Fractional K-BKZ Numerical Model of the Start-Up Flow for a Viscoelastic Shock Absorber

Abstract

This paper has proposed a fractional K-BKZ numerical model by adopting the framework of the classical K-BKZ model and the relaxation modulus of the fractional Maxwell model with quasiproperties to study the start-up flow of a viscoelastic shock absorber. The start-up flows in both the orifice and the gap of a shock absorber were simplified to unidirectional accelerated flows in a pipe and between two parallel plates where one plate is accelerating and the other is at rest. The fractional K-BKZ numerical model was then developed using the finite difference method with real-world initial and boundary conditions. Numerical simulation was then performed, and the results were validated through laboratory testing, based on a comparison of the maximum fluid level and the contact angle. The proposed fractional K-BKZ numerical model successfully simulated the characteristics of the viscoelastic material passing through the orifice or the gap of a shock absorber, as demonstrated by accurately capturing the change of the shape of the flow. This fractional K-BKZ numerical model provided better accuracy for the fluid’s viscoelasticity and can be used for shock absorber design.