Mathematical modeling and concepts to describe the dynamics in pressure transients for fuel systems in aerospace

Abstract

Purpose – The purpose of this study is to conduct a mathematical analysis and visualization of pressure dynamics in fluid-fuel systems. The numerical values for the given constants have been considered as those typical in aerospace applications. Design/methodology/approach – The author formulates a partial differential equation (PDE) to describe transient pressure behavior in fluid systems. This PDE is analyzed within travelling waves solutions and, in addition, is transformed into a weak formulation suitable for numerical approaches. The author uses Python’s NumPy and SciPy libraries for numerical integration and analysis. Findings – This paper develops a mathematical framework to analyze pressure transients in fluid-fuel systems using a weak formulation of the wave equation. A test functions with varying spatial and temporal frequencies is introduce so that the model can capture a wide spectrum of transient behaviors, including high-frequency dynamics. Numerical simulations highlight the potential of this approach to address complex phenomena such as pressure amplification and attenuation. The study emphasizes the importance of refining the model for higher frequency modes, and this is particularly relevant for future experimental validation. Originality/value – This research contributes to the field of modeling of pressure transients in pipelines, which is an important topic in aerospace applications. The originality resides in considering a form of wave-type differential equation along with a friction law and the resolution path followed based on travelling waves and a weak formulation of the differential equation obtained. In addition, the author uses an oscillatory test function aiming to capture short and long frequency interactions