Thermal Analysis of Solar Collectors

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1 Thermal Analysis of Solar Collectors Soteris A. Kalogirou Cyprus University of Technology Limassol, Cyprus Contents Types of collectors Stationary Sun tracking Thermal analysis of collectors Flat plate collectors Concentrating collectors Performance of solar collectors 1

2 Types of solar collectors Motion Stationary Single-axis tracking Two-axes tracking Collector type Absorber type Concentration ratio Indicative temperature range ( C) Flat plate collector (FPC) Flat Evacuated tube collector (ETC) Flat Compound parabolic collector (CPC) Tubular Linear Fresnel reflector (LFR) Tubular Parabolic trough collector (PTC) Tubular Cylindrical trough collector (CTC) Tubular Parabolic dish reflector (PDR) Point Heliostat field collector (HFC) Point Note: Concentration ratio is defined as the aperture area divided by the receiver/absorber area of the collector. Modes of Tracking 2

3 Comparison of energy absorbed for various modes of tracking Solar energy (kwh/m 2 ) Percent to full tracking Tracking mode E SS WS E SS WS Full tracking E-W Polar N-S Horizontal E-W Horizontal Note: E - Equinoxes, SS - Summer Solstice, WS - Winter Solstice Stationary collectors No concentration 3

4 Flat plate collector Flat plate Collector 4

5 Exploded view of a flat plate collector Gasket Header Glazing Riser tube Absorber plate Insulation Casing Types of flat plate collectors Water systems Glazing Riser Absorbing plate Glazing Riser Absorbing plate Insulation Insulation Glazing Riser Absorbing plate Glazing Riser Absorbing plate Insulation Insulation 5

6 Types of flat plate collectors Air systems Glazing Air passage Glazing Corrugated sheet Insulation Glazing Air flow Metal matrix Insulation Metallic foam Insulation Transpired air collector Hot air Fan Perforations Very suitable for BISTS Perforated absorber Ambient air Ambient air Plenum 6

7 Schematic diagram of an evacuated tube collector Evacuated tube collectors 7

8 Combination of collectors Collectors Flat diffuse reflector Reflector Evacuated tubes ICPC Collector Solar radiation Solar radiation Finned absorber 8

9 Stationary collectors Concentrating Flat plate collector with flat reflectors Sun rays Flat plate collector Flat reflector 9

10 Saw tooth arrangement Solar rays Collector Diffuse reflector Collector Horizontal roof Diffuse reflector Schematic diagram of a CPC collector 2θc 10

11 CPC types Application as flat plate collector Solar radiation Glass cover Absorber Casing Involute reflector 11

12 Sun tracking collectors Concentrating Schematic of a parabolic trough collector Sun rays Glass cover Receiver detail Parabola Receiver Receiver tube Tracking mechanism 12

13 Parabolic trough collectors Fresnel type parabolic trough collector Sun rays 13

14 Schematic diagram of a downward facing receiver illuminated from a Linear Fresnel Reflector (LFR) field Receiver Sun rays Tower Mirrors Schematic diagram showing interleaving of mirrors in a CLFR with reduced shading between mirrors Receiver Receiver Sun rays Tower Tower Mirrors 14

15 Photo of Fresnel system Schematic of a parabolic dish collector Sun rays Receiver Parabola Two-axes tracking mechanism 15

16 Schematic of central receiver system Thermal analysis of collectors 16

17 Flat plate collector thermal losses Flat plate collector thermal losses From the simple thermal network the collector thermal losses are: Tp Ta Qloss ULA c(tp T a) R L The total heat loss coefficient U L is given by: UL Ut Ub Ue (top, back, edges) The various relations can be obtained from basic heat transfer analysis 17

18 Empirical relation This relation gives adequate accuracy: U t 2 2 Tp Ta Tp Ta 1 Ng 1 2Ng f 1 N 0.33 C T p 0.05Ng1 p p T a 1 g Tp Ng f hw g Where: 2 w w g f 10.04h h N C h 8.6V L w The minimum value of wind heat loss coefficient, h w for still air is 5 W/m 2 K, so if above equation gives a lower value we use this value as a minimum. 2 18

19 Useful energy collected from a flat plate collector In the form of equation this is given by: Q u A c G t( ) UL Tp T a mcp To Ti Useful energy collected from a collector Flat plate General formula: Qu A c G t( ) UL Tp Ta mcp To Ti by substituting inlet fluid temperature (T i ) for the average plate temperature (T p ): Q A F G ( τα) U T T u c R t L i a Where F R is the heat removal factor 19

20 Heat removal factor Heat removal factor represents the ratio of the actual useful energy gain that would result if the collector absorbing surface had been at the local fluid temperature. Equation: mc p ULF'A c FR 1 Exp AU c L mc p F =collector efficiency factor Collector efficiency Finally, the collector efficiency can be obtained by dividing Q u by (G t A c ). Therefore: F R ( ) U L(Ti T a) G t 20

21 Concentration ratio The concentration ratio (C) is defined as the ratio of the aperture area to the receiver/absorber area, i.e.: For flat plate collectors with no reflectors, C=1. For concentrators C is always greater than 1. For a single axis tracking collector the maximum possible concentration is given by: 1 Cmax sin( m ) and for two axes tracking collector: 1 Cmax 2 sin ( ) m C A A a r where θ m is the half acceptance angle limited by the size of the sun s disk, small scale errors and irregularities of the reflector surface and tracking errors. Maximum concentration For a perfect collector and tracking system C max depends only on the sun s disk which has a width of 0.53 (32 ). Therefore: For single axis tracking: C max = 1/sin(16 ) = 216 For full tracking: C max = 1/sin 2 (16 ) = 46,747 21

22 Concentrating collectors The useful energy delivered from a concentrator is: Q G η A AU T T Where n o is the optical efficiency given by: And A f is the geometric factor given by: u b o a r L r a ηo ρταγ 1 Af tan( θ) cos( θ) A f 2 2 W a Wah p fwa f Concentrating collectors efficiency Similarly as for the flat plate collector the heat removal factor can be used: Q F G η A AU T T u R b o a r L i a And the collector efficiency can be obtained by dividing Q u by (G b A a ): n F η U R o L Ti T GC b a Note C in the denominator 22

23 PERFORMANCE OF SOLAR COLLECTORS The thermal performance of the solar collector is determined by obtaining: values of instantaneous efficiency for different combinations of incident radiation, ambient temperature, and inlet fluid temperature. the transient thermal response characteristics of the collector (time constant). the variation of steady state thermal efficiency with incident angles between the direct beam and the normal to collector aperture area at various sun and collector positions (incidence angle modifier). Collector efficiency For flat plate collectors: F( ) FU T T i a R R L G t For concentrating collectors: FU R L ( Ti Ta) η FRηo C G b 23

24 Efficiency plots More details on a special presentation η Flat plate collector η Concentrating collector Intercept = F R (τα) n Intercept = F R η ο Slope = -F R U L /C Slope = -F R U L ΔΤ/G t ΔΤ/G B Thank you for your attention, any questions please. 24

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