Inside cell dimensions

D = 5m, L = 10m,

Max volume ~ 25,000

gallons of liquid helium

equivalent

Outside dimensions

~7 m dia and ~20 m high

Refrigeration needed

< 200 W

Huge accelerator facilities

like CERN or BNL would

have plenty of liquid

helium on hand, used to

cool superconducting

magnets.

A proposed 10m high convection cell capable of Ra~1021 nearly

comparable to that characteristic of solar convection.

RHIC, BNL

Multiple use facility

―Over a two month period we tested more than two

hundred models of different types of wings. All of the

models were three to nine inches long. We finally

stopped our wind tunnel experiments just before

Christmas, 1901. We really concluded them rather

reluctantly because we had a bicycle business to

run and a lot of work to do for that as well.‖

---Wilber Wright

―We directed the air current from an old fan in the

back shop room into the opening of the wooden

box. Occasionally I had to yell at my brother to keep

him from moving even just a little in the room

because it would disturb the air flow and destroy the

accuracy of the test.‖

The Wright Brothers: 1st successful application of wind tunnel data

Testing applications

An historical digression

The main ―driving‖ force behind innovations in testing is for

applications where you hope that ―lift‖ never gets you off

the ground…

―On each little aircraft wing design we tested we located the center

of pressure and made measurements for lift…‖ Wilber Wright

At Old Dominion University

resides the largest University-

operated wind tunnel in the world.

―Customers include NASA, the

Navy, racecar teams (principally

NASCAR)…‖

Cryogenic testing facilities

In aerodynamic testing, one measures lift, drag and moments on a

model and infers the corresponding values on the prototype. Since Re can

often be very large in practical situations (of the order 108 or 109 for

commercial aircraft or modern submarines), it is difficult to match the

prototype Reynolds number if the same fluid is used for model testing.

Helium has an advantage over highly compressed air because the dynamic

pressure (1/2)ρU2 is substantially smaller for a given Reynolds number, and

hence the helium flow can be expected to exert significantly less force on the

models.

Another possibility with helium is the use of powerful superconducting

magnetic balance and suspension systems both to orient models without

the external arm or ―stinger‖, and to measure forces on them.

The National Transonic Facility (NTF) at the NASA Langley Research Center,

operating since 1984. Cryogenic liquid nitrogen is sprayed and evaporated into a

gas that is accelerated through the tunnel's test section up to a Mach number of

1.2. The 150-m long tunnel is powered by a 100 MW turbine motor. The figure on

the right shows the giant vanes that help air flow around a corner.

Re UL

A cryogenic tunnel

The physically largest wind tunnel in the world at NASA Ames. This subsonic tunnel can test

planes with wing spans of up to 100 feet. It is about 430 m long and 55 m high. Air is driven

through these test sections by six 15-bladed fans. Each fan has a diameter equal to the height

of a four-story building. The total power 100 MW.

Room temperature….

but large!

Helium wind tunnel

A 30 cm helium tunnel could be considered ―table-top‖ compared to the large wind

tunnels of NASA. A 125 cm model would reach comparable Re to any of them.

NASA AMES

Liquid helium tunnel

Testing applications :

If quantitative changes in measured data are ―slow‖, then it is reasonable to

obtain data at, say, Re=107 and extrapolate it to Re = 109.

However, the total flow field, including acoustics, is important. The

complexity of the flow fields and multiplicity of interactions among various

elements in naval and aeronautical testing makes extrapolations to higher

Reynolds number difficult.

Wing-tip vortices are an example: wind-tunnel tests give poor indication of

actual interactions (extrapolation of 2 orders of magnitude in Re).

wingtip vortices

Wingtip vortices reduce some of a

plane’s lift. They create dangerous

conditions during takeoff and landings,

both for the aircraft and perhaps

especially those that follow.

Geese have a very

practical knowledge of

wingtip vortices of the

goose in front of them.

A Boeing 747 flying into Hong Kong. Vortices shed from the wing can be seen

in smoke from a factory below.

fix: high

aspect ratio

wings and

winglets

Helium can be used very effectively for testing surface ships due to the ability to match

both Reynolds and Froude numbers simultaneously in reasonable tow tank circuits. This

results from the large ratio between the kinematic viscosities of helium and water.

Considering a ship 200 m long and moving at 32 knots, we can match both the Reynolds

and Froude numbers by using a 25:1 scale model towed at 3.3 m/s. In this case the ratio

of kinematic viscosities of air and helium is 121, while the ratio of velocity times length for

the ship and the model is 125.

1/2U/(gL)Fr

UL/νRe

Froude number: characterizes resistance

by wave generation

L/σρUWe 2

Weber number: characterizes surface

tension effects at the free surface

Advantage of helium II: high effective thermal conductivity increases temperature

homogeneity and reduces cavitation

Tow Tanks

Brass Ring19 mm diameter0.5 mm by 1 mm

Stainless wires0.23 mm diameterEpoxied to ring

0.2 mm

10 m quartz fiber

A start…

Bushnell’s Original Submarine

Remote-controlled ¼

scale models operated

in Lake Pond Oreille,

Idaho.

High Re-low Mach number: Submarines

Left: Leonardo Da Vinci’s systematic

studies of the vorticity resulting from

flow in channels and in the wake

behind obstacles.

The systematic study of fluid motions

Flow visualization has provided useful insights for centuries in classical

fluids—can we improve the situation in quantum fluids

Given these limited tools, it is remarkable that as much progress has

been made in quantum turbulence as is the case.

Turbulence in superfluid component takes form of tangled configurations

of quantized vortex lines. Much of our knowledge has come from

techniques for measuring the average density of these lines with poor

spatial resolution . As we saw the classical analog would be to measure

the mean square vorticity, also with poor spatial resolution.

As in classical turbulence there is likely to be a wide range of scales.

The smallest scale can be very small. Eg: for turbulence in 4He above 1K in

which the energy-containing eddies have size 1 cm and characteristic velocity 1

cm s-1, the smallest scale is of order 10 microns; the time scale ranges from 1 s

to a few milliseconds. Below 1K the need for a Kelvin wave cascade to dissipate

energy may take the smallest scale to 10 nm. Ideally our techniques ought to

cover these ranges.

Velocity correlation functions, which play an important role in classical turbulence

as we saw for finding deviations from Kolmogorov scaling (higher-order

moments).

Quantum turbulence

There is much interest in quantum turbulence in 4He at temperatures where the

density of normal fluid is negligible. The search for appropriate experimental

techniques for this temperature range poses major problems. The second sound does

not propagate at low temps so it has to be replaced with other techniques which can

be calibrated with the same level of success.

Ion trapping can in principle measure line densities, but there are still some gaps in

our knowledge of the capture cross-sections (which may be very small). A. Golov

(Manchester) has been leading the development in this area.

Laser Induced Fluorescence (LIF) can be adapted to LT helium use and may prove

more powerful than the use of ions.

Miniature pressure sensors may be useful if they have adequate sensitivity for the

study of decaying turbulence. G. Ihas, UF has been leading this effort.

Existing studies here have tended to rely on rather simple measurements

(e.g., vortex line densities), combined with extensive computer simulations

to see whether models can be developed to account for these rather coarse

observations. More detailed experimental evidence would be valuable, and

this must come from techniques that allow observation of (weak) turbulent

regimes that are neither homogeneous nor in a steady state.

The second sound measurements that were described in lecture 5 were

averaged over a large sample volume. To look at fluctuations in line density we

will need second sound transducers with better spatial resolution, while retaining

reasonable sensitivity.

QuickTime™ et undécompresseur TIFF (LZW)

sont requis pour visionner cette image.

Effective surface=

1mm*1mm

Thermometer (Al)

(transition edge ~ 1.5K)Heater (Cr)

Side view :

thermometer and heater

facing each others

Tip thickness

= 15 m

From Roche, et al.

Some later improvements in the hot wire sensor

We discussed in lecture 5 an experiment by Maurer and Tabeling in von Karman

swirling flow in helium II in which the pressure transducer probed only scales much

larger than the dissipation length (or the intervortex line spacing) Can pressure

sensors having a better spatial resolution and temporal response be developed?

Piezo Resistive Transducers made to work at Low T

Doped Germanium

With Vadim Mitin

**UF**

Pressure Transducer Requirements

sampling on micron scale

sensitivity: 0.1 Pascal

fast: 1 msec

function at low temperatures (20 – 100 mK)

transduction: as simple as possible

MEMS Technology Pressure Sensors

Piezo-resistive

Capacitive

Optical

Detecting Turbulence in Helium near T=0: Thermometry

Gary G. Ihas (University of Florida), DMR-Award # 0602778

One goal of hydrodynamic research is to

study very large phenomena, such as

hurricanes and sun spots, in the laboratory

by constructing a system which scales from

millions of meters in size to one meter in the

lab, retaining the same type of flows, such as

turbulence. Liquid and cryogenic (very cold)

gaseous helium enable this scaling because

their viscosities, a key parameter governing

turbulence, may be varied from that similar to

air to essentially zero. But measurements at

these temperatures require the development

of new sensors that function in this cold

environment. We have developed extremely

small electrical resistance thermometers

which have a fast reaction time (less than

1/10 sec.) and adjustable sensitivity for use

from 10 mK to 5 K. They measure both

ambient temperature and temperature

fluctuations prevalent in turbulent flow.

Cross section of thermometer-made using computer

chip technology. Ge (Germanium) layer is active

element, deposited on GaAs substrate. Heat

treatment cause various amounts of Ga and As to

become dopants in Ge, producing adjustable

sensitivity-see graph below chip.

Shadowgraphy (from P. Lucas, U. Manchester)

Rc = gd3 T Tc/ DT

The combination is the relevant factor: although n0 is very

close to 1 for helium, the expansion coefficient is relatively

large. This fact was first noticed by Sullivan, Steinberg and Ecke

(1993).

)1( 0nT

T

Examples of shadowgraph in helium convection (Lucas group, Manchester)

Electron bombardment can produce

He2 excimer molecules, mostly in the

states He2(A1 u+) and He2(a3 u+).

Molecules decay by emission

of 80 nm photons with lifetimes

1ns and 13 s for singlet and

triplet states

Laser-Induced Fluorescence (LIF)

A molecular counterpart to PIV

Cryogenic PIV experiment (grid flow)

Particle pairs

Velocity vectors

C.M. White, Ph.D. thesis, Yale University

Summary of apparatus size and mesh Reynolds numbers, RM, in a few grid

turbulence experiments

Source test section max RM

Kistler & Vrebalovich (1966) 2.6 m 3.5 m 2.3 million

(air at 4 atmospheres)

Comte-Bellot & Corrsin (1971) 1 m 1.3 m 34,000

(atmospheric air)

Towed grid (He I) 5 cm 5 cm 0.8 million

----------------------------------------------------------------------------------------------

Towed grid (He II) 1 cm 1 cm 0.5 million

Creating Turbulence in a Dissipationless Fluid

Gary G. Ihas (University of Florida) DMR-Award # 0602778

If we pull a wire mesh through a fluid with

zero viscosity, we might think that there

will be no drag force and that the fluid will

smoothly flow around the wires of the

mesh, creating no turbulence. Yet,

turbulence of sorts has been observed in

liquid helium near absolute zero, which

has vanishingly small viscosity. Once this

turbulence is created, it seems that there

is no mechanism except through viscosity

for it to decay. Yet again, it does decay.

Until now, no one had succeeded in

producing isotropic homogeneous

turbulence, as is often studied in classical

fluids, in a dissapationless fluid. We have

designed, built, and operated the

superconducting pulsed actuator (shown

schematically at right), which, when

mounted on a dilution refrigerator, allows

exactly such studies to be achieved.

Schematic of Cell

1. Pb plated Cu cell

2. Phenolic armature

3. Superconducting

solenoid

4. Superconducting

Nb can (2)

5. Capacitive

position sensor

6. Mesh grid

7. 300 µm thermistors

8. Resistive heater

If we knew how to precisely interpret it….

Optical Pressure Sensors

Optical techniques typically employ a

microsensor structure that deforms under

pressure resulting in change in optical

signal.

Diaphragm-based sensors, for example,

incorporate optical waveguides on the top

surface.