Transitional natural convection flow and heat transfer in an open channel

Abstract

The work presented here is an experimental study on natural convection flows in a differentially heated open channel configuration. The applications concern the free cooling of both the photovoltaic components integrated within the building envelope (double-skin configuration) and the building itself. Particular focus is given to the identification of integration configurations favorable to both heat transfer on the rear side of components and buoyancy enhancement. The test section consists of a vertical channel with two walls composed of different heating modules. In the present investigation the thermal configuration considers one wall heated uniformly while the other is not heated. We focus on the kinematic characteristics of the flow and convective heat transfer at the heated wall. A PIV system allows investigating the mean velocity field and velocity fluctuations at different levels of the channel height. The experimental procedure allows inferring the wall surface temperature, local heat transfer coefficient and local and average Nusselt numbers. The experimental evidence shows that the flow is neither really turbulent nor purely laminar for the range of Rayleigh numbers considered. Although the average characteristics of the flow seem perfectly consistent with the results obtained, changes of behavior seem to occur intermittently.

Introduction

The study of natural convection developing in vertical open channels is of major importance since it is found in many applications of different scales, from cooling micro-electronic components to cool nuclear reactors, in solar systems and in Trombe walls. In the medium term the application benefits of our studies will be dedicated to the design of photovoltaic panels integrated in double-facades of buildings to exploit their thermal operating characteristics. It is necessary to investigate both the heat transfers at the rear side of heated plates (PV panels) and the chimney effect in asymmetrically heated channels.

Laminar natural convection in open-ended channels has been subjected to extensive investigation for several decades. Pioneering on the analytical studies, Aung solved the governing equations by using a parabolic model in the developing flow region [1] and the fully developed limit [2] for both symmetrically and asymmetrically isothermal and isoflux plates. More recently most of the investigations have been carried out by means of experimental [3], [4], [5], [6] and numerical techniques [7], [8], [9], [10], [11]. These studies have covered various geometrical and thermo-physical aspects of the problem including variable heating and geometric parameters [4], [6], [12], [13], [14], the effect of radiation [15], [16], [17], [18], flow reversals [3], [5], heat transfer enhancement [6], influence of fluid properties [5], [7], [8], [21] and its transient development [10]. Nevertheless, the number of studies reported on transitional natural convection in vertical channels and concerning the flow kinematic and thermal behavior are limited, albeit the interest on this scenario of heat transfer enhancement. Indeed, this natural flow involving low velocities is sensitive to environmental conditions and thus difficult to measure. Numerical simulations are confronted by the same difficulties and a lack of experimental data. In addition to the recurring problem of selecting a CFD model suitable for this type of flow, both the appropriate boundaries of the computational domain and the proper definition of the kinematic (pressure and velocity) inlet/outlet boundary conditions still constitute considerable scientific barriers despite the large number of studies already performed. Intermittent flow reversal may occur at the outlet under conditions that are not clearly identified or systematically reported in either numerical or experimental studies. In general, whatever computer simulations and model used, there is a tendency to overestimate the kinematic characteristics of the flow [19] while the thermal characteristics are generally recovered. For example, Fedorov et al. [20] and Muresan et al. [21] found good agreements at the inlet boundary with the experiments of Miyamoto [22] by selecting a fairly high level of turbulent kinetic energy (15–20%). However their parametrical studies carried out with RANS models highlighted that the location of the transition depends strongly on the turbulent intensity imposed in the inlet section. These observations highlight the sensitive nature of the flow regarding environmental conditions. Minkowycz et al. [23] stressed again that the conditions at the inlet of the channel play a decisive role on the flow development process. Moreover, authors such as Zamora et al. [9] have shown that in the transitional range, the effects of initial turbulence intensity are more significant on the evolution of the induced mass flow rate rather than on the average Nusselt number. Numerical results have revealed a similar aspect of the flow pattern and the velocity boundary layer in the near wall region. This has been highlighted for different values of initial turbulence intensity I. However, for higher values of I, an increase of the vertical velocity component level is observed in the core region. That leads to a drastic increase of the mass flow rate.

The answer to these difficulties could find its origin in the unsteady nature of this flow which not only depends on the thermal and kinematical activity within the channel, but is also probably very highly correlated with pressure and temperature conditions outside the channel.

Most experimental investigations regarding natural convection in heated open channels are based on the determination of global or local correlations linking thermal (wall heat transfer) or kinematical (mass flow rate, pressure loss) quantities to the characteristic Rayleigh numbers. Most of them focused on determining heat transfer to walls by neglecting to collect information on the instantaneous kinematical structure of the flow [24], [25], [26]. Olsson [15] references many correlations linking trade flows to the walls or a dimensionless Rayleigh number in 2004. The laminar regime is actually that most documented for both the main wall boundary conditions, namely uniform wall temperature (UWT) and uniform wall heat flux (UWF). Most studies have dealt less with UWF [27] than with UWT. Elenbaas [28] was the first to report on experimental correlations and a specific theoretical solution for vertical parallel plates with fixed wall temperature. Aung et al. [2], carried out many numerical and experimental studies on laminar flows for UWT and UWF thermal boundary conditions. Few experimental studies have been dedicated to transition and turbulent regime. Wirtz and Stutzman [29] have conducted experiments on free convection for uniform and symmetric heat fluxes from 50 to 150 W/m² for four aspect ratios ranging from 1/38 to 1/17. Miyamoto [22] carried out an experimental study on natural convection in a 5 m vertical air channel with a UWF imposed on one wall, the other being adiabatic. The injected fluxes were 104 and 208 W/m² and the aspect ratios tested varied from 1/25 to 1/100. These studies showed that the wall temperature profile along the heated wall presents an inflexion point and then an increase of the heat transfer coefficient related to the transition process. In the limit case where the width of the channel is sufficiently large, both boundary layers develops independently and the location of the inflexion point corresponds to that obtained for a single vertical heated plate. The location of the inflexion point is shifted upward in the channel as the width of the channel decreases. Later, using the same bench Katoh et al. [30] investigated the influence of the inlet on the flow development. This influences both turbulent intensity and heat transfer at the inlet and a quasi-flat velocity profile was measured by LDA at this level. The transition zone seems to appear at a higher level in the channel. Using an LDA system, Yilmaz and Fraser [19] and Yilmaz and Gilchrist [31] studied a vertical channel (3 m high) with one wall at imposed temperature, facing a glass. The aspect ratio was 1/25 and more detailed results were provided for an injected heat flux density of 344 W/m². They also performed simultaneous instantaneous velocity and temperature measurements in the outlet section of the device and presented mean correlations of the Nusselt number with the Reynolds number. Moreover, they showed that the turbulent kinetic energy was relatively high at the channel inlet close to the glass wall; it decreased until the mid-height of the channel corresponding to a relaminarization zone of the flow and increased in the upper half of the channel. The turbulent kinetic energy profile became symmetrical in the outlet section, corresponding to the fully turbulent regime of the flow.

Very few works have examined the mechanisms of the destabilization of natural convective flows in double façades and evaluated the effect of these disturbances on heat transfer. Flow instabilities and unsteadiness were also studied in the case of mixed convection [32], [33], [34]. However instantaneous kinematical, thermal quantities and flow structures need to be measured and analyzed to better understand the transition process. Understanding the physical mechanisms leading to transition as well as linking instantaneous kinematical, thermal quantities and structures is useful in applications to control flow and monitor the wall heat transfer. A few similar investigations have been performed and although kinematical flow characteristics (mainly mean velocities) have been identified, there are few reports in literature of instantaneous velocity visualization data regarding natural convection flow in asymmetrically heated vertical channels with UWF boundary conditions. However this approach based on instantaneous flow measurements analysis has been adopted intensively for studying the boundary layer along a vertical flat plate in water [35] and in air [36]. Many studies have focused on turbulence transition mechanisms and are useful for analyzing the observations presented in this paper. Although the channel is a semi-open domain, the boundary walls generate a confined effect and thus the internal thermal and pressure conditions distinct from the outside ambiance. The influence of the external conditions is still not so obvious because thermal stratification and differences of pressure between the inlet and the outlet of the channel can dampen, neutralize or enhance the chimney effect. As an example Rodríguez Sevillano et al. [37], have determined experimentally the onset of transition in an inclined channel (α = 30°) which was heated asymmetrically and subjected to uniform wall temperature. They examined the increase of turbulence intensity from hot-wire measurements. Repetition tests showed a good reproduction of mean velocity profiles and a significant scatter of the turbulence intensity levels. Major differences between tests are found to appear in inlet and outlet sections. However, no information regarding the external conditions or the impact of these differences on other parameters, such as the Nusselt number or the flow rates have been provided. On the other hand, certain studies performed on mixed convection appear useful for interpretations, especially for the very high sensitivity of the flow kinematic to perturbations whereas the thermal state of the walls does not appear greatly affected [34], [38]. Obviously, this does not include the increase of mean convective heat transfer (around 30%) induced by the change of the flow regime from laminar to turbulent. We provide some explanations of mechanisms and flow behavior derived from these types of study.

This study is an additional step in an extensive collaboration conducted between the CETHIL laboratory (Lyon, France), the CFD laboratory (Sydney, Australia) and DIPTEM laboratory (Genova, Italy) during the recent years on different aspects of PV cooling via natural convection. Most of our studies have dealt with the thermal characterization of the flow by means of both experimental [25], [26], [39] and numerical investigations [21], [24], [39], [40]. Uniform and nonuniform heat flux configurations have been considered covering a large range of aspect ratios and Rayleigh numbers. Moreover, the kinematic aspect of the problem has been only approached numerically.

The aim of this investigation is to highlight, experimentally, the unsteady character of the flow for a vertical parallel channel heated asymmetrically and subjected to uniform wall heat flux. It is investigated by analyzing the repeatability of global and local quantities for both thermal and kinetic aspects and the identification of the typical flow patterns close to the walls. Mean wall temperature and velocity profiles as well as turbulent intensities are described beforehand. Since the shapes of the mean velocity and fluctuation profiles are conserved between the different tests implemented, the general trends are presented first and then repeatability is discussed in terms of discrepancies.

The repeatability of tests is investigated to show the sensitivity of the natural convection flows to the ambient conditions and then to analyze the influence of the inlet turbulent intensity on the flow development [9], [20], [23]. Moreover this is particularly important since it is not possible to scan the entire channel in only one test. According to the size of PIV frame and the required recording time to reach convergence of the mean values, the tests need to be conducted on several days. The results reported in this paper suggest the possibility of controlling the development of natural convection flows and thus heat transfer at the wall/fluid interface. Therefore this work also contributes to the constitution of a database of the fluctuating quantities measured, which will be very helpful for numerical simulations.

We have previously performed a parametric study covering the range of modified Rayleigh number of 3.86·10⁵ < Ra* < 6.5·10⁶ (corresponding to injected fluxes of 20, 50, 100, 225 and 475 W/m²). For the range of 3.86·10⁵ < Ra* < 1.86·10⁶ (qs = 20, 50 and 100 W/m²) the flow exhibits a laminar behavior and no distortion of the streamline pattern is observed. Increasing the modified Rayleigh number to Ra* = 3.5·10⁶, essential features of the early stages of the transitional kinetic scenario could be clearly distinguished. Thus, the evolving process to transition and the generation of turbulence mixing is what we would like to highlight in the present study. This stage is of significant interest as wall heat transfer rates are found to be highest.

At the highest modified Rayleigh number Ra* = 1.86·10⁶, it is really difficult to examine and identify the transition process due to non linear interactions between the governing mechanisms. Consequently, a modified Rayleigh number of 3.5·10⁶ has been chosen to be a reference case of study.

In the first part, we present the test rig, the instrumentation, the experimental procedure and the test room conditions. In the second part the thermal boundary conditions at the wall are characterized in terms of temperature and convective heat flux obtained from the energy balance between the electrical flux injected and the conjugated heat transfer achieved by natural convection, conduction and radiation. Then the flow is described through mean quantities, turbulent intensities and an instantaneous analysis of the velocity field.