# Cryogenic Pipe Calculations

Urban and Civil

Nov 15, 2013 (4 years and 8 months ago)

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Cryogenic Pipe Calculations

VB

Jan 2008

idea

Use superconducting pipe for atomic
beam experiments

cryopumping for better vacuum

exclusion of magnetic fields inside pipe

cost & complications

cryopump vibrations

basic concept

use simple pipe with superinsulation (MLI) & two cryocoolers

no liquids in the system (except in the cryocoolers themselves)

use two cryocoolers (~ 1W cooling @ 4 K)

use lead pipe (used for calculations)

device is NOT a magnet

Type I superconductor

high critical temp ( ~ 7 K)

Niobium has even higher critical temp (~9 K)

Can probably use Type
-
II superconductors below lower critical temp

cryocoolers

insulation

pipe

performance calculations

use MATLAB to simulate pipe performance

heat capacity as a function of temperature

cryocooling as a function of temperature

heat conductivity constant

insulation on pipe + heat leak at pipe ends

pipe divided into longitudinal segments

program calculates new temp profile every fraction of a second

for each segment

heat gain through insulation

arbitrary heat gain in a any segment (used for ends)

cryocooling heat loss (if present for the segment)

cryopumps turn on at an upper temp and off at a lower temp (for any
segment)

temp cannot go below 4 K (cryopump limit)

Superinsulation

http://www.cryogenicsociety.org/cryo_central/cryogenic_insulation/

An insulation material's performance under a large temperature difference is given in terms
of milliwatt per meter
-
kelvin (mW/m
-
K) and is referred to as the apparent thermal conductivity
or k
-
value.

To compare k
-
values for different materials one must understand the warm and
cold boundary temperatures, the vacuum level, the residual gas composition, and the
installed thickness.

The designer has a very wide range of k
-
values with which to work: as
low as
0.03 mW/m
-
K

for perforated MLI blankets up to approximately 40 mW/m
-
K for cellular
glass.

As in all good designs, the performance must justify the cost.

The performance of the
total thermal insulation system as it is actually put to use is defined as the overall k
-
value for
actual field installation or koafi.

Several test methods are usually needed to adequately test and evaluate the overall
performance of an insulation system.

Standardized material test methods can be employed
for basic thermal, mechanical, and compatibility properties.

Cryostat test methods provide
the apparent thermal conductivity values for the insulation systems.

Prototype testing is then
needed to determine the actual performance for a specific mechanical system.

The use of
MLI systems illustrates the need for this three step testing process.

The k
-
value for an MLI
system under ideal laboratory conditions may be around
0.05 mW/m
-
K

while the koafi can
easily be
10 times worse
.

Cryocooler Performance

SHI Cryogenics Group, a global manufacturer that includes the Cryogenics Division of
Sumitomo Heavy Industries, Ltd.

and the former APD Cryogenics, delivers innovative
solutions to the semiconductor, research, optical coating, and medical industries.

Curve used in calculations

(1.0 watts @ 4 K)

Heat Capacity

Handbook of Chemistry & Physics

page 2357 for low temp behavior for lead

Heat Conductivity

Handbook of Chemistry & Physics

page 2528 for lead, relatively flat, ~ 0.1 cal per sec per cm**2 for 1 cm thickness

http://prola.aps.org/pdf/PR/v80/i5/p859_1

evidence of superconducting behavior of heat capacity (factor of 2.5
enhancement of the heat conduction in the 4
-
15 K temprange)

Used a constant
value in calculations

(0.5 or 1.0)

MATLAB simulations parameters (data1)

rateloss=0.00003

% insulation heat loss W/meter/K

ncool=1.0

% de
-
rating factor for the 1.0 watt cryocooler

initT = 10

% starting temperature for the pipe

roomT = 300

% temperature of the laboratory

lowT = 5

% turn
-
off temp of cryocooler

highT = 5.75

% turn
-
back
-
on temp of cryocooler

Tmin=4.0

% min cryocooler temp

maxIn = 30000

% number of seconds to run simulation

pthick = 1.0

% pipe thickness in cm

plength = 1000

% pipe length in meters

pdensity = 13

% density of pipe g/cc

nsegs = 100

% number of pipe segments in length

cooling(8)=0.5 ; cooling(72)=0.5;

% cryocooler power in segments

heatleak(1)=0.1; heatleak(100)=0.0;

% heat leak in segments

secsegs = 2 ;

% number of time segments in a second

hcond=1.0 ;

% heat conductivity

Results

data1

temp contours

Results

data1

temp vs. time

Times on are 439 310 303 301 300 300 300 300 300 300

Times off are 2065 1769 1772 1771 1770 1770 1770 1770 1770

Uptime=85%

Cooldown from 300 K

100 hour timescale

Would be nice to get
faster cooling

Pre
-
cooling

Better distribution

MATLAB simulations parameters (data2)

rateloss=0.0001

% insulation heat loss W/meter/K

ncool=0.67

% de
-
rating factor for the 1.0 watt cryocooler

initT = 10

% starting temperature for the pipe

roomT = 300

% temperature of the laboratory

lowT = 5

% turn
-
off temp of cryocooler

highT = 5.75

% turn
-
back
-
on temp of cryocooler

Tmin=4.0

% min cryocooler temp

maxIn = 30000

% number of seconds to run simulation

pthick = 1.0

% pipe thickness in cm

plength = 1000

% pipe length in meters

pdensity = 13

% density of pipe g/cc

nsegs = 100

% number of pipe segments in length

cooling(8)=0.5 ; cooling(72)=0.5;

% cryocooler power in segments

heatleak(1)=0.1; heatleak(100)=0.0;

% heat leak in segments

secsegs = 2 ;

% number of time segments in a second

hcond=1.0 ;

% heat conductivity

Results

data2

Times on are 714 608 606 602 602 601 602 601 602 601

Times off are 1203 1084 1085 1084 1084 1084 1084 1084 1084

Uptime=64%

Results

data2

secsegs=10

Times on are 713 608 606 603 603 603 603 603 603 603

Times off are 1203 1084 1085 1085 1085 1085 1085 1085 1085

uptime=64%

MATLAB simulation parameters (data4)

rateloss=0.0001

% insulation heat loss W/meter/K

ncool=1.0

% de
-
rating factor for the 1.0 watt cryocooler

initT = 10

% starting temperature for the pipe

roomT = 300

% temperature of the laboratory

lowT = 5

% turn
-
off temp of cryocooler

highT = 5.75

% turn
-
back
-
on temp of cryocooler

Tmin=4.0

% min cryocooler temp

maxIn = 30000

% number of seconds to run simulation

pthick = 1.0

% pipe thickness in cm

plength = 1000

% pipe length in meters

pdensity = 13

% density of pipe g/cc

nsegs = 100

% number of pipe segments in length

cooling(8)=0.5 ; cooling(72)=0.5;

% cryocooler power in segments

heatleak(1)=0.2
; heatleak(100)=0.0;

% heat leak in segments

secsegs = 2 ;

% number of time segments in a second

hcond=1.0 ;

% heat conductivity

Results

data4

Times on are 275 268 265 265 264 265 264 264 264

Times off are 511 502 501 501 501 501 501 501 500

Uptime=65%

Cryocooler
-

Vibrations

Information from …

Vibration Reduction Methods:
Active Cancellation

[13]

Vibration reduction

PT cryocoolers

CC
sizes

Sumitomo
Heavy
Industries

~ 50 cm scale

Mounting & Other Issues

Need a system to support pipe vertically

Need to connect cryocoolers to pipe

Copper collars (Cu conductivity ~ 5
-
10 higher)

Can we use flexible metal hose between collars and
cryocoolers (reduce vibrations)

How many points on the pipe do we connect

What happens at the “warm” end that is connected to
rest of the apparatus

We have other options for metals (e.g. Nb)

CC Spec Sheet

Sumitomo
Heavy
Industry

Summary

Simple model of pipe shows promise

Timescales look reasonable

“brute force” vibration control (i.e. CC off)
works

Still have options to improve cooling and
vibrations

Next step

get professional help

Nuclear Instruments and Methods in Physics Research Section A: Accelerators,
Spectrometers, Detectors and Associated Equipment

Volume 538, Issues 1
-
3
, 11 February 2005, Pages 33
-
44

Reduction of field emission dark current for high
-
field gradient electron gun by using a molybdenum
cathode and titanium anode

Cathode flattop = 18 mm

Anode flattop = 2 mm

Enhancement effect of dark current by electron and ion

impact on electrodes.
(1)

Primary field emission,
(2)

Desorption

of ions and molecules by electron bombardment,
(3)

Ionization

by electron impact,
(4)

Back bombardment,
(5)

Emission of

secondary ions and electrons.

Nuclear Instruments and Methods in Physics Research Section A: Accelerators,
Spectrometers, Detectors and Associated Equipment

Volume 538, Issues 1
-
3
, 11 February 2005, Pages 33
-
44

Reduction of field emission dark current for high
-
field gradient electron gun by using a molybdenum
cathode and titanium anode

The free parameter
α

was
an average value of 0.4
±
0.02
for Ti and 1.0
±
0.04 for Mo. This
constancy of
α

over the entire
range of dark current indicates
that the gap separation
dependence is well
approximated by Eq.
(2)
.

E(I,10mm) = 124/(1+4) = 25 MV/m for Ti

E(I,10mm) = 170/(1+10) = 15.5 MV/m for Mo

Can we make a flat beam??

Nuclear Instruments and Methods in Physics Research Section A: Accelerators,
Spectrometers, Detectors and Associated Equipment

Volume 538, Issues 1
-
3
, 11 February 2005, Pages 33
-
44

Reduction of field emission dark current for high
-
field gradient electron gun by using a molybdenum
cathode and titanium anode

1 nA plots

Nuclear Instruments and Methods in Physics Research Section A: Accelerators,
Spectrometers, Detectors and Associated Equipment

Volume 538, Issues 1
-
3
, 11 February 2005, Pages 33
-
44

Reduction of field emission dark current for high
-
field gradient electron gun by using a molybdenum
cathode and titanium anode

Sacrificing some