1. 1 Part B5: System design/performance prediction

2. 2 B5.1System design Irradiance: Variables Latitude at the point of observation Orientation of the surface in relation to the sun Day of the year Hour of the day Atmospheric conditions

3. 3 G b = Beam Irradiance normal to the earth’s surface (W m -2 ) G b,n = Beam Irradiance (W m -2 )  z = Zenith angle B5.1System design Irradiance on a horizontal surface

4. 4

5. 5 G b,t = Beam Irradiance normal to a tilted surface (W m -2 ) G b,n = Beam Irradiance (W m -2 ) = Angle of incidence B5.1System design Irradiance on a tilted surface

6. 6 R b,t =Ratio of Beam Irradiance normal to the earth’s surface to Beam Irradiance normal to normal to a tilted surface B5.1System design Irradiance on a tilted surface

7. 7

8. 8 R b,t = ratio of beam radiation on the tilted surface to that on a horizontal surface  = Latitude (degrees)  = Surface angle  = Declination (degrees)  = Hour angle (degrees) B5.1System design Irradiance on a tilted surface (facing the equator) Northern hemisphere Southern hemisphere

9. 9 B5.1System design Irradiance on a tilted surface Beam radiation

10. 10  opt = Optimum surface angle (degrees)  = Latitude (degrees)  = Declination (degrees) B5.1System design Irradiance on a tilted surface: Optimum tilt

11. 11 Beam radiation Air mass 1.0 Air mass 1.5 B5.2System design Irradiance: the atmosphere

12. 12 B5.2System design Irradiance: the atmosphere

13. 13 Direct Beam Ground Reflected Building Reflected Reflected Diffuse Beam B5.2System design Irradiance: Beam, reflected and diffuse

14. 14 B5.2System design Irradiance: Beam and diffuse

15. 15 k = Hourly clearness index K = Daily clearness index I = Hourly global radiation on a horizontal surface (kJ m -2 h -1 ) I o = Hourly extraterrestrial radiation on a horizontal surface (kJ m -2 h -1 ) H = Daily global radiation on a horizontal surface (kJ m -2 day -1 ) H o = Daily extraterrestrial radiation on a horizontal surface (kJ m -2 day -1 ) B5.2System design Irradiance: Beam and diffuse: Clearness index

16. 16 B5.2System design Irradiance: measurement of global irradiance: pyranometer

17. 17 B5.2System design Irradiance: global irradiance

18. 18 B5.2System design Irradiance: global irradiance

19. 19 B5.2System design Irradiance: diffuse radiation on a tilted surface

20. 20 B5.2System design Irradiance: diffuse radiation on a tilted surface

21. 21 B5.2System design Irradiance: global radiation on a tilted surface: Optical efficiency

22. 22 K  = incidence angle modifier R b,t = ratio of beam radiation on the tilted surface to that on a horizontal surface G = global radiation on a horizontal surface (kJ m -2 ) G  d  = diffuse radiation on a horizontal surface (kJ m -2 ) G  t  = global radiation on a tilted surface (Kj m -2 )  = Surface angle (degrees) = Incidence angle (degrees)  = Ground albedo b  = incidence angle coefficient (-0.1 for single glazing, -0.17 for double glazing) B5.2System design Irradiance: global radiation on a tilted surface: Optical efficiency

23. 23 G t = Total irradiance on a tilted surface (W m -2 ) G d = Diffuse irradiance (W m- 2 ) G = Total irradiance on a horizontal surface (W m -2 ) R b,t = ratio of beam radiation on the tilted surface to that on a horizontal surface  = Surface angle  = Ground albedo (reflectivity) – 0.2 for bare earth  = Ground albedo (reflectivity) – 0.7 for snow B5.2System design Irradiance: global radiation on a tilted surface

24. 24 K = Monthly average clearness index H = Monthly average daily global radiation on a horizontal surface (kJ m 2 /day) H o = Monthly average daily extraterrestrial radiation on a horizontal surface (kJ m 2 /day) B5.3System design Calculating monthly average daily global radiation: Clearness index

25. 25 H = Monthly average daily global radiation on a horizontal surface (kJ m -2 day -1 ) H o = Monthly average daily extraterrestrial radiation on a horizontal surface (kJ m -2 day -1 ) a’ = Constant b’ = Constant n = Average day length (hours) n max = Maximum day length (hours) B5.3System design Calculating monthly average daily global radiation

26. 26 Sunshine hours as a % of maximum possible a’b’ LocationRangeAve Alburquerque (USA) 68-85780.410.37 Buenos Aires (Argentina) 47-68590.260.50 Darien (China) 55-81670.360.23 Hamburg (Germany) 11-49360.220.57 Honolulu (Hawaii) 57-77650.140.73 Malange (Angola) 41-84580.34 Nice (France) 49-76610.170.63 Poona (India) dry 25-49370.300.51 Poona (India) monsoon 65-89810.410.34 Kisangani (Zaire) 34-56480.280.39 Tamanrasset (Algeria) 76-88830.300.43 B5.3System design Calculating monthly average, daily irradiance

27. 27 H o = Monthly average daily extraterrestrial radiation on a horizontal surface (kJ m -2 day -1 ) G sc = Extraterrestrial irradiance (W m -2 )  = Latitude (degrees)  = Declination (degrees)  s = Sunset angle (degrees) B5.3System design Monthly average, daily extraterrestrial irradiance

28. 28 B5.3System design Monthly average, daily irradiance

29. 29 B5.3System design Monthly average, radiation on a sloped surface (NH, facing the equator) R b,T = monthly average ratio of beam radiation on the tilted surface to that on a horizontal surface  = Latitude  = Surface angle  = Declination  s = Sunset angle  ss = Sunset angle on the tilted surface

30. 30 B5.2System design Monthly average, radiation on a sloped surface

31. 31 B5.3System design Monthly average, daily irradiance

32. 32 MonthMean day number January 17 February 47 March 75 April 105 May 135 June 162 July 198 August 228 September 258 October 288 November 318 December 344 B5.3System design Monthly average, daily irradiance: Mean day in the month

33. 33 H t = Daily global radiation on a tilted surface (kJ/m 2 /day) H = Daily global radiation on a horizontal surface (kJ/m 2 /day) H d = Daily diffuse radiation on a horizontal surface (kJ/m 2 /day) R b,t = ratio of beam radiation on the tilted surface to that on a horizontal surface  = Surface angle  = Ground albedo (reflectivity) – 0.2 for bare earth  = Ground albedo (reflectivity) – 0.7 for snow B5.3System design Daily irradiance: global radiation on a sloped surface

34. 34 B5.3System design Daily irradiance: Diffuse radiation

35. 35 B5.3System design Daily irradiance: Diffuse radiation: Clearness index

36. 36 H = Monthly average daily global radiation on a horizontal surface (kJ/m 2 /day) H d = Monthly average daily extraterrestrial radiation on a horizontal surface (kJ/m 2 /day) K = Monthly average clearness index  s = Sunset angle B5.3System design Daily irradiance: Diffuse radiation: Clearness index

37. 37 Hourly global on a horizontal surface B5.4System design Disaggregating monthly data solar constant Extraterrestrial radiation per day in the month Sunshine hours per day in the month Mean global radiation on a horizontal surface per day in a particular month Measured Meteorological data Latitude month Monthly or daily/hourly? Diffuse component Frequency distribution of global radiation – mean is not sufficient Daily or hourly? Daily Diffuse component Daily global radiation on tilted collector Hourly global radiation on tilted collector Monthly Daily/hourly DailyHourly

38. 38 B5.4System design Calculating daily irradiance

39. 39 K = clearness index K max = maximum clearness index K min = minimum clearness index (0.05)  = Constant B5.4System design Calculating daily irradiance

40. 40 K = Monthly average clearness index K max = maximum clearness index B5.4System design Calculating daily irradiance Temperate Monsoon

41. 41 K = Monthly average clearness index K min = minimum clearness index K max = maximum clearness index  = Constant B5.4System design Calculating daily irradiance

42. 42 B5.4System design Calculating daily irradiance K = clearness index K min = minimum clearness index K max = maximum clearness index K = Monthly average clearness index  = Constant Where

43. 43 B5.4System design Calculating daily irradiance

44. 44 H = Daily global radiation on a horizontal surface (kJ/m 2 /day) H d = Daily diffuse radiation on a horizontal surface (kJ/m 2 /day) K = clearness index B5.4System design Calculating daily irradiance

45. 45 B5.4System design Calculating hourly irradiance

46. 46 I = Hourly global radiation on a horizontal surface (kJ/m 2 /h) H = Daily global radiation on a horizontal surface (kJ/m 2 /day)  = Hour angle (at the middle of the hour)  s = Sunset angle (hours) a = Constant ( 0.409 + 0.5016 sin(  s – 60) ) b = Constant ( 0.6609 + 0.4767 sin(  s – 60) ) B5.4System design Calculating hourly irradiance

47. 47 I d = Hourly diffuse radiation on a horizontal surface (kJ m -2 h -1 ) H d = Daily diffuse radiation on a horizontal surface (kJ m -2 day -1 )  = Hour angle (at the middle of the hour)  s = Sunset angle (hours) B5.4System design Calculating hourly irradiance

48. 48 B5.4System design Calculating hourly irradiance

49. 49 I = hourly global radiation on a horizontal surface (kJ m- 2 h) I d = hourly diffuse radiation on a horizontal surface (kJ m -2 h) k = Hourly clearness index I o = hourly beam extraterrestrial radiation (kJ m- 2 h) B5.4System design Calculating hourly irradiance

50. 50 B5.4System design Using hourly irradiance

51. 51 B5.5System design Performance prediction Detailed simulation –Most accurate method –Data and processing time hungry Utilisability –Uses statistics to generate daily, monthly or yearly output –T ci must be known and independent (not closed loop) Empirical methods –Based on detailed simulations and empirical correlations –Only applicable to a limited range of systems –Examples f-chart, BS5918 Simplified analytical approaches –Useful if thermal load is constant One-day repetitive method –Detailed simulation of statistically derived “day” – derivation of day is data hungry Commercial software

52. 52 B5.5System design Performance prediction UtilisabilityEmpirical correlationSimplified Analytical approach One-day repetitive HourlyDailyf-chartPhibar f-chart TMDMIRA ApplicationIndustrial process heat Space and domestic water heating Hot water and industrial process heat Industrial process hot water Any preheat application Thermal load characteristic Diurnally varying or constant Constant over time scale Pre- specified monthly load diurnal distribution Constant over time- scale of one month Constant over time- scale Diurnally varying or constant over time scale Solar thermal system configuration No- storage systems No-storage or seasonal systems Closed - loop Open-loopAny Types of solar thermal system Air and liquid systems Liquid systems Air and liquid systems

53. 53 B5.5System design Performance prediction UtilisabilityEmpirical correlationSimplified Analytical approach One-day repetitive HourlyDailyf-chartPhibar f-chart TMDMIRA Collector type developed for Flat plate Any Flat plate Collector type applicable to Any Flat plateAny Level of flexibility Restricted High Time scale originally developed for Monthly Yearly Monthly Time scale applicable to Seasonal and yearly YearlyMonthlySeasonalSeasonal and monthly OptimisationSearch method DirectSearch method Level of skill required Low Average

54. 54 B5.5.1System design Performance prediction: Utilisability Mainly used for industrial applications or applications with a large store If T ci (or how it varies) is known and repeats daily, for a month or a year –it is possible to simulate the contribution of each hour’s (say 11:00-12:00) collection over a period –By adding the hours the total energy collected in the month can be calculated Can only be used for closed loop systems if the input to the heat exchanger is known and constant

55. 55 Q cm = heat gained in a particular hour over the month A c = collector area (m 2 ) F R = heat removal coefficient  o = monthly average optical efficiency I t = monthly average hourly global radiation on a tilted surface (kJ m -2 h -1 )  = hourly utilisability N = number of days in the month i = ith hour B5.5.1System design Performance prediction: Utilisability

56. 56 B5.5.1System design Performance prediction: Utilisability: critical threshold From the HWB equation If heat losses balance heat gains – no output. So When Q =0 So for useful output Where I c is the critical radiation

57. 57 B5.5.1System design Performance prediction: Utilisability: critical threshold

58. 58 B5.5.1System design Performance prediction: Utilisability: hourly utilisability Summing Q over N days So A radiation statistic –The fraction of hourly radiation that can be converted into useful heat by an optically ideal collector

59. 59 X = Radiation ratio X c = Critical radiation ratio  i = hour collector utilisability I t = hourly global radiation on a tilted surface (kJ m -2 h -1 ) I c = hourly critical global radiation on a tilted surface (kJ m -2 h -1 ) I t = monthly average hourly global radiation on a tilted surface (kJ m -2 h -1 ) B5.5.1System design Performance prediction: Utilisability: hourly utilisability: radiation ratios If we define Then and

60. 60 B5.5.1System design Performance prediction: Utilisability: hourly utilisability

61. 61 B5.5.1System design Performance prediction: Utilisability: daily utilisability

62. 62 B5.5.1System design Performance prediction: Utilisability: daily utilisability  i = Daily collector utilisability N = number of days in the month n = number of hours in the day X = Daily radiation ratio X c = Daily critical radiation ratio I t = hourly global radiation on a tilted surface (kJ m -2 h -1 ) I c = hourly critical global radiation on a tilted surface (kJ m -2 h -1 ) I t = monthly average hourly global radiation on a tilted surface (kJ m -2 h -1 ) H t = monthly average daily global radiation on a tilted surface (kJ m -2 h -1 )

63. 63 B5.5.1System design Performance prediction: Utilisability: daily utilisability  i = hour collector utilisability K t = Monthly average clearness index X c = Critical radiation ratio R b,t = Monthly average ratio of beam radiation on the tilted surface to that on a horizontal surface

64. 64 B5.5.1System design Performance prediction: Utilisability: daily utilisability  = Monthly average daily utilisability X c,k = Monthly average critical radiation ratio R t = Monthly average ratio of global radiation on the tilted surface to that on a horizontal surface R t,noon = Monthly average ratio of global radiation on the tilted surface to that on a horizontal surface at noon K t = Monthly average clearness index

65. 65 B5.5.1System design Performance prediction: Utilisability: daily utilisability X c,k =monthly average critical radiation ratio I c =hourly critical global radiation on a tilted surface (kJ m -2 h -1 ) I t,noon =monthly average hourly global radiation on a tilted surface at noon (kJ m -2 h -1 ) r noon =monthly average ratio of hourly global radiation on a horizontal surface at noon to that on the same surface over the day R t,noon =monthly average ratio of global radiation on the tilted surface to that on a horizontal surface at noon H = monthly average daily global radiation on a horizontal surface (kJ m -2 h -1 )

66. 66 B5.5.1System design Performance prediction: Utilisability: hourly utilisability

67. 67 I = Monthly average hourly global radiation on a horizontal surface (kJ m -2 h -1 ) H = Monthly average daily global radiation on a horizontal surface (kJ m -2 day -1 )  = Hour angle (at the middle of the hour)  s = Sunset angle a = Constant ( 0.409 + 0.5016 sin(  s – 60) ) b = Constant ( 0.6609 + 0.4767 sin(  s – 60) ) B5.5.1System design Performance prediction: Utilisability: daily utilisability : Calculating hourly irradiance

68. 68 B5.5.1System design Performance prediction: Utilisability: daily utilisability R t,noon = Ratio of global radiation on the tilted surface to that on a horizontal surface at noon R b,t = Ratio of beam radiation on the tilted surface to that on a horizontal surface  = Surface angle I t = Hourly global radiation on a tilted surface (kJ m -2 h -1 ) I = Hourly global radiation on a horizontal surface (kJ m -2 h -1 ) H d = Daily diffuse radiation on a horizontal surface (kJ m -2 day -1 ) H = Daily global radiation on a horizontal surface (kJ m -2 day -1 ) r d = Ratio of hourly diffuse to daily diffuse radiation on a horizontal surface r = Ratio of hourly global to daily diffuse radiation on a horizontal surface Monthly average value of R at noon on an average day

69. 69 B5.5.1System design Performance prediction: Utilisability: energy dumping

70. 70 B5.5.1System design Performance prediction: Utilisability: energy dumping  u,i = Monthly average daily dump utilisability

71. 71 B5.5.2System design Performance prediction: Empirical correlations: f-chart Based on an empirical correlation from a large number of detailed simulations Only one calculation for each month Only applicable for a few standard systems One equation represents f m the fraction of the load met by solar energy

72. 72 B5.5.2System design Performance prediction: Empirical correlations: f-chart

73. 73 B5.5.2System design Performance prediction: Empirical correlations: f-chart

74. 74 A c = collector area (m 2 ) F’ R = De Winter heat exchange factor U L = Heat loss coefficient T REF = 100ºC T A = Monthly average ambient temperature  t = number of seconds in a month (3600 x 24 x N) Q LM = Monthly total load  o = monthly average optical efficiency H T = Monthly average daily radiation on the collector (J m -2 ) B5.5.2System design Performance prediction: Empirical correlations: f-chart

75. 75 B5.5.2System design Performance prediction: Empirical correlations: f-chart

76. 76 B5.5.2System design Performance prediction: Empirical correlations: f-chart f m = fraction of the load met by solar energy

77. 77 B5.5.2System design Performance prediction: Empirical correlations: f-chart: Assumptions

78. 78 Store volume – 75 l m -2 B5.5.2System design Performance prediction: Empirical correlations: f-chart: Assumptions For different volumes change X to X c : Valid for:

79. 79 B5.5.2System design Performance prediction: Empirical correlations: f-chart: Assumptions  L = load heat exchanger effectiveness For different values change Y to Y c : Valid for:

80. 80 B5.5.2System design Performance prediction: Empirical correlations: f-chart: Hot water only

81. 81 B5.5.2System design Performance prediction: Empirical correlations: f-chart: Hot water only

82. 82 B5.5.2System design Performance prediction: Empirical correlations: f-chart: Hot water only Valid for:  w = hot water temperature  m = mains (cold) water temperature   = mean ambient temperature

83. 83 B5.5.3System design Performance prediction: Empirical correlations: Philbar f-chart Similar to f-chart but for industrial applications Any water inlet temperature is allowed Any water outlet temperature is allowed Constant load over the whole month No load dumping

84. 84 B5.5.3System design Performance prediction: Empirical correlations: BS5918 Based on simulations in the UK using a reference system Assumes –Direct system with preheat –Preheat vessel with a volume >0.8 x load –Load 100 l/day at 55º C. Each person uses 30 l/day. –Cold water is about 14º C –Flow rate 0.02 kg/s/m 2 –Pump is on when T > 1.5º C and off when <4º C –The weather is based on London

85. 85 Class U/   Typical type B <3Advanced C 3-6Vacuum tube D 6-9Single glazed with selective surfaces E 9-13Single glazed with matt black coating F >13Unglazed B5.5.3System design Performance prediction: Empirical correlations: BS5918

86. 86 B5.5.3System design Performance prediction: Empirical correlations: BS5918

87. 87 B5.5.3System design Performance prediction: Empirical correlations: BS5918

88. 88 B5.5.4System design Performance prediction: Simplified analytical methods Single expression for annual output Useful in industrial applications –inlet temperature and load are known and constant throughout the year –The system runs when there is sunshine and doesn’t when there isn’t

89. 89 B5.5.4System design Performance prediction: Simplified analytical methods

90. 90 B5.5.4System design Performance prediction: Simplified analytical methods Q u = Total useful energy over the year (GJ m -2 y -1 )  = Latitude (radians) G b,n = Annual average beam radiation at usual incidence = 1.37K – 0.34 (kW m -2 ) A c = Collector area (m -2 ) F R = Heat removal factor  n = Optical efficiency at usual incidence  c = Critical radiation ˜ ˜

91. 91 B5.5.4System design Performance prediction: Simplified analytical methods Q u = Total useful energy over the year(GJ m -2 y -1 ) a = Local constant b = Local constant c = Local constant ˜ ˜ ˜

92. 92 B5.5.4System design Performance prediction: Simplified analytical methods P L = Thermal heat demand of the load (kW) m L = Flow rate across the load (kg s -1 ) C p = Specific heat (J kg -1 ) T Li = Temperature at the load inlet (K) T Xi = temperature of the mains water (K).

93. 93 B5.5.4System design Performance prediction: Simplified analytical methods Qu = Usable energy/year (kJ) P L = Thermal heat demand of the load (kW) a = Local constant b = Local constant c = Local constant ˜ ˜ ˜

94. 94 B5.5.4System design Performance prediction: One-day repetitive method Very flexible – most types of system can be modelled Uses a “typical meteorological day” (TMD) –Has the correct statistical distribution of all hourly radiation on the collector –Has the correct mean daily radiation –Is symmetrical about solar noon –Reaches a maximum at solar noon –Is zero at collector sunrise and sunset cumulative frequency distribution mirrored about noon satisfies these criteria

95. 95 B5.5.4System design Performance prediction: One-day repetitive method

96. 96 B5.5.4System design Irradiance: Beam and diffuse

97. 97 B5.5.4System design Performance prediction: One-day repetitive method A cumulative frequency distribution is generated and mirrored about noon to form the TMD An initial storage temperature is assumed System is simulated over the TMD repeatedly until the final storage temperature converges with the initial storage temperature

98. 98 Next - Concentrating collectors