Precursors of backflow events and their relationship with the near-wall self-sustaining process

This study examines the precursors and consequences of rare backflow events at the wall using direct numerical simulation of turbulent pipe flow with a high spatiotemporal resolution. The results obtained from conditionally averaged fields reveal that the precursor of a backflow event is the asymmetric collision between a high- and a low-speed streak (LSS) associated with the sinuous mode of the streaks. As the collision occurs, a lifted shear layer with high local azimuthal enstrophy is formed at the trailing end of the LSS. Subsequently, a spanwise or an oblique vortex spontaneously arises. The dominant nonlinear mechanism by which this vortex is engendered is enstrophy intensification due to direct stretching of the lifted vorticity lines in the azimuthal direction. As time progresses, this vortex tilts and orientates towards the streamwise direction and, as its enstrophy increases, it induces the breakdown of the LSS located below it. Subsequently, this vortical structure advects as a quasi-streamwise vortex, as it tilts and stretches with time. As a result, it is shown that reverse flow events at the wall are the signature of the nonlinear mechanism of the self-sustaining process occurring at the near-wall region. Additionally, each backflow event has been tracked in space and time, showing that approximately 50 % of these events are followed by at least one additional vortex generation that gives rise to new backflow events. It is also found that up to a maximum of seven regenerations occur after a backflow event has appeared for the first time.

One-point statistics for turbulent pipe flow up to

We study turbulent flows in a smooth straight pipe of circular cross-section up to friction Reynolds number $({\textit {Re}}_{\tau }) \approx 6000$ using direct numerical simulation (DNS) of the Navier–Stokes equations. The DNS results highlight systematic deviations from Prandtl friction law, amounting to approximately $2\,\%$ , which would extrapolate to approximately $4\,\%$ at extreme Reynolds numbers. Data fitting of the DNS friction coefficient yields an estimated von Kármán constant $k \approx 0.387$ , which nicely fits the mean velocity profile, and which supports universality of canonical wall-bounded flows. The same constant also applies to the pipe centreline velocity, thus providing support for the claim that the asymptotic state of pipe flow at extreme Reynolds numbers should be plug flow. At the Reynolds numbers under scrutiny, no evidence for saturation of the logarithmic growth of the inner peak of the axial velocity variance is found. Although no outer peak of the velocity variance directly emerges in our DNS, we provide strong evidence that it should appear at ${\textit {Re}}_{\tau } \gtrsim 10^4$ , as a result of turbulence production exceeding dissipation over a large part of the outer wall layer, thus invalidating the classical equilibrium hypothesis.

Measurement of energy spectrum by using 100 eyes Tomographic PIV

PIV is one of the methods to measure velocity in a flow field, but its dynamic velocity range is narrower than other flow velocimeter. This disadvantage is particularly apparent in measurements of spectrum in turbulent boundary layers, where the higher wave number side of the spectrum cannot be measured with high accuracy. In this study, we captured images of the same particle in the flow field from many different direction simultaneously, and reduced the measurement error of the particle displacement by averaging the acquired particle positions, so called ‘Multiple Eye PIV’ [Maekawa, A., Sakakibara, J., 2018, Meas. Sci. Tech., 29, 064011]. We applied this method to obtain the energy spectrum in a turbulent pipe flow aiming for resolving higher wave number. Particle images were captured by a single high-speed CMOS camera (Fastcam Nova S6, 6000 fps, Photron) through a mirror array consists of 110 flat mirrors arranged in the shape of an axisymmetric ellipsoid (Fig.1), as shown in Fig.2. The images were evaluated by Tomographic PIV method to resolve three-dimensional velocity field. Fig.3 shows energy spectrum in a pipe measured by Tomographic-PIV with number of mirrors, N, up to 100 in addition to the 2D2C-PIV with a single mirror. Although the spectrum curve for the result of Tomographic-PIV begins to depart from the reference curve at wavenumber beyond 10-1 , such wavenumber grows as N increases, and consequently the plateau of the curve appeared at lower energy. Such a downward shift of the plateau is expected due to the improvement of the dynamic velocityrange, which is approximately one order in energy, i.e. three times in velocity, found between N=4 and 100. Note that the cases of N=4 and 40 loses the dynamic range against the 2C2D-PIV case. From the above, we can summarize that the advantage of Multiple Eye PIV over the 2C2D-PIV is effective when the number of mirrors is more than 40. In this experiment, the issue is that particles images flickered. In order to resolve this issue, we tried to use fluorescent particles, and obtained a clear particle images in the following experiment. We are now analyzing whether the energy spectrum can be measured with higher accuracy due to improved resolution of the particles.

Experimental techniques against RANS method in a fully-developed turbulent pipe flow

Turbulence has been studied by scientists and engineers for decades as it appears in the majority of the fluids existent in nature and in engineering applications and because turbulent flow and its underlying behaviour are tremendously complex. The University of Manchester is widely viewed as the birthplace of turbulence due to the pioneering work of one of its prominent academics, Professor Osborne Reynolds (1842-1912). Building on this legacy, a classical experimental apparatus has been used in this paper to study a turbulent pipe flow with the aim of measuring the mean velocity field and wall shear stress using four experimental techniques, all developed in the 20th century, namely static pressure drop; mean square signals measured from a hot-wire; Preston tube; and the ‘Clauser Plot’. The experimental results have then been compared against those obtained using Computational Fluid Dynamics (CFD), utilising different two-equation turbulence models. The present work highlights the discrepancies evident in obtaining the value of the wall shear stress in each method. In addition, the scopes and limitations of each technique are discussed in detail, highlighting the clear evolution of turbulence study tools over the last 100 years.