Efficient simulation of flow and heat transfer in arbitrarily shaped pipes

Abstract

The transport of fluids through pipes is a very common application. Corrugated pipes have characteristics such as local stiffness and flexibility that makes them convenient in several application areas such as offshore LNG (Liquefied Natural Gas) transfer, cryogenic engineering, domestic appliances, etc. Nonetheless, the introduction of pipes with corrugated walls increases the difficulty of simulating flow and heat transfer in these type of pipes. The present thesis addresses the development of efficient models and numerical methods for simulating fluid flow and heat transfer in arbitrarily shaped pipes. The presented work combines both, numerical and analytical techniques with this goal in mind. We start by providing a general framework to the governing equations of fluid flow and heat transfer. We present the Boussinesq approximation and on basis we derive the governing equations for isothermal flow and non-isothermal flow. In the case of non-isothermal flow, we consider the limiting cases of forced and natural convection. We put special attention to the computation of the losses of mechanical energy and derive integral expressions for the friction factor (for periodic corrugated pipes) and for the loss coefficient (for arbitrary conduits). In the case of isothermal laminar flow we develop a very efficient analytical formula for computing the friction factor in slowly varying pipes. For non-slowly varying geometries we present an efficient numerical model which uses a periodicity decomposition in order to reduce the numerical domain to just one period. We use the numerical model for systematically evaluating the accuracy of the analytical formula. Based on the presented models, we also address the problem of wall-shape design. For the problem of non-isothermal laminar flow we consider two limiting cases, namely forced and natural convection. In the case of forced convection, we consider the problem of constant prescribed heat flux at the walls. As in the case of isothermal flow, we use periodicity decomposition for reducing the computational domain. For natural convection, first we take a more practically oriented approach and concentrate on an industrial application involving a cryogenic storage tank featuring a thermosyphon loop. We present a numerical model to simulate the involved phenomena. With this numerical model, we show that it is possible to optimize the wall-shape of the thermosyphon. However the computational cost of such a numerical model are considerable. This happens mainly because the problem does not allow for a periodicity decomposition and the whole extension of the domain needs to be considered. In addition, the corrugations introduce multiple scales which further increase the computational requirements for handling this problem. We provide a more efficient alternative for simulating natural convection by using the method of homogenization. The homogenization method allows us to replace the boundary conditions on a complex boundary by certain effective boundary condition on a homogenized (much simpler) boundary. This is advantageous from a computational point of view, the generation of an adequate mesh becomes straight forward and it is also easier to numerically solve the equations. At the same time, the effects of wall-shape are kept via the effective boundary conditions. The homogenized model is able to handle developing flows and can capture boundary layers. The homogenized model accurately predicts local and averaged quantities in a fraction of the costs of the direct numerical approach. We continue with the case of isothermal turbulent flow. We first present the (RANS) Reynolds averaged Navier-Stokes equations. On this framework, we introduce two turbulence models, the two-equation k-epsilon model and the algebraic LVEL model. We validate both models with experimental data and provide a comparison between both models.