dns of the turbulence decay in liquid metal flow under an...
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Introduction Case & Background Formulation & Methodology Results Concluding remarks
DNS of the Turbulence Decay in LiquidMetal Flow Under an Increasing Magnetic
Field
X.Albets-Chico , D. Grigoriadis, S. Kassinos
Department of Mechanical and Manufacturing EngineeringUniversity of Cyprus
International conference on MHD turbulenceDecember 21st-23rd, 2009. IIT Kanpur, India.
Introduction Case & Background Formulation & Methodology Results Concluding remarks
Outline
1 Introduction
2 Case & Background
3 Formulation & MethodologyFormulationNumerics
4 ResultsVerification & ValidationFinal Results
5 Concluding remarks
Introduction Case & Background Formulation & Methodology Results Concluding remarks
Motivation: Spatially varying magnetic fields
The nuclear fusion reaction takes placein the plasma confined in the tokamak
Introduction Case & Background Formulation & Methodology Results Concluding remarks
Motivation: Spatially varying magnetic fields
The nuclear fusion reaction takes placein the plasma confined in the tokamak
The energy (and other particles) isabsorbed by the blanket surroundingthe toroidal tokamak
Introduction Case & Background Formulation & Methodology Results Concluding remarks
Motivation: Spatially varying magnetic fields
The nuclear fusion reaction takes placein the plasma confined in the tokamak
The energy (and other particles) isabsorbed by the blanket surroundingthe toroidal tokamak
The blanket concept is based onliquid-metal flow
Introduction Case & Background Formulation & Methodology Results Concluding remarks
Motivation: Spatially varying magnetic fields
The nuclear fusion reaction takes placein the plasma confined in the tokamak
The energy (and other particles) isabsorbed by the blanket surroundingthe toroidal tokamak
The blanket concept is based onliquid-metal flow
The plasma is confined using a helicalmagnetic field
Introduction Case & Background Formulation & Methodology Results Concluding remarks
Motivation: Spatially varying magnetic fields
The nuclear fusion reaction takes placein the plasma confined in the tokamak
The energy (and other particles) isabsorbed by the blanket surroundingthe toroidal tokamak
The blanket concept is based onliquid-metal flow
The plasma is confined using a helicalmagnetic field
The section of the pipes is expected toby circular
Introduction Case & Background Formulation & Methodology Results Concluding remarks
Circular Pipe Turbulent Flow
Turbulence
Generallythree-dimensional
Introduction Case & Background Formulation & Methodology Results Concluding remarks
Circular Pipe Turbulent Flow
Turbulence
Generallythree-dimensional
Generated bywall instabilities
Introduction Case & Background Formulation & Methodology Results Concluding remarks
Circular Pipe Turbulent Flow
Turbulence
Generallythree-dimensional
Generated bywall instabilities
Mixing of heat ,momentum andmass is enhanced.
Introduction Case & Background Formulation & Methodology Results Concluding remarks
Circular Pipe Magnetohydrodynamic flow
Effect of the magnetic field on electrically conducting fluid
Induced currentsj → −∇φ + u × B
Introduction Case & Background Formulation & Methodology Results Concluding remarks
Circular Pipe Magnetohydrodynamic flow
Effect of the magnetic field on electrically conducting fluid
Induced currentsj → −∇φ + u × B
Lorentz Force →j × B ∼ u × B × B
Introduction Case & Background Formulation & Methodology Results Concluding remarks
Circular Pipe Magnetohydrodynamic flow
Effect of the magnetic field on electrically conducting fluid
Induced currentsj → −∇φ + u × B
Lorentz Force →j × B ∼ u × B × B
The current loopsdefine the localeffect of theLorentz force
Introduction Case & Background Formulation & Methodology Results Concluding remarks
Circular Pipe Magnetohydrodynamic flow
Effect of the magnetic field on electrically conducting fluid
Induced currentsj → −∇φ + u × B
Lorentz Force →j × B ∼ u × B × B
The current loopsdefine the localeffect of theLorentz force
Turbulence issystematically suppressedby magnetic fields(Ha/Re > 0.025)
Introduction Case & Background Formulation & Methodology Results Concluding remarks
Objective: Magnetohydrodynamics & Turbulence ?
The action of strong magnetic fields suppressesturbulence
Introduction Case & Background Formulation & Methodology Results Concluding remarks
Objective: Magnetohydrodynamics & Turbulence ?
The action of strong magnetic fields suppressesturbulence
Fringing magnetic fields are related to three-dimensionaleffects
Introduction Case & Background Formulation & Methodology Results Concluding remarks
Objective: Magnetohydrodynamics & Turbulence ?
The action of strong magnetic fields suppressesturbulence
Fringing magnetic fields are related to three-dimensionaleffects
Three-dimensional effects increase the complexity andinstabilities of the flow
Introduction Case & Background Formulation & Methodology Results Concluding remarks
Objective: Magnetohydrodynamics & Turbulence ?
The action of strong magnetic fields suppressesturbulence
Fringing magnetic fields are related to three-dimensionaleffects
Three-dimensional effects increase the complexity andinstabilities of the flow
Coexistence of the two phenomena is here investigated
Introduction Case & Background Formulation & Methodology Results Concluding remarks
Case
y
z
x
R
Magnet
14R
20R
B
C
F
D
Magnetic field = B yfit(x)
Flow
Magnet
A
E
30
34R
R
ExperimentalConfiguration.ALEX facility,Argonne NationalLab., Illinois, USA.
Introduction Case & Background Formulation & Methodology Results Concluding remarks
Case
y
z
x
R
Magnet
14R
20R
B
C
F
D
Magnetic field = B yfit(x)
Flow
Magnet
A
E
30
34R
R
Case reportedExperimentally[Picologlou(1986),Reed(1987)] andNumerically(Asymptoticmethods [forinstance,Reed(1987),Molokov(2003),Bülher(2006)], andrecently by DNS[Ni (2007),Albets(2009)])
Introduction Case & Background Formulation & Methodology Results Concluding remarks
Case
y
z
x
R
Magnet
14R
20R
B
C
F
D
Magnetic field = B yfit(x)
Flow
Magnet
A
E
30
34R
R
Case addressedby current work.Analyzed for thevery first time.Role of inertiadisqualifies theuse of asymptoticmethods. Thereare also importantexperimentalaccuracyproblems. Is DNSan option?
Introduction Case & Background Formulation & Methodology Results Concluding remarks
Background (i)Experimental work, decreasing magnetic field. Upstreamconditions Ha = 6640, N = 10700 (ALEX Results: Picologlouet al.. 1986, Reed et al.. 1987 )
Introduction Case & Background Formulation & Methodology Results Concluding remarks
Background (i)Experimental work, decreasing magnetic field. Upstreamconditions Ha = 6640, N = 10700 (ALEX Results: Picologlouet al.. 1986, Reed et al.. 1987 )Attention to the accuracy in Experiments!!
Introduction Case & Background Formulation & Methodology Results Concluding remarks
Background (i)Experimental work, decreasing magnetic field. Upstreamconditions Ha = 6640, N = 10700 (ALEX Results: Picologlouet al.. 1986, Reed et al.. 1987 )Attention to the accuracy in Experiments!!
Approximately 18R are needed to decrease from Ha = 6640 toHD conditions?
Introduction Case & Background Formulation & Methodology Results Concluding remarks
Background (i)Experimental work, decreasing magnetic field. Upstreamconditions Ha = 6640, N = 10700 (ALEX Results: Picologlouet al.. 1986, Reed et al.. 1987 )Attention to the accuracy in Experiments!!
Approximately 18R are needed to decrease from Ha = 6640 toHD conditions?The ERROR signal output of the local magnetic field becomesvery important (negative value!)... The last ACCEPTABLE valueis at Ha = 60! (17R dowstream of the high mag. field area)
Introduction Case & Background Formulation & Methodology Results Concluding remarks
Background (i)Experimental work, decreasing magnetic field. Upstreamconditions Ha = 6640, N = 10700 (ALEX Results: Picologlouet al.. 1986, Reed et al.. 1987 )Attention to the accuracy in Experiments!!
Approximately 18R are needed to decrease from Ha = 6640 toHD conditions?The ERROR signal output of the local magnetic field becomesvery important (negative value!)... The last ACCEPTABLE valueis at Ha = 60! (17R dowstream of the high mag. field area)For a Increasing Magnetic field: Experimental analysis presentenormous difficulties to provide accurate information about thetransition from (turbulent) HD flow to strong MHD flow(Ha/Re > 0.025, Ha ≈ 100 turbulence decayment)
Introduction Case & Background Formulation & Methodology Results Concluding remarks
Background (ii). Size of the problem?
How to characterize this area? What is the most reliabledescription of the evolution of the magnetic field from HDconditions to Ha ≈ 50 and beyond?
Introduction Case & Background Formulation & Methodology Results Concluding remarks
Background (ii). Size of the problem?
How to characterize this area? What is the most reliabledescription of the evolution of the magnetic field from HDconditions to Ha ≈ 50 and beyond?
tanh− based function can be applied By = Bd1+tanh[0.45(x/R)]
2(IEA Liquid Breeder Blanket SubTask, 2005) (mean error of 1%)
Introduction Case & Background Formulation & Methodology Results Concluding remarks
Background (ii). Size of the problem?
How to characterize this area? What is the most reliabledescription of the evolution of the magnetic field from HDconditions to Ha ≈ 50 and beyond?
tanh− based function can be applied By = Bd1+tanh[0.45(x/R)]
2(IEA Liquid Breeder Blanket SubTask, 2005) (mean error of 1%)
Consequences
Introduction Case & Background Formulation & Methodology Results Concluding remarks
Background (ii). Size of the problem?
How to characterize this area? What is the most reliabledescription of the evolution of the magnetic field from HDconditions to Ha ≈ 50 and beyond?
tanh− based function can be applied By = Bd1+tanh[0.45(x/R)]
2(IEA Liquid Breeder Blanket SubTask, 2005) (mean error of 1%)
Consequences
Required distance to evolve from HD conditions(Ha = 0.005, Ha ≈ 0) to strong MHD conditions(Ha = 6640) is 23R
Introduction Case & Background Formulation & Methodology Results Concluding remarks
Background (ii). Size of the problem?
How to characterize this area? What is the most reliabledescription of the evolution of the magnetic field from HDconditions to Ha ≈ 50 and beyond?
tanh− based function can be applied By = Bd1+tanh[0.45(x/R)]
2(IEA Liquid Breeder Blanket SubTask, 2005) (mean error of 1%)
Consequences
Required distance to evolve from HD conditions(Ha = 0.005, Ha ≈ 0) to strong MHD conditions(Ha = 6640) is 23RRequired distance to reach accurate fully-developedturbulent HD flow at experimental conditions (Reτ ≈ 520) isbetween 5 − 10D.
Introduction Case & Background Formulation & Methodology Results Concluding remarks
Background (ii). Size of the problem?
How to characterize this area? What is the most reliabledescription of the evolution of the magnetic field from HDconditions to Ha ≈ 50 and beyond?
tanh− based function can be applied By = Bd1+tanh[0.45(x/R)]
2(IEA Liquid Breeder Blanket SubTask, 2005) (mean error of 1%)
Consequences
Required distance to evolve from HD conditions(Ha = 0.005, Ha ≈ 0) to strong MHD conditions(Ha = 6640) is 23RRequired distance to reach accurate fully-developedturbulent HD flow at experimental conditions (Reτ ≈ 520) isbetween 5 − 10D.
Computational domain of at least 50R for conducting cases,even more for insulating cases! (development length!,three-dimensional effects of R ×O(Ha1/2) R. Holroyd and J.S. Walker, Journal of Fluid Mechanics 84, 79 (1978)
Introduction Case & Background Formulation & Methodology Results Concluding remarks
Governing EquationsConservation of mass, momentum and charge:
∇ · u = 0 (1)∂u∂t
+ u · ∇u = −∇p +1
Re∇2u + N(j × B) (2)
∇ · j = 0 (3)
Ohm’s Law:
j = σ(−∇φ + u × B) (4)
∇2φ = ∇ · (u × B) (5)
ν viscosityσ conductivityρ densityu velocityj current densityp pressuret timeφ electric potentialB magnetic field
Re = UbR/νN = RσB2/ρUb
Ha = RB√
σ/ρν
Introduction Case & Background Formulation & Methodology Results Concluding remarks
Boundary Conditions
Wall:~uwall = 0, (No slip)∂p∂n |wall = 0,∂φ∂n |wall = −[∇τ · (c∇τφw )], J. S. Walker, Journal de Mécanique 20, 79 (1981).
Inlet:~uinlet = definedpinlet → inlet penalty b.c.,∂φ∂n |inlet = 0
Outlet:∂~uoutlet
∂t + Uconv∂~uoutlet
∂n = 0, (Convective)poutlet → outlet penalty b.c.,∂φ∂n |outlet = 0
Introduction Case & Background Formulation & Methodology Results Concluding remarks
Numerical Method, Grid Generation
Unstructured Nodal-basedFinite Volume Code
Collocated scheme
Fractional-step method(Chorin, 1968)
Time discretization:Crank-Nicholson /Semi-implicit /Explicitintegration of the LorentzForce
Conservative computation ofthe Lorentz force (Ni, 2007)
Direct Numerical Simulation(no model used)
z/R
y/R
-1 -0.5 0 0.5 1-1
-0.5
0
0.5
1
θ
r
Hybrid quads/triangles b.layer/core
Very strong near-wall stretching toresolve Ha layers
Core designed to resolveturbulence scales
Introduction Case & Background Formulation & Methodology Results Concluding remarks
Numerical Method, Grid Generation
z/R
y/R
-1 -0.5 0 0.5 1-1
-0.5
0
0.5
1
θ
r
Very strong near-wallstretching to resolve Halayers (up to Ha ≈ 10000)→ ∆r+
min = 0.013→ ∆rmin/R = 0.00005
Core → turbulence scalesat Reτ ≈ 520 →∆x+ = 10.4,∆θ+
max=7.2,∆r+max ∼7
Introduction Case & Background Formulation & Methodology Results Concluding remarks
Numerical Method, Grid Generation
SUMMARY
Explicit Lorentz Force...TIME-STEPING REQUIREMENTS!∆t ≤ 2/σB2→ Ha = 7000 → 3 · 105 time-steps are neededto compute one turn-over time
(development length = 50R)ESTIMATED MESH REQUIREMENTS! → 17 M6
elements
Something needs to be done... impossible to address...
Introduction Case & Background Formulation & Methodology Results Concluding remarks
Numerical Strategy
D
A
B
C’Ha=500
Ha=0, N=0, Reb≈4000
Magnet
Magnet
A
20 R
Ha=500, N=62.7
Ha=50, N=0.62
B
C’’
Fully-developed hydrodynamicturbulent flow
C’
C’’
D
C’
Transition to low mag. field
Ha=50, N=0.62
Ha=50Ha=0.005 Ha=3
Ha=500, N=62.7
Ha=3
Flow
B
≈50 R
20 R
7 R
20 R
Introduction Case & Background Formulation & Methodology Results Concluding remarks
Numerical Strategy
Magnets’ magnetic field generates Ha = 50 conditionsBy = 501+tanh[0.45(x/R)]
2Magnets’ magnetic field generates Ha = 500 conditionsBy = 5001+tanh[0.45(x/R)]
2
−10 −5 0 5 100
100
200
300
400
500
600
X/R
Ha
−10 −5 0 50
20
40
60
80
100
X/R
Ha
−10 −5 0 50
20
40
60
80
100
X/R
Ha
it is possible to find a shift to match both values withoutassuming too much... why?
Introduction Case & Background Formulation & Methodology Results Concluding remarks
Numerical Strategy∂(tanh(x))
∂x = 1 − tanh2(x)...so...∂(tanh(x))
∂x → 0 faster than tanh(x)for x → −∞ we chooseappropriate x/R which, in combination with the shift (while matchingboth magnetic field values), produces a difference in the slope that issmall ...
−3.5 −3 −2.51
1.5
2
2.5
3
3.5
4
4.5
5
X/R
Ha
6%relativedifferencein slope
−10 −5 0 5 10 150
100
200
300
400
500
600
X/R
Ha
The investigateddomain is extended withoutincreasingcomputationalrequirements!
This feature allows to reuse computational information and extendfurther downstream our domain, very useful to assess inertia effects!!!
Introduction Case & Background Formulation & Methodology Results Concluding remarks
Numerical Strategy
20R
C
D
A
R
C
B
D
AB
BC
y
z
x
Flow
Constant magnetic field,fully-develped MHD flow?
Hydrodynamic flow Reb≈4000
Rapid transition to MHD flow, decayment of turbulence
Introduction Case & Background Formulation & Methodology Results Concluding remarks
Numerical Strategy
A
B
AB
20R
y
z
x
Flow
Time-history...t, u,v,w
Periodic Boundary-conditions
Flow
Hydrodynamic flow Reb≈4000
Introduction Case & Background Formulation & Methodology Results Concluding remarks
Numerical Strategy
D
R
B
20Ry
z
x
Flow: inlet defined in time and position
Introduction Case & Background Formulation & Methodology Results Concluding remarks
Numerical Strategy
7R
C’
D
R
C’’
B
D
BC’
C
C’C’’
20Ry
z
x
Flow: inlet defined in time and position
Constant magnetic field,fully-develped MHD flow?
Rapid transition to MHD flow (I) (low N, low Ha)
Rapid transition to MHD flow (II)
Introduction Case & Background Formulation & Methodology Results Concluding remarks
Numerical Strategy
20R
C’’
D
R
D
C’
C’’
C’
C’’
y
z
x
Flow: inlet defined (u,v,w)in time and position
Constant magnetic field,fully-develped MHD flow?
Rapid transition to MHD flow (II)
Introduction Case & Background Formulation & Methodology Results Concluding remarks
Results
Introduction Case & Background Formulation & Methodology Results Concluding remarks
Verification. Connecting magnetic fields
The information is accurately transferred to the newdomain, identical magnetic fields
x/R
P/R
σUbB
d2 ,u x/U
b
By/B
d
-15 -10 -5 0 5
0.2
0.4
0.6
0.8
1
1.2
0.2
0.4
0.6
0.8
1
Quasi-fully developed MHD flow(turbulent interaction)
Fully developed turbulent HD flow
Computation 1Computation 2
ux at z/R=0
P
ux at z/R=0.75
x/R-15 -10 -5 0 5 10
Computation 1Computation 2
N=0.62Ha=50
N ≈0Ha≈0
N=2.5e-3Ha=3.15
Increasing Magnetic field
Evaluation of the injection into higher magnetic field underprocess...
Introduction Case & Background Formulation & Methodology Results Concluding remarks
Validation &Verification . Hydrodynamic flow.Accurate resolution of the Fully-developed turbulent flow atReτ ≈ 520 →Resolution of the turbulence scales, near-wall viscoussublayer
100
1020
5
10
15
20
y+
u+ x
Present periodicPresentDurst et al.Wagner et al.Log law
100
1020
0.5
1
1.5
2
2.5
3
y+
(ux,u
r,u
θ)+ r
ms,
p+ rm
s
ux
uθ
ur
p
Present periodicPresentDurst et al.Wagner et al.
The injection profile is also assessed...while evaluatinginlet/outlet effects...perfect agreement regardingmomentum!!
Introduction Case & Background Formulation & Methodology Results Concluding remarks
Validation. MagnetoHydrodynamic flow.Accurate resolution of the fully-developed MHD flow up toHa = 7000Resolution of the Ha layers and side layersHa = 10, Ha = 50, Ha = 2000, Ha = 7000
−1 −0.5 0 0.5 10
0.02
0.04
0.06
0.08
0.1
y/R, z/R
ux
ν∂
p/∂
xR
2
Analytic (Gold, 1962)Computed
−1 −0.5 0 0.5 10
0.005
0.01
0.015
0.02
0.025
y/R, z/R
ux
ν∂
p/∂
xR
2
Analytic (Gold, 1962)Computed
−1 −0.5 0 0.5 10
1
2
3
4
5
x 10−4
y/R, z/R
ux
ν∂
p/∂
xR
2
Shercliff, 1962Computed
−1 −0.5 0 0.5 10
0.5
1
1.5x 10
−4
y/R, z/R
ux
ν∂
p/∂
xR
2
Shercliff, 1962Computed
Introduction Case & Background Formulation & Methodology Results Concluding remarks
Transition to low MHD conditions ( Ha = 50) (1/3).
Introduction Case & Background Formulation & Methodology Results Concluding remarks
Transition to low MHD conditions ( Ha = 50) (2/3).
ux at z/R=0.75=y/R=0.75
ux at z/R=0
y/R=0.75, z/R=0
z/R=0.75
x/R
u x/U
b
By/
Bd
-30 -20 -10 0 10
0.6
0.8
1
1.2
1.4
0.2
0.4
0.6
0.8
1
Conducting c=0.027
Fully-developed turbulent HD flow
Insulating
Quasi-fully developed MHD flow(turbulent interaction)
Conducting c=0.027
Fully developed turbulent HD flow
Insulating
x/R
P/R
σUbB
d2
By/B
d
-30 -20 -10 0 10
0
0.2
0.4
0.6
0.8
0.2
0.4
0.6
0.8
1
Quasi-fully developed MHD flow(turbulent interaction)
Fully developed turbulent HD flow
(ux’ ux
’)1/2 at z/R=0.95
(ux’ ux
’)1/2 at z/R=0
x/R
(ux’ u x’ )1/
2 /uτ
By/B
d
-30 -20 -10 0 100
0.5
1
1.5
2
2.5
3
0
0.2
0.4
0.6
0.8
1
Conducting c=0.027
Quasi-fully developed MHD flow(turbulent interaction)
Insulating
The mean velocity evolves to a "flatter"profile, Ha and Roberts layers effects
The MHD pressure drop is higher than theturbulent one. Conductivity effectsincrease the pressured-drop requirementsdue to the net braking Lorentz force.
The turbulent fluctuating levels decreasenon-homogeneously! Overall agreementwith experimental observation for theturbulence decay (Ha/Re > 0.025), as theturbulence indicators are not completelydampened out.
Introduction Case & Background Formulation & Methodology Results Concluding remarks
Transition to low MHD conditions ( Ha = 50) (3/3)
y/R-R, z/R-R
u+ xrm
s/u
τ0
10-3 10-2 10-10
0.5
1
1.5
2
2.5
3
z=0 c=0y=0 c=0Fully-Developed HDz=0 c=0.027y=0 c=0.027
x/R=-8 N ≈ 0
x/R=8 N = 0.62
(y-R)/R, (z-R)/R
u+ xrm
s/u
τ0
10-5 10-4 10-3 10-2 10-1 1000
0.1
0.2
0.3
0.4
0.5
z=0 c=0y=0 c=0z=0 c=0.027y=0 c=0.027
x/R=8 N = 0.62
Roberts layer effect
Ha layer effect
f,Hz
Su
100 101
10-1
100
101
102
103
104
105
HDMHD (Ha=0.55, N≈0))MHD (Ha=25, N=0.31)MHD (Ha=50, N=0.62)
Power Spectrum (4 turn-over time) z/R=0.95
2.95 ≈ 3
1.68 ≈ 5/3
The reduction of the fluctuating statistics isobserved for Ha > 25, N > 0.3...rapidslope of the magnetic field?
The reduction of the fluctuating statisticstakes places in a in-homogenous way,being the conducting Ha layer moreeffective to organize the flow and reducethe turbulence levels.
The inertial range of the power spectra isreduced by the magnetic field(−5/3 → −3) (agreement with spectralanalysis...)
Introduction Case & Background Formulation & Methodology Results Concluding remarks
Transition to moderate MHD conditions (1/4)Wall-conductivity effects ( c = 0.027, c = 0)
Introduction Case & Background Formulation & Methodology Results Concluding remarks
Transition to moderate MHD conditions (1/4)Wall-conductivity effects ( c = 0.027, c = 0)
c = 0.0
c = 0.027
Introduction Case & Background Formulation & Methodology Results Concluding remarks
Transition to moderate MHD conditions (2/4)Wall-conductivity effects ( c = 0.027, c = 0)
Introduction Case & Background Formulation & Methodology Results Concluding remarks
Transition to moderate MHD conditions (3/4)
x/R
u x/U
b
By/
Bd
-30 -25 -20 -15 -10 -5 0 5 10
0.6
0.8
1
1.2
1.4
1.6
0
0.2
0.4
0.6
0.8
1
Fully-Developed Turbulent flow
z/R=0.75
z/R=0.75 , y/R=0.75
y/R=0.75
center-line
x/R
P/R
σUbB
d2
By/
Bd
-30 -25 -20 -15 -10 -5 0 5 10
-0.06
-0.04
-0.02
0
0
0.2
0.4
0.6
0.8
1
Fully-Developed Turbulent flow
z/R=0.75
y/R=0.75
center-line
x/R
(ux’u
x’)
1/2/u
τ0
By/
Bd
-30 -25 -20 -15 -10 -5 0 5 10
0.5
1
1.5
0
0.2
0.4
0.6
0.8
1
Fully-Developed Turbulent flow
z/R=0.75z/R=0.75 , y/R=0.75
y/R=0.75
center-line
(Ha = 500, c = 0.0)
Overspeed-areas are generated due to thebraking Lorentz force. A fully-developedprofile is not completely achieved (inertialterms...)
Important three-dimensional effects takeplace. The MHD pressure drop is oneorder of magnitude larger than the HD one.
The (turbulent) fluctuations are completelydampened out for values Ha >≈ 300N >≈ 25...However, important fluctuatinglevels take place... LAMINAR magneticflow instabilities!!!
Introduction Case & Background Formulation & Methodology Results Concluding remarks
Transition to moderate MHD conditions (4/4)
x/R
u x/U
b
By/
Bd
-30 -25 -20 -15 -10 -5 0 5 10
0.8
1
1.2
1.4
0
0.2
0.4
0.6
0.8
1z/R=0.75
Fully-developed MHD flow
z/R=0.75, y/R=0.75
y/R=0.75
Fully-developed Turbulent flow
center-line
x/R
P/R
σUbB
d2
By/
Bd
-30 -25 -20 -15 -10 -5 0 5 10
-0.4
-0.35
-0.3
-0.25
-0.2
-0.15
-0.1
-0.05
0
0
0.2
0.4
0.6
0.8
1
z/R=0.75
Fully-developed MHD flow
center-line, z/R=0.75, y/R=0.75 center-line, y/R=0.75
Fully-developed Turbulent flow
x/R
(u x’
u x’)
1/2
/uτ0
By/
Bd
-30 -25 -20 -15 -10 -5 0 5 10
0.5
1
1.5
0
0.2
0.4
0.6
0.8
1
z/R=0.75
Fully-developed MHD flow
z/R=0.75, y/R=0.75
y/R=0.75
Fully-developed Turbulent flow
center-line
(Ha = 500, c = 0.027)
A rapid transition to the fully-developed flatprofile is achieved by the moderatemagnetic field. Important jets take place,but they are smaller respect the insulatingones (wall-conductivity effect)!
The HD pressure drop is negligible respectto the MHD one (2 orders!×HD) due to thestrong braking Lorentz force in thedownstream area. Inertial effects aremasked.
The (turbulent) fluctuations are completelydampened out for values Ha >≈ 300N >≈ 25, the fluctuating effect ofinsulating configurations does not takeplace... (wall-conductivity effect)...
Introduction Case & Background Formulation & Methodology Results Concluding remarks
Concluding Remarks
Present results agree with experiments (Ha/Re > 0.025)when predicting the decayment of the turbulence producedby the magnetic field.
Introduction Case & Background Formulation & Methodology Results Concluding remarks
Concluding Remarks
Present results agree with experiments (Ha/Re > 0.025)when predicting the decayment of the turbulence producedby the magnetic field.
Turbulence is suppressed in a non-homegenous way,Conductivity and Ha layers are the major actors...
Introduction Case & Background Formulation & Methodology Results Concluding remarks
Concluding Remarks
Present results agree with experiments (Ha/Re > 0.025)when predicting the decayment of the turbulence producedby the magnetic field.
Turbulence is suppressed in a non-homegenous way,Conductivity and Ha layers are the major actors...Important over-speed areas are generated by themoderate and strong increasing magnetic fields.Conductivity reduces the intensity of the jets and maskinertial terms role. Three-dimensional effects are quicklydissipated
Introduction Case & Background Formulation & Methodology Results Concluding remarks
Concluding Remarks
Present results agree with experiments (Ha/Re > 0.025)when predicting the decayment of the turbulence producedby the magnetic field.
Turbulence is suppressed in a non-homegenous way,Conductivity and Ha layers are the major actors...Important over-speed areas are generated by themoderate and strong increasing magnetic fields.Conductivity reduces the intensity of the jets and maskinertial terms role. Three-dimensional effects are quicklydissipated
Pulsating phenomena are generated close to theedge-pole face of the magnet for the insulating case.Turbulence is completely suppressed forN >≈ 25, Ha >≈ 300. Additional moderate mag. fieldsshould be analyzed...