Development and Implementation of a New Mathematical Model of the Tangential Exit Nozzles in Centrifugal Compressors
Authors: Drozdov A.A., Galerkin Y.B., Utsekhovskiy A.A. | Published: 27.06.2020 |
Published in issue: #6(723)/2020 | |
Category: Energy and Electrical Engineering | Chapter: Vacuum and Compressor Technology and Pneumatic Systems | |
Keywords: centrifugal compressor stage, tangential exit nozzles, scroll, annular chamber, mathematical model, loss coefficient |
Various engineering techniques are used for optimal gas-dynamic design of centrifugal compressors. This includes a universal modelling method that consists of software programs developed at Peter the Great St. Petersburg Polytechnic University. Tangential exit nozzles are elements of the centrifugal compressor flow path. The analysis of the results of the tangential exit nozzle calculations using the current mathematical model showed a need of improvement. The following main provisions formed a basis for a new model: the size of the passage is determined using the flow rate equation at the entrance and exit of the output unit (the calculated cross sections should be increased by 25–35% according to the recognized recommendations by Russian experts); the real nature of the flow in the output unit is taken into account by introducing an empirical coefficient in the equation of the circumferential component of velocity; the output diffuser is designed taking into account the optimal angle of expansion of an equivalent conical diffuser; the scroll tongue is shifted from a section with an angle of expansion of 0° to a section with an angle of expansion of 30°, which aids levelling the circumferential flow parameters and reduces total losses. To simplify the calculation process, a constant density along the scroll length is adopted in the mathematical model. The circumferential component of velocity is also determined approximately using the flow continuity equation without taking viscosity into account. Losses in scrolls and annular chambers are calculated in the radial and meridional planes. In the radial plane, the main losses are friction losses, whereas in the meridional plane, the main losses are due to expansion. For a trapezoid scroll, these pressure losses are determined depending on the scroll’s expansion angle. In the off-design operating modes, incidental losses due to impact flow around the scroll tongue are added. The presented model was implemented in the new version of the universal modeling method. The mathematical model was identified by the results of the commissioning test of the turboexpanders and turbochargers.
References
[1] Ris V.F. Tsentrobezhnye kompressornye mashiny [Centrifugal compressor machines]. Leningrad, Mashinostroenie publ., 1981. 351 p.
[2] Miftakhov A.A., Zykov V.I. Vkhodnyye i vykhodnyye ustroystva tsentrobezhnykh kompressorov [Input and output devices of centrifugal compressors]. Kazan, Fen publ., 1996. 198 p.
[3] Idel’chik I.E. Aerogidrodinamika tekhnologicheskikh apparatov: (podvod, otvod i raspredeleniye potoka po secheniyu apparatov) [Aerohydrodynamics of technological devices: (inlet, outlet and flow distribution over the cross section of devices)]. Moscow, Mashinostroyeniye publ., 1983. 350 p.
[4] Miftakhov A.A., Seleznev K.P. Experimental study of aerodynamics of scrolls of centrifugal compressors. Trudy KKHTI, 1971, iss. 49, pp. 40–54 (in Russ.).
[5] Nikitin A.A., Yaminov V.G. Calculation of the output devices of a centrifugal compressor. Povysh. effektiv. parov. i gazov. kholod. mashin i protsessov teplomassoperenosa. Sbornik trudov [Improving the efficiency of steam and gas refrigeration machines and heat and mass transfer processes. Collection of works]. Leningrad, LTIKHP publ., 1989, pp. 58–65 (in Russ.).
[6] Nikitin A.A., Tsukerman S.V. The research results of the output devices of unified centrifugal compressor machines (UTsKM). Konstruirovaniye, issledovaniye, tekhnologiya i organizatsiya proizvodstva kompressornykh mashin. Sb. tr. [Design, research, technology and organization of production of compressor machines. Collection of works]. Sumy, VNII-Kompressormash publ., 1976, pp. 60–66 (in Russ.).
[7] Miftakhov A.A., Voronov G.F. The output devices of centrifugal compressors: design and calculation. Kompressornaya tekhnika i pnevmatika, 1996, iss. 1–2 (10–11), pp. 5–9 (in Russ.).
[8] PCA Engineers Limited. Available at: https://www.pcaeng.co.uk/software (accessed 15 January 2020).
[9] Japikse D. Agile design system in the age of concurrent engineering. JANNAF Conference, Albuquerque, 1996, December, pp. 331–345.
[10] Japikse D., Bitter J. Effective two-zone modeling of diffusers and return channel systems for radial and mixed-flow pumps and compressors. Proceedings of the 11th International Symposium on Transport Phenomena and Dynamics of Rotating Machinery, 2006, vol. 2, pp. 511–520, doi: 10.1063/1.5122102
[11] Japikse D., Dubitsky O. Vaneless diffuser advanced model. Proceedings of the ASME Turbo Expo, 2005, vol. 6 pt. B, no. GT2005-68130, pp. 823–834, doi: 10.1115/GT2005-68130
[12] Qiu X., Japikse D., Zhao J., Anderson M.R. Analysis and Validation of a Unified Slip Factor Model for Impellers at Design and Off-Design Conditions. Journal of Turbomachinery, 2011, vol. 133(4), no. 041018, doi: 10.1115/1.4003022
[13] Drozdov A.V., Lunev A.T. The use of identification methods and multi-mode optimization in the design of centrifugal compressors. Potrebiteli-proizvoditeli kompressorov i kompressornogo oborudovaniya. Tr. 19 mezhdunar. simp. [Consumer manufacturers of compressors and compressor equipment. Proceedings of the 19th international symposium]. Sankt-Petersburg, SPbPU publ., 2015, pp. 69–73.
[14] Lunev A.T. The structure of the method for designing and testing the flow of the superchargers for pumping natural gas. Kompressornaya tekhnika i pnevmatika, 2001, no. 10, pp. 4–7 (in Russ.).
[15] Lunev A.T. Razrabotka vysokoeffektivnyh smennyh protochnyh chastey tsentrobezhnyh kompressorov gazoperekachivayushchih agregatov. Diss. kand. tekhn. nauk [Development of high-efficiency replaceable flow parts of centrifugal compressors of gas pumping units. Cand. tech. sci. diss.]. Kazan, 2005. 123 p.
[16] Galerkin Yu.B. Formation of views on work processes and the current state of gas-dynamic methods for designing industrial centrifugal compressors. Kompressornaya tekhnika i pnevmatika, 2000, no. 2, pp. 9–14 (in Russ.).
[17] Galerkin Y., Danilov K., Popova E. Design philosophy for industrial centrifugal compressors. Institution of Mechanical Engineers (IMechE) Conference Transactions, International Conference on Compressors and Their Systems, London, City University, 1999, pp. 465–480.
[18] Danilov K.A. Sozdaniye matematicheskoy modeli i programmnykh kompleksov dlya optimal’nogo gazodinamicheskogo proyektirovaniya kholodil’nykh tsentrobezhnykh kompressorov. Diss. kand. tekhn. nauk [Creation of a mathematical model and software systems for optimal gas-dynamic design of refrigeration centrifugal compressors. Cand. tech. sci. diss.]. Sankt-Petersburg, 1999. 176 p.
[19] Galerkin Y., Drozdov A. New generation of Universal modeling for centrifugal compressors calculation. IOP Conference Series: Materials Science and Engineering, 2015, vol. 90(1), no. 012040, doi: 10.1088/1757-899X/90/1/012040
[20] Galerkin Y., Rekstin A., Soldatova K., Drozdov A. Universal modeling method — the instrument for centrifugal compressor gas dynamic design. ASME Gas Turbine India Conference, 2015, no. 119665, doi: 10.1115/GTINDIA2015-1202
[21] Drozdov А., Galerkin Y. Modeling the non-incidence inlet flow rate coefficient in a centrifugal compressor impeller. AIP Conference Proceedings, 2018, vol. 2007, iss. 1, no. 030052, doi: 10.1063/1.5051913
[22] Rekstin А., Popova Y., Ucehovscy A. Centrifugal compressor stages efficiency analysis by means of the approximate algebraic equations. AIP Conference Proceedings, 2018, vol. 2007, no. 030036, doi: 10.1063/1.5051897
[23] Rekstin A.F., Drozdov A.A., Solovyeva O.A., Galerkin Y.B. Two mathematical models centrifugal compressor stage vaneless diffuser comparison. AIP Conference Proceedings, 2018, vol. 2007, no. 030035, doi: 10.1063/1.5051896
[24] Galerkin Yu.B., Rekstin A.F., Solovyeva O.A. Vaneless diffuser of the centrifugal compressor stage design method. AIP Conference Proceedings, 2019, vol. 2141, no. 030007, doi: 10.1063/1.5122057
[25] Galerkin Yu.B., Rekstin A.F., Soldatova K.V., Drozdov A.A. Analysis of geometric and gas-dynamic parameters of centrifugal compressor stages in tenfold range of design flow rate. AIP Conference Proceedings, 2019, vol. 2141, no. 030018, doi: 10.1063/1.5122068
[26] Rekstin A.F., Galerkin Yu.B., Soldatova K.V. Computer programs application for development a primary design recommendations of low-flow rate centrifugal compressor stages. AIP Conference Proceedings, 2019, vol. 2141, no. 030032, doi: 10.1063/1.5122082
[27] Rekstin A.F., Galerkin Yu.B. The primary design method development of centrifugal compressor impellers based on the analysis of the geometrical parameters. AIP Conference Proceedings, 2019, vol. 2141, no. 030052, doi: 10.1063/1.5122102
[28] Rekstin A.F., Soldatova K.V., Galerkin Yu.B. Experience of application the computer program based on a simplified mathematical model for industrial centrifugal compressors candidates. IOP Conference Series: Materials Science and Engineering, 2019, vol. 604, iss. 1, no. 012045, doi:10.1088/1757-899X/604/1/012045
[29] Galerkin Y., Drozdov A., Rekstin A. Centrifugal compressor impeller loading factor analysis. E3S Web of Conferences, 2019, vol. 124, no. 01005, doi: 10.1051/e3sconf/201912401005
[30] Rekstin A.F., Soldatova K.V., Galerkin Yu.B., Popova E.Y. Verification of a simplified mathematical model of centrifugal compressor stages. E3S Web of Conferences, 2019, vol. 124, no. 01005, doi: 10.1051/e3sconf/201912401007
[31] Galerkin Yu.B., Soldatova K.V. Modelirovaniye rabochego protsessa promyshlennykh tsentrobezhnykh kompressorov. Nauchnyye osnovy, etapy razvitiya, sovremennoye sostoyaniye [Modeling the workflow of industrial centrifugal compressors. Scientific basis, stages of development, current status]. Sankt-Petersburg, SPbPU publ., 2011. 327 p.
[32] Seleznev K.P., Galerkin K.P. Tsentrobezhnyye kompressory [Centrifugal compressors]. Leningrad, Mashinostroyeniye publ., 1982. 271 p.
[33] Galerkin Yu.B., Rekstin F.S. Metody issledovaniya tsentrobezhnykh kompressornykh mashin [Research Methods for Centrifugal Compressor Machines]. Leningrad, Mashinostroyeniye publ., 1969. 303 p.
[34] Soldatova K.V. Sozdaniye novoy matematicheskoy modeli protochnoy chasti tsentrobezhnykh kompressorov i bazy dannykh model’nykh stupeney. Dokt. Diss. [Creation of a new mathematical model of the flow part of centrifugal compressors and a database of model stages. Doct. Diss.]. Sankt-Petersburg, 2017. 357 p.
[35] Galerkin Yu.B. Turbokompressory [Turbochargers]. Sankt-Petersburg, KKHT publ., 2010. 650 p.
[36] Galerkin Yu.B., Rekstin A.F., Drozdov A.A., Kaminskiy R.V., Sibiryakov S.V., Turegulov T.I., Usenko A.E. Design experience for low-pressure turbocharger based on the modern version of the Universal Modeling Method. Kompressornaya tekhnika i pnevmatika, 2019, no. 2, pp. 2–10 (in Russ.).
[37] Galerkin Yu.B., Semenovskiy V.B., Soldatova K.V. Creating model stages of centrifugal compressor based on experimental data. AIP Conference Proceedings, 2019, vol. 2141, no. 030026, doi: 10.1063/1.5122076