55 research outputs found
Asymptotics of stream-wise Reynolds stress in wall turbulence
The scaling of different features of stream-wise normal stress profiles
in turbulent wall-bounded flows, in particular in
truly parallel flows, such as channel and pipe flows, is the subject of a long
running debate. Particular points of contention are the scaling of the "inner"
and "outer" peaks of at and , respectively, their infinite Reynolds number limit, and
the rate of logarithmic decay in the outer part of the flow. Inspired by the
landmark paper of Chen and Sreenivasan (2021), two terms of the inner
asymptotic expansion of in the small parameter
are extracted for the first time from a set of direct
numerical simulations (DNS) of channel flow. This inner expansion is completed
by a matching outer expansion, which not only fits the same set of channel DNS
within 1.5\% of the peak stress, but also provides a good match of laboratory
data in pipes and the near-wall part of boundary layers, up to the highest
's of order . The salient features of the new composite
expansion are first, an inner peak, which saturates at
11.3 and decreases as , followed by a short "wall loglaw" with
a slope that becomes positive for , leading up to an
outer peak, and an outer logarithmic overlap with a negative slope continuously
going to zero for .Comment: 10 pages, 4 figure
Vortex shedding dynamics in the laminar wake of cones
Experiments on two cones of different taper ratios have been performed in the periodic Reynolds number range between 40 and 180. The visualizations of the plan view of the wake with hydrogen bubbles allow to determine local instantaneous frequencies, wavelengths and shedding angles from digital movie. The shedding frequency adjusts in a stepwise manner to the continuous variation of the cone diameter. Our results lead to revisit the original work of Gaster
A novel tethered-sphere add-on to enhance grid turbulence
The new turbulence generator consists of a standard uniform grid with tethered spheres attached to its nodes and is capable of producing approximately twice the turbulence energy per unit pressure drop coefficient C p than the same bare grid without the spheres. At the same time, the Reynolds number Reλ based on the Taylor microscale is also amplified by a factor of roughly 2, and the turbulence anisotropy is reduced to a constant level of 10% at all downstream distances without further flow conditioning after the grid. The new grid's simple design makes it suitable for a variety of fluid-flow facilities, in particular smaller water tunnels. Its performance in comparison with the plain grid is documented by measurements of the streamwise decay of turbulence energy and velocity spectra in the Reλ range of 50-10
Grid turbulence in dilute polymer solutions: PEO in water
Grid turbulence of polyethylene oxide (PEO) solutions (Polyox WSR-301 in ) has been investigated experimentally for three concentrations of 25, 50 and 100 weight ppm, at a turbulence Reynolds number based on a Taylor microscale of . For the first time, time sequences of turbulence spectra have been acquired at a rate of 0.005Hz to reveal the spectral evolution due to mechanical degradation of the polymers. In contrast to spectra averaged over the entire degradation process, the sequence of spectra reveals a clear but time-dependent Lumley scale at which the energy spectrum changes abruptly from the Kolmogorov inertial range to a elastic range, in which the rate of strain is maintained constant by the polymers. The scaling of the initial Lumley length with Kolmogorov dissipation rate and molecular weight is determined, and a cascade model for the temporal decrease of molecular weight, i.e.for the breaking of polymer chains is presented. Finally, a heuristic model spectrum is developed which covers the cases of both maximum and partial turbulence reduction by polymer
Experimental investigation into localized instabilities of mixed Rayleigh-Bénard-Poiseuille convection
The stability of the Rayleigh-Bénard-Poiseuille flow in a channel with large transverse aspect ratio (ratio of width to vertical channel height) is studied experimentally. The onset of thermal convection in the form of ‘transverse rolls' (rolls with axes perpendicular to the Poiseuille flow direction) is determined in the Reynolds-Rayleigh number plane for two different working fluids: water and mineral oil with Prandtl numbers of approximately 6.5 and 450, respectively. By analysing experimental realizations of the system impulse response it is demonstrated that the observed onset of transverse rolls corresponds to their transition from convective to absolute instability. Finally, the system response to localized patches of supercriticality (in practice local ‘hot spots') is observed and compared with analytical and numerical results of Martinand, Carrière & Monkewitz (J. Fluid Mech., vol. 502, 2004, p. 175 and vol. 551, 2006, p. 275). The experimentally observed two-dimensional saturated global modes associated with these patches appear to be of the ‘steep' variety, analogous to the one-dimensional steep nonlinear modes of Pier, Huerre & Chomaz (Physica D, vol. 148, 2001, p. 49
The hunt for the K\'arm\'an "constant'' revisited
The logarithmic law of the wall, joining the inner, near-wall mean velocity
profile (MVP) to the outer region, has been a permanent fixture of turbulence
research for over hundred years, but there is still no general agreement on the
value of the pre-factor, the inverse of the K\'arm\'an ``constant'' or on its
universality. The choice diagnostic tool to locate logarithmic parts of the MVP
is to look for regions where the indicator function (equal to the
wall-normal coordinate times the mean velocity derivative \dd U^+/\dd
y^+) is constant. In pressure driven flows however, such as channel and pipe
flow, is significantly affected by a term proportional to the wall-normal
coordinate, of order \mathcal{O}(\Reytau^{-1}) in the inner expansion, but
moving up across the overlap to the leading in the outer
expansion. Here we show, that due to this linear overlap term, \Reytau's of
the order of and beyond are required to produce one decade of near
constant in channels and pipes. The problem is resolved by considering
the common part of the inner asymptotic expansion carried to
\mathcal{O}(\Reytau^{-1}), and the leading order of the outer expansion,
which is a \textit{superposition} of log law and linear term L_0
\,y^+\Reytau^{-1}. The approach provides a new and robust method to
simultaneously determine and in pressure driven flows at
currently accessible \Reytau's, and yields 's which are consistent
with the 's deduced from the Reynolds number dependence of centerline
velocities. A comparison with the zero-pressure-gradient turbulent boundary
layer, henceforth abbreviated ``ZPG TBL'', further clarifies the issues
Reynolds number required to accurately discriminate between proposed trends of skin friction and normal stress in wall turbulence
In Nagib, Chauhan and Monkewitz~\cite{NCM07} we concluded that nearly all
available relations for zero-pressure-gradient boundary layers are in
remarkable agreement over the entire range O(), provided
one coefficient is adjusted in each relation by anchoring it to accurate
measurements. Regarding the peak of the streamwise turbulence intensity
, we conclude here that accurate measurements in flows with
O() are required, especially when looking only at the peak
to discriminate between recently proposed trends. We also find remarkable
agreement between the three analyses of Monkewitz \cite{M22}, Chen and
Sreenivasan \cite{CS22} and Monkewitz and Nagib \cite{MN15}, with some
coefficients slightly modified, by underpinning them with the same accurate
measurements of from reliable channel and boundary layer data. All
the three analyses conclude that the inner peak of remains finite in
the limit of infinite Reynolds number, which is at variance with the unlimited
growth of as predicted by the attached eddy model
\cite{MM19}. Accurate measurements of high-order moments and the guidance of
consistent asymptotic expansions may help clarify the issue at lower
values.Comment: 6 pages, 6 figure
Grid turbulence in dilute polymer solutions: PEO in water
Grid turbulence of polyethylene oxide (PEO) solutions (Polyox WSR-301 in H2O) has been investigated experimentally for three concentrations of 25, 50 and 100 weight ppm, at a turbulence Reynolds number based on a Taylor microscale of Re-lambda approximate to 100. For the first time, time sequences of turbulence spectra have been acquired at a rate of 0.005 Hz to reveal the spectral evolution due to mechanical degradation of the polymers. In contrast to spectra averaged over the entire degradation process, the sequence of spectra reveals a clear but time-dependent Lumley scale at which the energy spectrum changes abruptly from the Kolmogorov kappa(-5/3) inertial range to a kappa(-3) elastic range, in which the rate of strain is maintained constant by the polymers. The scaling of the initial Lumley length with Kolmogorov dissipation rate epsilon(0) and molecular weight is determined, and a cascade model for the temporal decrease of molecular weight, i.e. for the breaking of polymer chains is presented. Finally, a heuristic model spectrum is developed which covers the cases of both maximum and partial turbulence reduction by polymers
A novel tethered-sphere add-on to enhance grid turbulence
The new turbulence generator consists of a standard uniform grid with tethered spheres attached to its nodes and is capable of producing approximately twice the turbulence energy per unit pressure drop coefficient C (p) than the same bare grid without the spheres. At the same time, the Reynolds number Re-lambda based on the Taylor microscale is also amplified by a factor of roughly 2, and the turbulence anisotropy is reduced to a constant level of 10% at all downstream distances without further flow conditioning after the grid. The new grid's simple design makes it suitable for a variety of fluid-flow facilities, in particular smaller water tunnels. Its performance in comparison with the plain grid is documented by measurements of the streamwise decay of turbulence energy and velocity spectra in the Re-lambda range of 50-100
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