NAVY ENVIRONMENTALLY SAFESHIPS PROGRAM

EXPERIMENTAL STUDIES OF RADIAL WAVETHERMOACOUSTIC ENGINES

ANNUAL REPORT

Gramnt #: N00014-93--1-125

Submitted to:

Office of Nava! Rese.rc.,,Phvsici Division ONR 331

800 North]Q-i c __. £3 l4 Arlington, Virginia 2.1217-5660 T .,

'AUtJGJ?4 kl9.

by:

Richard Rasper, Ilenrv E. Bass and Jay A. LightfixotNational Center for Physical Acois: cs

The Univerrsity of Nfi•s•i•iliUniversitv.y lissis:•ippi 31(;",7

1995"025 0IT

NAVY ENVIRONMENTALLY SAFESHIPS PROGRAM

EXPERIMENTAL STUDIES OF RADIAL WAVETHERMOACOUSTIC ENGINES

ANNUAL PEPORT

The Jamie WhittenNational Center forPhysical Acoustics

FDITIC

fA4 ~; BEST AVAILABLE COPY

I lnit~rr~lhl Uf fti~is'o

4 TITLE AND SUBTITLE 5 FUNDING NUMBERS

Experimiental Studies of Rad~ial Wave Thermoaccustic PE 61153NEngines G tN00014-93-1-1123

_______________________________________________TA 3i26973ess016ý AUTHOR%(S)

Kichard Rasper, Henry E. Bass and Jay A. Lilght Ac.,r

I. PERFORMING ORGANIZATION NAMF(Sý AND ADDRESS(ES) 18 PERFORMING ORGANIZATIONIREPORT NUMBER

Nation~al. Center for Physilcal AcoIusticsThe University of ý1issis~sippi j RR0795-01CrE~versitv, XS 38677 .

29 SPONSORING MONITOR NdG AGENCY NAME(S) AND AOORESS(ES) j10. SPONSORINGi'MONITOR;.N6

O~f ce o Naal Rsearh jAGENCY REPORT NUMBER

N, R 331800 !NCrth, Quincy StreatArlington, VA 22217-5661)j_____________

11. SUPPLEMENTARY NOTES

12a. DISTRIBUTION. AVAILA8i~iTY ITATEMENT 12lb. DISTRIBUTION CODE

Approved for public release: 31strliut ion. unlnmited

13. ABSTRACT ijrn 3 rs

The horizontal plate prime mo'ver !,"it beeii constructed and reported at the fallmeeting~ of the ASA in Austin~. IX. Trhe ana~lysis of horizontal plate tiierzaoacousticengines hiws been completed and tiubmitted for publication in J1ASA and a~ theoreticalcoinparisorn of plane and radial. wave thi--rmoacoustic engines was reported in Austin.AnalvsLi5 cý vertical plate therrnoarnustic engines has recently been completed andýa marluscrlpt is being reviewed. reiininarv vertical plate price mover resultswere reported at the spirng tneeting of the ASA in %as.hington, DC.

14. SUBJECT TERM;1' ~M ~CP'E

rhernacu~jc5,!fri~.e '*.r, H~izr,.t.<~ xetIC~ p'lartc. u, C

TABLE OF CONTENTS

Page

BRIEF DESCRIPTION OF ACCOMPLISHMENTS ........................ -I

I. Radial Prime Mover Prototype ................................. I

11. Horizontal Plate Thermoacoustic Engines ......................... 3

ill Thermoacoustic Engines i'ith Varying Plate Separation ........... ..... 3... ........ 3

A. Slopcd" engine wave equa-ion ........ ..................................................... 4B. Pressure and specific acoustic impedance differer.:hd equation. .... ................ 6C. Prime mover results ..... ...................................... .............. 7D. Plane w ave results ..............................................................................................E. Radial wave results ..................................... 10

IV. Thermoacoustic Helmholtz Rvsonalor ............................ ............

V. Reference, ....... ....... - ......... ...................................... i ...... .... 13

PUBLICATT(IN:PA TENTS/PRESENTATIONIONORS REPORT ........................... 27

S; t.::.,:,,:. (it

ira" Tor

fj

%.

EXPERIMENTAL STUDIES OF RADIAL WAVE_THERMOACOUSTIC ENGINES

ANNUAL REPORT

BRIEF DESCRIPTION OF ACCOM.NPLISHMIENTSThe horizonr4 pltrime mover has bencn trctd in collaboration with Dr. Arnott at

-tic Univer-sity off Nevada at Reno,=4dwa ~t tb, f-311 m,-tr~ t~f fli. Arrimvt-!)1 1ýwif

(If America in Austin, Texas. 1 Tlhe analysis of hcortwntal plate therrnoacoustic engines his becin

completed ands:ubrnitted for publication in the Jour-nal ot' the Acoustical Society of Ame-rica, 2

and a theoretical conmparisonc ~rcad ailwv h -o.4--oi Pnv~.none wrýpnrtwdfin

Austin.3 Report W. -s also made at Austin of a previously described Helmholtz resonator prime

moeiAnal) si or vertical plate thermoacoustic engines hits recently been completed and a

mnt~inIcript is being rcevewed. Pý,piNmin'Arvr n'it mrrm winii. e~ wnwtr

the spring meetingof the Acoustical Sc-ýiety of America in W'acshing-tor'.DC. 5

1. Radial Prime Mover Prototype

A schematic of the radial mode prime mover ,tack %%,ich Eas been contrucited is given inFio. I and the resonwior is s!w inFg 2. ThL Ivtn is oiu it-, Iu ~tr f6

frc,*urn and 4011 Argon at a prc5 sure of I atmb with an operating tz freuency f oIt .S klli.

The cylindrical. resonator is 12 inche:s in diz:.meter and 4 inches high. Li~ ote- rin- is alinvi~n Am

wdthe. top and bo~torn pfae are "r!'s e.'ie~d~i ~c ~af~~ ~njCt ih~

outer diameter of 10.3146 inchos and a-i inner diameter of 9.M62 inchcs. The theorctical

Caualirv factor gr I J II tI 11.nr~ AUipr:.. tCC ;U P V- rific d nI~

the heat exch;zm1:er cle~ien

Rascd i.n;o'l. nhe I, ~y~ ~xc~~n~a the 1 ~e.r fN~~s:'

S{

next to the stack, the initial cold heat exchanger design consisted of copper tubing to cool the top

and bottom pl.ates, and brass screen a.ns "Opp- t,,,%:,, r^,,,:.,,,, ., --,. -t ..- ,,mt,,r

The predicted onset temperature difference %%as about 200 K. TIhis design proved to be

oversimp'ified. A small increase in the quality factor of the system was measured, but the

maximum temperature differece achie.ve-d. ; was onl, habo 1 A more onnventionrl vertical

plate copper heat exchanger was constructed by Dr. Arnotr. The predicted omset temperature was

about 275 K. Although the capacity for heat exchange is much greater than that oif the former

heat exchaner. the atten uat.o *1 al.o mmr", trrpr nc j• evideced hc a sirnifanrlv nlrger

onset temperature. The greatest temperature difference achieved was about 150 K.

The hot side is heated by nichrome wire, and there appears to .- no problem supplying

enough heat in this -.-,y. The problem %k,,: Ltre h-ivinr in -naintairing, thik iaret t-nem rtire

difference across a short distance is one or cooling cap,,ability. Several potential problems have

been investigated: thernmal conduction across the stack through the top and bo,-ttom pltit oft

resonator and radiation frot the nicrome w.,,ire thryt,'h the sack. When the heater-stack-cold

heat exchanger system is removed from the casing and covered with insulation top and bottom

(effectively removing thermal conduction throug. h di top nd to p..... . t.. iarte....

t emperature difference achieved is 180 K, Therefore, cuttine down heat conducted across tie

resonator pnats c.n increase AT by up to 3 30 K. A brass screen was then wrapped around the

outnide of the stack in order to reduce the C...... .f ,,dxio, a....:d ...... , ,.

cold heat exeha|cer. while leavina the system, out of the casing and insulated on top and bottom.

The largest temperature difference achieved was 179 K. The 10 K difference between #he

ercenled result and theno - cree.ed rpct:!t h. n ,1 . . ,t,.rrn. !,, flI...ft

Therefore. it appears fthat radiafion is not signifi zantlv contributing to the heating of the co!d heat

excrmnaer. .

Since the troNibh is teto a difft-icut. tes,1k in~r. vo~fr'~-i .j

ut:erupt iz being r::a:de to roduce th•S ol-n:it'. . C.,L t.latu•sb,,, ita a s it;.vk te.-1t.a. to the

prexen; (thC pliced a rest::5atu 1 VtJ ,,::c' 'X ' i c;.. . ."iU

outside the pressure node to inside the pressure node, will reqjuire a .AT of 635 K for air at

zitnm:spheric pressure. For this sn-a!! 4T tk- rmci on~if h-.'it evi-h-tntc'c'r c" he 1'P '14 -hp e

hot heat exchanger. It remains only to construct a larger resonator and a new cold heat

exchanger. This will be -accomplished shortly.

11, Horizontal Plate Thermo-acoustic E~ngines,

A paper has been submitted describing thc fuil theory for horizonta! plate thermoacousliC

en-2i neS, including applicatio1M n tor~' nha!ticee ni-mmmilttic ý;nfe',rwosnv and a

theorefical comparison of plane and radial w&ave priine tmovers and refrige7LatorS.2 Dr. Arnot~s

report gives a detailed description of this wvork.

ft1. Therrnoacoustic Engines'with Varying Plate Separation

Swift showed for parallel plate thernolousf.tlcenne i~a ilia. vnr-Imized when the plate snacing is rouglyv %wiletetemlpntato et. er

realiCd thiat varying the plate spacirtg from the cotld side to thec "ot side of ather-moacoustic

engine had two poss le ocncr-ts "pp. 459 162o ~.7.Fr,~a!~~~ hra o:

between the flid and the engine. wa!i1 to bc closely approximnated througho-ut the en-irne. since

the thertnal penetraticrn depth varies with temiper.-ire. Second. it can rcdm e acousthc fos~es by'

matching impedance,'-t bothý i t.-rfe (,A r-,- C inca1 ir 1rwA~ntaker, %onn.8 Rert

formulated an analytic solution to the, problem by adopting Swift's parallel pInýe wave equation

(Eq. 54 of Ref. 6) and a!lowinL, for a co-starnt sju v-t bettween successlkve piates kpp 131. I 1 -32 of

Ref. 7).

Analvzling Bennett'sq work for application to radial wave. te:-iboacoustic ciwines, it became

th~frroa~coustic en'iasLv inriT a \ irvirwrT Lur' staixti '.ioll. Rolt conrectlv annoruacl cd this t\vnecf

problem while considering sound propagat ion in tu,bes ,•ith .v..triAe rs.s on Lby in-t.:-u, ,

the changirg tube cross-sectionat area inai the wave ecuation; as in Webster's horn equation

(Fq. 7-8.5 of Ref. 10). The theory of sloped engine thermnoacoumtics is described below and its

effect in pnme movers is numerically quantified.

A. "Shiped" enzinc wave equation

The thermoacousric wave equation for the pariteir plate thennoacousrtc enginte of Fig. 3 is

given by Fq. 28 of Ref. I1 to be

FO d 7) d dF 0.drL 9o dr + 2 a0 , ).T d -k

where

P (F : dTO,a(I. XT) ' ~ 222 1-C } ( " 2

Jr s', ir) = LYk ( - lj ....(.. . .c0 FQL

F (Y 1 :I / - 5/ ) tan h-617. P)

y is the ratio of fluid specific hear•. p. (r) is the ambi'ent fluid density, c is the speed of sound in

the fluid, o) is the o3!cJlatory angular frequency of the acotsli iciaiaahicls Pzt' is Olc col.Ud

pressure. t is ter coýffiient of thernmal rxpansx'n of Oh (n is the Pranri2 number of The

:.,,,' i hePla.f ube . h

XT~~ ~/ 3 (6)

6vf&) iss the thermal (viscous) penetration depth in tic fluid. and v is the plate separation.

Figure 4 shows a thermnoacousic engine with a con~stant slope between successive plates.

fiernet: accounted for a sloped engire by replacilng v Wit hl y (~r; -i,- #thII p arale PIate wvye%

* qu~ation (Eq. 1). where

y (r) yo + sr - (7)

y~is the plate separ~ation at the cote (Teft) side or the engine, s =L - 3.1; L i6 the slope of the

phatcs rellative to eachi (W e.I LA.; UI e J el 5i%. A IUL M) 'I* V. f.1.14~IS

*the hot (right) side of the engine, and r is the clistance from the cold (left) side of the engine.

Adopting* Bennett's method of allowing for a constant slope between successive piates.A

and A T in Eq. 1 are now 1-sitivit ArAl'nt cait~itp cinvp vnih heen r~Lenhe hv v tr;

fro,.ýever. exan.miation of Ro-tfs work with tubes11 ofý varying cross-section) rcvenls; the need for a

fundamental changec in Eq. I for s~loped enginles Nio ing for area changes, within individua,

pores in the stack As in Websicrs bortr Pq witin - in rwidition to nnak~nz and ;.7 rositior.

*deperndent. The corr-ecc wave equation for stucked p!ate thernioacoiistieý vnns~ ith ~~r n

plate spacirg is

__________r -"arF ' +~ :. + k-U., AI-)pi 0 ,(8),

'Apr) F,(.) Lr pý & dr

where Ap(r, is the cross -sec tion,,tl area we~.e ow pl:'tes at a location r (or tlhe pore cross-

seci~tiona area 1 in vii-, .en int -and Jlt 1,s~ x11-4it vr)~mn'LO. f In W/. 4~ ~T J tie rLWxa

araand is idenfical to prt-viotrý rt-smis.16

B. Pressure a',d spccifr aeon tric impedance differential eqatidons

"The derivation to follow is analogous to that of Ref. 11, w ith r dependence showving up in

some previox, y constant terms due to the changing cross-sectional area bet.een the plae...

Define as a pore the space between two plates. Let vJO) be the average particle velocity for a

particular pore cross-section, n the total number of pores in the engine, Arf Sr) the resonator

cross-see:iona! area at r. Ap(r) the cross-sectional area of" a porn at r, V; >h :c .... ,Ar tk.

resonator at r, and s2(r; the porosity or the ratio of open area to total area in the engine at r.

Volume velocity is Ares(r)l% = nAp(r)vr(r). but 12(r) = nAp(r)YArer); therefore, vdr) =

The equation of motion for the fluid in a pore is given in Eq. 13 of Ref iI as iopj,,vr =

flf) :dr) whi.ch. w he n-n...~......... L,,, fri ,- rn- tv w,-Nen !4k

Si~pO-3•- F "dpjFo"- (AL) d r . (9'i

"With the definition of specific "CoiiMt dancc

Z(r) (lO1S~Vrt,(r)•

the first order differentiall ea..... fo. prct:4re, j; f,,,n A e..., tfr-ri Eos.r9 I- ,-

• dp_.!r~d - ik (X ,?) 7T Z irt,ri zIll" '

wh r e7/f

where

= 2rF~ (k,) X-1)12

Thc inmpedance eq,,afion is dexrivecd bt ins~rtnornc 0q.9 10. An'd I I into tt Rq %Ot ih the rceratt

given by

c!7(r}~( 4= klq' Z,,.)L~ 1-dZ(r). (13)

Given ihe definition of 12'r) abov'e. Eq. 13 can also he writzen

dZr .(r) I)fj d

--rk(X.i)Zint (r}, I -*-- 12U 00t,T') + L ~ e() (r) . (14)di' A~~~ \es(T) dr

C. P'rime ineiver resukZS

T he heat exchanger tcmrcraturc difference (onset tem?,pcrwurc~) %t which Q -+for a givenl

by integration of Eqs. I I and 13. Numerical integratio of siar equat s is desctibed in Ref.

21 for radial wave prime movers and in Ref. I I for plane wam e prime rno% ers. The integrazion for

sloped stack, plane and rai- v~ve......................ve by Aaping the so'ution

described in Refs. 2 and I1I suc~h thaIt the varyircg plate spacing. cro~s-sectiona! area,a~nd porosity

Were included.

Arnott eftyl showecd rbhat for" pnaralitMlate thermoxoisoc:t engine,, the optinmal plate sva.i~ng

OccUri when 4T 3.2 (RvF. 11" whiAch corre.sponds to a pixle separation of 2.26 &(this is the

plate separarion ath e lho: end of the en g~tti c, ~i 1_1C! 4 ~ IM. 3.c;w d s- c P'

sepratir. rtheot ad hanat the col-! endn a 5,j is ni::2cr p- thecoldM siLc cf ancrneine. so for

al optimally spar-e'J Par:Iic'. pare et' g the pl'i~ 'c..Jat~~ ion the cold sidt i;ý Te~trer than the

pLive Kepardrion .Ohcic '.'ould ifl ý. 10'c'l IKAUA tiA( /(2f ';t7C' U............ .

of the actual engine slope s to the slo'e which gives optimal thermal contact, ahere optimal

thermal contact slope is determnd by s•,ti:-, ;T = 3 • at the hot and cold ends of the engine.

Positive (negative) sMope ratio corresponds to a wider plate spacing at the hot (cold) side of the

engine.

D. Platte ware rest!:s

Fig. 5 show; numerical calculations of AT, the onset temperature difference, as a function

of slope ratio for the prime r'ove" d,,';.l, ina"rI. The resonator int

to be square and the resonator length is held const:ant. The intecration is initially run for zero

slope to determine the optimal plate spacing for a parallel plate engine. This value is then

assigned to va at the cold side of the eine,. A, ithe s•loe is ehanrge-t the plate spacing at the hot

side of the engine. Yb. changes; which requires one cross-sectional dimension of the tibe on the

hot side of the engine to vary due to the spreading of the engine (the other ttibc- dimcns ... n -is also

varied to maintain a sqrare geometry). Porosities of the heat exchangers on the hot and cold

sides are held co sltant at all times. The process is then repeated for different values of YO to

determine the lowcst ons•et temperature achiev abe.

In Fig. 5. curve a provides the best thermal contact between the fluid and the solid at the

cold side. If thermal contact were the dominant factor in decreasing •T. one would expect curve

a with slope ratio I to prouce the low.t po ae..• since for curv-e a alone the lowest AT occurs %khen slope ratio 25. In addition, curves h. d.

and e, which have plate spaeirgs greater than 2.2; have much lower A"s than curve a. The

solid dots repre;ca the ""n a o c r .c... a r¾.mor...t data "S*C " ,I;f ...... xt,,;r .

The lowest AT achievable for the parallel plate engine (curve c with slope ratio = 0) is aNl~ut

137.5* C. while the overall minima (curve dv.i', storc ra:io# 7,8) is abot 131215s a carefulix

spaced and sloped .engi. cL I:... fL ..- e414:. v.i - byt.-p)., 6... .

6.5' C. Thete arc :wo additional thin,. to note. Fzr-t. curve d. which eives the lovwest Al. has a

wider plate -pacing at all points th-.t tLe lwe.t _11 xiarallel plate spa,,-ig. Seckond. the: sp

~ritilo which gives the lowest AT in'curvc d is large, so a smaller fraction of the fluid is in good

thermal contact with the sofid ('see i.6frapy;clitue.Te

one to Cor~clude that there is a trade-off between reducing acoustic losses via impedance

nmatchin- using sloped stacks (and thus changing the resonator cross-secr~n on the, hot end') and

having the ftuid in good thcri-al contact wit'h :heI =M.id .it .....nc ~''

dominant quartiy for reducing the onset temperature.

TABLE. 1. Sloped stack plane wave prime. rover specifications. "var- denotes quiantities whichvary with engine slope. Ambient temperature is 239 K,. ambientr pressure is 200 kP3, and tilefluid is Helium.

Specification Open Tube Open Tube Cold HX Engine R-ot, H-X Open Tube Open Tube

Legth (cm) M2.0 50 20 6.0, 2.D 5.0 176.0

Height (cm.) 10.0 1(0.0 10.0 var var var 1.0.0

Wiil~h (cm;) 1(030 10.0 10.0 1~ V.r A!r (

Left Side-Porosity 1.0 10.0 0.640 var 0.640 1.0 1.0

Ri'ght SidePiomsity 1.) V.0 0.6-40 var .0 io

PlateThickness(Inn') 0.60( U.457 0.6100

PlaxCMaeralcopper triuia COPper

i~!:cthe effects of therITMa LerUIC' anld ir.ptdtince rnat chin--. O)re o~f jmsepr~tflccr,,'s the

foc-.icron cif the --n-,i!, ir rthe ':,-. t%~ It"tt~si~a..1l~"l:TLI 4.

mir im>,:m AT for the mar~itIMl nmtcof rai'Wh-ts vmer is ~l,.c~t ~d~

even lower ATs arc achieved using a sloped engine by sliding the iheat exchanger - sta.k - hcat

excchanzcr system in the of" t-,- 14,. n'. ". n r-o- r - it C

inlrearce Nyond that -which gives the lowet AT in the original location.

E. Radiai wtae rcszdi...

Radial wave prime movers with "was•her'" style stacks have been investigated?2 and are

related to the plane wave parallel plate engines in the sense that both have a constnt plt-,ic

spacing fromi one side of the stack to the other Fg. 7 i. crh,.-nvir o th. tu n ri.ld Ic-

being compared, AT for two different radial wave prime movers with varying plate spac:ng hav-,

been pNotted against the slope ratio and have been compared with the AT achievable using a

"'washer" s:-yle ertine. in thi 5:me rscrnw,,rs and wit-h uhe vrre r diAd lcncrihs and h.:cauionF.

Note that the actual slope between the p!ates in the radial system is completely determincd by the

number of plates, the plate thickness. and the radial location of ihe st,., ;erfcre, it iN

impossible to choose at cold side spacig a•d swk:,-p through a racne of s!ores.

The first radial system considered is, a scaled version of the plane wave system described in

Table I such that the resonant q ECV 1f t rada-..... .... • .I. .:.. .... : ,. ..

resonator f314 llz) The dirmensions and specifications of the 314 Hz radial vertical stck svstem

are riven in Table 2, and Fig. 8 shows AT as a function of sl,.pe ratio. The mirtmim _ST

calculated for the vertical p!at prime. m"ovr Cs 1xO tf

"washer" style engine. The second~radaal system considered is a model presently being worked

on which has an oFerating frequency of about 1.37 kHz. The dimens!o;:n and speci::cainr ut

the 1.37 kIlz radial veric"al,- stack .-. ctpm -- , i-n Tahls I at Fir Q) chrn9 - AT wz t fnr.,-,;,.

of slope ratio. The minimum AT calculated for thc vertical plate prime mover is 253 ,9"

compared to a low of 255.4WC for the -washer-" btl I engie.

In MYoth Or the ra(d! sy.stems 'NYl.,- t-ie ;4 r;f'r X?:f flA IV1O 4v Itflllo t. t '••it'

rather thani a -'\aser' -" i

sloped engins are ceifir;ed to exncm:;. .o'x ;

dhe sh-ape ratio value %khich- gives. a minimum 3Pf for the plifne wave en2ine ofLthble 1. ihi..

merans that the spacing in the rd!vert ic .1.cgn~cr~iee!i ~~y~ih~ ~.rn

spacing in th'-e comparable "was-her" st! e en~gines. A higher Isiope rat'& is achievable by

decreasing the radial diqtance of the engine from the center, but this would tend to move df-.

cn-iPne from outside the prc:;ýsun~:~ nl* u insidc :! uc ce ýdýl .&&i, r'i

loocitions of the hct and cold sides Jf the engin. and caw~ing the icasin sope to be in the

w'rong direction. Therefore, the small advantazge ga i ne by a carefully spaced, vertical pl-te,

trdadl prTimel mover over a -vshe a 6N* le j .-. " .... .. ..

might be nece-stary in construc:tion of such an, engine. It had been hoped that the variation in

platc spacing intrinsic to the radial vertical engine (sloped) geometry would he advantageoixs:

C de o'j- der -d cr f Ah-op 0 ..n.I -n'A~ i0it Cv-W1'C 1;~tfl vri

In :AT is predicted bet%%ceer the radiat vertical engine- an~d the radial -washer" style (parale! plate)

IAitA s -2). 314 H7. radial prime m~over specifications. *var" denotes quantities which Vary U ithen-1ne slope. Amibi.tnt temperaaureý is 29% K. a~nb-enz Pressure is 2(~tk..adtefudiFeicu~m. Lengths ýirc radiia. Ifi stances (i.e. there are` 162 cm betx~cen the cenwer (if the re-so-1amrad the inside of th~e cold l'a:cxeclia-cer.

Spel:fiCjtti-r Ope lTie Ccl -TX En(-ine 1-lct FIX Open Tube

U.) 11 (Cni1) 162.0~ 2.0 ".0 2.0,2.

11dicht (cmT) .5. 5.0 5.0 5.0

Pooiy1.0, 0.640 var 0.640 LO

E'rate~~~~~~~~ r lcns mi..' ~ It'

ADA297855

TA\BLE 3. 137 kHz radial prime mover specifications. "var denotes quantities -- hich varywith engine slope. Ambient temperature is 293 K, ambient pressure is I atm, and the fluid is a5 cc; Helium 40% Argon mixture. Lengths are radial distances (i.e. there are 10.62 cm betweenthe center of the resonator and the inside of the cold heat exchanzer.

Specification Open Tuhe Cold [LX Engine Hot HX Open Tube

Lenzth (cm) 10.62 1.27 1.25 0.1 2.0

Fleight (cm) 10.16 I0.16 10.16 I0.16 10.16

Porosity 1.0 0.450 var' 0.70 1.0

Plate Thickness (Mm) 1.03-$ 0.1524 1.0

Plate Material copper mica copper

IV. Thermoacoustie Helmholtz Resonat.r

The construction of the thennoacousticallv driven Helniholt; resonator of Fig 10 was

described in last yatr's report. The advantage of this type of prime mover i, that it is a cCmIpa t,low-frequency round source. The operating frequency of thi5 small prime nover is about 220

Hz. Experiments were performed using a conventional copper fin cold heat cxchancer and using

a section of cooled open tube. 'hiee i-ueresri,'g ihitigs were fo.md. Fir;r, t0.11aý,J iM;,,!ia, of1

the heat exchanger - stack - heat exchanger svs:em (the location which gives the lowest AM) is

such that the first obstruction to air flow, occurs at the point where a un fonm velocitv is achievedin the body of the resonator. This occur- chscr Ao oo.

copper fin heat exchanger, since for the open :i;;g the first obstruction is the stack itself. Figures

locations wvith a ccd 1he: .... mc. r ,, . . .. v " ' ,' ..... T " ,,,,t.. . .... ;I ... . z.....: I11 and 12 that the open tube cooling cuts acoustic losstes and requires less polh\cr to bc

delivered to th-e nichrome wire hea:ter for o:.•e: w• occur. "ihbird. in ;a te~t o)f o,:r:;zl onrrlu~tnon it

wa; tor,-, ! r d -"rbv "," h "in a..... .. .r.-; ," , .. t... 07 " - in -.- ..... "~ *I.t .rn- f,-lwI.i,•

ADA297 855

hot side of the stack, requtires a much low,%er power to Ibc supplied to the nichrome wire heater for

.niset (when Q c) thin whlenl the neckils ry cingdwn (cpfxFic. I I

Anothler accidentala but interesting fir~di ng was that the radial prime mover described in the

previous section car, operate as a thcrmnoacoustically driven Ilernihol:7 resoinator. When 'he

temperature differnceiý was.. 'i nnrz th P ktvick an d the' microflhrinc nont Wns remonved, a

weak 106 Hzt tonle (h crirrcspond-s very nicely to the predicted Hl-lcm!'oltz resonance for this

Meso nator) was heard.

,V. References

J.3. A. Lightfoo, W. P. Arnott, R. Raspe: a nd H. E . Baý4. ")esl(;nI of a radial miodethermoacoustic prime mnover and cxcicx1obevtos". Aco0tis-. SOC. An . 9.6,3 22)1(1994).

2.W. P. Arrnott. J. A. Lightfoot, R. Raspet and FT. Moosmiillcr, "Rad-ial w-ave ther'MOUCOTsticenLin es: Theory ind examples, for refriger'xtors, prime move,-,, ,.!id high-giin riarrow-bandwidth photoacoustic spectrometers," (in prcparation).,

3. W. P. Arno-t, J. L~ightfoot, R. Raspet and H. E.Bass. "Radial versus plane wavethermoacoustic engines: Which is best?" J. Acoust. Soc. Am. 96. 32271 (1994).

4. R. Raspet. 3. A. Lightfoot, 1. R. Belche-r snd H. E. Bass, '1herinoacoustic ondSource inl'the H-elmholtz limii." J. Acoust. Soc. Am.'96, 3221 (1994.1

5. 1. A. Lightfoot, Rilchard Raspet, H. E. Bass and W. Patrick Arniu,, "Pla--e and radial wavethroacousw ung-Ines with Variable Plate spacing."iJ. Acoust. Soc. Am-. 971. 3410 (1995,.

0. G. W. Swift, "T=11aioaCOUS~ic an'-ines," J. Acou.,t. Soc. Ann. 184. i14 i.5- 11 6ý

7. ennett, "Active cooling for dow%-nhole ins~r, iment,)7on: A tninititre thermoaccnizticrefrigerator." dissertation from the University of New Mexico (1991).

S8. D). E. ffalL. BasirAoust.ýirs. (John Wi!ey and Sons, Inc.. New York. 9zs6) 286-2189.

9. N. Rotr and G. Zovzoulas, -Thenra~!!y eriven aCt-ns-ic usceil!1-ionc -art !V: Tv 1 CS wt~haiable cross-se~ction,- J. A-pp. Math. and Phys. 27, 197-224 (1976,ý.

-0.A. D. Pre.Acoustic-s: A4n liftrod~tclio to Its ph. Siczl r.c;,' dApiaw:.(Ameri-can lnstiture' of Physics, Ne%.r York, 199,

11. W. P. Ax-nott. 11. L. 1asý-. a!",! R<. Raspar `'Gtenerdft iunicli jh ~'~ !~ ~stacks h-avin' rirrm Thýqped pore cossccrz'; J. A cowu Soc \. -,1 f . 1283 ;7(199 I).

ADA297 855

Stackstainless steel topand bottom plates

swatne" steel~suppoft rods

7 -~ -

7-___ - -- - .A

o ~ -1034 i. od 0.253_in.___ -- 1034 in.

Id932 n a10in - -4- 9-6, n

MicadSack Miac a Slaners 0,4e2 Ptes5 c

stack height -4 in.# of micaI plates 177

F u Re : Radi;Il morle horIzo~ntu Plat fe t (o tiltA Zt ttt k,1V Iý.t T~ . Ih,f

ADA297855

Resonator

staioles od.t2eIn

groove o.d. 9.2 in.

groove depth 0 . 180 in.

* aluminum

-~.14 in.W~. 12 in.

hegh 4 in.

od. 1 14 i n.stainless steel hih .6 n

Figure 2: Raialcriigi ie. resonator.

ADA297855

(a) stack of plates

cold_ _ hot

: " r

(b)

Fluid

jSolid it.

Fluid Y

[ oid'I

Fluid

FigureI3 Parallel plate engite geometry. (a) Overall view, anti (Inx dd view. Pla-teshave thirknris t. and fluid layers have thicknsies y,

ADA297855

IS*lidFluid

.Figure 4: Sloped engi te, gecmlet ry. (a.vra 1vw ald (b xpwd vie. Pk,;thikkri&ss t, fluid layers havC thicktiess y(r), and yo0 is the' fluid Iaycr thickiticss at theleftsitle of the stack,

ADA297855

160

1655

150

c. 14 5 0

140

135 d

S~130

. * 11 * 3 ,1 * It ! * I i,, II,

-2 0 2 4 6 8 10 12 14 16 18

slope ratio

mmni . 2.6.6 l) .t, 4.8-7 mm, c) yg 0.919 m,. d9. M/ - f. 11), - 1 = 065

mm. S&didf dots represcnt minima in AT for curves similar to a,-" with Iifferent st va!,irs."The anbient heat exchanig-r temperature is 293 K.

ADA 297855

- -- - ~lowest ovrall ATlerbest c ~ira contact

LI~~~~~~ --------------------- Ki-2.268iK(cold) -2.268ic(hot)

--__ _ -- - - - - - - - -

l owestprle plate A

Figure 6: Simnple visual reptesentaition of plate spacings which provide the lowest overallAT, the lowest parallel plate AT , and the best thermial contaoct between the fluid and thesolid.

ADA297855

Svertical stack washer-style stack

e Tevertical stack wahe-syl sntack uvfiFigutre 7: Two different styles of radlial engines. The vertical stack ha a natural varyitgplate spacing, while the "washer* style stack is simllar to the plane parallel plate stack-since there is a constant plate sparing from one side to the other.

ADA297855

190

185

180

00 175

170/

165 160.0 OC

0.16 0.18 0.20 0.22 0.24 0.26 0.28

slope ratio~ur~ : h~~ rern~rdI ~ ~;~ t .~. - -

tical plate radial :zystcmfl The b.ywesf AT achieveff by~ a similar "washer- l~ vi W n is161.1 '(7.

ADA297855

280

275

270

"' 265

260253.9 0C

255

0.36 0.38 0.40 0.42 0.44 0.46 0,48

slope ratio

veruical plate radial s•stem. The lowest AT achieved •yya similar "washer !tyle enmine

is 255.4 0C.

ADA297855

Helmh:oltz Resonator

:Cold fIX or Coo)ing Ring

1"CrmwcStadck .2

Nichrorne Wire Heater _____

ADA297855

Helmholtz ResonatorWithout Heat Exchanger

90-Neck, Resonatc.,

85- Interface

S75-

70-

65-

4C I

60- S• 0 0.01 0.02 0.0"3 0.04, 0.05 0.6 0.07 0.0)8 0.0 0.1S!i!. stack location (fraction of wavdetnth)

Figure 11: Power dissipated in nirchro.n........ , ...... , .... .....................- with cooled openx tube.

ADA297855

Helmholtz ResonatorWith Heat Exchanger

125 - ~-A

Neck, ResonatorS~5 120-

Interface115-

C110-

105

100-

95-j

o 0.01 0.02 0.03 0.04 0.05 0.06 0 .07 0.08 0.09 0.1stack location (fraction of wavelingth)

'Fiatire -12: Thw I is-'ipatcd ki n>Lrft f~ ri 11 at *4--,t.ct or diffver'Tulsjt rL Jla Ck atjOj-is

with rctIf fie.-t c:hnr

ADA297855

Helmholtz Resonator0.05-4

AA

0.04 ACL A

C30.03- A

0 A

nA A

0.01 .

"0 1

0 20 40 60 0 100 120 140 160 18Wpower dissipated in hot wire (watts)

• ' :~ .M eckr~c•.n n NeckU.Ji Ak

Figure 13: I/Q a-- a fuiction (if uth power dissipated in the nicrirom, wile fiwur C ,i 1,1-W'nr. 1orientat ions of t he resonator.

ADA297855

-OFF1CE-IOF- NAVAL RFESFARCHPUBLICATIONS IPATENTS / PRESENTATIONS / IHONORS REPOR'T

I JUNE 1994 through 3 1 May 1995

R -T Ntinihc: 3'26973esMO

ContramLGr.int Number: N00014-93-1- 112;

Confract/,Cir~,m Tiiic: piCr¶!Si WxeTr c'q E~'

Prir.cipal hInve )r: Richard Raspct

Mailing Addres': National Ccn*.,r for Physical AcousricsThe University o~f mixd~zýippiUniversity, NIS 3S677

Phoic Numbmr O-Z25O

C MailI Addrcss: . UUsarc~;e

.1. Numernvof Patpem Suhrio!toI o Re'fereed JOurnal3 but not yc 5hbM~: .. j

l. Nuiu~cr of i'apzLrs PlutlishAd in, Refer,-'j~ 30Curnal: .Q....(list atwacheid)

C. NmKb~r of flcioký or (Thv~perN Sn'initined Imt nn ot N-iblu~isjhed.

d'. Numi~cr of Books or Ch, pte.rz Pub'isl.ed: ....Q...

e. ' Number ofPrintzc! Terhnic21 Repor-.Q A

f. Number of Paurenrý riikd: _Ql

g Nuber.~i'4teuts GranwLd:_JL

h. Number of Invited Pre~eln!rioims at Work~tops or Prof. Society Meetilnc\: .L

I. Number of Pr $f n-ations t' Work'tIops Cr Prof. Socrioly Meetingý:

Crad!SIAMBnt I a~ 'u:[,s_0_ inz~udm,n-

(r (Id Sttl~r i.;u N11 ii Irl I% Id r t'. f

ADA297855

OFFICE OF NAVAL RESEARCI IPUBLICATIONS I PATENTS / PRESENTArIONS / HONORS REPC)RT

I JUNE 199-1 through 31 May 1995

AITACHMNFNTS

a. Papers Submitted to Refereed Joarnal

W. Patrick Arnott, Jay A. Lighfoot, Ri~hard Raspet and lans Moos-nuller, "Radial Wavethermoacoustic engines: Theory and examples for refrigerators, prime movers. and highgain narrow bandwidth photoacoustic spectrometers," submitted to J. Acoust. Soc. Am.,January 1995