Energy saving by proper tree plantation

\ PERGAMON

Building and Environment 23 "0888# 454Ð469

Energy saving by proper tree plantation S[ Raeissi\ M[ Taheri Chemical Engineering Department\ Shiraz University\ Shiraz\ Iran Received 03 May 0886^ received in revised form 19 May 0887^ accepted 05 September 0887

Abstract A model is presented to predict the e}ect of trees as passive cooling options on buildings[ A computer program is written to calculate hourly cooling load requirements by the numerical solution of the energy balance equation for the building[ This simulation is validated by comparison with _eld data taken from an actual house in Shiraz\ Iran[ A guideline is presented for optimum tree plantation concerning energy saving[ Results indicate that for the house under study "of popular size in Shiraz# cooling loads may be reduced by 09Ð39) by appropriate tree plantation[ Þ 0888 Elsevier Science Ltd[ All rights reserved[ Keywords] Trees^ Shading^ Passive cooling

Nomenclature CF fractional cloud cover\ dimensionless D instantaneous di}use solar radiation ðW m−1Ł f "t# heat ~ux de_ned in eqn 3 ðW m−1Ł h heat transfer coe.cient ðW m−1 K−0Ł Ih instantaneous direct solar radiation on horizontal surface ðW m−1Ł k thermal conductivity ðW m−0 K−0Ł l\ m\ n direction cosines of sun beams\ dimensionless qsky sky radiation per unit area ðW m−1Ł QAI cooling load due to air in_ltration ðWŁ QC cooling load due to air conditioners ðWŁ Qdw heat transfer rate through doors and windows ðWŁ Qf heat transfer rate through ~oors ðWŁ QI cooling load due to lights\ appliances\ occupants\ etc[ ðWŁ QR heat transfer rate through roof ðWŁ Qw heat transfer rate through outer walls ðWŁ Rt radius of tree t time ðsŁ T temperature ðKŁ Tsky sky temperature ðKŁ x distance from outer surface of roof or walls ðmŁ lowest height of roof z9 Greek symbols a absorptivity of surface\ dimensionless

 Corresponding author[ Tel[] 99 87 60 292960^ fax] 99 87 60 41614

g gs o u uz s

wall azimuth angle solar azimuth angle emissivity\ dimensionless angle of incidence ðdegŁ zenith angle ðdegŁ Boltzmann constant ðW m−1 K−3Ł

Subscripts A ambient b center base of tree c center of spherical shaped tree g ground L inner surface of roof or walls N generic point in space R room "inside of building# T points on tree O outer surface of roof or walls

0[ Introduction In early times\ before the invention of mechanical forms of refrigeration\ ingenious uses were made of the available sources of coolness to provide thermal comfort in hot climates[ Due to the shortage of nonrenewable energy sources and environmental pollution problems\ once again e}ort is being made to reduce the high energy consuming methods of mechanical refrigeration and air conditioning\ and instead to establish systems which make use of {natural cooling| with even higher e.ciencies than in the past ð0Ł[ Of the many available systems for reaching this goal\ tree plantation is a delightful option

9259Ð0212:88:, ! see front matter Þ 0888 Elsevier Science Ltd[ All rights reserved PII] S 9 2 5 9 Ð 0 2 1 2 " 8 7 # 9 9 9 3 5 Ð 7

455

S[ Raeissi\ M[ Taheri : Buildin` and Environment 23 "0888# 454Ð469

achieving much more than just energy saving] reducing noise and air pollution\ modifying temperature and rela! tive humidity and having great psychological e}ects on humans[ Trees can modify both the microclimate around a building and the macroclimate of a region[ The sig! ni_cance of trees as passive options is in the charac! teristics of growing leaves in the hot summer months when shading is most needed and loosing them in the cool winter season when shading is not desired[ The variability of the elements involved in the treeÐ environment interaction\ makes the establishment of design guidelines very di.cult\ but there seems to be a growing interest in this subject in literature[ The advan! tage of using trees for summer shade has been pointed out in a large number of references\ but very little data can be found giving quantitative information about the e}ects of trees on shading[ Kay et al[ ð1Ł presented tech! niques using diagrams for the estimation of the solar access to buildings[ Maksoumi ð2Ł used scale models of trees for determining the resulting shadow patterns[ Budin and Budin ð3Ł and Sassi ð4Ł described mathematical models for shading calculations and Fanchiotti et al[ ð5Ł presented some applications of a computer program in determining the shadows cast by obstructions[ Sattler et al[ ð6Ł calculated the area and position of shadows cast by trees on a surface of any orientation and inclination[ In the present work a computer program is written which predicts the position of shadows cast by trees on buildings at di}erent hours in a day and di}erent days of the year[ The overall cooling load reduction caused by shadows on di}erent facing walls and windows is also predicted by the program and a guideline is presented for appropriate relative positioning between buildings and trees for Shi! raz and similar latitudes[ 1[ Theoretical model of the building

−k

1T 1x

b

 hL"TL−TR#

"1#

xL

Where L is the thickness of the roof[ At the outer surface\ other than convection from the ambient air\ there is also a net heat ~ux to the surface caused by radiation[ −k

1T 1x

b

 hA"TA−TO#¦f "t#

"2#

x9

The radiation ~ux denoted by f "t#\ may be divided into several parts\ each acting parallel to each other\ namely direct and di}use solar radiation and sky radiation[ For horizontal roofs\ f "t# will take the form ð7Ł f "t#  a"Ih¦D#¦qsky

"3#

Ih and D\ the instantaneous direct and di}use solar radi! ation on horizontal ~at surfaces in W m−1 are determined by the empirical equations given by Daneshyar ð09Ł for radiation in Iran Ih  "0−CF#"840[44ð0−exp=−9[964"89−uz#=Ł#"cos uz# "4# D  0[321¦1[096"89−uz#¦010[2CF

"5#

where CF is the fractional cloud cover\ and uz is the zenith angle in degrees[ The net radiation from the sky is calculated using qsky  os"T3sky−T3O#

To calculate cooling loads in summer\ by assuming that the air inside a building is at constant temperature\ the energy balance for the building is ð7Ł Qc  QR¦Qw¦Qdw¦Qf¦QI¦QAI

numerically[ This is done by dividing the roof and walls into three!dimensional space nodes and determining the temperature of each node at successive time intervals[ Assuming that the net radiation on the inner surfaces is negligible\ the boundary condition at these surfaces is ð7Ł]

"6#

in which Tsky  9[9441T0[4 A

"7#

"0#

Due to the time dependent terms on the right side\ this equation must be solved numerically[ 1[0[ Calculation of heat loads The loads due to the ~oor\ lights\ appliances\ occupants and in_ltration are estimated by the methods given in the ASHRAE Handbook of Fundamentals ð8Ł[ 1[1[ Heat ~ux through roof and walls Heat transfer through the roof and walls is determined by solving the unsteady state heat conduction equation

For vertical walls the net radiation ~ux takes the form ð7Ł]

6

f "t#  aIh

cos u D rg qsky ¦ ¦ "Ih¦D# ¦ cos uz 1 1 1

7

"8#

where u is the angle of incidence of solar radiation on the wall\ rg is the re~ectivity of the ground\ and the 0:1 multipliers are the shape factors of vertical surfaces to sky and ground[ Of course each wall is treated separately since the radiation incident upon it di}ers with direction[ In this manner the temperature pro_les of the roof and walls are set up for each time step\ from which the heat ~ux through the slab is easily obtained[

S[ Raeissi\ M[ Taheri : Buildin` and Environment 23 "0888# 454Ð469

456

1[2[ Heat ~ux through windows The transmittance\ re~ectance\ and absorptance of glass windows are functions of the angle of incidence of radiation\ which itself varies throughout the day[ Thus a precise numerical approach is set up which\ after esti! mating the angle of incidence of direct solar radiation at each time step\ will determine the transmissivity\ re~ect! ivity\ and absorptivity of the glass for both direct and di}use radiation at that time step[ This is followed by the estimation of the glass temperature by use of an energy balance written around the glass[ Finally the load due to windows is estimated as the sum of transmittance and conductance of the windows[ Windows facing di}erent directions are also treated separately due to the variations of incident solar radiation ð7Ł[ Fig[ 0[ The shadow of a spherical shaped tree[

2[ Simulation of trees In order to _nd where the shadows of a tree will be at di}erent hours of a day throughout the year\ three elements must be taken into account] the tree geometry\ the position of the sun in the sky at the required times and the position of the surfaces to be shaded[ It has been suggested that any tree can be typi_ed either as having a spherical\ conical or cylindrical shape or as being the result of some sort of combination of these shapes[ In this work the geometry of the shadows are obtained by the method of Sattler et al[ ð6Ł[ A system of coordinate axes is considered with origin O\ on the bottom left!hand corner of the surface in question\ so that the z!axis points to the zenith and the x! and y!axes are on the horizontal plane\ with the x!axis pointing outwards from the surface and the y!axis pointing to the right[ A sun ray can be referred to in relation to this system of coordinate axes by means of its direction cosines\ which are the cosines of the angles that the sun ray makes with the positive directions of the coordinate axes[ Thus\ if the surface to be shaded by the tree has a wall azimuth angle g\ solar azimuth angle gs\ and solar altitude angle hs\ then the direction ratios de_ning the sun beam will be l  cos hs cos "g−gs# p m  cos hs cos ¦g−gs 1

0

n  sin hs

"09#

1

Fig[ 0[ For a vertical wall de_ned by x  9\ the resulting ellipse will be ð6Ł "0−m1#y1"0−n1#z1−1mnyz¦1"mk−Yc#y ¦1"nk−Zc#z¦c  9

"02#

where k  lXc¦mYc¦nZc

"03#

and c  X 1c ¦Y 1c ¦Z 1c −k1−R 1t

"04#

On the other hand\ the roof can be expressed by z  zO−x tan a

"05#

where zO is the lowest z value on the roof\ and a is the inclination of the roof[ Thus\ the intersection of the cylindrical shade with the roof is given by ð6Ł ð0−"l−n tan a#1¦tan1 aŁx1¦"0−m1#y1 −1"l−n tan a#mxy−1ðXc¦zO tan a −Zc tan a¦"l−n tan a#"nzO−k#Łx −1ðYc¦m"nzO−k#Ły¦z1O

"00# "01#

−1ZOZc−n1z1O¦1knzO¦c  9

"06#

2[1[ The geometry of the shade of conical and cylindrical shaped trees

2[0[ The geometry of the shade of spherical shaped trees A spherical shaped tree will be speci_ed by the coor! dinates of its center Xc\ Yc\ and Zc\ and its radius Rt[ The intercepts of the sun|s rays with a spherical tree produce a cylinder of shade[ When incident on a ~at surface\ this cylinder of shade will de_ne an ellipse as can be seen in

In their simulation\ Sattler et al[ ð6Ł assume that both conical and cylindrical shaped trees have vertical axes and that they have bases normal to their axes[ In order to _nd their shadows it is necessary to project as many points as possible from two circles "cylinder# or one circle and one point "cone# onto a plane\ considering parallels

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457

"cone# or bases "cylinder# of the tree[ The pairs of coor! dinates found in this manner] "X0\ Y0#\ "X1\ Y1#\ [ [ [ \ "Xn\ Yn#\ together with the z!coordinate of the tree base\ can then replace the values of XN\ YN and ZN in eqn "19#\ thus determining as many points as needed to be pro! jected onto the walls[ In order to draw the contours of a shadow\ it is impor! tant to calculate the coordinates of the points positioned between straight lines and curves\ where a transition occurs on the contour of the shadow[ These points can be found by projecting the corresponding points on the tree surface\ with coordinates Zb or Zt belonging to the base of a cone or cylinder and XT and YT\ onto the plane in question[ XT and YT are estimated by

Fig[ 1[ The shadow of a conical shaped tree[

to the solar beam through these points and then to draw the contours of the shadows by linking these projections "see Figs 1 and 2#[ The base of a cone or cylinder is a circle that can be described by radius Rt and the coordinates of its center "Xb\ Yb\ Zb#\ with respect to the coordinate system[ The equation of this circle will be "x−Xb#1¦"y−Yb#1  R1t

"07#

and z  Zb

YT  Yb2Rt

XT  Xb¦

0

l1 m1¦l1

1

0 1

"10#

m "Yb−YT# l

"11#

Similarly\ the projection of the top of the cone can be found by replacing the value of ZN in eqn "19# by the corresponding z!value of the top of the cone and x and y by Xb and Yb[

"08#

The equation of the straight line parallel to the sun! beam containing a generic point in space with coordinates XN\ YN\ and ZN will be x−XN y−YN z−ZN   l m n

"19#

By giving an adequate value to y "or x# in eqn "07# the corresponding value of x "or y# is calculated[ This can be repeated for points 0\ 1\ [ [ [ \ n\ positioned on the base

3[ Experimental procedure The residential building under experiment is a one! storey house with no common walls with other buildings[ This case study is situated in Shiraz\ Iran\ at an altitude of 0380 m\ latitude angle of 18[5> N and longitude angle of 41[42> E and is directed towards the south[ It is cooled in summer by an evaporative water cooler[ The house has a ~oor area of 039[44 m1 and a height of 2 m[ Wall and glass areas are given in Table 0 for each side of the building ð7Ł[ A program is set up to simulate the thermal behavior of the house[ Cooling loads are calculated for each hour and summed up over 13 h to obtain the daily total cooling load[ Numerical values of the constant parameters used in this simulation are given in Table 1[

Table 0 Wall and window "glass# area of test building

Fig[ 2[ The shadow of a cylindrical shaped tree[

Direction

Wall area ðm1Ł

Glass area ðm1Ł

South West North East

16[14 21[16 35[09 17[58

13[51 2[65 4[84 6[02

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458

Table 1 Constant values used in the simulation of test building Ambient air] Wind velocity Average relative humidity Pressure Roof] Roof thickness Emissivity Conductivity Density Speci_c heat Walls] Wall thickness Emissivity Conductivity

09 km h−0 9[13 74299 Pa

9[21 m 9[77 9[610 W m−0 >C−0 0599 Kg m−2 739 J Kg−0 >C−0

9[21 m 9[4 9[78 W m−0 >C−0

4[ Results The validity of the simulation program has _rst been checked by comparing the actual sensible cooling and heating provided by the cooler and heater with loads estimated by the program for a few random days in summer and winter[ The results of these comparisons are given in our earlier paper ð7Ł[ Good matching was observed for both seasons[ This validated program was then used to study the e}ects of tree shadows on cooling loads of buildings[ As an optimum sunshine shielding system\ cylindrical trees were chosen side!by!side and touching each other[ By noting that the rays of sunshine are all parallel\ it is not the actual dimensions of the tree!wall geometry that are important\ but rather the various ratios of the lengths ð6Ł[ Thus the ratio of tree height to distance from wall "Zt:X# was varied for each wall of the house[ The day chosen for this analysis was 10 June since it is the longest day of the year[ The estimated results are shown in Figs 3 and 4[ The e}ect of the ratio of tree height to tree distance on heat ~ux through windows is given in Fig[ 3 for each side of the building and Fig[ 4 shows the same e}ect for the walls[ As shown\ heat ~uxes through south and north faces are not much altered by trees in summer^ north faces barely receive any sunshine and south faces receive high noon sunshine which is better blocked by overhangs than trees[ Both east and west windows and walls\ receiving low morning and afternoon sunshine\ are greatly a}ected by trees[ Increasing the tree height to distance ratio has larger e}ects at lower ratios but starts to level o} at ratios of 2Ð3[ As an overall energy guideline for tree plantation at latitudes of about 29>\ it is suggested to use coniferous trees on east and west faces of a building whenever these walls are exposed[ By taking into account the maximum obtainable height of the chosen trees\ they should be

Fig[ 3[ E}ect of tree height to tree distance on heat ~ux through window on 10 June\ Zb:X  9[1[

Fig[ 4[ E}ect of tree height to tree distance on heat ~ux through walls on 10 June\ Zb:X  9[1[

planted at a distance which ful_lls the criterion of height: distance × 2Ð3[ Evergreens are not desirable on east and west sides[ North facing walls and windows do not receive summer sun so design is not based on shadow e}ects\ but planting a condensed row of evergreen trees and bushes on this side can help block cold north winds in winter[ South face plantation is left to the personal preference of the habitants but use of evergreens should be discarded to prevent shadows in winter[ Tables 2 and 3 give the daily cooling load and the percentage of reduction of the load for the test building on 10 June for cases where there are no trees\ trees with height:distance  3 on east\ west\ and both east and west

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469

Table 2 E}ect of tree shadows on overall daily cooling load of test house on 10 June with no ambient air temperature reduction

perature reduction of green trees[ It is seen that up to 39) reduction is obtainable with correct plantation[

Trees on

Cooling load ð097 JŁ

) Reduction

5[ Conclusions

No sides East side West side East and West sides

6[34 6[99 6[03 5[58

* 5[9 3[1 09[1

Trees are ideal passive options decreasing summer loads by blocking sunshine and reducing ambient air temperature\ while having insigni_cant e}ects in winter by loosing their leaves[ Thus correct tree planation on each side of the building is important and can lead to desirable energy e}ects[ Trees can act complementary to window overhangs\ as they are better for blocking low morning and afternoon sun while overhangs are better barriers for high noon sunshine[

Table 3 E}ect of trees on overall daily cooling load of test building on 10 June with 2>C ambient air temperature reduction Trees on

Cooling load ð097 JŁ

) Reduction

No sides East side West side East and West sides

6[34 3[672 3[758 3[368

* 24[7 23[6 28[8

sides[ To show the e}ect of shading alone\ the results of Table 2 are for the imaginary case of no ambient temperature reduction caused by trees[ It is seen that tree shading alone reduces cooling load by 09)[ In reality\ trees contribute even more than this[ Due to their evap! oration and perspiration\ they can also reduce the tem! perature of the ambient air "either microclimate or macroclimate#[ Experimental measurements in Shiraz showed that in summer\ the temperature in a heavy tree populated area was about 1Ð4>C less than an area where very little trees were found[ The extent of ambient air temperature reduction caused by trees in a particular location is a very complicated function of the surface area covered by trees\ the number of trees per unit area\ size and type of trees\ and the rate of irrigation[ With present knowledge\ it is almost impossible to exactly determine the temperature e}ects of trees in a particular site[ But to have an approximate\ cooling loads were also estimated by taking an average ambient temperature reduction of 2>C caused by trees[ The results presented in Table 3 show the overall e}ect of shading and tem!

Acknowledgements The authors wish to acknowledge Shiraz University Research Council for their _nancial support[ References ð0Ł Raeissi S\ Taheri M[ Cooling load reduction of buildings using passive roof options[ Renewable Energy 0885^6[ ð1Ł Kay M\ Hora U\ Ballinger JA\ Harris S[ Energy!E.cient Site Planning Handbook[ Sydney] The Housing Commission of New South Wales\ 0871[ ð2Ł Maksoumi JM[ Low energy alternatives for site planning through the use of trees in a hot arid climate[ Proceedings of The Second International PLEA Conference[ Oxford] Pergamon Press\ 0872[ ð3Ł Budin R\ Budin L[ A mathematical model for shading calculations[ Solar Energy 0871^18[ ð4Ł Sassi G[ Some notes on shadow and blockage e}ects[ Solar Energy 0872^20[ ð5Ł Fanchiotti G\ Messina CV\ Rinonapoli A[ A computer code for determining the e}ect of shadows on the availability of solar radi! ation on facades of buildings[ Proceedings of The Second Inter! national PLEA Conference[ Oxford] Pergamon Press\ 0872[ ð6Ł Sattler MA\ Sharples S\ Page JK[ The geometry of the shading of buildings by various tree shapes[ Solar Energy 0876^27[ ð7Ł Raeissi S\ Taheri M[ Optimum overhang dimensions for energy saving[ Building and Environment 0887^22"4#[ ð8Ł ASHRAE Handbook of Fundamentals[ American Society of Heating\ Refrigerating and Air Conditioning Engineers\ Inc[\ 0861[ ð09Ł Daneshyar M[ Solar radiation statistics for Iran[ Solar Energy 0868^10[