid 150x50, 10’000 steps, density visualisationτ = 0.55 ν = 0.017 Re = 100
τ = 0.53 ν = 0.01 Re = 160
τ = 0.52 ν = 0.0067 Re = 240
FHP, Poiseuilleflow
LBM, Karmanvortex street
Beata Kowal
Outline
FHP
Poiseuille flow
Simulation results
Lattice BoltzmannmethodThe Boltzmann Equation
BGK
Reflection
Karman vortexstreet
Simulation results
Frequancy ofvortex structures
Frequancy of vortex structures
f - vortex frequency.d - diameter of the cylinderV - flow velocity.Strouhal number: St = fd
V
Strouhal number, for a range of Reynolds number between 250 < Re < 105, can be expressed as(calculated by G. I. Taylor (1886-1975)):
St = 0.198
(1−
19.7
Re
)”Simple Karman Street model”, Cecilia Tapia S. and Ryad Chellali,DOI: 10.1109/OCEANSSYD.2010.5603671
Model of a vortex street, Tubes, crossflow over, Bengt Sunden
FHP, Poiseuilleflow
LBM, Karmanvortex street
Beata Kowal
Outline
FHP
Poiseuille flow
Simulation results
Lattice BoltzmannmethodThe Boltzmann Equation
BGK
Reflection
Karman vortexstreet
Simulation results
Frequancy ofvortex structures
Frequancy of vortex structures
τ Re fs from simulation ff from formula |∆f |/fs0.55 100 0.00185 0.00153 17%0.53 160 0.00181 0.00167 8%0.52 240 0.00174 0.00175 0.6%
0.515 325 0.00178 0.00179 0.6%
FHP, Poiseuilleflow
LBM, Karmanvortex street
Beata Kowal
Outline
FHP
Poiseuille flow
Simulation results
Lattice BoltzmannmethodThe Boltzmann Equation
BGK
Reflection
Karman vortexstreet
Simulation results
Frequancy ofvortex structures
Bibliography
Sebastian Szczecina, Własności hydrodynamiczne modelugazu sieciowego FHP-III
Josue Njock, A Method of Evaluating the Presence ofFan-Blade-Rotation Induced Unsteadiness in Wind TunnelExperiments
Amir Masoud Abdol, Lattice Gas Automata
A Practical Introduction to the Lattice Boltzmann Method ,Alexander J.Wagner
Badanie zjawisk zachodzących w cieczach nieściśliwychmetodą cząstek znaczonych, M.Matyka
Simple Karman Street model, Cecilia Tapia S. and RyadChellali
Tubes, crossflow over, Bengt Sunden
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