Linear instability of Poiseuille flows with highly non-ideal fluids

The objective of this work is to investigate linear modal and algebraic instability in Poiseuille flows with fluids close to their vapour-liquid critical point. Close to this critical point, the ideal gas assumption does not hold and large non-ideal fluid behaviours occur. As a representative non-ideal fluid, we consider supercritical carbon dioxide (CO$_2$) at pressure of 80 bar, which is above its critical pressure of 73.9 bar. The Poiseuille flow is characterized by the Reynolds number ($Re=\rho_{w}^{*}u_{r}^{*}h^{*}/\mu_{w}^{*}$), the product of Prandtl ($Pr=\mu_{w}^{*}C_{pw}^{*}/\kappa_{w}^{*}$) and Eckert number ($Ec=u_{r}^{*2}/C_{pw}^{*}T_{w}^{*}$), and the wall temperature that in addition to pressure determines the thermodynamic reference condition. For low Eckert numbers, the flow is essentially isothermal and no difference with the well-known stability behaviour of incompressible flows is observed. However, if the Eckert number increases, the viscous heating causes gradients of thermodynamic and transport properties, and non-ideal gas effects become significant. Three regimes of the laminar base flow can be considered, subcritical (temperature in the channel is entirely below its pseudo-critical value), transcritical, and supercritical temperature regime. If compared to the linear stability of an ideal gas Poiseuille flow, we show that the base flow is more unstable in the subcritical regime, inviscid unstable in the transcritical regime, while significantly more stable in the supercritical regime. Following the corresponding states principle, we expect that qualitatively similar results will be obtained for other fluids at equivalent thermodynamic states.Comment: 34 pages, 22 figure

The influence of station keeping systems on tidal turbine structural performance when operating in combined-wave current sea states

This thesis reports on the performance and interactions of a tidal turbine and station keeping systems based on the adoption of a tension mooring system in different sea states. The capabilities of introducing damping are being investigated to reduce the peak loads that tidal turbines experience during operational life in high energy wave-current environments and extreme sea states. A neutrally buoyant turbine is supported from a tension cable based mooring system, where tension is introduced by a buoy fully submersed in water. The loading on the turbine rotor blades and buoy are calculated using a wave and current coupled BEMT. The modeling algorithm developed is based on an inverted triple pendulum, responding to different sea state conditions to understand the system response behavior and the blade load in different sea states, including extreme conditions. The results show the tension mooring system reduce speak thrust loading on the turbine, but it was found that there are certain limitation when using this design in extreme waves conditions.This thesis reports on the performance and interactions of a tidal turbine and station keeping systems based on the adoption of a tension mooring system in different sea states. The capabilities of introducing damping are being investigated to reduce the peak loads that tidal turbines experience during operational life in high energy wave-current environments and extreme sea states. A neutrally buoyant turbine is supported from a tension cable based mooring system, where tension is introduced by a buoy fully submersed in water. The loading on the turbine rotor blades and buoy are calculated using a wave and current coupled BEMT. The modeling algorithm developed is based on an inverted triple pendulum, responding to different sea state conditions to understand the system response behavior and the blade load in different sea states, including extreme conditions. The results show the tension mooring system reduce speak thrust loading on the turbine, but it was found that there are certain limitation when using this design in extreme waves conditions