Fluids are common substances in our daily life, for example, water, air, and blood, etc. A fluid is said to be Newtonian if its viscosity does not change with the flow shear rate (e.g., water and air), while a fluid is said to be non-Newtonian if its viscosity is dependent on the flow shear rate/history, etc. Many substances encountered in biological systems and industrial practices normally display non-Newtonian fluid behaviours, for example, blood, fish mucus and food, etc. Due to the shear rate (history) dependent viscosity, such non-Newtonian fluids display a variety of complex behaviours including shear-thinning and shear-thickening. Due to the pragmatic significance of non-Newtonian fluids in biological systems and process industries, research efforts herein have been concentrated on the development of computational tools to explore the insights of the complex fluid flow and heat transfer phenomena.
Most of previous investigations have presented numerical methods based on the stationary boundaries; however, observations have shown that many practically important flow processes involve the moving boundaries such as flexible interfaces and wavy channels. The tractable level of complexities further enhances, even for the simple fluids, in obtaining the solution of flow problems involving moving boundaries. Motivated by this simple but extremely important fact, Dr. Fang-Bao Tian at the Vanderbilt University (now at the University of New South Wales Canberra), collaborated with Prof. Ram P. Bharti at the Indian Institute of Technology Roorkee and Dr. Yuan-Qing Xu at the Beijing Institute of Technology, developed a variation of the deforming-spatial-domain/stabilized space-time method for the computations of non-Newtonian fluid flow and heat transfer with moving boundaries (Computational Mechanics 53, 257-271, 2014). In this method, the variational formulation is written over the space-time domain. Three sets of stabilization parameters are used for the continuity, momentum and thermal energy equations. This method allows the spatial domain at various time levels to vary and does not apply interpolation when a moving mesh is involved, and thus, is accurate and efficient. It makes the computations feasible with third-order accuracy in time, which is higher then most of the previous versions of the finite element method. The reliability and accuracy of this method has been established through the well-known benchmark problems such as channel-confined flow, flow in channel with wavy wall, and fish mucus, where the non-Newtonian fluid rheological behaviours are incorporated. This work (Computational Mechanics 53, 257-271, 2014) provides an accurate and efficient method for hydrodynamics and heat transfer problems involving complex fluids and moving boundaries.
For more details, please visit DOI: 10.1007/s00466-013-0905-0 or contact Dr. F.-B. Tian ([email protected]) at University of New South Wales Canberra, Australia or Prof. Ram P. Bharti ([email protected]) at Indian Institute of Technology Roorkee, India.
Computational Mechanics. February 2014, Volume 53, Issue 2, pp 257-271.
Fang-Bao Tian, Ram P. Bharti, Yuan-Qing Xu.
Department of Mechanical Engineering, Vanderbilt University, 2301 Vanderbilt Place, Nashville, TN, 37235-1592, USA &
Department of Chemical Engineering, Indian Institute of Technology Roorkee, Roorkee, 247667, India &
School of Life Science, Beijing Institute of Technology, Beijing, 100081, People’s Republic of China.
This work presents an extension of the Deforming-Spatial-Domain/Stabilized Space–Time (DSD/SST) method to non-Newtonian fluid flow and heat transfer with moving boundaries. In this method, the variational formulation is written over the space–time domain. Three sets of stabilization parameters are used for the continuity, momentum and thermal energy equations. The more efficient solution for highly non-linear problems is achieved by using the Newton–Raphson iterative method for non-linear terms and the generalized minimal residual method for algebraic equations. This work makes the computations feasible with third-order accuracy in time, which is higher then most versions of the FEM. To validate this method, it is used to solve the well-known benchmark problems such as channel-confined flow, lid-driven cavity, flow around a cylinder, and flow in channel with wavy wall, where the non-Newtonian fluid rheological behaviour is incorporated. In particular, the results in terms of the Nusselt number, wall shear stress (WSS), vorticity fields and streamlines are discussed. It shows that the flow and heat transfer characteristics are quite different if the moving boundaries are taken into account. In summary, this work provides an effective extension of the DSD/SST method to hydrodynamics and heat transfer problems involving complex fluids and moving boundaries.