ADIABATIC CAPILLARY TUBE FLOW IN A TRANSCRITICAL CARBON DIOXIDE HEAT PUMP

Transcription

1 ADIABATIC CAPILLARY TUBE FLOW IN A TRANSCRITICAL CARBON DIOXIDE HEAT PUMP Neeraj Arawa, Souvk Bhattacharyya Department of Mechanca Enneern Indan Insttute of Technooy Kharapur, Inda 730 ABSTRACT An adabatc homoeneous mode has been deveoped to nvestate the fow characterstcs n the capary tube of a transcrtca carbon doxde heat pump system. Mass, enery and momentum conservaton equatons are soved smutaneousy usn fnte dfference technque. The supercrtca sne phase fud fow and sub-crtca two phase fow are consdered separatey. Three frcton factor correatons (Church, Ln, and Frede) and four vscosty modes (Mcadams, Ccchtt, Ducker and Ln) are tested for comparatve sutabty. The extreme choked condton at the outet s aso nvestated for maxmum mass fow rate. Sub-crtca and super-crtca thermodynamc and transport propertes of CO are cacuated empoyn a precson property code. Numerca resuts show pressure radent to be consderaby hh for CO than the tradtona refrerants, yedn a shorter capary tube enth. Choce of vscosty mode eads to nsnfcant varaton n resuts unke that n CFC refrerants. Keywords: Capary tube, transcrtca, CO, adabatc, homoeneous two phase fow.. INTRODUCTION As a natura refrerant, CO s the preferred choce today for ts envronmentay benn nature and arey benefca heat transfer and safety characterstcs compared to the currenty used refrerants. Fow nsde the capary tube of a refreraton system s compex n nature. Numerous combnatons of bore and enth can be provded to obtan the desred restrcton. Tube dameter and enth at a ven operatn condtons s the man concern to desn a capary tube. In redesnn the system usn aternatve refrerants, therefore, t s vta and crtca to seect a capary tube whch s compatbe wth the system components. In a transcrtca CO refreraton cyce, pressure and temperature are two ndependent parameters unke the common sub-crtca cyce; thus functonn of the capary tube s expected to be dfferent as compared to sub-crtca cyce. Therefore, t s desrabe to nvestate the fow characterstcs n the capary tube for a transcrtca CO heat pump system. Severa studes have been reported on fow characterzaton of adabatc capary tube wth haocarbon and hydrocarbon refrerants. Bansa et a. [] deveoped a homoeneous two phase fow mode to study the performance of adabatc capary tubes for HFC-34a. Sam et a. [] proposed a numerca mode to predct the capary behavour for HCFC- aternatves R-40A, R-40B and R-407C under dfferent fow remes. Krtsadathkarn et a. [3] presented a numerca study on the oca pressure dstrbuton of some common tradtona and aternatve refrerants R, R34a, R409A and R409A. Yufen et a. [4] presented a homoeneous mode ncudn the metastabe qud and metastabe two-phase reon to assess the effect of varous frcton factor equatons, two-phase vscosty correatons on smuaton the behavour of capary tubes. Bansa and Wan [5] presented a homoeneous smuaton mode to account for the addtona choked fow condtons for pure refrerants R34a and R600a n adabatc capary tubes. It can be nferred that most studes concentrated on the HFCs, hydrocarbon refrerants and ther mxtures. Reatvey, Author for correspondence; te: ; souvk@mech.tkp.ernet.n 7 th IIR Gustav Lorentzen Conference on Natura Workn Fuds, Trondhem, Norway, May 8-3, 006

2 much ess nformaton s currenty avaabe n the open terature on fow characterstcs of capary tube n transcrtca CO systems. Chen and Gu [6] deveoped a non-adabatc homoeneous capary tube mode for a transcrtca CO cyce. They proposed a new transcrtca refreraton cyce combnn the characterstcs of heat transfer and expanson nto one capary tube by assembn the capary tube n an accumuator or sucton ne. Parametrc study for coon pressure, evaporatn temperature, ambent heat transfer coeffcent and capary sze was presented. Recenty, Madsen et a. [7] has reported a study on the adabatc capary tube n a transcrtca CO system. However, fow was consdered to be senthapc whch s not achevabe n reaty; crtca expanaton on the mathematca mode and reated assumptons were not ncuded n the artce. In the present study an adabatc homoeneous mode s empoyed a frst step to nvestate the fow characterstcs n the capary tube for a carbon doxde heat pump, where the fow s transcrtca n nature.. MATHEMATICAL MODEL The mode s based on of mass, enery and momentum conservaton equatons, whch are soved smutaneousy usn fnte dfference scheme and ncorporatn property varaton for better accuracy. The capary tube can be dvded nto three dstnct fow reons, namey, supercrtca fow reon -, transcrtca fow reon -3 and the subcrtca fow reon 3-4 as shown n Fures and. F.. Varous fow remes n an adabatc capary tube 40 0 Pressure (bar) Enthapy (kj/k) F.. Locaton of state ponts -4 n the cyce daram on p-h pane 7 th IIR Gustav Lorentzen Conference on Natura Workn Fuds, Trondhem, Norway, May 8-3, 006

3 p p3 p5 p7 p9 p F. 3. Lontudna dscretsaton for the capary tube The tota tube enth may be wrtten as: L = L sup + L subq + L The expanson process from pont to 4 s shown n F. on the pressure-enthapy pane. The mode s based on the foown assumptons: Straht capary tube wth constant nner dameter and rouhness Homoeneous and one dmensona fow throuh the capary tube Fow s adabatc wth no work done Thermodynamc equbrum prevas n the system Refrerant s free of o Fow throuh the capary tube s fuy deveoped turbuent fow Entrance osses are nebe The subsequent parametrc study ncudes the effect of varous desn parameters, namey, tube dameter, tube reatve rouhness and refrerant fow rate. The capary tube s dscretsed nto a number of ontudna eements (Fure 3) to enabe the sharp chanes n CO property to be ncuded n the anayss. The conservaton of mass for steady fow n an eement s ven by: AV d = 0 () υ Snce area s constant for a straht tube: V d = 0 () υ. AV AV+ m = = (3) υ υ + For steady state adabatc fow wth no externa work and neectn the eevaton dfference, the enery conservaton equaton ets smpfed to: G dh + dυ = 0 (4) Two phase enthapy and specfc voume are expressed as: h = h + xh, υ = υ + xυ (5) Substtutn Eq. (5) nto Eq. (4): G G ( ) ( ) υ x 0 h G υ υ x h h υ υ = (6) 7 th IIR Gustav Lorentzen Conference on Natura Workn Fuds, Trondhem, Norway, May 8-3, 006

4 Ths quadratc equaton can be soved for x +. From the conservaton of momentum equaton, the dfference n forces apped to the eement due to dra and pressure dfference on opposte ends of the eement shoud be equa to that needed to acceerate the fud, ven by: d V dp f G = GdV (7) D D ρ dp f G V dv d = From Eq. (), substtutn dv V d ρ = n Eq. (8) yeds: ρ (8) D d ρ d = f ρ ρ G dp (9) Ths needs to be nterated frst between and for the supercrtca reon and then between 3 and 4 for the post-saturated reon. The overnn equatons are couped equatons and are soved smutaneousy for capary tube enth empoyn fnte dfference approxmaton by an teratve technque. Pressure s taken as an ndependent parameter. Based on newy avaabe precson thermodynamc and transport property reatons, a computer code COPROP was deveoped and that has been nterated wth the fow mode to yed resuts presented n ths artce [8]. Church correaton for frcton factor s empoyed n sne-phase fow whe Ln and Frede correatons for frcton factor are used for two phase fow. Church correaton s expressed as: 8 Re where f = 8 + ( + ) A B ε 5.74 A = 0.5 o D Re 0.9 Ln correaton for frcton factor s ven by: f = φ f where sp υ sp υ ( A + B ) Re υ φ = x υ ( Asp + B sp ) Re sp, B = Re, Re GD = (0) () () 7 th IIR Gustav Lorentzen Conference on Natura Workn Fuds, Trondhem, Norway, May 8-3, 006

5 Frede frcton factor s expressed as: f = φ f (3) where 3.FH K Fr We φ = +, ( ) ρ f K = x + x, ρ f f ε 5.74 = 0.5 o D Re 0.9 ε 5.74 f 0.5 o D = +, 3.7 Re 0.9 ( ) 0.4 ρ 0.78 F = x x, H = ρ G GD ρ =, Fr =, We = x x + Dρ σρ ρ ρ Four methods for estmatn two-phase vscosty have been empoyed to factate estmaton of the two phase frcton factor at varous quaty condtons. These correatons are presented beow. ( x) McAdams (94) mode: x = + (4) Ccchtt (960) mode: = ( x) + x (5) Duker (964) mode: ( x) υ + xυ = ( x) υ + xυ (6) Ln (99) mode: =.4 + x (7). Choked fow anayss ( ) At the choked condton, the mass fow throuh the capary reaches the maxmum and the back pressure s desnated as choked pressure. The pont of neatve entropy chane can be used as a crteron to detect the choked fow condton n a capary tube n the enthapy-entropy pane as ustrated n Fure RESULTS The smuaton s performed for a as cooer pressure of 00 bar and temperature of 33 K. The evaporator temperature s taken as 88 K whe the capary tube dameter and nterna surface rouhness are taken as.0 mm and mm, respectvey. Mass fow rate s taken as 0.0 k/s based on expermenta desn reported n the terature [7]. Lenth of the capary tube s evauated at varous combnatons of frcton factor and vscosty correatons and subsequenty resuts are compared. A the operatn data seected for ths study pertann to a typca transcrtca CO based heat pump system reported earer [8]. Fures 4 and 5 show the pressure and temperature varaton aon the capary tube. It can be observed that pressure varaton s ndependent of frcton factor (F. 4). As the capary enth ncreases, the pressure decreases neary up to saturaton pont (.e. n the sne phase reon) as the temperature varaton s modest n the sne phase reon; however, t s not near n the two- 7 th IIR Gustav Lorentzen Conference on Natura Workn Fuds, Trondhem, Norway, May 8-3, 006

6 phase zone. The rate of chane of decrease n pressure and temperature ncreases beyond ths pont and n the two phase reon. It can be observed that for a ven as cooer and evaporator pressure, Frede frcton factor cacuates reatvey shorter enth than that estmated by Ln frcton factor as t consders the surface tenson effect. Varaton of pressure and temperature aon the tube and cacuaton of frcton factor are unaffected by choce of vscosty mode unke n R and R34a; ths can be attrbuted to the fact the CO qud vscosty s consderaby ess than that of tradtona refrerants. Moreover, the temperature varaton tends to be more non-near n the two-phase reon due to the presence of vapour. Reference [4] has reported the capary tube pressure radents for R and we observe that the present anayss for CO estmates reatvey hher radents and hence the obtaned enth for CO s comparatvey shorter. Pressure (bar) McAdams Frede Ccchtt Duker Ln Lenth (m) Fure 4. Pressure varaton aon the tube enth Temperature (K) Ln. Frede Lenth (m) Fure 5. Temperature varaton aon tube enth Dryness Fracton Lenth (m). Fure 6. Quaty varaton aon the capary n two phase zone Veocty (m/s) Lenth (m) Fure 7. Varaton of veocty aon tube enth Enthapy (kj/k) Lenth (m) Entropy (kj/k K) Lenth (m) Fure 8. Varaton of enthapy aon tube enth Fure 9. Varaton of entropy aon tube enth 7 th IIR Gustav Lorentzen Conference on Natura Workn Fuds, Trondhem, Norway, May 8-3, 006

7 Varaton of quaty aon the tube enth s exhbted n Fure 6. Intay quaty ncreases at a faster rate snce the ncrements of enth needed to drop the saturaton pressure become proressvey smaer and aso due to the ncepton of vaporzaton near the crtca pont. Fures 7 and 8 exhbt varaton n veocty and enthapy, respectvey. The varatons are qute modest up to the saturaton pont (.e. sne phase). However, they vary sharpy n the two phase reon due to the presence of vapour phase. Around the crtca pont, CO propertes fuctuate rather sharpy and that requre carefu and precse numerca smuaton. Narrow dscretsaton has been adopted to yed hher accuracy. F. 9 shows that even n sne phase, enthapy s not constant due to varaton n densty. F. 0 shows the enth requrement for varyn mass fow rates. The enth estmate for the supercrtca reon s reatvey arer due to ower frcton offered by aseous CO whe the enth cacuated n the subcooed reon and subsequenty n the two phase reon s reatvey ess due to hh frcton own to the qud phase. The enth cacuated n transcrtca reon s amost 65 % of the tota enth of the capary tube. As mentoned earer, the chokn condton s evauated on the bass of attanment of maxmum entropy. At the ven mass fow rate of 0.0 k/s, chokn occurs, whch s exhbted by the ext pressure of the capary ben hher than the evaporator pressure. The ext pressure s cacuated as 9.64 bar whe evaporator pressure and temperature are cacuated as 9. bar and 5. K respectvey at the chokn condton. For the ven capary tube dameter and enth, further reducton of evaporator pressure does not chane the mass fow rate. The choked condton s shown by the Fanno ne (Fure ). However, t must be noted that usuay n a typca CO heat pump system, evaporator pressure s not expected to drop to such eves and as such chokn w not usuay occur n these systems. Chokn anayss shows that for the ven as cooer pressure and capary tube dameter, capary tube can aow a arer mass fow rate despte a ower evaporator pressure. That s mportant when the ven capary enth s attached to the system and evaporator pressure vares due to varyn oad condtons. Lenth (m) Mass fow rate (k/s) Enthapy (kj/k) Entropy (kj/k K) Fure 0. Tube enth requrement varaton wth refrerant mass fow rate Fure. Fanno ne shown choked-fow condton on the h-s pane 4. CONCLUSIONS Anayss of capary fow wth CO as a refrerant s dfferent from other refrerants as the CO cyce s a transcrtca one. The ncepton of vaporzaton s near to crtca pont resutn n a comparatvey hh vapour fracton. Pressure radent s consderaby hher for CO than the tradtona refrerants yedn shorter capary tube enth. Varaton of pressure and temperature aon the tube and cacuaton of frcton factor are unaffected by choce of vscosty mode unke n R and R34a. In a comparatve anayss, use of Frede frcton factor n the mode yeds the 7 th IIR Gustav Lorentzen Conference on Natura Workn Fuds, Trondhem, Norway, May 8-3, 006

8 mnmum tube enth. Despte havn an adabatc tube, there s a varaton n enthapy aon the tube enth. However, varaton s ess than % n sne-phase qud reon as expected. There s amost 0 0 C temperature drop aon the tube even n the sne-phase reon unke the conventona refrerants where temperature remans amost constant n the sne phase reon. Such snfcant varaton n behavoura pattern vs-à-vs conventona refrerants pont to be fact the transcrtca CO capary fow needs cose attenton for better system desn. NOMENCLATURE p pressure (bar) L capary tube enth (m) D capary tube dameter (m) A cross-sectona area (m ) V veocty (m s - ) h specfc enthapy (J k - ) G mass fux (k m - s - ) x dryness fracton (-) f frcton factor (-) Re Reynods number(-) We Weber number (-) Fr Froude number(-) m mass fow rate (k s - ) Subscrpts sup supercrtca subq sub-cooed qud saturated qud saturated vapour qud vapour phase sp sne phase two phase r refrerant Greek symbos υ specfc voume (m 3 k - ) ρ densty (k m -3 ) ε nterna surface rouhness(-) dynamc vscosty (Pa s) φ two phase frctona mutper (-) σ surface tenson (N m - ) REFERENCES [] Bansa P. K., Rupasnhe A. S. 998, A homoeneous mode for adabatc capary tubes, Apped Therma Enneern, 8(3-4), [] Sam S. M., Matas H. 000, Numerca moden of aternatve refrerants to HCFC- throuh capary tubes, Internatona Journa of Enery Research, 4, [3] Krtsadathkarn P., Sonnetchaovat T., Lokathada N., Wonwses S. 00, Pressure dstrbuton of refrerant fow n an adabatc capary tube, Scence Asa, 8, [4] Yufen Z., Guobn Z., Hu X., Jn C. 005, An assessment of frcton and vscosty correatons for mode predcton of refrerant fow n capary tubes, Int. J of Enery Research, 9, [5] Bansa P.K., Wan G. 004, Numerca anayss of choked refrerant fow n adabatc capary tubes, Apped Therma Enneern, 4, [6] Chen Y., Gu J. 005, Non-adabatc capary tube fow of carbon doxde n a nove refreraton cyce, Apped Therma Enneern, 5(-), [7] Madsen K.B., Pousen C.S., Wesenfarth M. 005, Study of capary tubes n a transcrtca CO refreraton system, Int J of Refreraton, 8, -8. [8] Sarkar J, Bhattacharyya S, Ramopa M. 004, Optmzaton of transcrtca CO heat pump cyce for smutaneous coon and heatn appcatons. Int J of Refreraton; 7(8): th IIR Gustav Lorentzen Conference on Natura Workn Fuds, Trondhem, Norway, May 8-3, 006