The transition and optimisation of turbulence in pipe flow

Understanding transitional and full turbulence in pipe flow is of great significance for engineering applications. This thesis focuses on isothermal and heated pipe flow, which have different requirements of turbulence. The former needs flow to keep laminar to reduce frictional drag, while the latter prefers turbulence to enhance heat transfer. These two types of flow are researched to understand and optimise their transition between laminar and turbulence. The thesis first focuses on the isothermal pipe flow, and applies
the nonlinear variational method to find invariant solutions. Such a method allows for identifying the invariant solutions at low Reynolds number, making it possible to understand transition from the perspective of a dynamical system. Then, linear and nonlinear variational methods are developed to optimise laminarisation. The nonlinear method allows to identify a minimal force to laminarise turbulence, and the linear method targets reducing transient growth to eliminate turbulence. The focus next switches to the heated pipe, aiming to understand the buoyancy-affected transitional flow and heat transfer optimisation. A new DNS model is set up for the simulation of heated pipe flow, which considers a time-varying background temperature gradient and two types of temperature boundary conditions. The heated pipe flow at different buoyancy strengths (measured by a dimensionless parameter C, which is the ratio of buoyancy force to pumping force) is investigated by nonlinear nonmodal stability analysis. The amplitude of the minimal seed is found to be larger at a larger C. Some important invariant solutions, which represent the self-sustaining process of convective turbulence, are identified. Finally, the nonlinear variational method is applied to optimise heat transfer in heated pipe flow. Optimisations are performed in the laminar, shear turbulence and convective turbulence. A more efficient body force is found by optimisations for unsteady states, compared to optimisations for a steady laminar state.