Validation study of real gas models: Applied on a wide range of temperatures and pressures
Author
Larsen, Jeppe Mulvad
Term
2. term
Education
Publication year
2010
Pages
127
Abstract
En hydraulisk akkumulator bruger komprimeret gas til at lagre energi og udjævne tryk i et hydraulisk system. Dette projekt undersøger, hvordan kompleksitet i matematiske gasmodeller påvirker nøjagtigheden, når man beregner gastryk og gastemperatur i en akkumulator. Målet er at finde den model, der beskriver gastrykket mest præcist under en arbejdscyklus, samtidig med at kompleksitet holdes nede. Projektet er udført i samarbejde med Fritz Schur Energy. Efter en litteraturgennemgang blev fem realgas‑modeller valgt samt idealgasmodellen som reference: Van der Waals, Beattie‑Bridgeman, Benedict‑Webb‑Rubin, Jacobsen & Stewart og Bender. De varierer i kompleksitet med henholdsvis 3, 6, 9, 20 og 33 konstanter (idealgas har 1). To testrigge blev udviklet, med forskel i akkumulatorstørrelse (en lille og en stor). Der blev opstillet mekaniske og hydrauliske modeller (med begrænset fokus), en gastryksmodel baseret på litteraturen og en gastemperaturmodel baseret på energibalance på gassiden. Da energibalancen afhænger blandt andet af gastrykket, førte det til seks delmodeller. Testplanen fastlagde referencevariabler og betingelser: For den lille akkumulator blev position brugt som referencesignal for at kontrollere volumen. Forsøgene blev udført ved cirka 260 K, 300 K og 350 K. Testriggen blev først valideret og viste meget lav variabilitet, hvilket gør målingerne pålidelige. Derudover blev den termiske tidskonstant bestemt, dvs. hvor hurtigt trykket falder efter et hop i volumen, fordi gassen afgiver varme til omgivelserne. Resultaterne viser, at for den lille akkumulator matcher Van der Waals‑modellen målingerne bedst ved normale og varme omgivelser (ca. 300–350 K). Ved kolde forhold (ca. 260 K) anbefales Beattie‑Bridgeman. Generelt var forskellene i beregnet tryk mellem modellerne små. Problemer med testriggen begrænsede klare konklusioner for temperaturmodellerne og for den store akkumulator, men tendenserne støtter, at de samme konklusioner gælder. Samlet peger projektet på, at meget komplekse modeller ikke er nødvendige for at beregne tryk i hydrauliske akkumulatorer. De mindst komplekse realgasmodeller gav de mest nøjagtige resultater inden for de testede intervaller: temperaturer ca. 260–350 K, forladetryk 50–150 bar, maksimalt tryk ca. 250 bar og minimalt tryk ca. 40 bar.
A hydraulic accumulator uses compressed gas to store energy and smooth pressure in a hydraulic system. This project examines how the complexity of mathematical gas models affects accuracy when calculating gas pressure and temperature in an accumulator. The aim is to identify the model that most precisely describes gas pressure over a working cycle while keeping complexity reasonable. The project was carried out in collaboration with Fritz Schur Energy. After a literature review, five real‑gas equations of state and the ideal‑gas model (as a reference) were selected: Van der Waals, Beattie‑Bridgeman, Benedict‑Webb‑Rubin, Jacobsen & Stewart, and Bender. Their complexity ranges from 3, 6, 9, 20, to 33 constants (ideal gas has 1). Two test rigs were developed with different accumulator sizes (small and large). Mechanical and hydraulic models were set up (with limited focus), along with a gas‑pressure model based on the literature and a gas‑temperature model based on an energy balance on the gas side. Because the energy balance depends, among other things, on gas pressure, six sub‑models were created. The test plan defined reference variables and conditions: for the small accumulator, position was used as the reference signal to control volume. Tests were run at approximately 260 K, 300 K, and 350 K. The test rig was first validated and showed very low variability, making measurements reliable. The thermal time constant was also determined—the rate at which pressure drops after a step change in volume due to heat exchange with the surrounding air. Results show that for the small accumulator, the Van der Waals model matches measurements best at normal and warm ambient temperatures (about 300–350 K). In cold conditions (about 260 K), the Beattie‑Bridgeman model is recommended. Overall, differences in calculated pressure across models were small. Issues with the test rig limited clear conclusions for the temperature models and the large accumulator, but trends support applying the same conclusions. Overall, the project shows that highly complex models are not necessary to compute pressure in hydraulic accumulators. The least complex real‑gas models gave the most accurate results within the tested ranges: temperatures about 260–350 K, precharge pressures 50–150 bar, maximum pressures about 250 bar, and minimum pressures about 40 bar.
[This abstract was generated with the help of AI]
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