Determination of Hopf bifurcation sets of a chemicalreactors by two-parameter continuation method

• Autorzy: Berezowski Marek

Identyfikatory

DOI

10.24425/cpe.2020.132544

• Języki publikacji: EN

Abstrakty

EN

A two-parameter continuation method was developed and shown in the form of an example, allowingdetermination of Hopf bifurcation sets in a chemical reactor model. Exemplary calculations weremade for the continuous stirred tank reactor model (CSTR). The set of HB points limiting the rangeof oscillation in the reactor was determined. The results were confirmed on the bifurcation diagramof steady states and on time charts. The method is universal and can be used for various models ofchemical reactors.

Słowa kluczowe

EN

chemical reactor; Hopf bifurcation; thank reactor; bifurcation diagram; steady state; stability; dynamics

PL

reaktor chemiczny; Rozwidlenie Hopfa; diagram bifurkacji; stan stabilny; stabilność; dynamika

• Wydawca: Komitet Inżynierii Chemicznej i Procesowej Polskiej Akademii Nauk
• Czasopismo: Chemical and Process Engineering
• Rocznik: 2020
• Tom: Vol. 41, nr 3
• Strony: 221--–227
• Opis fizyczny: Bibliogr. 11 poz., rys.

Twórcy

autor

Berezowski Marek

• Faculty of Chemical Engineering and Technology, Cracow University of Technology,ul. Warszawska 24, 30-155 Kraków, Poland

Bibliografia

• 1. Agrawal P., Lee C, Lim H.C., Ramkrishna D., 1982. Theoretical investigations of dynamic behavior of isothermalcontinuous stirred tank biological reactors.Chem. Eng. Sci., 37, 453–462. DOI:10.1016/0009-2509(82)80098-5.
• 2. Antonelli R., Astolfi A., 2003. Continuous stirred tank reactors: easy to stabilise? Automatica, 39, 1817–1827.DOI:10.1016/S0005-1098(03)00177-8.
• 3. Berezowski M., 2010. The application of the parametric continuation method for determining steady state diagramsin chemical engineering.Chem. Eng. Sci., 65, 5411–5414. DOI:10.1016/j.ces.2010.07.003.
• 4. Berezowski M., 2017. Limit cycles that do not comprise steady states of chemical reactors.Appl. Math. Comput.,312, 129–133. DOI:10.1016/j.amc.2017.05.002.
• 5. Berezowski M., Kulik B., 2009. Periodicity of chaotic solutions of the model of thermally coupled cascades of chemical tank reactors with flow reversal.Chaos, Solitons Fractals, 40, 331–336. DOI:10.1016/j.chaos.2007.07.066.
• 6. Chen C.-C., Fu C.-C., Tsai C.-H., 1996. Stabilized chaotic dynamics of coupled nonisothermal CSTRs.Chem. Eng.Sci., 51(23), 5159–5169. DOI:10.1016/S0009-2509(96)00335-1.
• 7. Kubíček M., Hofmann H., Hlaváček V., Sinkule J., 1980. Multiplicity and stability in a sequence of two nonadiabaticnonisothermal CSTR.Chem. Eng. Sci., 35, 987–996. DOI:10.1016/00092509(80)85088-3.
• 8. Merta H., 2006. Characteristic time series and operation region of the system of two tank reactors (CSTR) with vari-able division of recirculation stream.Chaos, Solitons Fractals, 27, 279–285. DOI:10.1016/j.chaos.2005.03.028.
• 9. Starzak M., Zarzycki R., 1990. Podstawy teoretyczne i numeryczne analizy stanów asymptotycznych kaskadyreaktorów. II. Bifurkacje stanów stacjonarnych i oscylacyjnych okresowych.Inz. Chem. Proc., 4, 757–780.
• 10. Verazaluce-García J.C., Flores-Tlacuahuac A., Saldívar-Guerra E., 2000. Steady-state nonlinear bifurcation analysisof a high-impact polystyrene continuous stirred tank reactor.Ind. Eng. Chem. Res., 39, 1972–1979. DOI:10.1016/S15707946(05)80246-9.
• 11. Zukowski W., Berezowski M., 2000. Generation of chaotic oscillations in a system with flow reversal.Chem. Eng.Sci., 55, 339–343. DOI:10.1016/S0009-2509(99)00329-2.

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2020).