Free-form shape optimization of a U-shaped Coriolis Mass Flow Meter for enhanced measurement sensitivity

Coriolis Mass Flow Meters (CMFs) directly measure mass flow rate through tube deformation induced by Coriolis forces. This paper presents a high-fidelity, physics-based shape optimization framework to enhance the sensitivity of a U-shaped CMF while preserving its drive-mode frequency. A free-form approach is employed, treating all finite element nodes as design variables to enable an unbiased exploration of the geometric design space. A static mode-consistent torsional surrogate loading is introduced to mimic the deformation pattern of the Coriolis mode without requiring fully coupled high-fidelity fluid–structure interaction (FSI) simulations. The optimization is carried out using adjoint-based sensitivities, gradient-projection constraint handling, and vertex morphing with Helmholtz-type filtering within the ShapeOptimizationApplication of Kratos Multiphysics . The optimized design achieves about a 105% increase in relative sensors deformation while maintaining the drive frequency at 108.72 Hz. FSI-based verification confirms a corresponding increase in actual phase-shift. The resulting geometry exhibits localized ovalization and a transition toward a π -like shape. The proposed framework provides an efficient approach to sensitivity-driven CMF design, demonstrated here for a U-shaped measuring tube, with particular relevance for low-flow gas and hydrogen applications. • A free-form shape optimization framework is developed for Coriolis mass flow meters. • Eigenfrequency-based optimization is employed to enhance measurement sensitivity. • A static surrogate load reproduces the relevant torsional deformation pattern without full FSI. • Adjoint sensitivities and vertex morphing enable large-scale node-based optimization. • The optimized design achieves a significant increase in relative sensor deformation.