An Experimental Facility for Compressible Flow*

Transcription

1 Int. J. Engng Ed. Vol. 15, No. 1, pp. 58±63, X/91 $ rintd in Grat Britain. # 1999 TEMUS ublications. An Exprimntal Facility for Comprssibl Flow* C. Y. LAM and C. Y. LIU School of Mchanical and roduction Enginring, Nanyang Tchnological Univrsity, Singapor , Rpublic of Singapor. mcylam@ntu.du.sg This papr dscribs a low-cost, quit and portabl facility for th dmonstration of comprssibl air flow succssfully dvlopd by a group of tn mchanical nginring undrgraduat studnts during a two-wk projct modul of thir in-hous practical training programm. Th facility is abl to produc a flow of maximum Mach numbr of about 1.7 through a convrging-divrging nozzl. Th phnomnon of suprsonic flow such as choking and th formation of shock wavs can b dmonstratd. Th facility dvlopd is now bing usd as an undrgraduat projct xprimnt. Du to th quitnss and portability of th facility, it is also wll suitd for classroom dmonstrations. SUMMARY OF EDUCATIONAL ASECTS OF THE AER 1. Th papr dscribs nw quipmnt usful in mchanical and aronautical nginring courss.. Th lvl of studnts involvd in th us of th quipmnt is typically third-yar undrgraduats in mchanical nginring. 3. Th quipmnt dscribd is xtrmly low cost and portabl, and is comparativly quit, yt capabl of producing a suprsonic stram of Mach numbr of about 1.7. It is probably th first of its kind in trms of cost, portability and prformanc. 4. Th arrangmnt can b dvisd for cours work to dmonstrat comprssibl flow phnomnon and to study th flow through a convrgingdivrging nozzl from low to high spds, including th choking phnomnon and th dtrmination of shock wav movmnt insid such a nozzl basd on prssur masurmnts. 5. A suitabl accompanying txt is Fluid Mchanics, third dition, by Frank M. Whit, McGraw-Hill (1994). 6. Th rig dvlopd has bn usd by third-yar undrgraduats. It is found that th xprimnt succssfully rinforcs studnts' undrstanding of th comprssibl flow thory. Th studnts wr amazd by th high spd such a low cost and compact rig can achiv. INTRODUCTION IN GAS FLOWS of nginring intrst, th spd of flow is oftn sufficintly high that th * Accptd 1 Novmbr flow bcoms comprssibl. At such high spds, th flow xhibits som distinct faturs such as th choking phnomnon and th formation of shock wavs. Comprssibl flow has thus bn an important topic in nginring curriculum, particularly in th arospac nginring. Traditionally, comprssibl flow xprimnts ar carrid out in a suprsonic wind tunnl. Such xprimnts ar costly, noisy and th durations for taking masurmnts ar usually short, if th flow is not continuous. rior to masurmnts, prparation is oftn rquird to charg th air rsrvoir that producs a high total prssur for th air stram. Sinc th suprsonic wind tunnl is costly and bulky, it is sldom usd by undrgraduat studnts to study th comprssibl flow phnomnon. Th chapr and lss bulky altrnativ availabl is th bnch-top typ comprssibl flow rigs. Thy can b purchasd from ducational quipmnt supplirs. Ths rigs usually mploy a multi-stag cntrifugal comprssor drivn by a motor to dlivr th flow through a convrging-divrging nozzl. Th nois lvl is still quit high du to th multistag comprssor opration. With svral sts oprating, th studnts must war ar protctors. Vry oftn, th highst spd thy can produc is slightly ovr Mach 1 and th flow quickly bcoms subsonic in th divrging sction. As a rsult, thy do not provid masurmnt capability in th divrging sction. Th instrumntation of ths rigs is usually th primitiv U-tub manomtrs. Th siz and wight of such bnchtop unit ar still considrabl and th unit cannot b portabl. Th cost of a st of th bnch-top unit, although much chapr than th wind tunnl, is of th ordr of US$10,000. Th aim of th prsnt task is to dvlop a comprssibl flow facility which is low-cost, quit and portabl, yt abl to produc a suprsonic flow 58

2 An Exprimntal Facility for Comprssibl Flow 59 Duration Tabl 1. Th projct schdul Activitis and classroom dmonstrations. It was thrfor proposd as a projct for th projct modul. 3 days rojct familiarisation, planning and dsigning 4 days Fabrication days Tsting and final modifications days rparations of rport and oral prsntation high nough to dmonstrat th dvlopmnt and movmnt of a shock wav that is oftn part of a rlatd undrgraduat curriculum. Th dvlopmnt involvs diffrnt nginring procsss including th dsign, fabrication and tsting of th facility. It thus falls natly into th objctivs [1] of th rojct modul of th in-hous practical training programm dvisd in th School of Mchanical and roduction Enginring at th Nanyang Tchnological Univrsity for studnts to gain first-hand xprinc in dsign, manufactur, construction and assmbly of parts and tsting of th final product that nithr lcturs, tutorials nor laboratory sssions can offr. Th in-hous practical training programm, prviously rportd in rfrncs [] and [3], is an intnsiv tn-wk compulsory training programm undrtakn by th studnts at th nd of thir scond yar of study. It includs a two-wk projct modul in which studnts ar dividd into groups of about tn and ach group is rquird to work on a diffrnt mchanical nginring rlatd product right from scratch to finish. Th studnts ar motivatd by th fact that th projct modul poss a challng for thm to put th knowldg thy larn in producing a practical nginring product which thy can physically fl and driv satisfaction if th projct is succssful. For this rason, thy ar oftn nthusiastic and contribut good ffort and tamwork. Exampls of som products prviously dvlopd in th projct modul which hav bn publishd in th litratur ar a man-powrd aircraft [4] and a smok-wir flow visualisation rig [5]. In addition to provid th studnts an opportunity to larn comprssibl flow phnomnon and dvlop its associatd hardwar, th dvlopmnt of a comprssibl flow facility also srvs a dual purpos of producing a practical comprssibl flow rig that can b usd for laboratory invstigations THE LANNING OF THE ROJECT rior to th start of th projct, raw matrials and som quipmnt had bn purchasd for th studnts. Ths includd a solid cylindrical rspx rod, a rspx sht, silicon tubing, a domstic vacuum clanr with an lctronic spd controllr, a scanning valv, a prssur transducr, a DC powr supply, a digital mtr and an inclind manomtr. Th total duration of th projct was two wks, which was quivalnt to lvn working days. Th projct schdul is shown in Tabl 1. At th bginning of th projct, th studnts wr brifd on th thory of comprssibl flow through a convrging-divrging nozzl and th dsign rquirmnts of th facility. During th two projct wks, a tchnician was assignd to hlp th studnts in sourcing matrials not pr-providd and in particular to train and hlp th studnts in th fabrication phas. Tamwork was promotd by ltting th studnts organis and shar various activitis thmslvs. Consultation with th suprvisor was availabl at all tim. Short discussions with suprvisor wr also hld at th nd of ach day. In particular, lngthy discussions had bn hld to finalis th dsign bfor fabrication and bfor th oral prsntation on th last Saturday. Th following sctions dscrib th facility dvlopd and th tsting rsults. THE EXERIMENTAL FACILITY Th facility primarily consists of thr partsð namly th convrging-divrging nozzl to produc suprsonic flow, th driv unit to induc th flow through th nozzl and th instrumntation to facilitat th prssur masurmnts. In addition, a baromtr is rquird to masur th ambint prssur for data analysis. Th convrging-divrging nozzl was mad from a cylindrical rspx rod. Figur 1 shows th gomtry and dimnsions of th nozzl. Upstram Fig. 1. Th convrging-divrging nozzl. (All dimnsions ar in mm).

3 60 C. Lam and C. Liu Tabl. Locations of th prssur tappings (x 0 at B and incrass downstram) Tapping x mm ± of th convrging sction, thr is an inlt portion AB of lngth 53. mm and constant intrnal diamtr of 5.4 mm. Th inlt allows th mass flux _m to b dtrmind, if dsird, from a prssur masurmnt through a prssur tapping installd on it with th aid of carful calibration rsult. Th convrging sction BC of lngth 13 mm, has a contour of th shap of a circular arc of radius mm with cntr on th plan of th throat ntranc. This is to nsur th ara gradint to b continuous at position C so that th flow is smooth thr. Th convrging sction is rsponsibl to acclrat th flow from low subsonic spds to high subsonic spds. Th throat CD of th nozzl is of lngth 15.9 mm along with diamtr constant at 9.7 mm. Th throat is followd by a divrging sction of lngth mm and constant divrging angl of Th divrging angl is small to avoid possibl flow sparation undr advrs prssur gradint. At subsonic spds, th divrging sction is rsponsibl to dclrat th flow gradually for a smooth prssur rcovry. At high spds, aftr th nozzl is chokd, th divrging sction is rsponsibl to acclrat th flow to suprsonic spds up to th location of th normal shock wav, as dpictd by th suprsonic flow thory [6]. Aftr th divrging sction, th flow ntrs a sction EF of constant diamtr which can b attachd to th inlt of th driv unit via a flang. Machining of th nozzl was don using a convntional lath machin. Bcaus of th small intrnal diamtr of th nozzl as compard to its lngth, th nozzl was dividd into thr sctions. Each sction was machind and polishd sparatly bfor thy wr alignd and joind togthr. A total of thirtn prssur tappings, of diamtr 1 mm wr drilld along th nozzl for prssur masurmnts. Th numbring and th locations of th tappings ar givn in Tabl. Most of th tappings ar locatd at a short distanc downstram of th throat bcaus suprsonic flow and shock wavs ar producd in that rgion. Th driv unit consists of an AC motor attachd to a cntrifugal vacuum air pump with an lctronic spd controllr, which wr dismantld from a domstic vacuum clanr. Th spd of th pump can b varid from about 1,000 rpm to 5,000 rpm in ordr to crat diffrnt suction prssur. Th powr of th motor is 1400 W. To masur th low diffrntial prssur at th inlt of th nozzl, an inclind watr manomtr is connctd to tapping numbr 1. Th inclination of th manomtr can b adjustd to control th snsitivity of th manomtr, spcially at low spds. At th throat and along th divrging sction of th nozzl, th flow spd and hnc th diffrntial prssur is high and th prssur tappings ar connctd to a common strain gaug prssur transducr via a scanning valv, which allows a particular tapping to b slctd for masurmnt. Th output of th transducr is calibratd to prssur and is displayd on a digital mtr. For compactnss, th driv unit and th instrumnts ar housd in a box, masurd mrly 35 cm 30 cm 5 cm. Th wight of th ntir rig including th nozzl is lss than 4 kg. Figur shows a schmatic diagram of th facility. Th nozzl can b attachd on th air pump bfor masurmnts ar mad. With this st-up, th prssur variations along th nozzl at diffrnt flow spds can b masurd asily. Th total cost of th matrial of th facility was undr $1000. As it is quit and portabl, it can b usd in th laboratory as wll as in th classroom for dmonstrations. RESULTS AND DISCUSSION Th facility was first subjctd to a consistncy tst. During th tst, th motor was switchd on and was adjustd to maximum spd. Thr sts of prssur masurmnts along th nozzl wr takn at 15 minut intrvals. Th total running tim of th facility was thus mor than 30 minuts, which is much longr than th tim rquird to Fig.. Schmatic diagram of th facility.

4 An Exprimntal Facility for Comprssibl Flow 61 prform th comprssibl flow xprimnt. Th tst rsults showd that th maximum drift in diffrntial prssur was about 1.8%, wll within th xprimntal uncrtaintis. It can thus b concludd that th facility is consistnt. At diffrnt motor spd sttings, prssur masurmnts along th nozzl wr mad. From th xprimntal data, assuming isntropic flow, th local Mach numbr [6] for subsonic flow and flow upstram of shock wav is givn by: ÿ 1 M = ÿ 1 1 whr is th spcific hat ratio, 01 is th ambint prssur, and M ar th local prssur and Mach numbr rspctivly. Hr th prssur ratio = 01 can b obtaind from: 1 ÿ 01 ÿ whr 01 ÿ is th gaug prssur dirctly takn from th manomtr and th digital mtr. For flow downstram of shock wav, th local Mach numbr is givn by: ÿ 1 M = ÿ 1 whr 0 is th total prssur downstram of th shock wav. To dtrmin th Mach numbr, 0 is thus rquird which can b obtaind by considring th nozzl xit condition for which: 0 A A A 1 A 0 A A 3 whr A is th cross-sction ara of th nozzl; th subscripts 1, and rfr to upstram and downstram of th shock wav and xit of th nozzl; and th suprscript rfrs to th critical condition. Now from normal shock rlationships, w hav: and A A 8 ÿ 1 1 >< 1 M >: 1 8 >< 0 >: 1 1 ÿ 1 M M 9 >= >; 9 >= >; 1 = ÿ1 = ÿ 1 whr M is th Mach numbr at th xit of th nozzl. utting into (3) and rarranging, togthr with A 1 A t whr A t is th throat ara, yilds: " M ÿ 1 ÿ 1 1 ÿ 1 ÿ 1 1 = ÿ 1 # A t =A 1= 4a 1 = 01 For th nozzl usd, with 1:4 for air, 8 " M ÿ:5 6:5 0:0356 # 9 < ÿ 1= = : ; 01 1= 4b This givs M. Thn 0 can b obtaind by using () at th nozzl xit, i ÿ 1 = ÿ 1 M 5 whr 01 ÿ and 01 ÿ ar th gaug prssurs dirctly takn from th digital mtr. Th lattr corrsponds to prssur tapping 13. Th location of th shock wav must also b dtrmind so that th appropriat quation (1) or () can b applid to giv th corrct Mach numbrs. It can b dtrmind by finding th Mach numbr M 1 just upstram of th shock using th normal shock rlationship: M1 ÿ 1 M1 = ÿ 1 1 M1 ÿ ÿ 1 6 or by using th standard normal shock wav tabl. Having found M 1, th ara at th shock location A s can b dtrmind from th ara rlation: 8 ÿ 1 A s As A t A 1 >< 1 1 M 1 >: 1 M 1 9 >= >; 1 = ÿ 1 7 Knowing A s, th shock wav location x s can b found from th gomtry of th nozzl. For th nozzl usd, with 1:4, 8 " 9 < 1 1 0:M 3 = 1 4:85 #1=ÿ1 : M 1 1: ; x s tan :98 8:9 8 Th variations of prssur ratio and local Mach numbr in th stramwis dirction obtaind by using th abov procdur ar plottd in Figs 3 and 4 rspctivly. Whn th motor spd was low, th

5 6 C. Lam and C. Liu Fig. 3. Variations of prssur ratio = 01 with x. prssur droppd along th convrging sction and rachd a minimum at th throat aftr which it rcovrd along th divrging sction. This corrspondd to an incras in flow spd along th convrging sction followd by a dcras in flow spd along th divrging sction as dpictd by th incomprssibl continuity quation and as also shown in Fig. 4. As motor spd was incrasd, th prssur droppd and rcovry in th convrging sction as wll as in th divrging sction bcam mor rapid. Whn th prssur ratio at th throat was rducd to about 0.53, th xprimntal critical prssur ratio, th Mach numbr at th throat incrasd to about 1. At this point, th nozzl was chokd. Byond choking, at highr motor spds, th flow condition in th convrging sction and at th throat bcam indpndnt on motor spd. Fig. 4. Variations of local Mach numbr M with x.

6 An Exprimntal Facility for Comprssibl Flow 63 Tabl 3. Locations of th shock wavs Spd stting Shock location x s mm ±±±±±± ±±±± 40.6 ±--±--&±--± ±-±-±-4± -±-± 4.9 ÐÐÐÐÐÐ 46.0 ÐÐÐ&&ÐÐÐ 47.3 Th prssur continud to drop aftr th throat, indicating th occurrnc of suprsonic flow rgions. Furthr downstram, th prssur droppd to a minimum and thn rcovrd. Th prssur rcovry was rapid at first and thn bcam gradual. Th rapid rcovry of prssur in th divrging sction showd th formation of shock wavs across which nrgy dissipatd rapidly. Th locations of th shock wavs x s calculatd basd on th nozzl xit condition by using th procdur dscribd arlir ar tabulatd in Tabl 3 and ar indicatd by `s' in Figs 3 and 4. Aftr th shock wavs, th flow quickly bcam subsonic. It can b sn in Tabl 3 and in Figs 3 and 4 that th shock wav movd downstram as motor spd was incrasd. At maximum motor spd, th flow spd rachd to a maximum Mach numbr of about 1.7 at about 16.5 mm downstram of th throat. CONCLUDING REMARKS A low-cost, quit and portabl xprimntal facility for th dmonstration of suprsonic flow phnomnon has bn succssfully dsignd, fabricatd and tstd as a studnt practical training projct. Th facility can b usd in laboratory classs and can also b asily carrid to th classrooms for dmonstrations of comprssibl flow. It is abl to show th prssur and Mach numbr variations along a simpl convrgingdivrging nozzl from subsonic to suprsonic spd. With ths variations, th choking phnomnon, th dvlopmnt of suprsonic flow and th formation and movmnt of shock wavs can all b obsrvd. Th rsults agr wll with th comprssibl flow thory. Th highst Mach numbr achivabl is about 1.7, wll suitd for an undrgraduat xprimnt in th ara of arodynamics. REFERENCES 1. Information on In-hous ractical Training, School of Mchanical and roduction Enginring, Nanyang Tchnological Univrsity, Singapor (1994).. S. Thiruvarudchlvan, An undrgraduat in-hous practical training projct in mchanical and production nginring, roc. 1st Australasian Education and Enginring Confrnc, apr 7B5, Univrsity of Sydny (1989). 3. A. Amn, Effctivnss of projct modul as part of an in-hous practical training programm, Int. J. Mch. Eng. Edu., 18, (l990) pp. 187± R. S. J. almr and K. Shrwin, A man-powrd aircraft as a studnt projct, Int. J. Mch. Eng. Edu., 14, (1986) pp. 73± S. C. M. Yu and L.. Chua, Construction of a smok-wir rig for visualisation of complx thr-dimnsional flow, Int. J. Engng. Ed., 9, (1993) pp. 467± J. D. Andrson, Fundamntals of Arodynamics, nd d., McGraw-Hill (1991). C. Y. Lam holds a B.Sc.(Eng) dgr with first class honours and a h.d. dgr, both in Aronautical Enginring from th Univrsity of London. H is an associat profssor in th School of Mchanical and roduction Enginring at th Nanyang Tchnological Univrsity, Singapor. His currnt intrsts includ computational fluid dynamics, mathmatical modlling, micro-computr applications and anthropomtry. H is a Chartrd Enginr, a mmbr of th IMchE and a snior mmbr of AIAA. H is listd in Who's Who in th World. C. Y. Liu obtaind his h.d. in During th past 30 yars, h has taught in svral univrsitis in diffrnt countris. His currnt rsarch intrsts ar masurmnt tchniqus and hat transfr. H has just rtird rcntly. Currntly, h is an adjunct profssor in th School of Mchanical and roduction Enginring at th Nanyang Tchnological Univrsity.