NG43B-1492: Angular Momentum Transport in Turbulent ... · Taylor-Couette flow, see: Paoletti and...
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Daniel S. Zimmerman, S.A. Triana, and D.P. Lathrop University of Maryland Physics, Geology, IREAP NG43B-1492: Angular Momentum Transport in Turbulent Spherical Couette Flow 0.8 1.2 1.6 2 2.4 H L LL B Q E 10 0 10 1 10 2 0.8 1 1.2 1.4 1.6 1.8 Ro R Ro R Ro R Ro 10 0 10 1 10 2 Ro Long term mean Conditioned on state Three Meter Experiment & Parameters = r o − r i η = r i r o = 0.35 Ω o 3m Velocity, Pressure, Wall Shear Torque Dye Visualization ~1m r i r o Torque with Outer Stationary The experiment is an approximately 2.92m diameter spherical tank of water mounted on bearings with an independently rotating 1.02m diameter inner sphere. Maximum possible rotation rates are 4Hz for the outer sphere and about 12Hz for the inner sphere, driven by a pair of 250kW electric motors with variable frequency drives. The torques on the boundaries provide a global measurement of angular momentum flux Four ports in the lid allow measurements of pressure and wall shear stress 60cm distant from the axis and ultrasound velocimetry is possible 10-30cm from these ports. Turbulent Multiple Stability As the Rossby number Ro is varied, we observe many different turbulent flow states that are characterized by different torque demand and mean velocity profiles, and different large scale (m=1 and m=2 for Ro>2) coherent wave motions. In certain ranges of Ro the flow undergoes spontaneous transitions between adjacent states, leading to the bimodal distributions of torque and azimuthal velocity velocity shown on the right. One transition is analyzed in detail here: arxiv.org/abs/1107.5082 Phys. Fluids 23, 065104 (2011) H L LL 1.0 2.0 4.0 3.0 6 - 4 - 2 - 0 log(S(ω)) ω Ω o Ro 2 0 10 −13 10 −12 10 −11 10 −10 G Pr(G) 6 8 10 12 10 10 x 10 10 x 10 10 x 10 10 x H L −0.1 0 0.1 0.2 0.3 0.4 10 −2 10 0 L H u φ Ω o r o Pressure power spectral density vs. Ro, E = 1.6e-7 showing changes in large scale wave motions. Bimodal probability distributions of azimuthal velocity (top) and torque (bottom) Ro = 2.13, E = 2.1e-7 E = ν Ω o 2 9 ×10 −8 5 × 10 −6 < E < Ekman Number Ro = Ω i − Ω o Ω o -5 100 < Ro < Rossby Number Re = Ro E = (Ω i − Ω o ) 2 ν 2.5 ×10 5 5 × 10 7 < Re < Reynolds Number Ω i 10 6 10 7 10 8 10 9 10 10 10 11 10 12 10 13 Data G = 0.003 Re 1.89 Re = Ω i ν 2 ∞ ν ρ 2 r i G= T u φ Ω o r o Pr( ) 0 0.1 0.2 0 1000 2000 u φ Ω o r o 5 . 2 × 0 1 0 1 0 . 2 × 0 1 0 1 5 . 1 × 0 1 0 1 Ω o t 2π Time series of azimuthal velocity near port (top) and inner sphere torque (bottom) Ro = 2.33 E = 5e-7. ν ρ 2 r i G= Torque H L L L L H H YouTube Spin Test The torque with the outer sphere stationary depends on Reynolds number in a way that is typical of turbulent drag, torque nearly proportional to the square of Reynolds number. We use the fit to this data to normalize the torque when the outer sphere revolves as well. Shear Stress Concentration - Transport Inhomogeneity Ro ∞ G G 1 . 3 × 0 1 -7 6 . 2 × 0 1 -7 2 . 2 × 0 1 -7 8 . 1 × 0 1 -7 6 . 1 × 0 1 -7 3 . 1 × 0 1 -7 Ekman 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0.8 1 1.2 1.4 1.6 1.8 2 Err. H L LL -0.1 Ro + 1.8 0.03 Ro + 0.9 -0.05 Ro + 1.1 Normalizing measured torque by the torque predicted same Reynolds number without rotation nearly collapses the torque data for all measured parameters. Here the torque has been conditioned on flow state in those ranges of Ro where the torque is bimodal. The large scatter at low Rossby number is likely due to shaft seal drag dominating the torque. The implication of the collapse presented here is that the angular momentum transport factorizes, with a Rossby dependent prefactor unique to the geometry and a typical turbulent scaling with Re. The same behavior with a different Rossby dependence has been observed in Taylor-Couette flow, see: Paoletti and Lathrop, Phys. Rev. Lett. , 106 024501a (2011) and van Gils et al., Phys. Rev. Lett. 106, 024502 (2011). Torque with Overall Rotation G = f(Ro) g(Re) Angular Momentum Transport Barrier? Wall shear & Velocity Measurement Location Fast zonal transport barrier with waves? High Torque Low Torque Dye Movie QR Links Ro = 2.33 The data for the H/L state transition are consistent with the formation of an angular momentum transport barrier near the inner sphere. Fast fluid trapped at, above, and below the inner sphere lowers the drag. The further transitions may be related to intensification of the transport barrier. Dye visualization along with the torque and measurements far above the inner sphere corroborates faster flow at all vertical distances above the inner sphere in the L state, strongly reduced in the H state, but global velocimetry is needed to measure angular velocity profiles. complex.umd.edu We make measurements of the wall shear stress 60cm from the axis using a homemade constant temperature anemometry system with low cost RTD sensors. Using the wall shear stress in-situ calibration, we normalize the wall shear stress by that expected at the same Reynolds number with the outer sphere stationary. The normalized wall shear stress peaks at the same Ro where the normalized torque is minimized. ∞ τ τ ∞ G G − + In Out Gnd RTD, Omega F-2020 +24V Regulator FZT491A 1/2 AD8662 3x 0.1 µF 10 µF 10 µF PWR − + 100k Ω 100k Ω 330 Ω +15V 1/2 AD8662 Zero-Flow Offset 3x 0.1 µF OVH BNC Out PWR 8 4 +15V +15V One Per Channel 2 R 1 R R3 ∞ τ τ Measurement Locations ∞ G G 0.9 1 1.1 0 1000 2000 3000 4000 0.9 1 1.1 1.2 τ 〈 τ 〉 G 〈 G 〉 Ro=3.2 0.95 1 1.05 1.1 300 400 500 600 700 800 900 1000 0.8 0.9 1 1.1 τ 〈 τ 〉 G 〈 G 〉 Ω o 2 π Ro=6.3 The same anti-correlation between the long term mean wall shear stress on the outer sphere and the torque on the inner sphere is observed in shorter term fluctuations in those quantities at transition Rossby numbers, two of which are shown here. Torque (top) and wall shear stress (bottom) are normalized by their mean values. In all cases, the lower torque is concurrent with higher shear stress, implying a different pattern of wall shear stress on the outer sphere as Ro is varied. At about Ro = 7, there seems to be a peak in “upward” transport of angular momentum but an overall reduction in transport. Future Work - Hydromagnetic Experiments The hydrodynamic phase of this experiment using water has finished as we work to prepare for experiments with liquid sodium metal. As of this meeting the experiment is 73% full of sodium and we await shipment of the remaining material. Above left are the original drums that we have used, in the center is a thermal image of the sphere 66% full of warm sodium, and on the right is a drum with heaters and insulating mantle. We will recieve the remaining sodium this month and hope that the three meter experiment will soon show self-excited dynamo action in a laboratory experiment geometrically similar to Earth’s core. YouTube Sodium Fill Time Lapse t Ω o 2 π t Omega F-2020 RTD Array Low Cost CTA Schematic More information: Ph.D. Thesis complex.umd.edu/papers /zimmerman_thesis.pdf Taylor-Couette: Paoletti and Lathrop (2011) arxiv.org/abs/1011.3475 1 1) email: [email protected]
Transcript of NG43B-1492: Angular Momentum Transport in Turbulent ... · Taylor-Couette flow, see: Paoletti and...
Daniel S. Zimmerman, S.A. Triana, and D.P. Lathrop University of Maryland Physics, Geology, IREAP
NG43B-1492: Angular Momentum Transport in Turbulent Spherical Couette Flow
0.8
1.2
1.6
2
2.4
H
L
LLB
QE
100 101 1020.8
1
1.2
1.4
1.6
1.8
RoR
RoRRoR
Ro100 101 102
Ro
Long term meanConditioned on state
Three Meter Experiment & Parameters
= ro− ri
η =riro
= 0.35
Ωo
3m
Velocity,Pressure,Wall Shear
TorqueDye Visualization
~1m
ri
r o
Torque with Outer Stationary
The experiment is an approximately 2.92m diameter spherical tank of water mounted on bearings with an independently rotating 1.02m diameter inner sphere. Maximum possible rotation rates are 4Hz for the outer sphere and about 12Hz for the inner sphere, driven by a pair of 250kW electric motors with variable frequency drives. The torques on the boundariesprovide a global measurement of angular momentum flux Four ports in the lid allow measurements of pressure and wall shear stress 60cm distant from the axis and ultrasoundvelocimetry is possible 10-30cm from these ports.
Turbulent Multiple Stability
As the Rossby number Ro is varied, we observe many different turbulent flow states that arecharacterized by different torque demand and mean velocity profiles, and different large scale(m=1 and m=2 for Ro>2) coherent wave motions. In certain ranges of Ro the flow undergoes spontaneous transitions between adjacent states, leading to the bimodal distributions of torqueand azimuthal velocity velocity shown on the right. One transition is analyzed in detail here:
arxiv.org/abs/1107.5082Phys. Fluids 23, 065104 (2011)
H
L
LL
1.0 2.0 4.03.0
6-4-2-0 log(S(ω))
ωΩo
Ro
2
0
10−13
10−12
10−11
10−10
G
Pr(G)
6 8 10 121010x1010x 1010x 1010x
H
L
−0.1 0 0.1 0.2 0.3 0.4
10−2
100
LH
uφ
Ωoro
Pressure power spectral density vs. Ro, E = 1.6e-7 showing changes inlarge scale wave motions.
Bimodal probability distributionsof azimuthal velocity (top) and torque (bottom) Ro = 2.13, E = 2.1e-7
E =ν
Ωo2
9×10−8 5×10−6 < E <
Ekman Number
Ro =Ωi − Ωo
Ωo
-5 100 < Ro <
Rossby Number
Re =Ro
E=
(Ωi − Ωo)2
ν
2.5×105 5×107 < Re <
Reynolds Number
Ωi
106 107 108109
1010
1011
1012
1013
Data
G = 0.003 Re1.89
Re = Ω iν
2
∞
νρ 2 riG= T
uφ
ΩoroPr( )
0
0.1
0.2
0 1000 2000
uφ
Ωoro
5.2 × 01 01
0.2 × 01 01
5.1 × 01 01
Ωot2π
Time series of azimuthal velocity near port (top) and inner sphere torque (bottom) Ro = 2.33 E = 5e-7.
νρ 2 riG= Torque
HL L L LH H
YouTubeSpin Test
The torque with the outer sphere stationary depends on Reynolds number in a way that is typical of turbulent drag, torque nearly proportional to the square of Reynolds number. We use the fit to this data to normalize the torque when the outer sphere revolves as well.
Shear Stress Concentration - Transport Inhomogeneity
Ro
∞GG
1.3 × 01 -7
6.2 × 01 -7
2.2 × 01 -7
8.1 × 01 -7
6.1 × 01 -7
3.1 × 01 -7
Ekman
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
0.8
1
1.2
1.4
1.6
1.8
2
Err.
H
L
LL
-0.1 Ro + 1.8
0.03 Ro + 0.9
-0.05 Ro + 1.1
Normalizing measured torque by the torque predicted same Reynolds number withoutrotation nearly collapses the torque data for all measured parameters. Here the torque has been conditioned on flow state in those ranges of Ro where the torque is bimodal. The largescatter at low Rossby number is likely due to shaft seal drag dominating the torque. The implication of the collapse presented here is that the angular momentum transport factorizes, with a Rossby dependent prefactor unique to the geometry and a typical turbulent scaling withRe. The same behavior with a different Rossby dependence has been observed in Taylor-Couette flow, see: Paoletti and Lathrop, Phys. Rev. Lett. , 106 024501a (2011) andvan Gils et al., Phys. Rev. Lett. 106, 024502 (2011).
Torque with Overall Rotation
G = f(Ro) g(Re)
Angular Momentum Transport Barrier? Wall shear & VelocityMeasurement Location
Fast zonal transportbarrier with waves? High Torque Low Torque
Dye Movie QR Links Ro = 2.33
The data for the H/L state transition are consistent with the formation of an angular momentumtransport barrier near the inner sphere. Fast fluid trapped at, above, and below the inner spherelowers the drag. The further transitions may be related to intensification of the transport barrier.Dye visualization along with the torque and measurements far above the inner sphere corroborates faster flow at all vertical distances above the inner sphere in the L state, stronglyreduced in the H state, but global velocimetry is needed to measure angular velocity profiles.
complex.umd.edu
We make measurements of the wall shear stress 60cm from the axis using a homemadeconstant temperature anemometry system with low cost RTD sensors. Using the wall shear stress in-situ calibration, we normalize the wall shear stress by that expected at the sameReynolds number with the outer sphere stationary. The normalized wall shear stress peaks at the same Ro where the normalized torque is minimized.
∞
ττ
∞GG
−
+
In OutGnd
RTD, Omega F-2020
+24V Regulator
FZT491A
1/2 AD8662
3x 0.1 µF10µF10µF
PWR
−
+
100k Ω100k Ω
330 Ω
+15V
1/2 AD8662
Zero-Flow Offset
3x 0.1 µFOVH
BNC Out
PWR
8
4
+15V
+15V One Per Channel
2R1R
R3
∞
ττ
Measurement Locations
∞GG
0.9
1
1.1
0 1000 2000 3000 4000
0.9
1
1.1
1.2τ
⟨τ ⟩
G⟨G ⟩
Ro=3.20.95
1
1.05
1.1
300 400 500 600 700 800 900 10000.8
0.9
1
1.1
τ⟨τ ⟩
G⟨G ⟩
Ωo2π
Ro=6.3
The same anti-correlation between the long term mean wall shear stress on the outer sphere and the torque on the inner sphere is observed in shorter term fluctuations in those quantities at transition Rossby numbers, two of which are shown here. Torque (top) and wall shear stress(bottom) are normalized by their mean values. In all cases, the lower torque is concurrent with higher shear stress, implying a different pattern of wall shear stress on the outer sphere as Ro is varied. At about Ro = 7, there seems to be a peak in “upward” transport of angular momentum but an overall reduction in transport.
Future Work - Hydromagnetic Experiments
The hydrodynamic phase of this experiment using water has finished as we work to prepare for experiments with liquid sodium metal. As of this meeting the experiment is 73% full of sodium and we await shipment of the remaining material. Above left are the original drums that we have used, in the center is a thermal image of the sphere 66% full of warm sodium, and on the right is a drum with heaters and insulating mantle. We will recieve theremaining sodium this month and hope that the three meter experiment will soon show self-excited dynamo action in a laboratory experiment geometrically similar to Earth’s core.
YouTube Sodium Fill Time Lapse
tΩo2π
t
Omega F-2020RTD Array
Low Cost CTA Schematic
More information:Ph.D. Thesis
complex.umd.edu/papers/zimmerman_thesis.pdf
Taylor-Couette:Paoletti and Lathrop (2011)
arxiv.org/abs/1011.3475
11) email: [email protected]
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