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Basement heat loss studies at DBR/NRC
NATIONAL RESEARCH COUNCIL OF CANADA
DIVISION OF BUILDING RESEARCH
BASEMENT HEAT LOSS STUDIES AT DBR/NRC
by
G. P. Mitalas
DBR Paper No. 1045
of the
Division of Building Research
BASEMENT HEAT LOSS STUDIES AT DBR/NRC by G.P. M i t a l a s
ABSTRACT
A s i m p l i f i e d c a l c u l a t i o n method h a s been developed f o r p r e d i c t i n g : 1 ) maximum r a t e of h e a t l o s s from a basement
2) t h e basement t o t a l h e a t l o s s o v e r t h e h e a t i n g s e a s o n T h i s method d i f f e r s from p r e v i o u s o n e s mainly b e c a u s e i t
r e c o g n i z e s t h e a n n u a l v a r i a t i o n of basement h e a t l o s s a s a s i g n i f i c a n t component of t h e t o t a l basement h e a t l o s s . The development o f t h e method i s b a s e d o n b o t h e x p e r i m e n t a l and a n a l y t i c a l s t u d i e s of basement h e a t l o s s . The e s s e n t i a l d a t a needed t o c a l c u l a t e t h e basement h e a t l o s s a r e t h e s t e a d y - s t a t e and p e r i o d i c s h a p e f a c t o r s , t h e a m p l i t u d e a t t e n u a t i o n f a c t o r and t h e time-lag f a c t o r and ground s u r f a c e
t e m p e r a t u r e s . The basement h e a t l o s s f a c t o r s f o r s e v e r a l i n s u l a t i o n systems a s w e l l a s t h e ground t e m p e r a t u r e d a t a f o r s e v e r a l l o c a t i o n s i n , Canada a r e l i s t e d i n t h e pgper. A comparison of t h e c a l c u l a t e d and measured basement h e a t l o s s v a l u e s i n d i c a t e t h a t t h e method i s c a p a b l e of r e a s o n a b l y a c c u r a t e p r e d i c t i o n of basement h e a t l o s s .
LES ~ T U D E S DE LA DRBICNRC SUR LES PERTES DE CHALEUR PAR LES SOUS-SOLS p a r G.P. M i t a l a s
Une methode d e c a l c u l s i m p l i f i e e a 15tg mise a u p o i n t en vue d e p r b v o i r : 1 ) l e t a u x maximal d e d e p e r d i t i o n d e c h a l e u r p a r l e s o u s - s o l ; 2 ) l e t o t a l d e s p e r t e s d e c h a l e u r p a r l e sous-sol d u r a n t l a p g r i o d e d e c h a u f f a g e . C e t t e mgthode est l e r e s u l t a t d ' e t u d e s e x p g r i m e n t a l e s e t a n a l y t i q u e s . E l l e d i f f e r e d e s a u t r e s e n c e q u ' e l l e c o n s i d k r e l e s v a r i a t i o n s a n n u e l l e s de p e r t e s d e c h a l e u r comme un 6lement s i g n i f i c a t i f d e s p e r t e s t o t a l e s d e c h a l e u r . Les d o n n s e s n g c e s s a i r e s aux c a l c u l s d e s p e r t e s d e c h a l e u r p a r l e s s o u s - s o l s s o n t l e f a c t e u r de rggime permanent e t l e f a c t e u r p g r i o d i q u e d e forme, l e s f a c t e u r s d l a t t & n u a t i o n d ' a m p l i t u d e e t de temps m o r t , e t l e s t e m p e r a t u r e s s u p e r f i c i e l l e s du s o l . Les f a c t e u r s d e p e r t e s d e c h a l e u r d e p l u s i e u r s methodes d ' i s o l a t i o n , a i n s i que l e s donn6es r e l a t i v e s
B
l a t e m p g r a t u r e du s o l d e p l u s i e u r s e n d r o i t s a u Canada s o n t pr'esent'es d a n s l e document. Une comparaison e n t r e l e s p e r t e s d e c h a l e u r c a l c u l e e s e t mesurees i n d i q u e que c e t t e mgthode permet d e p r g v o i r a v e c u n e p r ' e c i s i o n r a i s o n n a b l e l e s p e r t e s d e c h a l e u r p a r l e s s o u s - s o l s .TABLE OF CONTENTS
NOMENCLATURE
...
INTRODUCTION...
DERIVATION OF CALCULATION PROCEDURE FOR BASEMENT HEATL O S S B a s e m e n t M o d e l
...
A b o v e - G r a d e H e a t L o s s...
B e l o w - G r a d e H e a t Loss...
D e t e r m i n i n g B a s e m e n t H e a t L o s s Factors...
C o r n e r H e a t Loss...
CALCULATION O F BASEMENT HEAT L O S S
...
EXPERIMENTAL MEASUREMENTS O F BASEMENT HEAT L O S S...
ANALYSIS OF T E S T DATA...
COMPARISON OF CALCULATED AND EXPERIMENTAL R E S U L T SP a g e 1
5
I n f l u e n c i n g Factors...
1 7 E x a m p l e C o m p a r i s o n s...
18 COMMENTS AND D I S C U S S I O N...
2 3 ACKNOWLEDGEMENTS...
24
REFERENCES...
2 5 TABLES I t o V I F I G U R E S 1 t o 17 APPENDICES:A
-
COMPUTER PROGRAMS USED I N CALCULATIONS B.
SAMPLE CALCULATION O F BASEMENT HEAT L O S S C.
DBR/NRC T E S T BASEMENTS( A l l dimensions used i n t h i s paper a r e i n
SI
u n i t s e x c e p t i f noted otherwise. ) NOMENCLATURE *n a r e a of segment n a n , b n , c n , and dn c o n s t a n t s t h a t a r e s p e c i f i c t o t h e basement t h e r m a l i n s u l a t i o n system n c o r n e r allowance f a c t o r s D h e i g h t of basement w a l l above g r a d eE ( t ) experimental energy consumption
G basement p e r i m e t e r H t o t a l h e i g h t of basement w a l l k lower and s o i l thermal c o n d u c t i v i t y k upper L basement l e n g t h M h e i g h t of i n s u l a t i o n coverage over w a l l m month number ( 1 t o 1 2 )
N
number of segments c o n s t i t u t i n g i n t e r i o r s u r f a c e a r e a of below-grade p o r t i o n of t h e basement P ( t > i n s t a n t a n e o u s h e a t s u p p l i e d t o t h e basement o r c a l o r i m e t e r (power)QT
annual basement h e a t l o s sQ( t )
h e a t l o s s from t h e below-grade p o r t i o n of t h e basementQw
below-grade basement h e a t l o s s f o r w i n t e r p e r i o d q a , n annual mean v a l u e of q n ( t )qv, n amplitude of t h e f i r s t harmonic of t h e h e a t f l u x v a r i a t i o n qv,n ( t ) v a r i a b l e component of t h e average h e a t f l u x through t h e
segment,
h ,
a t time tR thermal r e s i s t a n c e of basement i n s u l a t i o n
RT
o v e r - a l l thermal r e s i s t a n c e of basement w a l l above g r a d el e v e l
n shape f a c t o r t h e s t e a d y - s t a t e h e a t l o s s component
Sn(R) s t e a d y - s t a t e shape f a c t o r s f o r a basement i n s u l a t e d t o a thermal r e s i s t a n c e , R
t t ime
U o v e r - a l l thermal conductance of basement w a l l above g r a d e
l e v e l , l / R T
'n shape f a c t o r f o r t h e p e r i o d i c h e a t l o s s component Vn(R) s t e a d y - s t a t e and p e r i o d i c shape f a c t o r s f o r a basement
i n s u l a t e d t o a thermal r e s i s t a n c e , R
W basement width
*n c o r n e r allowance
Y and c o e f f i c i e n t s determined by a s t r a i g h t l i n e f i t t o t h e yo measured energy d a t a o v e r w i n t e r p e r i o d
Zo,Z1,Z2 and Z3 c o e f f i c i e n t s determined by " l e a s t s q u a r e s " f i t of Eq.
(8) t o measured d a t a S u b s c r i p t s a d e n o t e s s t e a d y - s t a t e component n d e n o t e s t h e segment of t h e i n t e r i o r s u r f a c e of below-grade p o r t i o n of basement v d e n o t e s v a r i a b l e component m month number ( 1 t o 1 2 ) Greek Symbols
a time l a g of power wave
t i m e l a g of t h e h e a t f l u x harmonic r e l a t i v e t o s u r f a c e t e m p e r a t u r e v a r i a t i o n
'
B
basement space a i r t e m p e r a t u r e'G
ground s u r f a c e t e m p e r a t u r e averaged o v e r b o t h time and a r e a ,which e q u a l s mean ground t e m p e r a t u r e
eo,m
monthly v a l u e of o u t d o o r a i r t e m p e r a t u r e e o ( t > outdoor a i r t e m p e r a t u r e a s f u n c t i o n of t i m e v a m p l i t u d e of t h e f i r s t harmonic of t h e ground s u r f a c e t e m p e r a t u r e 'n amplitude a t t e n u a t i o n f a c t o r w a n g u l a r v e l o c i t y of t h e f i r s t harmonic of t h e annual c y c l eBASEMENT HEAT LOSS STUDIES AT DBR/NRC by
G.P. M i t a l a s
INTRODUCTION
One a r e a of u n c e r t a i n t y i n t h e methods f o r c a l c u l a t i n g e n e r g y n e e d s f o r h e a t i n g i s t h e p r e d i c t i o n of basement h e a t l o s s . The methods used t o c a l c u l a t e t h i s l o s s a r e n o t s u f f i c i e n t l y s e n s i t i v e t o b e a b l e t o d i s t i n g u i s h between d i f f e r e n t i n s u l a t i o n methods o r t y p e s , e . g . , a r e a o f basement covered w i t h i n s u l a t i o n and t h i c k n e s s of i n s u l a t i o n . T h i s d e f i c i e n c y i s e s p e c i a l l y i m p o r t a n t today when h o u s e s a r e c o n s t r u c t e d w i t h more i n s u l a t i o n , b e t t e r f i t t i n g windows and a g r e a t e r d e g r e e o f a i r t i g h t n e s s . A s t h e basement h a s become a major component o f t h e t o t a l house h e a t i n g r e q u i r e m e n t , t h e r e i s need of a n a c c u r a t e method t o p r e d i c t basement h e a t l o s s s o t h a t d e s i g n e r s and r e g u l a t o r y o f f i c i a l s can make well-informed d e c i s i o n s r e g a r d i n g basement i n s u l a t i o n .
To s a t i s f y t h i s need, a house basement s t u d y was i n i t i a t e d a t t h e NRC D i v i s i o n of B u i l d i n g R e s e a r c h c o n s i s t i n g of b o t h a n e x p e r i m e n t a l and an a n a l y t i c a l component. The o b j e c t i v e of t h e s t u d y was t o d e v e l o p a s i m p l e c a l c u l a t i o n p r o c e d u r e f o r p r e d i c t i n g basement h e a t l o s s i n o r d e r t o d e t e r m i n e , f o r any g i v e n s i t u a t i o n ,
( 1 ) t h e maximum r a t e of h e a t l o s s from
a
basement, and( 2 ) t h e t o t a l h e a t l o s s from a basement o v e r t h e h e a t i n g s e a s o n . The basement h e a t l o s s problem h a s been s t u d i e d by many
i n v e s t i g a t o r s . Of more t h a n 30 p a p e r s o n t h i s s u b j e c t , t h e most r e l e v a n t a r e l i s t e d a s R e f e r e n c e s ( 1 ) t o ( 1 1 ) . Numerous c a l c u l a t i o n methods have been d e v e l o p e d and used. Many of t h e s e t r e a t basement h e a t l o s s a s a two-dimensional s t e a d y - s t a t e h e a t c o n d u c t i o n problem and have s o l v e d i t by p a p e r a n a l o g u e , f i n i t e - d i f f e r e n c e and f i n i t e - e l e m e n t c a l c u l a t i o n methods.
The paper by F.C. Houghten e t a 1 ( 1 ) was c i t e d f o r many y e a r s a s t h e s o u r c e of t h e basement h e a t l o s s f a c t o r s g i v e n i n t h e ASHRAE
Handbook of Fundamentals ( 2 ) . It d e s c r i b e s a d e t a i l e d e x p e r i m e n t a l s t u d y of basement h e a t l o s s and t e m p e r a t u r e c o n d u c t e d o n o n e basement. A q u e s t i o n h a s always e x i s t e d a s t o t h e a p p l i c a b i l i t y of t h e
e x p e r i m e n t a l r e s u l t s from o n e basement t o o t h e r s i t u a t i o n s .
The paper by G.G. B o i l e a u and
J.K.
L a t t a ( 3 ) d e s c r i b e s a n o v e l a p p r o a c h f o r d e r i v i n g h o u s e basement h e a t l o s s f a c t o r s . The h e a t f l o w p a t h s around t h e basement a r e assumed t o be c i r c u l a r and t h e l e n g t h of t h e s e p a t h s u s e d t o estimate t h e basement h e a t l o s s f a c t o r s .U n f o r t u n a t e l y , h e a t flow p a t h s a r e n o t n e c e s s a r i l y c i r c u l a r f o r a l l i n s u l a t i o n arrangements.
Any review of basement h e a t l o s s must acknowledge p e r t i n e n t Swedish s t u d i e s ( 4 ) . They r e c o g n i z e d t h e s i g n i f i c a n c e of below-grade h e a t l o s s i n t h e t o t a l house h e a t b a l a n c e and c a r r i e d o u t s t u d i e s t o a s s e s s t h e e f f e c t of i n s u l a t i n g below ground l e v e l . Although t h e Swedish a n a l y t i c a l s t u d i e s a r e based on s t e a d y - s t a t e h e a t conduction models, t h e i r r e p o r t s c o n t a i n a g r e a t d e a l of u s e f u l i n f o r m a t i o n on basement i n s u l a t i o n .
The paper by M.C. Swinton and R.E. P l a t t s ( 5 ) f o l l o w s an approach based on c o r r e l a t i n g e x p e r i m e n t a l l y determined basement h e a t l o s s w i t h "degree days" f o r d i f f e r e n t l e v e l s of i n s u l a t i o n . T h i s i s a
q u e s t i o n a b l e approach s i n c e t h e c o r r e l a t i o n of ground t e m p e r a t u r e and number of "degree days" h a s n o t been e s t a b l i s h e d .
The method i n t h i s paper d i f f e r s from t h e p r e v i o u s ones i n two major r e s p e c t s : i t r e c o g n i z e s t h e v a r i a t i o n of basement h e a t l o s s d u r i n g t h e y e a r a s a s i g n i f i c a n t f a c t o r i n t h e house h e a t b a l a n c e and u t i l i z e s a n a l y t i c a l a s w e l l a s e x p e r i m e n t a l d a t a t o d e v e l o p a proposed c a l c u l a t i o n method and t o e s t a b l i s h t h e s i g n i f i c a n t f a c t o r s involved i n t h e c a l c u l a t i o n of basement h e a t l o s s .
T h i s paper on t h e DBR basement h e a t l o s s s t u d i e s c o n s i s t s of s i x p a r t s :
( 1 ) D e s c r i p t i o n of t h e basement p h y s i c a l model and t h e d e r i v a t i o n of t h e c a l c u l a t i o n method,
( 2 ) D e t a i l e d d e s c r i p t i o n of t h e proposed c a l c u l a t i o n method,
( 3 ) D e s c r i p t i o n of t h e basement h e a t l o s s e x p e r i m e n t s , ( 4 ) A n a l y s i s of t e s t d a t a ,
( 5 ) Comparison of t h e e x p e r i m e n t a l and c a l c u l a t e d basement h e a t l o s s r e s u l t s , and f i n a l recommendations f o r basement h e a t l o s s c a l c u l a t i o n s f a c t o r s ,
( 6 ) Comments and d i s c u s s i o n .
1. DERIVATION OF CALCULATION PROCEDURE FOR BASEMENT HEAT LOSS 1.1 Basement Model
F i g u r e 1 shows a p h y s i c a l model of t h e e l e m e n t s i n v o l v e d i n t h e h e a t l o s s from a basement:
( a ) t h e basement w a l l ahove g r a d e ,
( b ) t h e basement w a l l and f l o o r below g r a d e , ( c ) t h e ground s u r f a c e a d j a c e n t t o t h e basement,
( d ) a lower thermal boundary at a constant temperature equal to
the mean ground temperature,
(e)
the conducting solid mass between the basement, the ground
surf
ace and the lower thermal boundary.
The model assumes that sufficient groundwater flow occurs to
maintain a constant temperature at some depth below the basement floor.
1.2 Above-Grade Heat Loss
The instantaneous heat flux through the above-grade portion of the
basement wall can be represented by
where
Ql
(t) =heat flux through the above-grade wall,
U
=over-all thermal conductance of the basement wall above
grade level, I/%,
RT
=over-all thermal resistance of the basement wall above
grade level,
OB
=basement space air temperature,
Oo(t)=
outdoor air temperature as a function of time,
t =
time.
1.3 Below-Grade Heat Loss
The instantaneous heat loss from the below-grade portion of the
basement can be expressed as
where
N
=number of segments constituting the interior surface area
of the below grade portion of the basement,
An
aarea of segment n,
q,(t)
=average heat flux through the segment area, An, at time
The a m p l i t u d e v a l u e s f o r t h e f i r s t and second harmonics o f t h e ground s u r f a c e t e m p e r a t u r e f o r s e v e r a l l o c a t i o n s i n Canada ( 1 2 ) , o b t a i n e d by a F o u r i e r s e r i e s a n a l y s i s , a r e shown i n T a b l e I .
S i n c e t h e second harmonic i s r e l a t i v e l y s m a l l , t h e a n n u a l ground s u r f a c e t e m p e r a t u r e v a r i a t i o n can b e approximated u s i n g o n l y t h e f i r s t harmonic of t h e a n n u a l c y c l e . The i n s t a n t a n e o u s h e a t f l u x e s , q n ( t ) , can t h u s be e x p r e s s e d a s q n ( t ) = qa,,
+
q,,, s i n ( w t ) where qa,, = a n n u a l mean v a l u e of q n ( t ) , q v , n = a m p l i t u d e of t h e f i r s t harmonic of t h e h e a t f l u x v a r i a t i o n , w = a n g u l a r v e l o c i t y of t h e f i r s t harmonic. Heat c o n d u c t i o n t h r , ~ u g h a l i n e a r t h e r m a l s y s t e m i s i n d i r e c t p r o p o r t i o n t o t h e t e m p e r a t u r e d i f f e r e n c e a c r o s s t h e s y s t e m and t h e o v e r - a l l conductance. The two components of q,,(t) g i v e n by Eq. ( 3 ) c a n , t h e r e f o r e , be e x p r e s s e d a s qa,, " Sn(QB
-
QG)
and q V , , ( t ) I Vn o n 0, s i n w ( t + A t n ) ( 5 where S, = shape f a c t o r f o r t h e s t e a d y - s t a t e h e a t l o s s component.I t i s assumed t h a t s t e a d y - s t a t e and mean a n n u a l h e a t l o s s a r e e q u a l .
OB = basement a i r t e m p e r a t u r e ,
OG = ground s u r f a c e t e m p e r a t u r e averaged o v e r b o t h t i m e and a r e a , which e q u a l s mean ground t e m p e r a t u r e ,
V,
= shape f a c t o r f o r t h e p e r i o d i c h e a t l o s s ,u,
= a m p l i t u d e a t t e n u a t i o n f a c t o r , 0, = a m p l i t u d e of t h e f i r s t harmonic of t h e ground s u r f a c e t e m p e r a t u r e , A t n = time l a g of t h e h e a t f l u x harmonic r e l a t i v e t o s u r f a c e t e m p e r a t u r e v a r i a t i o n .The shape f a c t o r , Sn, r e p r e s e n t s t h e o v e r - a l l conductance between t h e basement i n t e r i o r s u r f a c e segment n ( i n c l u d i n g t h e s u r f a c e h e a t t r a n s f e r c o e f f i c i e n t ) and t h e two b o u n d a r i e s ; and between t h e ground s u r f a c e a d j a c e n t t o t h e basement and t h e h y p o t h e t i c a l lower boundary plane a t mean ground t e m p e r a t u r e , a s i n d i c a t e d i n F i g u r e 1. The shape f a c t o r , Vn, r e p r e l s e n t s t h e o v e r - a l l conductance between o n l y t h e
basement i n t e r i o r s u r f a c e segment n and t h e ground s u r f a c e .
Thus t h e shape f a c t o r s f o r t h e s t e a d y - s t a t e and p e r i o d i c h e a t l o s s components a r e n o t t h e same. S t e a d y - s t a t e h e a t l o s s c o n s i s t s of two components: one between t h e i n t e r i o r s u r f a c e segment and t h e ground s u r f a c e , and t h e o t h e r between t h e i n t e r i o r s u r f a c e segment and t h e p l a n e a t a c o n s t a n t t e m p e r a t u r e below t h e basement f l o o r . P e r i o d i c h e a t l o s s , on t h e o t h e r hand, i s only between t h e i n t e r i o r s u r f a c e segment and t h e ground s u r f a c e , s i n c e t h e ground t e m p e r a t u r e deep down
i s assumed t o be c o n s t a n t .
1.4 Determining Basement Heat Loss F a c t o r s
Below-grade basement h e a t l o s s can be c a l c u l a t e d u s i n g Eqs. ( 2 ) t o
( 5 ) i f v a l u e s c a n b e a s s i g n e d t o : t h e shape f a c t o r s , Sn and V n ; t h e amplitude a t t e n u a t i o n f a c t o r , a n ; and t h e time l a g , A t n . The c r o s s - s e c t i o n a l model of a basement and t h e s u r r o u n d i n g ground ( F i g u r e 1 ) was used t o d e t e r m i n e t h e s e f a c t o r s . T h i s s i m p l e model assumes t h a t two- dimensional h e a t conduction p r e v a i l s around t h e basement. (The t h r e e - d i m e n s i o n a l h e a t c o n d u c t i o n e f f e c t of a n e x t e r i o r c o r n e r i n a
r e c t a n g u l a r basement w i l l be d i s c u s s e d l a t e r . ) F a c t o r s t h a t a r e n o t t a k e n i n t o a c c o u n t by t h i s model a r e :
-
time v a r i a t i o n s of t e m p e r a t u r e and l e v e l of t h e ground w a t e r ,-
t h e flow of r a i n o r melt water i n t o t h e s o i l s u r r o u n d i n g t h e basement,-
s p a t i a l v a r i a t i o n of ground t e m p e r a t u r e around a basement due t o s o l a r e f f e c t s , a d j a c e n t b u i l d i n g s and v a r i a t i o n s i n t h e snow c o v e r ,-
t h e d i f f e r e n c e i n t h e r m a l p r o p e r t i e s of b a c k f i l l and u n d i s t u r b e d s o i l , and of t h e s o i l above and below t h e f r e e z i n g plane.The model can a l l o w f o r some v a r i a t i o n i n s o i l t h e r m a l p r o p e r t i e s by a s s i g n i n g a d i f f e r e n t c o n d u c t i v i t y v a l u e t o t h e s o i l above and below t h e basement f l o o r l e v e l .
A set of shape f a c t o r s , Sn and Vn, f o r a g i v e n basement i n s u l a t i o n system was o b t a i n e d by c a l c u l a t i n g t h e h e a t f l u x , qn, through An u s i n g one c o n s t a n t u n i t f o r ground s u r f a c e and basement s p a c e t e m p e r a t u r e s . F i n i t e - e l e m e n t numerical methods were used t o d e t e r m i n e t h e h e a t f l u x through t h e basement i n t e r i o r s u r f a c e and s h o r t d e s c r i p t i o n s of t h e programs used i s g i v e n i n Appendix A.
An a n a l y s i s of t h e c a l c u l a t e d shape f a c t o r s i n d i c a t e s t h a t , i n most c a s e s , t h e basement i n s u l a t i o n t h e r m a l r e s i s t a n c e , R , and t h e shape f a c t o r s c a n be r e l a t e d by and f o r t h e range 1
<
R<
5
where S,(R) and Vn(R) = s t e a d y - s t a t e and p e r i o d i c s h a p e f a c t o r s f o r a basement i n s u l a t e d t o a t h e r m a l r e s i s t a n c e v a l u e , R , a n , b n , c n = c o n s t a n t s t h a t a r e s p e c i f i c t o t h e basement t h e r m a l i n s u l a t i o n system.The e x p r e s s i o n s of Sn and V n f o r s e v e r a l basement i n s u l a t i o n systems and f o r two s e t s of s o i l c o n d u c t i v i t y v a l u e s a r e l i s t e d i n T a b l e s I1 and 111.
The a t t e n u a t i o n f a c t o r , a n , and t h e time l a g f a c t o r , A t n , have been d e t e r m i n e d by c a l c u l a t i n g t h e p e r i o d i c h e a t f l u x u s i n g a s i n e wave v a r i a t i o n of t h e ground s u r f a c e t e m p e r a t u r e . C a l c u l a t e d a t t e n u a t i o n and time-lag f a c t o r s a r e p l o t t e d i n F i g u r e 2. Based on t h e s e c u r v e s , a s e t of a t t e n u a t i o n and time-lag f a c t o r s were d e r i v e d and a r e i n c l u d e d i n T a b l e 111.
E x p e r i m e n t a l s t u d i e s have i n d i c a t e d t h a t t h e v a r i a t i o n i n basement h e a t l o s s c a n b e a d e q u a t e l y d e s c r i b e d u s i n g monthly mean v a l u e s of t h e basement h e a t l o s s . Thus, a t i m e i n c r e m e n t , m , of one month was u s e d , w i t h J a n u a r y i d e n t i f i e d by m = 1 and a n g u l a r v e l o c i t y of 30 d e g r e e s p e r month.
1.5 Corner Heat Loss
Using F i g u r e 1 a s t h e b a s i c c r o s s - s e c t i o n of a t h r e e - d i m e n s i o n a l model, t h r e e - d i m e n s i o n a l h e a t c o n d u c t i o n c a l c u l a t i o n s were performed
f o r a basement e x t e r i o r c o r n e r w i t h two l e v e l s of i n s u l a t i o n : t h e w a l l i n s u l a t e d t o half-way down below g r a d e , and i n s u l a t i o n o v e r t h e
f u l l h e i g h t of t h e w a l l . The c a l c u l a t e d s u r f a c e h e a t f l u x v a l u e s f o r t h e two c a s e s a r e shown i n F i g u r e s 3a and 3b. Note t h a t t h e i n c r e a s e i n s u r f a c e h e a t f l u x towards t h e c o r n e r i s o n l y o f s i g n i f i c a n c e f o r t h e lower s e c t i o n of an u n i n s u l a t e d w a l l and f o r t h e f l o o r . Based on t h e s u r f a c e h e a t f l u x v a l u e s c a l c u l a t e d f o r t h e two l e v e l s of basement i n s u l a t i o n , a s e t of c o r n e r allowance f a c t o r s , 'n
was d e r i v e d f o r a l l t h e basement i n s u l a t i o n systems l i s t e d i n T a b l e 111.
2. CALCULATION OF BASEMENT HEAT LOSS
The i n s i d e s u r f a c e of t h e basement, a s shown i n F i g u r e 1, i s made up of t h e f o l l o w i n g f i v e segments:
Al
= i n s i d e s u r f a c e a r e a of w a l l above g r a d e , A2 = upper i n s i d e s u r f a c e a r e a of w a l l below g r a d e , A3 = lower i n s i d e s u r f a c e a r e a of w a l l below g r a d e , A4 = i n s i d e s u r f a c e a r e a of f l o o r s t r i p 1 m wide a d j a c e n t t o w a l l , and A5 = i n s i d e s u r f a c e a r e a of t h e remainder of t h e f l o o r . The basement f l o o r was d i v i d e d i n t o two r e g i o n s because h e a t f l u x c a l c u l a t i o n s have shown t h a t t h e f l o o r h e a t f l u x a d j a c e n t t o t h e w a l l d i f f e r s s u b s t a n t i a l l y from t h e h e a t f l u x through t h e remainder of t h e f l o o r .The e s s e n t i a l d a t a needed t o c a l c u l a t e t h e basement h e a t l o s s a r e t h e s t e a d y - s t a t e and p e r i o d i c s h a p e f a c t o r s , Sn and V n , t h e amplitude a t t e n u a t i o n f a c t o r , a n , and t h e time-lag f a c t o r , A t n . T a b l e I1 l i s t s c a l c u l a t e d h e a t l o s s f a c t o r s f o r s e v e r a l i n s u l a t i o n systems found i n t h e t e s t basements. (These v a l u e s a r e used i n t h e f o l l o w i n g s e c t i o n s t o compare c a l c u l a t e d and measured basement h e a t l o s s r e s u l t s . ) Based on t h i s comparison, t h e s t e a d y - s t a t e f l o o r s h a p e f a c t o r s were modified t o improve agreement between measured and c a l c u l a t e d r e s u l t s . These a d j u s t e d f a c t o r s (where t h e a d j u s t m e n t s are b a s e d o n e x p e r i m e n t a l r e s u l t s ) f o r a l a r g e number of basement i n s u l a t i o n systems a r e l i s t e d i n T a b l e 111.
It s h o u l d b e n o t e d t h a t t h e f a c t o r s f o r t h e c a s e s of t h e p a r t i a l l y i n s u l a t e d w a l l s were c a l c u l a t e d assuming a v e r t i c a l dimension (M-D) of 0.6 m f o r A 2 . The dimension, 0.6 m, was s e l e c t e d because t h a t i s t h e amount s p e c i f i e d i n some Canadian b u i l d i n g s t a n d a r d s . The f a c t o r s f o r t h e s e c a s e s can, however, b e used t o c a l c u l a t e t h e l o s s e s from o t h e r p a r t i a l l y i n s u l a t e d w a l l s where D 4 M
<
H.The f o l l o w i n g summarizes t h e s t e p s t o be t a k e n t o c a l c u l a t e t h e h e a t l o s s . For a s p e c i f i c basement: S t e p 1
-
S p e c i f y t h e r e q u i r e d i n p u t d a t a f o r : ( a ) I n s i d e basement dimensions-
l e n g t h , L,-
w i d t h , W ,-
t o t a l h e i g h t of w a l l , H ,-
h e i g h t of w a l l above g r a d e , D. ( b ) Basement i n s u l a t i o n-
o v e r - a l l thermal r e s i s t a n c e of w a l l above g r a d e , RT,-
r e s i s t a n c e v a l u e of i n s u l a t i o n , R,-
h e i g h t of i n s u l a t i o n coverage over w a l l , M ,-
e x t e n t of i n s u l a t i o n coverage over f l o o r (e.g., none, 1 m s t r i p a d j a c e n t t o w a l l , f u l l coverage).( c ) Temperature
-
basement space t e m p e r a t u r e , O B ,-
mean ground t e m p e r a t u r e , O G ( s e e Table 1 of Ref. 121,-
a m p l i t u d e of t h e f i r s t harmonic of t h e ground s u r f a c et e m p e r a t u r e v a r i a t i o n , O V , and t h e t i m e l a g of t h e f i r s t harmonic, A t n , i n months ( s e e Table I ) ,
-
monthly a v e r a g e outdoor a i r t e m p e r a t u r e , Oo,m, where i d e n t i f i e s t h e month ( s e e Ref. 13).S t e p 2
-
C a l c u l a t e t h e a r e a s of t h e segments c o n s t i t u t i n g t h e basement f l o o r and w a l l s .( a ) For a r e c t a n g u l a r basement of a d e t a c h e d house:
G = p e r i m e t e r = 2 (L+W) A 1 = G D ,
A4 = G
-
4 ,( i ) w i t h i n s u l a t i o n p a r t i a l l y c o v e r i n g t h e w a l l ,
( i i ) w i t h i n s u l a t i o n c o v e r i n g t h e e n t i r e w a l l , u s e t h e following:
(Even though b o t h A2 and
A3
a r e covered by i n s u l a t i o n , t h e y a r e t r e a t e d s e p a r a t e l y because of t h e manner i n which t h e f a c t o r s were d e r i v e d (Table 111).( b ) For a basement of a home t h a t is l o c a t e d i n t h e middle of a row of housing u n i t s , n o t e t h e f o l l o w i n g changes:
A4 = G , and
S t e p 3
-
S e l e c t an a p p r o p r i a t e v a l u e of s o i l thermal c o n d u c t i v i t y ; f o r t h e p a r t i c u l a r R-value of basement i n s u l a t i o n , e x t r a c t and c a l c u l a t e t h e f a c t o r s Sn, V,, C n , a, and A t n from Table 111. (The h i g h v a l u e of s o i l thermal c o n d u c t i v i t y would probably b e a p p r o p r i a t e f o r r o c k s andw e t sand; t h e lower v a l u e could be used f o r well-drained c l a y . )
S t e p 4
-
Using t h e s e l e c t e d c o r n e r allowance f a c t o r s , Cn, c a l c u l a t e t h e a c t u a l c o r n e r allowances, Xn, f o r t h e basement.( a ) For t h e two upper w a l l segments, t h e i n c r e a s e d h e a t l o s s due t o c o r n e r s c a n b e n e g l e c t e d , i . e . , X1 = X2 = 0.
( b ) For t h e bottom segment of t h e w a l l ,
X 3
= i C3 ( c ) For t h e one metre s t r i p of f l o o r ,X 4 = i C 4 , and ( d ) For t h e c e n t r a l a r e a of f l o o r ,
For a detached house, i =
4.
For a semi-detached o r end u n i t of arow of houses, i = 2. There a r e no c o r n e r s t o b e c o n s i d e r e d i n a middle u n i t of a row of houses, a l l X f a c t o r s a r e zero.
S t e p 5
-
C a l c u l a t e t h e monthly average h e a t l o s s r a t e (power) through t h e f i v e basement segments:where
"30" i s i n d e g r e e s p e r month which e q u a l s 2x112 r a d i a n s p e r month A t n and t = time i n months (m p l u s a number from 1 t o 1 2
i d e n t i f i e s t h e month)
(Note t h a t t h e c o r n e r allowance, Xn, i s n o t used i n t h e same f a s h i o n f o r a l l t h e segment h e a t l o s s c a l c u l a t i o n s . )
S t e p 6
-
C a l c u l a t e t h e annual h e a t l o s s (energy) from t h e f u l l basement:where
(730) (3600) = average number of seconds p e r month,
Step
7
-
Calculate below-grade basement heat loss for the winter
period, QW
I
where
m
=start of winter season
1
m2 =
end of winter season.
This equation can be rearranged as follows:
5
12+m2
+
0,C
An Vn
an
Csin w(m-t8+~t,).
n=2
ml
A sample calculation of basement heat loss is presented in
Appendix B.
3. EXPERIMENTAL MEASUREMENTS OF BASEMENT HEAT LOSS
During a three-year period (Sept. 1978 to Sept. 1981), heat loss
experiments were conducted on several basements by the Division and by
a private consultant under contract to DBR/NRC. These experiments were
conducted on:
1)
three experimental basements (A, B and C) constructed on the
NRC campus in Ottawa,
2)
basement of an experimental house (basement D) located near
the Ottawa International Airport,
3)
basements in two experimental houses (HUDAC Mark XI Houses H1
and H4) in Orleans, Ontario,
4)
three basements of houses in Gatineau, P.Q., and
5)
several basements in Saskatoon, Charlottetown, and Ottawa.
The majority of heat loss measurements were made with large
2
calorimeters with a test area of 2 m (14).
Total basement heat loss
measurements were only attempted in a few cases.
A
description of the
tests conducted by the contractor on basements in Gatineau, Ottawa,
Saskatoon and Charlottetown, are given in References 15 to 17. The
construction details of the HUDAC houses are given in Reference 18.
Test basements A, B, C and D are described in Appendix C.
4. ANALYSIS OF TEST DATA
It was found t h a t t h e energy consumption v a l u e s measured i n t h e s e e x p e r i m e n t s c o u l d be r e p r e s e n t e d q u i t e a c c u r a t e l y by t h e f o l l o w i n g e q u a t i o n : where E ( t ) = e x p e r i m e n t a l energy consumption, Zo Z1,Z2, and Z3 = c o e f f i c i e n t s determined by a " l e a s t s q u a r e s " 9 f i t of Eq. ( 8 ) t o measured d a t a ; w = 30 d e g r e e s per month.
The d i f f e r e n t i a t i o n of Eq. ( 8 ) g i v e s t h e power,
where
P ( t ) = i n s t a n t a n e o u s h e a t s u p p l i e d t o t h e basement o r c a l o r i m e t e r , Z1 = s t e a d y s t a t e o r t h e a v e r a g e power,
w *
4
Z$+
223 = t i m e l a g of t h e power wave where t h e r e f e r e n c ep o i n t i s t h e s t a r t i n g d a t e of t h e test.
The power was a l s o c a l c u l a t e d by numerical d i f f e r e n t i a t i o n , i.e.,
where
6 t = t i m e i n t e r v a l between t h e kWh meter r e a d i n g s E ( t ) and E ( t
+
6 t )The f o r e g o i n g a n a l y s i s was performed on a l l t h e measured h e a t l o s s d a t a f o r t h e DBR/NRC t e s t basements and t h e HUDAC Mark X I basements.
F i g u r e 5 d e m o n s t r a t e s t h e s t e p s used t o a r r i v e a t t h e h e a t l o s s r a t e ( o r power). The energy consumption d a t a p o i n t s and t h e c u r v e f i t r e p r e s e n t e d by Eq. ( 8 ) a r e i n d i c a t e d a s curve 1. Curve 2 r e p r e s e n t s t h e non-cyclic component of t h e h e a t l o s s , i.e., Zo
+
Z1 t. Curve 3 r e p r e s e n t s Eq. ( 9 ) , t h e d i f f e r e n t i a t i o n of t h e e n e r g y consumption curve. F i n a l l y , c u r v e4
r e p r e s e n t s t h e n u m e r i c a l d i f f e r e n t i a t i o n of t h e a c t u a l d a t a p o i n t s of curve 1 (Eq. (10).The comparison of measured and p r e d i c t e d h e a t l o s s v a l u e s f o r t h e HUDAC houses a r e g i v e n i n F i g u r e 4 and T a b l e I V . The comparison of
measured and p r e d i c t e d l o s s r a t e s f o r t h e DBR/NRC t e s t basements a r e shown i n F i g u r e s 5 t o 15.
T e s t d a t a were c o l l e c t e d o n l y d u r i n g t h e w i n t e r p e r i o d f o r t h e t e s t basements i n Ottawa, G a t i n e a u , S a s k a t o o n , and C h a r l o t t e t o w n . Values of t h e a v e r a g e h e a t i n g (power) o v e r t h e w i n t e r p e r i o d were o b t a i n e d by p e r f o r m i n g a s t r a i g h t l i n e f i t t o t h e d a t a , i . e . ,
where
Y1 = a v e r a g e power o v e r t h e t i m e p e r i o d u n d e r c o n s i d e r a t i o n . The e x p e r i m e n t a l l y - d e t e r m i n e d h e a t i n g i n p u t power and t h e c a l c u l a t e d h e a t l o s s r a t e f o r t h e s e basements a r e compared i n T a b l e s V and V I .
5. COMPARISON OF CALCULATED AND EXPERIMENTAL RESULTS 5.1 I n f l u e n c i n g F a c t o r s
Before comparing t h e c a l c u l a t e d and measured h e a t l o s s v a l u e s , i t might b e h e l p f u l t o d i s c u s s t h o s e f a c t o r s t h a t have a s i g n i f i c a n t e f f e c t on t h i s comparison. These f a c t o r s a r e :
( a ) t h e s e a s o n a l t e m p e r a t u r e of basement s p a c e a i r , ( b ) t h e s o i l t h e r m a l c o n d u c t i v i t y ,
( c ) t h e mean ground t e m p e r a t u r e ,
( d ) t h e w a t e r flow i n ground a d j a c e n t t o basement ( e . g.
,
f l o w a t f o o t i n g d r a i n ) ,( e l t h e l e v e l and f l o w of groundwater.
( a ) The basement a i r t e m p e r a t u r e i s one of t h e main f a c t o r s
c o n t r o l l i n g basement h e a t l o s s . I n most basements, a change of 1 K i n basement t e m p e r a t u r e c a n change basement h e a t l o s s by 5 t o 1 0 p e r c e n t
(19, 2 0 ) . Knowledge of t h e basement t e m p e r a t u r e i s e s s e n t i a l .
( b ) The c o m p u t a t i o n of basement h e a t l o s s r e q u i r e s a r e a s o n a b l y p r e c i s e e s t i m a t e of s o i l t h e r m a l c o n d u c t i v i t y , e s p e c i a l l y when a
s i g n i f i c a n t p o r t i o n of t h e t o t a l t h e r m a l r e s i s t a n c e i s provided by t h e s o i l . T h i s c o n d i t i o n p r e v a i l s w i t h b o t h t h e p a r t i a l l y i n s u l a t e d
basement w a l l and t h e e x t e r n a l i n s u l a t i o n t h a t g o e s down t h e w a l l and t h e n outwards. I n t h e l a t t e r c a s e , a s o i l w i t h a low t h e r m a l
r e s i s t a n c e l o c a t e d b e n e a t h t h e i n s u l a t i o n c o u l d n e g a t e much of t h e h e a t r e s i s t a n c e of t h e i n s u l a t i o n .
( c ) A change of 1 K i n t h e mean ground t e m p e r a t u r e c a n change t h e s t e a d y - s t a t e component of t h e basement h e a t l o s s by 5 t o 1 0 p e r c e n t .
Snow-cleared d r i v e w a y s , a t t a c h e d g a r a g e s , c a r p o r t s , walkways, and s o l a r s h a d i n g a r e a l l f a c t o r s t h a t c a n r e d u c e t h e mean ground t e m p e r a t u r e and, h e n c e , i n c r e a s e basement h e a t l o s s . C o n v e r s e l y , t h e p r o x i m i t y of a n e i g h b o u r i n g basement c o u l d i n c r e a s e t h e mean ground t e m p e r a t u r e and r e d u c e basement h e a t l o s s e s . U n f o r t u n a t e l y , t h e s e e f f e c t s a r e
d i f f i c u l t t o q u a n t i f y .
( d ) Basement h e a t l o s s e s i n c r e a s e w i t h an i n c r e a s e i n w a t e r f l o w a t t h e f o o t i n g . T h i s was i n d i c a t e d by t h e w a t e r f l o w s and h e a t l o s s r a t e s
measured i n t h e DBR t e s t basements i n 1978179.
( e ) The l e v e l and flow of groundwater a f f e c t t h e ground t e m p e r a t u r e f i e l d b e n e a t h t h e basement and, t h e r e f o r e , a f f e c t t h e f l o o r h e a t l o s s and, t o a l e s s e r e x t e n t , t h e w a l l h e a t l o s s . U n f o r t u n a t e l y t h e
i n f l u e n c e of w a t e r o n basement l o s s c a n n o t b e q u a n t i f i e d . Example Comparisons
5.2.1 S a s k a t o o n , Ottawa and C h a r l o t t e t o w n ( T a b l e V)
For t h e s e 6 h o u s e s , h e a t l o s s r a t e s from t h e basements were measured w i t h c a l o r i m e t e r s d u r i n g t h e h e a t i n g s e a s o n o n l y . Basement a i r t e m p e r a t u r e s were n o t c o n t r o l l e d d u r i n g t h e 1978179 t e s t y e a r , b u t t h e y were c l o s e l y c o n t r o l l e d i n s u b s e q u e n t y e a r s . The measured h e a t l o s s r a t e s l i s t e d i n T a b l e V a r e v a l u e s averaged o v e r t h e h e a t i n g season.
( a ) Basement A ( S a s k a t o o n )
-
The basement was u n i n s u l a t e d e x c e p t f o r a s e c t i o n of t h e n o r t h w a l l which was c o v e r e d w i t h i n s u l a t i o n (R = 1 . 6 ) 3.6 m wide and extended from t h e t o p of t h e w a l l down t o 0.6 m below grade. I n a l l c a s e s , t h e measured h e a t l o s s r a t e s were g r e a t e r t h a n t h e c a l c u l a t e d o n e s , but t h e d i f f e r e n c e between t h e two was somewhat l e s s f o r t h e i n s u l a t e d w a l l . T h i s would i n d i c a t e t h a t t h e a c t u a l ground t h e r m a l c o n d u c t i v i t y was g r e a t e r t h a n t h e v a l u e s assumed i n t h e c a l c u l a t i o n s ( i . e , 0.8 and 0.9 Wlm-K).A s a l r e a d y n o t e d , t h e basement a i r t e m p e r a t u r e was allowed t o v a r y
i n 1978179. It went from 14.5"C i n November t o 10°C i n J a n u a r y t o
13.5OC i n A p r i l . The e f f e c t of t h i s v a r i a t i o n i n s p a c e t e m p e r a t u r e was n o t a l l o w e d f o r i n t h e c a l c u l a t e d v a l u e s .
( b ) Basement B ( S a s k a t o o n )
- There was r e a s o n a b l e agreement between
t h e c a l c u l a t e d and measured h e a t l o s s v a l u e s .
( c ) Basement C ( S a s k a t o o n )
-
a s e c t i o n of t h e n o r t h w a l l was c o v e r e d w i t h i n s u l a t i o n (R = 1.32) on t h e e x t e r n a l f a c e (above g r a d e o n l y ) . Another s e c t i o n of t h e n o r t h w a l l was covered w i t h i n s u l a t i o n on t h e e x t e r n a l f a c e above g r a d e ; t h e i n s u l a t i o n p r o j e c t e d h o r i z o n t a l l y 1.2 m away from t h e w a l l on t h e g r a d e . The w i d t h of w a l l covered w i t h i n s u l a t i o n was 3.05 m which i s o n l y 2 m w i d e r t h a n t h e c a l o r i m e t e r . T h i s p r o b a b l y r e s u l t e d i n h e a t b y p a s s i n g t h e h o r i z o n t a l i n s u l a t i o n and e x p l a i n s t h e r e l a t i v e l y l a r g e d i f f e r e n c e between measured andThe f l o o r c a l o r i m e t e r was l o c a t e d n e a r t h e n o r t h e a s t c o r n e r of t h e basement and probably e x p e r i e n c e d t h r e e - d i m e n s i o n a l c o n d u c t i o n which was n o t a c c o u n t e d f o r i n t h e c a l c u l a t e d v a l u e . T h i s c o u l d e x p l a i n t h e d i f f e r e n c e between measured and c a l c u l a t e d f l o o r h e a t l o s s .
( d ) Basement E (Ottawa)
-
The measured and c a l c u l a t e d v a l u e s a g r e e q u i t e w e l l .( e ) Basement A ( C h a r l o t t e t o w n )
-
T h i s was a w e l l i n s u l a t e d basement (R = 3.52 i n 1979180) w i t h t h e e a r t h bermed up a g a i n s t t h e basement w a l l . The c a l c u l a t e d v a l u e s assumed g r a d e l e v e l was t h e h i g h e s t p o i n t of t h e e a r t h berm a g a i n s t t h e w a l l . I n a c t u a l f a c t , t h e t h e r m a lr e s i s t a n c e of t h e ground would be less t h a n t h a t assumed i n t h e
c a l c u l a t i o n d u e t o a r e d u c t i o n i n e a r t h c o v e r away from t h e w a l l . T h i s c o u l d be t h e r e a s o n f o r t h e h i g h e r measured h e a t l o s s r a t e s .
( f ) Basement D (Ottawa)
-
T h i s basement was c h a r a c t e r i z e d by a r e l a t i v e l y h i g h w a t e r t a b l e which would t e n d t o i n c r e a s e h e a t l o s s . T h i s was p r o b a b l y t h e r e a s o n why t h e measured l o s s from t h e u n i n s u l a t e d f l o o r was h i g h e r t h a n t h a t c a l c u l a t e d . The l o s s from t h e i n s u l a t e d w a l l s showed b e t t e r agreement between measured and c a l c u l a t e d v a l u e s .Houses i n G a t i n e a u
(P.Q.)
( T a b l e V I )I n t h e s e t h r e e homes an a t t e m p t was made t o i s o l a t e t h e basement t h e r m a l l y from t h e remainder of t h e house. The power i n p u t t o t h e e l e c t r i c h e a t e r t h a t m a i n t a i n e d t h e basement a t a c o n s t a n t a i r t e m p e r a t u r e was r e c o r d e d from December 1977 t o A p r i l 1978.
I s o l a t i o n of t h e basement from t h e house was o n l y p a r t i a l l y
s u c c e s s f u l a s t h e a i r i n f i l t r a t i o n i n t o t h e house t h r o u g h t h e basement could n o t be c o m p l e t e l y e l i m i n a t e d . An a l l o w a n c e f o r h e a t i n g
i n f i l t r a t i n g a i r was made, t h e r e f o r e t o a r r i v e a t t h e "measured" v a l u e s l i s t e d i n T a b l e V I I . These v a l u e s a l s o i n c o r p o r a t e a s m a l l c o r r e c t i o n f o r e x t r a n e o u s h e a t l o s s from t h e basement t h r o u g h t h e h e a v i l y
i n s u l a t e d house above. C o n s i d e r i n g a l l t h e s e f a c t o r s , T a b l e V I shows r e a s o n a b l y good agreement between e s t i m a t e d measured h e a t l o s s r a t e s and c a l c u l a t e d l o s s r a t e s .
5.2.3 HUDAC Mark X I Houses ( T a b l e I V , F i g u r e 4 )
The basement of house H 1 was i n s u l a t e d on t h e i n s i d e (R = 1 . 2 3 ) from t h e t o p of t h e w a l l t o 0.9 m below grade. The i n s u l a t i o n v a l u e was i n c r e a s e d t o R = 3.52 and c o v e r a g e was i n c r e a s e d t o f u l l h e i g h t i n November 1980. The basement of house H4 was i n s u l a t e d on t h e e x t e r i o r f a c e (R = 1.23) o v e r t h e f u l l h e i g h t of t h e w a l l . C a l o r i m e t e r s were mounted on t h e n o r t h w a l l of H 1 , and on t h e n o r t h and w e s t w a l l s and t h e f l o o r of H4.
The basement a i r t e m p e r a t u r e was h e l d a s c o n s t a n t a s p o s s i b l e u s i n g a r e s i d e n t i a l t h e r m o s t a t t h a t c o n t r o l l e d t h e f u r n a c e . The e n e r g y i n p u t s t o t h e f i v e e l e c t r i c c a l o r i m e t e r h e a t e r s were r e c o r d e d from J a n u a r y 1979 t o December 1 9 8 1 ( s e e F i g u r e 4 ) . Only t h e d a t a r e c o r d e d
up t o November 1980 (when t h e i n s u l a t i o n system i n H 1 was upgraded) were u s e d i n t h e comparison shown i n T a b l e I V .
Values of s o i l t h e r m a l c o n d u c t i v i t y , measured a l o n g a c o n d u c t i v i t y probe, were 0.72 W / ( ~ * K ) a d j a c e n t t o t h e basement w a l l , and 1.1 ~ / ( m - K ) 15 m from t h e house. The w a t e r f l o w a t t h e f o u n d a t i o n f o o t i n g , which was a l s o m o n i t o r e d , was i n t e r m i t t e n t w i t h a maximum f l o w r a t e of 30 L/h.
E x p r e s s i o n s d e s c r i b i n g t h e h e a t l o s s r a t e were d e r i v e d from t h e e x p e r i m e n t a l d a t a (1979 and 1980) and a r e p r e s e n t e d i n T a b l e I V . Loss r a t e e x p r e s s i o n s c a l c u l a t e d w i t h s o i l c o n d u c t i v i t y v a l u e s of 0.8 and 0.9 W/m*K a r e a l s o p r e s e n t e d . The H 1 v a l u e s a r e f o r t h e o r i g i n a l , p a r t i a l i n s u l a t i o n system.
The l a r g e d i f f e r e n c e i n measured l o s s t h r o u g h t h e n o r t h and w e s t w a l l s of H4 i s i m p o r t a n t . The r e a s o n s f o r t h i s d i f f e r e n c e c o u l d be t h a t : t h e west w a l l f a c e s a n o t h e r house which i s o n l y 4 m away; t h e n o r t h w a l l c a l o r i m e t e r was p l a c e d on a r e l a t i v e l y s h o r t s e c t i o n of w a l l and t h e r e f o r e t h e measured l o s s might be i n f l u e n c e d by t h e t h r e e - d i m e n s i o n a l e f f e c t of two c o r n e r s .
The c a l c u l a t e d v a l u e s f o r t h e west w a l l of house H4 a g r e e w i t h t h e measured l o s s v a l u e , b u t t h e r e i s a c o n s i d e r a b l e u n d e r e s t i m a t i o n of t h e h e a t l o s s t h r o u g h t h e n o r t h w a l l , even when t h e c o r n e r s of t h e n o r t h w a l l a r e c o n s i d e r e d . One r e a s o n f o r t h e h i g h e r measured l o s s t h r o u g h t h e n o r t h w a l l could be t h a t , b e c a u s e of s o l a r s h a d i n g , t h e a c t u a l ground t e m p e r a t u r e o n t h e n o r t h s i d e was lower t h a n t h e v a l u e of 8.9OC used i n t h e c a l c u l a t i o n .
A s noted e a r l i e r , t h e basement a i r t e m p e r a t u r e was i n d i r e c t l y c o n t r o l l e d by t h e s p a c e h e a t i n g t h e r m o s t a t l o c a t e d on t h e main f l o o r of t h e house. I t i s p o s s i b l e , t h e r e f o r e , t h a t t h e basement a i r
t e m p e r a t u r e was h i g h e r t h a n t h e 20.7OC t h e r m o s t a t t e m p e r a t u r e which was used t o c a l c u l a t e t h e l o s s e s . T h i s c o u l d e x p l a i n why t h e measured l o s s v a l u e s were always h i g h e r t h a n t h e c a l c u l a t e d o n e s . t h e measured f l o o r h e a t l o s s was s i g n i f i c a n t l y h i g h e r t h a n t h a t p r e d i c t e d , p o s s i b l y due t o some groundwater flow b e n e a t h t h e basement. T h i s i n d i c a t e s t h a t a h i g h e r v a l u e of s t e a d y - s t a t e , f l o o r shape f a c t o r s h o u l d have been used i n t h e h e a t l o s s p r e d i c t i o n .
DBR/NRC T e s t Basements ( F i g u r e s 5 t o 1 5 )
T e s t basements A , B and C , l o c a t e d on t h e NRC grounds i n Ottawa, a r e d e s c r i b e d i n Appendix C. Both c a l o r i m e t e r and t o t a l basement h e a t l o s s measurements were r e c o r d e d f o r t h e t h r e e - y e a r pe-riod (September 1978 t o September 1981). D a t a from t h e f i r s t y e a r a r e n o t i n c l u d e d i n t h e f o l l o w i n g d i s c u s s i o n b e c a u s e t h e t h e r m a l b a l a n c e o f t h e ground s u r r o u n d i n g t h e basements was i n a t r a n s i e n t s t a t e d u r i n g t h a t t i m e and b e c a u s e t h e groundwater flow was a b n o r m a l l y h i g h d u r i n g t h i s p e r i o d , a s
shown i n F i g u r e 16. A d r a i n a g e d i t c h was dug around t h e t e s t s i t e i n t h e summer of 1979 t o lower t h e w a t e r t a b l e u n i f o r m l y and t o reduce t h e w a t e r flow a t t h e f o o t i n g s t o a more "normal" r a t e .
The measured t e s t d a t a were a n a l y z e d a s d e s c r i b e d i n s e c t i o n 4 , and a r e p r e s e n t e d i n F i g u r e s 5 t o 15. The h e a t l o s s v a l u e s c a l c u l a t e d by t h e method p r e s e n t e d e a r l i e r a r e shown on t h e same f i g u r e s . The t o t a l h e a t l o s s v a l u e s f o r basements A , B and C a r e g i v e n i n F i g u r e s
5 ,
9 and 13, r e s p e c t i v e l y . The h e a t l o s s v a l u e s f o r s p e c i f i c s e c t i o n s oft h e basements a r e shown i n t h e o t h e r f i g u r e s i n t h a t group.
The f o l l o w i n g a r e some o b s e r v a t i o n s and comments t h a t a p p l y t o a l l t h r e e t e s t basements.
( a ) The groundwater t a b l e a f t e r c o n s t r u c t i o n of t h e d r a i n a g e d i t c h was a b o u t 0.5 m below t h e basement f l o o r s u r f a c e . The w a t e r l e v e l d i f f e r e n c e a c r o s s basement C (which had e x p e r i e n c e d t h e g r e a t e s t w a t e r flow a t t h e f o o t i n g d r a i n s ) was r e d u c e d t o p r a c t i c a l l y z e r o , i n d i c a t i n g v e r y l i t t l e groundwater flow p a s t t h e basement.
( b ) The basements were c o n s t r u c t e d i n an a r e a of Leda c l a y . The measured s o i l t h e r m a l c o n d u c t i v i t y v a l u e s a r e g i v e n i n Appendix C.
( F o r more i n f o r m a t i o n on s o i l t h e r m a l c o n d u c t i v i t y s e e Ref. 21.) ( c ) Each t e s t basement was d i v i d e d i n t o a n o r t h , a c e n t r e and a s o u t h
room, and e a c h room had i t s own e l e c t r i c h e a t e r . For a l l t h r e e basements, i t was found t h a t t h e n o r t h room r e q u i r e d more h e a t i n g energy i n p u t t h a n t h e s o u t h room:
-
8% more i n basement B ( p a r t i a l i n s u l a t i o n ) ,- 7%
more i n basement A ( f u l l - h e i g h t i n s u l a t i o n ) ,-
5% more i n basement C (down-and-out i n s u l a t i o n on e x t e r i o r ) . T h i s d i f f e r e n c e was p r o b a b l y due t o a lower t e m p e r a t u r e of t h e ground a d j a c e n t t o t h e n o r t h basement room c a u s e d , i n p a r t , by s o l a r s h a d i n g of t h e ground by t h e h u t s ( s e e Fig. C l ) , and by augmented ground h e a t l o s s from a pathway l e a d i n g t o t h e h u t s which was k e p t f r e e of snow a l l w i n t e r .Following a r e comments on e a c h of t h e s e t h r e e basements.
Basement A ( f u l l - h e i g h t w a l l i n s u l a t i o n on i n s i d e , f l o o r u n i n s u l a t e d ) F i g u r e s 5 t o 8 show t h a t t h e r e i s r e a s o n a b l e agreement between t h e measured and c a l c u l a t e d h e a t l o s s v a l u e s ( b o t h t o t a l and s e c t i o n a l ) e x c e p t f o r t h e f l o o r , where t h e measured v a l u e s a r e c o n s i d e r a b l y h i g h e r t h a n t h o s e c a l c u l a t e d . T h i s l a r g e d i f f e r e n c e c o u l d be d u e t o
groundwater e f f e c t s t h a t were n o t accounted f o r i n t h e c a l c u l a t i o n s , i . e . , t h e v a l u e s used i n t h e c a l c u l a t i o n s were t o o low t o approximate t h e conductance t o t h e lower boundary.
Basement B ( p a r t i a l - w a l l i n s u l a t i o n on i n s i d e , f l o o r u n i n s u l a t e d ) F i g u r e s 9 t o 12 show r e a s o n a b l e agreement between measured and c a l c u l a t e d h e a t l o s s v a l u e s . Again, a h i g h e r f l o o r h e a t l o s s was
measured t h a n was p r e d i c t e d p r o b a b l y because of unaccounted groundwater e f f e c t s .
S p e c i a l c a l o r i m e t e r s were used t o measure t h e s u r f a c e h e a t f l u x t h r o u g h t h e u p p e r ( i n s u l a t e d ) s e c t i o n of t h e e a s t w a l l and t h r o u g h t h e lower ( u n i n s u l a t e d ) s e c t i o n . For t h e i n s u l a t e d p o r t i o n of t h e w a l l , t h e measured h e a t l o s s was s l i g h t l y h i g h e r t h a n t h a t p r e d i c t e d ; f o r t h e u n i n s u l a t e d p o r t i o n , t h e measured h e a t l o s s was s i g n i f i c a n t l y h i g h e r t h a n t h a t p r e d i c t e d . The r e a s o n f o r t h e d i f f e r e n c e between measured and p r e d i c t e d l o s s f o r t h e lower s e c t i o n c o u l d be t h e same a s t h a t f o r t h e f l o o r , i . e . , e f f e c t s of groundwater.
Basement C ( e x t e r i o r i n s u l a t i o n t o 0.35 m below g r a d e , t h e n outwards 1.4 m; f l o o r u n i n s u l a t e d )
There was poor agreement between measured and c a l c u l a t e d h e a t l o s s v a l u e s when t h e c a l c u l a t i o n s assumed c l a y s o i l s u r r o u n d i n g t h e basement
( i . e . , k = 0.8 and 0.9 W/m*K f o r upper and lower s o i l ( F i g . I ) ,
r e s p e c t i v e l y ) . Agreement was much b e t t e r when l o s s e s were c a l c u l a t e d
assuming sandy s o i l ( i . e , k = 1.2 and 1.35 W/rn*K f o r upper and lower
s o i l , r e s p e c t i v e l y ) . These l a t t e r v a l u e s a r e compared w i t h measured v a l u e s i n F i g u r e s 13 t o 15.
C a l c u l a t i o n s u s i n g t h e h i g h c o n d u c t i v i t i e s may be a p p r o p r i a t e when
i t i s r e c a l l e d t h a t sand was used a s b a c k f i l l u n d e r n e a t h t h e i n s u l a t i n g
l a y e r p r o j e c t i n g outward from t h e basement w a l l ( s e e Appendix C).
Moreover, t h i s s a n d would have a r e l a t i v e l y hi.gh m o i s t u r e c o n t e n t (and h i g h c o n d u c t i v i t y ) s i n c e t h e w a t e r t a b l e a t t h e t e s t s i t e i s q u i t e high.
The t e s t r e s u l t s emphasize one p o t e n t i a l weakness of t h e "down- and-out" e x t e r i o r i n s u l a t i o n method. Because i t r e l i e s h e a v i l y on t h e t h e r m a l r e s i s t a n c e of t h e s o i l t o reduce w a l l h e a t l o s s , i t s use w i t h a h i g h c o n d u c t i v i t y s o i l o r i n a s o i l w i t h moving groundwater may n o t b e a d v i s a b l e . T h i s example a l s o i n d i c a t e s t h a t t h e s i m p l e p r e d i c t i o n method o u t l i n e d i n t h i s p a p e r h a s d i f f i c u l t y i n h a n d l i n g t h o s e i n s u l a t i o n systems t h a t r e l y p r i m a r i l y on t h e t h e r m a l r e s i s t a n c e of t h e s o i l . T h i s i s e s p e c i a l l y t r u e when t h e r e i s some u n c e r t a i n t y r e g a r d i n g t h e s o i l c o n d u c t i v i t y .
5.2.5 Recommendations: C a l c u l a t i o n P r o c e d u r e and F a c t o r s f o r Basement
Heat L o s s C a l c u l a t i o n s
I n g e n e r a l , comparison of t h e e x p e r i m e n t a l and c a l c u l a t e d basement h e a t l o s s e s i n d i c a t e s t h a t t h e proposed c a l c u l a t i o n p r o c e d u r e f o r
basement h e a t l o s s i s c a p a b l e of a c c o u n t i n g r e a s o n a b l y w e l l f o r a l l t h e s i g n i f i c a n t w e a t h e r p a r a m e t e r s and basement s h a p e s . The q u e s t i o n a b l e p a r t of t h e p r o c e d u r e i s t h e f a c t o r s used t o p r e d i c t f l o o r - s u r f a c e h e a t l o s s s i n c e , i n n e a r l y a l l c a s e s , t h e p r e d i c t e d l o s s e s were l e s s t h a n t h e measured v a l u e s . The u n d e r p r e d i c t i o n of l o s s s u g g e s t s t h a t t h e a c t u a l c o n d u c t a n c e between t h e basement and t h e l o w e r t h e r m a l boundary i s g r e a t e r t h a n t h a t c a l c u l a t e d on t h e b a s i s of t h e basement model
shown i n F i g u r e 1 ( i . e . , t h e n u m e r i c a l v a l u e s of t h e f l o o r - s u r f a c e s t e a d y - s t a t e s h a p e f a c t o r s g i v e n i n T a b l e
I1
a r e t o o low).The v a l u e s of t h e f l o o r s h a p e f a c t o r were i n c r e a s e d by assuming t h a t t h e conductance between t h e basement and t h e lower boundary i s 1 . 5 t i m e s t h e v a l u e s c a l c u l a t e d f o r t h e basement model ( F i g u r e 1 ) . The f l o o r s h a p e f a c t o r s l i s t e d i n T a b l e 111
i n c l u d e t h i s i n c r e a s e i n t h e r m a l conductance.
The change i n t h e f l o o r - s u r f a c e s t e a d y - s t a t e s h a p e f a c t o r s
improves t h e match between c a l c u l a t e d and measured v a l u e s ( F i g u r e 1 7 ) . I n t h i s F i g u r e t h e measured s t e a d y - s t a t e h e a t l o s s v a l u e s f o r DBR/NRC t e s t basements a r e p l o t t e d v e r s u s t h e c a l c u l a t e d v a l u e s b a s e d on t h e f l o o r - s u r f a c e s t e a d y - s t a t e shape f a c t o r s g i v e n i n T a b l e s I1 and 111. The improvement i n agreement between t h e measured and c a l c u l a t e d v a l u e s u s i n g t h e m o d i f i e d f a c t o r i s a p p a r e n t .
It s h o u l d be n o t e d t h a t t h e a m p l i t u d e a t t e n u a t i o n f a c t o r s f o r f l o o r s u r f a c e were a l s o changed ( i . e . , n u m e r i c a l l y i n c r e a s e d ) t o i n c r e a s e t h e c a l c u l a t e d a n n u a l v a r i a t i o n of t h e f l o o r s u r f a c e h e a t f l u x . T h i s improves t h e match between t h e c a l c u l a t e d and measured annual h e a t l o s s v a r i a t i o n s .
T a b l e I11 l i s t s f a c t o r s f o r a l a r g e number of basement i n s u l a t i o n systems. The f l o o r f a c t o r s have been m o d i f i e d t o p r o v i d e a b e t t e r match between t h e measured and p r e d i c t e d l o s s e s . I t i s recommended,
t h e r e f o r e , t h a t t h e s e f a c t o r s b e used i n p r e d i c t i n g basement h e a t l o s s .
6. COMMENTS AND DISCUSSION
From t h i s comparison between measured and p r e d i c t e d basement h e a t , l o s s v a l u e s , i t c a n b e concluded t h a t :
( a ) The two-dimensional s t e a d y - s t a t e h e a t c o n d u c t i o n model f o r house basements i s a d e q u a t e f o r c a l c u l a t i n g t h e s h a p e f a c t o r s r e q u i r e d f o r t h e s i m p l i f i e d basement h e a t l o s s c a l c u l a t i o n method.
( b ) The a n n u a l v a r i a t i o n of ground s u r f a c e t e m p e r a t u r e c a n b e
accommodated by u s i n g a p e r i o d i c h e a t f l o w c a l c u l a t i o n a p p r o a c h , i . e . , by u s i n g a m p l i t u d e decrement and time-delay f a c t o r s .
Because t h e p r e d i c t e d basement h e a t l o s s i s n o t a s t r o n g f u n c t i o n of t h e s e f a c t o r s , o n l y an a p p r o x i m a t i o n of a m p l i t u d e r e d u c t i o n and
time l a g i s s u f f i c i e n t and t h e f a c t o r s d o n o t have t o b e c a l c u l a t e d f o r e v e r y c a s e .
( c ) Basements w i t h s i m p l e r e c t a n g u l a r s h a p e s c a n be t r e a t e d r e a s o n a b l y w e l l by u s i n g s h a p e f a c t o r s d e t e r m i n e d f o r s t r a i g h t w a l l s e c t i o n s and c o r n e r a l l o w a n c e f a c t o r s t o accommodate t h r e e - d i m e n s i o n a l h e a t
flow a t o u t s i d e c o r n e r s . The t h r e e - d i m e n s i o n a l h e a t flow of basements w i t h i r r e g u l a r s h a p e s ( s u c h a s t h o s e w i t h i n s i d e c o r n e r s ) c a n n o t b e accommodated by t h i s s i m p l e method. It i s
