Abstract
The unrestrained free surface oscillation of liquid hydrogen in a rectangular tank due to external forces are analyzed using a mapping technology called sigma transformation. Here the governing equation and boundary conditions were developed using potential flow theory for irrotational and incompressible fluid flow. The function sigma is used for transforming the non-linear physical domain into a fixed rectangular domain and thereby reducing the complexity of analysis by avoiding the re-meshing of the liquid domain in each time step. The numerical investigation is done for medium steepness non-breaking inviscid flow conditions under horizontal excitations due to turning and lane change accelerations. For shallow waves, the viscous effect becomes more evident. Sloshing behaviour of the liquid hydrogen was analyzed by generating wave profiles, elevation, phase plane and sloshing force diagram. The non-linearity of waves was also investigated using a fast Fourier transform. This method seems to be more simple and accurate at medium steepness, for higher steepness waves non-linear effect become more significant, this is due to the development of low energy level frequencies, which can be understood from the spectrum analysis. At high steepness phase plane diagram changes its circular shape to oval.
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Abbreviations
- x :
-
Horizontal distance from left wall (in m)
- y :
-
Vertical distance from mean level (in m)
- t :
-
Time (in s)
- \({\Phi }\) :
-
Potential function \(\left( {x,y,t} \right)\)
- \(\zeta\) :
-
Change in liquid hydrogen level from the free surface (in m)
- g :
-
Acceleration due to gravity (in \({\text{m}}/{\text{s}}^{2}\))
- \(\ddot{Y}_{t}\) :
-
Acceleration of container in vertical direction (in \({\text{m}}/{\text{s}}^{2}\))
- \(\ddot{X}_{t}\) :
-
Acceleration of container in horizontal direction (in \({\text{m}}/{\text{s}}^{2}\))
- p :
-
Pressure (in \({\text{N}}/{\text{m}}^{2}\))
- \(\sigma\) :
-
Mapping function
- \(\phi\) :
-
Potential function in sigma transformed domain \(\left( {x,\sigma ,t} \right)\)
- \(\rho\) :
-
Density (in \({\text{kg}}/{\text{m}}^{3}\))
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Sreeraj, R., Anbarasu, S. (2022). Numerical Investigation of Cryogenic Liquid Sloshing—A Sigma Transformation Approach. In: Palanisamy, M., Natarajan, S.K., Jayaraj, S., Sivalingam, M. (eds) Innovations in Energy, Power and Thermal Engineering . Lecture Notes in Mechanical Engineering. Springer, Singapore. https://doi.org/10.1007/978-981-16-4489-4_18
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DOI: https://doi.org/10.1007/978-981-16-4489-4_18
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