A weakly compressible flow direct numerical simulation of a controlled-diffusion aerofoil at geometrical angle of attack, a chord-based Reynolds number of and a Mach number of based on the free-stream velocity relevant to many industrial applications was conducted to improve the understanding of the impact of the pressure gradient on the development of turbulent structures. The evolution equations for the two invariants and of the velocity-gradient tensor have been studied at various locations along the aerofoil chord on its suction side. The shape of the mean evolution of the velocity-gradient tensor invariants were found to vary strongly when the flow encounters favourable, zero and adverse pressure gradients and as well for different wall-normal locations. The coupling between the pressure-Hessian tensor and the velocity-gradient tensor was found to be the major factor that causes these changes and is greatly influenced by the mean pressure-gradient condition and the wall-normal distance. Striking differences exist from the mean trajectories of this coupling at least in the log layer and outer layer subject to different mean pressure gradients. The nonlinearity and viscous diffusion effects keep their respective invariant characters regardless of the pressure-gradient effects and wall-normal locations. The wall and the mean adverse pressure gradient were both found to suppress the vortical stretching features of the flow. These features are of great importance for the development of future turbulence models on wall-bounded flows, especially on surfaces with significant curvature such as cambered aerofoils and blades for which significant mean pressure gradients exist.

Effects of pressure gradient on the evolution of velocity-gradient tensor invariant dynamics on a controlled-diffusion aerofoil at

Reconstructing pressure fields from 2D or 3D velocimetry data involves a pressure gradient integration procedure. This paper proposes a spectral decomposition-based fast pressure integration (SD-FPI) algorithm to integrate a gridded pressure gradient field. The algorithm seeks the least-square solution for the discrete momentum conservation equation by matrix decompositions, which allows for the use of various difference schemes. The recently proposed fast Fourier transform (FFT) integration method (Huhn et al. Exp Fluids 57:151, 2016) could be viewed as a special example of SD-FPI when adopting a special circulant difference scheme. The inherent relationship between SD-FPI and the Poisson reconstruction is also revealed in theory. An iterative strategy for SD-FPI is developed to integrate the pressure gradient fields with missing data. The accuracy and efficiency of SD-FPI with various difference schemes including the FFT-based approaches are compared based on a synthetic pressure field. We conclude that while the computing efficiency is always high, the accuracy of SD-FPI depends on the difference scheme and error types of the pressure gradients.

Spectral decomposition-based fast pressure integration algorithm

This study examines the interactions of a compliant wall with a turbulent boundary layer as the deformation scale increases from submicron to several wall units (δν). The friction velocity Reynolds number ranges between 1435 and 5179, and , with the direct numerical simulation results of Rosti and Brandt (J. Fluid Mech., vol. 830, 2017, pp. 708–735).

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022112020004462

On the interaction of a compliant wall with a turbulent boundary layer

We address the fluid–structure interaction of flexible fin models oscillating in a water flow. Here, we investigate in particular the dependence of hydrodynamic force distributions on fin geometry and flapping frequency. For this purpose, we employ state-of-the-art techniques in pressure evaluation to describe fluid force maps with high temporal and spatial resolution on the deforming surfaces of the hydrofoils. Particle tracking velocimetry is used to measure the three-dimensional fluid velocity field, and the hydrodynamic stress tensor is subsequently calculated based on the Navier–Stokes equation. The shape and kinematics of the fin-like foils are linked to their ability to generate propulsive thrust efficiently, as well as the accumulation of external contact forces and the resulting internal tension throughout a flapping cycle.

How shape and flapping rate affect the distribution of fluid forces on flexible hydrofoils

Effects of heat transfer on separated boundary layer behavior under adverse pressure gradients

Abstract This study focuses on the effects of mean (favourable) and large-scale fluctuating pressure gradients on boundary layer turbulence. Two-dimensional (2D) particle image velocimetry (PIV) measurements, some of which are time-resolved, have been performed upstream of and within a sink flow for two inlet Reynolds numbers, ${Re}_{\theta }(x_{1})=3360$ and 5285. The corresponding acceleration parameters, $K$ , are ${1.3\times 10^{-6}}$ and ${0.6\times 10^{-6}}$ . The time-resolved data at ${Re}_{\theta }(x_{1})=3360$ enables us to calculate the instantaneous pressure distributions by integrating the planar projection of the fluid material acceleration. As expected, all the locally normalized Reynolds stresses in the favourable pressure gradient (FPG) boundary layer are lower than those in the zero pressure gradient (ZPG) domain. However, the un-scaled stresses in the FPG region increase close to the wall and decay in the outer layer, indicating slow diffusion of near-wall turbulence into the outer region. Indeed, newly generated vortical structures remain confined to the near-wall region. An approximate analysis shows that this trend is caused by higher values of the streamwise and wall-normal gradients of mean streamwise velocity, combined with a slightly weaker strength of vortices in the FPG region. In both boundary layers, adverse pressure gradient fluctuations are mostly associated with sweeps, as the fluid approaching the wall decelerates. Conversely, FPG fluctuations are more likely to accompany ejections. In the ZPG boundary layer, loss of momentum near the wall during periods of strong large-scale adverse pressure gradient fluctuations and sweeps causes a phenomenon resembling local 3D flow separation. It is followed by a growing region of ejection. The flow deceleration before separation causes elevated near-wall small-scale turbulence, while high wall-normal momentum transfer occurs in the ejection region underneath the sweeps. In the FPG boundary layer, the instantaneous near-wall large-scale pressure gradient rarely becomes positive, as the pressure gradient fluctuations are weaker than the mean FPG. As a result, the separation-like phenomenon is markedly less pronounced and the sweeps do not show elevated small-scale turbulence and momentum transfer underneath them. In both boundary layers, periods of acceleration accompanying large-scale ejections involve near-wall spanwise contraction, and a high wall-normal momentum flux at all elevations. In the ZPG boundary layer, although some of the ejections are preceded, and presumably initiated, by regions of adverse pressure gradients and sweeps upstream, others are not. Conversely, in the FPG boundary layer, there is no evidence of sweeps or adverse pressure gradients immediately upstream of ejections. Apparently, the mechanisms initiating these ejections are either different from those involving large-scale sweeps or occur far upstream of the peak in FPG fluctuations.

The effect of mean and fluctuating pressure gradients on boundary layer turbulence

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The effect of mean and fluctuating pressure gradients on boundary layer turbulence