182 research outputs found
Polymers in Fluid Flows
The interaction of flexible polymers with fluid flows leads to a number of
intriguing phenomena observed in laboratory experiments, namely drag reduction,
elastic turbulence and heat transport modification in natural convection, and
is one of the most challenging subjects in soft matter physics. In this paper
we review our present knowledge on the subject. Our present knowledge is mostly
based on direct numerical simulations performed in the last twenty years, which
have successfully explained, at least qualitatively, most of the experimental
results. Our goal is to disentangle as much as possible the basic mechanisms
acting in the system in order to capture the basic features underlying
different theoretical approaches and explanations
Dependence of heat transport on the strength and shear rate of prescribed circulating flows
We study numerically the dependence of heat transport on the maximum velocity
and shear rate of physical circulating flows, which are prescribed to have the
key characteristics of the large-scale mean flow observed in turbulent
convection. When the side-boundary thermal layer is thinner than the viscous
boundary layer, the Nusselt number (Nu), which measures the heat transport,
scales with the normalized shear rate to an exponent 1/3. On the other hand,
when the side-boundary thermal layer is thicker, the dependence of Nu on the
Peclet number, which measures the maximum velocity, or the normalized shear
rate when the viscous boundary layer thickness is fixed, is generally not a
power law. Scaling behavior is obtained only in an asymptotic regime. The
relevance of our results to the problem of heat transport in turbulent
convection is also discussed.Comment: 7 pages, 7 figures, submitted to European Physical Journal
Mean Temperature Profiles in Turbulent Thermal Convection
To predict the mean temperature profiles in turbulent thermal convection, the
thermal boundary layer (BL) equation including the effects of fluctuations has
to be solved. In Shishkina et al., Phys. Rev. Lett. 114 (2015), the thermal BL
equation with the fluctuations taken into account as an eddy thermal
diffusivity has been solved for large Prandtl-number fluids for which the eddy
thermal diffusivity and the velocity field can be approximated respectively as
a cubic and a linear function of the distance from the plate. In the present
work we make use of the idea of Prandtl's mixing length model and relate the
eddy thermal diffusivity to the stream function. With this proposed relation,
we can solve the thermal BL equation and obtain a closed-form expression for
the dimensionless mean temperature profile in terms of two independent
parameters for fluids with a general Prandtl number. With a proper choice of
the parameters, our predictions of the temperature profiles are in excellent
agreement with the results of our direct numerical simulations for a wide range
of Prandtl numbers from 0.01 to 2547.9 and Rayleigh numbers from 10^7 to 10^9.Comment: 8 pages, 4 figure
Heat transport by laminar boundary layer flow with polymers
Motivated by recent experimental observations, we consider a steady-state
Prandtl-Blasius boundary layer flow with polymers above a slightly heated
horizontal plate and study how the heat transport might be affected by the
polymers. We discuss how a set of equations can be derived for the problem and
how these equations can be solved numerically by an iterative scheme. By
carrying out such a scheme, we find that the effect of the polymers is
equivalent to producing a space-dependent effective viscosity that first
increases from the zero-shear value at the plate then decreases rapidly back to
the zero-shear value far from the plate. We further show that such an effective
viscosity leads to an enhancement in the drag, which in turn leads to a
reduction in heat transport.Comment: 7 pages, 8 figures, 1 tabl
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