Efficacy of single-component MTV to measure turbulent wall-flow velocity derivative profiles at high resolution

Abstract

Physical interpretations and especially analytical considerations benefit from the ability to accurately estimate derivatives of experimentally measured statistical profiles. Toward this aim, experiments were conducted to investigate the efficacy of single-component molecular tagging velocimetry (1c-MTV) to measure mean velocity profiles that can be differentiated multiple times. Critical effects here pertain to finite measurement uncertainty in the presence of high spatial resolution. Measurements acquired in fully developed turbulent channel flow over a friction Reynolds number range from 390 to 1800 are used to investigate these issues. Each measured profile contains about 880 equally spaced data points that span from near the edge of the viscous sublayer to the channel centreline. As a result of the high spatial resolution, even very small levels of uncertainty in the data adversely affect the capacity to produce smooth velocity derivative profiles. It is demonstrated that the present 1c-MTV measurements can be differentiated twice, with the resulting profile remaining smooth and accurate. The experimental mean velocity profiles and their wall-normal derivatives up to second order are shown to convincingly agree with existing DNS data, including the apparent variations with Reynolds number.