Cryogenic Pipe Calculations

petnamelessUrban and Civil

Nov 15, 2013 (3 years and 11 months ago)

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Cryogenic Pipe Calculations

VB

Jan 2008

idea


Use superconducting pipe for atomic
beam experiments


advantages


cryopumping for better vacuum


exclusion of magnetic fields inside pipe


disadvantages


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


load map


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


conduction from adjacent segments


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.




http://www.shicryogenics.com/index.php?option=com_content&task=blogcategory&id=22&Itemid=169

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


pradius = 5.0



% pipe radius in cm


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


pradius = 5.0



% pipe radius in cm


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


pradius = 5.0



% pipe radius in cm


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


ES&H issues with lead?


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
adjusted in each case, but had
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
gradient can greatly
reduce the dark current

Surface preparation
and cleaning is
critically important