A simple method for determining the heating requirements of direct-gain passive solar houses

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A simple method for determining the heating requirements of

direct-gain passive solar houses

Ser

TZl

A SIMPLE METHOD FOR DETERMINING

THE

OF

DIREfl-GAIN PASSIVE SOLAR

S.A.

D,M.

A simple method to calculate the heating energy requirements

of direct-gain passive solar houses is presented. The calculation

procedure is baeed on the concept of solar utilization factor,

which i s d e f i n e d a s that fraction of the t o t a l solar gain through

all windows of a house that contributes to the reduction of

heating requtrements, The method is incorporated into a graphical procedure that can be easily used during the design process to

f i n d the combinatloa af south w i n d w area and t h e m 1 storage maea

that d n l m i z e s purchased space heatkng energy.

It

"S

houses to ovlnass sun-tempered ones.

LNTRODUCT ION

The need

for

of a hwee is widely recognized. Such an estimating technique could be used

for comparing alternatfves i n the design proceas and for evaluating house designs t o determine their canpliance with energy standards.

An important aspect of such a method is the a b i l i t y to estimate the amount of solar energy collected through the windows of a house and u t i l i z e d t o o f f a e t heat losses.

A number of methods have been developed to eetimate the net salar contrtbution t o apace heating f o r dlrect-gain passive salar de81gns.

The ~olar-load-ratio method, (SLR), developed by the LOB ATamos Scientific Laboratorylr2 is widely used

In

the SLR method is easy t o use, the range of parametere that can be

considered ia l i m i t e d to those used tn the reference d e s i g n s .

In

it cannot be used t o examine the effects,

em

such as the number of glaziaga and the amount of t h e m 1 storage. The

SLR

method

hae,

maw

computerized t echniquea.

Another approach t o estimating the solar contrfbution is the

method relfes on solar radiation s t a t i s t i c s to detemlne the fraction of s o l a r gain that is not useful and t h a t must be e l f d n a t e d to prevent overheating. Hore parameters can be considered than with the SLR method, but more calculations and greater involvement with radiation data are

required.

It

Recently, hawever, the "un-utilizability" s y s t e m was made easier t o apply

through the use of tables and graphs4.

'She procedure presented in this paper combines the s i m p l i c i t y of the

SLR

It

w e l l as direct-gain passive solar houses, and is applicable t o the complete

range of housing types, from the high-mass direct-gain to the l o w s s

sun-tempered.

The

basis. T b l s makes it e a s l e r to uee, and a h a p e r m i t s it: to be incorporated

into a graphicdl technique whtch cam be a p p l i e d to determine the optimum* combination of s o u t k f a c i n g window area and thermal storage mass. The

graphical technique can a180 be uaed to i l l u s t r a t e t h e sensitivity of

seasonal heating energy requirements to change8 i n glaas area, type of

glazing, or thermal mass. Examples for a Canadian location ( O t t a w a ) indicate that thfs s e n s f t i v i t y i s less than might be commonly expected.

The energy con8umption values measured in the NRC passive t e s t units

d u r i q the 1981-82 heatfng season have been compared arb the corresponding

values calculated using this method5. The calculated values w e r e in close

agreement w i t h the measured results, the maldrrmm difference amounting t o

less than 5%.

TEE UTILIZATION FACTOR

The calculatioe procedure is baaed on the concept of the solar

u t i l i z a t i o n factor. T h i s factor, qs Is defined as that fraction of the

t o t a l solar gain, through all w%ndows of a hwse, that contributes t o the

reduction of the heating requirement; that is,

= Useful salar gain

9s %local solar galn

The useful solar gain far any hour includes the solar gain used to o f f s e t h e a t losses during that hour, plus the portion etored In the t h e m 1 mass

and used to offset losses a t a l a t e r time. It does not include the excese gain t h a t m a t be discarded to prevent roam temperature from exceeding a

preset maximum, nor any gain u t i l i z e d t o offset additional losses caused by

a rise in room temperature above the thermostat setting.

The seasonal heating energy requlsement (H)

for

where:

L

q, = utilization factor for solar gains,

6, = total ~ o l a r heat galas through windows.

The

solar

(GLR)

mass-gain ratio"

(MGR).

The galn-load ratio is the ratio of solar gain through d n d w s , Gs,

to the net heating load, L, or:

This gain-load r a t i o d i f f e r s from the solar load ratlo (SLR), as

d e f i n e d in Reference 2,

In

the windcrws, n o t only those f a d n g s mth.

The mass-gain r a t i o reflects the thermal storage characteristics of

the b u i l d i n g as well as the area, type and osientatfon of the glazfng.

It is defined as,

where: C = thermal capacity of the building interior

CMJIK),

gs = average hourly solar gain f a r season (MJ/hs),

( g s = Gs/houra in heating season).

The thermal capackty, C,

is

b u t l d i n g multiplied by its specific heat. The effective mass is the mass

actually available to store heat as a result of direct solar gains, or that

in close contact with ram af r so that any change

in

air

affects the mass temperature,

This

insulating layer of the walls and ceilings, but excludes the exposed

concrete of uninsulated basement walls and floors. Typical, thermal capacity

values for

four

are

Solar u t i l i z a t i o n factor^ were derived using hour-by-haw computer simulation

of

space heating load, thermal storage mass, solar gain and allowable

temperature awing for f i v e Canadian location&

.

factore w e r e correlated using the parameters GZR and MGR, and w e r e

independent of geographical laslation as a h m in Figure

1.

the solar utflizatioa factor platted against the GZ,R

for

MGR and a room temperature rise of 5 . 5 " C . Curves for the cases of O* and

2.75"C temperature rises are a l s o available in Reference 5.

C A L G W T I O H OF

HEATING

The basis of the c a l c u l a t i o n method is the simple heat balance equation

of the house, as &pea by Equation (1).

The seasonal net heating h a d , L, is calculated as:

where: La, = total heat losses due to transmission through exterior walls,

windows, c e i l i n g s , etc.

,

t, = t o t a l heat losses due to indoor-outdoor aSr exchange (in£ i l t r a t i o n

+

Lb = total belou-grade heat loss,

ni

Gi = total heat galas f rorn internal sources ( l i g h t s , equipment, people, e t c * ),

The seasonal t o t a l of heat losses due to transmissbon through the exterior

w a l l s , wiudcws and c e i l i n g is calculated ae:

where: M = number of hours in the heating season,

-

B1 = average indoor a i r temperature ( O C ) ,

go

UA

windms

(WIK).

The conductance values, UA, can be calculated as described tn the AS-

andb book^,

8,

The heat losses due t o indoor-outdoor air exchange,

La,

calculated from the equation:

where:

Am

v

1.

The total below-grade losses can

be

recently developed by Mftalas8

.

The mgnktude of the fntcrnal gains, G depends on the occupancy of the house. While date concerning the rate $'heat release by various

appliances are available, tt is always necessary to make arbitrary

assumptions regarding occupant behaviour and, therefore, of the internal

gains. For m o s t s i t u a t i a n ~ in which GI is less than 25X of the heat losses,

all of the internal gaim are assumed to be u s e f u l

(rr

The seasonal t o t a l solar gain through the windows is calculated as

where the subscript 1 represents the orientatLon of window and:

4% = glass area,

SCI = shading coefficient: of window,

Q i = t o t a l solar gain through unit area of a single sheet of standard glass, given by Of = 0.83 B i ,

where Hi is the total seaeonal solar radiation incident on the window

E U ~ f B C ~

Values of the total monthly solar radiation incident on surfaces of

different orf entations and t iltg are tabulated for a number of locations.

In

Service as 10-yeas averages for 130 locations. The

seasonal

be obtained by summing the values f o r the appropriate months.

Equatiom

(2)

M X .

found

1

SAMPLE CALCULATION

The method w i l l be i l l u s t r a t e d by calculations for a two-story h w s t

located in Ot taws, Canada. The assmed heatlng season runs from October to

April incluskve (5064 hours). Far t h i s period the average outdoor

temperature is -3.25OC and the gofar cner incident on south- and

north-faefng surfaces is 2910 and 510 XI/

,

indoor temperature 18 assmed to be

21°C.

S

The house is w e l l insulated (B6 walls,

R10

w a l l s ) and of frame c o n ~ t r u c t i a n . It has

7

of

14

south-facing double glazed windows. The characteristics of the house are as

follcws: floor area u house v o h e = IJA (walls) =

UA

(south

in£

d

w/a

23.2

WIK

6

0.25 a t r changes per hour.

A, Ealculatioa of Lt, from Equation ( 5 ) ,

Lt

-

B. Calcvlatioa of la, fro. Equation ( 6 ) .

L = 31

loo

w

a

C

.

5 ,

8,

D, Internal gains art assumed t o

be

-

K

l

i

E. Calculation of

L,

G. Gain-load ratio, from Equation (21, GLR = 3 2 4Q0 _{= 0.36}

90 5130

H. Mass-gasn ratio from Equatlw ( 3 ) and aaswning thermal capacity of

0.06 W/K p e r U? of floor area (Table

11,

1. From F i g u r e 1,

ns =

0.88

J.

GRAPHICAL DESIGN METHOD

Solar utilization may a l s o be presented as the f r a c t i o n of the net

heating load

which

(Fh), wlll be referred t o as the "purchaaad heating fraction"\ (It is, in

f a c t , equal to one minus the solar heating fraction.)

Figure

2

These curves a p p l y for a maximum allmable temperature swfag of 5.5-C;

graphs for other temperature s d n g s are given in Reference 5.

The heating energy requirement far the house can then be obtained from:

The above procedure can be incorporated into a simple graphical methad

to examine the effect of south-facing windm type and area, as well aa

thermal storage, on the heating requirement of a house.

Figure 2 can be reformatted aa shown in Figure 3. On the same sheet

t h e follming can be p l o t t e d againat south windm area for a particular house design:

A . Solar gain,

G,,

window area, a s s d n g that the areas of windows on the ather

orientatf ons remain f i x e d :

where

Go

solar

south.

B. N e t house load, L, calculated as a linear function of south window

a r ea:

where

L'

south-facing rindov (Asouth =

0)

C. GLR, obtained by dividing G g by L at a number of p o i n t s .

D. MGR, obtained by computing C N/GB for a number of values of %mth

-

The procedure t o construct the relationship between window area and

purchased heating requirement %s as follms (Figure 3 ) :

I . For any south window area, draw a vertical l i n e to intersect the

solar gain line, the net load l i n e , the

GLR

curve at pointa A, B,

C

D,

2. Ilrm a horizontal l f n e from point: C to intersect: the purchased

heating fraction plot for t h e appropriate MGR (measured at D) at point E {same interpolation between MGR curves may be necessary).

This determines the purcha~ed heating fraction, Fh

.

requiremnt, R, is then equal t o t h e product of Q, and L. T h i s

is obtained graphically in the next three steps.

3. Draw a horizontal l i n e from point B

to

of Fh = 1.0 at

X,

X

Y

( p o i n t of interaectfon of the vertical l i n e thraugh Fh

-

4 . Draw a vertical l i n e from point E to meet t h e l i n e XY at F.

5, Drew a horizontal l i n e from point F t o meet t h e o r i g i n a l vertical

line of S t e p 1 at p o i n t G. The energy value a t p o i n t G represents t h e purchased heating energy assaciated with t h i s south wfndow

area.

6, Repeat: steps 1 through

5

A change in thermal storage for the same house can be accommodated simply by calculating new values of MCX

and

in window type requires repetition a f the entire procedure b e g h n i n g by

recalculation of both G, and L.

Examples are presented in Ffgures 4 and

5

envelope constructions {thermal resistance] in Ottawa, Canada. For each example, three optfons were evaluated:

1. light frame constructien with all vindows d o u b l e g l a z e d ,

2, same as

L

3, l i g h t construction with all windows t r i p l e g l a z e d .

Details of the six cases examined are given in Table 2 alang d t h the

minimum purchased heating required far each case and t h e optimum south window area.

S€?MMAKY AND OBSERVATIONS

T h i s s i m p l e graphical procedure may

be

construction, the optimum combination o f 6011th window area, windm type and

thermal storage mass. The method w i l l subsequently be used to develop

guidelines f o r t h e desfgn of df rect-gain passive solar houses in Canada. The fallowing observations regarding direct-gain passive solar houses in the Canadian clfmate were arrlved at by application of t h i s method t o a

number of house designs for the Ottawa climate.

The

very shallow around the optimum area.

In

change i n purchased energy requirement (a maximmi a £ 4% in the s i x cases

The oprimum south windm area decreases for the mare energy conserving houses. For d o u b l e g l a z e d w i n d m s and light-weight construction, the

o p t i m a area is about 8X of flaor area for aa 80 GJ house (House 1). This

reduces to 3.5% of f l o a r area for the more cnerjy conscrvlng 48 GJ house

(House 2).

While en increase in

the

results i n a reduction in purchased energy, a larger reduction in purchased energy c m be achieved with a smaller area of triple-glazed windows. Taking

the optimr d a u b l r g l s z i n g cascs as the b a s i s for comparison, a fourfold

increase in the mass results in a 7% reduction in purchased heating for

Rouse 1 and 24: f o r Rouse 2. The use of triplwglazing results

In

of 15% and 21I f o r Houees 1 and 2 , rtspectivcly.

REFERENCES

1. Wray, W.O. Design

and

tA-8885+S, Los M m o s Scientific Laboratory, 1981.

2. Balcomb, J.D., et al. Passive Solar Design Randbook, Vol. 2, Passive

Solar Design Analysis, USDOE/CS-O~ 27/2, 1980.

3. Honeen, W.A,, S.A. Klein and W-A. Beckman. Ptedfcting of Direct Gain

Solar Heating System Performance, Solar Energy, Vol. 27, No. 2,

pp. 143-147, 1981.

4. Klein, S.A., e t al. Tabular Data for the Un-Utilizabifity Passive Solar Design Method, Proc. 6th National Passive Solar Conference, Portland,

pp. 328-332, 1981.

5 . Barakat,

S.A.

Windms for Heating Houses",

BRN

184,

Natlonal Research Council of Canada, Ottawa,

1982.

6 . ASHElAE Handbook af Fundamentals. Amtrican S o d e t y of Fiesting,

R e f rigeration and Air Conditioning Engineers, New 'Pork, Chapter 22,

1981

7. Canadian EFosmals-Temperature. Atmosphtric Environment Service, Dawnsvicw, Ontario, 1975.

8. MitaEas, G.P. Basement Reat Loss Studies at

DBRIW,

Building Rtseazch, Natkonal Research Council of Canada, (DBR Paper

T h c m l Capacity

Floor Area

WJ/rn2~)

TABLE 1. SAMPLE HOUSE WEIGHTS

Construction

L i ht

-

&-

c e i l f n g s , carpet over wooden f l o o r .

Medium

-

As

0.415 Heavy

-

101.6 m b r i c k , 12.7 mm gypsum board f i n i s h

on c e i l i n g , carpet over wooden f l o o r .

Very Heavy

-

TABLE 2.

House 2

Case Case Caac Case Case Case

1 2 3 1 2 3

Floor area, m2 207 207 207 207 207 207

Thermal capacity, W / K 12

.4

m2Ww

Ceflf ng thermal rcslstance, m 2 ~ / W 5 . 2 5.2 5 -2

Glazing type Double Double T r i p l e

South s o l a r gain,

w/m2

Basement heat los~,

GJ

Internal gains, GJ 15 15 15

A i r change rare, 1/h 0.25 0.25 0 -25 Heat loss coefficient

(at *Borrth

-

M t n f m u m purchased

heating, GJ

*

F I G U R E I

SEASOHAL SOLAR U T l l l Z A f l O N FACTOR !ROOM rEMPERAKURE S W I N G

-

a 0.3 0.6 0 . 9 1.2 1.5

GLR

SE4SDHAl PURCHASEO H E A T I N G FRACTION l R O O M rEMPERkTURE S W l H G . 5.5"CI

r

N A M E

-

F I G U R E 3

N AMZ D B R

PROJECT

O T T A W A , C A N A D A

F I G U R E 4