Amplitude-Frequency Characteristics of the System “Mixing–Mixing” Heat Exchanger + Heat Transfer”

Background. Mathematical modeling of continuous technological processes in non-stationary conditions caused by actions of various destabilizing factors is an actual problem. At the same time, analytical solutions have significant advantages over numerical ones, since they allow us to find out the na...

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Main Authors: Igor D. Lucheyko, Roman V. Kotsiurko
Format: Article
Language:English
Published: Igor Sikorsky Kyiv Polytechnic Institute 2018-11-01
Series:Наукові вісті Національного технічного університету України "Київський політехнічний інститут"
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Online Access:http://bulletin.kpi.ua/article/view/147067
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spelling doaj-9ad693ee06d14c27a298d7e0ffa09b1a2021-02-02T04:33:44ZengIgor Sikorsky Kyiv Polytechnic InstituteНаукові вісті Національного технічного університету України "Київський політехнічний інститут"1810-05462519-88902018-11-0105374410.20535/1810-0546.2018.5.147067147067Amplitude-Frequency Characteristics of the System “Mixing–Mixing” Heat Exchanger + Heat Transfer”Igor D. Lucheyko0Roman V. Kotsiurko1Ternopil Ivan Puluj National Technical UniversityTernopil Ivan Puluj National Technical UniversityBackground. Mathematical modeling of continuous technological processes in non-stationary conditions caused by actions of various destabilizing factors is an actual problem. At the same time, analytical solutions have significant advantages over numerical ones, since they allow us to find out the nature of causation links in the analyzed properties of the modeling object and, as a practical result, to give physically well-founded recommendations for improving the efficiency of its functioning. The possible fluctuations in the temperature of heat carrier (HC) at the inputs of the flow heat exchanger (HE) cause instabilities for heat exchange processes. This usually leads to the efficiency decrease of the HE. Therefore, the calculation of its amplitude-frequency characteristics (AFC) has a significant (weighty) value. Objective. The aim of the paper is to find out the behavior of the ideal “mixing–mixing” HE in stationary mode and harmonic fluctuations of temperature at the inputs of the apparatus and calculation of its AFC. Methods. Known mathematical model in the form of a system of linear differential equations (reduced summed to dimensionless form) to calculate the effect of harmonic fluctuations of temperature on the stationary mode of the system “HE + heat transfer” was used. Results. It is shown that the efficiency of the stationary mode of operation of the ideal “mixing – mixing” HE can be estimated by the efficiency indicator , where  – transfer number (k – heat transfer coefficient across the surface area F ;  – the volumetric flow rates of HC and their heat capacities). When , when  (the process of heat transfer is much more intense compared with the process of heat outlet by flows from HE). AFC  of the system is calculated, where  – the simplex of the amplitudes of temperature fluctuations at the inputs and outputs;  – frequency complex (w – cyclic frequency, t02 – average time of stay of cold HC in HE). Conclusions. In the case of common-phase fluctuations of temperatures at the inputs of HE AFC don’t depend on Ai, i.e. they are equal to the AFC of HE as two flow devices of the ideal mixing. In the case of antiphase fluctuations of temperature the values  are equal when the formal rearrangement of values Ai: , which is a reflection of the thermal “equality” of HC. When ; when  at . In the case  (the intense heat transfer reduces the amplitudes of temperature fluctuations at the outputs of the HC). At relatively high frequencies, stationary mode is practically not violated at any values of Ai: . Therefore, in order to ensure practically stationary mode of HE operation, it is necessary to get rid of low  harmonics of possible temperature fluctuations at the inputs.http://bulletin.kpi.ua/article/view/147067Mathematical modeling“Mixing–mixing” heat exchangerPerformance indicatorHarmonic temperature fluctuationsAmplitude-frequency characteristic
collection DOAJ
language English
format Article
sources DOAJ
author Igor D. Lucheyko
Roman V. Kotsiurko
spellingShingle Igor D. Lucheyko
Roman V. Kotsiurko
Amplitude-Frequency Characteristics of the System “Mixing–Mixing” Heat Exchanger + Heat Transfer”
Наукові вісті Національного технічного університету України "Київський політехнічний інститут"
Mathematical modeling
“Mixing–mixing” heat exchanger
Performance indicator
Harmonic temperature fluctuations
Amplitude-frequency characteristic
author_facet Igor D. Lucheyko
Roman V. Kotsiurko
author_sort Igor D. Lucheyko
title Amplitude-Frequency Characteristics of the System “Mixing–Mixing” Heat Exchanger + Heat Transfer”
title_short Amplitude-Frequency Characteristics of the System “Mixing–Mixing” Heat Exchanger + Heat Transfer”
title_full Amplitude-Frequency Characteristics of the System “Mixing–Mixing” Heat Exchanger + Heat Transfer”
title_fullStr Amplitude-Frequency Characteristics of the System “Mixing–Mixing” Heat Exchanger + Heat Transfer”
title_full_unstemmed Amplitude-Frequency Characteristics of the System “Mixing–Mixing” Heat Exchanger + Heat Transfer”
title_sort amplitude-frequency characteristics of the system “mixing–mixing” heat exchanger + heat transfer”
publisher Igor Sikorsky Kyiv Polytechnic Institute
series Наукові вісті Національного технічного університету України "Київський політехнічний інститут"
issn 1810-0546
2519-8890
publishDate 2018-11-01
description Background. Mathematical modeling of continuous technological processes in non-stationary conditions caused by actions of various destabilizing factors is an actual problem. At the same time, analytical solutions have significant advantages over numerical ones, since they allow us to find out the nature of causation links in the analyzed properties of the modeling object and, as a practical result, to give physically well-founded recommendations for improving the efficiency of its functioning. The possible fluctuations in the temperature of heat carrier (HC) at the inputs of the flow heat exchanger (HE) cause instabilities for heat exchange processes. This usually leads to the efficiency decrease of the HE. Therefore, the calculation of its amplitude-frequency characteristics (AFC) has a significant (weighty) value. Objective. The aim of the paper is to find out the behavior of the ideal “mixing–mixing” HE in stationary mode and harmonic fluctuations of temperature at the inputs of the apparatus and calculation of its AFC. Methods. Known mathematical model in the form of a system of linear differential equations (reduced summed to dimensionless form) to calculate the effect of harmonic fluctuations of temperature on the stationary mode of the system “HE + heat transfer” was used. Results. It is shown that the efficiency of the stationary mode of operation of the ideal “mixing – mixing” HE can be estimated by the efficiency indicator , where  – transfer number (k – heat transfer coefficient across the surface area F ;  – the volumetric flow rates of HC and their heat capacities). When , when  (the process of heat transfer is much more intense compared with the process of heat outlet by flows from HE). AFC  of the system is calculated, where  – the simplex of the amplitudes of temperature fluctuations at the inputs and outputs;  – frequency complex (w – cyclic frequency, t02 – average time of stay of cold HC in HE). Conclusions. In the case of common-phase fluctuations of temperatures at the inputs of HE AFC don’t depend on Ai, i.e. they are equal to the AFC of HE as two flow devices of the ideal mixing. In the case of antiphase fluctuations of temperature the values  are equal when the formal rearrangement of values Ai: , which is a reflection of the thermal “equality” of HC. When ; when  at . In the case  (the intense heat transfer reduces the amplitudes of temperature fluctuations at the outputs of the HC). At relatively high frequencies, stationary mode is practically not violated at any values of Ai: . Therefore, in order to ensure practically stationary mode of HE operation, it is necessary to get rid of low  harmonics of possible temperature fluctuations at the inputs.
topic Mathematical modeling
“Mixing–mixing” heat exchanger
Performance indicator
Harmonic temperature fluctuations
Amplitude-frequency characteristic
url http://bulletin.kpi.ua/article/view/147067
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