Phenomenological models of cavitation erosion kinetics

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8 International Cavitation Erosion Test Seminar, Sopot, 1-2 June 2000∆V, mm 3∆V, mm 320018016014012010080604020IMP PAN (RD) 1H18N9TStellerNoskievic, Sitnik00 200 400 600 800 1000 12005040302010Stellerczas, minIMP PAN (RD) 1H18N9TNoskievicSitnik00 100 200 300 400 500czas, minFig.5 Erosion curves obtained at the IMP PAN rotatingdisk facility (the exposure period of 20 h duration isanalysed)∆V, mm 35040302010IMP PAN (RD) 1H18N9TSitnikNoskievicSteller00 100 200 300 400czas, minFig.6 Erosion curves obtained at the IMP PAN rotatingdisk facility (the exposure period of 6 h duration isanalysed)The work on ensuring full reliabilityof calculations according tothe J.Noskievič model is now in progressand is expected to end successfullyin a short time. Neverthelessthe authors are reluctant to recommendit as an element of more sophisticatedalgorithms due to a rathercomplicated form of formula (5),incorporating additionally some periodicalfunctions.No numerical problems havebeen encountered when testing themodel of K.Steller. However, oneshould notice the non-vanishing firstderivative of formula (7) at the beginningof the process, which canresult in improper modelling of theincubation period and improper assessmentof the maximum instantaneouserosion rate (Fig.5b). On theother hand side, if the analysis isconfined to the period precedingattainment of the maximum cumulativeerosion rate (CER max ), the modelcan describe the reality even betterthan the other ones (Fig.6)Following the model ofL.Sitnik, the erosion rate in the initialstage of damage is always equalzero. The curves obtained show avery smooth pattern, hardly dependenton the duration of analysed period.Therefore, under some circumstances,the model can describe materialperformance in the initial damageperiod worse than the other ones.An obvious advantage is the veryfact that the model has been developedbasing on considerations of thestochastic nature of the cavitationerosion phenomenon. Thus, themodel is a continuation of the originalconcept of F.J.Heymann, somehowrelated to the contemporarymethods of modelling the fatiguephenomena [11].
J.Steller, P.Kaczmarzyk: Phenomenological models of cavitation erosion progress. 9REFERENCES1. Steller J.: International Cavitation Erosion Test. Preliminary Report. Part I: Coordinator'sReport. IMP PAN Int. Rep. no. 19/19982. Steller J.(ed.): International Cavitation Erosion Test. Preliminary Report. Part II: ExperimentalData. IMP PAN Int. Rep. no. 20/19983. Steller J.: International Cavitation Erosion Test and quantitative assessment of materialresistance to cavitation. Wear, Vol.233-235, December 1999, pp.51-644. Heymann F.J.: On the time dependence of the rate of erosion due to impingement or cavitation.[in:] "Erosion by Cavitation or Impingement", A symposium presented at the 69 thAnnual Meeting, ASTM, Atlantic City, 1966. ASTM Special Technical Publicationno.408, pp.70-1005. Noskievič J.: Dynamics of the cavitation damage, Joint Symposium on Design and Operationof Fluid Machinery, ASCE/IAHR/ASME, Colorado State University, Fort Collins,June 1978, pp.453-4626. Steller K.: Nowa koncepcja oceny odporności materiału na erozję kawitacyjną.Prace IMP, z.76, 1978, s.127-1507. Thiruvengadam A.P.: The concept of erosion strength. Erosion by cavitation or impingement[in:] "Erosion by Cavitation or Impingement", A symposium presented at the 69 thAnnual Meeting, ASTM, Atlantic City, 1966. ASTM Special Technical Publicationno.408, pp.22-358. Sitnik L.: Mathematical description of the cavitation erosion process and its utilizationfor increasing the materials resistance to cavitation. [in:] "Cavitation in Hydraulic Structuresand Turbomachinery". The Joint ASCE/ASME Mechanics Conf., Albuquerque,New Mexico, 1985, pp.21-309. Press W.H., Teukolsky S.A., Vetterling W.T., Flannery B.P.: Numerical Recipes in FOR-TRAN 77. The Art of Scientific Computing. Cambridge University Press, 199210. Kaczmarzyk P.: Kinetics of the cavitation erosion process in view of the InternationalCavitation Erosion Test results (in Polish). MSc Thesis, Faculty of Technical Physicsand Applied Mathematics, Technical University of Gdansk, Gdansk, 2000(under preparation)11. Sobczyk K., Spencer B.F.: Stochastyczne modele zmęczenia materiałów,WNT, Warszawa, 1996AuthorsDr Janusz StellerInstytut Maszyn Przepływowych PANul. Gen. J. Fiszera 1480-952 Gdańsk, Polandphone: +48 58 341 12 71 ext. 139e-mail: steller@imp.pg.gda.plPiotr KaczmarzykPolitechnika GdańskaWydział Fizyki Techniczneji Matematyki Stosowanej,ul. G. Narutowicza 1180-952 Gdańsk, Poland
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