NATIONAL BUREAU OF STANDARDS REPORT

NBS PROJECT NBS REPORT

1003-20-4702 June 4, 1953 2546

PROGRESS REPORT

Air Conditioning in Underground Structures

November 1, 1952 to April 30, 1953.

by

B. A. Peavy

Heating and Air Conditioning Section

Building Technology Division.

U. S. DEPARTMENT OF COMMERCE

NATIONAL BUREAU OF STANDARDS

The publication, reprin

unless permission isobt

25, D. C, Such permls*

cal ly prepared If that

Approved for public release by the

Director of the National Institute of

Standards and Technology (NIST)

on October 9, 2015.

iart, Is prohibited

ards, Washington

I has been speclfi-

't for Its own use,

PROGRESS REPORT

Air Conditioning in Underground Structures

I, IkTRvUrSTIQj

During the period from November 1, 1952 to April 31

»

1953, tests have been continued in the underground test

chamber at Mount Weather, mathematical approaches to

the theory ©f heat transfer to a rock mass bounding

an underground space have been studied and are compiled

and presented in this report,, data from previous tests

were analysed, revisions were made in the Engineering

Manual, Fart 3TX, Chapter 3, and preparations were made

for future testing at Mount -feather, 7a# and Fort RStchie,

Maryland#

II# TESTS PERFORMED XU TOERGBCTOD TEST . CHASER

Test Condition & - Determination of heat and moisture

load without ventilation or simulated occupancy

from November 10 to November 26 while maintaining

constant conditions of 75* DB and 50$ R#H# with the

air conditioning system.

Test Condition 9 « Conditions were the same as test condition $ except condenser water reheat was used to

reduce the electric reheat November 26 >to December 5#

Test Condition 10 - Steady state heat at ?5*F air temperature from .December 5 to January 5 t 1953# Ho dshuEsidlfication*

Test Condition 11 - Steady state heating at 75e F air

temperature with ventilation air from January 5

to February 11#

Test Condition 12 - Test condition 10 repeat from

February 11 to .March 30,

Test Condition 13 - Test condition 11 repeat now in

progress#
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- 2 - m. mmmktickt approaches to heat

TRANSFER TO W3DERGROUKB SPACES

A review of the mathemyir! cal approaches to the

transfer of heat to the rock surrounding an underground

chamber ©hows that mathematical treatment of the elementary shapes such as the plane surface, circular cylinder and

sphere bounded by a ssedium approaching infinite thickness

is found in Carsi aw and Jaeger, "Conduction of Heat in

Solids" • Jhile for the most part the actual equations

involving heat transfer are complicated, they nay be reduced by numerical integration or approximation and plotted

in graphical or tabular form for design application.

Configuration of actual underground installations

say be approximated by one or more of t‘ e elementary

shapes. * Considering an underground room to be an assembly

of plane surface© (floor, ceiling and walls) neglects the

heat flow into the corners and edges, whereas likening it

to a cylinder (lateral surface) neglects the heat flow

into ends of the cylinder. A sphere would rarely be an

approximation for an actual installation.

To the above named shapes two different boundary

conditions can be applied; namely, the constant heat

flux case and the constant surface temperature case.

1. Heat transferred to a solid bounding an elementary

share with a constant heat flux and the initial

temperature of the solid equal to sero ©n an arbitrary datum plane.

A. Linear heat flow to a medium of semi-infinite

depth from a plane surface.

1. I’emper&fcrre at depth x

2 ierfc

2 v' «

Values of *2 ierfc’ of the argument arr- shown In tabular form in Table 2.

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2. Temperature at x * 0.

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B. Heat flow to the solid bounded internally

by a circular cylinder {radius * a).

1* Temperature at r/> a in the operational

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if*

Solution of this operational form can be made

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C. Heat flow to the solid bounded internally by a

sphere (radius ** a).

1. Temperature at radius r > a.

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in tabular form in Table 2*
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2. Temperature at radius r « a.

II. Heat transferred to a solid bounding an elementary

shape with & constant surface temperature and the

initial temperature of the solid equal to Kero on

an arbitrary datum plane. It must be noted that

for these conditions the heat flux is infinite

for time equal to zero and therefore the equations

are valid for t greater than zero.

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IT. RE7IS10KS OF miMEEUlia MANUAL

Fart 171 • Chapter 3

Certain tentative revisions *n the Engineering Manual,

XVI Chapter 3, eating, Ventilating and Moisture Control11 , were mad© by B. A, Peavy of this Bureau and J# C. Letts of

the 0,0. I, The additions to the manual were mainly concerned with three conditions of occupancy for which the

•performance of an air conditioning system and related

equipment must be designed, Some deletions were made In

the manual because of their redundancy. Copies of the

manual with these tentative revisions were presented to

interested parties for their comment and review. Further

work to be accomplished in writing of the manual will be

concerned with work now being performed by this Bureau.

f. FUTURE EXPES1MEII TATIGk - MT. WEATHER , ¥A.

1* Underground Test Chamber

Test Condition 14 - Test condition 3 repeat temperature

drop with minimum heat supply and no ventilation.

Test Condition 15 - Apply refrigeration to chamber until

room temperature reaches 40'°F.

Test Condition 16 - Test condition 15 with use of

ventilation air.
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- 7 - Test Condition 1? - Repeat test condition 1, constant

heat input at about 75,000 BTU/br until temperature of chamber is

2, Underground Spray Pond Heat Exchanger

The spray pond was ready to operate before tie

finish of this period, but interference due tc blasting by Bureau of Mines operations halted this test.

Testing will begin May 11, with the test conditions

for the various spray pond tests controlled as follows:

Test Condition 1 - A constant heat input rate to the

spray water of approximately 60,000 BTU/hr will be

used until the temperature of the pond water

reaches lOOfF.

Test Condition 2 - Maintain the temperature of the pond

water at 100* F.

Test Conditions 3 and 4. Repeat test conditions 1 and 2

with use of stagnant pond instead of using sprays*

3* Tunnel Ventilation

F reparations are being made for determining the

heat exchange between tunnel walls and an air stream.

Tests will begin during the month of June.

VI. U3E OF m OCCUPIED UUBERGRCUKD

SPACE FOR TEMPERATURE STUDIES.

Background

Following a visit to an underground space near Port

Ritchie, Maryland, it was concluded that some of the

data needed for correlation with present studies at

Mount Feather, Va. could be obtained by making appropriate tests in the underground space there. Seasonal

heating or cooling of the ventilation air by rock wall

shafts will occur at this site and the amount of heat

exchanged between ventilation air and the rock mass

could be evaluated. Also studies of the heat transferred

to the rock mass surrounding the occupied structure

could be made.
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Proposed ^ork to b© Done;

Temperature sensing elements will be installed

on the rock surface and at selected depths in the

rock in the ventilation air shafts and inside and out*

side of the structure proper. Other instruments will

b© provided to measure air flow, heat flux to rock

»ass, and relative humidity. These instrument r and

their locations will be carefully selected that

measurements would provide data for computations of

heat transfer rates. During this reporting period

thermocouples were installed at six positions cm the

rock surface and at selected depths in 'the rock. The

remaining work will be finished during the mouth of

June*
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TABLE 1 B r Ci| B f (B)

001 *0321 0.050 .2302

002 .0495 0.052 .2341

004 • 0694 0.054 .2332

.006 • Of- 44 0.056 .2422

DOB .097; 0.057 .2461

.010

,012

•ioai

,1176

0.060 .2499

014 .1269 0.065 .2591

016 .1342 0.070 .2677

OU .1430 0.075 .2765

020 .1503 0.0BO .2-743

022 .1572 G.Q$5 .2921

024 • 16 36 0.090 .2996

026 • 1700

02B •1760 0.10 .3133

030 .1619 0.11 .3273

032 .1059 0.12 . 3401

034 .1910 0.13 .3519

036 .1963 0.14 .3633

03a .2009 0.15 .3741

040 .2074 0.16 .3747

042

044

04^ • 2123

.2210 • 225^

0.17 .3937
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TABLE, 2

Table of Functions Used in Heat Transfer Equations

y erfc y 2 ierfc y 1 (0, 1; y)

0.00 1.0000 1.1234 ** .01 .9337 1.1035 15.122

.92 .9774 1.0333 11.033

.03 .9662 1.0694 9.213

.04 .9549 1.0502 3.135

.05 0.9436 1.0312 7.359

.06 .9324 1.0124 6.346

.07 .9212 0.9939 6.421

.03 ..9099 0.9756 6.076

.09 .3937 0.9575 5.790

0.10 .3375 0.9396 5.549

.11 . 3764 0.9220 5.340

.12 .3633 0.9046 5.153

.13 .3542 0.3374 4.993

.14 .3431 0.3704 4.354

.15 .3320 0.0537 4.726

.16 .3210 0.3371 4.609

.17 .3101 0.3203 4.503

.13 .7991 .3047 4.405

.19 .7332 .7339 4.315

0,20 .7773 .7732 4.232

.21 .7665 .7573 4.155

.22 .7557 .7426 4.033

.23 .7450 .7275 4.016

.24 .7343 .7123 3.953

.25 .7237 .6932 3.394

• 26 .7131 .6333 3.333

.27 .7026 .6697 3.735

.23 .6922 .6557 3.735

.29 .6313 .6420 3.633

.30 .6714 .6234 3.643

.31 ,6611 .6151 3.600

.32 .6509 .6020 3.559

.33 . 6403 .5391 3.520

.34 .6307 .5764 3.432

.35 .6206 .5639 3.446

.36 .6106 .5515 3.412

.37 .6003 .5394 3.379

.33 .5909 .5275 3.343

.39 .5313 .5X53 3.317
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y erf

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.40 .5716 .5043 3.288

.41 .5620 .4929 3.259

.42 .5526 ,4818 3.232

-.43 .5431 .4708 3.206

• 44 .5338 .4600 3.180

.45 .5245 .4495 3.156

.46 .5154 .4391 3.132

.47 .5063 .4289 3.109

• 48 .4973 .4188 3.086

.49 • 4 & 84 .4090 3.065

.50 .4795 .3993 3.044

.51 .4708 .3898 3.023

.52 .4621 .3805 3.003

.53 .4535 .3713 2.984

.54 .4451 .3623 2.965

.55 .4367 .3535 2.947

.56 .4284 .3448 2.929

.57 .4202 .3364 2.912

.58 .4121 .3280 2.895

.59 .4041 .3199 2.878

.60 .3961 .3119 2.862

.61 .3883 .3040 2.847

.62 .3806 .2963 2.831

.63 .3729 .2888 2.816

.64 .3654 .2814 2.802

.65 .3580 .2742 2.787

.66 .3506 .2671 2.773

.67 .3434 .2602 2.760

.66 .3362 .2545 2.746

.69 .3292 .2467 2.733

0.70 .3222 .2402 2.720

.71 .3154 .2338 2.708

.72 .3086 .2276 2.695

.73 .3019 .2215 22683

.74 .2953 .2155 2.671

.75 .2888 .2097 2.660

.76 .2825 .2040 2.648

.77 .2762 .1984 2.637

.78 .2699 .1929 2.626

.79 .2639 .1876 2.616
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.32 . 2462 .1723 2.534

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,34 .2349 .1626 2.565

-S5 .2293 .1530 2.555

.36 .2239 .1535 2.545

.37 .2136 .1490 2.536

.33 .2133 .1447 2.527

.39 .2032 .1405 2.513

0.90 .2031 .1364 2.509

0.91 .1931 .1324 2.500

0.92 .1932 .1235 2.492

0.93 .1334 .1247 2.433

0.94 .1337 .1209 2.475

0.95 .1791 .1173 2.46?

0.96 .1746 .1133 2.459

0.97 .1701 .1103 2.451

0,93 .1653 .1070 2.443

0.99 .1615 .1037 2.435

1.00 .1573 .1005 2.427

1.02 .1492 .0944

1.04 .1414 .0336

1.06 .1339 .0331

1.03 .1267 .0779

1.10 .1197 .0729 2.357

1.12 .1132 .0633

1.14 11069 .0639

1.16 .1009 .0597

1.13 .0952 .0553

1.20 .0397 .0521 2.259

1.25 .0771 .0433

1.30 .0660 ,0366 2.240

1.35 .0562 .0305

1.40 .0477 .0253 2.191

1.50 2.147

1.60 2.106

1.70 2.069

1.30 2.036

1.90 2.004
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- 9 -

VII. RESULTS

PERIOD - APRli 23 TO RAY 15, 1952.

Object

The object of this test was to determine the time

needed to bring the temperature of an underground chamber

up to a temperature within the human occupancy comfort

range by the means of a constant heat input rate, and

also to determine empirically the equations of heat transfer to the mass bounding the chamber and the relation of

these empirical equations to the theoretical approaches

listed in Part III of this report.

Description of Underground Chamber a.- d -Rtuinmar-t

The underground chamber, the dimensions of which are

10G*x35 , xlG! high, is contained in and adjacent to an experimental mine operated by the Bureau of fines at fount

leather, Virginia. The chamber is approximately 215 feet

below the surfae " round and 1200 feet from the surface in a horizontal direction. The rock mass bounding

the chamber consists isainly of greenstone with a scattering of epidcte and quartz, and traces of various other

minerals . Petrographically , the greenstone is a metamorphic

basalt partially colored green by the presence of chlorite*

Measurements of the surface area of the walls, floor

and ceiling were made and showed that the projected surface

area was approximately 10,000 square feet. Physical determinations of greenstone rock from the excavation were

made at this Bureau and the results were:

Density, p = 186 lbs/ft^

Specific heat, c * 0.2 BTU/lb. ft F

Thermal Conductivity (cores), k * 1.45 BTU/hr.ft. *f

• A Vit

".

r , c< ~ 0.039 ft2

,/hr

The apparent porosity of greenstone saw; Its tested by the

bureau of Tines was 0.50 percent.

As shown in Figures 11 and 12, the walls and ceiling

are painted white and the floor paved with concrete.

Figure I shows plan and elevation views of the chamber

and arrangement of mechanical equipment and air distribution ductwork. Air was forced by the circulating fan

(1) into the ductwork past electric strip boaters (5)

to the diffusers (6) and the air from the chamber was returned to the circulating fan through the air return

filters (7) and the plenum chamber.
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- 10 - Fifteen twelve-foot long thermocouple poles were

placed at selected positions (Figure 2) in the rock.

Thermocouples had been previously attached to these

poles at intervals —one half foot intervals up to six

feet and one foot intervals from six to twelve feet.

Room air temperatures were measured at twenty plan positions and at each plan position at heights of 2, 30 # 60,

and 90 inches from the floor. The thermocouples were

copper-constantan and temperatures were measured by

them in conjunction with an indicating potentiometer

located in an instrument shed built within the chamber.

Test Fro ce dure:

With the initial temperature in the rock up to

12 feet in depth practically uniform at 53»5°F, a constant heat input of 17 .

8

kilowatt or 6Q,$0Q BTU/hr was

supplied to the test chamber. At regular intervals

during the test, temperatures of the rock surface, rock

depth room air, wet and dry bulb were recorded as well

as the electric energy input as measured by kilowatthour meters.

The test was arbitrarily terminated at the time when

the average plane rock surface temperature reached 70 C F.

This time was 522 hours or 21.75 days.

Results

Figure 3 is a plot of the average rock temperature

(computed from the average of the temperatures on the

fifteen poles) against depth in the rock, with time from

the start of the test as a parameter. Figures 4-& show

temperature distributions at various crossections in the

rock.

Figure 9 is a log-log plot of time against average

temperature rise above the initial rock temperature of

53«5°F with depth in the rock as a parameter, and also

trie average temperature rise of the room air with time.

The average room air temperature was approximately 6°F

above that of the rock surface temperature throughout

the test and like the rock surface temperature rise plots

as a substantially straight line on log-log paper. The

heat transfer from the room air to the rock surface appears to obey Newtons Law:

Q - h A T (1)

where the coefficient , h* in this case was approximately

1.0 BTU/hr fu °F.
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- 11

An empirical equation of average rock surface

temperature rise with time has been computed from the

data by the method of averages, namely:

9 * o . egt

1 '2

(2)

Referring to Part III of this report, equations relating temperature rise at the rock surface, with the

©lapsed time of heating for a constant heat flux, into a

mass approaching infinite thickness, are for the plane

surface, and the cylindrical case:

9 « 2 : I

3/2

- * t

4a

( « t)

4a2

{ Tr V5 - ufill

32

respectively (for nomenclature refer to Part III of this

report-}, -where the first term In the cylindrical case is

the same as that for the plane surface*

Using the experimental surface temperature data, the

constants determined at the Bureau for thermal conductivity

and diffusivity, and assuming the equivalent cylindrical

radius of the chamber was the average of the radii computed

from a) the perimeter and b) the crosssectional area, the

heat flux was determined to be 4*49 and 4*9 » Bft/hr.ffe 2

for the plane surface and cylindrical case, respectively*

Using these values for determining temperatures at a depth

in the rock the calculated values are compared with the

actual experimental values in figure 10#

Following is a table showing the heat input to the

chamber from reading’s of watt hour meters compared with

the heat stored in the rock computed from the mean temperature rise at various times from th© start of the test.

Also the depth of perceptible heat penetration is noted.

Time, Hrs. Electric Heat Heat in Rock Heat Penetration

. Incut. BTU BTU ft

49 3,010,300 2,900,000 5.5

100 5,960,000 6,700,000 7.

a

170 10,256,000 11,450,000 9.0

290 17,92$, 000 19,020,000 11.2
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- 12 - Discussion and Conclusion:

1. For the duration of this test, the temperature rise

at the rock surface was proportional to the square

root of the time (Equation 2). This is substantiated

by theory {Equations 3 and 4) where the second, third

and fourth terns of equation 4 are small in comparison

to the first terra for small values of time,

2. The coefficient of heat transfer between the air and

rock was approximately 1.0 BTU/hr ft** (deg F). This

value is approximately what would be expected for this

case wherein heat transfer was by natural convection

from nearly still air, with no radiation because all

surfaces were nearly at the same temperature .

3. The heat balance showed that the heat stored in the

rock as computed from the observed temperatures of the

rock agreed to within 5^ of the measured electrical

heat input.

4. Figure 10 shows that the use of the -equation for heat

transfer to a medium surrounding a cylinder gave

footer agreement with the experimental data than the

equation for heat transfer from a plane surface to

a semi-infinite medium. (Refer to Part III of this

report, sections I,A,i and For the cylindrical case, the agreement between the experimental and

computed values was improved with increase in depth

from the exposed rock surface.

5. Figures 4 through £ show isotherms in the rock at

various crossections. The isotherms tend to approach

elliptical shape, especially in the smaller crosaections.

6. The constant rate of energy input to the chamber, as

measured electrically, was 60* TOO BTU/hr, which gives

an average heat flux of 6 t 0£ liTIl/br ftm for the measured

X04 square feet of projected surface area. The heat

flux computed from the heat transfer equations on the

basis of surface temperatures and measured rock

properties was 4.49 and 4.90 STU/hrft*' for the plane

surface and cylindrical equations, respectively.

The discrepancy between measured and calculated heat

flux is believed to be due to the fact that heat flow

from the chamber surfaces took place in three dimensions

(diverging as do the radii of a sphere), whereas the

equations apply strictly to one-dimensional flow

(plane equation) or two dimensional flow (cylinder
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- 13 -

equation). The difference between the measured

average input flux and that calculated fro® the

equations is considered due to the extra bulk

of rock beyond edges and corners, which caused

greater flux at nearby surface areas than at

other areas of the chamber, thus causing the

average flux to be greater than the value at

other areas where the stated equations apply

more correctly. For the chamber investigated,

the flux which appears appropriate for use in

the cited equations was about o0;l of the

measured input flux*

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CONS' HIXTOS NOTES

section C-C

scale *r- ro*

V.A.6 0*

A A_L SLCtVI

A LiNTtL OPENINGS PROViOtD

BY OTHHJ B TAN N»l SUPPORT . i.lliM ANGLES «• r • »/•• a- leg oown C COOLING COIL SUPPORT- » L_| , s' % GUO 0 COOL INC COIL SUPPORT 4 (.*• l-l/t* S/0* IBLG C 0OCTN0RK INSTAl I ATlON TO TERMINATE AT THIS POINT INSTALLATION TO OUTSIDE SV OTHERS P CON JENSER WATER PIPING TO TERMINATE AT THIS POINT INSTALLATION TO COOLING TOWER GT OTHERS G OOCTWORP » CONOUIT SUPPORT- G- L't S*K 5* K 1/4* EOPT LONG INSTALLATION GV OTHERS H DUCTWORK SUPPORT- t-L* GPT LONG

INSTALLATION GT OTHERS

EQUIPMENT LIST

•ooo cm rrp 4G#

v *f go-, MO CPM *1* TP 4 40 V >4 GO - WO CPU IP TP 4 40 V If GO —

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ANEXT MG

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HUMIOIST AT MODULATING THCNMOSTAT HS-SO’P) MOOULATINQ THERMOSTAT OOCT TTH (IS GS'P !

CHILLI0 WATER CONTROL (0 TO

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I

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MECHANICAL PLAN

WTONAL BUREAU OF STANDARDS

WAIHNGTON OC

THOMAS

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Temperature

in

°F

TEST CONDITION 1 (CONSTANT HEAT INPL

AVERAGE TEMPERATURE vs DEPTH Off ROCK

Depth in feet



SECHC. N AA

•

SCALE

TEST CONDITION No I- HEATING UP PHASE

TEMPERATURE DISTRIBUTION IN ROCK

AFTER 521 HOURS

FIGURE 4



5

1

SECTION 3-9

SCALE- ’/4

"

: l -Q11

TEST CONDITION No. I- HEATING UP PHASE

TEMPERATURE DISTRIBUTION IN ROCK

AFTER 521 HOURS

FIGURE 5

A

a



.

SECTIO N C -C

SCALX >4

» I'-C

"

TEST CONDITION No. I - HEATING UP PHASE

TEMPERATURE DISTRIBUTION IN ROCK

AFTER 521 HOURS

FIGURE 6

I

10



5

i

H

SECTION D-D

SCALE Va" - l‘- 0

"

TEST CONDITION No. I-HEATING UP PHASE

TEMPERATURE DISTRIBUTION IN ROCK

AFTER 521 HOURS

i 2

*3|

FIGURE 7

> I

", - 0 v.

I?

\

c • ,









o o c O O

o o o O O

in ro CO — SdOOH 31/Mll

TEMPERATURE

DIFFERENCE

-(Tx

-53.5)

FIGURE

10

Figure 11. Underground Chamber - entrance door on rimht,

door to plenum chamber on left.

Figure 12 Underground Chamber Rear