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Evaluation of periodic processes with two modulated inputs based on nonlinear frequency response analysis. Case study: CSTR with modulation of the inlet concentration and flow-rate

Authorized Users Only
2013
Authors
Nikolić-Paunić, Daliborka
Petkovska, Menka
Article (Published version)
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Abstract
In our previous work, a new, fast and easy, nonlinear frequency response method for analysing potential improvements of reactor performance by forced periodic operation was presented. This method, which is based on Volterra series, generalized Fourier transform and the concept of higher-order frequency response functions (FRFs), gives an approximate value of the average process performance directly, without numerical simulation of the complete process. It was shown that the asymmetrical second order frequency response function, (G(2)(omega, -omega)) corresponds to the dominant term of the non-periodic (DC) component of the periodic steady-state response and determines the average performance of the periodic process. Thus, in order to evaluate the potential of a periodic reactor operation, it is enough to derive and analyse this function. In this work this method is extended to evaluating periodic operations with forced oscillations of two modulated inputs. In this case the nonlinear sy...stem has to be defined by three sets of frequency response functions, two of thorn correlating the output to each of the inputs and one set of cross-FRFs. The general methodology for this case is developed. It is further used to analyse the time-average performance of an isothermal continuous stirred tank reactor (CSTR) with forced periodic modulation of the inlet concentration and flow-rate, for a simple nth order homogeneous reaction. The analysis is performed for cases when the inlet concentration and flow-rate are modulated simultaneously. The optimal choice of the phase shift between the two inputs is discussed in detail.

Keywords:
Nonlinear dynamics / Chemical reactors / Mathematical modelling / Simulation / Two modulated inputs / Frequency response functions
Source:
Chemical Engineering Science, 2013, 104, 208-219
Publisher:
  • Oxford : Pergamon-Elsevier Science Ltd
Funding / projects:
  • The development of efficient chemical-engineering processes based on the transport phenomena research and process intensification principles (RS-172022)
  • Nanostructured Functional and Composite Materials in Catalytic and Sorption Processes (RS-45001)

DOI: 10.1016/j.ces.2013.09.009

ISSN: 0009-2509

WoS: 000327735900021

Scopus: 2-s2.0-84884753540
[ Google Scholar ]
18
16
URI
https://cer.ihtm.bg.ac.rs/handle/123456789/1236
Collections
  • Radovi istraživača / Researchers' publications
Institution/Community
IHTM
TY  - JOUR
AU  - Nikolić-Paunić, Daliborka
AU  - Petkovska, Menka
PY  - 2013
UR  - https://cer.ihtm.bg.ac.rs/handle/123456789/1236
AB  - In our previous work, a new, fast and easy, nonlinear frequency response method for analysing potential improvements of reactor performance by forced periodic operation was presented. This method, which is based on Volterra series, generalized Fourier transform and the concept of higher-order frequency response functions (FRFs), gives an approximate value of the average process performance directly, without numerical simulation of the complete process. It was shown that the asymmetrical second order frequency response function, (G(2)(omega, -omega)) corresponds to the dominant term of the non-periodic (DC) component of the periodic steady-state response and determines the average performance of the periodic process. Thus, in order to evaluate the potential of a periodic reactor operation, it is enough to derive and analyse this function. In this work this method is extended to evaluating periodic operations with forced oscillations of two modulated inputs. In this case the nonlinear system has to be defined by three sets of frequency response functions, two of thorn correlating the output to each of the inputs and one set of cross-FRFs. The general methodology for this case is developed. It is further used to analyse the time-average performance of an isothermal continuous stirred tank reactor (CSTR) with forced periodic modulation of the inlet concentration and flow-rate, for a simple nth order homogeneous reaction. The analysis is performed for cases when the inlet concentration and flow-rate are modulated simultaneously. The optimal choice of the phase shift between the two inputs is discussed in detail.
PB  - Oxford : Pergamon-Elsevier Science Ltd
T2  - Chemical Engineering Science
T1  - Evaluation of periodic processes with two modulated inputs based on nonlinear frequency response analysis. Case study: CSTR with modulation of the inlet concentration and flow-rate
VL  - 104
SP  - 208
EP  - 219
DO  - 10.1016/j.ces.2013.09.009
ER  - 
@article{
author = "Nikolić-Paunić, Daliborka and Petkovska, Menka",
year = "2013",
abstract = "In our previous work, a new, fast and easy, nonlinear frequency response method for analysing potential improvements of reactor performance by forced periodic operation was presented. This method, which is based on Volterra series, generalized Fourier transform and the concept of higher-order frequency response functions (FRFs), gives an approximate value of the average process performance directly, without numerical simulation of the complete process. It was shown that the asymmetrical second order frequency response function, (G(2)(omega, -omega)) corresponds to the dominant term of the non-periodic (DC) component of the periodic steady-state response and determines the average performance of the periodic process. Thus, in order to evaluate the potential of a periodic reactor operation, it is enough to derive and analyse this function. In this work this method is extended to evaluating periodic operations with forced oscillations of two modulated inputs. In this case the nonlinear system has to be defined by three sets of frequency response functions, two of thorn correlating the output to each of the inputs and one set of cross-FRFs. The general methodology for this case is developed. It is further used to analyse the time-average performance of an isothermal continuous stirred tank reactor (CSTR) with forced periodic modulation of the inlet concentration and flow-rate, for a simple nth order homogeneous reaction. The analysis is performed for cases when the inlet concentration and flow-rate are modulated simultaneously. The optimal choice of the phase shift between the two inputs is discussed in detail.",
publisher = "Oxford : Pergamon-Elsevier Science Ltd",
journal = "Chemical Engineering Science",
title = "Evaluation of periodic processes with two modulated inputs based on nonlinear frequency response analysis. Case study: CSTR with modulation of the inlet concentration and flow-rate",
volume = "104",
pages = "208-219",
doi = "10.1016/j.ces.2013.09.009"
}
Nikolić-Paunić, D.,& Petkovska, M.. (2013). Evaluation of periodic processes with two modulated inputs based on nonlinear frequency response analysis. Case study: CSTR with modulation of the inlet concentration and flow-rate. in Chemical Engineering Science
Oxford : Pergamon-Elsevier Science Ltd., 104, 208-219.
https://doi.org/10.1016/j.ces.2013.09.009
Nikolić-Paunić D, Petkovska M. Evaluation of periodic processes with two modulated inputs based on nonlinear frequency response analysis. Case study: CSTR with modulation of the inlet concentration and flow-rate. in Chemical Engineering Science. 2013;104:208-219.
doi:10.1016/j.ces.2013.09.009 .
Nikolić-Paunić, Daliborka, Petkovska, Menka, "Evaluation of periodic processes with two modulated inputs based on nonlinear frequency response analysis. Case study: CSTR with modulation of the inlet concentration and flow-rate" in Chemical Engineering Science, 104 (2013):208-219,
https://doi.org/10.1016/j.ces.2013.09.009 . .

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