Compactness factors for rolled, stacked-screen regenerative heat exchangers

Cryogenics38 (1998) 959–965 1998 Elsevier Science Ltd. All rights reserved

Printed in Great BritainPII: S0011-2275(98)00061-7 0011-2275/98/$ - see front matter

Compactness factors for rolled, stacked-screen regenerative heat exchangersTim Murphy*† and W. Jerry Bowman‡

†Air Force Research Laboratory, Kirtland AFB, NM 87117, USA‡Department of Mechanical Engineering, Brigham Young University, Provo, UT84602, USA

Received 9 March 1998; revised 26 April 1998

The objective for the current research was to determine how the heat transfer andpressure drop characteristics changed in a stacked, wire-screen regenerative heatexchanger (regenerator), if the screens which were used to construct the matrix wererolled to decrease their thickness. More of the rolled screens would fit into a regener-ator with a reduction in gas volume in the regenerator. During the course of theresearch, an improved method for determining the heat transfer characteristics of aporous medium regenerator was developed. The results show that the compactnessfactor (jH/f) was adversely affected by rolling. Flattening the screens by 15%, 30%, or50%, did not improve the heat transfer rate to the matrix, but it did increase the totalpressure drop. Rolling the screens caused a decrease in both wetted surface area andpore size. The heat transfer which is proportioned to the wetted surface area wasreduced. The pressure drop, which is strongly dependent on pore size, increased. Rol-ling the screens also reduced the effectiveness of the regenerator. 1998 ElsevierScience Ltd. All rights reserved

Keywords: regenerative heat exchanger; regenerator; porous media; compactness fac-tor; heat transfer coefficient; friction factor

Cryocoolers are used in space-based assets to cool elec-tronics1. Numerous efforts are under way to improve theefficiency of cryocoolers2. The measure of efficiency forcryocoolers is the coefficient of performance (COP). Anintegral component of many cryocooler systems is a regen-erator. A figure of merit for regenerators is its compactnessfactor, which is the ratio of its heat transfer characteristicsas measured by the Colburnj-factor, to its pressure dropcharacteristics as measured by the friction factor. The COPof the cryocooler is improved with higher regenerator com-pactness factor3.

Although the compactness factor is an important para-meter influencing system COP4, researchers have alsoshown that reducing the dead volume in the cryocooler alsoimproves system COP5. Hence, if a way could be found toreduce the dead volume without causing the compactnessfactor to decrease, a better COP could be achieved. Oneway to reduce the dead volume is to flatten the screenswhich when stacked together constitute the matrix com-monly used to construct the regenerator. Flattening thescreens reduces the porosity of the regenerator matrix,allowing for more matrix mass in the regenerator and lessvoid for gas. Even though flattening the screen will reduce

*To whom correspondence should be addressed.

Cryogenics 1998 Volume 38, Number 10 959

the void fraction, its effect on compactness factor isunknown. Consequently, the heat transfer coefficient andfriction factor for flattened screen regenerators need to bemeasured to determine the effect on the compactness factor.

An improved approach for measuring the heat transfercoefficient in a porous matrix was developed. A total of 12regenerators were tested using the new technique. Meshsizes of 100, 180, and 250 per inch at screen thicknessreductions of 15%, 30% and 50% were studied. The regen-erators were test for a Reynolds number range of 50 to 600.

Experimental method

The classic step-change transient technique for determiningthe heat transfer coefficient of a regenerator was originallydescribed by Pucciet al.6. For their method, gas flows inone direction through a regenerative heat exchanger. Thetechnique uses a step change in gas temperature at theregenerator inlet to cause heat transfer between the gas andthe regenerator matrix. The heat transfer coefficient isdetermined by studying the temperature trace at the regen-erator outlet. Pucci showed that with the introduction of theappropriate dimensionless variables, along with an adia-batic boundary condition and the step-change initial con-dition, the temperature of the gas could be calculated as a

Compactness factors for regenerative heat exchangers: T. Murphy and W. J. Bowman

function of time and location in the regenerator. Locke7

showed that the maximum slope of the temperature at thematrix outlet is solely a function of the heat transfer coef-ficient. This solution to the governing equations of the step-change transient approach offered an elegant method fordetermining the heat transfer coefficient: provide a step-change in inlet temperature and measure the maximumslope of the outlet temperature trace. From the gradient oftemperature at the outlet, with respect to time, a value forNtu (number of thermal units) can be determined. SinceNtu 5 (hconvA)/(mcp), whereA is the surface area for heattransfer (m2), m is the mass flow rate (kg/s), andcp is thespecific heat of the gas (J/kg/K); the heat transfer coef-ficient, hconv, can be calculated.

There are three major problems with this technique. First,obtaining an exact step change in inlet temperature in thelaboratory is difficult. Second, it is very difficult to obtainan accurate slope from experimental data. Third, the modelignores heat transfer between the gas and the regeneratorwall.

The importance of energy exchange with the wall can beseen inFigure 1, where a temperature transient for anempty regenerator (no matrix material) is shown. The inletand outlet temperatures start the test run at the same steady-state value. When the transient begins, the inlet tempera-ture, Tg1, abruptly falls, and soon begins to converge on anew steady-state value. Similarly, the outlet temperaturetrace,Tg2, falls sharply, but the temperature drop lags thedrop inTg1 due to heat transfer from the regenerator wall tothe gas. The wall is supplying enough energy to measurablyinfluence the temperature of the gas for a significant time.A simple calculation shows that the thermal time constantof the wall and environment is much larger than the thermaltime constant of the matrix. If the wall and matrix are madefrom the same material and treated in a lumped parametersense, and if the heat transfer coefficient between the gasand the wall is considered the same as between the gas andthe matrix, the ratio of time constants for heat transfer fora unit length of regenerator wall to that for a unit lengthof regenerator matrix is written:

tw

tm5

FrVchAG

wall

FrVchAG

matrix

5FVAGwall

FVAGmatrix

5tw

S1 2 f

a D (1)

Figure 1 Temperature lag at empty regenerator outlet

960 Cryogenics 1998 Volume 38, Number 10

wheretw is the time constant for wall (s),tm is the timeconstant for matrix (s),tw is the wall thickness (m),f isthe porosity of the matrix (dead volume/total volume) anda is the surface area for heat transfer per unit volume ofthe matrix (m−1).

For the 12 regenerators used in the current research, thisratio ranged from 16.4 (100 mesh, no reduction inthickness), to 47.2 (250 mesh, 50% reduction in thickness).Consequently, the time constant for the regenerator matrixis much quicker than that for the wall. If this is the case,the early-time heat transfer should be studied to get the bestestimate of the heat transfer coefficient for the matrix. But,the step-change transient technique concentrates on rela-tively late-time events (when the maximum temperatureslope occurs) where the influence of the wall is present.

Three modifications to the classical method describedabove were made in the current research. The first was toeliminate the assumption that an exact step-change in tem-perature occurs at the inlet. This was accomplished by mea-suring the true inlet temperature trace for each experimentaltest run. The method used the measure inlet and outlet tem-perature traces and an inverse method to predict the heattransfer coefficient between the gas and the regeneratormatrix.

The second major improvement to the model was theinclusion of the energy transfer to the regenerator wall. Alumped parameter approach was taken. The heat transfercoefficient between the gas and the wall was assumed tobe the same as between the gas and the matrix, and thewall temperature was allowed to vary in the axial directionand with time.

The third major improvement deals with the criteria usedin the inverse method to select the most accurate heat trans-fer coefficient. In the earlier model, the heat transfer coef-ficient was selected by studying the maximum slope of out-let temperature trace. Because the wall effect is lessimportant early in the transient, an earlier time in the transi-ent was used for the convergence criteria. This time is dis-cussed below.

A characteristic of porous media is that it acts like athermal sponge. The sponge effect of a regenerator can bedemonstrated by comparingFigure 1andFigure 2. For theempty regenerator inFigure 1, the outlet temperature tracechanges almost immediately, in tandem with the inlet tem-perature trace. However, when a matrix material is present

Figure 2 Regenerator sponge effect delay time


as inFigure 2, the outlet gas stays at the initial temperaturefor some time before it begins to change. The definition ofthe sponge effect delay time is as follows: it is the time ittakes for the outlet gas temperature to change a measurableamount. For the current research, the definition of a measur-able change is a deviation in outlet temperature from itsrunning average by more than twice the accuracy of thetemperature measuring devices, or about 0.4°C for thiswork.

Using the sponge effect delay time gave a better valuefor the heat transfer coefficient than using the maximumoutlet temperature slope. Two arguments can be made tosubstantiate this claim. First, the most accurate value forthe heat transfer coefficient will be found by studying theearly transient when heat transfer between the gas and thematrix dominates. The second argument for the improve-ment can be seen fromFigure 3. Whereas a wide range ofoutlet temperature traces can be achieved depending onhow much the tube affects the flow, the delay time is nearlyinsensitive to these extraneous factors. For the example inFigure 3, the maximum slopes differ for the two cases byapproximately 150%, whereas the delay times are only dif-ferent by about 5%. Hence, the sponge effect delay time isan easily measured parameter of the regenerator that canbe used to calculate more accurate heat transfer coefficients.

Experimental procedure and apparatus

The apparatus used is represented byFigure 4. It consistedof three main subsections. The first subsection was a sourceof both hot (around 35°C) and cold (10°C) helium. Thesecond subsection consisted of a test section which con-tained a mounting bracket which held the regenerator (#11in Figure 2), instrumentation (fast-response thermistors(#10) and differential-pressure transducers (#15)) to meas-ure the temperatures and pressures at the inlet and outletto the regenerator, a four-way valve (#9) which divertedthe flow from cold to hot, producing the transient, and aventuri flowmeter (#12). The third subsection was the dataacquisition system (#16).

The procedure was straightforward. After steady-stateflow was achieved at the appropriate pressure and massflow rate at the cold gas temperature, the four-way valvewas switched to hot flow and the transient inlet and outlet

Figure 3 Comparison of outlet temperature trace with andwithout a wall


Figure 4 Diagram of experimental apparatus

temperature traces were measured, as well as the pressuredrop across the regenerator and the gas mass flow rate.

The raw data consisted of temperature traces measuredat the inlet and outlet to the test section; pressure and press-ure drop readings from the three pressure stations in thetest section; and an average value of the mass flow rate.The first parameters determined from the data were theactual start and end times of the transient. The raw tempera-ture data were filtered with a 20th order finite impulse resol-ution filter. The start timet0 was selected to be the timewhen the inlet temperature changed by more than two stan-dard deviations from the initial, steady state value. The endtime was selected at a time after which the maximum slopein the outlet temperature trace had obviously occurred,between 10 and 15 regenerator matrix time constantsafter t0.

Once the beginning and end times were identified, thesponge effect delay timing was found,t2. The time betweenwhen the transient begins,t0, and when the outlet tempera-ture trace began to change measurably was defined aboveas the sponge effect delay time. The determination oft2

was done in a similar manner as fort0; it occurs when theoutlet temperature trace changed by more than two standarddeviations from its running average.

The final step in the reduction process was collecting allthe data into a read file for each experimental run. Resultsfrom the raw data file such as mass flow rate and pressureswere assembled at the beginning. Next, some geometricproperties of the regenerators such as mass, pore size, andlength were added to the file. Then, the filtered temperaturetraces were appended to the file. Finally, the time para-meters described above were included. All these data wereused by the numerical model described below to determinea heat transfer coefficient.

A numerical model was developed to model the flow. Itused an explicit, finite difference method to solve theenergy equations that modeled the regenerator during thetransient. The model was the same as the one used in theapproach of Pucci6 for the step-change transient solutionexcept for the three modifications mentioned above.Assumptions in the model included no axial conduction, noconduction between the wall and the matrix, perfect gasrelations, constant properties, low Mach numbers, one-dimensional flow, incompressible flow, and a constant heattransfer coefficient. With these assumptions, the continuity


equation shows the mass flow rate, and consequently, themass velocity, is a constant. Conservation of energy forthree control volumes, one representing the gas, one rep-resenting the regenerator matrix and one representing theregenerator wall, are:

Gas:2 mcp

∂Tg

∂xDx 1 hconvAm(Tm 2 Tg) (2)

1 HconvAw(Tw 2 Tg) 5 rcvAfDx∂Tg

∂t

Regenerator matrix: (3)

2 hconvAm(Tm 2 Tg) 5 rmcmA(1 2 f)DX∂Tg

∂t

Tube:kAwx

∂2Tw

∂x2 − hconvAw(Tw − Tg) = rwcwAwxDX∂Tw

∂t

(4)

where m is the gas mass flow rate (kg/s)cp, cv are thespecific heat of the gas at constant pressure/volume(J/kg/K),hconv is the heat transfer coefficient (W/m2/K), Am

is the matrix surface area for convection (m2), Aw is thewall surface area for convection (m2), Awx is the wall cross-sectional area associated with axial conduction (m2), Tg,Tm, Tw are the gas, matrix, and wall temperatures, (K),ris the gas density (kg/m3), A is the cross-sectional area ofthe regenerator (m2), f is the porosity,rm is the density ofthe matrix (kg/m3), cm is the specific heat of matrix(J/kg/K), andDx is the length of the control volume.

Using a first-order accurate forward difference in time,and a second-order accurate central difference in space, theequations were numerically integrated to predict the gas,matrix and wall temperatures as functions of time andspace. Several sample problems with known solutions wereused to validate the accuracy of the model and the numeri-cal grid selected3.

The initial condition was the same for each of the threeequations. The gas, regenerator, and wall were all at thesame initial, steady-state temperature. During the transient,the experimentally measured inlet gas temperature was usedas a boundary condition for the model.

Using the model, a numerically generated outlet tempera-ture trace could be obtained for an approximate value ofthe heat transfer coefficient. The heat transfer coefficientwas determined by requiring that at the sponge effect delaytime the calculated outlet temperature trace match theexperimental temperature trace. Root solving methods wereemployed to find the convection heat transfer coefficientwhich produced the closest match between the experimentaland numerical outlet temperatures. For comparison, thetheoretical heat transfer coefficient based on the approachof Pucci6 was also found.

Two comparisons were made to give confidence in themethod. The first can be seen inFigure 5 where resultsfor friction factor and Nusselt number are compared withpublished correlations for friction factors and Nusselt num-bers for unrolled screens. In the case of the friction factors,Armour and Cannons’8 study included similar mesh sizesand a Reynolds number range, 1.0, Re, 100. The agree-ment is very good with a mean difference of6 2.5%. Thepublished Nusselt number data are due to Hamaguchi9, who


Figure 5 Friction and Nusselt number comparison

also used identical mesh sizes, and a Reynolds numberrange of 1.0, Re , 900.

Another test of confidence for the methodology is repeat-ability. In Figure 5, data is shown for both friction factorand Nusselt number for four sets of test runs. The test runswere done on different days but with approximately thesame operating conditions. The test runs were chosen atrandom and cover a range of Reynolds numbers. The fric-tion data is particularly good, with a mean difference ofonly 2.0% between the members of each set. The fit forthe Nusselt numbers is also good, with a mean differenceof 8.4% between members of the same set. Since the resultscan be duplicated so closely from one test run to the next,confidence in the measurements is warranted.

Experimental data

Two preliminary items are addressed to facilitate using thedata which follows: the first is the definition of the charac-teristic length used to define Reynolds and Nusselt num-bers. The second is an explanation of how the specific sur-face area for each matrix was found.

Many definitions for the characteristic length for heattransfer/fluid flow in a porous medium appear in the litera-ture. One common length used was presented in an articleby Armour and Cannon8. Their definition for the character-istic length isLA 5 1/(a2 3 D), whereLA is the character-istic length,a is the surface area per unit volume of thematrix, and D is the pore diameter. The pore diameter wasfound by taking the cube root of the free volume betweenthe wire threads that make up the screen matrix. The sidesof the volume have length (1/n 2 dw). The volume wasassumed to have a depth of 2dw. Thus, the pore diameter is:

D 5 [(2dw)(1/n 2 dw)2]1/3 (5)

wheren is the mesh number (m−1) anddw is the wire diam-eter (m).

In order to use the Armour and Cannon dimension, thesurface area per unit volume (a) needed to be determinedfor each regenerator. Wiese10 took electron microscopephotographs of the screens which he rolled to the samereduction factors as those used in the current research. Thephotographs show that the rolling caused the round wiresurfaces to be flattened where wires crossed. When screen


Figure 6 Specific surface area vs. reduction factor

disks are stacked one against another, the flattened areascan contact each other, and reduce the surface area avail-able for heat transfer from the fluid to the regeneratormatrix. For this work, it was assumed that the wetted sur-face area of the regenerator matrix was reduced by the flat-tened regions on the rolled screens. The magnitude of thearea of the flattened regions was estimated from the photo-graphs taken of the screen. The results are presented inFigure 6.

To use this figure, the area per unit volume for theunrolled screen (as) is required. It was calculated byassuming the screen wires were woven cylinders and thescreen thickness was equal to one wire diameter. Theresulting relationship for the area to volume ratio is:

as 5 2pn2[d2w 1 (1/n)2]1/2 (6)

This value foras is multiplied by the appropriate ratioobtained fromFigure 6 to get the modified surface area perunit volume for rolled screen (a).

The Nusselt number is defined as Nu5 hconv 3 LA/k,where hconv is the convective heat transfer coefficientbetween the gas and the matrix,LA is the Armour and Can-non dimension, andk is the thermal conductivity of the gas.The experimental results and a least-squares curve fit forNusselt number versus Reynolds number are shown inFig-ure 7.

Figure 7 Nusselt number as a function of Reynolds number


In Figure 8 Nusselt number is plotted as a function ofreduction factor. It is interesting to note that there does notseem to be a strong dependence. During the first attemptto reduce the data, the surface area of the regenerator wasassumed to be the same for the reduced thickness screensand for the unrolled screens of the same mesh number.When this was the case, the Nusselt number was smallerfor the rolled screens. When the reduction in wetted surfacearea was taken into account (discussed earlier,Figure 6,by using a characteristic length which included the effectsof surface area reduction) the Nusselt number was nolonger dependent on the reduction factor. The plot showsthat within the accuracy of the testing, changing thereduction factor had no effect on the Nusselt number. Whenconsidering the heat transfer from a gas to a regeneratormatrix, a regenerator matrix made from rolled screen wouldexperience less heat transfer. This is due to either a smallerarea for heat transfer or a decrease in the heat transfer coef-ficient or some combination of the two effects.

The friction factor is defined as follows8:

f 5Dpgcf

2DLrU2

g(7)

where Dp is the pressure drop across the regenerator(N/m2), f is the porosity,D is the pore diameter (m),L isthe matrix length (m),r is the gas density (kg/m3), andUg

is the gas approach velocity (m/s).The behavior of the friction factor differs from the

behavior of the Nusselt number. The reduction factor playsa significant role in the value of the total pressure drop.The experimental results and a least-squares curve fit forfriction factor versus Reynolds number is shown inFigure9. The solid line is the relationship by Armour and Cannon8

for unrolled screens. The first thing to notice about theexperimental data is the group of points which are in theupper left-hand corner of the figure. All of these data pointsare for test runs with a reduction factor5 0.5. Apparently,reducing the thickness of the screen by 50% causes a largeincrease in the friction coefficient. The second thing tonotice in Figure 9 is that the remaining data points fallclose to the line with only a 6% mean difference. To insurethis was the case, the friction factor was plotted as areduced friction factor inFigure 10. The reduced frictionfactor was defined as the friction factor for a specific screenunit divided by the friction factor for the unrolled screen

Figure 8 Nusselt number as a function of reduction factor


Figure 9 Friction factor as a function of Reynolds number

unit operating at the same Reynolds number. It appears thatthe friction factor increases for all values of screen thick-ness reduction, but most pronouncedly so for reductionsgreater than 30%.

An important result from the current research is themeasurement of compactness factor. The definition of com-pactness factor is CF5 jH/f, where jH is the Colburnj-factor, andf is the friction factor11. The Colburnj-factor isdefined asjH 5 St 3 Pr1/3, where St is the Stanton numberand Pr is the Prandtl number.

In Figure 11, the results for the compactness factor as afunction of reduction factor are shown for each mesh size.For the 100 and 180 mesh screens, the trend is clear: thecompactness factor decreases with decreasing reductionfactor. Hence, rolling the screens tends to reduce the com-pactness factor. For the 250 mesh screens, the compactnessfactor seems to increase at a reduction factor of 0.7. Thedata for this case was examined more closely, and whereasthe heat transfer coefficient is about what one would expect(compared to the other data,) the friction factor is smallerthan expected. The reason for this discrepancy is not appar-ent. Since all of the other data follow a predictable trend,it is considered an outlier.

A reduced compactness factor was defined to be the ratioof the compactness factor for rolled screen to the com-

Figure 10 Reduced friction factor as a function of reductionfactor


Figure 11 Compactness factor for each screen mesh size

pactness factor for unrolled screens. The reduced com-pactness factors data is plotted inFigure 12, along with aleast-squares curve fit. The spread is moderate (a standarddeviation of 21.5% from the best-fit curve). The trendclearly shows a reduction in the compactness factor as thescreen thickness gets smaller.

Another remark can be made about the use of the com-pactness factor in numerical models. Due to the lack of heattransfer data for regenerators, some researchers resort tomeasuring the friction factor and applying Reynolds anal-ogy12. For Reynolds analogy to apply to flow in a regener-ator, the compactness factor should be a constant. If theresults for flow in a tube are used, Reynolds analogy statesthe compactness factor should be 0.125. For the unrolledscreens, this is not a bad guess, being 16.7% high versusthe average of the unrolled values. But the analogy breaksdown at smaller reduction factors, reaching a mean valueof 0.031 for a 50% reduction in screen thickness.

Another parameter was used to evaluate the merit ofreducing the thickness of the screens. Effectiveness isdefined for regenerators in terms of the ability of the regen-erator to remove the maximum amount of energy from thegas relative to an ideal case. Effectiveness,h, can bedefined for the case of one-directional flow as

h 5mcpt2

msucm(8)

Figure 12 Reduced compactness factor vs. reduction factor


Figure 13 Reduced effectiveness vs. reduction factor

wherem is the mass flow rate (kg/s),cp is the specific heatof the gas (J/kg/K),msu is the mass of matrix (kg),cm isthe specific heat of the matrix (J/kg/K), andt2 is the spongeeffect delay time (s)3.

In Figure 13, the reduced effectiveness is shown as afunction of the reduction factor. Effectiveness is the domi-nant parameter in cryocooler systems performance4,13. Thedata show a reduction in effectiveness whenever the screenthickness (reduction factor) is reduced. The effect is smallat reduction factors of 0.7 and 0.85, and falls to about a13% decrement in effectiveness at a reduction factor of 0.5.Again, these results would rule out any benefit of reducingthe screen thickness by 50%. The interesting thing aboutthe figures is that one would expect the effectiveness toincrease by making pore sizes smaller. Rolling the screensdoes not change the material properties of the gas or matrix,hence another reason must exist for the decrement. Asnoted above, rolling the screens does reduce the wetted sur-face area of the matrix since abutting round wires have asmall area of contact while flattened surfaces can have alarger contact area. Large surface-area-to-volume ratio isone of the factors responsible for the large effectivenessof wire-screen matrices. Since the wetted surface area isdiminished when flattened surfaces are introduced by rol-ling the screens, the effectiveness is also reduced.

Conclusions

The results presented in this paper give a convincing expla-nation for the conclusion that rolling the screens to reducetheir thickness causes the ratio of heat transfer coefficientto the friction factor to decrease. The data show that theheat transfer between the gas and the matrix is reduced forregenerators made from rolled screens. This reduction is aresult of reduced wetted surface area or reduced convectionheat transfer coefficient. The friction factor, however,


increased marginally for small thickness reductions, butsubstantially for the 50% reduction case.

The crux of the matter with regard to the compactnessfactor is how the geometry of the matrix changes due torolling. Rolling the screens causes the round surface areasof wires to be replaced with flattened areas with abruptedges. These flattened areas abut against one another, caus-ing the total wetted surface area in the matrix to decrease.This reduces the heat transfer. Also, the smaller pore sizesand sharp edges cause the inertial component of the press-ure drop to increase to the point where the total pressuredrop is higher. The overall effect of the geometry changeis to increase the compactness factor.

The effect of reducing the screen thickness on cryocoolerCOP was not addressed. It was shown that reducing thescreen thickness caused a decrease in regenerator effective-ness which will have a negative impact on COP. However,reducing the screen thickness should also decrease the voidfraction in a cryocooler, which will have a positive impacton COP. The optimum screen thickness for best COP stillneeds to be studied.

References

1. Chan, C. K., et al., Overview of cryocooler technologies for space-based electronics and sensors.Advances in Cryogenic Engineering,1990,35, 1239–1250.

2. Thomas, P. J., SDIO and Air Force cryocooler technology develop-ments at USAF Phillips Laboratory. InProceedings of the 7th Inter-national Cryocooler Conference, Santa Fe, NM, November 1992,pp. 3–13.

3. Murphy, T. J., How reducing the thickness of the round wire screensin a porous medium regenerator affects its compactness factor (jH/f).PhD dissertation, AFIT/DS/ENY/96-5, School of Engineering, AirForce Institute of Technology (AU), Wright-Patterson AFB, OH,June 1996.

4. Urieli, I. and Berchowitz, D. M.,Stirling Cycle Engine Analysis.Adam Hilger, Bristol, UK, 1984.

5. Atria, M. D., et al., Microcomputer aided cyclic analysis of the Stir-ling cryocooler with different regenerator meshes.Cryogenics(September Supplement), 1990,30, 236–240.

6. Pucci, P. F., et al., The single blow transient testing technique forcompact heat exchangers surfaces.Journal of Engineering forPower, 1967,89, 29–40.

7. Locke, G. L., Heat transfer and flow friction characteristics of poroussolids. Test Report No. 10, Department of Mechanical Engineering,Stanford University, Stanford, CA, 1 June 1950.

8. Armour, J. C. and Cannon, J. N., Fluid flow through woven screens.AICHE Journal, 1968,14(3), 415–420.

9. Hamaguchi, K.et al., Effects of regenerator size change on Stirlingengine performance. InProceedings of the 26th IECEC, Vol. 5.1991, pp. 293–298.

10. Wiese, J. L., Experimental analysis of heat transfer characteristicsand pressure drop through screen regenerative heat exchangers. Mas-ters thesis, AFIT/GAE/ENY/93D-30, School of Engineering, AirForce Institute of Technology (AU), Wright-Patterson AFB, OH,December 1993.

11. Kays, W. M. and London, A. L.,Compact Heat Exchangers, 3rdedn. McGraw-Hill, New York, 1984.

12. Radebaugh, R. and Louie, B., A simple 1st step to optimizing regen-erator geometry. InProceedings of the 3rd Cryocooler Conference,Boulder, CO, 17–18 September 1986, pp. 177–198.

13. Martini, W. R., Stirling Engine Design Manual. NASA CR-135382 (1980).

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Compactness factors for rolled, stacked-screen regenerative heat exchangers