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Investigation of the energy flows for transparent and nontransparent building facade
Solar Energy Vol. 51, No. 6, pp. 481-493, 1993 Printed in the U.S.A.
0038-092X/93 $6.00 + .00 Copyright © 1993 Pergamon Press Ltd.
INVESTIGATION OF THE ENERGY FLOWS FOR TRANSPARENT A N D NONTRANSPARENT BUILDING FACADE R. KRAUS,* E. R. F. WINTER,** and W. IBELE*** *Baureferat, Hochbau 7, Landeshauptstadt Miinchen, **Lehrstuhl C ftir Thermodynamik (K~iltetechnik) Technical University, Munich, ***Heat Transfer Laboratory, Mechanical EngineeringDepartment University of Minnesota, Minneapolis, MN 55455, U.S.A. Abstract--Based on extensive measurements of energy usage for a variety of building facades, a computer model has been developed for calculating in advance the heating and cooling requirements of test rooms equipped with arbitrary facades. To simplifythe predictive calculation,the three-dimensionalphysical model was transformed to a one-dimensional, linear, computational model. The computer model uses the results of arl earlier sensitivityanalysis. This permits the precise numerical modeling of the measured results and gives special value to the adaptation of this model for describingthe geometric and thermal relations investigated experimentally. The results of the numerical calculations are found to be in good agreement with the measurements for six test rooms. This agreementjustifies the linear numerical model and the computer program for predicting the energy flows in differentroom structures. Further, the computer model not only provides results which follow the course of weather conditions for the test year but yields results as well for a Standard Reference Year for the region.
l. INTRODUCTION
The facade or shell of a building may be considered to be a separating surface between the natural external environment and the artificial internal climate. The provision of heating and cooling in order to maintain a dependable, comfortable, internal climate often involves factors which are in opposition. Even now, the planning and design of new buildings require that economic and ecological requirements, often conflicting, be taken into account and reconciled. Thus careful regard should be given to our environment, the growing "greenhouse effect," the increased scarcity of raw materials, and energy requirements when new structures are designed. The result should be to utilize technical materials in order to make available a heat barrier and sun protection for buildings at a somewhat higher but justified cost. The building plan should require a wise use of energy, particularly the development of an energy-etticient facade, exact knowledge of the specific influence parameters, as well as fundamental information about the energy behavior for the planned rooms and building. The research project "Energy Transport Through Transparent and Non-transparent Outer Walls of Different Construction," represents a contribution toward this end. The energy effectiveness of six representative facade designs were investigated in long-term tests of one year. For that purpose six, identical, thermostatically controlled rooms, were equipped with different window designs, and their thermal performance (heating and cooling) measured continuously over an entire calendar year. Because of the severe time demands for the quantitative evaluations of the measured energy characteristics of the different facade constructions, a computer model was developed. With this model the yearly mea-
sured energy requirements of the research rooms given in Schulz et a/.[l]can be reproduced and the thermal and energy characteristics of any facade construction predicted depending upon pertinent weather data of a Standard Reference Year (SRY) [2]. Calculations of heating and cooling needs by digital computer have already (1963) been published[3]. A number of investigators [ 4-6 ], in the same fashion, also developed computer models for this end, however the special features of the test rooms cannot be taken into consideration with precision, hence these earlier approaches are not applicable here. 2. DESCRIPTIONOF THE COMPUTER MODEL Based on the findings of the sensitivity analysis by Troeltsch [ 6 ], and the particular geometrical, thermal, and energy characteristics for the research rooms, a model room was developed as shown schematically in Fig. 1. For all room surfaces (facade, sidewalls, backwall, floor, and ceiling) an energy exchange occurs between the room and its surroundings, as shown by the two-way arrows. In addition, the room heat exchanger provides convective heat flow to or from the room air Qwr~c. This quantity also includes the heat emitted by longwave radiation when the radiation exchange (longand shortwave) of room surfaces is considered. For the model shown, numerical calculations are effective in determining the thermal behavior of the rooms. Because of the three-dimensional nature of the heat transfer between the room surfaces and the associated expense and time involved, an extensive simplification of the model became necessary; the final result of which is a "quasi" one-dimensional model. This simplified model is shown in Fig. 2 which sketches a linear numerical model for the energy balance of the rooms. In the figure all room surfaces as well as the heat exchanger
481
R. KRAUS,E. R. F. WINTER,and W. IBELE
482
heatexchanger
K
profiles in a single nontransparent layer is given by Fourier's equation in the form
Ot
o-~ =
)x 02t c~'Ox --~
(l)
radiation
where the temperature t is a function of time z and position x. For transparent parts of the building where material absorbs shortwave radiation, the temperature profile equation is expanded to
Ot O~
Radiation exchange in Room Heat flow through surfaces surrounding the room
Fig. 1. Simplemodel simulating the thermal and energy relations for research rooms.
become confined to a plane surface upon which the heat flows, indicated by two-way arrows, and may be superimposed. The contributions of long- and shortwave radiation are also linearized, despite their spatial nature, and symbolized by common lines with directional arrows. No other direct heat transport between the surfaces surrounding the rooms occurs. In the transparent facade part, should an air flow through the window be present, an enthalpy flow running perpendicular to the direction of heat flow will take this into account. The model room facade structure consists of the support structure, window frame, glasswork of a given number of layers, and any specified type of sunshield (e.g., Jalousie Sunshade or Rollo in German) providing temporary protection from direct sunlight. The remaining surfaces enclosing the room (floor, ceiling, sidewalls, and backwall) can be constructed of several different layers. Inhomogeneous walls due to a door, a recess for a radiator, or additional insulation, can be treated in the same way as a radiator installation. The concept of the test facilities allows the window glasswork and sunshield device to be modeled precisely and an exact account of the long- and shortwave radiation exchange within the room. Thus for the simplified model, in particular the simplified wall calculations, the effective assumptions are summarized• • The heat conduction in the opaque parts of the structure is assumed to one-dimensional. • The air in the model room is homogeneous and takes no part in the radiation exchange. • The nontransparent walls of the model room remain as plane, parallel layers with constant properties. • The heat exchange between individual walls and between parts of wall surfaces occurs by way of convection in the room air and long- and shortwave radiation. Based on the above assumptions the basic differential equation for the description of the temperature
~ 02t I~ cq OX2 + cq
(2)
in which the absorbed part of the shortwave radiation is represented by an inner heat source of strength I~ (jm-3 s -I ). For the upper surface of the building receiving longand shortwave radiation (SLw and Ssw), extending boundary condition 3 gives: Ot
-X-~x = ac(t - tA) + SLw(T 4) + Ssw(r).
(3)
An energy balance on the control volume of room air where convective heat flow to (Oto) or from (O:rom) may occur results in the following equation ( ato, i - O f tom,i)'~ OH "~ QC = i
cnnqnavR ~ u7
. (4)
This equation relates the room air temperature tea with the heating On or cooling Oc effects required to maintain a specified room air temperature. With the simulation of the heat exchanger as an extended surface, the hot and cool energy transport rates are contained in the convective part of Qw and Qfro,~, respectively. The solution of the foregoing system of differential equations occurs by different methods; in this instance a difference method, specifically a fully implicit method, is used. For this method a time interval of 10-15 minutes was chosen. This choice was identified as most suitable because of a sensitivity analysis which considered the influence of different computer models and discretization on calculation times and the occurance of oscillations in the numerical results[6]. In this article, the discretization in the nontransparent part of the structure does not require a detailed explanation. It may be considered as an analog of the following account for transparent parts of the structure (a detailed description is given in Kraus's dissertation[7]).
2.1 Description of the computer model for the window The calculation of energy transport through the window of the testroom was based on the work of Klas [ 8]who developed a multi-plate model in which not only was there an arbitrary number of arbitrary kinds of glassplate (e.g., two-layer, insulated glasswork,
483
Investigation of the energy flows
QWT
roo_~air -~
~j
heatexchanger
i~
I
I
sldewall
w n °w
radiational
~
l~mll~ ~ ',~
I I~
,
1
~ ~ l o n g and short I= ~N~ eW~V~anr~i~t~r_
i---L~.F= j
I/J SUrr°undings~-----~--~---~ ~
)
i
i- ~I
FF__~_..~/AL.-i--.-',
i~
',-r//J-
i
i
l I_ ~ l
I I
I i
i !
I I
II~ surroundings (Hot-Box)
~ ~
I
J si~ewa~
/~ backwall ~I
I floo~
convective heat flow Fig. 2. Linear numerical model simulating the thermal and energy relations for research rooms.
or three-layer thermally protected glasswork), but also various internal and external sunshields, composite windows, and exhaust air windows could be taken into consideration as well. This model will be explained with the help of an arbitrarily chosen example as shown in Fig. 3. Here we consider a fictitious structure comprising a two-layer thermally protected glasswork ( 1), a sunscreen (2), and a simple glass pane (3). The space between the first two glass panes (Sp 1) is sealed at the top and bottom; forced through-flow occurs in the second space (Sp 2); and the third space (Sp 3) is subject to natural convective flow. Because of air flow the
transport of energy occurs in the vertical as well as the horizontal direction. The total window height h is subdivided by a number of vertical steps (here three). Despite the resulting two-dimensional field of junction points (grid), which with no through-flow (nontransparent structure) the section becomes one-dimensional, the calculation of energy transport and the temperature behavior of the window can be carried out as if they were quasi-two-dimensional. In this case it is assumed that the energy in the vertical direction only occurs through air streams. The neglect of heat conduction in the y-direction is justified, for the natural temperature and radiation conditions and the range of flow
484
R. KRAUS,E. R. F. WINTER,and W. IBELE model room, which also allowed simultaneous temperature distribution in the window to be determined, would require excessive calculation time. This difficulty is dealt with, when calculating the energy transport through the window glasswork at the time rz+~, by determining the longwave radiation exchanges with the rest of the room surfaces whose surface temperatures are those for the time rz. In this way the energy which passes through the window to the room air and the new window surface temperature are connected with the determination of the temperature behavior of the rest of the structure and the energy need for the entire room applied at time rz+~.
2 ©
2.2 Division o f surrounding room surfaces into parts In order to consider the exchange of thermal radiation between the room surfaces, including those nontransparent walls containing inhomogeneties, the effect of direct sunlight passing through the window must be J =1 2 3 4 5 6 78 9 10 11 considered. Some surfaces receive solar radiation diSp 1 Sp 2 Sp 3 rectly, others remain in shadow, thus a subdivision of Fig. 3. Multisurface model to determine the energy flow the surrounding room surfaces must be carried out. through a window. The procedure followed, shown with the help of Fig. 4, results in a fictitious sidewall. The door ® in the wall and a radiator eventually velocities anticipated for the space enclosed by the first located in a wall recess ® represent inhomogeneties in two panes. The inequality the construction of the wall 0). When the sun's rays fall directly on the facade surface, those passing through Atx Atr --~ the window will illuminate certain interior surfaces. ~-~x~>~ -} 4x>>qy (5) The boundaries of this illuminated area correspond to the projection of the window perimeter in the direction describes the distribution of heat flow in the horizontal of the suns's rays on the surfaces surrounding the room. and vertical directions for the prevailing conditions. The surfaces are thus divided into those directly illuThe energy balance at an individual grid point is built minated by the sun in this fashion ~) and nonillumiin each case only for the different control volumes nated ~ parts as shown in Fig. 4b. In order to calculate formed by the vertical steps. The individual vertical the energy transport through the transparent wall with steps are coupled with one another through the en- the required precision, in the presence of such surface differences, a subdivision of the wall surface is necessary thalpy balance for the airstream. Because of solar radiation the temperature field in (Fig. 4c). The rectangular subdivision, particularly the transparent sections of the building envelope changes designation of illumination numbers (values), offers more rapidly than in nontransparent parts; conse- the greatest advantage. The calculation of the sun's quently the coefficient for convective heat transfer a c position at a given moment for any arbitrarily chosen and that for longwave radiation exchange aLw, for the place in the northern hemisphere follows from the actual time step, must be found by iteration. While procedure reported in [ 9 ]. the calculation method can perform this task, the conThe respective positions of the sun's shadow edges sideration of a complete system of equations for the for the example above are shown in Fig. 5. They result
~
,.•
Wall
\
Area i n shadow
\
I a)
~Radiator ~surface
b)
~Sun]it ~area
Fig. 4. Composition of the surrounding room surfaces.
c)
485
Investigationof the energy flows
Backwallk = 5 ~
N
I
I
Fig. 5. Determination of shadow edges in a room and the discreet surface parts.
n
from the relationship between the four window corners (F1 • • • F4) and how that relationship becomes represented on the room surfaces. With the help of straightline equations parallel to the sun's rays and equations for the plane surfaces, the window corners projection points (Pl • • • P4) on the walls and floor were determined. In this way a partition may be drawn between areas bathed in sunlight (hatched) and those not. The sunlit part xk for a surface k is given by ABS,k xk = - Atot,k
(6)
where Ass, k is the sunlit area and Ato~,kis the total area. With the knowledge of the shapefactors ~0between individual surfaces, which is easily determined according to the procedure described in Gross et a/.[10], it is now possible to determine with precision, the shortand longwave radiation exchange in the room. 2.3 Shortwave radiation exchange in the room In order to determine the shortwave radiation exchange in the room the outgoing, shortwave radiation for the individual surface Hsw, i [ W / m 2] must be described. It depends upon the individual radiosity of the surface and on the reflections from the illuminated portions of the remaining surfaces and their radiosities. In the procedure proposed here, the incidence angle of direct solar radiation is prescribed in calculations and a distinction is made between those parts of the surrounding room surfaces directly illuminated by the sun and those not. For the surface materials generally employed in rooms, the reflections, both for direct as well as diffuse radiation, can be assumed to be fully diffuse. This means that only the outgoing radiation intensity from the window has a directed component; after one reflection the radiosities corresponding to the shapefactors are evenly distributed. For the radiosity of the window surface the valid equation is:
Hsw,o = Esw,o + rsw,D,O ~ (~O0.k"HSW,k)
(7)
k=l
where the subscript 0 (zero) designates its special basic position. The radiosity Hsw,o thus combines the individual radiosity of the window (surface) Esw,o with the part of the irradiation intensities X~po.kHsw,k, which become reflected from the window surface ( rsw,D is the reflectivity for shortwave diffuse radiation). The individual radiosity
Es~o = D o + S ~ , 0 " c o s ~o
(8)
can be calculated from the diffuse part of the radiation Do and from the part Sx,o, which passes through the window and enters the room as shortwave radiation. The angle cI, lies between the direction of the incident sunbeams and the respective normals to the surfaces. For a nontransparent surface i, whose individual radiosity Esw,~ is always zero [W/m2], the intensity of emitted radiation Hsw, i is given by
Hs~i =Hs~D,i + H s ~ s , i
(9)
where Hsw,D,~ is the diffuse radiosity based on the reflection of diffuse radiation and Hsw~o,~ is the diffuse radiosity resulting from the reflection of direct radiation entering through the window. From the following equation for the diffuse radiosity of the i-th surface n
Hsw, D,i.hi : rsw,D,i ~ (~ok,i'Ak. Hsw, k,D) k=O
(10)
and the reciprocity relation for the irradiation between two surfaces Ai°~i,k = Ak'~k,i
(11)
R. KRAUS,E. R. F. WINTER,and W. IBELE
486 there follows the relation
The calculation of longwave radiation exchange in the room follows analogously from the so-called "Brutto Method." This is described in detail by Kasp a r e k [ l l ] a n d needs no further explanation.
n
Hsw, z,,i = rsw,D,~ ~ (9~,k"
Hsw,,,~)
(12)
k=O
2.4 Shortwave radiation balance on window The balancing of energy streams for each individual pane is the foundation of the numerical method for calculating the passage of shortwave radiation through the window and the absorption of radiation energy in separate window components• This requires the use of such optical properties as transmissivity rsw, reflectivity rsw, and absorbtivity asw. In this case we distinguish between diffuse and direct radiation as was done earlier when the total radiation on the facade was taken as being comprised of a diffuse part DrAs and a direct part SeAs. For these two kinds of radiation there will be different values for the optical properties mentioned above• In this connection the radiosity for the window surface, which reflects radiation back and out of the room, H~,ee is viewed as fully diffuse. In Fig. 6 the radiosities Hsw and the flux of absorbed heat flows qsw, together with the window installation consisting of N glass plates, sun-shade, or like components (Sl • • • Ss), are sketched• [Because of the detailed representation, the index S W (shortwave) has not been used•] As an example, for the chosen internal radiosity H2,3 of layer $2, the figure allows the equation
in which Hsw, k,n is the diffuse part of the radiosity. The diffuse radiosity Hsw,s,~ can be written (13)
nsw.s,i .Ai = rsw,s,i .S±,o.A±,i
In this relation the projection of surface A~ normal to the radiation direction A±,~, can be written A~,i = cos Ct "Ai.
(14)
Since for the i-th surface only a part becomes directly sunlit, an approximation is found through the use of the sunlit area fraction defined in subsection 2.2. Thus the radiosity for the i-th surface caused through reflection of direct radiation becomes Hsw, s,i = rsw,s,i" cos ¢i" SJ_.oXi.
(15)
If the diffuse Do and direct radiation S.,0 entering the room are known, the foregoing equations may be combined into a system of linear equations. The radiosities find use with the calculation of the heat flows O.sw,i, which are caused by the absorption of shortwave solar radiation striking the building surfaces. During its calculation, a balance over the incoming and outgoing energy streams is obtained from which follows the absorbed heat flow rate
112,3 = r2,iH3,2 + r2,aHi,2
to be written, in which the reflectivity r2 and the transmissivity z2 of the second pane are considered• The index i describes the radiation direction from an inner to an outer or external surface; the index a stands for the reverse direction• The radiosity H3,2 is, by analogy,
Qsw, i = ( ~, (@i,k. Hsw,~,D) - Hsw,~ k + S±,o" cos ~ . x~ )A~.
(16)
//32
®
@ Ia
3a
2t
h,al
a2,a[
a2,l,a!a2,2,a H2,3
1,\1 al,l,iJal,2, ial,i
HSI,I
I
I
H2,1
~
a2,1,1[a2,2,i ~--ff[ 'r2,i a2, i
HS1,2 HS2,1
Na
3i
a3,1,a a3,2,a
ql,l lql,2
=
HS2, 2
H3,2
N, i TN,a I
.,4 HN-I.~ aN,l,a aN,2,a HN,N+I'HF_[,P&
i.t '/ I
a3,1,i a3,2,i .~ x3,t [ a3,4 HS3,1
(18)
@
111 ,
r3,an2,3 + T3,in4,3.
a3 ,a I._m." "r3,a
'2,71-"
HO,I'HFAs al,%,alal,2,a H1,2
=
@
2a
Ii
(17)
--
HS3, 2
Fig. 6. Shortwave radiation balance for window.
N+| ,N=IIRA,FE
- I aN'l'i[ aN,2,i
JJ
HSN,1
I "N,| HSN,2
487
Investigation of the energy flows The generalization of the two previous equations leads to Hj,k = rj,iHk,j + rj, aHj-i,k-I
(19)
Hk,j = rk,attj,k + "rk,ink+l,j+l.
(20)
The energy balances for all the unknown radiosities yields a system of linear equations of the form M.H=
O
(21)
in which the matrix M contains the material properties of the layers and the vector b comprises the known radiosity HrAs (either DFAS or Sr~s) and the room-toinner window surface back reflection radiosity H~,rE. With the absorbtivity for the individual layers, the heat flux due to absorbtion can be calculated directly for the two different directions of radiation: {lj,l,i = aj,,.i Hj+l,s
(22)
(lj,2.i = aj, z.i Hj+Lj
(23)
dlj,L. = aj,,.~Hj_~,j
(24)
[b,2,~ : aj,2,~Hj Lj.
(25)
2.5 Convective a n d longwave heat transfer Basic convective heat transfer can in general be described by Newton's law of cooling. Previous work has used an overall coefficient of convection both for free
convection as well as mixed forced and free convective heat transfer and, in this manner, the respective surfaces of the room (outside, inside, air cavity surfaces, etc.) found consideration. The influence of longwave radiation of the facade is taken into consideration through the energy balances over the emissions of the various building surfaces as well the reflected radiation from the surroundings and atmosphere. This follows the work of Kondratyev[12]and others by means of an empirical equation given by Schaube [13]. Taking as a basis the numerical model concisely described here (a more detailed description can be found in Kraus's dissertation[7]), a simulation program for determining the thermal and energy behavior of the testroom can be developed. The computer program language "C", employed for this choice, appeared to have the highest probability of lasting use despite the availability of widely different computer architecture. In addition, because of the versatility of this language, the numerical calculations create results which are essential for the optimal management and control (heating, cooling and shading) of large buildings.
3. RETROSPECTIVE CALCULATIONOF THE ANNUAL TOTAL ENERGY BUDGET FOR THE TESTROOMS The retrospective calculation of the annual heating and cooling budgets for the research rooms under working and weather conditions prevailing during the test year 1988 was carried out.
3.0-
1988
2.5
ID
2.0
Calculated
n~
>~
Measured \
1.5
ID
1.0. ro o
0.5 0.0 Room1/88 ~measured
I
Room 2/88
Room3/88
~Heating e n e r g y ~
[T7~calculatedJNeed
Room4/88
Room 5/88
Room6/88
measured ~Cooling energy
~---~calculated JNeed
Window types: REF -reference, VB/FR -composite with sunshade AB/FR -exhaust air, WS-insulated, TWS-insulated with controlled shutters ~g. 7. Comparison of measu~d and calcula~d annual heating and cooling ~quirements ~r six tearooms.
488
R. KRAUS,E. R. F. WINTER,and W. IBELE
The respective measured annual energy budget, divided into heating and cooling requirements, and the corresponding calculated annual energy budget are shown as bar graphs in Fig. 7. For the numerical calculations, test-facade construction details are given in Table 1. The comparison of the calculated energy requirement for heating of test room 1/88 (thermopane) with the measured value shows a deviation of somewhat less than 10%. For the cooling, energy needed the calculated value amounts to 93% of the measured value. In the following, the percentage given always refers to the measured value for the respective room. Thus the calculated relative total energy budget for research room 1/88 shows a value of 98%. For testroom 2/88 (composite window with sunshade) a larger deviation exists; the relative heating need amounts to 90% and the relative cooling need amounts to 85%. The deviation of the calculated total energy budget from the experimentally determined value amounts in this case to about 12%. The energy behavior of testroom 3/88 which, as in the case oftestroom 2/88, is furnished with a composite window with a sunshade, is closely replicated by the computer program. The relative values for heating and cooling energy needs for the room amount to 101% and 91%, respectively, which yield a relative total energy value of 95%. In the instance of testroom 4/88, although it is equipped with an exhaust air window, the results shown are for zero flow ( ITASL= 0 m3/h) of exhaust air. The relative heating energy need of 101% almost matches the measured value. The calculated cooling energy need is 25% higher than the measured value, a result which can be explained by the fact that the simulation calculation does not consider the large-scale air circulation, and related heat transfer from the inner surfaces and sunshade, within the exhaust air chamber of this window type. The simulation calculations for testroom 5/88 with a facade equipped with a three-pane thermopane gave, for the heating case as well as the cooling case, good agreement with the measured results. The relative heating energy requirement amounts to 91% and the cooling requirement to 101% of the measured needs, from which a relative total energy budget of 97% obtains. Similarly, for testroom 6/88, equipped with different rotating temporary shutters and heat barrier (insulation) which could be controlled during the course of the investigation, a good agreement was found. The relative values for heating and cooling were 99 and 102%, respectively, and the calculated total energy budget was the same as that measured. The results for the numerical simulations and measurements indicate, that despite some minor differences the computer program provides for a very good simulation of the temperature and energy behavior of the testrooms. It is therefore capable of calculating in advance the energy budgets for rooms of different and complex construction and equipped with arbitrary facades.
4. STANDARD REFERENCE YEAR
In order to be able to make a convincing prediction of the energy behavior of the testrooms over a representative time span, the meteorological boundary conditions for the area of southern Bavaria, as represented by the weather data for a SRY, were imposed on the various facades and testrooms. The SRY represents a collection of data for certain weather characteristics, whose mean values correspond to the long standing ( 10 to 15 years) average climate. The test reference year for a typical regional climate in the German Federal Republic (preunification) was developed according to the general research goal of the federal ministry for research and technology (BMFT). The SRY described here is the one developed by Troeltsch [6 ]and meets the observation of Jahn[14]that the most realistic model of building spaces possible can only be based on real, simultaneously measured data from a weather station. Thus, given the presence of hourly data, the following weather parameters should be included: • • • • • • • • • •
air temperature, background radiation (on the horizontal plane), sky radiation (on the horizontal plane), sunshine duration--hourly or relative of coverage, wind velocity, wind direction, relative humidity, air pressure, ground temperature, and snow cover.
For the construction of a suitable SRY the actual weather records for 12 individual months (not necessarily successive) were taken from sequential data for several years. The selection of a month as a time period is a compromise, because considering the thermal response of the rooms, it already represents a long time period; on the other hand a multi-year average of the behavior of individual weather variables is desirable for the development of a good model. The selection of the individual months follows the procedure given in Jahn's research[14]. There, not only do the monthly and annual averages find consideration, but the average values over the heating and summer seasons do as well. The SRY months of January, February and June, and July were selected first. Within these months the maximum and minimum for the comparison parameters as well as the averages of the outside air temperature, total background radiation, and the sunshine duration should lie close to the respective means and totals recorded over many years for these months. Subsequently, the months of August and December were selected so that their usual climatic conditions corresponded to the respective quarterly average values. These six months were not changed. To complete the selection, the months of a transition period (March, April, May, and September, October, November) were assigned weather conditions corresponding to the annual means and totals of long standing. For the greater Munich area, measurements taken
g
Foil shade
2.1 1.7
--
3.0 2.2
2-panes insulated glass
Plain glass
Composite window
2
1.1 1.1
2-panes insulated glass (Argon) Foil shade
Plain glass
Composite window
3
* The values given are for open sun shades and open shutters.
Sun shield, movable insulation u-value* ugt, [W/m 2 K)] ufa,. [W/(m 2 K)]
2-panes insulated glass
--
Construction outer
inner
Reference
1
Test element
Room number facade
1.1 1.1
Foil shade
2 -panes insulated glass (Argon) Plain glass
Exhaust air window V = 0 m3/h
4
0.9 0.95
--
3-panes insulated glass (Argon)
Insulated window
5
3.0 2.2
Insulated movable shutters
2-panes insulated glass
Insulated movable shutters
6
Table 1. Construction of test facades
1.1 1.1
Foil shade
2-panes insulated glass (Argon) Plain glass
Exhaust air window V = 50 m3/h
7 (see No. 4) 8
<0.9 <0.95
3-panes insulated glass (Argon) Foil shade
Plain glass
Composite window
(see No. 3)
0.6 0.8
3-panes insulated glass (Krypton) Movable shutters (glass)
Special construction - const.
9
0.6 0.8
(Krypton) Movable shutters (glass)
glass
3-panes insulated
Special construction = const.
10 (see No. 9)
R. KRAUS,E, R. F. WINTER,and W. IBELE
490
Table 2. Composition of the SRY and summary for the SRY of outside air average temperature and total radiation on a vertical surface (C~ras = 198 °) Month Out of Composition Calendar of the SRY year
January February March April May June July August September October November December
1977
1972
1975
1974 1977 1977 1977 1977
1978
1978
1978
1973
toA = 7.5°C. qSOL.O= 830 [kW h/mS].
at the Weihenstephan Weather Station were employed, with which the m o n t h s o f different calendar years were compiled to f o r m t h e SRY (Table 2). For the two most important parameters: (a) outside air temperature ton and ( b ) the total o f shortwave irradiation on a vertical surface qSOL.O, the table also gives the m e a n and total values for the SRY. The daily trace of the outside
tOA
air temperature and total radiation Gens on the facade surface during the SRY is shown in Fig. 8. 5. ADVANCE CALCULATION OF THE ANNUAL ENERGY BUDGET OF ROOMS WITH DIFFERENT TEST-FACADES As a result o f the comparison o f experiments and the c o m p u t e r model predictions, it is now possible to
20
[°C] -20
GFAS [W/m 2]
Fig. 8. Course of outside air temperature tAL and the total radiation for a vertical surface (aFAS = 198 ° ) during the SRY.
Investigationof the energy flows calculate the thermal and energy behavior for any given facade and arbitrary room dependent upon the weather data of the standard reference year. Here, six individual, experimentally investigated facades are considered. The numerical calculations were extended to other window types of improved performance (as shown in Table l, under the headings 7, 8, 9, and 10). The first newly added facade (No. 7) involves a modem exhaust-air window construction similar to the type installed in testroom 4/88. In this facade variation, however, the computation of the annual energy budget is carried out with a given through-flow in the space between the two innermost glass panes, of 12AsL= 50 m 3 h - l , which corresponds to a turnover of room air ofn ~ 1.5 h -~ . This differs from facade 4/88 in which the air gap between the panes was sealed. Another facade type (No. 8) consisted of an composite window with an internal, three-pane thermopane and a rolling sunshade, as well as an outward facing glass pane. The heat shielded glasswork corresponds to that of testroom 5/88 and the shade has the same properties as that employed for facades 2 and 3, the support structure and frame as well. The third new facade type is similar to a prototype currently installed by the Gartner firm. The construction consists of a three-pane heat shielded glasswork, whose infrared reflecting coating has an emissivity value, ~ ~ 0.05, and whose space between panes is filled with krypton gas. The thermally isolated frame has a k-value of approximately 1.7 [ W / m : K]. An externally installed, reflecting jalousie system serves as a sunshield and makes it possible to distribute daylight in the room for optimal illumination. Under these conditions it is extremely difficult to specify a radiation transmissivity for this sunshield. Therefore, assuming computer control of the jalousie, the system adjusted for optimal energy conditions using integral radiation transmissivities in the range of r s s v = 0.2 to 0.8 (No. 10). For the purpose of comparison, the annual calculation was carried out with a constant transmissivity of r s s v = 0.4 which implies a fixed sunshield position (No. 9). The annual energy profile for the test facades is complete in the sense that the simulation calculations are determined for a weather course which considers every single day of the SRY. Summing the energy flows, heating, and cooling for 366 days yields the annual total energy budget for the respective test facades. The results of these calculations for all window types are shown in Fig. 9. As before, the lower hatched area represents the heating part of the total energy budget and the upper area the cooling part. The total energy turnover of 2.8 MW h / a n n u m calculated for testroom 1/SRY is larger than that measured for testroom I/88 because of higher total radiation and lower outside air average temperatures during the SRY (see Fig. 7). In considering the results shown in Fig. 9, it should be noted that for rooms 2/SRY through 6/SRY there were differences between the respective experimental and numerically determined values (see Fig. 7). The
491
reasons for these differences may be attributed to the different weather conditions during the test year in contrast with those of the standard-reference-year as well as different control of the sunshades (jalousies). These difference are only slight however as verified by the interpretation of the test results for the six rooms I/SRY through 6/SRY as given in Schulz et al.'s report [ 1] and Kraus's dissertation [ 7 ]. The calculated results for room 7/SRY show that the through-flow of room air in the space between the innermost panes caused a dramatic reduction of the relative energy requirements when compared with those of testroom 4/SRY. The latter resembles room 7/SRY but had no through-flow. The calculated savings amounted to about 25% for heating and 30% for cooling. It should be noted that the ventilating air flowing between the inner panes is provided from the room at the constant temperature maintained there, a condition assumed in the calculations. The heating and cooling energy required for this exhaust air stream can be taken into consideration specifically in future numerical simulations. The complete climate control of a building can be accomplished using exhaust windows throughout for greatest energy economy. This is especially true if during the period of intensive solar radiation on the south-facing windows the waste heat generated is used to heat the northerly rooms. An improved version of the composite window construction oftestroom 3/SRY, through the insertion of a three-pane-heat shielded glasswork, reduced the heating requirements about 15%. The cooling requirements for such a room (8/SRY) compared with the original testroom 3/SRY are reduced to 87%. Whether this and the above listed energy savings justify the increased capital costs must in each individual case be proven through established economic analysis. The special construction of facades 9/SRY and I0/ SRY, although expensive to fabricate, offer definite advantages in energy savings when the radiation transmission of the sunshield is optimally adjusted for the prevailing weather conditions. For the two modes of operation, room 9 / SRY-sunshield position fixed and room 10/SRY-sunshield position varied, there are performance differences of 11% for heating and 40% for cooling. With a computercontrolled sunshield operating under the conditions described earlier, room 10/SRY saves 27% of the energy needs of room 9/SRY with its less than optimum sunshield, and 81% of the energy needs of room l / SRY. Further possibilities of optimization, for example, an improved illumination of the spaces with daylight or the adjustment of illumination conditions for videoscreen work stations, remain to be considered. 6. SUMMARY By means of a numerical analysis, preceeded by extensive measurements on six testrooms, an investigation was undertaken to develop a readily used computer program. The program accurately reproduces the measured results for the BMFT-sponsored tests as well
R. KRAUS,E. R. F. WINTER,and W. IBELE
492 3,0"
\
~' 2,5
SRY c"
~
2,0-
°
\
"
\
_J
\
1,5
S.
° 0
~-
1,0-
¢
0,5
~/
O. 1/SRY
2/SRY 3/SRY 4/SRY 5/SRY 6/SRY 7/SRY 8/SRY 9/SRY IO/SRY WS z:const, x#const.
•
Heating requirement
~Cooling
requirement
Fig. 9. Calculated annual energy budget of research rooms with various test facades.
as predicting the heating and cooling energy requirements of the testrooms, equipped with arbitrary facades, for the weather conditions of a SRY. In the course of developing the program, the varying thermal and energy behaviors of the rooms were determined using a fully implicit finite difference procedure. Before undertaking the calculations the three-dimensional physical model was simplified by conversion to a onedimensional, linear numerical model. The deviations from one-dimensionalitywere also found by calculating the energy transport for exhaust-air windows and the long- and shortwave thermal radiation exchange in the rooms. To guarantee that the numerical calculations of testroom thermal and energy behavior were exact as possible, particular emphasis was placed on adjusting the model to correspond to the geometrical and thermal conditions which held for the experimentally investigated testrooms. However, the development of the program allows the thermodynamic behavior of other room designs of light, moderately heavy, and heavy construction to be determined. Further, the energetics of the ventilating air stream and internal heat sources as well as artificial illumination can be treated. The results of numerical modeling are found to be in good agreement with the measured energy exchange record for the six testrooms. Confidence in the applicability of the linearized numerical model and the computer model for predicting the energy exchanges for rooms of various construction is based upon this agreement between measurement and calculation. In summary, the computer model here described, secured by extensive experimental data, offers the possibility of replacing additional measurements on other types of facade constructions with rapid calculation
and substantial cost savings. Due to improvements in microelectronics, high capacity computer systems are no longer required, so such numerical calculations can enter into the planning of every building. This will influence the part of building design and construction dealing with energy considerations, and shape future, carefully directed, experiments which provide the foundation for continuing research.
Acknowledgments--This research was partially supported by the Minister of Research and Technology(Germany) and the J. Gartner Company, Gundelfingen (Germany). REFERENCES
1. H. Schulz, W. Heusler, E. R. F. Winter, and R. Kraus, Energietransport durch transparente und nichttransparente Aul3enwandkonstruktionunterschiedlichenAutbaus, final report, BMFF FE 03E 8134 A (1989). 2. R. Kraus, E. R. F. Winter, H. Schulz, and W. Heusler, Energietransport durch transparente und nichttransparente AuBenwandkonstruktionunterschiedlichenAutbaus, Bauphysik 13, H. 6; 239-242, H 7; 19-22 ( 1991 ). 3. G. Brown, 1Vletodfor datamaskin ber~ihningav kyloch v~irmebehov, V VS 34 i 1, 40 I-410 (1963). 4. L. Rouvel, Analoges und digitales Rechenverfahren far die Interdependenzdes w~metechnischen Verhaltensvon Raumumschliel3ungsfl~ichenbei dynamischer W~irmebelastung, Dissertation, Technical University Munich (1972). 5. G. Hauser, Rechnerische Vorherbestimmung des W~irmeverhaltens grol3er Bauten, Dissertation, University of Stuttgart (1977). 6. M. Troeltsch, Numerische Simulation des W~rmeverbrauchs und des Temperaturverhaltens von l~umen als repr~isentativeTeile von Geb~iuden,Dissertation, Technical University Munich (1986). 7. R. Kraus, Experimentelleund numerischeUntersuchung des Energieverbrauchsan transparenten Fassaden, Dissertation, Technical University Munich (1990).
Investigation of the energy flows 8. J. Klas, Numerische Simulation des Energieverhaltens luftdurchstr6mter, lichtdurchl~ssiger Fassaden, Diplomarbeit, Lehrstuhl C ftir Thermodynamik, TU MiJnchen (1987). 9. DIN 5034, Tageslicht in Innenrfiumen, Beuth, Berlin (1985). 10. U. Gross, K. Spindler, and E. Hahne, Shapefactor-equations for radiation heat transfer between plane rectangular surfaces of arbitrary position and size with parallel boundaries, Letters in Heat Mass Transfer 8, 219-227 ( 1981 ). 11. G. Kasparek, Der Energieaustausch durch W~irmestrah-
493
lung zwischen Feststoffoberfl/ichen, BrennstoffWSrmeKraft 24, 6, S. 229-233 (1972). 12. K. Y. Kondratyev, Radiation in the atmosphere, International geophysics series, vol. 12, Academic Press, New York (1969). 13. H. Schaube, Untersuchungen fiber Wiirmetibergangskoel~zienten an Fenstern mit und ohne W~irmeschutzeinrichtungen unter natiirlichen Klimabedingungen, Fraunhofer-lnstitut ftir Bauphysik, Bericht EB-I 5/1986 (1986). 14. A. Jahn, Das Test-Referenzjahr, Eine Sammlung sttindlicher Werte interessierender Wetterelemente, HLH 28 (19177), 199-206, 257-265, 295-299 (1977).
0038-092X/93 $6.00 + .00 Copyright © 1993 Pergamon Press Ltd.
INVESTIGATION OF THE ENERGY FLOWS FOR TRANSPARENT A N D NONTRANSPARENT BUILDING FACADE R. KRAUS,* E. R. F. WINTER,** and W. IBELE*** *Baureferat, Hochbau 7, Landeshauptstadt Miinchen, **Lehrstuhl C ftir Thermodynamik (K~iltetechnik) Technical University, Munich, ***Heat Transfer Laboratory, Mechanical EngineeringDepartment University of Minnesota, Minneapolis, MN 55455, U.S.A. Abstract--Based on extensive measurements of energy usage for a variety of building facades, a computer model has been developed for calculating in advance the heating and cooling requirements of test rooms equipped with arbitrary facades. To simplifythe predictive calculation,the three-dimensionalphysical model was transformed to a one-dimensional, linear, computational model. The computer model uses the results of arl earlier sensitivityanalysis. This permits the precise numerical modeling of the measured results and gives special value to the adaptation of this model for describingthe geometric and thermal relations investigated experimentally. The results of the numerical calculations are found to be in good agreement with the measurements for six test rooms. This agreementjustifies the linear numerical model and the computer program for predicting the energy flows in differentroom structures. Further, the computer model not only provides results which follow the course of weather conditions for the test year but yields results as well for a Standard Reference Year for the region.
l. INTRODUCTION
The facade or shell of a building may be considered to be a separating surface between the natural external environment and the artificial internal climate. The provision of heating and cooling in order to maintain a dependable, comfortable, internal climate often involves factors which are in opposition. Even now, the planning and design of new buildings require that economic and ecological requirements, often conflicting, be taken into account and reconciled. Thus careful regard should be given to our environment, the growing "greenhouse effect," the increased scarcity of raw materials, and energy requirements when new structures are designed. The result should be to utilize technical materials in order to make available a heat barrier and sun protection for buildings at a somewhat higher but justified cost. The building plan should require a wise use of energy, particularly the development of an energy-etticient facade, exact knowledge of the specific influence parameters, as well as fundamental information about the energy behavior for the planned rooms and building. The research project "Energy Transport Through Transparent and Non-transparent Outer Walls of Different Construction," represents a contribution toward this end. The energy effectiveness of six representative facade designs were investigated in long-term tests of one year. For that purpose six, identical, thermostatically controlled rooms, were equipped with different window designs, and their thermal performance (heating and cooling) measured continuously over an entire calendar year. Because of the severe time demands for the quantitative evaluations of the measured energy characteristics of the different facade constructions, a computer model was developed. With this model the yearly mea-
sured energy requirements of the research rooms given in Schulz et a/.[l]can be reproduced and the thermal and energy characteristics of any facade construction predicted depending upon pertinent weather data of a Standard Reference Year (SRY) [2]. Calculations of heating and cooling needs by digital computer have already (1963) been published[3]. A number of investigators [ 4-6 ], in the same fashion, also developed computer models for this end, however the special features of the test rooms cannot be taken into consideration with precision, hence these earlier approaches are not applicable here. 2. DESCRIPTIONOF THE COMPUTER MODEL Based on the findings of the sensitivity analysis by Troeltsch [ 6 ], and the particular geometrical, thermal, and energy characteristics for the research rooms, a model room was developed as shown schematically in Fig. 1. For all room surfaces (facade, sidewalls, backwall, floor, and ceiling) an energy exchange occurs between the room and its surroundings, as shown by the two-way arrows. In addition, the room heat exchanger provides convective heat flow to or from the room air Qwr~c. This quantity also includes the heat emitted by longwave radiation when the radiation exchange (longand shortwave) of room surfaces is considered. For the model shown, numerical calculations are effective in determining the thermal behavior of the rooms. Because of the three-dimensional nature of the heat transfer between the room surfaces and the associated expense and time involved, an extensive simplification of the model became necessary; the final result of which is a "quasi" one-dimensional model. This simplified model is shown in Fig. 2 which sketches a linear numerical model for the energy balance of the rooms. In the figure all room surfaces as well as the heat exchanger
481
R. KRAUS,E. R. F. WINTER,and W. IBELE
482
heatexchanger
K
profiles in a single nontransparent layer is given by Fourier's equation in the form
Ot
o-~ =
)x 02t c~'Ox --~
(l)
radiation
where the temperature t is a function of time z and position x. For transparent parts of the building where material absorbs shortwave radiation, the temperature profile equation is expanded to
Ot O~
Radiation exchange in Room Heat flow through surfaces surrounding the room
Fig. 1. Simplemodel simulating the thermal and energy relations for research rooms.
become confined to a plane surface upon which the heat flows, indicated by two-way arrows, and may be superimposed. The contributions of long- and shortwave radiation are also linearized, despite their spatial nature, and symbolized by common lines with directional arrows. No other direct heat transport between the surfaces surrounding the rooms occurs. In the transparent facade part, should an air flow through the window be present, an enthalpy flow running perpendicular to the direction of heat flow will take this into account. The model room facade structure consists of the support structure, window frame, glasswork of a given number of layers, and any specified type of sunshield (e.g., Jalousie Sunshade or Rollo in German) providing temporary protection from direct sunlight. The remaining surfaces enclosing the room (floor, ceiling, sidewalls, and backwall) can be constructed of several different layers. Inhomogeneous walls due to a door, a recess for a radiator, or additional insulation, can be treated in the same way as a radiator installation. The concept of the test facilities allows the window glasswork and sunshield device to be modeled precisely and an exact account of the long- and shortwave radiation exchange within the room. Thus for the simplified model, in particular the simplified wall calculations, the effective assumptions are summarized• • The heat conduction in the opaque parts of the structure is assumed to one-dimensional. • The air in the model room is homogeneous and takes no part in the radiation exchange. • The nontransparent walls of the model room remain as plane, parallel layers with constant properties. • The heat exchange between individual walls and between parts of wall surfaces occurs by way of convection in the room air and long- and shortwave radiation. Based on the above assumptions the basic differential equation for the description of the temperature
~ 02t I~ cq OX2 + cq
(2)
in which the absorbed part of the shortwave radiation is represented by an inner heat source of strength I~ (jm-3 s -I ). For the upper surface of the building receiving longand shortwave radiation (SLw and Ssw), extending boundary condition 3 gives: Ot
-X-~x = ac(t - tA) + SLw(T 4) + Ssw(r).
(3)
An energy balance on the control volume of room air where convective heat flow to (Oto) or from (O:rom) may occur results in the following equation ( ato, i - O f tom,i)'~ OH "~ QC = i
cnnqnavR ~ u7
. (4)
This equation relates the room air temperature tea with the heating On or cooling Oc effects required to maintain a specified room air temperature. With the simulation of the heat exchanger as an extended surface, the hot and cool energy transport rates are contained in the convective part of Qw and Qfro,~, respectively. The solution of the foregoing system of differential equations occurs by different methods; in this instance a difference method, specifically a fully implicit method, is used. For this method a time interval of 10-15 minutes was chosen. This choice was identified as most suitable because of a sensitivity analysis which considered the influence of different computer models and discretization on calculation times and the occurance of oscillations in the numerical results[6]. In this article, the discretization in the nontransparent part of the structure does not require a detailed explanation. It may be considered as an analog of the following account for transparent parts of the structure (a detailed description is given in Kraus's dissertation[7]).
2.1 Description of the computer model for the window The calculation of energy transport through the window of the testroom was based on the work of Klas [ 8]who developed a multi-plate model in which not only was there an arbitrary number of arbitrary kinds of glassplate (e.g., two-layer, insulated glasswork,
483
Investigation of the energy flows
QWT
roo_~air -~
~j
heatexchanger
i~
I
I
sldewall
w n °w
radiational
~
l~mll~ ~ ',~
I I~
,
1
~ ~ l o n g and short I= ~N~ eW~V~anr~i~t~r_
i---L~.F= j
I/J SUrr°undings~-----~--~---~ ~
)
i
i- ~I
FF__~_..~/AL.-i--.-',
i~
',-r//J-
i
i
l I_ ~ l
I I
I i
i !
I I
II~ surroundings (Hot-Box)
~ ~
I
J si~ewa~
/~ backwall ~I
I floo~
convective heat flow Fig. 2. Linear numerical model simulating the thermal and energy relations for research rooms.
or three-layer thermally protected glasswork), but also various internal and external sunshields, composite windows, and exhaust air windows could be taken into consideration as well. This model will be explained with the help of an arbitrarily chosen example as shown in Fig. 3. Here we consider a fictitious structure comprising a two-layer thermally protected glasswork ( 1), a sunscreen (2), and a simple glass pane (3). The space between the first two glass panes (Sp 1) is sealed at the top and bottom; forced through-flow occurs in the second space (Sp 2); and the third space (Sp 3) is subject to natural convective flow. Because of air flow the
transport of energy occurs in the vertical as well as the horizontal direction. The total window height h is subdivided by a number of vertical steps (here three). Despite the resulting two-dimensional field of junction points (grid), which with no through-flow (nontransparent structure) the section becomes one-dimensional, the calculation of energy transport and the temperature behavior of the window can be carried out as if they were quasi-two-dimensional. In this case it is assumed that the energy in the vertical direction only occurs through air streams. The neglect of heat conduction in the y-direction is justified, for the natural temperature and radiation conditions and the range of flow
484
R. KRAUS,E. R. F. WINTER,and W. IBELE model room, which also allowed simultaneous temperature distribution in the window to be determined, would require excessive calculation time. This difficulty is dealt with, when calculating the energy transport through the window glasswork at the time rz+~, by determining the longwave radiation exchanges with the rest of the room surfaces whose surface temperatures are those for the time rz. In this way the energy which passes through the window to the room air and the new window surface temperature are connected with the determination of the temperature behavior of the rest of the structure and the energy need for the entire room applied at time rz+~.
2 ©
2.2 Division o f surrounding room surfaces into parts In order to consider the exchange of thermal radiation between the room surfaces, including those nontransparent walls containing inhomogeneties, the effect of direct sunlight passing through the window must be J =1 2 3 4 5 6 78 9 10 11 considered. Some surfaces receive solar radiation diSp 1 Sp 2 Sp 3 rectly, others remain in shadow, thus a subdivision of Fig. 3. Multisurface model to determine the energy flow the surrounding room surfaces must be carried out. through a window. The procedure followed, shown with the help of Fig. 4, results in a fictitious sidewall. The door ® in the wall and a radiator eventually velocities anticipated for the space enclosed by the first located in a wall recess ® represent inhomogeneties in two panes. The inequality the construction of the wall 0). When the sun's rays fall directly on the facade surface, those passing through Atx Atr --~ the window will illuminate certain interior surfaces. ~-~x~>~ -} 4x>>qy (5) The boundaries of this illuminated area correspond to the projection of the window perimeter in the direction describes the distribution of heat flow in the horizontal of the suns's rays on the surfaces surrounding the room. and vertical directions for the prevailing conditions. The surfaces are thus divided into those directly illuThe energy balance at an individual grid point is built minated by the sun in this fashion ~) and nonillumiin each case only for the different control volumes nated ~ parts as shown in Fig. 4b. In order to calculate formed by the vertical steps. The individual vertical the energy transport through the transparent wall with steps are coupled with one another through the en- the required precision, in the presence of such surface differences, a subdivision of the wall surface is necessary thalpy balance for the airstream. Because of solar radiation the temperature field in (Fig. 4c). The rectangular subdivision, particularly the transparent sections of the building envelope changes designation of illumination numbers (values), offers more rapidly than in nontransparent parts; conse- the greatest advantage. The calculation of the sun's quently the coefficient for convective heat transfer a c position at a given moment for any arbitrarily chosen and that for longwave radiation exchange aLw, for the place in the northern hemisphere follows from the actual time step, must be found by iteration. While procedure reported in [ 9 ]. the calculation method can perform this task, the conThe respective positions of the sun's shadow edges sideration of a complete system of equations for the for the example above are shown in Fig. 5. They result
~
,.•
Wall
\
Area i n shadow
\
I a)
~Radiator ~surface
b)
~Sun]it ~area
Fig. 4. Composition of the surrounding room surfaces.
c)
485
Investigationof the energy flows
Backwallk = 5 ~
N
I
I
Fig. 5. Determination of shadow edges in a room and the discreet surface parts.
n
from the relationship between the four window corners (F1 • • • F4) and how that relationship becomes represented on the room surfaces. With the help of straightline equations parallel to the sun's rays and equations for the plane surfaces, the window corners projection points (Pl • • • P4) on the walls and floor were determined. In this way a partition may be drawn between areas bathed in sunlight (hatched) and those not. The sunlit part xk for a surface k is given by ABS,k xk = - Atot,k
(6)
where Ass, k is the sunlit area and Ato~,kis the total area. With the knowledge of the shapefactors ~0between individual surfaces, which is easily determined according to the procedure described in Gross et a/.[10], it is now possible to determine with precision, the shortand longwave radiation exchange in the room. 2.3 Shortwave radiation exchange in the room In order to determine the shortwave radiation exchange in the room the outgoing, shortwave radiation for the individual surface Hsw, i [ W / m 2] must be described. It depends upon the individual radiosity of the surface and on the reflections from the illuminated portions of the remaining surfaces and their radiosities. In the procedure proposed here, the incidence angle of direct solar radiation is prescribed in calculations and a distinction is made between those parts of the surrounding room surfaces directly illuminated by the sun and those not. For the surface materials generally employed in rooms, the reflections, both for direct as well as diffuse radiation, can be assumed to be fully diffuse. This means that only the outgoing radiation intensity from the window has a directed component; after one reflection the radiosities corresponding to the shapefactors are evenly distributed. For the radiosity of the window surface the valid equation is:
Hsw,o = Esw,o + rsw,D,O ~ (~O0.k"HSW,k)
(7)
k=l
where the subscript 0 (zero) designates its special basic position. The radiosity Hsw,o thus combines the individual radiosity of the window (surface) Esw,o with the part of the irradiation intensities X~po.kHsw,k, which become reflected from the window surface ( rsw,D is the reflectivity for shortwave diffuse radiation). The individual radiosity
Es~o = D o + S ~ , 0 " c o s ~o
(8)
can be calculated from the diffuse part of the radiation Do and from the part Sx,o, which passes through the window and enters the room as shortwave radiation. The angle cI, lies between the direction of the incident sunbeams and the respective normals to the surfaces. For a nontransparent surface i, whose individual radiosity Esw,~ is always zero [W/m2], the intensity of emitted radiation Hsw, i is given by
Hs~i =Hs~D,i + H s ~ s , i
(9)
where Hsw,D,~ is the diffuse radiosity based on the reflection of diffuse radiation and Hsw~o,~ is the diffuse radiosity resulting from the reflection of direct radiation entering through the window. From the following equation for the diffuse radiosity of the i-th surface n
Hsw, D,i.hi : rsw,D,i ~ (~ok,i'Ak. Hsw, k,D) k=O
(10)
and the reciprocity relation for the irradiation between two surfaces Ai°~i,k = Ak'~k,i
(11)
R. KRAUS,E. R. F. WINTER,and W. IBELE
486 there follows the relation
The calculation of longwave radiation exchange in the room follows analogously from the so-called "Brutto Method." This is described in detail by Kasp a r e k [ l l ] a n d needs no further explanation.
n
Hsw, z,,i = rsw,D,~ ~ (9~,k"
Hsw,,,~)
(12)
k=O
2.4 Shortwave radiation balance on window The balancing of energy streams for each individual pane is the foundation of the numerical method for calculating the passage of shortwave radiation through the window and the absorption of radiation energy in separate window components• This requires the use of such optical properties as transmissivity rsw, reflectivity rsw, and absorbtivity asw. In this case we distinguish between diffuse and direct radiation as was done earlier when the total radiation on the facade was taken as being comprised of a diffuse part DrAs and a direct part SeAs. For these two kinds of radiation there will be different values for the optical properties mentioned above• In this connection the radiosity for the window surface, which reflects radiation back and out of the room, H~,ee is viewed as fully diffuse. In Fig. 6 the radiosities Hsw and the flux of absorbed heat flows qsw, together with the window installation consisting of N glass plates, sun-shade, or like components (Sl • • • Ss), are sketched• [Because of the detailed representation, the index S W (shortwave) has not been used•] As an example, for the chosen internal radiosity H2,3 of layer $2, the figure allows the equation
in which Hsw, k,n is the diffuse part of the radiosity. The diffuse radiosity Hsw,s,~ can be written (13)
nsw.s,i .Ai = rsw,s,i .S±,o.A±,i
In this relation the projection of surface A~ normal to the radiation direction A±,~, can be written A~,i = cos Ct "Ai.
(14)
Since for the i-th surface only a part becomes directly sunlit, an approximation is found through the use of the sunlit area fraction defined in subsection 2.2. Thus the radiosity for the i-th surface caused through reflection of direct radiation becomes Hsw, s,i = rsw,s,i" cos ¢i" SJ_.oXi.
(15)
If the diffuse Do and direct radiation S.,0 entering the room are known, the foregoing equations may be combined into a system of linear equations. The radiosities find use with the calculation of the heat flows O.sw,i, which are caused by the absorption of shortwave solar radiation striking the building surfaces. During its calculation, a balance over the incoming and outgoing energy streams is obtained from which follows the absorbed heat flow rate
112,3 = r2,iH3,2 + r2,aHi,2
to be written, in which the reflectivity r2 and the transmissivity z2 of the second pane are considered• The index i describes the radiation direction from an inner to an outer or external surface; the index a stands for the reverse direction• The radiosity H3,2 is, by analogy,
Qsw, i = ( ~, (@i,k. Hsw,~,D) - Hsw,~ k + S±,o" cos ~ . x~ )A~.
(16)
//32
®
@ Ia
3a
2t
h,al
a2,a[
a2,l,a!a2,2,a H2,3
1,\1 al,l,iJal,2, ial,i
HSI,I
I
I
H2,1
~
a2,1,1[a2,2,i ~--ff[ 'r2,i a2, i
HS1,2 HS2,1
Na
3i
a3,1,a a3,2,a
ql,l lql,2
=
HS2, 2
H3,2
N, i TN,a I
.,4 HN-I.~ aN,l,a aN,2,a HN,N+I'HF_[,P&
i.t '/ I
a3,1,i a3,2,i .~ x3,t [ a3,4 HS3,1
(18)
@
111 ,
r3,an2,3 + T3,in4,3.
a3 ,a I._m." "r3,a
'2,71-"
HO,I'HFAs al,%,alal,2,a H1,2
=
@
2a
Ii
(17)
--
HS3, 2
Fig. 6. Shortwave radiation balance for window.
N+| ,N=IIRA,FE
- I aN'l'i[ aN,2,i
JJ
HSN,1
I "N,| HSN,2
487
Investigation of the energy flows The generalization of the two previous equations leads to Hj,k = rj,iHk,j + rj, aHj-i,k-I
(19)
Hk,j = rk,attj,k + "rk,ink+l,j+l.
(20)
The energy balances for all the unknown radiosities yields a system of linear equations of the form M.H=
O
(21)
in which the matrix M contains the material properties of the layers and the vector b comprises the known radiosity HrAs (either DFAS or Sr~s) and the room-toinner window surface back reflection radiosity H~,rE. With the absorbtivity for the individual layers, the heat flux due to absorbtion can be calculated directly for the two different directions of radiation: {lj,l,i = aj,,.i Hj+l,s
(22)
(lj,2.i = aj, z.i Hj+Lj
(23)
dlj,L. = aj,,.~Hj_~,j
(24)
[b,2,~ : aj,2,~Hj Lj.
(25)
2.5 Convective a n d longwave heat transfer Basic convective heat transfer can in general be described by Newton's law of cooling. Previous work has used an overall coefficient of convection both for free
convection as well as mixed forced and free convective heat transfer and, in this manner, the respective surfaces of the room (outside, inside, air cavity surfaces, etc.) found consideration. The influence of longwave radiation of the facade is taken into consideration through the energy balances over the emissions of the various building surfaces as well the reflected radiation from the surroundings and atmosphere. This follows the work of Kondratyev[12]and others by means of an empirical equation given by Schaube [13]. Taking as a basis the numerical model concisely described here (a more detailed description can be found in Kraus's dissertation[7]), a simulation program for determining the thermal and energy behavior of the testroom can be developed. The computer program language "C", employed for this choice, appeared to have the highest probability of lasting use despite the availability of widely different computer architecture. In addition, because of the versatility of this language, the numerical calculations create results which are essential for the optimal management and control (heating, cooling and shading) of large buildings.
3. RETROSPECTIVE CALCULATIONOF THE ANNUAL TOTAL ENERGY BUDGET FOR THE TESTROOMS The retrospective calculation of the annual heating and cooling budgets for the research rooms under working and weather conditions prevailing during the test year 1988 was carried out.
3.0-
1988
2.5
ID
2.0
Calculated
n~
>~
Measured \
1.5
ID
1.0. ro o
0.5 0.0 Room1/88 ~measured
I
Room 2/88
Room3/88
~Heating e n e r g y ~
[T7~calculatedJNeed
Room4/88
Room 5/88
Room6/88
measured ~Cooling energy
~---~calculated JNeed
Window types: REF -reference, VB/FR -composite with sunshade AB/FR -exhaust air, WS-insulated, TWS-insulated with controlled shutters ~g. 7. Comparison of measu~d and calcula~d annual heating and cooling ~quirements ~r six tearooms.
488
R. KRAUS,E. R. F. WINTER,and W. IBELE
The respective measured annual energy budget, divided into heating and cooling requirements, and the corresponding calculated annual energy budget are shown as bar graphs in Fig. 7. For the numerical calculations, test-facade construction details are given in Table 1. The comparison of the calculated energy requirement for heating of test room 1/88 (thermopane) with the measured value shows a deviation of somewhat less than 10%. For the cooling, energy needed the calculated value amounts to 93% of the measured value. In the following, the percentage given always refers to the measured value for the respective room. Thus the calculated relative total energy budget for research room 1/88 shows a value of 98%. For testroom 2/88 (composite window with sunshade) a larger deviation exists; the relative heating need amounts to 90% and the relative cooling need amounts to 85%. The deviation of the calculated total energy budget from the experimentally determined value amounts in this case to about 12%. The energy behavior of testroom 3/88 which, as in the case oftestroom 2/88, is furnished with a composite window with a sunshade, is closely replicated by the computer program. The relative values for heating and cooling energy needs for the room amount to 101% and 91%, respectively, which yield a relative total energy value of 95%. In the instance of testroom 4/88, although it is equipped with an exhaust air window, the results shown are for zero flow ( ITASL= 0 m3/h) of exhaust air. The relative heating energy need of 101% almost matches the measured value. The calculated cooling energy need is 25% higher than the measured value, a result which can be explained by the fact that the simulation calculation does not consider the large-scale air circulation, and related heat transfer from the inner surfaces and sunshade, within the exhaust air chamber of this window type. The simulation calculations for testroom 5/88 with a facade equipped with a three-pane thermopane gave, for the heating case as well as the cooling case, good agreement with the measured results. The relative heating energy requirement amounts to 91% and the cooling requirement to 101% of the measured needs, from which a relative total energy budget of 97% obtains. Similarly, for testroom 6/88, equipped with different rotating temporary shutters and heat barrier (insulation) which could be controlled during the course of the investigation, a good agreement was found. The relative values for heating and cooling were 99 and 102%, respectively, and the calculated total energy budget was the same as that measured. The results for the numerical simulations and measurements indicate, that despite some minor differences the computer program provides for a very good simulation of the temperature and energy behavior of the testrooms. It is therefore capable of calculating in advance the energy budgets for rooms of different and complex construction and equipped with arbitrary facades.
4. STANDARD REFERENCE YEAR
In order to be able to make a convincing prediction of the energy behavior of the testrooms over a representative time span, the meteorological boundary conditions for the area of southern Bavaria, as represented by the weather data for a SRY, were imposed on the various facades and testrooms. The SRY represents a collection of data for certain weather characteristics, whose mean values correspond to the long standing ( 10 to 15 years) average climate. The test reference year for a typical regional climate in the German Federal Republic (preunification) was developed according to the general research goal of the federal ministry for research and technology (BMFT). The SRY described here is the one developed by Troeltsch [6 ]and meets the observation of Jahn[14]that the most realistic model of building spaces possible can only be based on real, simultaneously measured data from a weather station. Thus, given the presence of hourly data, the following weather parameters should be included: • • • • • • • • • •
air temperature, background radiation (on the horizontal plane), sky radiation (on the horizontal plane), sunshine duration--hourly or relative of coverage, wind velocity, wind direction, relative humidity, air pressure, ground temperature, and snow cover.
For the construction of a suitable SRY the actual weather records for 12 individual months (not necessarily successive) were taken from sequential data for several years. The selection of a month as a time period is a compromise, because considering the thermal response of the rooms, it already represents a long time period; on the other hand a multi-year average of the behavior of individual weather variables is desirable for the development of a good model. The selection of the individual months follows the procedure given in Jahn's research[14]. There, not only do the monthly and annual averages find consideration, but the average values over the heating and summer seasons do as well. The SRY months of January, February and June, and July were selected first. Within these months the maximum and minimum for the comparison parameters as well as the averages of the outside air temperature, total background radiation, and the sunshine duration should lie close to the respective means and totals recorded over many years for these months. Subsequently, the months of August and December were selected so that their usual climatic conditions corresponded to the respective quarterly average values. These six months were not changed. To complete the selection, the months of a transition period (March, April, May, and September, October, November) were assigned weather conditions corresponding to the annual means and totals of long standing. For the greater Munich area, measurements taken
g
Foil shade
2.1 1.7
--
3.0 2.2
2-panes insulated glass
Plain glass
Composite window
2
1.1 1.1
2-panes insulated glass (Argon) Foil shade
Plain glass
Composite window
3
* The values given are for open sun shades and open shutters.
Sun shield, movable insulation u-value* ugt, [W/m 2 K)] ufa,. [W/(m 2 K)]
2-panes insulated glass
--
Construction outer
inner
Reference
1
Test element
Room number facade
1.1 1.1
Foil shade
2 -panes insulated glass (Argon) Plain glass
Exhaust air window V = 0 m3/h
4
0.9 0.95
--
3-panes insulated glass (Argon)
Insulated window
5
3.0 2.2
Insulated movable shutters
2-panes insulated glass
Insulated movable shutters
6
Table 1. Construction of test facades
1.1 1.1
Foil shade
2-panes insulated glass (Argon) Plain glass
Exhaust air window V = 50 m3/h
7 (see No. 4) 8
<0.9 <0.95
3-panes insulated glass (Argon) Foil shade
Plain glass
Composite window
(see No. 3)
0.6 0.8
3-panes insulated glass (Krypton) Movable shutters (glass)
Special construction - const.
9
0.6 0.8
(Krypton) Movable shutters (glass)
glass
3-panes insulated
Special construction = const.
10 (see No. 9)
R. KRAUS,E, R. F. WINTER,and W. IBELE
490
Table 2. Composition of the SRY and summary for the SRY of outside air average temperature and total radiation on a vertical surface (C~ras = 198 °) Month Out of Composition Calendar of the SRY year
January February March April May June July August September October November December
1977
1972
1975
1974 1977 1977 1977 1977
1978
1978
1978
1973
toA = 7.5°C. qSOL.O= 830 [kW h/mS].
at the Weihenstephan Weather Station were employed, with which the m o n t h s o f different calendar years were compiled to f o r m t h e SRY (Table 2). For the two most important parameters: (a) outside air temperature ton and ( b ) the total o f shortwave irradiation on a vertical surface qSOL.O, the table also gives the m e a n and total values for the SRY. The daily trace of the outside
tOA
air temperature and total radiation Gens on the facade surface during the SRY is shown in Fig. 8. 5. ADVANCE CALCULATION OF THE ANNUAL ENERGY BUDGET OF ROOMS WITH DIFFERENT TEST-FACADES As a result o f the comparison o f experiments and the c o m p u t e r model predictions, it is now possible to
20
[°C] -20
GFAS [W/m 2]
Fig. 8. Course of outside air temperature tAL and the total radiation for a vertical surface (aFAS = 198 ° ) during the SRY.
Investigationof the energy flows calculate the thermal and energy behavior for any given facade and arbitrary room dependent upon the weather data of the standard reference year. Here, six individual, experimentally investigated facades are considered. The numerical calculations were extended to other window types of improved performance (as shown in Table l, under the headings 7, 8, 9, and 10). The first newly added facade (No. 7) involves a modem exhaust-air window construction similar to the type installed in testroom 4/88. In this facade variation, however, the computation of the annual energy budget is carried out with a given through-flow in the space between the two innermost glass panes, of 12AsL= 50 m 3 h - l , which corresponds to a turnover of room air ofn ~ 1.5 h -~ . This differs from facade 4/88 in which the air gap between the panes was sealed. Another facade type (No. 8) consisted of an composite window with an internal, three-pane thermopane and a rolling sunshade, as well as an outward facing glass pane. The heat shielded glasswork corresponds to that of testroom 5/88 and the shade has the same properties as that employed for facades 2 and 3, the support structure and frame as well. The third new facade type is similar to a prototype currently installed by the Gartner firm. The construction consists of a three-pane heat shielded glasswork, whose infrared reflecting coating has an emissivity value, ~ ~ 0.05, and whose space between panes is filled with krypton gas. The thermally isolated frame has a k-value of approximately 1.7 [ W / m : K]. An externally installed, reflecting jalousie system serves as a sunshield and makes it possible to distribute daylight in the room for optimal illumination. Under these conditions it is extremely difficult to specify a radiation transmissivity for this sunshield. Therefore, assuming computer control of the jalousie, the system adjusted for optimal energy conditions using integral radiation transmissivities in the range of r s s v = 0.2 to 0.8 (No. 10). For the purpose of comparison, the annual calculation was carried out with a constant transmissivity of r s s v = 0.4 which implies a fixed sunshield position (No. 9). The annual energy profile for the test facades is complete in the sense that the simulation calculations are determined for a weather course which considers every single day of the SRY. Summing the energy flows, heating, and cooling for 366 days yields the annual total energy budget for the respective test facades. The results of these calculations for all window types are shown in Fig. 9. As before, the lower hatched area represents the heating part of the total energy budget and the upper area the cooling part. The total energy turnover of 2.8 MW h / a n n u m calculated for testroom 1/SRY is larger than that measured for testroom I/88 because of higher total radiation and lower outside air average temperatures during the SRY (see Fig. 7). In considering the results shown in Fig. 9, it should be noted that for rooms 2/SRY through 6/SRY there were differences between the respective experimental and numerically determined values (see Fig. 7). The
491
reasons for these differences may be attributed to the different weather conditions during the test year in contrast with those of the standard-reference-year as well as different control of the sunshades (jalousies). These difference are only slight however as verified by the interpretation of the test results for the six rooms I/SRY through 6/SRY as given in Schulz et al.'s report [ 1] and Kraus's dissertation [ 7 ]. The calculated results for room 7/SRY show that the through-flow of room air in the space between the innermost panes caused a dramatic reduction of the relative energy requirements when compared with those of testroom 4/SRY. The latter resembles room 7/SRY but had no through-flow. The calculated savings amounted to about 25% for heating and 30% for cooling. It should be noted that the ventilating air flowing between the inner panes is provided from the room at the constant temperature maintained there, a condition assumed in the calculations. The heating and cooling energy required for this exhaust air stream can be taken into consideration specifically in future numerical simulations. The complete climate control of a building can be accomplished using exhaust windows throughout for greatest energy economy. This is especially true if during the period of intensive solar radiation on the south-facing windows the waste heat generated is used to heat the northerly rooms. An improved version of the composite window construction oftestroom 3/SRY, through the insertion of a three-pane-heat shielded glasswork, reduced the heating requirements about 15%. The cooling requirements for such a room (8/SRY) compared with the original testroom 3/SRY are reduced to 87%. Whether this and the above listed energy savings justify the increased capital costs must in each individual case be proven through established economic analysis. The special construction of facades 9/SRY and I0/ SRY, although expensive to fabricate, offer definite advantages in energy savings when the radiation transmission of the sunshield is optimally adjusted for the prevailing weather conditions. For the two modes of operation, room 9 / SRY-sunshield position fixed and room 10/SRY-sunshield position varied, there are performance differences of 11% for heating and 40% for cooling. With a computercontrolled sunshield operating under the conditions described earlier, room 10/SRY saves 27% of the energy needs of room 9/SRY with its less than optimum sunshield, and 81% of the energy needs of room l / SRY. Further possibilities of optimization, for example, an improved illumination of the spaces with daylight or the adjustment of illumination conditions for videoscreen work stations, remain to be considered. 6. SUMMARY By means of a numerical analysis, preceeded by extensive measurements on six testrooms, an investigation was undertaken to develop a readily used computer program. The program accurately reproduces the measured results for the BMFT-sponsored tests as well
R. KRAUS,E. R. F. WINTER,and W. IBELE
492 3,0"
\
~' 2,5
SRY c"
~
2,0-
°
\
"
\
_J
\
1,5
S.
° 0
~-
1,0-
¢
0,5
~/
O. 1/SRY
2/SRY 3/SRY 4/SRY 5/SRY 6/SRY 7/SRY 8/SRY 9/SRY IO/SRY WS z:const, x#const.
•
Heating requirement
~Cooling
requirement
Fig. 9. Calculated annual energy budget of research rooms with various test facades.
as predicting the heating and cooling energy requirements of the testrooms, equipped with arbitrary facades, for the weather conditions of a SRY. In the course of developing the program, the varying thermal and energy behaviors of the rooms were determined using a fully implicit finite difference procedure. Before undertaking the calculations the three-dimensional physical model was simplified by conversion to a onedimensional, linear numerical model. The deviations from one-dimensionalitywere also found by calculating the energy transport for exhaust-air windows and the long- and shortwave thermal radiation exchange in the rooms. To guarantee that the numerical calculations of testroom thermal and energy behavior were exact as possible, particular emphasis was placed on adjusting the model to correspond to the geometrical and thermal conditions which held for the experimentally investigated testrooms. However, the development of the program allows the thermodynamic behavior of other room designs of light, moderately heavy, and heavy construction to be determined. Further, the energetics of the ventilating air stream and internal heat sources as well as artificial illumination can be treated. The results of numerical modeling are found to be in good agreement with the measured energy exchange record for the six testrooms. Confidence in the applicability of the linearized numerical model and the computer model for predicting the energy exchanges for rooms of various construction is based upon this agreement between measurement and calculation. In summary, the computer model here described, secured by extensive experimental data, offers the possibility of replacing additional measurements on other types of facade constructions with rapid calculation
and substantial cost savings. Due to improvements in microelectronics, high capacity computer systems are no longer required, so such numerical calculations can enter into the planning of every building. This will influence the part of building design and construction dealing with energy considerations, and shape future, carefully directed, experiments which provide the foundation for continuing research.
Acknowledgments--This research was partially supported by the Minister of Research and Technology(Germany) and the J. Gartner Company, Gundelfingen (Germany). REFERENCES
1. H. Schulz, W. Heusler, E. R. F. Winter, and R. Kraus, Energietransport durch transparente und nichttransparente Aul3enwandkonstruktionunterschiedlichenAutbaus, final report, BMFF FE 03E 8134 A (1989). 2. R. Kraus, E. R. F. Winter, H. Schulz, and W. Heusler, Energietransport durch transparente und nichttransparente AuBenwandkonstruktionunterschiedlichenAutbaus, Bauphysik 13, H. 6; 239-242, H 7; 19-22 ( 1991 ). 3. G. Brown, 1Vletodfor datamaskin ber~ihningav kyloch v~irmebehov, V VS 34 i 1, 40 I-410 (1963). 4. L. Rouvel, Analoges und digitales Rechenverfahren far die Interdependenzdes w~metechnischen Verhaltensvon Raumumschliel3ungsfl~ichenbei dynamischer W~irmebelastung, Dissertation, Technical University Munich (1972). 5. G. Hauser, Rechnerische Vorherbestimmung des W~irmeverhaltens grol3er Bauten, Dissertation, University of Stuttgart (1977). 6. M. Troeltsch, Numerische Simulation des W~rmeverbrauchs und des Temperaturverhaltens von l~umen als repr~isentativeTeile von Geb~iuden,Dissertation, Technical University Munich (1986). 7. R. Kraus, Experimentelleund numerischeUntersuchung des Energieverbrauchsan transparenten Fassaden, Dissertation, Technical University Munich (1990).
Investigation of the energy flows 8. J. Klas, Numerische Simulation des Energieverhaltens luftdurchstr6mter, lichtdurchl~ssiger Fassaden, Diplomarbeit, Lehrstuhl C ftir Thermodynamik, TU MiJnchen (1987). 9. DIN 5034, Tageslicht in Innenrfiumen, Beuth, Berlin (1985). 10. U. Gross, K. Spindler, and E. Hahne, Shapefactor-equations for radiation heat transfer between plane rectangular surfaces of arbitrary position and size with parallel boundaries, Letters in Heat Mass Transfer 8, 219-227 ( 1981 ). 11. G. Kasparek, Der Energieaustausch durch W~irmestrah-
493
lung zwischen Feststoffoberfl/ichen, BrennstoffWSrmeKraft 24, 6, S. 229-233 (1972). 12. K. Y. Kondratyev, Radiation in the atmosphere, International geophysics series, vol. 12, Academic Press, New York (1969). 13. H. Schaube, Untersuchungen fiber Wiirmetibergangskoel~zienten an Fenstern mit und ohne W~irmeschutzeinrichtungen unter natiirlichen Klimabedingungen, Fraunhofer-lnstitut ftir Bauphysik, Bericht EB-I 5/1986 (1986). 14. A. Jahn, Das Test-Referenzjahr, Eine Sammlung sttindlicher Werte interessierender Wetterelemente, HLH 28 (19177), 199-206, 257-265, 295-299 (1977).