Ser m B92

NaRimd Research Conseil national

no. 245 C w n d Canada de h e - C m d a

c - 2 l nstitute for lnstitut de IUdX Research in recherche en

Construction construction

Experimental Investigation of the Dynamic Thermal Response of Houses

by S.A. Barakat

BRN 245 ANALYZED

EXPERTMENTAL INVESTIGATION OF THE DYNAMIC THERMAL RESPONSE OF HOUSES

by S.A. Barakat Building Servic- Section ,

Institute for Research in Construction

BRN 245 ISSN 0701 -5232 Ottawa, April 1986 BNational Research Council Canada 1986

Serving the construction Industry Au sedce de la consiruction

TABLE OF CONTENTS

A B S T R A C T / ~ S ~

1 NTRODUCrIOPI

THE Z-TRANSPEP FUNCl'LON MEWOI)

THE OUTD(XIB TEST FACILITY

EXPEXIWeMTAL PROCE WBE

DATA ANALYSIS

RXSULTS

DISCUSSION

SUMMARY

REFERENCES

Page

1

1

2

5

6

EXPERIHENTAL INVBSTZGATION OF THE DYNAMIC THERHAL RESPONSE OF HOUSES

by

S.A. Barakat

ABST urn

Specially designed experiments were performed at an outdoor test facility to determine the cooling-load s-transfer funcrion coefficients due to solar gain input, as well as the roomair transfer fuuctioa coefficients* Three sets of coefficients were obtained for different mass levels in wood-frame houses. These levels, whfch cover a range lower than those cove-red in the A S H W Handbook, are particularly useful for energy calculations for houses. The mass levels examined are based on 4 6 , 130 and 535 kg/m2 ( 9 . 4 , 26.6 and 110 lb / f t2) of floor area.

On a effect&, dana une installarion d'essai extgrfeure, des expEriences spSciales en vue de dsterminer les coefficients de fonctton de transfert z de la charge de refroidfssement due 3 l'apport solaire, ainsi que les coefficfencs de fonction de transfert local-air. Trois ssries de coefficients ont 6t6 obtenues pour des maisons 3 ossature 'bofs I6gSre ayant diffsrents niveaux de masse. Ces niveaux, q u i sont mtns QlevBs- que ceux indiquss dans le manuel de llASBRAE pour les construct..lons IggSres, sont particulisremnt utiles pou? l'analyse Snerggtique dea misons. IRs niveaux de masse gtudiea sone bas& sur 46, 130 et 535 kg/m2 ( 9 , 4 , 26,b et 110 lbIpi2) d'aire de plancher.

INTRODUCTION

The e-transfer function technique (also called the thermal response factor or the weighting factor aethod),. introduced by Hitalas and Stephenson (1-41, is a well-known method for energy analysis of buf ldlngs. With th i s technique, hourly thermal loads can be calculated based on the physical description of rhe building and the ambient weather condition. These loads are then used, together with idormation about the heatinglcooling system, to calculate the space air temperature and heat additi.oa/extraction rates, To perform these caLculatfons, the method utilizes sets of precalculated transfer function coefficients. These are givea in the A S U W procedures (5) for three room mass levels; namely, light, medium and heavy, characterized respectively by 146, 341 and 635 kg/m2 (30, 70 and 130 lb / f t2 ) of floor area,

An examinatton of canveational wood-frame houses y i e l d s a room specific mass value as low as 50-60 k g / d (10-12 l b / f t 2 ) , which is mch lower than ASBRAE values for 1Lghtwefght buildings, The precalculated response factors given in (5) are, therefore, not appropriate for most houses, This is confirmed by the lack of agreement between measured and predtcted energy coasumption when ASHRAE values are used in an energy analysis program (6) to simulate the performance of a wood-frame structure. Figure 1 shows t b

1 1 1 1 1 1 1 1 1 1 1 1 1 1

- a ) S O U T H ROOM T K M P E R A T U R E -

- -

- -

- -

- -

- M E A S U R E D

-------- P R E D I C T E D A

I I I I t I I I I I L I 1 I

D E C 1980 D A Y OF MONTH JAN 1981

2 4 0 0 1 I I I I I I 1 1 1 1 1

F i g u r e 1. 'ENCOREr simulation results for Unit 1 ( l i ght ) uslng AS- response factors

2000

where O ( z ) = 2-transform of the output I(z) = z-transform of the input G ( z ) = system transfer Eunctfon

b ) TOTAL POWER C O N S U M P T I O N - -

results of one such calculation. T h i s lack of agreement indicates that the simulated performance consistently implies a mttch heavier building.

In t h i s study, experiments were carried out to determine the cooling-load transfer function coefficients Eor solar heat gain input and the room-air trans£ e r function coefficients for three dif ferent maes l e v e l s of houses correspondin to 4 6 , 130 4 and 535 kgjm (9 .4 , 26.6 and 110 lb/ft2) of floor area.

THE 2-TRANSFER FUNCTION METBO D

For a dynamic heat transfer system, dependent and independent variables can be related by dif ferenrial equations. The solution of these equations may take several forms. In t h i s case the input and output z-transforms (i. e . , transforms of Independent and dependent variables) are related by a z-transfer function as follows :

me z-transformation of a time-dependent function (e.g., solar radiation, outside air temperature) is a sequence of values of the function at equal time i n t e r v a l s (usua l ly one hour); that i s , it is a time series representation of the function.

The most: important characteristic of t h e z-transfer function method, as compared with other calculation methods, is that the tnputs and the outputs are sequences of values equally spaced In t i m e - Thus, the weather records of ourside air temperature and solar radiation, which are given on an hourly basis, caa be w e d as input with Ltttle or aa preprocessing. The main l i d t a r i o n of the z-transfer method is that the system under consideration m s t be constant wlth t i m e , and linear; ( in other words, the thermal properties and heat transfer coefficients used in the system must be constant, and independent of temperature).

The z-transfer function method for energy calculations is explained Ln Chapter 26 of the 1985 edition of the A5HRAE Handbook of Fundamentals (4) - The calculation consists of two steps. In the f irst step, the space air temperature I s assumed t o be constant at sme reference value and the instantaneous heat gains/losses for the room are catcufated. These include solar and Internal heat gains and envelope conductton and Infiltration losses. A coolfng/heating load for the room (defined as the rate at which heat mst be removedjadded t o maintain the air temperature in the room at the constant reference value) is calculated for each component of tnstantaneous heat gainlloss.

The z-trarisfer function that relates the z-rransForms of the room heat gain I(z) to the raum coaling+ load Q ( z ) may be expressed as

where vg, vl and wl are the z-transfer function caefficients. While vo and v1 are different for each type of heat gain, wl I s the same for all types and depends only on the tllermal storage characteristTcs of the room. In the tLm domain, the room cooling load is gtven by

where t is the time and A is the time interval between successive values, usually one hour.

At the end of the ffrst step, the coolhg loads From varlous heat gafas are added to gat the total cooling load for the ram.

In the second step, the net heat Lnput to the room (total ~ o o l i n g load less any heat axtractfort or addition provided by the HVAC system) is used to calculate the devLation of the space air temperature from the reference value set during the cooling load calculation.

The z-traasfer functton that relates the z-transforms of the space temperature deviation from the reference, 0(z), to the net hear input to the space, QNlz), is termed the room-air (or ai r-temperature) transfer function and is given by

%o avoid repaticioa, references to heating loads will be eliminated; these loads can always be considered as negative cooltng loads.

and p are the transfer function coefficients. The value pl is equal to vl for the same room mass. The net heat

input and space tempctature are related by

S o w intetesting properties of the transfer function coefftcients can be obtained by applying the steady-state conditions. For the cooling-load transfer function coefficients, -Lt can be shown that

where f represents the fraction of the steady-state heat gain that appears as a cooling load. The caefficients given i n the A S W Handbook of Fundamentals (4) are such that f = 1. An estimate ot f can be made using the procedure in Chapter 26 of Reference 4. The v caefficients can be adjusted accordingly.

Similarly, under steady-state conditions, Equation (4) can be rearranged t o give

where KT is the thermal conductance of the room, including all heat flow paths .

In ASHME literature, the air-temperature coefftcients are presented as normalized factors to remove the effect- of variations in room thermal conductance, and the effect of room size. The normallzed transfer function coefficients are calculated as

where Af is the f loor area. Equation (7) becomes

Another property inherent in the a€r temperature coefficients is a measure of the heat capacity of the room. It can be shown that the heat

capacity, C, i s given by

THE OUTDOOR TEST FACILITY

The test facility, described in d e t a i l i n Reference 7, consists of 3 one-storey insulated wood-frame buildings with basements. They are div ided into four 2 r o o m units and four l-roam units, Three of the four 27aom units (Units 1 t o 3) were used for the experiments, Construction detafls and thermal resistance values of the w a l l s and cetUngs are given In Tables 1 and 2.

Table 1, Characteristics of T e s t Units

Wall thermal resistance (m2 OC/W) Cegllng thermal reststance ( m 2 Q ~ f ~ ) Floor thermal res.is tance ( r n z a ~ / ~ ) South-indow glass area (m2) Morth-wiadow glass area (m2) Window thermal resistance (m2 "c/w) Floor area per room <m2) Room hefght (m)

Table 2. Thermal Storage Charactertstics of Teat: Units

T e s t Thermal capacitya unit (m/K)

Light - Standard wood-frame, 12.7 wm gypsum board finish on w a l l s and ceilings, carpet over wooden floor.

Medium - As above, but 50,8 rum gypsum board finish on walls and 25.4 mm f i d i s h on cell ling.

Heavy - Interior wall finish of 101.6 mu brfck, 12.7 rrrm gypsum board finish on ce i l lng , carpet over wooden floor.

aIncludes framing in walls and ceiling

Each of the 2-room units consists of a south and a north room with a connecting door. Each south room has a south-facing window with a aet glass area of 2.6 m2; each north room has a 1 m2 window faclng north. The three

units d i f f e r only in the type and amount of thermal masa used as I n t e r i o r f in i sh of the walls, as given i n Table 2. A l l rooms in the facility are heated to 20°C with an electric baseboard heater controlled by a precision controller to w i t h i n Q.l°C. To eliminate any heating load due t o outdoor air InELltration, a slight p o s i t i v e pressure is maintatned i n all rooms, using air preheated to the same temperature as the aXr in the test room.

Measurements were taken of the following: the average indoor air temperature at mld-height of each room (1.2 Q above the floor); the temperature oE the att ic alr and the corridor air; the solar radiation incident on a horixoncal surface, and on a south- and a north-facing vertical surface; the d i r e c t normal component of the solar radiation; the electric space-heating energy consumption of each room; and the wind speed and direction.

A data logger was used to scan and record the daLa on magnetic tape. Wind data, radiation and temperature values were scanned every minute, averaged over a speciftc period, and recorded. kergy consumption values were accumulated and recorded for the same period.

EXPERIMENTAL PROCEDURE

In prfnciple, the experiments were based on measuring the room response (heating-system power output or room-air temperature) to a known input (solar gain or perturbation in the system input to the room). Application of the transfer function relationships of Equation (2) or (4) using the measured i n p u t and output data would then yield the values of the coeff icimts, Since the t e s t units are located outdoors, the overall measured output contained a second sigaiftcant component, which is the overall response of the room to the outdoor weather parameters. This component had t o be subtracted before the transfer function c w l d be obtained.

To e l idnate the dyaamic effect of solar gain through windows and the associated overheating of the space on sunny days, both windows o f each unit were shaded from solar rad-lation-by en external, vertical shade about 40 cm ia froat of the uiodow.

For the solar transfer function experiments, the shade on the south window was totally or partially removed on a sunny day to allow solar gain through the window for 1 hour. This created a l+our solar input pulse on the room. The magnitude of the pulse (size of opening) was chosen so that the room-air temperature would not exceed the set point (reference) temperature. All the parameters, -including the electric heating power consumption for the room, @ere measured every 5 mlnutes. &d+our values were then used for the analysis.

For: rhe room-air transfer Eunction experiments, the window remained fu l ly shaded and an additional electric heater, placed i n the ceorre'of the unit, was starred at a prescribed time during the night, and kept on for 3 or 4 hours, causing the room t o overheat. The temperature rise above the reference value (set point) is the output response for Equation (5) (or input for Equatton ( 4 ) ) .

Tables 3 and 4 give particulars for both t y p e s of experiments. Figures 2 and 3 represent examples of the measured parameters and outdoor weather conditions during a solar pulse experiment, and dnring a hear-addition pulse experiment, respect ive ly .

Table 3. L i s t of Solar Rrlse T e s t s .

Date Time N e t window area T e s t unit Solar inteasi tp (1981) exposed (m2) m / m 2

Jan. 30 12:OO 0.45 L,fl,H 984 Feb. 5 12:OO 1.67 L,M,H 6 22 Feb. 13 12:OO 0.84 L, H 98 1 Feb. 14 12:OO 0.84 H, 8 12 Feb. 15 15:OO 1-67 H 55 1

Table 4. List pf RoonrAir Pulse T e s t s - -- -

Date T e s t unit Pulse duration E'ulse magnitude (h) (W)

( 1981 1 Apr. I6

19 2 1

Apr. 16 19 2 1

(1983) Jan, 24

27 3 i

Feb. 5 17

Mar. 11

Jan. 24 3 1

Feb. 24

TIME. h FEB 13. 1981

Figure 2. Example o f measured values during a solar pulse input

TIME, h FE8 24. 1981

Figure 3. Example of measured values during a hea.t input pulse

DATA ANALYSIS

In both pulse experiments, the total output; that is, the change in power consumption for the solar gain ~xperiments, and the rise in room temperature for the heat addi t ion experiments, was the result of two simultaneous inputs: the intentionally generated perturbation, and the outdoor weather parameters (ambient temperature, wind and solar radiation on the butlding surfaces). To separate the net output due to the pulse, the component due t o outdoor weather variation Qas f irst subtracted from the total output. A transfer function relationship was then established between the input pulse and the corresponding net output, and the coefficients were determined, The procedure is described in detail in the Eollowing paragraphs.

Step 1. Measurinjq room response to outdoor weather parameters

A number of periods were chosen during which no pulses were applied and the room temperature remained at a set point, The measured power consumption therefore represented the response t o the outdoor weather parameters. Using multiple linear regression, a transfer function was obtained l inking the input parameters and the room power consumptian E,. This function has the form

In the t h e domain this translates inro

where AT* is a weighted temperature diEEerence defined as

and UA = overall heat transfer coefficfenr for a particular wall, window or cei l ing

AT = T, - Tr, for outside walls = Ta - Tf, for partition walls and celling = To - T,, for windows

T, = sol-alr temperature of the outside surface T, = air temperature of the adjacent room or a t t i c To = outdoor air temperature Tr = room temperature (set at 20°C)

The overall. heak transfer coeffictents, UA, were calculated based on the construction detafls. Sol-air temperatures w e r e calculated using the followXng data: surface absorptance; solar radiation incident on the surface (measured for south and north walls and calcuLated from horizontal measurements for east and west walls ( 8 ) ); and the outdoor f i l m heat transfer coefficient calculated hourly as a function of wind speed ( 4 ) .

The coefficients (ao, al and bl) of Equation (12) were determined using multiple ltnear regression, The adequacy of these coefficients was checked by using them to prsdfct the power consumption during other periods. Figure 4 shows measured power consumption for a 4day period in January 1983; it also shows the predfcted pwer uslag the transfer function coefficients calculated for the same data, with the first value as an initial condition. Figure 5 shows the measured pwer values for a dif ferent period In March 1983 compared wLth the values predicted using the coefficients produced for the data in Figure 4. The prediction, which has an r m s error of less than 25 W (compared with an average power of 380 W over the period), is good. Figures 6 and 7, based on data for January and February 1981, respectively, provide additional examples. The r m s error between the measured and predicted data in Figure 7 5s only 11 W (compared with an average power of 451 W).

Step 2, Gemrating an input pu l se

For a period w i t h an input pu l se , the coefficients generated in S t e p 1 were used t o predict the room response due to ambient weather, E,( t) , using Bquatloo(12). The net ourput response due to the pulse E p ( t ) was then calculated as

1200' I I I I 700

I A N U A R Y 20-24, 1981 6 00 -

3 500

ar w 400 3

0 a a rz 300

600 - 2 00

400 I I I I 100 0 20 40 60 80 100 0 25 50 75 100 125 1.50 175

TIME, h TIME. h

Figure 4. - measured and -- predicted power (E,) for Unit 1, using coefficients generated for January 20-24, 1981

- -

- -

- MARCH 22-26, 1983

I 1 I I 1 300 0 24 48 - 7 2 96 120 144

TIME, h

Figure 6 . - measured and --- predicted power (B,) for Unit 3, usTng coef f ic ients generated for mr& 22-26, 1983

Figure 5. - measured and --- predicted power (Ear for Unit i , using coefficients fat: January 20-24, 1981

200 1 i I I I 1 I

0 24 4 8 72 96 120 144

TIME. h

Fi.gure 7. - measured and - predicted power (E,) for Unit 3, using coefficients for March 22-26, 1983

where E (t) represents Qt for the solar gain experiments (Quation ( 2 ) ) and QN forPthe mom-air temperature experiments (Equation ( 4 ) ) , and E ( t ) is the t total power wasumption of the room (including additional heater input in the room-air temperature experiments). Step 2 is i l lu s tra ted in Figure 8 for a solar pulse at noon in the south room of Untt 2 and in Figure 9 for a heat-addition pulse in hit 1. In these fAgures, and a l l those that follow, the hourly discrete data points are joined by straight lines for both measured and predicted results. k t a used t o produce the response factor start only at the pulse t i m e .

. For the solar pulse, the input fs calculated as

I I I I I L I 5 10 15 20 2 5 30 35

TIME, h

Ffgure 8. Net output response to a solar gain pulse

PULSE

,FRED ICTED. En I M E A S U R E D , E u

500 - --. .-' /TEMPERATURE

* R I S E i 'a

0 \-----

-500 -

10001 1 ' 1 ' ' I l l 1-10 0 1 U 20 30 40 5 0

TIME, h

Figure 9. N e t input and output for: a room-air pulse

where I is the average solar radiation intensity over the I-hour pulse period, F is the solar gain factor far double glazing calculated f o r that hour ( 8 ) , and A is the net glazing area exposed during the period.

Step 3. Calculating the transfer function coefficients

Multiple linear regression analysis w a s used to produce a first approximation to the transfer function coefficients in Equations (2) and ( 4 ) . These coefficients w e r e then used as fnitlal assumptions for a sophisticated prediction program to generate more accurate values of the coefficfents. The prediction program DFMFP, of the IBM scientific subroutine library, w a s used (91, which calculates the local miniwm of a function (the error value) of several variables (the coefficients) using the method of Fletcher and Powell (10). This is the same method commonly used for the design of recursive d ig i ta l f i lters (11). The minimized functlon was the square of the difference between the measured and predicted responses. The method substitutes the predicted value for the previous hour in Equations (2) or ( 4 ) to calculate tk value and error for the present hour, rather than the measured value for the previous hour, as in regression calculations.

RESULTS

Solar Etesponse Factors

A total of 11 experiments were performed during Lhe 1980/81 heating season in the south rooms of Units 1, 2 and 3 of t h e t e s t facility. Table gives the average calculated values of the transfer functfon coefficients for a l l experiments and the average far each room (light, raedium, heavy). The table also gives values of the rms difference between the measured and predicted responses, In addition, Figures 10 to 12 show examples of both the measured and predicted cooling load response to a solar pulse for each of the light, medium and heavy rooms,

Table 5. Solar Transfer Function Coefficients

Date (1981)

1 RMS fit error (W 1

Jan. 30 Feb, 5 Feb. 13

Aver age

Medium

Jaa. 30 Feb. 5 Feb, 14

Aver age

Jan. 30 Feb. 5 Feb. 13 Feb. 14 Feb. 15

Average

As w i t h the response factors in the ASHRAE handbook, the coefficients presented in Table 5 are normalized, as explained earlier in th i s Note,, to give an f value (in Equation ( 6 ) ) of 1. Befbre normalXzarion, average calculated values of f were 0.7, 0.89 and 0.86 for the three room mass levels , respectively.

I I 1 I I I

Figure 10. - measured and --- predicted response to a solar galn pulse I n U n i t I, -south room

-

-

9 0 5

ZZ

& -loo w & -100

a l F E B R U A R Y 5. 1981 I

150 0 L

100'

5 0

0

-5 0

I I I I I 1

4

-50 0 5 10 I5 20 25 30 35

TIME, h

a 1 F E B R U A R Y 5 , 1981 -

0 5 I 0 IS 20 25 30 35 0 5 1 0 IS 20 25 30 33

TIME. h TIME. h

- 5 0 ~ I I I 1 T I I E 150 # I I I I 1

Ffgure 12, - measured and --- predicted response t o a solar gain pulse i n lh f t : 3, south room

LY 400 0 e

300

200

100

D

-100

I I I f I I

b ) JANUARY 30. l98I

0 a

100

50

-

-

Figure 11. - measured and - predicted response t o a solar. gain pulse in hit 2 , south room

-

-

I I t 4 1 I I

b) FEBRUARY 15, 198.1 - 4

0

-

-

I I I 1 1 I

- -

b l FEBRUARY 14 , 1981 -

-

-500

3

& -1000 W 3 3000 1 , 1 1 ' 1 '

0 a b ) FEBRUARY 5, 1983

-

-

1 I 1 1 1 1 1 1 j '

a ) J A N U A R Y 27, 1983

Figure 13. - measured and ---- predicted response t o a room temperature pulse, hit 1 ( l i g h t )

I I 1 I I 1

-

-

k -

- - -

i f 1 1 1 1 1 1

I I 1 1 1 1 I I 1

TIME, h

-

- -

2 000 I l l l l l l l I - 1500 - b) APRIL 21, 1981 -

Figure 14, - measured and -- Figure 15, - measured and -- predicted response to a room predicted response t o a room temperature pulse, Unit 2 ( m e d i u n ) temperature pulse , Unit 3 (heavy)

a l A P R I L 21. 1981 -

-

-

-

1000

500

Boom-Air Response Factors

- - I 1 I I t I I 1

Experlmenrs were performed In two heating seasons, 1980/81 and 1982183. Between the two periods, an additional external layer of insulation was applied t o the walls and ceilings of a l l test uni ts , The change in thermal characteristics is reflected in the data in Table 1. In 1980181, experiments were performed in all three 2-rom units for both rooms s id taneous ly (partition door open). In 1982/83, the medium-weight unit was not available for further experiments. Details of the experiments performed during both heating seasons (19 in all) are given in Table 4. Figures 13 ra 15 show examples of the measured and predicted net heat: input ta the room (output) corresponding to the measured variation in room temperature (input) for: each of the three room mass values, The resulting average response factors for all the experiments are listed in Table 6.

0 I

-500 -

-

-

Due t o measurement errors, the transfer function coefficients obtained d i d not exactly sat is fy the steady-state condition given by Equation (7). To sa t i s fy this condition, the g2 coefficient was calculated from this equation. The overall thermal conductance of the unit, KT, w a s obtained by adding the corridorwall conductance L a the indoofoutdoor UA value of the unit obtained in a previous investigation (7). The. maximum change 14 any g2 value was less than 10%.

-

In addition, t o be conststent with the ASHRAE presentation, the room-air response factors w e r e normalized using Equation (8). These

Table 6 . Room-Air Eksponse Factors

RMS f i t error (W) Date

Light

(1981) Apr. 16 Apr, 19 Apr. 21

Average Corrected g2

(1983) Jan. 24 Jan. 27 Jan. 31 Feb. 5 Feb. 17 Mar. 11

Average Corrected g2

Medium

(1981) Apr. 16 Apr. 19 Apr. 21

Average ~orrected gZ

Heavy

(1981) Apr. 16 Apr. 19 Apr. 21

Average 453.7 Corrected g2 453.7

( 1983) Jan, 24 Jan. 27 Jan, 31 Feb. 24

Average 400.3 -452.2 51.4 -0.895 Corrected g p 400.3 -452-2 56.3 -0.895

Table 7. Normalized RoorAir Response Factors - - - -. - . - - .

The ma1 Unit Data capacity

( J l K )

Light

Average 11-16

Average 13.84 -16.29 2.45 -0.898 11,18(11;62~

a~alues in brackets are from Table 2

Table 8. Bxperimntal and ASRRAE Response Factors

Exptl. Exptl. A S H W A S H W E x p t l . ASHRAE l ight medium lgght medium heavy hsavy

S p e c i f i c mass (kg /m2 1

of floor area

Solar -

adjusted and normalized factors are presented in Table 7 far the three mass levels.

As indicated earlier, the thermal capacity of a building can be deterrained using Equation (10). Table 7 gives the resulting values far the three units, as well as the values calculated f r o m the construction d e t a i l s , the building elements and the specific heat of each element (taken from

Table 2) . The data i n the table show good agreement between the two sets of t h e m 1 capaci'ty values.

DISCUSSION

The response factors obtained in this study, together with the values in t h e ASHBAE Handbook, are summarized fn Table 8. Exadnation of the decay coefficients (wl and p l ) shows that the new values are consistent with the mass levels of the building. The new response factor values, therefore, fill the gap that existed for wood-frame houses. Additional work is needed, however, t o produce the remaining sets of cooling load response factors (conduction, l lghts, etc.).

.Work I s underway to calculaLe the z-transfer function coefficients analytically,- for the same m a s levels reported in thie study, uslng the procedure developed by Wtalas (12'). Preliminary results of these calculations (13) are reported in Table 9. Calculated values for the solar

Table 9, Calculated Response Factors

S p e c i f i c mass ( W m 2

of floor area

Solar -

Conduction

Lighting (incandescent)

boarair temperature

cooling load and the room-aair transfer function coefficients show f a i r l y good agreement with experimental values. The large values of the n e w g coefficients of the room-air transfer function are probably due to the

l l l l l l l l l 1 l l l l -

a) SOUTH ROOM ILIEASURED 20.5'~ AVERAGE TWIPERATURE - - - - - - - - - - PREDICTED 20.6"~ AVERAGE -

- -

New sets of z-transfer function coefficients were generated experimentally for the solar cooling load and the room-air temperature. The coeEftcients were obtained for wood-frame houses with three different

locations of heat input

-

4 0

3 5

," 30

w 0: a + 25 4 E w o s bJ 20 *

15

10

L

I h

and temperature measurement. As mentioned previously, temperature was measured as the average (of 12 locations) at room mid-height. However, %f the measured average temperature is less than the true mixed average assumed in any calculation, this w i l l resul t in higher values sf the g coefficients wmpared wlth those calculated analytically,

- -

1 1 1 1 1 1 1 1 1 1 1 1 1 1

2400 In addition, such b) TOTAL PWKR MEASURED 342.0 mm TOTAL differences may account

------a PRED l CTED 38.9 lrWh TOTAL for the discrepancy 2000 between the assumed

3 linear indoor convective

= 2500 fL1m coefficients used in w iz the calculation, and the 0 a actual convective -+ 1200 = coefficients for the 4 walls of the test units. J - 800 =I

4 The response factors in Table 9 w e r e used in the

4 00 ENCORE Program (6) to simlate the performance

o of Unit 1 of the test 29 3 0 3 1 1 2 3 4 5 6 7 8 9 1 0 1 1 facility far the same

OEC 1980 D A Y OF MONTH JAN 1981 period shorn in Figure 1. h o r n temperature and

Figure 16. ' E ~ ~ ~ ' sinmulation results for power cansumptian are Unit 1 ( l i g h t ) using new transfer function compared with measured coeff icf enrs (Table 9) values in FZgure 16. The

new response factor values gave results that

corresponded much better to actual monitored performance for such lightweight buildings. Further improvement in the s i m l a t l o n results, particularly for heavyweight buildings, can be expected if more coefficients are used t o express the z-transfer function.

specific mass levels: 4 6 , 130 and 535 kg/m2 of floor area. These coefficients improved the thermal performance prediction capability of energy analysis programs based on the response factor principle . The response factors reported i n this Note complement those in the ASHRAE Handbook and increase the scope of the response factor method.

REFERENCES

1. Stephenson, D.G., and G.P. Mitalas, Cooling b a d Calculation by the Thermal Response Factor Method. A S W Transactions, Vol. 73, Part 1, 1967.

2. Mitalas, G.P., Transfer Function Method of Calculating Cooling Loads, Heat Extraction and Space Temperature, ASBRAE Journal, Vol . 14, No, 12, pp. 54-56, December 1972.

3. Piitalas, G.P . , Comments on the 2-Transfer Function Hethod for Calculating b a t Transfer i n Buildings, ASRRAE Transactions, V o l . 84, Part 1, pp. 667-674, 1978,

4. A S H W 1985 Handbook of Fundamentals, American Society of Heating, Refrigerating and Air Conditioning Engineers, Chapters 23 and 26, Atlanta, GA.

5. Procedure for Determining Heating and Cooling b a d e for Computerizing Energy Calculatfons: Algorithms for Building Heat Transfer Subroutines, A S m E Task Group on Energy Fkquirements for Heating and Cooling of Buildings, American Society af Heating, Refrigerating and Air Conditioning Engineers, hc., New York, NY 10017 (1975).

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9, IBM System 360, Scientific Subroutine Package, Version 111, Progr-rs Manual, IBM Data Processing Mvislon, mite Plains, NY, 1968,

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11. S t e i g l i t z , K., Computer-Mded Design of Recursive Mgital Filters, IEEE Transactions on Audio and Electroacousrics, Vo1, AU-18, Plo. 2, pp. 123-129, 1970.

12. Mttalas, G . P . , Room Dynamic Thermal Response, Ptoceedings of the 4th hrernational Symposium on the U s e of Computers for EnvLronmentaL Engineering Related to Buildings, pp. 25-3 1, Tokyo, Japan, 1983. . . . . .

Zanaer, D.M., Division of 6d'faing Research, National Research Council of Canada, pr lvate communicatiom, 1985.