R. Jason Hearst

Scale-by-scale energy budget in fractal element grid-generated turbulence

Measurements were conducted downstream of a square-fractal-element grid at , where L0 is the size of the largest element in the grid. The scale-by-scale energy budget for grid turbulence is used to investigate the phenomenological change in the turbulence between the inhomogeneous and homogeneous regions downstream of the grid, providing greater insight into the evolution of the turbulence in these two regions. It is shown that in the far field, x/L0 ≥ 20, where the flow is approximately homogeneous and isotropic, the scale-by-scale energy budget for grid turbulence is well balanced. In the near field, x/L0 < 20, the same energy budget is not satisfied, with the imbalance of the budget occurring at scales in the range λ ≲ r ≲ L0. It is proposed that the imbalance is caused by non-zero transverse transport of turbulent kinetic energy and production due to transverse mean velocity gradients. Approach of the spectra to k−5/3 behaviour with a decade long scaling range in the inhomogeneous region is attributed...

Modelling high Reynolds number wall-turbulence interactions in laboratory experiments using large-scale free-stream turbulence

A turbulent boundary layer subjected to free-stream turbulence is investigated in order to ascertain the scale interactions that dominate the near-wall region. The results are discussed in relation to a canonical high Reynolds number turbulent boundary layer because previous studies have reported considerable similarities between these two flows. Measurements were acquired simultaneously from four hot wires mounted to a rake which was traversed through the boundary layer. Particular focus is given to two main features of both canonical high Reynolds number boundary layers and boundary layers subjected to free-stream turbulence: (i) the footprint of the large scales in the logarithmic region on the near-wall small scales, specifically the modulating interaction between these scales, and (ii) the phase difference in amplitude modulation. The potential for a turbulent boundary layer subjected to free-stream turbulence to ‘simulate’ high Reynolds number wall–turbulence interactions is discussed. The results of this study have encouraging implications for future investigations of the fundamental scale interactions that take place in high Reynolds number flows as it demonstrates that these can be achieved at typical laboratory scales. This article is part of the themed issue ‘Toward the development of high-fidelity models of wall turbulence at large Reynolds number’.

Interaction layer between a turbulent boundary layer and free-stream turbulence

The interaction between a turbulent free-stream and a turbulent boundary layer is investigated through particle image velocimetry measurements. An ‘interaction layer’ located between \(0.12 \le y/\delta \le 0.19\), at the end of the log layer, is identified whereby the kinetic energy in this layer describes the flow above it. Conditional averages about the interaction layer indicate that it is home to peaks in the Reynolds stresses and that it is the location of a change in the vortical structure. Furthermore, the conditional information identifies that low kinetic energy deficit states in the interaction layer result in a more full boundary layer profile due to increased movement of the bulk flow towards the wall.

A parametric study of high Reynolds number grid-generated turbulence

An active grid is used to generate high-intensity homogeneous isotropic turbulence (HIT) with large integral length scales. The grid is designed such that the motion of adjacent wings may be decoupled allowing for the transient blockage of the grid to take on a more random form than attainable by previous grids. The grid produces high Reynolds number turbulence that is a reasonable approximation of HIT. Based on an exhaustive parametric study conducted with this new grid, the three primary factors that inuence the turbulence produced by the grid are the mean rotational velocity of the wings, , the mean ow velocity, U, and the wing geometry. A maximum Reynolds number of Re = 426 was obtained and the largest integral length scales measured were Lux= 7:16M (or 57 cm). Variations in Lux were found to be dominated by the low frequency energy produced by certain grid settings, typically with low values of .