New Version of the Universal Modeling for Centrifugal Compressor Gas Dynamic Design

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1 Purdue University Purdue e-pubs International Compressor Engineering Conerence School o Mechanical Engineering 014 New Version o the Universal Modeling or Centriugal Compressor Gas Dynamic Design Kristina Soldatova Sankt-Peterburg State Polytechnical University, Russian Federation, buck0@list.ru Galerkin Yuri Sankt-Peterburg State Polytechnical University, Russian Federation, galerkin@pe.spbstu.ru Drozdov Aleksandr Sankt-Peterburg State Polytechnical University, Russian Federation, a_drozdi@mail.ru Follow this and additional works at: Soldatova, Kristina; Yuri, Galerkin; and Aleksandr, Drozdov, "New Version o the Universal Modeling or Centriugal Compressor Gas Dynamic Design" (014). International Compressor Engineering Conerence. Paper This document has been made available through Purdue e-pubs, a service o the Purdue University Libraries. Please contact epubs@purdue.edu or additional inormation. Complete proceedings may be acquired in print and on CD-ROM directly rom the Ray W. Herrick Laboratories at Herrick/Events/orderlit.html

2 1197, Page 1 NEW VERSION OF THE UNIVERSAL MODELING FOR CENTRIFUGAL COMPRESSOR GAS DYNAMIC DESIGN Y.B. Galerkin, K.V. Soldatova, A.A. Drozdov TU Saint-Petersburg, Russia buck0@list.ru ABSTRACT The 4 th generation model o the known TU SPb Universal modeling programs or gas dynamic design were perect enough to predict design point eiciency with accuracy about,5% i a single set o coeicients was applied. To raise accuracy o calculations to 1% or less dierent sets o empirical coeicients were necessary or stages with dierent low rate and work coeicients. The proposed text is ocused on scientiic background and realization o model improvements that leads to accuracy about 0,5% o design eiciency prediction with a single set o empirical coeicients or all types o stages and compressors. Samples o application are given. Key words: compressor design, loss model, perormance prediction, test data, model stages, low rate coeicient, work coeicient. Decades ago at pre computer era design process consisted o empirically based set o rules application to choose main low path dimensions. Serious model tests were obligatory beore compressor manuacturing to check delivery pressure and eiciency. Better low physical models and computer progress made possible to develop quickly operating programs to predict gas dynamic perormance curves o an arbitrary low path. TU SPb set o computer programs was named The Universal modeling method and its application still in mid 1990 th had lead to elimination o model tests in a design process o industrial centriugal compressors [1,, 3, 4, 5, 6]. Set o algebraic equations describe surace riction losses, low separation and ollowing mixing losses. Flow deceleration along suraces and velocity gradient along a normal to suraces are taken into account. Schematically represented blade velocity diagram parameters are an important part o the model. Several dozens o compressor with delivery pressure up to 1,5 MPa, number o stages 1-8, power up to 5 mwt were designed or some Russian and oreign manuacturers by the preceding generation programs. Amount o compressor installed exceeds 400 with total power close to kwt. In all cases the design parameters were achieved without model tests. The sample o typical -stage pipeline compressor is shown in the Fig. 1. Fig. 1. Cross section o -stage pipeline centriugal compressor The previous models are able to predict design point eiciency with accuracy about,5% i a single set o coeicients was applied. There are necessary to apply dierent sets o coeicients or dierent types o impellers to increase prediction accuracy to 1%. The scientiic background and realization o the new model with better abilities are presented in [7, 8, 9, 10]. New model or mixing mosses calculation was developed. Surace roughness and shroud labyrinth seal leakage inluence on low at an impeller inlet were taken into account. One o important improvements was new blade velocity diagram schematization very close to non viscid diagram. (Two) Old and new ways o schematization are demonstrated by Fig..

3 1197, Page Fig.. Non-viscid velocity diagrams along normalized length at a shroud blade-to-blade D impeller surace. Let old simpliied schematization (solid lines), right new schematization by numerical experiment math reduction The ollowing equations demonstrate why characteristic velocities o a diagram w s1, w s, wp1 w p, w thr1 shown in the Fig. are important or perormance curve(s) modeling. For instance, riction loss coeicient o impeller blades is equal: and: z S bl w w s p r pro m cws ws cwp wp wthr1 wthr1 There are members o Eq. 1 that include characteristic velocities: Drag orce coeicient [11]; Xi Xi ws / u w s cws 1 Xi 4 Xi 1 Rbl / D w s1 wp / u w p cwp 1 Xi 4 Xi1 Rbl / D w p1 X i X i ws 0,5ws 1w s, p 0,5 p1 p. (1), (), (3) w w w, (4) ws 0,5ws 1w s, p 0,5 p1 p w w w, (5) in Eq. 1 is calculated by ormulae or a thin plate with smooth or (o) rough surace X - hydraulically smooth surace, (6) i 1/7 Rew 1 X - rough surace. (7) i lg Rz/ lbl

4 1197, Page 3 w / The member p u 4 in Eq., 3 represents dimensionless velocity gradient normal to a surace. It Rbl / D inluences a normal component o turbulent pulsations. Characteristic velocities on a suction side are participating in calculation o mixing losses. The scheme o separation and mixing process are shown in the Fig. 3. Fig. 3. Scheme o wake ormation due to low separation at a suction side (let) and low mixing at an impeller exit (right) The separation point position depends on normal velocity gradient that suppresses normal pulsations on a suction side o blades; w w X X w / u. (8) s s s i 1 i 4 w s1 Rbl / D Mixing loss coeicient corresponds to scheme o sudden expansion: Empirical coeicients values o the math model. i w 1 r se Xi wssin w1 w1 c X i. (9) X ( i 1 60 ) depends on their position in presented above and other equations Models o 4 th and earlier versions operate with simpliied deinition o characteristic velocities as shown in the Fig. (let). Non-viscid velocity diagram is very close to a real one at design low rates at least [1]. Simpliied deinition is based on a mean blade load. For instance in case o D impeller a mean load is equal: 1 T w sin. (10) z 1D1 Blade load distribution along a blade length (or any impeller) must be estimated by a program user arbitrarily and result is presented by solid lines in the Fig. (let). To achieve principally better velocity diagram description the Authors applied results o numerical experiment presented at [7, 8]. About one hundred o impellers in range o low rate coeicients 0,00 0,090, Euler work coeicients 0,45 0,80, relative hub 0,0 0,45 were designed and their velocity diagrams were calculated and mathematically reduced. The last version o the equation or maximum local velocity on a blade w was proposed by one o the Authors: 1, ,5,06 b ws wthr 0, 61T des 1,69D1 w. (11) mean 1D1 Result o velocity diagram schematization by Eq. (11) and alike is demonstrated in Fig. (right), (let). Special attention was paid to more correct modeling o 3D impellers. Input menu o the 6 th version program in the Fig. 4 shows more detailed description o an impeller meridian shape. s1

5 1197, Page 4 Fig.4. Input menu or a 3D impeller meridian shape (6 th version o the model) In the 7 th version o the model low parameters in 3D impellers are calculated in Q-3D mode on ive blade to blade suraces. The sample o low parameters at 3D impeller exit is presented in the Fig. 5. The new model identiication and veriication validated proposed improvements. Test data on TU SPb model stages 0CE amily [13] were used. The accuracy o eiciency calculations at design low rate with a single set o empirical coeicients is about 0,6% or a wide range o model stages ( 0,08 0,064, T des 0,45 0,68, 0,5 0,373 D, hub D4 1, 43 1,6 (VLD), etc.). des

6 1197, Page 5 Fig. 5. Loss coeicients and loss o eiciency o a 3D impeller along blade height at an exit Fig. 6 represents comparison o measured and calculated perormances o several model stages. Fig. 6. Comparison o measured and calculated perormances or several model stages. Dotted line - experiment, continuous line calculation Fig. 7. Low low rate stage measured and calculated perormances. Red M u = 0,435, blue line - experiment, continuous line - calculation M u = 0,80. Dotted

7 1197, Page 6 Validation o the new model and the empirical coeicient set was made by comparison o measured and calculated perormances o several low low rate stages developed by one o compressor manuacturers. The typical result is presented in the Fig. 7. Low low rate stage with geometry parameters b 0, 057, b3 0,0103 D hub 0,31 was tested at M u = 0,435 and 0,80. D, 4 1,33, The new model and 5 th generation programs were applied to model plant test perormances o 16 compressors ( 8 stages, power 4,5-5 MW, delivery pressure up to 1,5 MPa). Some inormation on results was presented also in [8, 9, 10]. Sample o modeling is presented in the Fig.8. test, - Fig. 8. Four stage 16 MWt booster compressor. Plant test perormances and their modeling. calculation The important result o plant test perormance modeling - all perormances were well correlated with calculations on the base o a single set o empirical coeicients or all 16 compressors [7, 14, 15]. The stages o the compressors can be considered as 99 model stages with range o design parameters des = 0,05 0,064, T des = 0,40 0,85. The new versions o the model and computer programs were also successully applied to design 3 MWt single stage pipeline compressor, 16 MWt 6-stage booster compressor and in other designs and analytic projects (works). NOMENCLATURE b height; c absolute velocity; c r radial velocity; cu tangential velocity; c skin riction coeicient; c drag orce coeicient; w D diameter; l bl blade length; M u rotational Mach number; Re Reynolds number; R bl radius o blade curvature; Rz roughness; S blade area; bl U impeller periphery speed; V volumetric low; w relative gas velocity; z number o blades in a blade row, number o vanes; stage low coeicient;

8 1197, Page 7 t total polytropic eiciency; blade blockage coeicient; compressibility coeicient; e T Euler coeicient; stage work coeicient; low angle; z loss coeicient. Subscripts 1 impeller blade inlet condition; impeller tip condition; 3 vaned diuser inlet condition; 4 diuser exit condition; des r inl max p pro s se thr c c / u, b b / D design regime; riction; inlet; maximum; pressure side; proile; suction side; sudden expansion; throat; superlinear line mean, that speed is carried to character impeller periphery speed, the linear size is carried to the character linear size (impeller periphery diameter) REFERENCE 1. Galerkin Y., Popova E. Industrial centriugal compressors gas dynamic calculation and optimization concepts. Texts o the Union o the German engineers. Aachen. Germany Galerkin Y.B., Danilov K.A., Popova E.Y. Universal Modelling or Centriugal Compressors-Gas Dynamic Design and Optimization Consepts and Application. Yokohama International Gas Turbine Congress. Yokohama Galerkin Y.B., Popova E.Y., Danilov., Mitroanov V.P. Quasi-3d Calculations in Centriugal Impeller Design. VDI Berichte Hannover Galerkin Y., Danilov K., Popova E. Design philosophy or industrial centriugal compressor. // International Conerence on Compressors and their systems. London: City University. UK Galerkin Y., Mitroanov V., Geller M., Toews F. Experimental and numerical investigation o low in industrial centriugal impeller. // International Conerence on Compressors and their systems. London: City University. UK Galerkin Y. Pipeline Centriugal Compressors Principles o Gas Dynamic Design. International Symposium «SYMKOM-05». Compressor & Turbine Flow Systems. Theory & Application Areas. Lodz. 18. Vol Galerkin, Y. B., Soldatova, K.V. Operational process modeling o industrial centriugal compressors. Scientiic bases, development stages, current state. Monograph. [text] // SPbTU (In Russian). 8. Galerkin, Y. B., Drozdov A. A., Soldatova, K.V. Centriugal compressor eiciency types and rational application. // International Conerence on Compressors and their systems. London: City University. UK Galerkin, Y. B., Soldatova, K.V. Universal modeling method application or development o centriugal compressor model stages. // International Conerence on Compressors and their systems. London: City University. UK Seume J.R., Sextro T., Soldatova K.V. Modeling o small turbocharger compressors perormance curves. // International Conerence on Compressors and their systems. London: City University. UK Lojtsanskij L. Mechanics o liquid and gas. Moscow (In Russian). 1. Seleznev K., Galerkin Y. Centriugal compressors. //Leningrad. 198 (In Russian). 13. Galerkin, Y. B. Turbo compressors. // LTD inormation and publishing center. - Moscow (In Russian). 14. Galerkin, Y. B., Soldatova, K.V. Development o "virtual" model stages by means o 5th generation o the Universal modeling programs. [Text] // Scientiic and technical journal SPbSTU P

9 1197, Page Galerkin, Y. B., Soldatova, K.V. Development o model stages by the results o new generation industrial centriugal compressors tests. [Text] // Proc. o 15 Intern. Compressors scientiic and technical conerence. Vol. 1. Kazan., 011. P (In Russian)