In this paper, the effect of a fractional constitutive model on the rheological properties of fluids and its application in numerical simulation are investigated, which is important to characterize the rheological properties of fluids and physical characteristics of materials more accurately. Based on this consideration, numerical simulation and analytical study of unsteady fractional Oldroyd-B viscoelastic flow are carried out. In order to improve the degree of accuracy, the mixed partial derivative including the fractional derivative in the differential equation is converted effectively by integrating by parts instead of by direct discretization. Then, the stability, convergence, and unique solvability of the difference scheme are verified. The validity of the finite difference method is tested by making comparisons with analytical solutions for two kinds of fractional Oldroyd-B viscoelastic flow. Numerical results obtained using the finite difference method are in good agreement with analytical solutions obtained via the variable separation method. Viscoelastic characteristics of the unsteady Poiseuille flow are similar to the second-order fluid or integer-order Oldroyd-B fluid when the parameter is close to 0 or to 1. Oscillation characteristics of fractional viscoelastic oscillatory flow are similar to those of the classical viscoelastic fluid under the same condition. Compared with the previous research, the present work studies the rheological properties of fluids with the finite difference method, and the application of fractional constitutive models in describing the rheological properties of fluids is developed. Meanwhile, more cases reflecting the fractional-order characteristics are given. The present method can accurately capture the flow characteristics of unsteady fractional Oldroyd-B viscoelastic fluid and is applicable for the generalized fractional fluid.
A hybrid computational aeroacoustic method with permeable boundary is developed to evaluate non-compact noise induced by low Mach number flow over arbitrarily shaped bodies. Based on Lighthill’s equation and the boundary element method, the unified integral equations are established in which the integral boundary surrounding the objects can be selected arbitrarily. Validation studies are developed for noise induced by two-dimensional NACA0012 airfoil and three-dimensional circular cylinder. For NACA0012 airfoil, the directivity patterns of calculated noise with different permeable boundaries agree well with Howe’s analytical solution for trailing edge model. The acoustic noise generated by circular cylinder has a good agreement with Revell’s experimental data and FW-H equation. It demonstrates that the noise predicted by different permeable boundary is as accurate as that calculated by the body surface.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
customersupport@researchsolutions.com
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.