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.
Highlights
Viscoelastic materials belong to the class of non-Newtonian pseudoplastic fluids
The fractional K-BKZ numerical model was proposed in order to study the start-up flows of the viscoelastic material in a shock absorber
According to the actual flow conditions of a viscoelastic material in the orifice and the gap of a shock absorber, the flow behavior was simplified to two forms: the accelerated flow of the viscoelastic fluid in a pipe and the flow of the viscoelastic fluid between two parallel plates with one plate accelerating and the other at rest
Summary
Viscoelastic materials belong to the class of non-Newtonian pseudoplastic fluids. According to the mechanical structure of a shock absorber, the start-up flow forms of the viscoelastic material in the shock absorber can be divided into two types: the gap flow and the orifice flow. Carrera et al [11] studied the fractional Maxwell model containing the relaxation process presenting non-Newtonian viscous behavior, and they analyzed and calculated the storage and loss modulus corresponding to the frequency and the amplitude function They analyzed the stability of the function and found that the model’s results agreed well with the experimental results. On the basis of the converse ladder Maxwell model, Yao [12] introduced the tensor and different fractional derivative definitions to apply the fractional dashpot model to the simulation for the flow process of a nonlinear viscoelastic fluid under large deformation. Comparative analysis of classical K-BKZ numerical model, the fractional Maxwell numerical model, and the Newtonian fluid model have been performed, and the unidirectional accelerated start-up flows of viscoelastic fluid in the orifice and the gap have been studied. A start-up flow test system was designed, and it captured the flow process of a viscoelastic material in the orifice of a shock absorber when the flow starts up, which validated the accuracy of the fractional K-BKZ numerical model
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