Investigating conjugate heat transfer in a square cylinder via Lattice boltzmann method

Abstract

Conjugate heat transfer (CHT) is an approach that involves combination of heat transfer in fluids and solids. Unlike general heat transfer phenomena, conjugate heat transfer involves simultaneous analysis of fluid flow and thermal behavior. In practical applications, the interaction between fluid flow and heat transfer is common, necessitating conjugate approach for conducting analysis. Conventional heat transfer analyses with constant thermal properties often do not consider the influence of fluid flow on the temperature distribution. Conjugate heat transfer studies become imperative when the effects of fluid motion on temperature variations cannot be neglected. Conjugate heat transfer finds applications across various fields that include aerospace engineering, automotive design, biomedical engineering and industrial processes. Examples include thermal management in high-speed aircraft engines, cooling systems for electronic devices and optimizing heat dissipation in manufacturing processes etc. Beyond traditional engineering disciplines, conjugate heat transfer is also relevant in biomedical sciences (e.g., thermal modeling for drug delivery systems), geophysical studies (e.g., modeling heat transfer in earth sciences), and chemical engineering (e.g., optimizing reactor designs). Presently, numerical simulations using the Lattice Boltzmann Method (LBM) offer a powerful and effective alternative to classical CFD methods for studying conjugate heat transfer. This is because LBM is inherently parallelly programmable and does not require a conjugate boundary condition for solving CHT problems. Advancements in computational techniques particularly utilizing the parallel processing capabilities of Graphics Processing Units (GPUs) have revolutionized the numerical solvers that are parallelly programmable. High-performance computing centers enable researchers to tackle complex problems efficiently by harnessing the computational power of GPUs. This is particularly advantageous in problems such as conjugate heat transfer that involves intricate thermal-fluid dynamics. Since, LBM is inherently adaptable to run parallel computations, it is ideal for simulating CHT problems. Therefore, LBM with its GPU-based parallel computing capabilities not only enables research and studies in this field with unprecedented accuracy and computational efficiency but also eliminates the need for conjugate boundary conditions, thereby reducing computational costs significantly. In this thesis, an in-house developed Lattice Boltzmann solver is employed to simulate conjugate heat transfer. Non-isothermal viscous flow around a 2-D bluff body i.e. a thermally conductive square cylinder confined in a duct is the primary focus of analysis. The LBM solver is versatile and can be easily adapted to various other geometric configurations and can also be extended to solve multi-phase flows by incorporating relevant phase equations in the numerical solver. The computational setup of the LBM-CHT solver includes a flow solver and a heat solver integrated together in a single framework of a CUDA file (.cu). The solver is implemented using CUDA C++ programming model that is built to be executed on NVIDIA GPUs. Chapter 1 introduces the basic GPU programming principles that were used to develop the solver. Chapter 2 covers the theoretical aspect of Lattice Boltzmann method giving insights into the early developments, schemes used for relaxation models and different lattice arrangements in 1-D, 2-D and 3-D problems. Chapter 3 discusses the developments in the field of conjugate heat transfer and its numerical implementation using LBM. Numerical stability and boundary conditions are also discussed. Finally, we start our numerical study in chapter 5. We begin with the validation of our flow and heat solvers. The geometrical definition of our problem setup, boundary conditions, flow and thermophysical properties used for CHT investigation are discussed. The whole workflow of the numerical solver is provided in a flowchart followed by mesh dependency test. Post-processed results given as contours of flow field and temperature distribution are illustrated through a series of figures that are generated with .vtk extension and visualised in PARAVIEW. Each figure is unique to user-defined input for Prandtl number, solid to fluid conductivity ratio and Reynolds number. Chapter 5 is dedicated to discussion and analysing the key findings. The fluid flow in this study pertains to unsteady time periodic regime that commences at a critical threshold of Re greater than 50 for the square cylinder in the channel with blockage ratio H/D=4. The periodic nature of flow affects the temperature distribution and heat transfer in the system. To summarise and parameterise all the findings of this study, time-averaged Biot number of the cylinder is calculated to judge its performance. Finally, the concluding remarks about this study are highlighted in chapter 6. This study contributes to the understanding of conjugate heat transfer phenomena through computational modeling and numerical simulations. The findings provide valuable insights into the effect of fluid flow on heat transfer and temperature distribution. This can help in paving the way for optimized design and performance of thermal systems.