Empirical Determination and Analysis of Hourly Solar Heat Gain Factors in Wa, Ghana

Empirical Determination and Analysis of Hourly Solar Heat Gain Factors in Wa, Ghana

Emmanuel A. Sarsah, Felix A. Uba

Mechanical Engineering Department, Wa Polytechnic, Wa.

Abstract

The main purpose of the air conditioning system is to provide suitable internal thermal conditions of comfort to occupants or manufacturing applications. It is therefore necessary to perform cooling load calculations. By proper design and orientation of the building, the overall energy cost (initial and operational) can be reduced. Solar heat gain, through fenestration, particularly on vertical surfaces, is therefore a significant factor in determining the cooling load of commercial buildings; thus enabling proper sizing of air- conditioning equipment. SHGFs are site-dependent. In this work, SHGFs have been obtained from empirical correlations on the horizontal surface and for surfaces facing the four main cardinal points: North, South, East and West (N, S, E and W) for Wa (latitude 10.01°N, longitude 2.5°W) using design days of each month. Results show that SHGFs are dependent on the suns position in the sky and the direction of scattering of its radiation. It was also found out that horizontal and north-facing surfaces receive maximum annual mean solar heat

gains; values of about 418 W/m2. We also found out that substantial amount of solar heat gains could be avoided if more windows are placed in the southern and western directions. The SHGFs obtained will

help architects and building engineers in Wa to take into account solar geometry for calculating air- conditioning cooling loads.

Keywords: Solar Heat Gain Factors, horizontal surface, vertical surface, suns radiation.

1. Introduction

   Ghana has been experiencing a steady growth in electric power demand as a result of increasing economic activity and improvement in the standard of living such as the use of air conditioners (A/C) in both commercial and residential buildings. As a result, demand for electricity today far outstrips

   supply resulting in unstable and poor quality supply and load shedding. To meet this increasing demand

   for electricity and improve supply quality requires two approaches, namely, generate more power and/or economize the use of available power by avoiding wastage [1]. From surveys carried out by the Energy Foundation in Ghana, among others, air conditioners represent over 60% of the power usage in air- conditioned buildings [2]. Thus, energy-efficient air- conditioner usage in buildings will contribute immensely to reduce energy misuse in buildings and thereby reduce the strain on the national electricity grid. Solar heat gains come about as a result of direct solar radiation being transmitted through glazing to the building interior and indirect admittance of solar radiation to the building interior due to absorptance of solar radiation by the glazing. In the design of space to be air-conditioned, most architects and building engineers in Wa do not take into account solar geometry for the location as an energy consideration for the buildings orientation. This usually accounts for high energy requirements of the air conditioning equipment.It is necessary to have SHGF data that represent the prevailing weather conditions [3]. This is because SHGFs can be used to estimate solar heat gains for calculating air- conditioning cooling loads. The American Society of Heating, Refrigeration and Air-Conditioning Engineers Handbook(ASHRAE) [4] provides solar heat gain factors on cloudless days for daylight hours of 21st day of each month for a given window orientation at a particular latitude and time of year [3]. However, the effects of the suns position and the prevailing climatic conditions are the two essential variables for SHGF analysis. Hence, SHGFs are site- dependent.

   In this paper, we determined monthly hourly SHGFs empirically using the solar radiation data measured at Wa Polytechnic weather station on horizontal surface based on the formulae by [3], using monthly design days of Wa given by [5]. The monthly hourly SHGFs were determined for the horizontal surface and the four principal vertical orientations (N,S,E and W), based on available weather data from 7 am to 4 pm. We then explained the trend in the hourly values

   based on the suns position, the hour of the day and the atmospheric conditions.

2. Empirical Relations

   where is standard time, is the standard meridian (longitude) for the local time zone; = 0 for GMT zones like Ghana. is the longitude of the location (in degree west); = +2.5° and E

   is the equation of time, in minutes.

   1. Horizontal Surface

      Hourly SHGF (W/m2) for a horizontal surface,

      SHGFh, is given by [3]:

      SHGFh (I Id )(b Nib )

      E 9.87sin 2B 7.53cos B 1.5sin B

      and

      B (n 1) 360

      365

      (8)

      (9)

      I (0.799 0.0544N )

      (1)

      For an hourly period (e.g. 7 am – 8 am), the hour

      d i

      where

      is hourly horizontal radiation (W/m2), is hourly diffuse radiation (W/m2), is transmittance of the reference glazing for direct radiation, is

      angle is found at 7 am and at 8 am. 2 is the larger of the two values determined. Now [3] determined the following relations;

      absorptance of the reference glazing for direct

      radiation and is the inward flowing fraction of the absorbed radiation. The weather station at Wa Polytechnic measures the hourly horizontal radiation. The diffuse component of I, Idis determined empirically from a number of relations, outlined below. [6] determined

      0.00885 2.71235 cos 0.62062 cos2

      b

      b

      7.07329 cos3 9.75995 cos4

      3.89922 cos5

      b

      b

      0.001154 0.77674 cos 3.94657 cos2

      +8.57881cos3 8.38135 cos4

      +3.01188 cos5

      (10)

      (11)

      1 0.09 for kT 0.22

      I 0.9511 0.1604k 4.388k 2 16.638k 3

      d

      T T T

      T T

      T T

      I 12.336k 4 for 0.22 k

      0.165 for kT 0.80

      The clearness index,kTis given by

      0.80

      (2)

      The angle of incidence, is determined from [7]

      cos sin sin cos sin cos sin cos

      • cos cos cos cos

      • cos sin sin cos cos

        kT I / I0

        (3)

        • cos sin sin sin

      0 is the hourly extraterrestrial radiation on a horizontal surface given by [7]

      where

      (12)

      12 3600

      I G

      0 sc

      1 0.033 cos 360n

      365

      =slope; = 0 for horizontal surface and = 90 for

      vertical surface. =surface azimuth angle; zero due south, east negative and west positive. For a

      (cos cos (sin 2 sin 1 )

      (4)

      horizontal surface, = 0.

      /180(

      2 1 ) sin sin )

      Ni is given by [3]

      8.29

      where 2 > 1. is the solar constant (1367 W/m2), is the latitude of the location n is the day of

      Ni

      (8.29 (16.21Vs

      0.452 ))

      (13)

      the year, 1 365, is the declination angle given by

      Vs is the near surface wind speed obtained from the following relations;

      23.45 sin 360 284 n

      (5)

      Vs 0.68Vw 0.5

      (14)

      365

      for wind incidence angles of 20-160°, and

      The hour angle, is given by

      V 0.157V 0.027

      (15)

      (150 p )(t

      solar

      12h)

      (6)

      s w

      for oter wind incidence angles. Vw is the measured wind speed in m/s. Wind data were obtained from the

      The solar time,tsolar, is also given by

      tsolar tstd 4(Lst Lloc ) E

      (7)

      Wa Meteorological station from 2000-2012 since

      wind data for the Wa Polytechnic weather station could not be traced.

   2. Vertical Surface

      Hourly SHGF (W/m2) for a vertical surface, SHGFv,

      the particular orientation;, , cos, b, b, Ivd, Ivb, Rb

      and Iv.

      In order to relate the SHGFs obtained with the suns apparent movement in the sky, the following angles were computed; the solar altitude angle, s and the solar azimuth angle, s (as in Fig. 1).

      is given by [3]:

      SHGF H ( N ) I (0.799 (16)

      v v b i b g

      0.0544Ni )

      is hourly direct radiation on the plane of the vertical glazing, W/m2.

      H

      H

      I Id cos

      v sin

      (17)

      is the solar altitude angle given by

      z

      z

      90

      The zenith angle, is determined from

      (18)

      Figure 1:Sun's position in the sky [9]

      z

      z

      cos

      cos cos cos sin sin

      (19)

      90

      (26)

      s z

      s z

      I I H

      (20)

      sin cos cos cos sin

      s

      s

      g v v

      is the measured hourly global radiation on the

      cos

      (27)

      s

      s

      cos

      plane of the vertical glazing in W/m2. Here again, is determined from empirical relations since the weather station at Wa Polytechnic only measures I.

      Also, the sun does not rise exactly due east and set exactly due south. Instead, the sun may rise further north of east or further south of east, depending on

      I I I

      (21)

      the locations latitude and longitude. The sun-path

      v vb vd

      The diffuse component of I on the vertical surface,

      vd d

      vd d

      Ivdis given by [7]

      across the sky may be seen from Fig. 2.

      1 cos

      I I

      • I

      • I

      b d

      b d

      2

      I

      (22)

      2

      2

      1 cos

      is the hourly horizontal beam radiation (W/m2) and is found from

      b d

      b d

      I I I

      (23)

      R I

      R I

      I

      I

      The beam component of I on the vertical surface, Ivbis also given by

      Figure 2.Sun's Rise [10]

      where

      vb b b

      (24)

      A script file in MATLAB was written to aid in the

      cos( ) cos cos

      R

      R

      sin( ) sin (25)

      b cos

      calculations.

      z

      , the ground albedo is taken as 0.22 [8].

      In determining the SHGFv for the four main cardinal points, the following parameters were redefined for

3. RESULTS AND DISCUSSION

   SHGFs obtained from the empirical procedure outlined from section 2 are in Tables 1-4 for design days given by [5]

   Table 1.SHGF (W/m2): January-March

   Table 2.SHGF (W/m2): April-June

   Table 3.SHGF (W/m2): July-September

   Table 4.SHGF (W/m2): October-December

   The solar azimuth angles obtained indicate the sun rises north of east for the months of January, February, March, September, October, November and December. The sun rises south of east for the months of April to August. To avoid repetitive explanations, the trend in SHGF values for the

   months of January and June representing different rise of the sun have been explained in the next sections.

   1. January Trend

      At 7 am solar time, the solar azimuth and solar altitude angles are 115° and 13° respectively. This means the sun rises 25° north of east and is at a very low elevation. A surface facing North at this hour then experiences a higher solar heat gain than the horizontal surface because of the high diffuse component of the hourly radiation. There is also a high value of the heat gain for the east-facing surface compared to the horizontal surface (Figs. 3 and 4).

      January

      A south-facing surface obviously will have a low solar heat gain because of the rise of the sun at this hour. The value of the west-facing surface at this hour was found to be -333 W/m2. This means, the suns radiation had not reached the western-side at this hour; hence the surface looses heat. For purposes of solar heat gain, this value is accordingly set to zero. All other values of zero for other month represent the case of heat loss. At 8 am, the sun is a bit high in the atmosphere. The horizontal surface experiences an increase in value because there is an increase in the kT value meaning the sky is becoming clearer. The west-facing surface now experiences solar radiation and gains heat. There is a gradual increase in values for the other surfaces. Higher solar

      heat gains at solar hours of 9 am and 10 am for the

      600

      500

      SHGF (W/m 2)

      SHGF (W/m 2)

      400

      300

      200

      100

      0

      Horizontal

      North

      South East West

      7 8 9 10 11 12 13 14 15 16 17

      Solar Time

      west-facing surface means that most of the suns radiation is scattered westwards during the month of January at these hours. The atmosphere is clearer at

      11 am because of high kT value. The horizontal surface therefore has a higher heat gain compared to surfaces facing south, east and west. The east-facing surface has the lowest value at this hour because the suns radiation is focused westwards (relative to east direction). The sun is at its highest position at 12 pm with an azimuth angle of 175° and an altitude angle of 59°. There is more scattering towards the eastern direction hence a high value of solar heat gain for the

      Figure 3.SHGFs for horizontal and four vertical surfaces in January

      Sun-path diagram

      east-facing surface compared to the west-facing surface. The suns radiation is almost perpendicular to the horizontal surface. SHGF is still high because more of the suns radiation is focused onto the north

      and horizontal facing-surfaces. At 1 pm, the east-

      60

      55

      50

      Solar altitude, degrees

      Solar altitude, degrees

      45

      40

      9 am

      35

      30

      25 8 am

      20

      15

      7 am

      10

      1. am

      2. am

      3. pm

      1 pm

      2 pm

      3 pm

      4 pm

      facing surface shows an increase in value than the corresponding value at 12 pm, indicating that the suns radiation is scattered eastwards at this hour. From the hourly analysis, it can be concluded that most of the suns radiation is focused onto the north- facing surface.

   2. June Trend

      At solar time of 7 am, the solar azimuth and solar altitude angles are 69° and 22° respectively. This

      100 150 Solar azimuth, degrees 200 250

      Figure 4.Sun-path diagram: 15th January

      means the sun rises south of east and is relatively high in the sky. All surfaces receive radiation (Figs. 5 and 6). The diffuse component of solar radiation at this hour is very high.

      700

      600

      500

      SHGF (W/m2)

      SHGF (W/m2)

      400

      300

      200

      100

      0

      June

      Horizontal

      North South

      East

      West

      Horizontal

      North South

      East

      West

      7 8 9 10 11 12 13 14 15 16 17

      Solar Time

      facing surface and horizontal surface at 2 pm solar time indicate the fact that even though the sun is in the south-west position, most of its radiation is scattered eastwards and horizontally. At 4 pm there is no solar heat gain for the east-facing surface. The suns intensity is low and its scattering does not reach the east-facing surface.

      In order to obtain data that would be helpful for building engineers to assess the energy performance of buildings during the initial design stage, average hourly SHGFs were computed and are in Table 5.

      Table 5.Aerage SHGFs for Wa

      Figure 5.SHGFs for horizontal and four vertical surfaces in June

      Figure 6.Sun-path diagram: 24th June

      This is not surprising because the month of June is a rainy month in Ghana. The heat gains are therefore very small, with the horizontal surfaces receiving the highest heat gain. Values of SHGF indicate that there is more scattering of solar radiation onto horizontal surfaces for all hours for the month of June. Between 8 am and 9 am solar time, values increase because the sun is still rising (s=36° to 49°), with the southern and horizontal surfaces receiving higher heat gains. The high value of heat gain for the west-facing surface indicates scattering of the suns radiation westwards. This trend continues to 10 am solar time and 11 am solar time. There is now scattering of the suns radiation towards the north and continues up to 1 pm solar time. The higher heat gain values of east-

      The maximum average SHGF for the dry season months occurs on the north-facing surface. Values range from 436 W/m2 in January to 1183 W/m2 in December. The maximum mean SHGF for the rainy- season months occurs on the horizontal surface. Values range from 335 W/m2 in April to 566 W/m2 in May. The maximum horizontal average SHGF occurs in May. This indicates more clear days in May and more scattering of solar radiation onto the horizontal surface. For the vertical surfaces, the average SHGF ranges from 42 W/m2 in May for the north-facing surface to 1183 W/m2 in December still for the north- facing surface. The low value of SHGF in May indicates less solar intensity onto the north-facing surface. The high SHGF in December indicates diffuse sky conditions (e.g. due to the Harmattan) with more scattering of solar radiation onto the north-

      facing surface. Values of the SHGFs for the east- facing surface and west-facing surface are not symmetrical due to the same reasons outlined above. The 6-month dry season has higher SHGFs for all orientations compared to the 6-month rainy season. This means that due to the sun-path in Wa, all surfaces (i.e. H,N,S,E,W) receive more direct solar radiation than the diffuse component of solar radiation. Generally, electricity consumption due to air-conditioning equipment in the dry-season will be higher than that for the rainy-season.

      The maximum annual average SHGF occurs on the horizontal and north-facing surfaces followed by the east-facing surface, the west-facing surface and finally the south-facing surface. Values range from 222 W/m2 for the south-facing surface to 418 W/m2 for the horizontal surface. These have design implications. The very high values of SHGF for the horizontal surface imply that roof design with skylight is not desirable in Wa. More windows should be placed in the southern and western directions because of the relatively low values of SHGFs. For example, a building having 6 windows (1m2 area) distributed as follows; north=2, south=1, east=2,west=1, will have a total SHGF of 2172 W/m2. If the distribution is done as follows; south=3,west=2,east=1, the total SHGF will be 1589 W/m2. An extra 583 W/m2 is avoided and the air- conditioners consumption due to solar heat gain by fenestration is reduced. Calculations of this nature are required so as to give the arrangement with the least SHGF, hence the need to have SHGFs data.

4. Conclusion

SHGFs data is valuable for air-conditioning equipment sizing. In this paper, SHGFs based on empirical correlations have been determined for the horizontal surface and for surfaces facing the four main cardinal points: north, south, east and west. It was found out that SHGFs are dependent on the suns position in the sky and the direction of scattering of its radiation. For the dry season (October-March), it was found out that most of the suns radiation is focused onto the north-facing surface. Most of the suns radiation, however, is focused onto the horizontal surface in the rainy season (April- September). Annual average of SHGFs also showed

that the horizontal and north-facing surfaces receive almost equal amount of solar heat gain. For this reason, roof design with skylights is not recommended for residential and commercial buildings in Wa; except for commercial building application where lighting levels cannot be compromised. This is not surprising because most buildings in Wa do not have skylights. Buildings should be designed with more windows facing the southern and western surfaces based on the SHGF obtained. For already existing buildings with more windows facing the north, shading designs (e.g. using overhangs, blinds, frosted louver blades, etc.) should be provided. Further works, however, will be carried out to find the optimum angle and dimensions of overhangs for correct lighting levels in rooms.

Acknowledgement

The authors will like to thank the staff of the Agricultural Engineering Department, Wa Polytechnic, for their initiative for setting up the weather station for academic work.

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