Step by Step Derivation of the Optimum Multistage Compression Ratio and an Application Case
The optimum pressure ratio for the stages of a multistage compression process is calculated with a well known formula that assigns an equal ratio for all stages, based on the hypotheses that all isentropic efficiencies are also equal. Although the derivation of this formula for two stages is relativ...
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-06-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/22/6/678 |
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| author | Ignacio López-Paniagua Javier Rodríguez-Martín Susana Sánchez-Orgaz Juan José Roncal-Casano |
| author_facet | Ignacio López-Paniagua Javier Rodríguez-Martín Susana Sánchez-Orgaz Juan José Roncal-Casano |
| author_sort | Ignacio López-Paniagua |
| collection | DOAJ |
| description | The optimum pressure ratio for the stages of a multistage compression process is calculated with a well known formula that assigns an equal ratio for all stages, based on the hypotheses that all isentropic efficiencies are also equal. Although the derivation of this formula for two stages is relatively easy to find, it is more difficult to find for any number of stages, and the examples that are found in the literature employ complex mathematical methods. The case when the stages have different isentropic efficiencies is only treated numerically. Here, a step by step derivation of the general formula and of the formula for different stage efficiencies are carried out using Lagrange multipliers. A main objective has been to maintain the engineering considerations explicitly, so that the hypotheses and reasoning are clear throughout, and will enable the readers to generalise or adapt the methodology to specific problems. As the actual design of multistage compression processes frequently meet engineering restrictions, a practical example has been developed where the previous formulae have been applied to the design of a multistage compression plant with reciprocating compressors. Special attention has been put into engineering considerations. |
| first_indexed | 2024-03-10T19:05:18Z |
| format | Article |
| id | doaj.art-a5c9e861782745f189ba45f36884db94 |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-03-10T19:05:18Z |
| publishDate | 2020-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-a5c9e861782745f189ba45f36884db942023-11-20T04:11:43ZengMDPI AGEntropy1099-43002020-06-0122667810.3390/e22060678Step by Step Derivation of the Optimum Multistage Compression Ratio and an Application CaseIgnacio López-Paniagua0Javier Rodríguez-Martín1Susana Sánchez-Orgaz2Juan José Roncal-Casano3ETSI Industriales, Universidad Politécnica de Madrid (UPM), José Gutiérrez Abascal 2, 28006 Madrid, SpainETSI Industriales, Universidad Politécnica de Madrid (UPM), José Gutiérrez Abascal 2, 28006 Madrid, SpainETSI Industriales, Universidad Politécnica de Madrid (UPM), José Gutiérrez Abascal 2, 28006 Madrid, SpainETSI Industriales, Universidad Politécnica de Madrid (UPM), José Gutiérrez Abascal 2, 28006 Madrid, SpainThe optimum pressure ratio for the stages of a multistage compression process is calculated with a well known formula that assigns an equal ratio for all stages, based on the hypotheses that all isentropic efficiencies are also equal. Although the derivation of this formula for two stages is relatively easy to find, it is more difficult to find for any number of stages, and the examples that are found in the literature employ complex mathematical methods. The case when the stages have different isentropic efficiencies is only treated numerically. Here, a step by step derivation of the general formula and of the formula for different stage efficiencies are carried out using Lagrange multipliers. A main objective has been to maintain the engineering considerations explicitly, so that the hypotheses and reasoning are clear throughout, and will enable the readers to generalise or adapt the methodology to specific problems. As the actual design of multistage compression processes frequently meet engineering restrictions, a practical example has been developed where the previous formulae have been applied to the design of a multistage compression plant with reciprocating compressors. Special attention has been put into engineering considerations.https://www.mdpi.com/1099-4300/22/6/678compressorspressuremultistagenon-equal efficiencymultistage compressionoptimisation |
| spellingShingle | Ignacio López-Paniagua Javier Rodríguez-Martín Susana Sánchez-Orgaz Juan José Roncal-Casano Step by Step Derivation of the Optimum Multistage Compression Ratio and an Application Case Entropy compressors pressure multistage non-equal efficiency multistage compression optimisation |
| title | Step by Step Derivation of the Optimum Multistage Compression Ratio and an Application Case |
| title_full | Step by Step Derivation of the Optimum Multistage Compression Ratio and an Application Case |
| title_fullStr | Step by Step Derivation of the Optimum Multistage Compression Ratio and an Application Case |
| title_full_unstemmed | Step by Step Derivation of the Optimum Multistage Compression Ratio and an Application Case |
| title_short | Step by Step Derivation of the Optimum Multistage Compression Ratio and an Application Case |
| title_sort | step by step derivation of the optimum multistage compression ratio and an application case |
| topic | compressors pressure multistage non-equal efficiency multistage compression optimisation |
| url | https://www.mdpi.com/1099-4300/22/6/678 |
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