The Finite Element Numerical Investigation of Free Surface Newtonian and Non-Newtonian Fluid Flows in the Rectangular Tanks

Abstract

In this paper, we develop a new computational framework to investigate the sloshing free surface flow of Newtonian and non-Newtonian fluids in the rectangular tanks. We simulate the flow via a two-phase model and employ the fixed unstructured mesh in the computation to avoid the mesh distortion and reconstruction. As for the solution of Navier–Stokes equation, we utilize the SUPG finite element method based on the splitting scheme. The same order interpolation functions are then used for velocity and pressure. Moreover, the moving interface is captured via the concise level set method. We take advantage of the implicit discontinuous Galerkin method to handle the solution of level set and its reinitialization equations. A mass correction technique is also added to ensure the mass conservation property. The dam break-free surface flow is simulated firstly to demonstrate the validity of our mathematical model. In addition, the sloshing Newtonian fluid in the tank with flat and rough bottoms is considered to illustrate the feasibility and robustness of our computational scheme. Finally, the development of free surface for non-Newtonian fluid is also studied in the two tanks, and the influence of power-law index on the sloshing fluid flow is analyzed.

Compressible Non-Newtonian Fluid Based Road Traffic Flow Equation Solved by Physical-Informed Rational Neural Network

“…Non-Newtonian fluid, as a type of fluid that can describe viscoelastic characteristics, have unique advantages in reflecting velocity fields that do not strictly possess traditional fluid properties, and have received widespread attention from scholars in recent years [23][24]. In the field of life and health, Redfearn et al (2018) have applied non-Newtonian fluid to explain the rheology behavior of different food in mouth, and have discussed the compression characteristics of tongue and upper jaw on food fluids during eating [25]; have used non-Newtonian fluid theory to simulate the physical characteristics of bleeding, incorporating the effects of tension and platelets on the viscosity of bleeding particles into the non-Newtonian fluid equation, making the theoretical description closer to the true biological characteristics of bleeding [26]; Bhatti et al (2022) have studied the motion of metal suspended substances in nanofluids and explained the delivery law of magnetic drugs in narrow arteries using non-Newtonian fluid theory [27].…”