Numerical resolution of mass, momentum, and energy equations in 3D steady-state and transient models; Application to next generation of HVAC&R components and equipment

Abstract

The rising global demand for energy, particularly in the context of heating, ventilation, air conditioning, and refrigeration (HVAC&R) systems, necessitates the development of more efficient and environmentally sustainable solutions. This thesis focuses on the numerical resolution of the mass, momentum, and energy Navier-Stokes equations, using both steady-state and transient computational models. The work presents a comprehensive review of turbulence theory and modeling, including Direct Numerical Simulation (DNS), Large-Eddy Simulation (LES), and Reynolds-Averaged Navier-Stokes (RANS) approaches. The main emphasis is placed on the development, implementation, and validation of robust numerical algorithms using the Finite Volume Method (FVM), staggered meshing, and different temporal and spatial discretization schemes. The simulations were performed using the C++ programming language. Benchmark cases, such as 2D transient heat conduction, the SmithHutton problem, the Lid-driven cavity, and Differentially heated cavity flows, are simulated and analyzed to assess the impact of various numerical solution factors on solution accuracy, stability, and computational performance. Particular attention was given to the comparison of different convective schemes, with a main focus on the Central Difference (CDS), Upwind Difference (UDS), Second-Order Upwind Linear Extrapolation (SUDS), and Quadratic Upwind Interpolation for Convective Kinematics (QUICK) convective schemes, as well as the mesh convergence studies. Furthermore, the numerical results were verified by comparing them to benchmark solutions. Additionally, energy budgets were discussed, with the analysis of the convective schemes impact. The findings advance the understanding of CFD methodologies applied to HVAC&R systems, providing a basis for future research aimed at optimizing the design of next-generation thermal components and equipment, with the goal of reaching a solution to the ever-growing environmental issues caused by the excessive energy demand.