Low cost and high performance screen laminate regenerator matrix.pdf

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Low cost and high performance screen laminate regenerator matrix

Uri Bin-Nun *, Dan Manitakos

FLIR Systems, 16 Esquire Road, North Billerica, MA 01862, USA

Abstract

A laminate screen matrix regenerator with 47 elements has been designed, analyzed, fabricated and tested. The laminate was

fabricated from stainless steel screen sheets that were stacked on top of each other at certain angular orientation and then bonded at

high temperature and pressure environment utilizing a sintering process. This laminate is a porous structure media with highly

repeatable properties that can be controlled by varying mesh size, weave type, wire size and laminate sheet to sheet orientation. The

flow direction in relation to the weave plan can be varied by cutting a cylindrical or rectangular laminate element along or across theweave. The regenerator flow resistance, thermal conductance losses, dead volume, surface area and heat transfer coefficient are

analyzed. Regenerator cost and performance comparison data between the conventional widely used method of stacked screens and

the new stacked laminate matrix regenerator is discussed. Also, a square stainless steel screen laminate was manufactured in a way

which permits gas to flow along the screen wire instead of across it.

2004 Published by Elsevier Ltd.

Keywords: Convection (C); Heat transfer (C); Regenerators (E); Stirling (E); Thermal conductivity (C)

1. The common Stirling cycle regenerator

The common Stirling cycle regenerator is a one way

bidirectional heat exchanger in which thermal energy

flows in and out of the matrix and to or from the

working fluid. The heat exchanging media (matrix) is

usually made of light felt like mass of fine wire stacked

in a well insulated tube as shown in Fig. 1. The fine wire

mesh is commonly obtained in a form of woven screen

at variety of wire sizes, weave structures, mesh density

and materials. Other types of regenerator matrix are

also used such as spheres made of stainless steel, bronze,

lead and erbium to name a few. The common Stirling

cycle regenerator matrix usually has large thermal

capacity, large surface area, low flow impedance, small

void volume and large axial thermal resistance which areall essential to achieving high regenerator effectiveness.

Cooler performance is very sensitive to regenerator

effectiveness. A regenerator is considered 100% effective

when the temperature of the working fluid exiting the

regenerator is equal to the temperature of working fluid

entering it. If the temperature of the gas leaving the

regenerator at the compressor end is colder than the

entering gas it indicates that not enough thermal energy

was remove from the regenerator matrix. This causes the

regenerator to be warmer than it could have been and

thus reducing the pre-cooling of the incoming gas prior

to it entering the expansion space.

2. Screen laminate sintering process

Sintering is the fundamental processing step for all

porous metal products. This means bonding of powder

particles by diffusion process at high pressure and tem-

perature just below the melting point of the sintered

metal. After the sintering process is complete, no phys-

ical limits exist at the boundaries of the original particlesand they become fused at the contact points.

Similarly screen laminate is manufactured by a sin-

tering process in which the powder particles are replaced

with woven stainless steel screen sheets as the base

material. The screen sheets are placed on top of each

other at 45 (any other angle is possible) alternating

angle relative to wire weave direction. The stack of

screens is then placed in an environmental chamber at

high pressure and temperature just below the melting

point. The laminate is kept in this heated and com-

pressed state for a certain period of time until a bond is

* Corresponding author. Tel.: +1-978-901-8242; fax: +1-978-901-

8441.

E-mail address: [email protected] (U. Bin-Nun).

0011-2275/$ - see front matter 2004 Published by Elsevier Ltd.

doi:10.1016/j.cryogenics.2004.03.015

Cryogenics 44 (2004) 439444

www.elsevier.com/locate/cryogenics
http://mail%20to:%[email protected]/http://mail%20to:%[email protected]/http://mail%20to:%[email protected]/


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formed at the contact points between the screen wires.

The bonding is achieved by diffusion of material at the

point of contact resulting in a fused solid structure at the

contact boundaries of the screen wires. The screen

laminate is then laser cut, electro discharge machined(EDM), or die cut to form a cylindrical shape. The

cylindrical laminate elements are usually oriented so

that the flow is vertical to weave plan (Fig. 2).

In order to resolve cost and yield issue involving

regenerator manufacturing FLIR SystemsBoston

developed a new regenerator matrix element (Fig. 2) as

described in the following paragraph.

The laminate element can be cut from a thick lami-

nate screen stock, such that the flow axis is parallel or

normal to the weave plan (along the wire axis) as shown

in Fig. 3.

The final parts are solid, rigid and relatively thick

porous structures having more surface area and less

dead volume per unit length than a stack of individual

single screens. The laminate screen element thermal

conductance is much higher than an equivalent stack of

single screen disks causing a larger heat loss along

the regenerator axis. To remedy this problem, the lam-

inate thickness was reduced. This resulted in an increase

of the number of laminate screens and thus increas-

ing thermal contact resistances along the regenera-

tor axis thus reducing heat loss. The final product

thickness was optimized to achieve minimum number of

laminates (Fig. 2) while minimizing heat flow, maxi-

mizing surface area, reducing dead volume and maxi-

mizing rigidity.

3. Refrigeration losses due to regenerator effectiveness

The equation which determines refrigeration loss as a

function expansion ratio V4=V3, temperature ratioT2=T3, specific heat ratio, c Cp=Cv and regeneratoreffectiveness, e is shown below [1].

Nomenclature

e regenerator effectiveness, none

f friction factor, none

dk hydraulic diameter, ft (m)

h matrix convection coefficient, W/in.2 C, (W/

m2 K)oP=oX pressure drop per unit length, psi/in. (N/m3)As regenerator matrix surface area, in.

2 (m2)

c Cp=Cv specific heat ratio, noneq fluid local density, lb s2/ft4 (N s2/m4)

b porosity, none

l viscosity, lb s/ft2 (N s2/m2)

DQ refrigeration loss per cycle, BTU (J)

Re the flow Reynolds number, none

Pe Peclet number, none

Pr Prandtl number, none

Q ideal refrigeration per cycle, BTU (J)

Rpf regenerator performance factor, W/C psi/in.(W m3/N)

T2 temperature, R (K)

T3 temperature, R (K)

u fluid velocity, ft/s (m/s)

V3 volume, in.3 (m3)

V4 volume, in.3 (m3)

Fig. 2. Screen laminate element.

Fig. 1. Single screen mesh stacked regenerator made of 650 screen

disks.

Fig. 3. Laminate screen block.

440 U. Bin-Nun, D. Manitakos / Cryogenics 44 (2004) 439444


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DQ

Qideal

1 e

c 1

T2=T3 1

lnV4=V3

1

For example:

e 0:99 regenerator effectivenessc 1:67 specific heat ratio Cp=CvT2 540 R (300 K) rejection temperatureT3 140 R (77.7 K) cold end temperatureV4=V3 1:24 expansion ratioe regenerator effectiveness

T2 rejection temperature

T3 cold end temperature

V3 volume of expansion space at beginning of

expansion process

V4 volume of expansion space at end of expansion

process

A cryo-cooler with 1.24 expansion ratio operating

between 540 R (300 K) rejection temperature and140 R (77.7 K) cold end temperature, using Helium as a

working fluid will lose 20% of its refrigeration power if

the regenerator effectiveness is 99% instead of 100%.

This example emphasizes the critical role of the regen-

erator in Stirling cycle refrigerators performance and

efficiency.

4. Single screen disk regenerator matrix

The current regenerator design and assembly meth-

ods make it extremely difficult and costly to manufac-ture regenerators in production environment that meet

high effectiveness requirements consistently and in rea-

sonable yield. Regenerator effectiveness is depended on

and extremely sensitive to variations in surface area,

void volume (also known as dead volume), flow rate,

stacking pressure, mesh placement/orientation, screen

contamination and more. These variables are affected by

workmanship, process control and manufacturing tol-

erances. Also, it is extremely difficult to fabricate screen

elements of thin wire due to required die tolerances.

Most of these manufacturing problems (discussed

below) are due to the fact that the current regenerator

matrix element (Fig. 4) is very small, light and can beeasily bent or damaged during the fill process. The

regenerator tube fill process requires the technician to

handle 850 elements or more per tube, making the task

time consuming, difficult to control and inconsistent.

Stacking errors are practically unavoidable resulting in

low manufacturing yield and low performance.

Surface area of a filled regenerator is proportional to

the number of screen elements in the regenerator tube.

The number of screens in the tube can vary greatly due

to the wire diameter of the screen and the technicians

ability to maintain the required stacking pressure.

Void volume can vary greatly among regenerators due

to wire size tolerances, stacking pressure, screen element

size, screen disk flatness, regenerator tube internal

diameter manufacturing tolerances and the presence of

folded or bent screens.

Flow rate varies due to stacking pressure variations

caused by regenerator fill error, screen to screen weave

alignment and all the variables controlling surface areaand void volume mentioned previously.

Thermal contact resistance value depends on stacking

pressure, total number of screens in the tube, screen to

screen orientation and screen wire surface finish. Any

variation in the above stacking parameter will result in

refrigeration loses.

4.1. Analysisregenerator performance

In general the regenerator performance is directly

proportional to the matrix surface area and convection

coefficient and inversely proportional to pressure dropper unit length of the regenerator matrix. The relation-

ship between these three matrix design parameters is the

Regenerator Performance Factor and defined as follows:

Rpf Ash

op=ox2

where Rpf regenerator performance factor, W/(C psi/in.); As regenerator matrix surface area, in.

2; hmatrix convection coefficient, W/in.2 C; oP=oXpressure drop per matrix unit length, psi/in.

The matrix Rpf value is calculated at a given volu-

metric flow rate and it is the ratio between the energyflow per C, DT and the matrix local pressure gradient.

The goal is to maximize this value by increasing surface

area, convection coefficient and minimizing pressure

gradient.

As, regenerator matrix surface area calculations: sur-

face area of a given matrix is simply the total effective

area of the screen wires making direct contact with the

fluid. This value can be calculated or obtained from the

manufacturer. The area is dependent on wire size, weave

type, mesh density (wire weaved per in.) and total

number of screen elements in the matrix.

Fig. 4. Single screen elements.

U. Bin-Nun, D. Manitakos / Cryogenics 44 (2004) 439444 441


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oP=oX, pressure gradient calculations: the calculationof pressure drop in porous media is given by the fol-

lowing equation [2,3]:

op

ox

f

dh

qu2

23

where f friction factor; q fluid local density;dk hydraulic diameter; u fluid velocity.

dh hydraulic diameter and friction factor calcula-tions: the hydraulic diameter is the matrix wire diameter

modified by the porosity and it allows us to determine

the local Reynolds number of the flow by simulating it

as a simplified case of flow across a cylindrical body.

The end result is that the drag produced by flow in

porous media of certain wire diameter is equivalent to

drag produced by free flow over a cylinder with diameter

dk.

The hydraulic diameter equation is [2]:

dh b

1 b dw 4

where b porosity, porosity defined as: void volume/total matrix volume; Re the flow Reynolds numberequation is [2]:

Re qudh=l 5

where dk hydraulic diameter, calculated using Eq. (4);l viscosity; f friction.

Darcy-type friction factor calculation: the equation

for calculating the friction factor is based on Ergun

equation (Table 2) which was modified to better track

observed test data.

The equation is [2]:

f 129=Re 2:91Re0:103 6

where Reynolds number is determined by Eq. (5).

We are now ready to calculate the pressure drop

using Eq. (3) by substituting the values of f, friction

factor and dk, hydraulic diameter.

To calculate the regenerator performance factor Rpf,

we will have to determine the convection coefficient h.

h convection coefficient. The convection coefficienth, is a function of Nusselt number, the fluid conductivity

k and the hydraulic diameter dk. It can be calculated

using the following equation [2]:

h Nuk

dh7

Nusselt number is a function of Peclet number Nu and

the porosity b and calculated using the following equa-

tions [2]:

Nu 1 0:99Pe0:66b1:79 8

where b porosity; PePeclet number.Peclet number can be calculated using the Reynolds

number which has been determined previously and

Prandtl which can be calculated using the following

equations:

Pe RePr

Prandtl number is a function of fluid viscosity l, thermal

conductivity k and specific heat Cp of the working fluid

and can be calculated using the following equation:

PrPrandtl number

Pr lCp=k 9

We are now able to calculate the convection coefficient

and the regenerator performance factor using Eqs. (3)

and (7) and the total surface area As.

5. Test program

Using the above analysis model we calculated the

Regenerator Performance Factor for a variety of lami-

nate and single screen filled regenerators which wereconstructed from different types of mesh. Two regener-

ators were filled with single screen disk elements 400

mesh 0.0012 twill weave (FLIR Systems standard pro-

duction regenerator matrix) and the second one was

filled with a 400 mesh 0.0009 wire diameter plain weave.

Both regenerators were filled according to FLIRs man-

ufacturing methods and processes.

Three additional regenerators were filled with differ-

ent laminates.

The first regenerator was filled with 400 mesh 0.0012

twill weave laminate to 2/3 of the standard length in

order to maintain adequate flow rate. The second

regenerator was filled to the entire length with a 325

mesh 0.0014 wire laminate.

And the third one was filled to the entire length with a

mix of different laminates made from 400, 200, and 325

mesh in order to maximize Rpf number. Additional

laminates were tested and are identified in Table 1.

The Rpf number was calculated at room temperature

using Helium as a working fluid and at a flow velocity of

2.58 ft/s. The analysis results of few mesh types are

summarized at the Table 1. Few regenerators were built

(Table 2) and integrated into the same integrated cooler

Dewar assembly (IDCA) (Table 3). The cooling power

was measured at 77 at 300 K ambient (Fig. 5) using aDewar with active heat load and a temperature diode

mounted on the cold tip of the Dewar. The test results

are summarized in the Table 2.

6. Summary

A new type of regenerator matrix (Fig. 6) has recently

been developed at FLIR SystemsBoston. The alter-

nate design is essentially a woven screen laminate fab-

ricated by bonding screen sheets using a sintering



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process. Three laminate and two screen disk regenera-

tors were analyzed, built and tested. The cooling power

was measured, summarized in Table 2 and plotted as a

function of the Regenerator Performance Factor Rpf.

The performance plot clearly demonstrates that the

correlation between the calculated Performance Factor

and Cooling Power is strong and linear. In general,

regenerators with high Rpf always performed better. We

Table 1

Regenerator matrix details summary

dk, in. (m) b dw, in. (m) op=ox, psi/in.(N/m3)

h, W/in.2/C

(W/m2/K)

As, in2 (m2) Rpf, regenerator

performance

factor, W in./Cpsi

(W m3/KN)

Laminate 400

mesh 0.0012 twill

0.0014

(3.56E)

05)

0.54 0.0012

(3.05E)

05)

3.30

(3.73E)

01)

3.12

(2.01E)

03)

27.0

(1.74E)

02)

25.4 (9.4E)05)

Laminate 325

mesh 0.0014 twill

0.00177

(4.5E)05)

0.56 0.0014

(3.56E)05)

2.15

(2.43E)01)

2.92

(1.88E)03)

32.3

(2.08E)02)

43.9 (1.62-04)

Laminate 200

mesh 0.0021 twill

0.003

(7.62E)05)

0.59 0.0021

(5.33E)05)

0.782

(8.83E)02)

2.45 (1.58-03) 21.2

(1.37E)02)

66.6* (2.45E)04)

Mixed laminates (4)

400 mesh 0.0012

n/a n/a n/a 1.75

(8.83E)02)

Length

weighted

average

2.82

(1.82E)03)

Surface area

weighted

average

28.9

(1.86E)02)

Total surface

area

46.5 (3.84E)04)

(26) 325 mesh 0.0014

(17) 200 mesh 0.0021

Laminate 280

mesh 0.0013 plain

0.0018

(4.52E)05)

0.583 0.0013

(3.30E)05)

2.04

(2.30E)01)

3.11

(2.01E)03)

34.75

(2.24E)02)

53.0* (1.95E)04)

Laminate 325

mesh 0.0011 plain

0.00158

(4.01E)05)

0.59 0.0011

(2.79E)05)

2.66

(3.01E)01)

3.42

(2.21E)03)

40.59

(2.62E)02)

52.3 (1.92E)04)

Laminate 250

mesh 0.0014 plain

0.0021

(3.05E)

05)

0.598 0.0014

(3.56E)

05)

1.58

(1.79E)

01)

3.03

(1.95E)

03)

31.45

(2.03E)

02)

60.5* (2.22E)04)

Laminate 230

mesh 0.0014 plain

0.00236

(5.99E)05)

0.63 0.0014

(3.56E)05)

1.24

(1.40E)01)

3.1 (2.00E)03) 29.72

(1.92E)02)

74.4* (2.74E)04)

Single screen element

400 mesh 0.0012 twill

0.0017

(4.32E)05)

0.59 0.0012

(3.05E)05)

2.25

(2.54E)01)

3.27

(2.11E)03)

35.83

(2.31E)02)

52.1 (1.92E)04)

Single screen element

400 mesh 0.0009 plain

0.0015

(3.81E)05)

0.63 0.0009

(2.29E)05)

2.83 (3.2E)01) 3.92

(2.53E)02)

44.24

(2.85E)02)

61.4 (2.26E)04)

Table 2

Cooling power test results summary

Rege ne rator type de script ion Rege ne rator performance c oe . W in./K/psi (W m3/KN) Cooling power test (mW)

400 Mesh twill 0.0012, (31) laminates 25.4 (9.4E)05) 350

325 Mesh twill 0.0014, (48) laminates 43.9 (1.62E)

05) 386Mesh twilla 0.0012, (650) single screen disks 52.07 (1.92E)04) 420

400 Mesh plain 0.0009, (850) single screen disks 61.36 (2.26E)04) 466

Mixed laminate matrix regen 46.45 (3.84E)04) 400

(4) 400 Mesh 0.0012 wire dia. twill laminate



325 Mesh plain weave (49) laminate sand blasted 52.3 (1.92E)04) 430

325 Mesh four layer laminate 64.8 (2.38E)04) 469

325 And 400 mesh mixed 66 and 150 4 layer laminates 64.6 (2.37E)04) 478a Baseline design.

Table 3

Cost analysisscreen disk vs. laminate matrixItem Unit material

cost

Units required Material cost

total

Labor hours Hourly rate Labor cost total Total regenerator cost

Laminate $1.00 50 $50.0 0.3 $35 $10.5 $60.5

Screen disk 0.070 850.0 $59.5 3.0 $35 $105.0 $164.5

Delta )$9.5 )$94.5 )$104.5

Total savings: $104.5 per unit ($209,000 per year at current production rate).

U. Bin-Nun, D. Manitakos / Cryogenics 44 (2004) 439444 443


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managed to reduce conductive losses by increasing the

laminate surface roughness.

The cooling power of the standard matrix regenerator

currently in production is in the range of 380440 mW

with an average 410 mW, while the laminate design

regenerator was able to produce 400478 mW with an

average 440 mW of refrigeration depending on thelaminate type (Table 2). The measured cooling power

shows that the laminate regenerator performance is

similar or better than the average single screen disk

regenerator and cost 63% less to manufacture.

We plan to further optimize the design by using dif-

ferent mesh laminates in a regenerator to match the

temperature gradient along it. This allows us to take

advantage of the change in viscosity ofHe as a function

of temperature. Also, we plan to test laminate fabricated

in a variety of orientations.

7. Conclusions

So far, the performance of the new laminate regener-

ator is equal or better than the average standard sin-

gle screen filled matrix regenerator currently in

production.

The correlation between the calculated Rpf and cool-

ing power is good.

The potential for higher performance laminate is sig-

nificant.

The reduction in the number of matrix elements per

regenerator provides more than 63% reduction in

cost.

The ability to design a regenerator with mixed lami-

nates provides an additional system optimization

method.

Fabrication of ultra fine mesh disks will not be prac-

tical with out the use of laminates.

References

[1] Flynn TM. Cryogenic engineering. New York: Marcel Dekker, Inc.;

1997. p. 327.[2] Gedeon D. Baseline Stirling modeling. Athens, OH: Gedeon

Associates; 1999.

[3] Macdonald IF, El-Sayed MS, Mow K, Dullien FAL. Flow through

porous media-Ergun equation revisited. Ind Eng Chem Fundam

1979;(18):199208.

Fig. 5. IDCA cooling power vs. regenerator performance factor.

Fig. 6. Screen laminate regenerator.


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