DESIGN OF BACKWARD SWEPT TURBINE WHEEL FOR CRYOGENIC TURBOEXPANDER

Journal of Engineering Science and Technology Vol. 9, No. 4 (014) 43-431 School of Engineering, Taylor Univerity DESIGN OF BACKWARD SWEPT TURBINE WHEEL FOR CRYOGENIC TURBOEXPANDER BALAJI K. CHOUDHURY *, RANJIT K. SAHOO, SUNIL K. SARANGI Department of Mechanical Engineering, NIT Rourkela-769008, Odiha, India *Correponding Author: balajichoudhury@gmail.com Abtract With upport from the Department of Atomic Energy, our intitute ha initiated a programme on development and tudy of a low capacity (0 liter/hr.) turboexpander baed Nitrogen liquefier. Hence a proce deign wa carried out and a turboexpander wa deigned to meet the requirement of the liquefier. The turboexpander i ued for lowering the temperature of the proce ga (Nitrogen) by the ienthalpic expanion. The efficiency of the turboexpander mainly depend on the pecific peed and pecific diameter of the turbine wheel. The paper explain a general methodology for the deign of any type of turbine wheel (radial, backward wept and forward wept) for any preure ratio with different proce gae. The deign of turbine wheel include the determination of dimenion, blade profile and velocity triangle at inlet and outlet of the turbine wheel. Generally radial turbine wheel are ued but in thi cae to achieve the high efficiency at deired peed, backward curved blade are ued to maintain the Mach number of the proce ga at the nozzle exit, cloe to unity. If the velocity of fluid exceed the peed of ound, the flow get choked leading to the creation of hock wave and flow at the exit of the nozzle will be non-ientropic. Keyword: Turboexpander, Turbine wheel, Backward wept blade. 1. Introduction The performance of all cryogenic refrigeration and liquefaction plant mainly depend on the efficiency of turboexpander. The turboexpander i an expanion device where the proce ga i expanded by lowering it temperature at turbine ide and imultaneouly rejecting heat at the brake compreor ide. Hence the dimenion of turbine and it blade profile play a vital role in expanding the proce ga and lowering the temperature of the ga. The turboexpander conit 43

44 B. K. Choudhury et al. Nomenclature b Height (nozzle, impeller blade), m C Abolute velocity of fluid tream, m/ C o Spouting velocity, m/ C Velocity of ound, m/ D Diameter, m d Specific diameter, dimenionle h Enthalpy, kj/kg k 1 Preure recovery factor k Temperature and denity recovery factor M Mach number m& Ma of nitrogen flow through turboexpander, kg/ N Rotational peed, rpm n Specific peed P Power output of the turbine, W p Preure, N/m Q Volumetric flow rate, m 3 / Specific entropy, kj/kg K T Temperature, K t Blade thickne, m U Blade velocity (in tangential direction), m/ Z Number of blade Greek Symbol α Abolute velocity angle, radian α Inlet flow angle, radian 0 α Throat angle, radian t α Ma fraction of nitrogen diverted through turboexpander tr β Relative velocity angle, radian η Ientropic efficiency λ Hub diameter to tip diameter ratio tr ρ Denity, kg/m 3 ξ Inlet turbine impeller diameter to exit tip diameter ratio ω Rotational peed, rad/ Subcript o Stagnation condition hub Hub of turbine impeller at exit m Meridional direction max Maximum mean Average of tip and hub min Minimum r Radial direction Ientropic t Throat tip Tip of turbine impeller at exit θ Tangential direction Journal of Engineering Science and Technology Augut 014, Vol. 9(4)

Deign of Backward Swept Turbine Wheel for Cryogenic Turboexpander 45 of a turbine impeller and a brake compreor at the two end of a vertically placed haft. The haft i upported by two number of tilting pad journal bearing and two number of aerotatic thrut bearing. The whole component are place inide a bearing houing. At the lower end of bearing houing, cold end houing i attached. The cold end houing conit of nozzle and diffuer. At the top of bearing houing, warm end houing preent. It conit of nozzle to the brake compreor. The ectional view of the turboexpander i hown in Fig. 1 and the deign input parameter are hown in Table 1. Fig. 1. Sectional View of Turboexpander Aembly. Table 1. Deign Input Parameter. Working fluid Turbine inlet temperature, T in Turbine inlet preure, Dicharge preure, Ma flow rate, m& p ex p in Nitrogen 14 K 7.97 bar 1. bar 76.46 kg/ Working of Turboexpander The proce ga enter from the bottom end and get expanded by paing through the nozzle and turbine impeller and come out from the diffuer. The tate point at nozzle, turbine impeller and diffuer are hown in Fig.. Due to the Journal of Engineering Science and Technology Augut 014, Vol. 9(4)

46 B. K. Choudhury et al. ienthalpic expanion of the proce ga the temperature decreae along with the preure. Preure recovery occur due to the preence of diffuer. The T- diagram of the turboexpander expanion proce i hown in Fig. 3. The deign of turboexpander need a fixed tate of proce tream parameter or deign point. The deign point i fixed a per the proce deign done for turboexpander baed Nitrogen liquefier [1]. The literature of deign method for turboexpander [-5] are available for low expanion ratio with purely radial turbine. But the required deign point have high expanion ratio (i.e., 6.64). The high expanion ratio i achieved by uing backward curved vane [6] which increae the tangential force on the blade thereby increaing the turbine peed for higher efficiency. The preent deign procedure ha following characteritic: Deign for any expanion ratio. Deign of radial, backward or forward turbine. Fig.. State Point at Nozzle, Turbine Impeller and Diffuer. Fig. 3. T- Diagram of Turboexpander. Journal of Engineering Science and Technology Augut 014, Vol. 9(4)

Deign of Backward Swept Turbine Wheel for Cryogenic Turboexpander 47. Deign of Turbine Wheel The major dimenion of the turbine wheel and it inlet and exit velocity triangle are uniquely determined by the two dimenionle parameter [7], i.e., pecific peed and pecific diameter. The pecific peed and pecific diameter are expreed by the following equation n d Specific peed, = ω Q 3 3/ 4 ( h ) in 3, Specific diameter, ( h ) 1/ 4 D in 3, = () Q3 where Q 3 i the volumetric flow rate at the exit of the turbine impeller and h in-3, i the ientropic enthalpy drop from inlet to the turbine exit. The value of pecific peed and pecific diameter are choen o that Mach number of the fluid at the nozzle exit i maintained at or cloe to unity. If the velocity of fluid exceed the peed of ound, the flow get choked leading to the creation of hock wave and flow at the exit of the nozzle will be non-ientropic. To achieve the maximum poible efficiency within the ubonic zone the pecific peed and pecific diameter are choen o a 0.5471 and 3.478 repectively. At known inlet input preure and temperature all the ret thermodynamic propertie can be calculated uing property package ALLPROPS [8]. Conidering reaonable turboexpander efficiency of 75%, enthalpy at exit, hex i calculated by following equation, h = h η( h h ) (3) ex in in ex, Power produced, ( ) P = m& h in h ex (4) Q ex and volume flow rate at diffuer exit, = m& / ρ (5) ex The tate at the inlet and exit of the turboexpander are known. But tate at turbine exit are not known. There i the difference between the tate 3 and ex caued by preure recovery and conequent rie in temperature and denity in the diffuer. The two factor k 1 and k are taken in account, where k1 = Q3 Qex (6) and k = ( h h ) h h (7) in 3 in ex, The value of 1 k i aumed to be 1.11 a taken by Ghoh [] and k value i taken a 1.03 from the uggetion of Kun and Sentz [5]. Subtituting the value of (1) Journal of Engineering Science and Technology Augut 014, Vol. 9(4)

48 B. K. Choudhury et al. k 1 and k in Eq. (6) and (7) repectively we get, ientropic enthalpy drop from turbine hin 3, and volumetric flow rate at exit of turbine impeller Q 3. Putting the value of hin 3, and Q 3 into Eq. (1) and () give the peed and diameter of the turbine. The velocity ratio i calculated from the ratio of blade velocity to pouting velocity, where pouting velocity, C o 1 h ex, = ( h ) (8) A all radial turbine are found to produce maximum efficiencie over the range of velocity ratio 0.65 to 0.70 [9], the current deign i limit to within limiting value. Rohlik [10] precribe that; ξ the ratio of eye tip diameter to inlet diameter hould be limited to a maximum value of 0.7 to avoid exceive hroud curvature. The value of ξ i taken a 0.6, correponding to the maximum efficiency within the ubonic zone and for obtaining longer blade paage. Again from Reference [10], the exit hub to tip diameter ratio hould be limited to a minimum value of 0.4 to avoid exceive hub blade blockage and energy lo. Kun and Sentz [5] have taken the ratio a 0.35 while Ino et al. [6] have choen a value of 0.588. For current deign the value of λ i taken a 0.45. Table give the etimated value of turbine impeller. Table. Etimated Value of Turbine Impeller. Inlet diameter 9.6 mm Rotational peed 138777 rpm Eye tip diameter 17.8 mm Hub diameter 8.9 mm Power output 85.3 W Velocity ratio 0.68.1. Turbine exit velocitie For mall turbine, the number of blade depend on the hub circumference at exit and availability of diameter of milling cutter. So number of blade i taken Z = 10 []. Conidering uniform thickne of blade i 0.6 mm []. Auming abolute meridian velocity, C m3 and exit angle, α3 a 95 o [6] other velocity component are calculated along with mean blade angle at exit uing following equation. Abolute velocity at turbine exit, C m 3 C3 = (9) inα 3 Abolute tangential component, C = C co( 3 ) (10) θ 3 3 α Relative velocity at turbine exit, W = C + U C U co( α ) (11) 3 3 3 3 3 3 Journal of Engineering Science and Technology Augut 014, Vol. 9(4)

Deign of Backward Swept Turbine Wheel for Cryogenic Turboexpander 49 β 3, mean = tan C in( α ) 1 3 3 U C co( α ) 3, mean 3 3 (1) Flow through turbine ( 3, 3, ) π Zt D D Q3 = C3 in( α3) ( D3, tip D3, hub ) 4 in β tr tip hub 3, mean (13) Comparing the value of Q3 in Eq. Error! Reference ource not found. with the previouly calculated value from Eq. (5), if they are not equal then change the value of C m3 until both the value are equal... Turbine inlet velocitie Aume incidence angle, α a 6 o [3]. The amount of work can be extracted from a turbine i calculated from change in momentum of the fluid in it paage through the turbine impeller. So implifying the energy conervation equation for turbo machine [9], abolute velocity i calculated a C C 1000( h h ) + U C co( α ) 0 03 3 3 3 = (14) U co( α ) And ret of the velocitie etimated a follow. = C co( α ) (15) θ C = C in( α ) (16) m W = Cm + ( U C θ ) (17) β = tan 1 C m ( U ) C ϑ (18) It can be een from Fig. 4 that the turbine impeller ha backward wept blade. The blade profile ha been worked out uing the technique of Haelgruber [11], which ha been modified for the backward curved vane. Fig. 4. Velocity Triangle at Inlet ant Exit of the Turbine Impeller. Journal of Engineering Science and Technology Augut 014, Vol. 9(4)

430 B. K. Choudhury et al. Figure 5 how the different type blade profile. In backward curved blade, u > C coα give a the blade are inclined away from the direction of motion ( ) higher value of blade velocity, u for the given pouting velocity, C0 and nozzle angle. Or, in other word, the ame blade velocity give a lower value of jet velocity compared to other type of blade. Thi permit more preure drop in the nozzle, thu permitting the ue of high expanion ratio within the ubonic zone. Fig. 5. Different Type of Blade..3. Thermodynamic tate at dicharge (tate at 3) Neglecting loe in the diffuer, Stagnation enthalpy at turbine exit, h03 i equal to Stagnation enthalpy at diffuer exit h 04. From the tagnation enthalpy at turbine exit, tatic enthalpy at turbine exit i calculated. The denity wa found out by knowing the value of ma flow and volume flow at turbine exit by following equation ρ 3 = m& / Q 3 (19) From h 3 and ρ 3, all the other propertie at the turbine outlet are calculated from fluid property calculation oftware ALLPROPS [8]..4. Thermodynamic tate at inlet (tate at ) For computing the thermodynamic propertie at impeller inlet (tate ), the efficiency of the expanion proce till tate i aumed. Auming ientropic expanion in the vane le pace, the efficiency of the nozzle along with the vane le pace i defined a h ηn = h in in h h From Eq. (0), taking the nozzle efficiency η n a 93% [5, 6, and 1], the ientropic enthalpy at turbine inlet i calculated. Alo due to ientropic at inlet to nozzle i equal to inlet to turbine, i.e., in = 1 =. Knowing h and, the other propertie at turbine inlet are calculated along with the velocity of ound. Then abolute Mach number at the exit from the nozzle or inlet to the turbine impeller i calculated from the following equation which i to be le than 1 (i.e., 0.9388) (0) Journal of Engineering Science and Technology Augut 014, Vol. 9(4)

Deign of Backward Swept Turbine Wheel for Cryogenic Turboexpander 431 M = C C (1) / From continuity equation, the blade height at entrance to the impeller i computed from Eq. () a 0.709 mm. b = m& ( πd Z trttr ) ρ Cm () 3. Concluion The requirement of turboexpander to operate at high preure ratio and with high velocitie for better efficiency a backward curved turbine impeller i deigned. It maintain the Mach number at inlet to the turbine and take care of the velocity ratio (i.e., ratio of blade velocity to the pouting velocity) which i about 0.68. Reference 1. Alur, S.A.; Choudhury, B.K.; Sahoo, R.K.; and Sarangi, S.K. (010). Simulation of turboexpander baed nitrogen liquefier. Proceeding of the 0 th National and 9th International ISHMT-ASME Heat and Ma Tranfer Conference, January 4-6, Mumbai, India.. Ghoh, P. (00). Analytical and experimental tudie on cryogenic turboexpander. Ph.D. Thei, Indian Intitute of Technology Kharagpur, India. 3. Ghoh, S.K. (008). Experimental and computational tudie on cryogenic turboexpander. Ph.D. Thei. National Intitute of Technology Rourkela, India. 4. Kun, L.C. (1988). Expanion turbine and refrigeration for ga eparation and liquefaction. Advance in Cryogenic Engineering, 33, 963-973. 5. Kun, L.C.; and Sentz, R.N. (1985). High efficiency expanion turbine in air eparation and liquefaction plant. Proc. International Conference on Production and Purification of Coal Ga & Separation of Air, 1-1. 6. Ino, N.; Machida, A.; Ttugawa, K.; and Arai, Y. (199). Development of high expanion ratio Helium turbo expander. Advance in Cryogenic Engineering, 37B, 835-844. 7. Balje, O.E. (1981). Turbomachine. John Wiley and Son. 8. Lemmon, E.W.; Jacoben, R.T.; Penoncello, S.G.; and Beyerlein, S.W. (1995). ALLPROPS 4. Computer program for calculating thermodynamic propertie of fluid of engineering interet. Centre for Applied Thermodynamic Studie, Univerity of Idaho. 9. Blackford, J.E.; Halford P.; and Tantam, D.H. (1971). Expander and pump in G.G. Haelden (Ed.) Cryogenic Fundamental. Academic Pre London, 403-449. 10. RohliK, H.E. (1968). Analytical determination of radial inflow turbine geometry for maximum efficiency. NASA TN D-4384. 11. Haelgruber, H. (1958). Stromunggerechte getaltung der laufrader von radialkompreoren mit axialem laufradeintrict Kontruction (in German). 10(1), 1-. 1. Sixmith, H.; and Swift W.L. (1986). Cryogenic turbine and pump in Hand. Cryogenic Engineering Academic Pre, 341-35. Journal of Engineering Science and Technology Augut 014, Vol. 9(4)