Heat transfer modification of a natural convection flow in a differentially heated cavity by means of a localized obstacle

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Abstract

In this experimental study, a natural convection flow in a differentially heated cavity has been disturbed in order to modify heat transfers. The disturbance is achieved by introducing a localized obstacle which acts as a small spatial extent passive system. The obstacle is placed inside the hot boundary layer of the cavity flow. Measurements have been carried out in terms of velocity fields, temperature profiles and heat transfers. The influence of the length and the vertical location for an insulating and a conducting obstacle have been analyzed. For the insulating obstacle, a part of the flow is deviated inside the colder core region in front of the obstacle, which leads to an increase of the downstream heat transfers as the deviated colder flow returns along the hot wall. For the conducting obstacle, a hot thermal plume is generated, which counters the obstacle effect observed for the insulating obstacle. In that case, the downstream heat transfer is increased or reduced depending on the vertical location of the obstacle. Relative changes on heat transfers compared to the case without obstacle are larger for longer obstacles and for higher vertical locations of the obstacle, for any conductivity. For instance, a relative heat transfer increase up to 83% is observed downstream the insulating obstacle for the largest length and highest vertical location.

Introduction

Natural convection occurs in nature in many meteorological and geophysical situations as well as in many industrial applications. Close cavities are good candidates to study natural convection since boundary conditions are well defined which is crucial to understand the underlying physics or for further numerical simulations. Natural convection in enclosed parallelepipedic cavities usually appears into two configurations: the Rayleigh-Benard (RB) configuration and the Differentially Heated Cavity (DHC) configuration, for which the isothermal walls are respectively orthogonal and parallel to the direction of gravity. In this work, the DHC has been considered. This configuration is encountered in a wide range of applications such as cooling processes for electronic devices, solar collectors, nuclear power plants, in the under-hood space of cars or in building design for thermal comfort. In this configuration, due to the temperature difference between the vertical isothermal walls, a movement of the fluid arises. When this difference increases, the flow turns into a vertical boundary layer flow with jets along the horizontal walls, whereas the central zone remains almost at rest and stratified in temperature. In the past decades, differentially heated cavities have been widely studied theoretically, experimentally and numerically from laminar to transient and turbulent flows [[1], [2], [3], [4], [5], [6]].

Heat transfer enhancement has been studied in this configuration through several strategies. Indeed, the flow developing in a DHC can be disturbed within the objective of acting on heat transfers of the isothermal walls. Several studies have shown that the flow can be actively modified by mechanical [7], acoustic [8] or thermal [9,10] disturbances or cavity inclination [11]. These modifications by active systems require a continuous external action and induce an additional energy consumption and maintenance. Another solution is the use of a passive disturbance.

One way to act on a natural convection flow passively is to introduce wall roughness, the walls being normally considered as smooth walls. Several shapes and sizes of roughnesses have been previously studied both in RB and DHC configurations. In the RB configuration, Du and Tong [12] studied experimentally the influence of pyramidal grooves on the isothermal walls. For 109Ra1011, the authors observed an increase of 76% of heat transfer compared to the smooth wall case. Salort et al. [13] placed square-studs on the hot bottom wall. They observed that on the rough wall the overall Nusselt number is larger due to a local increase in transfers above the studs, which is greater than their reduction in the notches. In the DHC configuration, Yousaf and Usman [14] placed sinusoidal roughness elements on the vertical walls of a square cavity. At Ra=106 and for 10 roughness elements, the authors observed a reduction in the overall Nusselt number up to 17%.

Another passive disturbance in the DHC configuration is the insertion of one or more fins positioned on the walls. These fins are either insulating or highly conducting, and a variety of sizes and locations have been studied. One of the first studies with this kind of perturbation disturbance was done by Shakerin et al. [15]. For a conducting fin placed on the hot wall of a square cavity, the calculation of the global heat transfer indicated an increase of the Nusselt number of 12%. This increase is limited by the deviation of the flow and the resulting thickening of the boundary layer upstream and downstream the fin. Nag et al. [16] studied numerically the influence of an infinitesimal-thick fin on the hot wall for several lengths and locations. The authors showed that the Nusselt number on the cold side increases with a perfectly conducting fin and decreases with an adiabatic one. Polidori and Padet [17] positioned three adiabatic fins on a vertical plate heated with a uniform heat flux and immersed in a water tank. The authors noted a circulation of the fluid in the area between the fins, an increase of the convective exchange coefficient close to the lower fin and a reduction close to the upper one. Tasnim and Collins [18] studied numerically, in a square cavity, the influence of a thin and perfectly conducting fin for Rayleigh numbers up to 105. An increase of overall heat transfers is observed, especially when the fin length is large (up to 31% for the largest size). In several experimental and numerical studies, Xu et al. [19,20] and Xu [21] positioned an adiabatic fin at the mid-height of a DHC with a vertical shape ratio equal to 0.24 and filled with water. The authors showed that above a certain Rayleigh number, the fin creates an unsteady flow by the periodic formation of thermal plumes. Therefore, with a fin on each active wall, the Nusselt number increases by 7%. Recently, Ghalambaz et al. [22] used a flexible fin at mid-height with a sinusoidal oscillation imposed at the end of the fin. At Ra=106, the authors showed that, compared to a static fin, the overall Nusselt number increases slightly with amplitude and period. In addition, the gain is more important when the fin is more flexible. To sum up, in absence of a change in the flow regime, adding a fin leads to an increase in global heat transfers if the fin is conducting and to a decrease if the fin is insulating.

A last category of passive disturbance of a natural convection flow in a confined enclosure is the use of discrete elements or obstacles. Unlike fins, they are not necessarily located on the walls and can have a large size. Merrikh and Lage [23] placed several solid blocks within a square cavity. They showed that the deviation of the flow into the inner core of the cavity reduces drastically the wall heat transfers. Laguerre et al. [24] positioned in a rectangular cavity an arrangement of 40 cylindrical obstacles parallel to the cold wall. These obstacles are 10 times smaller in size than the width of the cavity. The fluid is humid air and the flow is described in terms of temperature, flow velocity and moisture. They observed a modification of the cold boundary layer flow due to the presence of obstacles, which induces a flow circulation in the areas between them.

These studies demonstrate the possibility to act on natural convection flows by means of fins and obstacles, in order to modify heat transfers. These disturbances occupy generally a large space within the cavity. In order to reduce the size and therefore the mass and the cost of such devices, a localized disturbance is used in this experimental study. The disturbance is a cylindrical obstacle of small spatial extent, with a maximal length equal to 4% of the height of the cavity. The obstacle is placed on the hot wall of the cavity.

The purpose of this work is to study the modification of heat transfers downstream an obstacle. We will first introduce the DHC experimental set-up and the measurement methods that have been used to investigate the flow and the associated heat transfers. Then the results concerning the disturbed flow (especially in terms of velocity fields and temperature profiles) and the associated heat transfers are analyzed and compared to those of the undisturbed flow.

Section snippets

DHC description

The Differentially Heated Cavity (DHC) used in this study is a parallelepiped with the following internal dimensions: width L=12 cm, depth D=14 cm, height H=48cm (see Fig. 1). Those three dimensions are respectively associated with the x, y and z axes. The vertical and horizontal aspect ratios are equal to Avert=HL=4 and Ahori=DL=1.167.

The vertical walls, with an imposed temperature, are made of duralumin (conductivity λ=164W.m−1.K−1, emissivity ε[0.1;0.2]) with a thickness of 5 mm. A vertical

Influence of the obstacle length

Three obstacle lengths are studied in this part. These lengths are equal to 0.5 cm, 1 cm and 2 cm, which corresponds to dimensionless lengths of l=0.010, l=0.021 and l=0.042 respectively. They are chosen so that the obstacles are smaller or almost reach the size of the dynamic boundary layer (described in the next paragraph). The CO center is located at ZCO=0.25, i.e. at the beginning of the boundary layer and outside the recirculation zone at the bottom of the cavity. This also enables to

Conclusions and perspectives

A natural convection flow in a differentially heated cavity of aspect ratio 4 was disturbed by means of a localized cylindrical obstacle. The obstacle was placed on the hot wall in the mid-depth plane of the cavity.

Two kinds of obstacles are considered: an insulating obstacle that only influences on its own the dynamics of the flow that rounds it and a conductive obstacle that influences on its own both the dynamics and the temperature of the flow that rounds it.

The effects, in the mid-depth

Acknowledgments

The authors would thank CPER (2015–2020) and ERDF (2014–2020) grants for supporting this work through the funding of experimental equipment. The authors would also like to thank H. Arlaud who built the micro-thermocouples and the experimental set-up, C. Fuentes for her help with laser techniques and C. Calbrix for his help for the measurements.

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