Initial Hydrodynamic Results from the Princeton MRI Experiment

M.J. Burin1,3, H. Ji2,3, J. Goodman1,3, E. Schartman2, W. Liu2,3

1. Princeton University Department of Astrophysical Sciences2. Princeton Plasma Physics Laboratory3. Center for Magnetic Self-Organization (CMSO)

CMSO general meeting Oct. 5-7 2005

Outline

Motivation and background

Brief description of apparatus

Result I. obtaining a Keplerian-like* flow

Result II. on subcritical hydrodynamic shear instability

Progress report on Gallium use (towards MRI)

Motivation: The Cause of Turbulence in Astrophysical Accretion Disks: What Instability(s) are Relevant?

•If sufficiently ionized and magnetized MRI probably responsible, but perhaps not solely

•If not? (e.g. some protostellar disks). The presence and relevance of various hydrodynamic instabilities is uncertain; subcritical shear instabilities are possible, but simulations and experiments so far appear to disagree.

•Hope: that a laboratory experiment which can create suitable velocity/shear profiles with sufficient Re/Rm can simulate accretion disk type instabilities in a controlled and repeatable environment.

?Taylor-Couette Flow

Experimental Apparatus: Overview

Rotating vessel components are of cast acrylic except for inner cylinder.

Phenolic gear (1/6)connects to motor via belt

Teflon seal (1/5)

(Tie-rods are usedto reinforce the outer cylinder)

Inter-nested stainlesssteel shafts aligned by cam followers.Shafts are co-supported with roller/thrust collars

Roller/Thrust Bearing

Roller Bearing

Note: this is mechanically nontrivial

Inner cylinder: R1=7cm, 1 < 4000rpmOuter cylinder: R2=21cm, 2 < 500rpmChamber height: H=28cm; Aspect Ratio ~ 2; ‘wide-gap’

Unique: Independently-Driven Intermediate Rings as End-Caps

Fluids: water, Gallium alloy (soon)

When we operate at full speeds:Max Re ~ 107

Max Rem ~ 10-100

Experimental Apparatus: Detail of Rotating Vessel

Rotating Apparatus Design: Use of Intermediary Rings to Reduce Ekman Circulation

In most experiments the end caps rotate as a solid body with the outer cylinder. A resulting pressure imbalance drives a circulation, which efficiently (and undesirably) transports angular momentum radially.

data(from prototype)

ideal (pure radial flux)

It was found numerically that just a couple intermediary rings, rotating at intermediary speeds, can significantly reduce the Ekman effect.

(Kageyama et al. 2004)

Use of Intermediary Rings to Reduce Ekman Circulation: Initial Results

Use of differentially rotating end rings successfully reduces Ekman circulation, allowing the ideal profile to be approached, which in turn allows for Keplerian-like profiles to be realized.

w/ solid end-caps

w/ differentialend-caps

Low-Speed “PIV” Data: Re ~ 2 x 105

2D simulation: Re ~3600 by W. Liu

Results submitted to Experiments in Fluids, August 2005

Being able to establish a high-Re Keplerian-like shear flow, we ask: * what instabilities/fluctuations may now be observed? * what sort/amount of transport results from them? in the absence of magnetic, kinetic, and stratification effects.

This is a very reduced but fundamental question, with a sparse and debatable history… It needs to be addressed first.

Because:

* The question is relevant for (at least) cool unmagnetized disks

* The question is relevant to a laboratory study of MRI: E.g., Is the background state is already turbulent?

Subcritical Shear Instability: Background Comments

Subcritical Shear Instability: Recent Observations (?)

dr

drS

CentrifugallyUnstable-1 < R < 0

Kep

leri

an

R > 0 Cyclonic Case

Richard & Zhan 1999, Richard 2001

Also relevant:Rotation Number R

SR

2

w/ shear

“?”grey areas of subcritical instability

Ray

leig

h st

abili

ty b

ound

ary

?

?

Example point

R =

-4/3

Subcritical Shear Instability: what does the data mean?I.e., What makes for an instability signature (“x”)?

u~

The stability boundary data given (“x”s) do not appear to represent a sudden subcritical transitionto relatively high fluctuation levels

Unconvincing. Boundary flows (e.g. Ekman circulation) are suspect

Not exactly sudden

Not exactly increasing

U

u~

Re0

8 %

Subcritical Shear Instability: Simulations

• ‘Shearing-box’ simulations by Balbus, Hawley, and Stone/Winters (1996/1999) conclude hydrodynamic stability even for slightly centrifugally stable flows. (Re ~ 104) • New numerical work by Lesur & Longaretti (2005) give a similar claim.• New work also ongoing by J. Stone and collaborators …

Rg = Critical Refor transition

Lesur & Longaretti (2005)

Subcritical Shear Instability: An Experimental Test

Ray

leig

h st

abili

ty b

ound

ary

From Keplerian-likeconditions to a centrifugally-unstable regime … and back again(check for hysteresis).

Note: actual Re #’s used are about two orders of magnitude higher

Fluctuations start and return to near-quiescent levels (~1%)

•Initial evidence for subcritical stability

•No evidence for hysteresis

Re ~ 1e6R ~ -1.05

Initial Result: No Significant Fluctuation Power for high Re Keplerian-like Flow

V

data from midplane

V

v~

Conclusions

• Ekman circulation can be significantly reduced in a wide-gap rotating flow, allowing for Keplerian-like profiles to be obtained.

• There is no significant hydrodynamic turbulence in a Keplerian-like flow up to Re ~ 1e6. This is in accord with simulations and in tentative disagreement with the experimental data of Richard & Zahn. More thorough experiments are planned.

And then onto MHD and MRI …

Addendum: Plans for MRI study

• Replacement of vessel with stainless steel version to withstand large rotation pressures (~25 atm.)

• Creation of axial B field (~ 6000 G) via 6 electromagnets

• Diagnostics: pickup coils for magnetic fluctuations and motor torque (via load cells) for gross radial angular momentum transport. Possible use of ultrasound and acoustics to assess the interior flow state. An invasive fin featuring pressure and Hall probes may be used as well.

• Some initial Gallium data may be seen later this month at APS-DPP.

** Go on Lab Tour ** See Poster by E. Schartman **