Theoretical and experimental investigations of similarity solutions in turbulent flows

Abstract

An investigation of turbulent flows is performed through seeking similarity solutions to their governing equations. A combination of theoretical, experimental, and numerical approaches are utilized to validate the resulting scaling parameters and solutions.

A two-point, two-time similarity solution is found for the velocity correlation in a decaying homogeneous turbulence field. The solution reduces to previous single-point, single-time solutions when the appropriate limit is taken. Relations to classic isotropic results are investigated, with additional symmetries to the equation of motion proposed. The implications on the simplifications of the Lumley POD integral are discussed.

A new theory for the temperature distribution in a developing turbulent thermal boundary layer is obtained, resulting in two different possible sets of scaling parameters for the inner and outer flows. The overlap-layer profile and resulting heat transfer law are both described by a power law. Extending the scaling and similarity analysis to the temperature variance field results in power laws for both the overlap-layer profile and so-called “variance law,” which is found to be directly tied to the heat transfer law. An additional Reynolds number dependent parameter, unique to the variance field, is discussed.

New velocity and temperature sensors are developed for flow measurements to assist in these investigations. Initial utilization of nanoscale wires to measure temperature in a water channel resulted in conflated velocity and temperature measurements, prompting this new sensor development. Theoretical models inform the design, while experimental results show their performance in the turbulent boundary layer as well as laminar flow applications. The velocity sensors are demonstrated as mechanically and electrically minimalistic compared to classic devices, with future design considerations made for thermal applications.