CFD Analysis of Supersonic Ejector in Ejector Refrigeration System for Air Conditioning Application

Transcription

1 Proceedngs of the World Congress on Engneerng 2017 Vol II, July 5-7, 2017, London, U.K. CFD Analyss of Supersonc Eector n Eector Refrgeraton System for Ar Condtonng Applcaton Jame Honra, Menandro S. Berana, Lous Angelo M. Danao, and Mark Chrstan E. Manuel Abstract Researches on supersonc eector for refrgeraton applcaton s ncreasngly becomng very attractve due to ts smplcty and sgnfcant reducton n overall cost. However, most of the studes are stll lmted to one-dmensonal mathematcal modellng and physcal expermentaton. Data acquston from physcal nvestgatons requres extensve effort and consderable tme and s very expensve; whereas, Computatonal Flud Dynamcs (CFD) could be a more effcent dagnostc tool for eector desgn analyss and performance optmzaton than one-dmensonal mathematcal modellng pror to actual expermentaton. Ths study presents CFD smulaton results of an eector for ar condtonng applcatons usng popular commercal CFD software and attempts to have a hghly dependable smulaton that features a model based on the nterpolaton of real flud propertes from NIST-REFPROP database embedded through user-defned functons (UDF s) wth R134a as the workng flud. Prmarly, densty and speed of sound are polynomal functons of both pressure and temperature. In addton, a comparson s made between the results of the sad model wth that of the deal gas model, whch s one of the conventonal models employed n dealng wth compressble flows nsde eectors. Index Terms computatonal flud dynamcs, refrgeraton, supersonc eector, user-defned functon T I. INTRODUCTION HE low-grade thermal energy such as waste heat from ndustral processes and equpment, nternal combuston engne exhaust heat, geothermal energy and solar energy can Manuscrpt receved March 20, 2017; revsed Aprl 10, The dssemnaton of ths research s sponsored by the Engneerng Research and Development Program (ERDT) of the Department of Scence and Technology (DOST) of the Republc of the Phlppnes. The program s beng managed and mplemented by the College of Engneerng of Unversty of the Phlppnes Dlman. J. Honra s wth the School of Mechancal and Manufacturng Engneerng, Mapua Insttute of Technology, Intramuros, Manla, 1002 Phlppnes (phone: , loc 2105; e-mal: ameshonra@yahoo.com). M. S. Berana s wth the Department of Mechancal Engneerng, College of Engneerng, Unversty of the Phlppnes Dlman, Quezon Cty, 1101 Phlppnes (phone: , loc 3130; fax: ; e-mal: menandro.berana@coe.upd.edu.ph). L. A. M. Danao s wth the Department of Mechancal Engneerng, College of Engneerng, Unversty of the Phlppnes Dlman, Quezon Cty, 1101 Phlppnes (phone: , loc 3130; fax: ; e-mal: lousdanao@gmal.com). M. C. E. Manuel s wth the School of Mechancal and Manufacturng Engneerng, Mapua Insttute of Technology, Intramuros, Manla, 1002 Phlppnes (phone: , loc 2105; e-mal: mcemanuel@mapua.edu.ph). be tapped as heat sources to power an eector refrgeraton system. Ths refrgeraton system uses an eector and a lqud pump n leu of the electrcty-drven compressor n conventonal vapor compresson refrgeraton system. The lqud pump typcally consumes only 1% of the heat nput to the eector system from low-grade heat sources or approxmately 16-19% of the electrcty consumpton of the compressor n conventonal system, gven the same refrgeratng capacty [1]. Ths translates to enormous potental savngs n energy consumpton when eector refrgeraton technology becomes mature and fully developed for commercal and ndustral applcatons. A. Eector Theory II. THEORY Eector refrgeraton system uses an eector, a lqud pump and a vapor generator to replace the mechancal compressor. Fg. 1 llustrates a smple eector refrgeraton system wth ts maor components labelled. The generator receves heat from a low-cost, low-grade thermal energy source and heats up the refrgerant to produce hgh pressure and hgh temperature vapor known as the prmary flud that enters the eector and accelerates through the eector nozzle where the et ssung from t entrans the low-pressure secondary flow comng from the evaporator. The resultng flud mxture whch s at an ntermedate pressure passes through the condenser, where heat reecton process occurs, and leaves as lqud refrgerant. Most of the refrgerant leavng the condenser s pumped back to the generator and the rest enters the expanson valve to reduce ts pressure down to that of the evaporator where another heat absorpton process takes place. Wp Lqud Pump 1 Lqud Recever Expanson Valve 6 5 Qg Generator Qc Condenser Evaporator Fg. 1. A Typcal Eector Refrgeraton System. QE Eector ISSN: (Prnt); ISSN: (Onlne)

2 Proceedngs of the World Congress on Engneerng 2017 Vol II, July 5-7, 2017, London, U.K. One of the maor parts of eector s the convergngdvergng nozzle as shown n Fg. 2. Prmary flud enters the nozzle at subsonc speed and leaves at supersonc condton wth ncreased knetc energy at the expense of pressure. The resultng dfference n pressure between the nozzle ext and the secondary flud nlet creates the entranment effect where secondary flud s sucked from the sucton chamber. The mxture flows through the mxng chamber at constant pressure untl t reaches the dffuser at subsonc velocty. The mxture s recompressed to the desred condenser pressure as t passes through the dffuser. Prmary Flow Sucton Chamber Nozzle Secondary Flow Fg. 2. Basc Eector Geometry. Mxng Chamber Dffuser The system s performance s best descrbed by ts Coeffcent of Performance (COP) and the eector s entranment rato (ER). Mathematcally, they are defned as, QE COP Q W (1) m ER m s p g p B. Computatonal Flud Dynamcs (CFD) Theory The governng equatons for flud flow such as equatons for conservaton of mass, momentum, and energy form a set of coupled, nonlnear partal dfferental equatons. Analytcal methods may not be possble to solve these equatons for most engneerng problems, but, computatonal flud dynamcs s capable of dealng wth these types of equatons. CFD s a branch of flud mechancs and s the scence of predctng flud flow, heat and mass transfer, chemcal reactons, and related phenomena [2]. Its core part s the solver that uses a numercal calculaton scheme. The doman s dscretzed nto fnte sets of control volume where the equatons n the form of Naver-Stokes partal dfferental equatons are solved. These equatons are converted nto a set of algebrac equatons at dscrete ponts whch are then solved numercally to render a soluton wth the approprate boundary condtons. The postprocessor gves the calculated results nto convenent formats, ether graphcally or numercally. Flud flow through the eector can be consdered compressble, turbulent, steady-state and axsymmetrc. The Naver-Stokes contnuty, momentum and energy equatons provde the foundaton n CFD smulaton of flud moton. The average values of flow quanttes ncludng velocty are usually determned by tme averagng over large ntervals, sftng out small varatons, but small enough to mantan large scale tme varatons. Ths results n Reynoldsaveraged Naver-Stokes (RANS) equatons. To fnd closure (2) to ths, a popular approach to turbulence modellng employs the Boussnesq hypothess to relate the Reynolds stresses to the mean velocty gradents [2], [3]. The subsequent equatons are wrtten n Cartesan tensor form as: u 0 (3) t x t u u u The stress tensor and energy equatons are gven n equatons 5 and 6, respectvely. The total energy equaton takes nto account the effects of vscous forces on flud moton as ths ncorporates the vscous dsspaton n t. A. Eector Geometry x u eff x t x u x p x E u E P. eff III. EJECTOR MODELLING Eector, beng the most crtcal component dctates the overall performance of the eector refrgeraton system. Thus, ts confguraton and geometry must be carefully determned and desgned. Intally, recommended eector dmensons from ASHRAE and ESDU and non-dmensonal parameters for eector confguraton from publshed ournals are followed [4]-[9]. Combnatons of such dmensons and parameters are tred on n the CFD smulaton one by one untl near-optmum geometry s establshed whch gves maxmum entranment rato at the desred operatng condtons of the refrgeraton system for R134a refrgerant. Table 1 gves the acqured specfcatons for the eector geometry. x 2 uk eff 3 xk T x u TABLE I EJECTOR GEOMETRY SPECIFICATION Nozzle Inlet Dameter 10 mm Throat Dameter 2.24 mm Nozzle Ext Dameter 3.65 mm Nozzle Convergng Angle 60 Nozzle Dvergng Angle 10 Sucton Dameter 32 mm Sucton Convergng Angle 42 Dstance of Nozzle from Mxng Secton 5 mm Mxng Secton Dameter 5.1mm Mxng Secton Length 39 mm Dffuser Outlet Dameter mm Dffuser Length 50 mm Dffuser Angle 5 Total Eector Length mm Mxng secton Length to Dameter Rato 7.6 Nozzle Ext Dameter to Throat Dameter Rato 1.63 (4) (5) (6) ISSN: (Prnt); ISSN: (Onlne)

3 Proceedngs of the World Congress on Engneerng 2017 Vol II, July 5-7, 2017, London, U.K. B. CFD Implementaton Two-dmensonal (2-D) axsymmetrc model of the flow doman s used to mnmze computatonal tme. Quad mesh s employed usng Ansys Meshng due to geometrc smplcty; and s mported to Ansys Fluent v.14.5, for mesh checkng and subsequently, for the smulaton. Temperature gradent adaptaton s set to automatcally refne meshes at regons where large temperature dfferences exst. Ths helps prevent dvergng soluton and makes the smulaton process smooth. In addton, solver selected s densty-based type wth mplct formulaton on the account that the flow s compressble. Ths type of solver computes the governng equatons of contnuty, momentum, and energy and speces transport smultaneously; and afterwards, governng equatons for addtonal scalars such as turbulence wll be solved sequentally. For steady-state assumpton wth travellng shocks, mplct formulaton may be more effcent. Although steady-state s appled, from the standpont of numercal solutons, the unsteady term s conserved and governng equatons are calculated wth a tme-marchng technque. Convectve transport varables are dscretzed usng thrd-order MUSCL; whle, the dscretzed system s solved wth Least Squares Cell-based gradent calculatons. Fnally, Shear-Stress Transport (SST) k-ω turbulence model s used whch takes nto consderaton the transport of the turbulent shear stress. Ths s the most recommended turbulence model for turbulent compressble flows [10], [11]. Sngle-phase flow assumpton s consdered snce both flow nlet condtons are n the vapor states; although phase change can happen, t s lkely to exst temporarly n small local regons and can be neglgble. Boundary Condtons In ths CFD analyss, the fxed eector geometry used s ntended for an eector refrgeraton system for ar-cooled ar-condtonng applcatons for specfc on-desgn operatng condtons sutable for tropcal countres lke the Phlppnes, as follows: evaporator temperature, 10 C; condenser temperature, approxmately 40 C and generator temperature, 95 C. The same geometry wll also be evaluated at off-desgn condtons by varyng the generator, condenser and evaporator temperatures (T g, T C, T E) at ranges C, C, and 5-15 C, respectvely. Pressure boundary condtons are mposed for both prmary and secondary flows as well as at the dffuser outlet. Real Flud Propertes The approach s manly concentrated on the calculaton of densty and speed of sound as polynomal functons of pressure and temperature to nearly depct propertes of the refrgerant as prescrbed by NIST-REFPROP [12]. Userdefned functon s formulated to ncorporate densty and speed of sound computatons n the CFD platform. Thermal conductvty and vscosty are essentally made polynomal functons of temperature only, as ther varatons wth temperature are generally found to be of neglgble effects. Specfc heat s largely lnear wth temperature, but the relatonshp vares at relatvely small ranges of temperature to accurately predct the propertes stpulated n the NIST REFPROP database. Ideal Gas Model Propertes The smplest equaton of state that relates pressure, temperature and molar or specfc volume s the deal gas law. Ths equaton whch s approxmately vald for the lowpressure gas regons s gven as, P R M w T IV. RESULTS AND DISCUSSION For the gven on-desgn condtons for both nlets, the analyss predcts a back pressure or condenser pressure, P C=1,041,262 Pa, whch corresponds to a desred saturaton temperature, T C = K (40.9 C). The entranment rato and ext temperature are and K, respectvely. Ths ndcates that the ext state s superheated. The computatonal doman conssts of approxmately 12,700 elements where very few of them fall wthn the mxture regon, as plotted n the Fg. 3. Smlar pattern also happens for deal gas assumpton. Thus, from a statstcal pont of vew, the flow s bascally sngle phase. Fg. 3. Pressure-Temperature Plot of Computatonal Elements. The contours of the velocty magntudes llustrated n Fg. 4 reveals a near optmal eector operaton as the profle descrbes the exstence of a seres of oblque shock waves for the prmary flud downstream the nozzle ext and a weak (7) Fg. 4. Contours of Velocty Profle and Exstence of Oblque Shocks. ISSN: (Prnt); ISSN: (Onlne)

4 Proceedngs of the World Congress on Engneerng 2017 Vol II, July 5-7, 2017, London, U.K. sngle shock wave of the mxture flow at the dffuser nlet [13], [14]. Ths renders effectve recompresson of the flud to the requred dffuser outlet pressure, P C. The occurrence of shock tran s also vsble n the outlne of pressure profle n Fg. 5 and densty profle n Fg. 6. Shock waves are characterzed by abrupt changes n pressure wth varaton n denstes. The predcted denstes and speeds of sound are accurate wthn 96% confdence level; whle, specfc heat, vscosty and thermal conductvty are at 95% confdence level. Table 2 compares the resultng propertes wth the values from NIST-REFPROP [12]. The effects of varyng nlet and outlet condtons are also evaluated wth results shown n Tables 3 to 5. Increasng the outlet pressure results n decreasng entranment rato and consequently, decreasng the COP of the refrgeraton system. Decrease of secondary pressure at lower T E and reducton n prmary pressure at lesser T g, lkewse lead to dmnshng entranment rato. The latter also results n some reverse flows through secondary nlet at T g = K, whch sgnfes eector falure. It s also noteworthy that n Table 5, prmary mass flow rate, m p drops due to nsuffcent motve pressure to push the prmary flud through the nozzle throat. TABLE III EFFECT OF INCREASING CONDENSER PRESSURE ON ENTRAINMENT RATIO Boundary Condtons PC, MPa TC, K mp, kg/s ms, kg/s ER Ths s at constant prmary and secondary nlet condtons: Pg= MPa at Tg =368.15K and PE= MPa at TE= K Fg. 5. Contours of Pressure n Pa TABLE IV EFFECT OF DECREASING EVAPORATOR PRESSURE ON ENTRAINMENT RATIO Boundary Condtons PE, MPa TE, K mp, kg/s ms, kg/s ER Ths s at constant prmary nlet and dffuser outlet condtons: Pg= MPa at Tg =368.15K and PC= MPa at TC= K TABLE V EFFECT OF DECREASING PRIMARY PRESSURE ON ENTRAINMENT RATIO Boundary Condtons Pg, MPa Tg, K mp, kg/s ms, kg/s ER Ths s at constant secondary nlet and dffuser outlet condtons: PE= MPa at TE= K and PC= MPa at TC= K Fg. 6. Contours of Densty n kg/m 3. TABLE II COMPARISON OF SIMULATION RESULT AND NIST PROPERTY VALUES Densty, kg/m 3 Speed of Sound, m/s Result NIST Result NIST Prmary Inlet Secondary nlet Dffuser Outlet The same fxed geometry s also utlzed usng the deal gas model on the same on-desgn condtons; and the results are compared wth the earler smulaton model. Table 6 shows the varaton n the entranment rato, slght ncrease n dffuser outlet pressure and the dfference n the outlet temperatures. The large devaton n the prmary mass flow rates s due to the huge dfference n the prmary nlet denstes. Hgher densty for the prmary flud results n greater amount of flow through the nozzle throat gven the same cross-sectonal area. Ths also causes more secondary ISSN: (Prnt); ISSN: (Onlne)

5 Proceedngs of the World Congress on Engneerng 2017 Vol II, July 5-7, 2017, London, U.K. flud entranment that tends to ncrease the entranment rato and the refrgeraton system s COP. In the frst smulaton the prmary flud densty at nlet s kg/m 3 whle for the deal gas, t s only kg/m 3. TABLE 6 COMPARISON BETWEEN THE REAL FLUID PROPERTY AND THE IDEAL GAS MODELS Real Flud Property Ideal Gas mp, kg/s ms, kg/s ER PC, MPa TC, K T, K COP For further comparson of the two (2) models, Fg. 7 llustrates the functonal relatonshp of densty at varyng temperatures gven a constant pressure. Also Fg. 6 shows speed of sound, whch largely depends on the densty partcularly for the real flud property, as functon of temperature at constant pressure. For real flud property, both densty and speed of sound are polynomal functons of temperature at a gven pressure, that s, densty ncreases more rapdly wth the decrease n temperature and as the temperature reduces the speed of sound decreases at a faster rate. In deal gas model, both densty and speed of sound almost vary drectly wth temperature. Fg. 7. Varaton of Densty wth Temperature at Constant Pressure V. CONCLUSION At specfc refrgeraton operatng condtons, there s a correspondng eector of fxed confguraton that wll operate at optmal condton. In ths study, a fxed-geometry eector s determned for the gven on-desgn condtons that works on a near optmal eector operaton. A near optmal eector operaton s characterzed by a number of oblque shocks that gradually fades nto a weak shock at the end of the mxng secton for an effectve recompresson. Overexpanson and under-expanson of the et comng from the nozzle ndcate neffectve recompresson and lower entranments, respectvely. The Real Flud Property smulaton predcts more accurately the thermodynamc propertes prescrbed n the NIST-REFPROP Database than the Ideal Gas Model. The former also gves hgher entranment rato and COP, thus, t can be consdered a more relable approach. However, such advantages cannot be construed to say that one model s better than the other unless an expermental valdaton s done n the future to further verfy ths clam. NOMENCLATURE CFD Computatonal Flud Dynamcs (-) COP Coeffcent of Performance (-) ER entranment rato (-) E Total Energy (J) m mass flow rate (kg/s) M w Molecular weght (kg/kmol) P pressure (Pa) Q heat (W) RANS Reynolds-averaged Naver-Stokes (-) R Unversal Gas Constant (J/kmol-K) T temperature (K) UDF User-defned Functon (-) ρ densty (kg/m 3 ) u velocty (m/s) stress tensor (-) x, y, z coordnates (-) α thermal conductvty (W/m-K) μ dynamc vscosty (kg/m-s) k turbulent knetc energy (J) δ Kronecker symbol (-) Subscrpts C condenser E evaporator eff effectve g generator, space components p prmary flow, pump s secondary flow Fg. 8. Varaton of the Speed of Sound wth Temperature at Constant Pressure ISSN: (Prnt); ISSN: (Onlne) ACKNOWLEDGMENT The authors express ther sncerest grattude to the Engneerng Research and Development for Technology (ERDT) Program of the Department of Scence and Technology Scence Educaton Insttute (DOST SEI) of the Republc of the Phlppnes for fundng ths research and ts dssemnaton.

6 Proceedngs of the World Congress on Engneerng 2017 Vol II, July 5-7, 2017, London, U.K. REFERENCES [1] X. Chen, S. Omer, M. Worall, and S. Rffat, Recent Developments n Eector Refrgeraton Technologes, Renewable and Sustanable Energy Revews, vol.19, pp , [2] Ansys, Inc. (2011). Avalable: [3] Y. Bartosewcz, Z. Adoun, and Y. Mercader, Numercal Assessment of Eector Operaton for Refrgeraton Applcatons based on CFD, Appled Thermal Engneerng, vol. 26, pp , [4] R. Yapc, H.K. Ersoy, A. Aktoprakoglu, H.S. Halkacı, and O. Ygt, Expermental Determnaton of the Optmum Performance of Eector Refrgeraton System Dependng on Eector Area Rato, Internatonal Journal of Refrgeraton, vol. 31, pp , [5] A. Selvarau, and A. Man, Expermental Investgaton on R134a Vapour Eector Refrgeraton System, Internatonal Journal of Refrgeraton, vol. 29, pp , [6] ASHRAE, Steam-Jet Refrgeraton Equpment, Equpment Handbook, vol.13, pp , [7] ESDU, Eectors and Jet Pumps, Desgn for Steam Drven Flow, Engneerng Scence Data tem 86030, Engneerng Scence Data Unt, London, [8] B.J. Huang, J.M. Chang, C.P. Wang, and V.A. Petrenko, A 1-D Analyss of Eector Performance, Internatonal Journal of Refrgeraton, vol. 22, pp , [9] R.H. Yen, B.J. Huang, C.Y. Chen, T.Y. Shu, C.W. Cheng, S.S. Chen, and K. Shestopalov, Performance Optmzaton for a Varable Throat Eector n a Solar Refrgeraton System, Internatonal Journal of Refrgeraton, vol. 36, pp , [10] Y. Zhu, and P. Jang, Hybrd Vapor Compresson Refrgeraton System wth an Integrated Eector Coolng Cycle, Internatonal Journal of Refrgeraton, vol. 35, pp , [11] Y. Bartosewcz, Z. Adoun, P. Desevaux, and Y. Mercader, Numercal and Expermental Investgatons on Supersonc Eectors, Internatonal Journal of Heat and Flud Flow, vol. 26, pp , [12] E. W. Lemmon, M. O. McLnden, and M. L. Huber, NIST Standard Reference Database 23: Reference Flud Thermodynamc and Transport Propertes-REFPROP, Verson 9.1, Natonal Insttute of Standards and Technology (NIST), Gathersburg, Maryland, [13] J. Chen, H. Havtun, and B. Palm, Investgaton of Eectors n Refrgeraton System: Optmum Performance Evaluaton and Eector Area Ratos Perspectves, Appled Thermal Engneerng, vol. 64, pp , [14] Y. Allouche, C. Bouden, and S. Varga, A CFD Analyss of the Flow Structure nsde a Steam Eector to Identfy the Sutable Expermental Operatng Condtons for a Solar-drven Refrgeraton System, Internatonal Journal of Refrgeraton, vol. 30, pp. 1-10, ISSN: (Prnt); ISSN: (Onlne)