NUMERICAL SIMULATIONS OF DIRECT ABSORPTION OF SOLAR RADIATION BY A LIQUID

NUMERICAL SIMULATIONS OF DIRECT ABSORPTION OF SOLAR RADIATION BY A LIQUID Ram Satish Kaluri Srinivasan Dattarajan Ganapathisubbu S Siemens Corporate Research & Technologies Bangalore, India 561 ramsatish.k@siemens.com srinivasan.dattarajan@siemens.com ganapathisubbu.s@siemens.com ABSTRACT The performance of a direct absorption collector of solar radiation is reported in this study with the aid of numerical simulations. Since the entire volume of the working fluid of a direct absorption collector participates in the conversion of solar energy, in contrast to just the surface of a conventional solar-thermal collector, the former has the potential to deliver higher collector efficiencies. Nevertheless, there are relatively few studies in literature that document the effect of various collector design parameters on its performance. In this paper, a numerical model for the direct absorption of solar radiation is studied on a collector comprising 2-D flow of a liquid between two parallel walls, one of which is permeable to solar radiation. The effects of key flow and radiation parameters on collector performance have been systematically evaluated, and are reported. The collector efficiency was found to increase with both fluid inlet velocity and collector depth up to certain respective values, beyond which there was no significant dependence on either parameter. The collector efficiency increased, and subsequently decreased with increasing fluid absorptivity. The collector was more efficient when the wall impermeable to solar radiation was emitting than when it was reflective. 1. INTRODUCTION Conventional solar thermal receivers provide for concentrated solar radiation to impinge on the surface of an opaque metal tube, beneath which the flow of a working fluid is maintained. This radiatively heated tube transfers heat to the working fluid via convection and conduction. As shown in Fig. 1(a), solar energy is transferred to the working fluid in two steps. This arrangement suffers from two performance drawbacks resulting from the tube surface inevitably reaching high temperatures. First, the receiver undergoes high convective and radiative heat loss. Secondly, the tube wall undergoes material degradation owing to the imposed thermal stress. These two factors limit how much radiative flux the receiver can be subjected to. (a) (b) Incident radiation Incident radiation Opaque wall Opaque wall Semi-transparent wall Opaque wall Emission losses Emission losses Fig. 1 Schematic of (a) surface absorption collector and (b) direct absorption and collector In a Direct Absorption Collector (DAC), incident radiation is directly absorbed by the working fluid, as shown in Fig. 1(b). The top wall is semi-transparent to solar radiation. The entire volume of the working fluid of a DAC participates in conversion of solar energy to thermal energy via absorption of radiation, as opposed to only the surface of a conventional receiver previously discussed. As can be appreciated, the former has the potential to do so more 1

efficiently. The potential advantages of the DAC concept over a conventional solar-thermal receiver are summarized below: The walls of the tube enclosing the working fluid of a DAC do not participate appreciably in the absorption process, and hence do not attain soaring temperatures resulting in reduced heat loss from the surface There are no limitations on the magnitude and uniformity of flux imposed by conventional designs. A well-known example of direct absorption collection system is the solar pond [1]. Over the years, many novel collector designs for direct absorption of solar energy have been proposed, such as black liquid collectors [2], trickle collectors [3] [4], volume-trap solar collectors [5], particleladen collectors [6], nanofluid collectors [7] [8] etc. The concept of direct absorption has been proposed for enhancing the efficiency of cavity-type collectors in power towers by Copeland et al. [9]. In this type of receivers, a thin film of molten salt flows over an inclined surface due to gravity, and is exposed to highly concentrated solar radiation. Several studies on development of mathematical framework for modeling of solar radiation absorption in thin films have been reported. A detailed mathematical model for absorption of solar radiation in particulate-laden falling liquid film has been proposed by Kumar and Tien [6]. The model accounts for radiative and convective transport, absorption, emission, scattering, and spectral and angular variations of radiation and radiative properties. Effects of particle loading, particle diameter, film thickness and variable thermo- physical properties on temperature distribution within the fluid layer are analyzed. Houf et al. [1] developed a three-dimensional laminar flow model to predict effects of liquid velocities, radiative properties of liquid and substrate, intensity of solar irradiation and influence of buoyancy forces on hydrodynamic and thermal conditions. Webb and Viskanta [11] numerically investigate the heat transfer characteristics of gravity-driven semitransparent molten salts flowing over an opaque substrate subjected to solar irradiation. The effects of model parameters such as substrate emissivity, fluid layer opacity, spectral nature of incident radiative flux, flow model, and fluid layer physical thickness on collector efficiency are investigated. Vaxman and Sokolov [12] develop a simple analytical model for heat removal factor and collector efficiency based on mass and energy balance for a free flow solar collector. Numerical studies by Lazardis et al. [13] indicate that steep temperature gradients of the order of 1 C exist within very thin fluid layers (<.5 mm). in fluids were limited only to one-dimensional analysis of radiative transfer. Even in the studies where momentum and energy equations are considered three-dimensional, the radiative transfer equation is still considered to be onedimensional, assuming that the thickness of fluid layer is considerably small [1]. A detailed two- and threedimensional modeling and analysis of solar radiation absorption in liquids is yet to appear in literature. The main objective of the present study is to analyze the influence of flow and radiative parameters on collector performance based on two-dimensional modeling of fluid flow and radiative heat transfer. 2. MATHEMATICAL MODEL 2.1. Flow geometry The direct absorption collector that was numerically simulated in this study comprised a liquid of absorptivity flowing between two parallel walls, as shown in Fig. 2. The top wall was semi-transparent to solar radiation, and the bottom wall was opaque. Inlet y Incident radiation x Fig. 2 Schematic of the physical domain considered for this study. 2.2. Governing equations Semi-transparent wall The governing equations mass, momentum and energy for two-dimensional steady-state, incompressible, laminar flow may be given as u v x y Midline Opaque wall u u P u u u v x y x x y Emission Losses Outlet Convective Losses (1) (2) Owing to the complexities and computational effort involved in solving an integro-differential radiative transfer equation, earlier studies on modeling of radiation absorption v v P v v u v x y y x y (3) 2

T T T T C u v k x y x y p q r where u, v, are velocities in x and y directions, respectively, is the density, P is the pressure, C p is the specific heat, is the fluid viscosity, T is the temperature, k is the thermal conductivity and q r is the heat flux due to radiation. The last term on right hand side of Eq. (4) is the volumetric source term due to radiation and is given by (4) (5) where is the wavelength, is the spectral absorption coefficient, I is the blackbody intensity given by the Planck function. The intensity I at the position in the direction s r in the fluid region is obtained by solving the Radiative Transfer Equation (RTE): ( I ( r, s) s) ( ) I ( r, s) n 4 q r 4I b I ( r, s) d (6) where, n is the refractive index, s is the scattering coefficient, s is the scattering direction vector, is the solid angle, is the phase function. Eq. 6 above is the generalized equation for absorbing, emitting and scattering medium. In the present study, scattering of energy within the fluid is ignored as the experimental studies on scattering of radiation in pure water indicate that the scattering phase function is highly forward in nature [14] i.e., the scattered energy propagates in the direction of incident beam. As suggested by Cengel and Ozisik [1], the highly forward nature of phase function may be approximated such that there is no scattering at all, since all non-absorbed energy propagates in its original direction. 2.3. Input parameters 4 2 I b ) s s I ( r, s) ( s, s d 4 The parametric studies were carried with the following boundary conditions and input parameters. The depth of the collector, i.e. the distance between its top and bottom walls, was.1 m, and the collector width, i.e. the distance between its inlet and outlet, was.5 m. The width and depth of the fluid channel were.5m and.1m, respectively. The incident radiation was assumed to be gray with an intensity of 2 kw/m 2 and was incident normally on the top wall. Convective heat loss coefficient, h was specified at both top and bottom walls. The h was assumed to be 8 W/m 2 -K, which is a typical value for heat loss due to natural convection. The fluid inlet temperature and ambient temperature were both 3 K. The semi-transparent top wall was considered to be glass with thermal conductivity 1.5 W/m-K and specific heat 83 J/kg-K. The opaque bottom wall was considered to be aluminum with thermal conductivity of 22.4 W/m-K and specific heat 871 J/kg-K. The refractive index of the semi-transparent glass wall was 1.5 and that of the fluid, 1.. The emissivity and diffuse fraction of the bottom wall were maintained at 1 and, respectively. The density, specific heat, thermal conductivity and viscosity of the fluid were the same as those of water. The computational domain shown in Fig. 2 was spatially discretized using a 15 x 5 mesh along the width and depth, respectively. Mesh points were spaced more closely near the top and bottom walls. 3. NUMERICAL SOLUTION & VALIDATION The governing equations for mass, momentum and energy discussed in the previous section were solved using the commercially available general purpose CFD solver FLUENT 13.. The radiative transfer equation (Eq. 6) was solved by the Discrete Ordinate (DO) method. In the DO method, the radiation field is divided into a number of discrete directions, and the RTE written and solved separately for each of these directions using a conservative variant of the DO model [15]. In this approach, the RTE is integrated over both control angles and control volumes unlike in the regular DO method, wherein the RTE for different directions is integrated over control volumes only. TABLE 1: INPUT CONDITIONS FOR FIVE DIFFERENT CASES REPORTED IN BEARD et al. [3]. Case I (W/m 2 ) m (kg/s) T amb (K) T in (K) 1 853.7.127 28 37.1 2 191.3.125 284.5 314.7 3 852.9.125 29 322.5 4 839.78 277 293.1 5 957.5.77 283 294.8 In order to validate the current numerical model, the free flow direct absorption collector experimentally studied by Beard et al. [3] was simulated employing the numerical model described in the previous section. Only the comparison of numerical results and experimental data for the flow conditions listed in Table 1 are presented here. For details on the experimental setup and problem description, the reader is referred to [3]. Fig. 3 shows the comparison of bulk outlet temperature predicted by current numerical model with that of experimental data of Beard et al. [3]. The results show that the numerical results are in good agreement with experimental data. The error between the experimental and numerical results is less than 1.2% for all the five cases. 3

Outlet temperature, T out (K) 335 33 325 32 315 31 Experimental (Beard et al [5]) Numerical (Present) At low velocities, the time delay between the entry and exit of a given fluid parcel into and out of the collector, i.e. the fluid residence time, was high, allowing for the fluid temperature to rise more. This is illustrated in Fig. 5, which shows declining temperature rise in the fluid across the width of the collector with increasing velocity. Since emission of radiation from the fluid scales with the fourth power of temperature, the fluid suffered higher emissive losses at lower velocities, which resulted in smaller collector efficiencies. 35 1 2 3 4 5 6 Fig. 3 Comparison of bulk outlet temperature (T out ) between experimental data [3] and present numerical data for five different cases (see Table 1). The error bars show 1% deviation. 4. RESULTS AND DISCUSSION Detailed simulations were carried out to study the effect flow and radiative parameters on the collector efficiency, defined as ratio of the enthalpy rise in the fluid across the collector inlet and outlet, to the total incident radiation, The efficiency has been used here as a measure of collector performance. The effects of the various parameters on collector efficiency are discussed below. 4.1. Effect of flow/geometric parameters The effects of bulk flow velocity at the inlet and the depth of the collector on the efficiency were studied, and are presented below. The collector depth was held fixed when the velocity was parametrically varied, and vice-versa. In both cases, the mass flow rate of fluid through the collector was determined by the particular choice of velocity and collector height. 4.1.1. Bulk inlet velocity Cases mc p ( Tout Tin) I The effect of inlet velocity on collector efficiency is shown in Fig. 4. Values of the fluid absorptivity, and the diffuse fraction f d and the emissivity w of bottom wall are indicated in the caption. The efficiency increased with velocity for small flow rates, and was found to be independent for higher velocities. (7) Collector efficiency, 1.9.8.7.6.5.4.3.2.1.1.1.1.1.1 Velocity (m/s) =15 m -1 Fig. 4 Effect of inlet velocity on collector efficiency. Here, = 15 m -1, f d = and w = 1. The collector depth was.1m. Temperature (K) 8 7 6 5 4 3 2.2.4.6.8 1 Normalized distance from the bottom wall v=1e-5 m/s v=.1 m/s v=.1 m/s v=.1 m/s v=.1 m/s Fig. 5 Temperature profiles at the midline of the collector, corresponding to the conditions in Fig. 4. In the abscissa, distance from the bottom wall is normalized by the collector depth. At higher velocities, though, the temperature rise in the fluid itself was small, and differences therein across velocities were still smaller. This resulted in a progressively weaker effect of emissive losses described above, and hence, collector efficiencies were seen to be independent of velocity at higher values. 4

4.1.2. Collector depth Since radiation was incident normal to the top wall of the collector, the collector depth determined what fraction of the incident radiation was absorbed before it impinged on the bottom wall. The effect of collector depth on the efficiency is shown in Fig. 6. The collector efficiency initially increased with collector depth for small values of depth, and subsequently became independent of depth for large values of collector depth. Collector efficiency, Fig. 6 Effect of the collector depth on the collector efficiency. Here, = 15 m -1, f d = and w = 1. The fluid inlet velocity was.1 m/s. For small values of depth, the radiation incident onto the top wall penetrated the fluid layer in the collector, and impinged on the bottom wall after being partly absorbed by the fluid. Since the bottom wall was non-reflective, any radiation impinging on it got absorbed, subsequently raising the fluid temperature in its vicinity as shown in Fig. 7. As indicated before, this temperature rise resulted in higher emissive loss, thereby reducing collector efficiency. Temperature (K) 1.95.9.85.8.75.7 5 48 46 44 42 4 38 36 34 32 3 =15 m -1 v=.1 m/s.1.2.3.4.5 Collector depth, D (m) 28.2.4.6.8 1 Normalized distance from bottom wall v=.1 m/s D=.1 m D=.3 m D=.5 m D=.1 m D=.2 m D=.4 m Fig. 7 Temperature profiles at the collector midline, corresponding to the conditions in Fig. 6. In the abscissa, distance from the bottom wall for various curves is normalized by the respective collector depth. For large collector depths, most of the radiation incident on the top wall was absorbed by the fluid before it reached the bottom, thereby avoiding the formation of high temperature regions near the bottom wall and giving higher collector efficiency. This is evident from the temperature near the bottom wall in Fig. 7. However, increasing the collector depth had no added advantage beyond a point in preventing fluid heating near the bottom wall. Hence the collector efficiency was independent of collector depth for high values of depth. The trend reported in Fig. 6 is consistent with that predicted in Fig. 2 of Sokolov et al. [16]. 4.1.3. Inlet temperature The rate at which a fluid parcel emits radiation is proportional to the fourth power of its absolute temperature. Collector efficiency,.94.92.9.88.86.84.82.8.78 3 32 34 36 38 Inlet temperature (K) Fig. 8 Effect of fluid inlet temperature on collector efficiency. Here, f d = and w = 1. The fluid inlet velocity and collector depth were.1 m/s and.1 m, respectively. So fluid entering the collector at a lower temperature emitted less total radiation than that entering the collector at higher temperature. Since the fluid absorptivity was held fixed, the collector efficiency was lower in the former case. This trend is captured in Fig. 8. 4.2. Effect of fluid and wall radiative properties The collector fluid interacted with the radiation incident on the collector via absorption and emission. For reasons outlined in Section 2, scattering of radiation by the fluid was not modeled. In section 4.2.1 below, the effect of the fluid absorptivity on the performance of the collector is quantified. The effects of the radiative properties of the bottom wall, viz. emissivity and diffuse fraction, are discussed subsequently in sections 4.2.2 and 4.2.3. 4.2.1. Fluid absorptivity = 15 m -1 = 8 m -1 The fraction of radiation incident on a fluid parcel that is 5

absorbed by it is proportional to the fluid absorptivity. For a fixed collector depth and inlet velocity, the collector efficiency at various values is shown in Fig. 9. The efficiency peaked at certain value, and increased and decreased with for lower and higher value, respectively. This was the consequence of two competing effects at play with increasing, as explained below. 1 wall absorbed most of the radiation incident on it, allowing little radiation to penetrate the fluid layer and reach the bottom wall. This resulted in a high temperature region near the top wall, with the attendant emissive losses and drop in collector efficiency. The trade-off between the two effects at low and high values described above accounts for the trend seen in Fig. 9. 4.2.2. Emissivity of bottom wall Collector efficiency,.9.8.7.6.5 v=.1 m/s v=.1 m/s v=.1 m/s v=.1 m/s The effect of the emissivity of the bottom wall on the performance of the collector is shown in Fig. 11. The bottom wall emissivity is seen to have a sizeable effect on collector efficiency only at low values of fluid absorptivity, i.e. when a significant fraction of the incident solar radiation reached the bottom wall..4 2 4 6 8 1 Absorption coefficient, (m -1 ) Fig. 9 Effect of fluid absorptivity on collector efficiency. Here, f d = and w = 1. The collector depth was.1 m. For very low, most of the radiation incident on the top wall penetrated all the way through the fluid layer to the bottom wall, causing the latter wall to absorb all the radiation impinging on it, since it was non-reflecting. This raised the fluid temperature adjacent to the bottom wall, as shown in Fig. 1. Collector efficiency, 7 6 5 4 3 2 1.2.4.6.8 1 Normalized distance from bottom wall = 1 m -1 = 15 m -1 = 4 m -1 = 1 m -1 Fig. 1 Temperature profiles at the collector midline, corresponding to the conditions in Fig. 9. In the abscissa, distance from the bottom wall is normalized by the collector depth. As noted previously, regions of high temperature in the flow field lead to greater emissive losses, bringing down the enthalpy retained by the collector fluid, and hence the collector efficiency. Thus, the collector efficiency increased with at low. For very high, fluid adjacent to the top Collector efficiency,.9.8.7.6.5.4.3.2.1.2.4.6.8 1 Emissivity of bottom wall ( w ) f d = = 2.48 m -1 = 1 m -1 = 24.8 m -1 Fig. 11 Effect of emissivity of the bottom wall on collector efficiency. Here, f d =.The fluid inlet velocity and collector depth are.1 m/s and.1 m, respectively. When w =, i.e. the bottom wall was reflective, solar radiation incident on the top wall was partly absorbed by the fluid before it reached the bottom, where it got reflected back into the fluid. This reflected radiation was again absorbed partly by the fluid before being transmitted out of the domain through the semi-transparent top wall. In the process, the fluid underwent a modest rise in temperature, as shown in Fig. 12. However, at w = 1, the bottom wall was non-reflective, and any radiation reaching there was absorbed by it. This caused the temperature of the bottom wall to rise significantly, and that of the fluid in its vicinity, as seen in Fig. 12. Thus, even though the consequent emissive losses were higher when w = 1, the sensible enthalpy required to bring about the temperature rise near the bottom was retained by the fluid. This resulted in a higher mean fluid temperature at the collector exit, and hence a higher collector efficiency. The observed collector efficiencies in Fig. 11 at intermediate values of w can be similarly explained. 6

Temperature (K) Fig. 12 Temperature profiles at the collector midline, corresponding to the conditions in Fig. 11. Only the profiles at = 2.48 m -1 and w =,.5 and 1 are shown. 4.2.3. Diffuse fraction of bottom wall The diffuse fraction of a wall is defined as the fraction of radiation incident on that wall which is reflected diffusely, i.e. in all directions on the same side of the wall. The rest of the radiation undergoes specular reflection. Collector efficiency, 7 6 5 4 3 2 1.2.4.6.8 1 Normalized distance from bottom wall.9.8.7.6.5.4.3.2.1.2.4.6.8 1 Diffuse fraction of bottom wall = 2.48 m -1 w = w = w =.5 w = 1 = 2.48 m -1 = 1 m -1 = 24.8 m -1 Fig. 13 Effect of diffuse fraction (f d ) of the bottom wall on collector efficiency. Here, w =, the fluid inlet velocity and collector depth are.1 m/s and.1 m, respectively. As in section 4.2.2, the diffuse fraction of the bottom wall had a sizeable effect on the collector efficiency only at low values of, i.e. when a significant fraction of the incident solar radiation reached the bottom wall. This effect is shown in Fig. 13. Solar radiation incident on the top wall of the collector that penetrated the fluid layer impinged normally onto the bottom wall. When it reflected off diffusely in all directions, it afforded the fluid layer a greater effective distance over which to re-absorb that radiation before it reached the top wall, than when the reflections from the bottom wall were specular. This accounts for the observed increase in collector efficiency at higher diffuse fractions of the bottom wall shown in Fig. 13. 5. CONCLUSIONS The effects of key flow and radiation parameters of a direct absorption solar collector have been studied. An idealized two dimensional model was used in order to keep the flow field simple, and to avoid getting locked into the specifics of the geometry of any one collector. Although the results presented in this paper are in dimensional form, we believe the findings will be valuable to the designer of a practical direct absorption collector. The flow parameters studied herein were the fluid inlet velocity and the collector depth. The effect of fluid velocity, which in essence is a fluid residence-time effect, implies that any collector design that tends to increase fluid residence time within the collector would cause its temperature to rise, leading to higher emissive losses and diminishing efficiencies. The collector depth, an increase in which ceases to influence collector performance significantly beyond a point, should be kept low in order to ease the requirement on the amount of collector fluid needed to operate the collector. The radiation parameters studied were the fluid absorptivity, and the bottom wall emissivity and diffuse fraction, the last of which had a relatively minor influence on collector performance. Since the absorptivity of a fluid determines the fraction of radiation coming its way that it absorbs, one might be tempted to conclude that collector performance ought to indefinitely improve with increasing fluid absorptivity. However, as this study shows, emissive losses dominate at high values absorptivity and bring the collector efficiency down, thereby rendering the efficiency maximum at a certain absorptivity. An emitting wall is seen to perform better than a reflecting one, especially at low values of optical depth, despite the fluid reaching significantly higher temperatures near the bottom wall in the former case. 6. ACKNOWLEDGMENTS The authors gratefully acknowledge the support and funding from Decentralized Renewable Energy Technologies, Siemens Corporate Research and Technologies, India. 7. REFERENCES [1] Y. A. Cengel and M. N. Ozisik, Solar radiation absorption in ponds, Solar Energy, vol. 33, 1984 7

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