## Validation study of real gas models: Applied on a wide range of temperatures and pressures

Student thesis: Master thesis (including HD thesis)

- Jeppe Mulvad Larsen

2. term, Electro-Mechanical System Design, Master (Master Programme)

The objectives of the project have been to investigate the correlation between complexity and accuracy when calculating the gas pressure and gas temperature in a hydraulic accumulator for a number of real gas models. The problem thesis of the project is \emph{What mathematical model describes the gas pressure during a cycle in a hydraulic accumulator most precisely, when comparing accuracy with complexity} and this will be studied throughout the report which the following chapters. The project have been performed in cooperation with Fritz Schur Energy.
In the first chapter of the project the results of a literature survey are presented. This survey have been carried out to identify which real gas models that should be used in the project. In total five real gas models was selected together with the ideal gas model. The five real gas models are; Van der Waals, Beattie-Bridgeman, Benedicte-Webb-Rubin, Jacobsen \& Stewart and Bender equation of state. They range in complexity with three, six, nine, 20 and 33 constants respectively where the ideal gas model only have one.
To validate the models two test rig where developed and modeled. The difference between the two test rigs was the size of the accumulator. The next five chapters in the report are presenting the models. In total four models was presented, namely a mechanical, a hydraulic, a gas pressure and a gas temperature model. The first two was not of big interest of the project which is why they have only been given little focus. The third model, the gas pressure model, was based on the literature survey. The last model, the gas temperature model, was based on an energy balance for the gas side of the accumulator. It turned out that this balance was a function of among others the pressure of the gas, which his way in total six sub models was produced.
Above part is followed by two chapter dealing with test variables and the test schedule. A discussion about what variable should be working as the reference is presented. For the small accumulator the position should work as the reference signal. In this way there will be total control of the volume of the accumulator, which is beneficial due to some sub experiments that should be performed. Furthermore the chapter describe at what temperatures the test runs should be performed. Three temperatures was chosen, namely ~260 Kelvin, ~300 Kelvin and ~350 Kelvin. The latter chapter presents a full test schedule to be followed during the test runs.
Finally four chapters presents the outcome from a number of validations. Firstly the test rig itself are validated to determine the variability. This gives an picture of how reliable the measure data is. The conclusion was that the test rig has a very low variability. Secondly the result from the experiment for determining the thermal time constant was presented. The thermal time constant is a measure for how fast the pressure drops when the accumulator is exposed to a step change is volume. The pressure drops because the temperature drops as it interacts with the surround air. Finally two chapters presents the outcome from the validation of the models found in the literature survey.
Some problems with the test rig has unfortunately resulted in problems with drawing clear conclusions for the temperature models and the large accumulator. But for the small accumulator it is clear to see, that the Van der Waals equation of state is the most precise for normal and warm ambient temperature ranging from ~300 Kelvin to ~350 Kelvin. No significant differences was to be found when comparing pressures. Furthermore it turned out that for cold ambient temperatures, the Van der Waals equation of state was not the best equation to use. In this case the Beattie-Bridgeman equation of state was recommended. It should be mentioned that the large accumulator showed a tendency that supports the conclusion that the same is valed for the large accumulator as for the small. Finally although no clear conclusions can be made for the temperature model, it is also assumed that the same conclusions are valid for this as well. This is assumed as the temperature and pressure models are closely linked and that the approach for calculating the temperature are supported by other sources.
The project has therefore shown that it is not necessary to use very complex models to obtain accurate results when calculating the pressure in a hydraulic accumulator. The opposite has actually shown to be the case, namely that the least complex real gas models resulted in the most accurate results. The above is valid for temperatures ranges from ~260 Kelvin to ~350 Kelvin, precharge pressures from 50 bar to 150 bar, maximum pressures of ~250 bar and minimum pressures of ~40 bar.

Language | English |
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Publication date | 2010 |

Number of pages | 127 |

Publishing institution | Institut for Energiteknik |

Keywords | hydraulic accumulator |
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