Etapa 3 Análisis de la situación proyectada

In§2.2.4 the effects of boundary layer three-dimensionality on the coherent turbu-

lent structures was briefly reviewed. In this section, a similar review is made into the effects of favourable pressure gradients. Though still complicated by the flow types and the various investigation methods employed, a more coherent picture is emerging for streamwise acceleration effects. This may be explained in part, by the relatively simpler design of favourable pressure gradient experiments and the fewer complicating practical factors.

Schraub and Kline (1965) used large acceleration rates in a low-speed water channel to investigate the viscous sublayer streaks using hydrogen bubble visual- isation. To observe the near-wall bursting activity, dye was injected through the wall and the number of ejections, defined by recognised patterns of violent streak behaviour, were counted for a given time and distance. The streaks were found to be largely unaffected by the pressure gradient within the range: -2×10−6<_K<_1.5×₁₀−6_, but significant changes occurred for larger accelerations; most notably for the streak spacing and bursting rates. For adverse pressure gradients, the burst rate tended to increase and decreased under favourable gradients. For very large negative pres- sure gradients (K> 3.5×10−6_{) the bursting eventually ceased entirely. The non-}

dimensional mean spanwise spacing of the low-speed streaks (λ+) was also found to

increase at strong favourable streamwise gradients, rising toλ+=180 forK=3×10−6

and up to 240 for K≈4×10−6_{. Quiescent (laminar-like) regions of bubbles begin to}

appear at the wall and streaks become more fixed in space, i.e. ‘wiggling’ less. Even- tually, turbulent production in the boundary layer is assumed to cease entirely with the bursting, leading to a laminar state. Further experimental confirmation of the increase in streak spacing is provided by Talamelli et al. (2002) who use time-space correlations of the velocity signals from two spanwise separated hot-wire probes.

They measured a rise inλ+ by up to 170% atK=3.1×10−6

Piomelli et al. (2000) visualised the near-wall turbulence structure using con- tours of streamwise velocity and vorticity magnitudes for the instantaneous flow field obtained in their LES. Like Schraub and Kline (1965), a slight decrease in the num- ber of low-speed streaks was seen using a mild acceleration suggesting a slight rise

in λ+. With stronger accelerations the streaks became longer and straighter; ap-

pearing in general more ‘orderly’ which suggests less bursting activity. In absolute terms, the magnitude of the streamwise velocity fluctuations rises near the wall, which Piomelli et al. interpret as ‘stronger’ streaks.

Contours of vorticity magnitude reveal a thinner inner-layer overall, as evi- denced by a reduction in the wall-normal extension of vorticity away from the wall. The absolute values of vorticity magnitude also increased, which Piomelli et al. sug- gest is due to shear between the streaks rather than changes to the quasi-streamwise vortices themselves. Iso-surfaces of the vortices show them to be longer and more aligned in the streamwise direction similarly to the streaks. The vortex strength (the magnitude of streamwise vorticity fluctuations) is not increased however, despite the streamwise stretching caused by the strain. The numbers of vortices are reduced though, which Piomelli et al. explain is caused by the vortex stretching, which reduces their diameter and makes them more susceptible to viscous diffusion. Al- most identical behaviour was observed in the sink flow DNS by Spalart (1986). The intense vortical regions which protrude upwards from the wall in a zero-pressure- gradient turbulent boundary layer are more aligned with the wall in the sink flow. The region of intense rotational motion is therefore shallower overall. Streak velocity contours at y+

=11 reveals small regions of quiescent flow, with localised decreases in the number streaks and increased streak spacing and length. Local reductions in the friction velocity and vorticity were also found at these locations.

Bourassa and Thomas (2009) examine the near-wall turbulence behaviour via conditional analysis of their hot-wire measurements. Their strong pressure gradient causes a reduction in the total number of near-wall turbulent events (ejections and

sweeps), but the strength of the upward ejections of fluid increases. The authors reason that the ‘mutual induction’ between the streamwise vortices is increased by the streamwise straining. This causes a rise in their spanwise separation with an accompanying increase in the spacing of the low-speed streaks. They expect that

the reduction in the streak spacing attenuates the local wall-normal vorticity, ωy,

whilst at the same time the streamwise strain increases the local spanwise vorticity,

ωz≈dU/dy. Reduced local ωy might also follow from the reduction in streak ‘wig-

gling’. From the observations of Schoppa and Hussain (2002), that the strength of the ejections is determined by the ratio of the ‘lifted streak flank’ wall-normal vortic- ity (ωy) to localωz, Bourassa and Thomas (2009) conclude that fewer ‘lifted’ streaks from ejections will be produced overall, leading to further reductions in streamwise vortex formation and a stabilisation of the near-wall flow. Though the total number of streamwise vortices declines, the streamwise strain increases their angular veloc- ity, resulting in more robust, ‘vigorous’ wall-normal motions. This disagrees with Piomelli et al. (2000) who suggested that it was the increased susceptibility of the vortices to dissipation, due to their reduced diameter, which lead to a reduction in their numbers.