Modern State of the Universal Modeling for Centrifugal Compressors Y. Galerkin, K. Soldatova, A. Drozdov

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1 World Academy of Scence, Engneerng and Technology Internatonal Journal of Industral and Manufacturng Engneerng Vol:9, No:, 05 Modern State of the Unversal Modelng for Centrfugal Compressors Y. Galerkn, K. Soldatova, A. Drozdov Internatonal Scence Index, Industral and Manufacturng Engneerng Vol:9, No:, 05 waset.org/pucaton/ Abstract The 6th verson of Unversal modelng method for centrfugal compressor stage calculaton s crbed. Identfcaton of the new mathematcal model was made. As a result of dentfcaton the unform set of emprcal coeffcents s receved. The effcency defnton error s 0,86 % at a gn pont. The effcency defnton error at fve flow rate ponts (except a pont of the maxmum flow rate) s, %. Several varants of the stage wth 3D mpellers gned by 6 th verson program and quas threedmensonal calculaton programs were compared by ther gas dynamc performances CFD (NUMECA FINE TURBO). Performance comparson demonstrated general prncples of gn valdty and leads to some gn recommendatons. Keywords Compressor gn, loss model, performance predcton, test data, model stages, flow rate coeffcent, work coeffcent. b c r c w wdth radal velocty NOMENCLATURE resstance force coeffcent D dameter angle of ncdence Kn specfc speed l ade heght М Mach number w p pressure R gas constant R radus Re u Reynolds number Rz roughness S area t ade ptch T temperature u ade speed X emprcal coeffcent w relatve velocty β ade angle related to tangental drecton β flow angle related to tangental drecton z number of a Yur Borsovch Galerkn s wth the S.-Peterbugd Poltechncal Ynversty, Russan Federaton, S-Peresburg, Polytechncal st. 9 (phone: ; fax: ; e-mal: yur_galerkn@ mal.ru). Krstna Valerevna Soldatova s wth the S.-Peterbugd Poltechncal Ynversty, Russan Federaton, S-Peresburg, Polytechncal st. 9 (phone: fax: ; e-mal: buck0@lst.ru). Aleksandr Aleksandrovch Drozdov s wth the S.-Peterbugd Poltechncal Ynversty, Russan Federaton, S-Peresburg, Polytechncal st. 9 (phone: ; fax: ; e-mal: a_drozd@ mal.ru). ϕ ψ T ζ ε m flow rate coeffcent work coeffcent losses effcency compressty coeffcent Subscrpts mpeller nlet mpeller ext ade gn m merdonal p pressure sde s sucton sde thr throat T І. GOAL AND OBJECTS OF MODELING OTAL power of centrfugal compressors nstalled s measured by dozens and dozens MWt n ndustral countres. The smplest of centrfugal compressors for ppe lne ndustry s shown n Fg.. These machnes have power n range 4-3 MWt, ext pressure to,5 MPa, number of stages up to 8 n one body. Compressors for other ndustres are more complcated usually. Power consumpton depends on many factors but the sound gas dynamc gn s the frst of them. Desgn procedure conssted of more or less proven rules to estash man flow path dmensons at pre-pc era. Numerous model tests at specal test rgs were ogatory before new compressor fabrcaton. The modern gas dynamc gn becomes easer and more relae. I.e. gven compressor pressure rato s guaranteed at gven mass flow rate wth good effcency. Expermental check and mprovement followed are not ogatory n many cases [4], [5]. Three-step numercal procedure s appled usually. The frst step of gn conssts of some mean lne feld type calculatons to fnd the best flow path man dmensons. The TU SPb R&D Laboratory of compressor proems was very actve n th. The TU SPb compressor school founded by Prof. K. Seleznev s one of the leadng Russan R & D centers [3]. Flow behavor study has lead to the physcal model formulaton and ts mathematcal crpton. The gn procedure scentfc background and practcal applcaton are well presented []-[6], [8]-[0]. Fg. shows that measured and calculated velocty dagrams at mpeller a are rather smlar at gn flow rate but the ext area where the wake s formatted []. Internatonal Scholarly and Scentfc Research & Innovaton 9() scholar.waset.org/ /

2 World Academy of Scence, Engneerng and Technology Internatonal Journal of Industral and Manufacturng Engneerng Vol:9, No:, 05 Internatonal Scence Index, Industral and Manufacturng Engneerng Vol:9, No:, 05 waset.org/pucaton/ Fg. Typcal two-stage ppe lne centrfugal compressor Fg. Measured (sold) and non vscd calculated velocty dagrams at D mpeller a Ths smlarty has proved Q3D non vscd calculaton effectve applcaton. A powder pant nserted n a flow path stcks to surfaces where shear stress are close to zero. Ths way wake and separaton zones formaton can be vsualzed. Fg. 3 demonstrates flow behavor n the D mpeller wth work coeffcent ψ 0,65. T 3D wake zone at the second part of the sucton sde of the ade s vse. Flow separaton never occurs at hub/shroud surfaces and mpeller ade pressure s, etc. Flow vsualzaton at Fg. 4 demonstrates wake zone and secondary flows on a sucton sde of an mpeller at close to surge flow rate and flow separaton n a vane dffuser at a gn flow rate. Fg. 3 Low shear stress zones n a D mpeller Fg. 4 Flow vsualzaton n stage components Sucton sde of a D mpeller ade, surge flow rate and flow separaton zone n a vane dffuser ІІ. UNIVERSAL MODELING BASIC FEATURES AND ACHIEVEMENTS Based on the physcal model the feld type Unversal modelng method s well presented to specalsts ([7]-[0], [4], [5]) so the basc nformaton s presented below only. The math model dentfcaton s based on gas dynamc performances of model stages. Loss of a head s calculated on each surface of a flow path and s summarzed. Shear stress force coeffcent and mxng loss coeffcents are presented as functons of flow velocty gradents along surfaces and along normal drecton. A velocty dagram of non vscd flow s crbed schematcally. Inlet and ext veloctes at two s of a ade are used for calculatons (are marked wth dots at Fg. 5). Internatonal Scholarly and Scentfc Research & Innovaton 9() 05 5 scholar.waset.org/ /

3 World Academy of Scence, Engneerng and Technology Internatonal Journal of Industral and Manufacturng Engneerng Vol:9, No:, 05 ζ fr prof w. (5) η fr prof = ψt Frcton loss coeffcents for hub and shroud surfaces are calculated on the same prncple. The physcal model s based on the absence of flow separaton everywhere n an mpeller but a sucton sde of a ade. The separaton pont s calculated by (6): X w s ws / u wɺ s = = X + X 4. (6) w s R / D Internatonal Scence Index, Industral and Manufacturng Engneerng Vol:9, No:, 05 waset.org/pucaton/ Fg. 5 Velocty dagram of non vscd flow on an mpeller ade and a scheme of flow separaton A frcton force coeffcent s presented s (a sample for a sucton sde): X ws / u w s cws = с f X 4 + X R / D w s X. () Two members of () present normal ws / u and R / D tangental w s velocty gradents. The basc value of the ws drag force coeffcent с f s the coeffcent of a thn plate []: с с f f hydraulcally smooth surface, () = X Re = X / 7 w lg Rz / l.5 - rough surface. (3) Emprcal coeffcents gradents X are subjects of model dentfcaton by balance of calculaton and measured performance curves. Ther numbers are ndvdual and show coeffcent s poston n the equatons. Equatons (4), (5) connect drag force coeffcents on both ade surfaces wth the frcton loss coeffcent of mpeller a and the last one wth an effcency loss: ζ = ε + π z S w w s p fr prof m cws ws cwp wp Ф wthr wthr, (4) The normalzed normal velocty gradent presents n (6) and reflects Rossby number nfluence on a boundary layer condton. Mxng loss coeffcent corresponds to scheme of sudden expanson: w з c r ζ mx = X wɺ s sn β. (7) w w The emprcal equatons and the proper coeffcents serve for off-gn regmes calculaton and take nto account 3-D flow character and compressty nfluence. The equatons for stator elements of a stage also present n the math model. The 4 th verson of computer programs was wdely used n academc and gn practce. Several dozens of compressor wth delvery pressure up to,5 MPa, number of stages -8, power up to 5 MWt were gned for some Russan and foregn manufacturers. Amount of compressor nstalled exceeds 400 peces wth total power close to KWt. In all cases the gn parameters were acheved wthout model tests. But one proem exsted for a gner. The math model basc prncple s that emprcal coeffcents X are ndependent of a stage parameters and smlarty crtera. It means that a sngle set of X must crbe gas dynamc performances of any stage at any condton wth accuracy of experments. The 4 th verson accuracy for gn pont effcency s nsde % that s not suffcent for gn practce. There are dfferent sets of for dfferent types of model stages partcpated n dentfcaton process. A gner had to choose proper sets for the gned objects. Ths dsadvantage also ponted out that the physcal and math models do not reflect all mportant factors. ІІІ. NEW VERSION OF MATH MODEL IDENTIFICATION AND VERIFICATION RESULTS The stuaton was revsed and several mportant novels were ntroduced n 5 th verson [7]-[0], [4], [5] and n the next, 6 th one too [0]. The flow path man dmensons nput are more precse and complete for 3-D mpellers especally. X X Internatonal Scholarly and Scentfc Research & Innovaton 9() 05 5 scholar.waset.org/ /

4 World Academy of Scence, Engneerng and Technology Internatonal Journal of Industral and Manufacturng Engneerng Vol:9, No:, 05 Velocty dagram schematzaton (Fg. 5) s made on the base of numercal experment by Q-3-D calculatons [7], [8]. Leakage n labyrnth seals s taken nto account, etc. The man novel n the math model s connected wth mxng losses calculaton. The emprcal coeffcent X n (6) s presented as a functon of two gas dynamc parameters of an mpeller: Internatonal Scence Index, Industral and Manufacturng Engneerng Vol:9, No:, 05 waset.org/pucaton/ X X X X X X w mx = + ψ T +. (8) w The new model dentfcaton was made wth the use of 37 tests of 8 basc model stages wth parameters Φ = 0,08 0,075, ψ T d es = 0,4-0,75 tested at M u = 0,60 0,86. Basc stages have varants wth dfferent hub rato, vaneless dffuser wdth, number of dffuser vanes, mpeller ade tralng edge confguraton. Fg. 6 Results of the 6th verson model dentfcaton Measured performances stroke lnes, calculated performances sold lnes The dentfcaton was made for all tests and a sngle set of the emprcal coeffcents was created. The average accuracy of effcency calculaton for all 37 tests s,09% - all flow rate range but the stall regme. The last s not mportant for ndustral compressors. The average accuracy for gn flow rate s 0,88%. Fg. 6 presents graphc nformaton about matchng of measured and calculated performances. Three compressors were chosen for the new model verfcaton. The 4-stage booster ppe lne compressor Fg. 7 0,5 0,75 wth optmal specfc speed of stages K = Φ / ψ n T [3] was gned by the Unversal modelng method. Fg. 7 Flow path scheme of the 6 MWt compressor wth delvery pressure 7,45Mpa Good correlaton of measured and calculated performances was expected Fg 8. Fg. 8 Sample of gas dynamc performance modelng. Four stage 6 MWt compressor wth delvery pressure 7,45M. P modelng, - test data The two stage booster compressor wth parameters close to the compressor above was qute unusual as the hgher pressure rse was acheved n two stages only. As result specfc speed was very far from optmal range. The frst stage parameters were Φ = 0,08, ψ T = 0,8. As result very narrow channels wth hgh level of frcton losses and mpeller a wth ext angle β = 04 0 Fg. 9. The second example compressor was gned by the Unversal modelng method too (4 th verson), but ts stages had no analogs. Anyway, the compressor demonstrated gn parameters at the plant test and at the nstallaton. The most satsfactory performance modelng result s shown at Fg. 0. The thrd sample compressor was gned by ts manufacturer on the base of model stages gned deca ago. Fg. shows unusual now a merdan shape of mpeller channels wth b b. It leads to excessve flow deceleraton w / w < 0,5 (recommendaton [7] w / w 0,60 0,65 ). Internatonal Scholarly and Scentfc Research & Innovaton 9() scholar.waset.org/ /

5 World Academy of Scence, Engneerng and Technology Internatonal Journal of Industral and Manufacturng Engneerng Vol:9, No:, 05 Hgh mxng losses lead to low effcency. Anyway, the modelng result s satsfactory n ths case too - Fg.. Internatonal Scence Index, Industral and Manufacturng Engneerng Vol:9, No:, 05 waset.org/pucaton/ Fg. 9 Scheme of the flow path of two stage 6 MWt compressor wth delvery pressure 7,45MP Fg. 0 Sample of gas dynamc performance modelng. Two stage 6 MWt compressor wth delvery pressure 7,45MP Fg. Scheme of the flow path of four stage 6 MWt compressor wth delvery pressure 7,45MP. Outdated gn Fg. Sample 3 of gas dynamc performance modelng. Outdated four stage 6 MWt compressor wth delvery pressure 7,45MP One more object of calculatons was the tested stage wth 3D mpeller and vaneless dffuser. Gas dynamc performances are compared at Fg. 3. ІV. SAMPLE OF OPTIMIZATION PRACTICE Results of dentfcaton and verfcaton of the 6 th verson of the model demonstrate ts valdty. It gves the possty to optmze man flow path dmensons by varants comparson. Several mportant aspects of gn cannot be solved by the smplfed approach of Unversal modelng though. The attractve way s to apply CFD calculatons to the proem. The test results shown at Fg. 4 are compared wth NUMECA FINE TURBO calculated performances Fg. 5. The result of the calculaton s qute typcal. CFD calculatons overestmate work coeffcent and underestmated ncdence losses at negatve ncdence angle ( Φ > Φ ). The same results were obtaned wth ANSYS CFX applcaton and wth other types of stages. The common postve result s that effcency predcton s qute satsfactory at Φ Φ. The stage wth Φ = 0,05, ψ T =0,56 was gned on prncples [3] and optmzed by 6 th verson computer program. Several approaches of 3D mpeller confguraton choce were compared by calculatons of effcency at Φ Φ. The mportant proem s 3D confguraton choce. The geometry prncple s qute smple. Blade angles are lnear functons of merdan length. The alternatve s to choose a confguraton by velocty dagram β = f l are optmzaton. The compared functons ( ) presented at Fg. 6. CFD calculaton has shown that η s m Internatonal Scholarly and Scentfc Research & Innovaton 9() scholar.waset.org/ /

6 World Academy of Scence, Engneerng and Technology Internatonal Journal of Industral and Manufacturng Engneerng Vol:9, No:, 05 0,4% hgher n the second case and the advantage s hgher at Φ > Φ. Internatonal Scence Index, Industral and Manufacturng Engneerng Vol:9, No:, 05 waset.org/pucaton/ Fg. 3 Model stage wth 3D mpeller and vaneless dffuser gas dynamc performances. Dots test, sold calculaton 6 th verson Unversal modelng 0.95 η Fg. 4 Model stage wth 3D mpeller and vaneless dffuser gas dynamc performances. Red test, ue CFD calculaton There s the opnon that ncrease of the work coeffcent along tralng edge from hub to shroud drecton n 3D mpellers can mprove flow unformty and dmnsh head losses n dffusers. The mpeller varant wth ψ T = f ( b ) = const was compared wth the varant wth ψ T s =,03ψ. T h It appeared that the flow feld unformty s nferor n case of ψ T = f ( b ) = var but the stage effcency s hgher at 0,% anyway. VІ. CONCLUSION Several other proems were studed by varants comparson. It could be concluded that general rules well proven n prevous gns are vald for hgh flow rate stages wth 3D mpellers too. Some detals of gn are constantly mproved by varants comparson and more precse gn recommendatons are formulated as result. Ф Fg. 5 3D mpeller merdan shape and two varants of ade β = f l confguraton defned by functon ( ) (a) (b) Fg. 6 Absolute velocty feld at the mpeller outlet. (a) ψ T s =, 03ψ T h, (b) ψ T = f ( b ) = const REFERENCES [] Galerkn Y., Popova E. Industral centrfugal compressors gas dynamc calculaton and optmzaton concepts. Texts of the Unon of the German engneers. Aachen. Germany m Internatonal Scholarly and Scentfc Research & Innovaton 9() scholar.waset.org/ /

7 World Academy of Scence, Engneerng and Technology Internatonal Journal of Industral and Manufacturng Engneerng Vol:9, No:, 05 Internatonal Scence Index, Industral and Manufacturng Engneerng Vol:9, No:, 05 waset.org/pucaton/ [] Galerkn Y.B., Danlov K.A., Popova E.Y. Unversal Modellng for Centrfugal Compressors-Gas Dynamc Desgn and Optmzaton Consepts and Applcaton. Yokohama Internatonal Gas Turbne Congress. Yokohama [3] Galerkn Y.B., Popova E.Y., Danlov К.А., Mtrofanov V.P. Quas-3d Calculatons n Centrfugal Impeller Desgn. VDI Berchte. 45. Hannover [4] Galerkn Y., Danlov K., Popova E. Desgn phlosophy for ndustral centrfugal compressor. // Internatonal Conference on Compressors and ther systems. London: Cty Unversty. UK [5] Galerkn Y., Mtrofanov V., Geller M., Toews F. Expermental and numercal nvestgaton of flow n ndustral centrfugal mpeller. // Internatonal Conference on Compressors and ther systems. London: Cty Unversty. UK. 00. [6] Galerkn Y. Ppelne Centrfugal Compressors Prncples of Gas Dynamc Desgn. Internatonal Symposum «SYMKOM-05». Compressor & Turbne Flow Systems. Theory & Applcaton Areas. Lodz. 8. Vol Р [7] Galerkn, Y. B., Soldatova, K.V. Operatonal process modelng of ndustral centrfugal compressors. Scentfc bases, development stages, current state. Monograph. (text) // SPbTU. 0. (In Russan). [8] Galerkn, Y. B., Drozdov A. A., Soldatova, K.V. Centrfugal compressor effcency types and ratonal applcaton. // Internatonal Conference on Compressors and ther systems. London: Cty Unversty. UK. 03. [9] Galerkn, Y. B., Soldatova, K.V. Unversal modelng method applcaton for development of centrfugal compressor model stages. // Internatonal Conference on Compressors and ther systems. London: Cty Unversty. UK. 03. [0] Soldatova K.V. Modelng of small turbocharger compressors performance curves. // Internatonal Conference on Compressors and ther systems. London: Cty Unversty. UK. 03. [] Lojtsanskj L. Mechancs of lqud and gas. Moscow. 978 (In Russan). [] Seleznev K., Galerkn Y. Centrfugal compressors. //Lenngrad. 98 (In Russan). [3] Galerkn, Y. B. Turbo compressors. // LTD nformaton and pushng center. - Moscow. 00. (In Russan). [4] Galerkn, Y. B., Soldatova, K.V. Development of "vrtual" model stages by means of 5th generaton of the Unversal modelng programs. (Text) // Scentfc and techncal journal SPbSTU P [5] Galerkn, Y. B., Soldatova, K.V. Development of model stages by the results of new generaton ndustral centrfugal compressors tests. (Text) // Proc. of 5 Intern. Compressors scentfc and techncal conference. Vol.. Kazan., 0. P (In Russan). Internatonal Scholarly and Scentfc Research & Innovaton 9() scholar.waset.org/ /