EFFECT OF OPERATING PARAMETERS ON THE PERFORMANCE OF WIRE SCREEN MATRIX PACKED SOLAR AIR HEATER
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1 EFFECT OF OPERATING PARAMETERS ON THE PERFORMANCE OF WIRE SCREEN MATRIX PACKED SOLAR AIR HEATER P. Verma 1, L. Varshney 1 * 1 Department of Mechanical Engineering, College of Technology, G.B. Pant University of Agriculture & Technology, Pantnagar , Uttaranchal, India. ABSTRACT A mathematical model has been developed to investigate the effect of operating parameters on the thermohydraulic performance of a wire screen matrix packed solar air heater. A mathematical model is developed to predict the thermo-hydraulic performance of a packed bed solar air heater packed with wire screen matrices considering various energy transfers. Governing equations are solved numerically using relevant empirical correlations for heat transfer coefficient for such solar collectors. For solving the equations a computer programme is developed in C++ to estimate the effective efficiency of the solar air heater. The effective efficiency values clearly indicate that the performance of solar air heater is governed by the operating parameters like mass flow rate, wind heat transfer coefficient and insolation, and there exists an optimum value of mass flow rate for best thermo-hydraulic performance. Among all the matrices, best effective efficiency is obtained for a particular matrix and the optimum value of thermohydraulic performance corresponds to mass flow rate range of 0.02 to kg/s KEYWORDS: Solar air heater, effective efficiency, wire screen matrix, pressure drop I. INTRODUCTION Due to increasing demand of energy consumption day by day there is a need for use of alternative energy sources; solar energy is a potential alternate energy source. Solar radiation received by sun is vast and can be converted into thermal energy using a collector. The primary component which takes part in the conversion is a collector which could be flat or concentrating type depending upon the end use of energy or temperature requirement. A solar collector is a device which converts the incident solar radiation into thermal energy via a heat transfer fluid (HTF). Solar air heaters use air as HTF. Though there are numerous applications of solar air heaters (SAHS) but for low and moderate temperature applications such as crop drying, drying of fruits and vegetables, timber seasoning and certain other industrial applications, SAHS are best suited as it does not require any auxiliary power. The drawback with SAHS is that their thermal efficiency is low due to low specific heat of air and higher heat loss to the surroundings as the h c between the absorber plate and the flowing air is low. Thermal performance of SAHS can be appreciably improved by increasing the convective heat transfer coefficient from absorber plate to air and this can be done by providing specific geometry shaped artificial roughness on absorber plate or by fixing ribs, baffles, wires, blocks, expanded metal mesh to the heat transfer surface. A review of literature available shows the use of multi V ribs by Hans et al., Multi V shaped ribs with gap by Kumar et al., Discrete V shaped ribs by Sukhmeet et al., combination of inclined and transverse ribs by Varun et al., dimple shaped roughness geometry by Saini and Verma, arc shaped and expanded metal by Saini and Saini [1-7] are a few of the variations which have been used to enhance the thermal performance of the solar air heater. Another effective way to improve the thermal performance of solar collectors is by packing the air flow duct with porous packing like wire screens as used by Varhney and Saini, slit and expanded metal foils by 263 Vol. 7, Issue 1, pp
2 Chiou et al. and Chiou and El- Wakil, glass beads by Hasatani et al., granular carbon by Saxena et al., paraffin based phase change material by Charvat et al., rasching rings by Özturk and Demiriel, steel wool by Sopian et al. and metal wool by Lansing et al. [8-16]. An attempt to enhance the heat transfer is always accompanied with an increase in pressure drop, and thus the pumping power requirement is increased. It is, therefore, desirable to optimize the system to maximize the heat transfer while keeping frictional losses at a minimum possible level..in this paper a mathematical heat transfer model of a packed bed solar air heater (PBSAH) having its duct packed with wire screen matrices has been formulated considering various energy transfers to predict the performance of the solar air heater. Performance of the packed bed has been investigated in terms of η th and effective efficiency and the effect of various operating parameters has been investigated. II. MATHEMATICAL MODEL For investigation of thermohydraulic performance (THP) of the system, a set of five matrices as used by Varshney and Saini [8] has been considered. The geometrical parameters of the matrix used are tabulated in Table 1. The Schematic diagram of the system used and the geometry of the wire screen used for making matrix inside the flow duct are shown in Fig. 1. Matrix Table 1 :Geometrical parameters of wire screen matrices of the PBSAH [8] Matrix Wire dia d w (mm) No. of layers, n Pitch, p t (mm) Hydraulic radius, r h 10 3 ( m) Porosity, P Extinction coefficient, ϑ (m -1 ) M M M M M4(a) Heat transfer in the bed is assumed to take place by combination of conduction, convection and radiation. Following the procedure of Hasatani et al. [11] the heat balance equations for PBSAH are written. The following assumptions are made to simplify the analysis. The temperature distribution within individual packing element and glass cover is uniform. Conductive heat transfer in the flow direction is negligible. Natural convection is not generated in the flow duct. The physical properties of the packed bed material are independent of the temperature. Fig.1. Heat transfer mechanism of PBSAH 264 Vol. 7, Issue 1, pp
3 Heat balance equations are modified for quasi steady state conditions in the analysis of the collector bed. While writing the heat balance equations, conduction losses through the side and back walls have been neglected. The following relations can be written for irradiation, I, and radiosity R tg, based on the transmitted and reflected radiation inside the bed as has been shown in Fig. 1. R tg = r c I + I 1 (τ) eff (1) R bg = I(τ) eff + r c I 1 (2) I 1 = R bp e τ o (3) I 2 = R bg e τ o (4) R bp = (1 ε p )I 2 (5) I y = R bg e τ (6) R y = R bp e (τ o τ) (7) Q r = I y R y = R bg e τ R bp e (τ o τ) (8) Further, the environmental temperature and wind velocity have been assumed uniform and constant. The heat balance equations can be obtained as follows for the PBSAH operating under actual outdoor conditions: Net heat flux entering the element due to conduction + Net heat flux due to radiation = Rate of heat gained by the air by means of convection from matrix to air (9) Rate of rise in the sensible heat of air = Rate of energy carried away by the air (10) The mathematical expression of Eq. (9) can be given as: [k t b y eff Q y r] = h c a v (t p t g ) (11) Assuming the bed temperature t b to be average of matrix temperature t p and air temperature t g. Therefore Eq. (11) can be represented as: [k t b y eff Q y r] = 2h c a v (t b t g ) (12) Similarly mathematical expression of Eq. (10) can be represented as: G o C p [ t g x ] = 2h ca v (t b t g ) (13) Applying boundary conditions for Eq. (12) the following equations are obtained: At y = 0, i.e. the top of boundary k eff t b y U t(t b t a ) = 0 (14) At y = D i.e. the bottom of bed k eff t b y Q r = 0 (15) At x = 0, boundary condition for Eq. (13) at the entry can be given as: t g = t i (16) For the calculation of heat transfer and friction factor, the following correlations as reported by Varshney and Saini [8] have been used. J h = [ 1 np ( P t d w )] Re P 0.55 (17) f p = [ 1 ( P t )] Re np d P (18) w The non-dimensional parameters introduced in order to normalize the above equations are given in Appendix (a). Respective equations (12) to (16) can be rewritten in the normalized form as under with the help of non dimensional parameters. For convenience non-dimensional bed temperature t b has been designated by p and non-dimensional air temperature t g by q. Hence, Eq. (12) can be written as: 2 u Q r = h (p τ 2 τ v q) (19) By substituting Q r we get, 2 u + R τ 2 bge τ R bp e (τo τ ) = h (p v q) (20) By applying boundary conditions on equations (14) and (15) can be rewritten as: 265 Vol. 7, Issue 1, pp
4 u U (p τ t t a ) = 0 (21) u Q τ r = 0 (22) For air Eq. (13) can be written as: u h x v (p q) = 0 (23) And its boundary condition Eq. (16) will be: q =1 (24) Equations (20) to (24) are two dimensional non-linear partial differential equations which can be solved by finite difference method. In order to cover a two dimensional region of the collector bed, a rectangular mesh is formed. The length and height of the mesh is divided into equal number of nodes. Governing equations are solved using Gauss elimination method through a computer programme developed in C++. Values of system parameters used for evaluation of effective efficiency are given in Table 2. Table 2 :Numerical values of system and operating parameters used in analytical calculation of PBSAH S. No. Input data Numerical value 1 Width of collector duct( W) 0.41 m 2 Length of collector(l) 2.0 m 3 Depth of collector( D) 0.03 m 4 Air mass flow rate ( m ) kg/s 5 Inlet air temperature (t i) 30 C 6 Ambient temperature ( t a) 30 C 7 Insolation (I) 620 W/m 2 8 Cover glass reflectivity of (r c) Cover glass absorptivity of ( c) Wire mesh screen emissivity of ( ) Bottom plate emissivity of ( p) Thermal conductivity of air ( k a) W/(m K) 13 Thermal conductivity of matrix ( k s) W/(m K) 14 Refractive index of mesh material, (n ) Air Viscosity ( μ) kg/(m s) 16 Wind heat transfer coefficient (h w) 10.2 W/(m 2 K) 17 Effective transmissivity of covers (τ) eff 0.72 The estimated air temperatures for given operating conditions are used to calculate the q u, thermal efficiency P m, P, and effective efficiency, for performance optimization using the following relations given in Appendix (b). The value of C recommended by Cortes and Piacentini [17] is used as III. VALIDATION OF MATHEMATICAL MODEL The mathematical model (MM) is tested for matrix M2 using three different correlations of U t given respectively by Klein [18] for model A, Agarwal and Larson [19] for model B and Malhotra et al. [20] for model C against the experimental results obtained by Varshney [21] for model D, and the model which is in agreement with experimental results is selected for the investigations on THP. Comparison 266 Vol. 7, Issue 1, pp
5 of obtained result for thermal efficiency using different U t is compared in Fig. 4 with experimental results, reported by Varshney [21]. 70 Thermal efficiency, η th Model A (predicted ηth) Model B (predicted ηth) Model C (predicted ηth) Model D(experimental ηth) Mass flow rate, m (kg/s) Fig.4. Comparison of predicted values with experimental values. It is found that relation of U t given by Klein [18] for model A used for the prediction of thermal efficiency for the MM fairly agrees with the experimental values of thermal efficiency obtained by Varshney [21] with an average deviation of 3.8 %. Hence the correlation given by Klein [18] for U t is used for further investigation of thermal performance. IV. RESULTS AND DISCUSSION In order to study the effect of operating parameters, it has been desired to evaluate performance in terms of effective efficiency rather than thermal efficiency as effective efficiency also takes into account the effect of pressure drop, effective efficiency has been evaluated by following the procedure proposed by Cortes and Piacentini [17] i.e. by subtracting the equivalent pumping power from thermal energy gain. Figure 5 shows the effect of the R ep on the thermal energy gain and the pumping power for a typical matrix M2. It has been observed that, at higher R ep, the rate of increase in pumping power is very high, while the rate of the thermal energy gain becomes nearly constant. It is notable that at lower R ep, the rate of increase in power required to force the air through the duct is low, while the rate of useful energy gain is substantial. Therefore, with the increase in R ep, a stage is reached where we get the optimum value of energy gain. It is evident from the Fig. 5 that at higher value of R ep, the benefit of net energy gain might eventually be lost. It has been observed that effective efficiency is the major concern parameter of the THP of PBSAH. Therefore the efforts have been made to investigate the effect of various operating and system parameters on effective efficiency of the PBSAH. 267 Vol. 7, Issue 1, pp
6 Effective efficiency, η eff (%) Thermal Energy Gain (W) Pumping Power (W) International Journal of Advances in Engineering & Technology, Mar., I= 620 W/m 2 t a = 30 C Maximum Gain (q u -P m /C) Thermal energy gain (qu) Pumping power (Pm/c) Reynold's no, (Rep x 10-2 ) Fig.5. R ep vs. thermal energy gain and pumping power for matrix M2 4.1 Effect of operating parameters on effective efficiency Figure 6 shows the effect of the m on the effective efficiency. It has been seen that as the airflow rate increases, the effective efficiency increases up to a particular value of the R ep or m, attains a maxima, and then decreases sharply Mass flow rate, m (kg/s) M1 M2 M3 M4 M4(a) Fig.6. Mass flow rate versus effective efficiency for different matrices There exists an optimum value of effective efficiency for a given matrix. This is due to the fact that the R ep is a strong parameter that affects the pumping power there by affecting the effective efficiency. It is evident that optimum THP is obtained for m varying from 0.02 to kg/s for different matrices used for investigation and best is obtained for matrix M4 (a). Effect of wind heat transfer coefficient on effective efficiency is investigated considering a typical matrix M2.Figure 7 shows the effect of variation of wind heat transfer coefficient on effective efficiency. It has been found that as the wind heat transfer coefficient is increased there is marginal drop in the effective 268 Vol. 7, Issue 1, pp
7 Effective efficiency, η eff (%) Effective efficiency, η eff (%) International Journal of Advances in Engineering & Technology, Mar., efficiency of PBSAH for a particular m, which is due to the higher losses from the top of the collector that results in the drop of thermal energy gain and consequently the effective efficiency. 100 m= m= m=.03 m= Wind heat transfer coefficient, h w (W/m 2 K) Fig.7. wind heat transfer coefficient versus effective efficiency for matrix M2 In order to check the effect of insolation on effective efficiency, Fig. 8 is drawn between insolation ranging from 600 W/m 2 to 1100 W/m 2 and effective efficiency for different values of mass flow rates. It is observed that the effective efficiency of solar air collector increases significantly with the increase in insolation due to the increase in thermal energy gain as compared to the losses for higher values of insolation m=.01 m=.02 m=.03 m=.04 m= Insolation, (W/m 2 ) Fig.8. Insolation versus effective efficiency for matrix M2 V. CONCLUSION A mathematical model has been developed to predict the thermohydraulic performance of a solar collector in terms of effective efficiency, η eff. It has been investigated that the correlation proposed by Klein for estimation of top loss coefficient, U t in the mathematical model is found to predict results fairly in agreement with the experimental values. Among all the matrices, matrix designated by M4 (a) is found to result in best effective efficiency. It has been observed that the effective efficiency increases with increase in mass flow rate up to a certain limit and then it starts decreasing as the 269 Vol. 7, Issue 1, pp
8 pressure drop becomes more predominant as compared to energy gain. Increase in wind heat transfer coefficient results in marginal drop of effective efficiency for a particular mass flow rate. Effective efficiency of packed bed solar air heater has been found to increase significantly with the increase in insolation. Thermal performance of packed bed solar collector depends on the heat transfer behavior from packing element to flowing air and the pressure drop encountered. It is proposed to investigate the behavior of various packing elements which can have better heat transfer coefficient with minimum pressure drop penalty. Also effect of geometrical parameters needs to be studied and optimization can be done to propose values of geometrical parameters of packing element. Nomenclature A c collector plate area, m 2 A f frontal area of collector bed, m 2 a v C C p D D e d w f p heat transfer area per unit volume of bed conversion factor specific heat of air, J/kg K depth of bed, m equivalent diameter of particle (=6/a v), m wire diameter of screen, m friction factor in packed bed G air mass flow rate per unit collector area, kg/(sm 2 ) G o mass velocity of air, Kg/(s m 2 ) h c convection heat transfer coefficient between air and matrices, W/(m 2 K) h v volumetric heat transfer coefficient, W/(m 3 K) h w Wind heat transfer coefficient, W/(m 2 K) I intensity of solar radiation, W/m 2 I 1 irradiation at the inner surface of lower glass cover, W/m 2 I 2 irradiation at the bottom plate of packed bed collector, W/m 2 I y intensity of solar radiation at depth y from top surface of the bed, W/m 2 J h Colburn J-factor (=StPr 2/3 ) K a thermal conductivity of air, W/ (m K) K eff effective thermal conductivity of packed bed, W/ (m K) L length of collector bed, m m, m mass flow rate of air, kg/s n number of screens in a matrix P Porosity P m P r p t Mechanical Power, W Prandtl number pitch of wire mesh, m 270 Vol. 7, Issue 1, pp
9 ΔP pressure drop in the duct, N/m 2 q u useful heat gain, W Q volume flow rate, m 3 /s Q r radiative heat flux at a distance y, W/m 2 r c r h reflectivity of glass cover hydraulic radius (=Pd w/(4 (1 -P)), m R tg radiosity at the top surface of upper glass cover, W/m 2 R bg radiosity at the bottom surface of lower glass cover, W/m 2 R bp radiosity at the bottom plate, W/m 2 R y radiosity at a distance y from top surface, W/m 2 R ep packed bed Reynolds number (=2G ode/3(1 -P) µ) r c r h S t t a t b t g t i t o t p reflectivity of glass cover hydraulic radius (=Pd w/4(1-p)), m Stanton number (=h c/(c pg o)) ambient temperature, o C bed temperature, o C air temperature, o C air inlet temperature, o C air outlet temperature, o C temperature of packing material, o C U t top loss coefficient, W/ (m 2 K) V x y velocity of air in the duct, m/s distance in horizontal direction from inlet, m distance in vertical direction from top surface, m ϑ extinction coefficient, m -1 η eff η f η m η tr η th effective efficiency efficiency of fan or blower efficiency of the electric motor used for driving fan efficiency of electrical transmission from power plant thermal conversion efficiency of power plant Greek symbols ε p emissivity of back plate µ dynamic viscosity of fluid, N s/m 2 ρ density of air, kg/m 3 τ transmissivity of cover glass τ o optical depth at y = D (=ϑ D) 271 Vol. 7, Issue 1, pp
10 (τ) eff effective transmittance for double glass cover system REFERENCES [1]. Hans VS, Saini RP, Saini JS, (2010) Heat transfer and friction factor correlations for a solar air heater duct roughened artificially with multiple V ribs. Sol Energy, 84, pp [2]. Kumar A, Saini RP, Saini JS, (2012) Experimental investigation on heat transfer and fluid flow characteristics of air flow in a rectangular duct with Multi V-shaped rib with gap roughness on the heated plate, Sol Energy,86, pp [3]. Sukhmeet S, Chandar S, Saini JS, (2012) Investigations on thermo-hydraulic performance due to flow-attack-angle in V-down rib with gap in a rectangular duct of solar air heater. Applied Energy, 97, pp [4]. Varun, Saini RP, Singal SK, (2008) Investigation of thermal performance of solar air heater having roughness elements as a combination of inclined and transverse ribs on the absorber plate, Renew Energy, 33, pp [5]. Saini RP, Verma J, (2008) Heat transfer and friction factor correlations for a duct having dimple-shape artificial roughness for solar air heaters. Energy, 33, pp [6]. Saini SK, Saini RP. Development of correlations for Nusselt number and friction factor for solar air heater with roughened duct having arc-shaped wire as artificial roughness. Sol Energy 2008, 82, pp [7]. Saini RP, Saini JS. Heat transfer and friction factor correlations for artificially roughened ducts with expended metal mesh as roughness element. Int J Heat Mass Transfer 1997, 40, pp [8]. Varshney L, Saini JS. Heat transfer and friction factor correlations for rectangular solar air heater duct packed with wire mesh screen matrices. Solar Energy 1998, 62 (4), pp [9]. Chiou JP, El-Wakil MM, Duffie JA. A slit and expended aluminum foil matrix solar collector. Solar Energy1965, 9, pp [10]. Chiou JP, El-Wakil MM. Heat transfer and flow characteristics of porous matrices with radiations as heat source. J of Heat Transfer 1966, 88, pp [11]. Hasatani M, Itaya Y. and Adachi K. Heat transfer and thermal storage characteristics of optically semitransparent material packed bed solar air heater, Current Researches in Heat and Mass transfer. A Compendium and Festchrift for Prof. A Ramachandran, ISHMT, Dept. of Mechanical Engg., I.I.T., Madras, India, 1985, pp [12]. Saxena Abhishek, Agarwal Nitin, Srivastava Ghanshyam. Design and performance of a solar air heater with long term heat storage. International Journal of Heat and Mass Transfer 2013, 60, pp [13]. Charvat Pavel, Klimes Lubomir, Ostry Milan. Numerical and experimental investigation of a PCM based thermal storage unit for solar air systems. Energy and Buildings 2014, 68, pp [14]. Özturk HH, Demiriel Y. Exergy based performance analysis of packed bed solar air heaters. Int. J. Energy Res. 2004, 28, pp [15]. Sopian K, Alghoul MA, Alfegi Ebrahim M, Sulaiman MY, Musa EA. Evaluation of thermal efficiency of double pass solar collector with porous-nonporous media. Renewable Energy 2009, 34, pp [16]. Lansing FL, Clarke V, Reynold R. A high performance porous flat-plate solar collector. Energy, 1979, 4, pp [17]. Cortes A, Piacentini R. Improvement of efficiency of a bare solar collector by means of turbulence promoters. Appl. Energy. 1990, 36, pp [18]. Klein SA. Calculation of flat plate collector loss coefficients. Solar Energy 1975, 17, pp [19]. Agarwal VK, Larson DC. Calculation of top loss coefficient of a flat plate collector. Solar Energy 1981, 2 pp [20]. Malhotra A, Garg HP, Palit A. Heat loss calculation of flat plate solar collectors, The J. of Thermal Engineering 1981, 2(2), pp [21]. L. Varhney. Investigations on thermohydraulic performance of packed bed solar air heaters. Ph.D. Thesis Department of Mechanical and Industrial Engineering, University of Roorkee. Roorkee (India). APPENDIX (a) Non dimensional parameters τ = ϑy t b = t b t i 272 Vol. 7, Issue 1, pp
11 t g = t g t i t a = t a t i x = x L h v = 2h vl (G o C p ) h v = 2h v (k eff ϑ 2 ) Q Q r r = (k eff ϑt i ) U t = U t (k eff ϑ) R bg = R bg (k eff ϑt i ) where h v = h c a v R bp = R bp (k eff ϑt i ) Q r = R bg e τ R bp e (τo τ ) (b) Relations used for analysis of THP optimization q u = m C P (t o t i ) η th = q u IA c P m = Q P P = f PLρv 2 2r h η eff = q u P m C IA c AUTHORS Prashant Verma has done his B.Tech from college of Technology, G.B.P.U.A.& T, Pantnagar University in 1997 and completed his M.Tech from U.P Technical University in the year He is having a teaching experience of 14 years and industrial experience of 3 years Lokesh Varshney has been working as a Professor in Department of Mechanical Engg., College of Technology G.B.P.U.A. & T, Pantnagar University since last 27 years. He has done his Ph.D from IIT Roorkee in the year He has been the recipient of several awards such as University Gold Medal in M.Sc. Engg. He is also life member of several institutions. 273 Vol. 7, Issue 1, pp
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