14:00
Turbulent Convection 2
14:00
15 mins
#61
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How surface roughness reduces heat transport in turbulent Rayleigh-B\'{e}nard convection
Quan Zhou, Yi-Zhao Zhang, Chao Sun
Abstract: Turbulent convection is ubiquitous in nature and in many industrial processes, and Rayleigh-B\'{e}nard (RB) convection, i.e. a working fluid layer in a closed system heated from below and cooled from above, has long been proposed as a most classical and yet simple paradigm to study the convection phenomenon. The RB convection has also been adopted as an ideal model system to search for ways to enhance heat transport of natural conveciton. Effectively increasing convective heat transfer is of vital importance in many engineering applications, and introducing wall roughness has been expected to be an effective means for that. To study fundamentals of heat transfer over rough surfaces, many experimental, numerical and theoretical studies on turbulent RB convection over rough plates have been carried out. Up to now, it has been widely accepted that introducing roughness on conducing plates could efficiently enhance the heat transport through the RB system.
In this talk, however, we show that roughness does not always mean a heat-transfer enhancement, but in some cases it can also reduce the overall heat transport through the system. To reveal this, we carry out direct numerical simulations (DNS) of turbulent RB convection over rough conducting plates \cite{bib:zhou2018jfm}. Our study includes two-dimensional (2D) simulations over the Rayleigh number range of $10^7\leqslant Ra\leqslant10^{11}$ and three-dimensional (3D) simulations at $Ra=10^8$. The Prandtl number is fixed to $Pr=0.7$ for both 2D and 3D cases. At a fixed Rayleigh number $Ra$, the reduction of the Nusselt number $Nu$ is observed for small roughness height $h$, whereas the heat-transport enhancement occurs for large $h$ [see figure \ref{fig1}(\emph{e})]. The crossover between the two regimes yields a critical roughness height $h_c$, which is found to decrease with increasing $Ra$ as $h_c\sim Ra^{-0.6}$. Through dimensional analysis, we provide a physical explanation for this dependence. The physical reason for $Nu$-reduction is that the hot/cold fluid is trapped and accumulated inside the cavity regions between the rough elements, leading to much thicker thermal boundary layer (BL) and thus impeding the overall heat flux through the system [see figure \ref{fig1}(\emph{b},\emph{c})].
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14:15
15 mins
#384
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About the influence of rough boundaries on the heat transport in highly turbulent thermal convection
Stephan Weiss, Chien-Chia Liu, Xiaozhou He, Guenter Ahlers, Eberhard Bodenschatz
Abstract: Thermal convection is one of the most effective mechanism for the transport of thermal energy and as
such plays a major role in many engineering applications as well as in geo- and astrophysical
systems. In these systems, the flow is in general highly turbulent. Many numerical and experimental
investigations on turbulent convection have been conducted in the Rayleigh-B\'enard (RB) setup,
where a fluid is confined between two horizontal plates, where the bottom plate is heated and the
upper one is cooled. The state of the boundary layers that form at the interface between the fluid
and the plates is of utter importance for the vertical heat transport, as their thermal resistance
is in general significantly larger than that of the convective bulk.
Recently, research has focused on the study of RB convection with rough boundaries at the bottom and
the top (i.e., \cite{SW11,ZSVL17}). The reason for these investigations is twofold. For one, in
many natural systems the bottom boundaries are not flat but modulated due to the natural terrain,
which significantly influences the heat transport. On the other hand predictions on the heat
transport for very large thermal driving (expressed by the Rayleigh number - Ra), assume that the
boundary layers become turbulent under sufficient shear stress leading to a significantly enhanced
heat transport. This regime is called the {\em Kraichnan regime} \cite{Kr62}. A rough boundary
causes stronger advection within the boundary layer and thus activates a turbulent-like boundary
layer, under which the
heat transport is expected to be similar to that in the Kraichnan regime.
We study RB convection with rough plates in 1.1\,m tall cylindrical convection cells that are filled
with pressurized sulfur hexafluoride (SF$_6$) of up to 19\,bar - the {\em Uboot of G\"ottingen}
(see \cite{AHFB12} for details). With this setup we
reach Rayleigh numbers of up to $5\times 10^{13}$ at Prandtl numbers Pr = 0.79 \ldots 0.86. The roughness
consists of periodically arranged pyramids with a square bottom cross section of side length as well
as height of 5\,mm. We investigate the heat flux in terms of the dimensionless Nusselt number (Nu).
We find $Nu\propto Ra^{0.42}$ in the investigated Ra-range. In this presentation, we also compare the
vertical temperature profiles measured close to the sidewalls in the current study, with those
in the same cell yet with smooth bottom and top plates.
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14:30
15 mins
#486
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Investigating Reynolds Analogy Over Riblet Roughened Surfaces
Amirreza Rouhi, Davide Modesti, Sebastian Endrikat, Nicholas Hutchins, Daniel Chung
Abstract: Heat transfer augmentation is important in many systems such as gas turbine surfaces~\cite{bunker2013}. An effective surface is one that, relative to the smooth surface, yields a larger fractional increase in heat transfer than in drag, i.e.\ favourably breaks Reynolds analogy (above the dashed line in Figure~\ref{fig1}\textit{c,d}). Riblets appear as a potential candidate for this purpose, having an increased wetted area without pressure drag, however, results in the literature are diverse~\cite{stalio2003,walsh1979}. The discrepancy could be due to: 1) measurement uncertainties~\cite{stalio2003}, 2) modelling assumptions~\cite{stalio2003}, 3) different riblet shapes or 4) different riblet spacings. Here, by performing direct numerical simulation (DNS) we ensure that our results are not influenced by 1) or 2), and by changing riblet shapes and spacings, we investigate 3) and 4), attempting to devise a roadmap for favourably breaking Reynolds analogy.
The domain is minimal open channel \cite{macdonald2019} with periodic boundary conditions in the streamwise ($x$) and spanwise ($y$) directions, and no-slip and isothermal bottom wall condition, $u_i = \theta = 0$. The Prandtl number $Pr \equiv \nu/\kappa$ is $0.7$, and the friction Reynolds number $Re_\tau \equiv u_\tau h/\nu = 395$, based on the friction velocity $u_\tau$ and domain height $h$. Among the 14 DNS cases (Figure~\ref{fig1}\textit{a,b}), 6 are over triangular riblets with varying tooth angles $\alpha$, 4 are over blade riblets and 4 are over trapezoidal riblets. The results reveal that Kelvin--Helmholtz rollers play a favourable role in breaking Reynolds analogy. This is inferred from flow visualisation (Figure~\ref{fig1}\textit{e,f}) and analysis of skin-friction coefficient $C_f$ and Stanton number $C_h$ (Figure~\ref{fig1}\textit{c,d}). Among all cases, only the triangular riblet at $\alpha = 30^o, s^+ = 21$ ($\times$) generates strong Kelvin-Helmholtz rollers (Figure~\ref{fig1}\textit{e}), which create local flow reversals ($\tau_w<0$), while $q_w$ is always positive. Thus, this case breaks Reynolds analogy in a favourable way (case $\times$ falls above the dashed line in Figure~\ref{fig1}\textit{d}). The analogy between $\tau_w$ and $q_w$ is quantified in figure~\ref{fig1}(\textit{a,b}), showing their correlation coefficient (of fluctuations) $\rho_{\tau q}$. For triangular riblets that trigger Kelvin-Helmholtz rollers, $\rho_{\tau q}$ decreases by increasing $s^+$ or decreasing $\alpha$, with minimum of $\rho_{\tau q} = 0.2$ achieved at $\alpha = 30^o, s^+ = 21$ ($\times$). For blade or trapezoidal riblets $\rho_{\tau q}$ remains above $0.7$, and they all fall in the unfavourable region of Figure~\ref{fig1}(\textit{c,d}) (below the dashed line). However, their departure from Reynolds analogy line remains mild compared to a conventional three-dimensional rough surface ($\bullet$) \cite{macdonald2019}. Our analysis shows that riblets are to date the only passive control strategy with heat-transfer efficiency close to or better than a smooth surface.
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14:45
15 mins
#513
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Boundary layer structure for different plate boundary conditions
Najmeh Foroozani, Dmitry Krasnov, Jörg Schumacher
Abstract: In order to study the influence of the thermal properties of the plates at the top and bottom of a closed cell on the heat transfer and the boundary layer structure, we solve the three-dimensional Boussinesq equations numerically via direct numerical simulations. The flow develops in a cylindrical cell of aspect ratio $\Gamma =1/2$ and fixed Prandtl number $Pr=0.7$. All surfaces of the cell satisfy no-slip conditions and the side walls are adiabatic. The conventional Rayleigh number defined as $Ra=\frac{ \alpha g H^3}{ \nu_f \kappa_f} \Theta$, where $\alpha_f$, $\nu_f$, $\kappa_f$ $H$, and $\Theta$ are the fluid- isobaric thermal expansion coefficient, kinematic viscosity, thermal diffusivity, depth and horizontally- and time-averaged temperature drop across the interfaces between the fluid and the plates, respectively.
We present results for three different boundary conditions at the plates. These are: \textit{i}) \textbf{fixed-temperature} condition (Dirichlet) where $\Theta= \Delta T_{RBC}$ \cite{bib:Foroozani}, \textit{ii}) \textbf{fixed-flux} condition (Neumann) where $\beta=\partial_z T |_{z=0,1}$ and thus $ \Theta=\beta H$ \cite{bib:Verzicco, bib:Jahnson}, and \textit{iii}) \textbf{conjugate heat transfer} condition for which the fluid is bounded above and below by finite conducting solid plates with fixed temperature imposed at the outer boundary.
We consider solid plates of thickness $h_s=0.2H$ with a thermal diffusivity $\kappa_s=5\kappa_f$ and thermal conductivity $\lambda_s=\rho_s c_{p,s}\kappa_s$. At the fluid-plate interfaces we require the continuity of temperature ($T_s=T_f$) and heat flux ($\lambda_s \partial_z T_s=\lambda_f \partial_z T_f$).
We note that, the total temperature drop between the fluid-plates interfaces ($T_{sf}$) is $\Theta=\Delta T_{CHT}= \overline{T}_{sf,b}-\overline{T}_{sf,t} \simeq 0.5$ which is computed after the end of computation carried out. In this investigation, the reference value of the Rayleigh number is approximately equal to $10^7$ in all cases such that they are directly comparable to each other. Figure 1(a) shows the normalized mean temperature profile along the vertical direction of all cases. Our first findings indicate that the temperature profile of case \textit{iii} collapses almost perfectly with case \textit{i} and that case \textit{ii} deviates slightly.
In figure 1(b) we plot the snapshot of the normalized temperature field at the bottom plate for the conjugate heat transfer setting which indicates that the distribution of temperature is non-uniform. As a next step we are going to extend the analysis to a liquid metal in which the conductivity of the fluid is not that much smaller than the conductivity of the copper plates.
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15:00
15 mins
#48
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Pore-scale-resolving Direct Numerical Simulations of Turbulent Natural Convection in Porous Media
Stefan Gasow, Andrey V. Kuznetsov, Marc Avila, Yan Jin
Abstract: Natural convection in porous media is an important process in nature and industry. Two examples are the long-term storage of CO 2 in deep saline aquifers and thermal-energy storage. Natural convection in porous media is usually calculated by solving macroscopic equations. The numerical solution of volume-averaged Darcy-Oberbeck-Boussinesq (DOB) equations is of particular interest, due to its relatively low computational costs. However, the DOB equations only account for the microscopic properties of the porous medium via the permeability. Their key underlying simplification is that the only control parameter of convection in porous media is the Rayleigh-Darcy number, or Rayleigh number (Ra=HβΔTgK/a m ν with H the chamber height, β the thermal expansion coefficient, ΔT the temperature difference, g the gravity, K the permeability, a m the effective thermal diffusivity and ν the kinematic viscosity) for short. This hypothesis may be at the root of the discrepancies between the Nusselt-scaling from DOB simulations and laboratory experiments. Hence, by performing pore-scale-resolving direct numerical simulations (DNS) of convection in porous media and comparing those to traditional DOB simulations, we investigated whether natural convection in porous media is influenced by parameters other than Ra through additional physical mechanisms. The macroscopic fields were obtained from DNS by volume-averaging over each representative elementary volume (REV) of the porous medium. The two-dimensional generic porous matrix (GPM) used here consisted of periodically arranged square obstacles. In our study different pore sizes and porosities were simulated for a Ra-range of [1,000; 20,000], which covers the macroscopic turbulence regime. The main conclusion of our pore-scale-resolving DNS is that the pore-scale has significant effects on convection in porous media. Macroscopic features most impacted by the pore-scale structures include the width of mega-plumes in the interior region, the thickness of the boundary layer, and the r.m.s temperature and velocity fields. It is also observed that the Sherwood and Nusselt numbers which characterize mass and heat transfer, respectively, decrease with increasing porosity. This trend is also shown in previous experimental studies [6]. None of these pore-scale effects can be captured by state-of-the-art DOB simulations. Our study thus paves the way for the extension and parametrization of improved DOB equations including non-Darcy terms accounting for the effect of porosity and pore-scale structures.
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15:15
15 mins
#330
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HEAT TRANSFERT AT THE ROUGHNESS SCALE IN TURBULENT RAYLEIGH-BÉNARD CONVECTION
Mebarek Belkadi, Anne Sergent, Bérengère Podvin, Yann Fraigneau
Abstract: Turbulent convection is a spontaneous physical process present in many natural systems as well as in engineering appli-
cations. However most of these systems are non-ideal in terms of underlying surfaces involving specific topography or
small-scale roughness. Moreover interactions between buoyant flow and plate roughness result in a global heat transfer
enhancement and in some cases, in an increase of the heat transfer scaling exponent (see for ex. [2]). In this study, we
consider thermal convection over a regularly roughened plate in a Rayleigh Bénard cell. The objective is to clarify inter-
actions between the large scale circulation filling the box and the flow around the roughness elements by means of direct
numerical simulations. Three successive heat transfer regimes are investigated from inactive roughness to a regime where
the heat transfer relative increase is larger than the relative surface increase induced by roughness addition.
The simulations are performed in a box-shaped cell of aspect ratio (depth over cell height) equal to 1/2 with water as
working fluid for a Rayleigh number Ra ranging from 5 × 10 5 to 5 × 10 9 . The roughness is introduced on the bottom
plate by a set of square based obstacles regularly spaced, modelled by using an immersed boundary method, while the top
plate is kept smooth.
Results are validated against experimental and numerical data from literature. As expected, it exhibits an enhancement
of heat transfer measured by the Nusselt number N u, depending on the relative sizes of the mean boundary-layers and
the obstacle height in agreement with previous studies from the literature [3, 1, 4]. Then, we investigate the different heat
transport mechanisms at the roughness scale for three successive regimes (fig. 1). Our study reveals that the change of
heat transport regime is mainly governed by physical features of fluid zone surrounding the obstacles. Flow dynamics and
boundary layer structure near rough surface are also reported.
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