Comparison of One-Dimensional Analysis with Experiment for CO2 Two-Phase Nozzle Flow

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1 Open Journa of Fuid Dynamics, 2014, 4, Pubished One December 2014 SciRes. Comparison of One-Dimensiona Anaysis with Eperiment for CO2 Two-Phase Nozze Fow Wakana Tsuru, Satoshi Ueno, Yoichi Koue, Norimasa Shiomi Department of Mechanica Eneer, Saa University, Saa, Japan Emai: Received 15 October 2014; revised 6 November 2014; accepted 5 December 2014 Copyriht 2014 by authors and Scientific Research Pubish Inc. This work is icensed under the Creative Commons Attribution Internationa License (CC BY). Abstract The aim of this study is to vestiate CO 2 two-phase nozze fow terms of both eperimenta and anaytica aspects for the optimum desin of two-phase fow nozze of CO 2 two-phase fow ejector. In the eperiment, it is measured that the temperature profie the stream-wise direction of a diverent-converent nozze throuh which CO 2 the supercritica pressure condition is bown down to the atmosphere. In the anaysis, a one-dimensiona mode which assumes steady, adiabatic, frictioness, and equiibrium is proposed. In the converent part of the nozze the fow is treated as se-phase fow of iquid, whereas the diverent part the fow is treated as separated two-phase fow with saturated condition. The anaytica resuts dicate that the temperature and the pressure decrease rapidy the diverent part, and the void fraction creases immediatey near the throat. Athouh this anaysis is quite simpe, the anaytica resuts can foow the eperimenta resuts we with this study. Keywords Carbon Dioide, Hih-Speed Nozze Fow, Gas-Liquid Two-Phase Fow with Phase Chane, Bow down Test, One-Dimensiona Anaysis 1. Introduction In recent years, natura refrierants are rearded as refrierants of refrieration cyces. Because of the hihy safety and the sma oba warm coefficient, carbon dioide (CO 2 ) is especiay focused. However, wasted avaiabe enery which is discarded a pressure reduction process at an epansion vave the cyce of us CO 2 is three times as much as that of us R-134a. Therefore, it is important to recover the avaiabe enery, How to cite this paper: Tsuru, W., Ueno, S., Koue, Y. and Shiomi, N. (2014) Comparison of One-Dimensiona Anaysis with Eperiment for CO2 Two-Phase Nozze Fow. Open Journa of Fuid Dynamics, 4,

2 W. Tsuru et a. and a as-iquid two-phase fow ejector (two-phase fow ejector) is used to recover the enery [1] [2]. A two-phase fow ejector consists of a driv fow nozze, a suction chamber, a mi section and a diffuser, respectivey. Many researches for se-phase fow ejectors have been carried out. However for two-phase fow ejectors, the mechanisms of the terna fow with phase chane have not been sufficienty made cear yet because of the compey of the fow. This study is carried out on a as-iquid two-phase fow nozze (two-phase fow nozze) of a driv nozze fow section which is the most important section. A diverent-converent nozze is eneray used as a two-phase fow nozze [3]. In actua CO 2 refrieration cyce, the typica vaue of the et pressure of the epansion vave is 9 MPa which eceeds the critica pressure of CO 2, 7.38 MPa. Therefore, a CO 2 two-phase fow nozze, the pressure of the nozze et and the converent section pressure are the supercritica pressure. And the fow the diverent section is the saturated twophase fow with phase chane (boi). The CO 2 two-phase fow the nozze is a compicated hih-speed fow with are chanes both temperature and pressure. For the optimum desin of the nozze which has these characteristics, the vestiation of the fuid mechanics of the hih speed as-iquid two-phase fow is important. For the two-phase nozze fow there are studies conducted by Nakaawa et a. [3]-[6]. Nakaawa et a. vestiated nozze shapes eperimentay [3] [4], and proposed a one-dimensiona anaytica mode for the fow [5] [6]. In their study, they anayzed a shock wave caused by a veocity reaation and a temperature reaation with the one-dimensiona mode. A phenomenon that the fow the nozze is not acceerated we ow to the eistence of a shock wave has been epaed by the anaysis. On the other hand, it is necessary to anayze a phenomenon for the case that the fow the nozze acceerates and the pressure decreases sufficienty. The purpose of this study is to conduct eperimenta and anaytica vestiations of the fow the two-phase fow nozze. In the eperiment, the simiar way used by Nakaawa et a. [4], the CO 2 fow that oes throuh the diverent-converent nozze to the atmosphere is researched, where the temperature and the pressure distribution the mastream direction are vestiated. In the anaysis, one-dimensiona anaytica mode assumed to be steady, adiabatic process, frictioness and equiibrium is vestiated. The mode refers to the formuarization by Sudo and Katto [7] for the study of the critica fow rate of a compressibe as-iquid two-phase fow. A method to predict various distributions of fow properties aon the mastream is considered by sov fundamenta equations, which are obtaed from appy conservation of mass, momentum and enery to the fow the two-phase fow nozze, simutaneousy. 2. Eperimenta Apparatus and Procedure Fiure 1 is the schematic diaram of eperimenta apparatus based on Nakaawa et a. [4]. The eperimenta apparatus may consists of a hih-pressure tank and a test section. The hih-pressure tank is fied up with ases the order of CO 2 and N 2, and hih-pressure CO 2 can be obtaed. The test section consists of the pressure measur part at the nozze et and the nozze. Fiure 2 shows the rectanuar nozze [4] used for the nozze part, where z is the distance from the nozze et the mastream direction. Thermocoupes are set on a side wa of the nozze as shown Fiure 2, and the temperature side the nozze is measured. The pressure is cacuated by us assumption of saturated condition and the measured temperature. CO 2 is emitted throuh the test section to the atmosphere. The pressure the hih pressure tank is set four staes from 7.2 MPa to 10.3 MPa, and the CO 2 as is eft unti the tank temperature is the same temperature of the room of K. At the time of start the eperiment, vave 3 and vave 4 Fiure 1 are opened to fow CO 2 the nozze. The outputs of the thermocoupes and the oad ce are saved on a computer. The weiht of the tank is measured at before and after the test, and the CO 2 mass fow rate is cacuated from the duration time of the emission. 3. One-Dimensiona Anaysis 3.1. Anaytica Mode In the CO 2 nozze fow, the temperature and the pressure distributions chane rapidy, and the phase condition chanes from supercritica to saturated two-phase condition. To et the most important aspect of the compe fow, this study, a one-dimensiona anaytica mode is used. For this anaysis, the fow is assumed to be steady, adiabatic, no friction and equiibrium. The fow the converent part of the nozze is treated as a se-phase fow. Fiure 3 shows the sephase fow mode. Where u is the veocity, P is the pressure, T is the temperature, ρ is the density, 416

3 W. Tsuru et a. Fiure 1. Eperimenta apparatus. Fiure 2. Detais of nozze. Fiure 3. Se-phase fow mode for onedimensiona anaysis. h the enthapy, and A is the area of the cross section. App the aws of conservation of mass, momentum and enery to a mute section shown Fiure 3, Equations (1) to (3) is obtaed, ρ ρ ρu u dt + u dp+ ρdu = da T P A p T 1 dp + du = 0 (2) ρu (1) 417

4 W. Tsuru et a. h h dt + dp + udu = 0 T P P where da is positive. To obta the temperature, the pressure and the veocity variations, dt, dp and du, Equations (1) to (3) are soved simutaneousy. The fow the diverent section is treated as a saturated separated two-phase fow. A mode of the separated as-iquid two-phase fow is shown Fiure 4. App the aws of conservation of mass, momentum and enery of each phase to a mute section as shown Fiure 4, Equations (4) to (7) is obtaed, ρ d u ρ ρu dρ ρu ρu ρu ρu + ( 1 ) dp+ du + ( 1 ) du + ( ρu ρu) d = da ρ dp ρ dp u u m ρ u T ( ) dp+ u d + u u d= 0 (5) i 1 d P + ( 1 ) d u + ( u i u ) d = 0 (6) ρ u dh dh ( 1 ) dp + udu + ( 1 ) udu + h + u + h + u d = 0 dp dp 2 2 where m, and u i Fiure 4 are the mass fow rate, the quaity and the veocity of the terface of the phases, and of subscripts dicate the as and the iquid phase, and da is positive. The pressure, the as veocity, the iquid veocity and the quaity variations of the separated saturated as-iquid two-phase fow, dp, du, du and d, are obtaed by sov Equations (4) to (7) simutaneousy. In Fiure 4 and Equations (4) to (7), the phase chane mode as chan from iquid to as is appied to the mute mass fow rate, dm = m d, which correspond to the quaity variation mute section, d. Simpe and typica modes of a as-iquid two-phase fow are a separated fow mode neect friction between the phases and a homoeneous fow mode neect veocity difference between the phases. In the diverent section of the two-phase fow nozze, sce it is epected that the distribution of the void fraction chanes sinificanty from 0 to 1, appropriate appication of the two modes is desirabe. However, this study, the whoe fow the diverent section of the two-phase fow nozze is simpy treated as a separated fow Anaytica Object and Methods The anaysis is carried out on the fow the converent-diverent nozze [4] shown Fiure 2. The fow the rectanuar nozze that is 3 mm wide is anayzed the mastream direction. The nozze that the tota enth (3) (4) (7) Fiure 4. Two-phase fow mode for one-dimensiona anaysis. 418

5 W. Tsuru et a. is 84 mm is divided to 8400 ces (each section terva is 0.01 mm), and the fow is numericay anayzed by us fundamenta equations which is appropriate for each section. There are not much difference between the resuts of the cases of 8400, 4200 and ces. Needed CO 2 properties for the cacuation process are obtaed by PROPATH. In the converent section of the nozze which fow is treated as the se-phase fow, a fow which reached saturated condition is addressed as saturated iquid. Therefore, ecud dt Equations (1) and (3), dp and du is cacuated. In the diverent section of the nozze which fow is treated as the separated as-iquid two-phase fow, the veocity at the terface between the phases is the iquid veocity case of d > 0, namey ui = u. The itia quaity is at the throat. The eperimenta resuts are appied to the et boundary conditions of the anaysis. Thus, the temperature measured by the thermocoupe CH1 shown Fiure 2 and the measured pressure, P, shown Fiure 1 are used as the et temperature and the pressure respectivey. For the mass fow rate, the vaue cacuated by us the eperimenta resuts is used. 4. Resuts and Discussions 4.1. Eperimenta Resuts The eperimenta conditions at the nozze et are isted Tabe 1. The distribution of the temperature measured by the thermocoupes the mastream direction is shown Fiure 5. The CO 2 temperature the nozze decreases sharpy, and the case of the tank pressure of 7.2 MPa the difference temperature between the et and the outet is 80 K. As the tank pressure creases, the temperature at the nozze outet aso creases. The nozze outet temperature for the tank pressure of 10.3 MPa is approimatey 17 K arer than that of the tank pressure of 7.2 MPa. Fiure 6 shows the pressure distribution the mastream direction the nozze obtaed by us the assumption of saturated condition and the temperature Fiure 5. The CO 2 pressure decreases sharpy the nozze as we as the temperature. Thus, it coud be considered that CO 2 acceerates sufficienty the nozze. As the tank pressure creases, the nozze outet pressure aso creases. Reard the nozze outet pressure, the one for the case of the tank pressure of 10.3 MPa is approimatey 0.6 MPa arer than that of 7.2 MPa Comparison of Eperiment and Anaysis The comparison of the eperimenta and the anaytica resuts of the temperature distribution (a) or the pressure distribution (b) the cases that the tank pressure is set to 7.2, 8.0, 9.2 and 10.3 MPa are shown Fiures In the case of the tank pressure of 7.2 MPa, as shown Fiure 7, the eperimenta and the anaytica resuts can be considered amost the same. Sce the condition of the nozze et is approimatey saturated, the fow the converent section of the nozze is treated as saturated iquid. In the case of the tank pressure of 8.0 MPa, as shown Fiure 8, the temperature distribution of the anaysis is amost the same as that of the eperiment. In the pressure distribution the anaytica resuts the converent section are different from the eperimenta resuts, whereas, the diverent section, the anaytica resuts approimate to the eperimenta resuts. In the converent section, sce the critica pressure of CO 2 is 7.38 MPa, it can be considered that the discrepancy is caused by the sett of the tank pressure to the supercritica pressure and the condition is not saturated the eperiment. Reard Fiure 9 of the tank pressure of 9.2 MPa, for above reasons, the pressure difference between the eperimenta and the anaytica resuts the nozze converent section is caused. For the pressure the diverent section and the temperature distribution of the anaysis, the anaytica resuts are rather smaer than the Tabe 1. Eperimenta conditions. Tank pressure (MPa) Inet temperature (K) Inet pressure (MPa) Inet veocity (m/s) Mass fow rate (k/m 3 )

6 W. Tsuru et a. Fiure 5. Temperature distributions of eperiment. P (MPa) T ank Pressure 7.2MPa 8.0MPa 9.2MPa 10.3MPa T (K) Fiure 6. Pressure distributions of eperiment. 220 Eperiment Anaysis 200 (a) Fiure 7. Comparison of anaysis with eperiment (tank pressure = 7.2 MPa). (a) Temperature; (b) Pressure. P (MPa) (b) Eperiment Anaysis 420

7 W. Tsuru et a. T (K) Eperiment Anaysis 200 (a) Fiure 8. Comparison of anaysis with eperiment (tank pressure = 8.0 MPa). (a) Temperature; (b) Pressure. T (K) 220 Eperiment Anaysis 200 (a) Fiure 9. Comparison of anaysis with eperiment (tank pressure = 9.2 MPa). (a) Temperature; (b) Pressure. T (K) Eperiment Anaysis 200 (a) Fiure 10. Comparison of anaysis with eperiment (tank pressure = 10.3 MPa). (a) Temperature; (b) Pressure. eperimenta resuts around the throat. However, area ecept the near throat, the anaytica and the eperimenta resuts are approimatey the same. For the pressure the diverent section and the temperature distribution the case of the tank pressure of 10.3 MPa shown Fiure 10, the differences between the anaytica and the eperimenta resuts at the near throat is arer than that of 9.2 MPa. Whereas, ecept the near throat, the anaytica and the eperimenta resuts are we matched. P (MPa) P (MPa) P (MPa) (b) (b) (b) Eperiment Anaysis Eperiment Anaysis Eperiment Anaysis 421

8 W. Tsuru et a Anaytica Resuts Fiures show the anaytica fow property distributions of the cases that the tank pressure set to 7.2, 8.0, 9.2 and 10.3 MPa, respectivey. In Fiures 11-14, the anaytica resuts are marked with dotted e for cross sectiona area, AA ( A : cross sectiona area at the nozze et), bod soid e for the temperature, TT ( T : the nozze et temperature), sma soid e for the pressure, PP ( P : the nozze et pressure), bod broken e for the quaity,, sma broken e for the void fraction,, bod cha e for the as-phase veocity, u u 100 ( u : the nozze et veocity, these vaues are dicated Fiures respectivey), bod two-dot cha e for the iquid-phase veocity, u u 100, sma cha e for the as-phase sonic veocity and sma two-dot cha e for c u 100, and the iquid-phase sonic veocity, c u 100. To see these fiures ceary, u, u, c and c are divided by 100. The se-phase and the two-phase sonic veocity and the void fraction are cacuated by foow formuas, { } ( ) ( 1 ) = ρ u ρ u + ρ u (8) ( d d ) c = P ρ (9) ( d d ) c = P ρ (10) ( d d ) where c the converent section is marked with the same sma cha e as A/A T/T p/p u /u /100 u /u /100 c /u /100 c /u /100 Fiure 11. Anaytica resuts (tank pressure = 7.2 MPa). A/A T/T p/p u /u /100 u /u /100 c /u /100 c /u / A/A T/T p / P i n Fiure 12. Anaytica resuts (tank pressure = 8.0 MPa). c = P ρ (11) u /u /100 c is marked with. u /u /100 c /u /100 c /u / A/A T/T p / P i n u /u /100 u /u /100 c /u /100 c /u /

9 W. Tsuru et a. Fiure 13. Anaytica resuts (tank pressure = 9.2 MPa). Fiure 14. Anaytica resuts (tank pressure = 10.3 MPa). In the case of the tank pressure of 7.2 MPa, as shown Fiure 11, the quaity,, is approimatey 0.45, the void fraction,, is approimatey 0.95, the as-phase veocity, u, is 1.3, and the iquid-phase veocity, u, is Mutipied u and 100, u and u are approimatey 400 m/s and 160 m/s respectivey. In these anaytica resuts, satisfactory acceerat performance of the nozze is dicated. To eucidate the vaidity of these anaytica resuts, it is necessary to vestiate these fow properties eperimentay. Compared with the sonic veocity defed this paper, the as-phase and the iquid-phase veocity is arer. From perspective of the sonic veocity defed this paper, the fow the diverent section can be considered as the supersonic fow. In the case that the tank pressure is set to 8.0 MPa, as shown Fiure 12, enera trend is the same as the tank pressure of 7.2 MPa. However, the veocity the case of the tank pressure of 8.0 MPa is smaer than that of the case of 7.2 MPa despite the arer et veocity the case of 8.0 MPa. As shown Fiure 13 and Fiure 14, it can be considered that the hiher pressure tank is set, the smaer veocity is cacuated. 5. Summary A/A T/T p/p u /u /100 u /u /100 c /u /100 c /u /100 A/A T/T p/p u /u /100 u /u /100 c /u /100 c /u / A/A T/T p / P i n u /u /100 u /u /100 c /u /100 c /u / A/A T/T p / P i n u /u /100 u /u /100 c /u /100 c /u / The fow fied of the carbon dioide hih-speed two-phase nozze fow has been vestiated by the eperiment and the one-dimensiona anaysis. Obtaed resuts are as foows. 1) For the nozze form used this research and the eperimenta condition, the CO 2 temperature and the pressure have been sinificanty and monotonousy decreased the nozze, and satisfactory acceerat performance has been presumed. 2) For the nozze fow, the one-dimensiona anaytica mode which assumes to be steady, adiabatic, no friction and equiibrium is proposed. In this anaytica mode, the nozze converent section is assumed to be se- 423

10 W. Tsuru et a. phase fow, and the nozze diverent section is assumed to be separated as-iquid two-phase fow. 3) The proposed anaytica mode is simpe, and the assumption that the fow is the separated saturated asiquid two-phase fow does not necessariy satisfy the actua fow. However, this eperimenta condition, these anaytica resuts satisfactoriy predicted these eperimenta resuts. 4) By the one-dimensiona anaysis, the veocity distribution the mastream direction the nozze is obtaed, and the satisfactory acceerat performance has been dicated. Further, it is made cear that from the perspective of the sonic veocity defed this anaysis the fow the diverent section can be considered as the supersonic fow. References [1] Nakaawa, M. (2004) Refrieration Cyce with Two-Phase Ejector. Refrieration, 79, [2] Akai, S., Dan, C.B. and Hihara, E. (2006) Eperimenta Research of Two-Phase Ejector Carbon Dioide Heat Pump Cyce. Journas of Japan Society of Refrierat and Air Condition Eneers, 23, [3] Nakaawa, M., Takeuchi, H. and Yokozaki, A. (1998) Performance of Two-Phase Nozzes Us the Refrierant R134a. Transactions of Japan Society of Mechanica Eneers, Series B, 64, [4] Nakaawa, M., Takeuchi, H. and Berana, M.S. (2006) Supersonic Characteristics and Shock Waves Two-Phase Fow aon a Nozze of a Carbon Dioide Ejector. Proceeds of the 3rd Asian Conference on Refrieration and Air-Condition, 1, [5] Nakaawa, M. and Suiura, T. (2000) Shock Waves Caused by Veocity Reaation Hih Speed Mist Fow. Transactions of Japan Society of Mechanica Eneers, Series B, 66, [6] Suiura, T. and Nakaawa, M. (2001) Shock Waves Caused by the Veocity and Temperature Reaation of Subsonic Mist Fow a Nozze. Transactions of Japan Society of Mechanica Eneers, Series B, 67, [7] Sudo, Y. and Katto, Y. (1975) Study of Compressibe Two-Phase Critica Fows: 1st Report, Prcipe of Occurrence of Critica Fow. Transactions of Japan Society of Mechanica Eneers, 41,

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