Heat-exchange relations for unglazed transpired solar collectors with circular holes on a square or triangular pitch

Abstract

The unglazed transpired solar collector is now an established solar air heater for heating outside air directly. Sample applications include pre-heating ventilation air and heating air for crop drying. The outside air in question is drawn straight from ambient, uniformly through the whole surface of a perforated blackened plate (the absorber plate) exposed to the sun. An important parameter in fixing the collector’s efficiency is the heat exchange effectiveness, ϵ. Once ϵ is known, finding the collector’s efficiency is straightforward. This paper presents measurements of ϵ for the case where the plate is perforated with circular holes on either a square or triangular layout, covering a range of wind speeds extending from zero to 5 m/s. These data extend the earlier measurements of Kutscher to a wider range of plate thicknesses, hole spacings (pitch), suction velocities, and to include a square layout of the holes. In the region where the two experiments overlap, agreement between the two is excellent. A new predictive model is developed that is based on breaking down the total heat transfer into contributions from each of the plate sections: the front, the hole and the back. Excellent agreement was found between modelled and measured ϵ; the new measured data were predicted with a 4.2% root mean squared error (RMSE) and Kutscher’s measured data is predicted within 6.3% RMSE.

Introduction

Unglazed, transpired solar collectors (Hollick and Peter, 1990, Kutscher et al., 1991, Kutscher et al., 1993) have been the subject of a number of recent investigations (Gunnewiek et al., 1997, Dymond and Kutscher, 1997; Arulanandam et al., 2000). They are effective devices for applications where outside air is to be heated directly, such as in heating ventilation air for buildings and crop drying. The outside air in question is drawn straight from ambient, through the whole surface of a transpired, dark-coloured plate (the absorber plate), which has been perforated with holes, typically with a porosity of about 0.5%. Tests conducted on several installations indicate that the unglazed transpired collector (UTC) works very well with annual solar collection efficiencies reaching 72% (Carpenter and Kokko, 1991). Over 70 large systems, each having collector areas between 500 and 10,000 m², have been installed and are successfully operating for fresh-air heating in Canada, the United States, Germany, and Japan and heating process air for crop drying in countries throughout the world.

The Hottel-Whillier (H-W) equation (Duffie and Beckman, 1991), which is customarily used to model standard flat plate solar collectors, can be made to model the UTC as well. For an unglazed collector, the H-W equation takes on the form: η=F_Rα_s−F_RU_L(T_i−T_∞)/G, where η is the efficiency, α_s is the plate solar absorptivity, U_L is the heat loss coefficient, T_i is the fluid inlet temperature, T_∞ is the ambient air temperature, G is the incident solar irradiance, and F_R is the heat removal factor. For the UTC, the fluid to be heated is air taken straight from ambient, so T_i=T_∞, and the equation reduces to η=F_Rα_s. Current theoretical modelling is aimed at determining the heat removal factor, F_R, appropriate to the UTC.

Such modelling started with the work of Kutscher et al. (1991), and the more recent modelling work has been summarized by Hollands (1998). Kutscher et al. (1991) argued that, under the range of wind and suction speeds relevant for the UTC operating with moderate temperature rises, there should be no significant convective heat loss from the UTC. Long-wave radiative heat transfer from the plate to the surroundings remains as the only important heat-loss mechanism (it should be noted, however, that convection is still important, in that it is the convective heat transfer between the plate and the air that is decisive in establishing the plate temperature and the radiant loss). Assuming an isothermal plate, Kutscher et al. (1991) developed an expression for the collector efficiency that (with an appropriate interpretation of h_r) can be made to reduce to

$$\text{η=α}{}_{\mathrm{<mtext>s</mtext>}}\text{/(1+h}{}_{\mathrm{<mtext>r</mtext>}}\text{/(ϵρC}{}_{\mathrm{<mtext>p</mtext>}}\text{V}{}_{\mathrm{<mtext>s</mtext>}}\text{))}$$

where h_r is the radiative heat loss coefficient from plate to ambient, V_s is the superficial suction velocity (rate at which air is sucked through the plate, per unit plate area), ρ and C_p are the density and specific heat of the air, respectively, and ϵ is the ‘heat exchange effectiveness’, to be defined presently. This means that the H-W equation applies to the UTC provided that one takes 1/(1+h_r/(ϵρC_pV_s)) to be the appropriate UTC expression for F_R. In practice, values of η ranging from 50 to 80% have been commonly achieved, with V_s ranging from 0.03 to 0.08 m/s.

The key item in the above equations for η and F_R is the effectiveness, ϵ, defined by

$$\text{ϵ≡}\text{T}{}_0\text{−T}{}_{\mathrm{\infty }}\text{T}{}_{\mathrm{<mtext>p</mtext>}}\text{−T}{}_{\mathrm{\infty }}\text{,}$$

where T₀ is the mean air temperature leaving the plate at the back-side, T_∞ is the ambient air temperature, and T_p is the plate temperature. (A similar equation for ϵ can be readily derived for the case where the plate temperature varies from the isothermal state assumed by Kutscher et al.; in this case, T_p is to be interpreted as the mean temperature of the outside surface of the plate. A further discussion on this point is given in Appendix A.) Effectiveness, ϵ, has to be evaluated, either from experimental data, or from analysis, but, once it has been evaluated, determining η and F_R is straightforward.

The expression for ϵ will depend on how the holes are laid out on the plate, and it will also depend on the nature of the wind. Cao et al. (1993), Golneshan (1994), and Golneshan and Hollands, 1998, Golneshan and Hollands, 2000 reported numerical and experimental correlation equations for ϵ for a plate with holes in the form of an array of slits, the wind being assumed to be transverse to the slits but parallel to the plate. Kutscher (1994) presented an empirical model for relatively thin plates, with circular holes on a triangular layout, with the wind parallel to the plate (grazing wind). Using computational fluid dynamics (CFD) methods, Arulanandam et al. (2000) analysed a plate having circular holes on a square layout, obtaining a correlation equation for the corresponding ϵ, but only under no wind conditions, and only accounting for the heat transfer on the front face of the plate and in the holes (i.e., it neglected the heat transfer at the back of the plate). Gawlik (1995) investigated the effect of having a low plate conductivity and the effect of corrugating the plate.

This paper presents new experimental data for thick and thin plates with circular holes on a square or triangular layout over a range of typical suction velocities and wind speeds, including zero wind. It extends the data of Kutscher to a wider range of plate thicknesses and hole pitch, as well as to the square pitch layout. In the region where the two studies overlap, the agreement between the two sets of data is very good, generally within about 3%, which is comparable to the accuracy of the experiments. A new predictive model is proposed for the effectiveness; one that gives a breakdown of the contribution to the heat transfer on each of the parts of the plate: that is, on the outside face, the hole, and the back of the plate. The additional information contained in this breakdown should be useful for plate-design purposes.