Implementation of Adaptive Observer and Mathematical Model Validation of the Evaporator of an Absorption Heat Transformer

This article presents the implementation of an adaptive observer to validate a falling film evaporator mathematical model. The evaporator consists of four coils, and each coil has four tubes. The heating flow in the first and third coils flows from bottom to top. Meanwhile, the heating flow in the s...

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Main Authors: Ricardo Fabricio Escobar-Jiménez, Isaac Justine Canela-Sánchez, Manuel Adam-Medina, Abisai Acevedo-Quiroz, Armando Huicochea-Rodríguez, David Juárez-Romero
Format: Article
Language:English
Published: MDPI AG 2024-11-01
Series:Mathematics
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Online Access:https://www.mdpi.com/2227-7390/12/23/3637
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author Ricardo Fabricio Escobar-Jiménez
Isaac Justine Canela-Sánchez
Manuel Adam-Medina
Abisai Acevedo-Quiroz
Armando Huicochea-Rodríguez
David Juárez-Romero
author_facet Ricardo Fabricio Escobar-Jiménez
Isaac Justine Canela-Sánchez
Manuel Adam-Medina
Abisai Acevedo-Quiroz
Armando Huicochea-Rodríguez
David Juárez-Romero
author_sort Ricardo Fabricio Escobar-Jiménez
collection DOAJ
description This article presents the implementation of an adaptive observer to validate a falling film evaporator mathematical model. The evaporator consists of four coils, and each coil has four tubes. The heating flow in the first and third coils flows from bottom to top. Meanwhile, the heating flow in the second and fourth coils flows from top to bottom. The mathematical model of the evaporator is parameterized with the geometry data of the experimental device. Since the mathematical model depends on the film breakdown onset Reynolds number (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>R</mi><msub><mi>e</mi><mrow><mi>O</mi><mi>n</mi><mi>s</mi><mi>e</mi><mi>t</mi></mrow></msub></mrow></semantics></math></inline-formula>) to estimate the evaporator temperatures, an adaptive observer is applied to estimate this unknown parameter (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>R</mi><msub><mi>e</mi><mrow><mi>O</mi><mi>n</mi><mi>s</mi><mi>e</mi><mi>t</mi></mrow></msub></mrow></semantics></math></inline-formula>). The observer design is developed through the evaporator mathematical model. The research aims to estimate the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>R</mi><msub><mi>e</mi><mrow><mi>O</mi><mi>n</mi><mi>s</mi><mi>e</mi><mi>t</mi></mrow></msub></mrow></semantics></math></inline-formula> at different operating conditions to accurately estimate the evaporator temperatures since there is no general correlation for estimating it or a sensor to measure this parameter. Once the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>R</mi><msub><mi>e</mi><mrow><mi>O</mi><mi>n</mi><mi>s</mi><mi>e</mi><mi>t</mi></mrow></msub></mrow></semantics></math></inline-formula> is estimated at different operating conditions, the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>R</mi><msub><mi>e</mi><mrow><mi>O</mi><mi>n</mi><mi>s</mi><mi>e</mi><mi>t</mi></mrow></msub></mrow></semantics></math></inline-formula> results are injected into the model for validation. The results of implementing the observer showed that the temperature estimation errors are between 0.00003% and 0.02815%. Moreover, the temperatures simulated with the model using the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>R</mi><msub><mi>e</mi><mrow><mi>O</mi><mi>n</mi><mi>s</mi><mi>e</mi><mi>t</mi></mrow></msub></mrow></semantics></math></inline-formula> estimated with the observers had errors between 0.04012% and 0.14160%.
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spelling doaj-art-fce3fefc51b244c8aad929f893320cda2025-08-20T01:55:45ZengMDPI AGMathematics2227-73902024-11-011223363710.3390/math12233637Implementation of Adaptive Observer and Mathematical Model Validation of the Evaporator of an Absorption Heat TransformerRicardo Fabricio Escobar-Jiménez0Isaac Justine Canela-Sánchez1Manuel Adam-Medina2Abisai Acevedo-Quiroz3Armando Huicochea-Rodríguez4David Juárez-Romero5Centro Nacional de Investigación y Desarrollo Tecnológico, Tecnológico Nacional de México, Int. Internado Palmira S/N, Palmira, Cuernavaca 62490, Morelos, MexicoCentro Nacional de Investigación y Desarrollo Tecnológico, Tecnológico Nacional de México, Int. Internado Palmira S/N, Palmira, Cuernavaca 62490, Morelos, MexicoCentro Nacional de Investigación y Desarrollo Tecnológico, Tecnológico Nacional de México, Int. Internado Palmira S/N, Palmira, Cuernavaca 62490, Morelos, MexicoCentro Nacional de Investigación y Desarrollo Tecnológico, Tecnológico Nacional de México, Int. Internado Palmira S/N, Palmira, Cuernavaca 62490, Morelos, MexicoCentro de Investigación en Ingeniería y Ciencias Aplicadas, UAEM. Av. Universidad No. 1001, Col. Chamilpa, Cuernavaca 62209, Morelos, MexicoCentro de Investigación en Ingeniería y Ciencias Aplicadas, UAEM. Av. Universidad No. 1001, Col. Chamilpa, Cuernavaca 62209, Morelos, MexicoThis article presents the implementation of an adaptive observer to validate a falling film evaporator mathematical model. The evaporator consists of four coils, and each coil has four tubes. The heating flow in the first and third coils flows from bottom to top. Meanwhile, the heating flow in the second and fourth coils flows from top to bottom. The mathematical model of the evaporator is parameterized with the geometry data of the experimental device. Since the mathematical model depends on the film breakdown onset Reynolds number (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>R</mi><msub><mi>e</mi><mrow><mi>O</mi><mi>n</mi><mi>s</mi><mi>e</mi><mi>t</mi></mrow></msub></mrow></semantics></math></inline-formula>) to estimate the evaporator temperatures, an adaptive observer is applied to estimate this unknown parameter (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>R</mi><msub><mi>e</mi><mrow><mi>O</mi><mi>n</mi><mi>s</mi><mi>e</mi><mi>t</mi></mrow></msub></mrow></semantics></math></inline-formula>). The observer design is developed through the evaporator mathematical model. The research aims to estimate the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>R</mi><msub><mi>e</mi><mrow><mi>O</mi><mi>n</mi><mi>s</mi><mi>e</mi><mi>t</mi></mrow></msub></mrow></semantics></math></inline-formula> at different operating conditions to accurately estimate the evaporator temperatures since there is no general correlation for estimating it or a sensor to measure this parameter. Once the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>R</mi><msub><mi>e</mi><mrow><mi>O</mi><mi>n</mi><mi>s</mi><mi>e</mi><mi>t</mi></mrow></msub></mrow></semantics></math></inline-formula> is estimated at different operating conditions, the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>R</mi><msub><mi>e</mi><mrow><mi>O</mi><mi>n</mi><mi>s</mi><mi>e</mi><mi>t</mi></mrow></msub></mrow></semantics></math></inline-formula> results are injected into the model for validation. The results of implementing the observer showed that the temperature estimation errors are between 0.00003% and 0.02815%. Moreover, the temperatures simulated with the model using the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>R</mi><msub><mi>e</mi><mrow><mi>O</mi><mi>n</mi><mi>s</mi><mi>e</mi><mi>t</mi></mrow></msub></mrow></semantics></math></inline-formula> estimated with the observers had errors between 0.04012% and 0.14160%.https://www.mdpi.com/2227-7390/12/23/3637adaptive observerheat transferabsorption heat transformerevaporation processnested helical heat exchanger
spellingShingle Ricardo Fabricio Escobar-Jiménez
Isaac Justine Canela-Sánchez
Manuel Adam-Medina
Abisai Acevedo-Quiroz
Armando Huicochea-Rodríguez
David Juárez-Romero
Implementation of Adaptive Observer and Mathematical Model Validation of the Evaporator of an Absorption Heat Transformer
Mathematics
adaptive observer
heat transfer
absorption heat transformer
evaporation process
nested helical heat exchanger
title Implementation of Adaptive Observer and Mathematical Model Validation of the Evaporator of an Absorption Heat Transformer
title_full Implementation of Adaptive Observer and Mathematical Model Validation of the Evaporator of an Absorption Heat Transformer
title_fullStr Implementation of Adaptive Observer and Mathematical Model Validation of the Evaporator of an Absorption Heat Transformer
title_full_unstemmed Implementation of Adaptive Observer and Mathematical Model Validation of the Evaporator of an Absorption Heat Transformer
title_short Implementation of Adaptive Observer and Mathematical Model Validation of the Evaporator of an Absorption Heat Transformer
title_sort implementation of adaptive observer and mathematical model validation of the evaporator of an absorption heat transformer
topic adaptive observer
heat transfer
absorption heat transformer
evaporation process
nested helical heat exchanger
url https://www.mdpi.com/2227-7390/12/23/3637
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