<p>Direct numerical simulation has been performed in order to study ressure-driven turbulent flow in a rod-roughened channel at Reynolds number Reτ = 400 (based on the mean pressure gradient). Square rods were attached to both channel walls and protruded only 0.034 of the channel’s half-height into the flow. Roughness elements were spaced at 7 heights, which corresponded to the so-called “k–type” laboratory roughness.</p><p>The classical logarithmic variation of the mean velocity was found to be maintained in the rough-wall channel flow. The only effect roughness had was to shift the log-profile downwards, the magnitude of which was about 7.1. This, corresponded to the upper limit of the transitionally rough region, based on the associated equivalent sand-grain roughness height. Within the layer of thickness about 3-5 times roughness height (roughness sublayer ), the dependency of the mean velocity and turbulence properties on the streamwise location with respect to the rods was revealed.</p><p>Instead of viscous sublayer, an intensive shear layer was formed emanated from the crest of roughness elements. It was observed that the wall-ward transport of the kinetic energy was substantially increased very close to the wall while the transport of the kinetic energy away from the wall was relatively reduced at just about the edge of the roughness sublayer. Visualizations of the fluctuating velocities and vortices in this region revealed the presence of elongated streaky structures very similar to those routinely observed in the structure of the smooth-wall turbulence, with much shorter coherence in the streamwise direction and less organization in the spanwise direction. The intensity of the vorticity fluctuations in the roughness sublayer were increased whereas in the outer layer, they remained unaffected. The anisotropy invariant maps for the smooth and rough cases clearly showed that the state of the near-wall turbulence for the two cases were substantially different, whereas in the regions away from the wall, the two cases exhibited similarities. Generally, the results obtained from this study supported the classical wall similarity hypothesis.</p>

Direct numerical simulation has been performed in order to study ressure-driven turbulent flow in a rod-roughened channel at Reynolds number Reτ = 400 (based on the mean pressure gradient). Square rods were attached to both channel walls and protruded only 0.034 of the channel’s half-height into the flow. Roughness elements were spaced at 7 heights, which corresponded to the so-called “k–type” laboratory roughness. The classical logarithmic variation of the mean velocity was found to be maintained in the rough-wall channel flow. The only effect roughness had was to shift the log-profile downwards, the magnitude of which was about 7.1. This, corresponded to the upper limit of the transitionally rough region, based on the associated equivalent sand-grain roughness height. Within the layer of thickness about 3-5 times roughness height (roughness sublayer ), the dependency of the mean velocity and turbulence properties on the streamwise location with respect to the rods was revealed. Instead of viscous sublayer, an intensive shear layer was formed emanated from the crest of roughness elements. It was observed that the wall-ward transport of the kinetic energy was substantially increased very close to the wall while the transport of the kinetic energy away from the wall was relatively reduced at just about the edge of the roughness sublayer. Visualizations of the fluctuating velocities and vortices in this region revealed the presence of elongated streaky structures very similar to those routinely observed in the structure of the smooth-wall turbulence, with much shorter coherence in the streamwise direction and less organization in the spanwise direction. The intensity of the vorticity fluctuations in the roughness sublayer were increased whereas in the outer layer, they remained unaffected. The anisotropy invariant maps for the smooth and rough cases clearly showed that the state of the near-wall turbulence for the two cases were substantially different, whereas in the regions away from the wall, the two cases exhibited similarities. Generally, the results obtained from this study supported the classical wall similarity hypothesis.

<p>This thesis deals with the construction of a numerical method for solving two-dimensional elliptic interface problems, such as fully developed stratified flow in pipes. Interface problems are characterized by its non-smooth and often discontinuous behaviour along a sharp boundary separating the fluids or other materials. Classical numerical schemes are not suitable for these problems due to the irregular geometry of the interface. Standard finite difference discretization across the interface violates the interfacial boundary conditions; therefore special care must be taken at irregular grid nodes.</p><p>In this thesis a decomposed immersed interface method is presented. The immersed interface method is a numerical technique formulated to solve partial differential equations in the presence of an interface where the solution and its derivatives may be discontinuous and non-smooth. Componentwise corrections terms are added to the finite difference stencil in order to make the discretization well-defined across the interface. A method that approximates the correction terms is also proposed. Results from numerical experiments show that the rate of convergence is approximately of second order.</p><p>Moreover, the immersed interface method is applied to stratified multiphase flow in pipes. The flow is assumed to be fully developed and in steady-state. For turbulent flow, both a low Reynolds number turbulence model and a two-layer turbulence model are adopted in order to imitate turbulence in the flow field and in the vicinity of the boundaries. The latter turbulence model is modified accordingly to account for the effects of a wavy interface. In this case, the concept of interfacial roughness is used to model the wavy nature of the interface.</p><p>Numerical results are compared with analytical solutions for laminar flow and experimental data for turbulent flow. It is also demonstrated that the current numerical method offers more flexibility in simulating stratified pipe flow problems with complex shaped interfaces, including three-phase flow, than seen in any previous approach.</p> / Paper I reprinted with kind permission of Elsevier, Sciencedirect

This thesis deals with the construction of a numerical method for solving two-dimensional elliptic interface problems, such as fully developed stratified flow in pipes. Interface problems are characterized by its non-smooth and often discontinuous behaviour along a sharp boundary separating the fluids or other materials. Classical numerical schemes are not suitable for these problems due to the irregular geometry of the interface. Standard finite difference discretization across the interface violates the interfacial boundary conditions; therefore special care must be taken at irregular grid nodes. In this thesis a decomposed immersed interface method is presented. The immersed interface method is a numerical technique formulated to solve partial differential equations in the presence of an interface where the solution and its derivatives may be discontinuous and non-smooth. Componentwise corrections terms are added to the finite difference stencil in order to make the discretization well-defined across the interface. A method that approximates the correction terms is also proposed. Results from numerical experiments show that the rate of convergence is approximately of second order. Moreover, the immersed interface method is applied to stratified multiphase flow in pipes. The flow is assumed to be fully developed and in steady-state. For turbulent flow, both a low Reynolds number turbulence model and a two-layer turbulence model are adopted in order to imitate turbulence in the flow field and in the vicinity of the boundaries. The latter turbulence model is modified accordingly to account for the effects of a wavy interface. In this case, the concept of interfacial roughness is used to model the wavy nature of the interface. Numerical results are compared with analytical solutions for laminar flow and experimental data for turbulent flow. It is also demonstrated that the current numerical method offers more flexibility in simulating stratified pipe flow problems with complex shaped interfaces, including three-phase flow, than seen in any previous approach. / Paper I reprinted with kind permission of Elsevier, Sciencedirect