Calculations of thermal performance of a building and its air conditioning plant by hybrid computer

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Calculations of thermal performance of a building and its air

conditioning plant by hybrid computer

Mitalas, G. P.

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___ _

NATIONAL RESEARCH COUNCIL CANADA

DIVISION OF BUILDING RESEARCH

CALCULATIONS OF THERMAL

PERFORMANCE OF A BUILDING AND ITS AIR CONDITIONING

PLANT BY HYBltiD COMPUTER

/

/ by

G. P. Mitalas

Computer Program No. 21

of the

Division of Building Research

Ottawa

(4)

·_·..,.

. ｾ＠

,.

}.

CALCULATIONS OF THERMAL PERFORMANCE OF A BUILDING AND ITS AIR CONDITIONING

PLANT BY HYBRID COMPUTER by

G, P. Mitalas

The temperature of the air in an air conditioned room depends on the rate at which heat enters the room, the rate at which heat is removed from the room, and the heat storage capacity of the structure, The calculation of room air temperature or room cooling load is quite involved as the ambient conditions, the characteristics of the cooling plant and the characteristics of the structure must all be considered together, The calculation involves the solution of several equations, both algebraiJZ and differential, that describe the performance of the cooling. ｳｹｳｴｾｭ＠ and the structure. These

equations can be solved qui.te readily by an electronic computer. This report describes the way that the NRC computer facilities have been used to make air conditioning design calculations.

Computer Facilities Available

The Analysis Section of the NRC Division of Mechanical Engineering has a Pace analogue computer, a Bendix G-15 digital

computer, and an analogue-digital digital-analogue coupling unit that allows the two computers to be interconnected, ·These machines have been used for air conditioning design calculations. The coupled analogue -digital machine is particularly well suited for this type of calculation because the problem involves algebraic and differential equations. The analogue is best suited for solving ·the differential equations and the digital is superior at algebraic equations. The digital is also used to generate the ambient conditions that are the driving functions for the problem, and the results are recorded in digital form and finally typed by the typewriter associated with the digital machine.

Mathematical Model of the Thermal Eaergy Balance of a Room and an Air Conditioning Plant

The heat interchange within a room, the heat flow.,through

u

a room envelope and the heat interchange between an outside wall and its environment, can be described by a set of linear algebraic

(5)

ﾷｾﾷﾷﾷ＠

t

c .e.

t

l l t

and by a set of differential equations:

e.

_l =

D. e. 1

t

D. e.

- D.e.

t-1 1- ttl ttl t t

where

C .. , K, and D. are coefficients

Jt t t

=

= K.I. J J

e.

t

=

room envelope inner surface temperature

... (1)

... (2)

(Ref. 1)

=

time dependent variable (i. e. solar radiation, outside air temperature, etc,).

The number of equations in a set is governed by the number and the construction of room envelope components. A room thermal ·response can be described by approximately ten differential and ten

linear algebraic equations.

where

The room air temperature is given by:

=

t

MR

=

J

(clel

t

czez

t ...

0

=

room air temperature Q = heat addition or extraction

a*

_R

=

minimum allowable room air temperature (i.e. stat setting),

/)

• . • (3)

(Ref, 1)

thermo-The continuous solution of the above .equations is possible using the three basic analogue circuits given in Figure 1.

(6)

. ·,,

3

-The mechanical equipment to control the inside climate in large buildings usually consists of:

(a) chiller

(b) primary air unit

(c) secondary water coils.

Figure 2 is a schematic diagram of this equipment and the

room.

The chiller cooling water outlet temperature, at constant water flows and compressor speed, depends on the cooling water inlet temperature and the outside air wet-bulb temperature, and is given by:

where

8 A A 8 A 8 2 - 8

*

/';. wo=

l + 2 Win+ 3 Win WO

8w.

_tn 8

wo

=

inlet cooling water temperature (• F)

outlet cooling water temperature ( • F)

a and b

=

constants that are functions of the particular chiller design

8 ｾＧ＠

wo

=

minimum allowable outlet cooling water temperature _{(• F).}

[)

The maximum heat extraction --per square foot of

nominal face area by the primary air unit at the design air and water flows --is a function of the temperature of the chilled water entering

(7)

,

__

this unit, Bwo; of the inlet air dry bulb, BoB;· and of the inlet air dew-point, Bop• temperatures. It is given by one of the three following expressions depending on (Bop - Bwol difference:

where where

=

/

=

c, d, e, f, g and m are constants that are functions of the particular primary air unit design. The temperatures are in • F and Qp is in Btu/hr ft2,

E.

1n

M

a

The enthalpy of the outlet air is given by: E

=

E. .., (Qp)/(M')

o 1n a

=

enthalpy of outside air (inlet air to primary air unit) (Btu)/(lb of air)

=

mass flow rate of air through primary air unit (lb)/(hr ft2).

If it is assumed that the outlet air is saturated, which is a reasonable assumption for a unit with four or more rows of sprayed coils, the outlet air temperature is given by the following equation:

B

oa

=

(-2. 69

+

_n

3. 51 E _o - 0. 0518 E 2 _o

+

0, 000333 E 3) •F. _o The heat extraction by the secondary coils is:

(8)

where

u

₌

=

5

-constant which depends on the particular coil design and water and air flow rates.

inlet water temperature to the secondary coil, oF

9R

=

room air temperature, oF

X

=

bypass factor, i.e. the ratio of cooling water flow through the chiller to the cooling water flow through the primary air unit

.,

=

water flow rate through t.!J.e primary air unit, (lb)/(hr ftZ).

/

The sensible cooling of room air by secondary coils and primary air is:

where

S

=

primary air unit coil nominal face area allocated for this room, ftZ.

The cooling water temperature entering the chiller is:

The equations describing the heat balance in the room and the cooling plant must be solved simultaneously because ·of the interdependence of room air temperature and heat extraction by secondary coils. The

solution of this set of equations on a hybrid computer is not a straight-forward operation because of the operational difference of the two computers; the digital computer sample_s the analogue voltages repre-senting 9w in and 9R at the time, ts· Using these sampled values it calculates ( 9₀a) ts and ( 9wr>· ts but the calculations require a small time interval,. and therefore the values (9₀a) ts and (9wr> ts are "late".

This diff:cbulty can be overcome by noting that the driving functions are ·periodic with 24-hr period, and that only the periodic steady state

(9)

Ｍｾ＠

I)

6

-calculated for the time, ts, are stored in the computer memory and held there until the time, ts

+

24 hr. At this time the values are transmitted to the analogue computer.

Hybrid Computer

The hybrid computer at the Division of Mechanical Engineering, NRC, used for these calculations is made up of:

(a) a Bendix G-15 digital computer, two magnetic tape units, a typewriter, puncl)ed paper tape reader and punch.

(b) a Pace 131R electronic analogue computer made up basically of 96 amplifiers, 160 potentiom'eters,

4 relay amplifiers,. digit.al vo:Jtmeters and an analogue

/

recorder.

(c) an Epsco addaverter with an 8 D:..A (digital to

analogue) and an 8 A-D (analogue to digital) channel capacity.

The D-A converter accepts lZ binary bits with sign, accuracy± 0. 5 bits or 0. OZ per cent over the working range of ± 10 volts and the time for conversion "" 0. 1 ms.

The A-D converter gives lZ binary bits with sign, accuracy ± Z bits, i.e. 0. 1 per cent and time for conver·sion of 8 channels

"" Z ms.

The interval between the conversions can be controlled by the addaverter clock or by the Bendix G-15.

Operation Procedure

The procedure for the solution of the e.quations describing the room thermal performance and the air conditioning plant can be divided into four major steps:

(1) Preparation of the driving functions

(Z)

Setting up and checking the analogue circuit (3) Solution of the equations on the hybrid computer ( 4) Tabulation of results.

(10)

7

-Preparation of the Driving Functions

The driving functions are calculated by "A Program to Calculate Design Data for Air Conditioning Calculations". This program is designed to calculate various weather parameters from the basic data, to store these in memory and to punch them on paper tape. The detailed description and operational procedure of this program are given in Ref. 2.

The punched paper tape produced by this program is not directly usable as an input for the "Running Program" which is described in the following sections. The numbers listed on the punched paper tape must be converted to the special format accept-able by the D-A converter. The "Driving Function Conversion Pro-gram" was written to convert the numbers to the r,equired format, to calculate A1, Az, and A3 constfnts and to store these on magnetic tape. The detailed description of this program and its operational procedure are given in Appendix I.

Setting Up and Checking of the Analogue Circuit

The method and the detailed description of how to set up an analogue circuit is given by G. P. Mitalas et al {1). Before this circuit is used, it is desirable to check the circuit and the settings of the

potentiometers. This can be done simply by noting that:

(a) the temperatures of the room envelope and the room air at steady state conditions must be equal to the temperature at the outside surface of the room envelope, when the other inputs are zero; (b) the heat extracted from the room air must be

equal to the solar radiation input to the room, when the heat flow through the room envelope an.d the internal heat sources are zero.

Once these verifications are carried put it is reasonable to assume that the analogue circuit and the potentiometer settings are corre.ct and that the analogue circuit components are functioning correctly.

Procedure for Operating the Hybrid Computer

(1) Mount the magnetic tape containing the driving functions on the magnetic tape unit No. 0.

(11)

(Z) Mount a reel of blank magnetic tape on tape unit No, 1.

(3) Set the addaverter controls:

( 4)

(5)

a) channel capacity

=

8

b) channel 8 on "Data" channel c) time on clock

=

1. Z sec.

Load "Running Program" (the .description of this program and its operational procedure· are given in Appendix II), search the magnetic tape for the required driving functions, and load thi,s set into the computer,

Turn on the analogue recorder and set the

analogue computer in operating mode. This puts the hybrid computer in operation.

(6) The heat extraction from the room air can be varied by:

a) a change in bypass factor, X

b) a change in primary air unit coil nominal face area, S

c) a change in constant, U,

{7) The strip chart record of the analogue voltages indicates if the solution is proceeding satisfactorily, and it also indicates when the periodic steady

state conditions are reached.

(8) When these latter conditions are reached, the results of this calculation, the driving functions used, and the several constap.ts are recorded on the magnetic tape on unit No. 1. The procedure for this is given in Appendix II.

(12)

9

-Tabulation of Results

The "Tabulation Program" was written to type the recorded results from the magnetic tape. This program also performs a limited amount of calculations to present the results in a more comprehensive form. The description of this program and its operational procedure are given in Appendix III.

Acknowledgement

The author wishes to acknowledge the assistance of Mr. G. P, Van Blockland of NRC Mechanical Engineering Division, Analysis Section, who prepared the programs described in

Appendices I and II.

References

/

1. _{Mitalas, G. P,, D. G. Stephenson and D. C, Baxter, Use of' An}

Analog Computer for Room Air -conditioning Calculations. Research Paper No, 114 of the Division of Building

Research, Ottawa, December 1960 (NRC 6099).

2. _{Mitalas, G. P, A Program to Calculate Design Data for Air} Conditioning Calculations. National Research Council,

Division of Building Research, DBR Computer Program No. 20, January 1965,

(13)

FIGURE 1

ANALOGUE Cl RCU IT FOR THE SOLUTION OF

a) linear algebraic equations

b) Ordinary differential equations

-el.,.l - eH D· _l-1

}---:::=::--t

., G)) ｾｃｬ＠ +9, • +

Where

Potentiometer

Relay amplifier

･Ｌｾ･ｯ＠

e

0

=

Ke,

e,

ｋｾ＠ 1.

e,

<

0

e

₃

=

_e.

Summer

e

=

e,

6 ･Ｌｾ･Ｐ＠

_-eo

_e,

+

e

₁. +

e3

e,>

0

e3

_e

₃

₌

_e+

Integrator

_t ･ｾ＠

=

e7

･Ｌｾ･ｯ＠

_-eo

₌

J

_{I e'}

₊

_e,

_+-

_{e3 ) dt}

_e+

_e7

e.

e3

0 (J 317:1-t

(14)

Iogue

<!:der

Ana

Reco

v

FIGURE 2

Analogue

.,

....

,..

,

ｾ＠

Results

Room

' "'

I

Secondary

Q"*

_Water

Coils

I

'

I

'

I \ ' /

.

I

I ,

I

ewi

I

I I

I

Digital

"

Computer

,

Memory

ew&

ｾ＠

Cooling

'

Tower

r---ew

in

_,

_...

Chiller

ewr?

'

j

ｂｹｰ｡ｳｳｾ＠

Valve

--Ｌｾ＠

'

I

e"s

Primary

eDP

"

_{Air Plant}

fin

eo

a.

. I

Driving

.

Functions

(15)

CONVERSION PROGRAM by

G. P. Van Blockland

The driving functions on the punched paper tape

generated by the "Program to Calculate Design Data for Air Con.;. ditioning Calculations" {2) cannot be used directly as an input to the "Running Program", as the numbers for this program must be

specially-scaled machine language numbers. Therefore, this pro-gram was written to perform the following operations:

{a) to read punched paper Ｍｾ｡ｰ･＠ prepared by the "Program ｴｯＭｃ｡ｫｾｬ｡ｴ･＠ Design Data for Air Conditioning Calculations",

{b) to convert these data to machine language numbers and to shift some of these numbers to the 13 least significant bits of the 29 bit word {this is the number format acceptable by the D-A converter).

(c) to arrange the converted numbers in arrays in such a way that they are ･｡ｳｩｾｹ＠ available for transmission to the D-A converter by the "Running Program 11_,

{d) to calculate A l• A2 and A3 coefficients (A's are defined on page 3) to store the con-verted numbers and the coefficients in one file on magnetic tape.

All the input is by punched ｰｾｰ･ｲ＠ tape except the pro-vision by which the driving function set number No can be entered by typewriter. The order of the data on punched paper tape is given in Appendix I. The first paper tape channel read is stored in line 06, the second in 07 and the third in

C.d.

(16)

I-2

Arithmetic Operations

This program calculates scaled A1, A2 and A3 coefficients.

=

Locations of Constants 0109 _{a 1/200} / 0115 b1/200 0127 _a2 0114 _b2 0132 200 a 3 0135 200 b3 Output

The converted numbers and A1, A2 and A3 coefficients are· stored in one file on magnetic tape in the following order:

First line = copy of computer memory line 09

Word location Data

96-4t A₁/200

97

-4;.';

A

2

+

L

10-5 2-16

(17)

96 97 98 99 No/1000 S/100 Ag/1000 H/10

Second line

=

copy of computer memory line 10

96-4t 97-4t 98-4t / 99-4t 96 97 e₀p x 1/zoo e_{0 B} x 1/zoo E X 1/100 r 1 x 1/1oo x z-16 Aw/100 No/1000

Third line

=

copy of computer memory line 11

96-4t 97 -4t 98-4t 99-4t where t

=

1(1)24. Memory Allocations rTD x 1/1oo x z- 16 ew x 1jzoo x z- 16 eg x 1/zoo x z- 16 rT x 1/soo x z-16

Lines 00, 01, 02, 03 and 04 are used for program and word location.

(18)

I-4

ZO:OO mask

ZO:Ol 9WB

x

1/100

ZO:OZ T for pickup

20:03 T for storing 21:00 number to be extracted 21 :01 scale factor Z2:00 temporary storage 22:01 , temporary storage 22:02 temporar)l" storage / 22:03 temporary storage. Operation Instructions

1. Mount magnetic tape containing driving functions on

mag-netic tape unit No. 0. Position the reading-writing head in the blank tape past the last information block.

2. Load the "Driving Function Conversion Program". Enable

ON, type P; after the first block has been read, compute GO.

3. Mount input data tape (output of the "Program to Calculate Design Data for Air Conditioning Calculations") on photo reader.

4.

Start the program. Enable ON, type

@

c£, compute GO.

5. Three blocks of paper tape containing the driving functions

will be read, These functions will be converted arid written on magnetic tape.

The program halts automatically as soon as all the input data tape is read and processed.

CJ 6. The driving function set number can be changed by the

(19)

(a) compute switch to BP while the computer is in the process of reading punched paper tape (b) when all of the three blocks are read,

com-puter halts

(c) Enable ON, type

®

cf, compute GO. Type No x 1/1000 in seven-decimal digit format,

e. g. No

=

5, type 0050000 tab

® .

The number No read from the punched paper tape is replaced by the number entered by the typewriter.

/

(20)

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NOTES

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68

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-N.R. C.

ｾ＠ OIV. OF MECHANICAL ENGINEERING

-DIGITAL COMPUTER LABORATORY

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