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FACTORS AFFECTING THE DESIGN OF
A SOLAR ENERGY STORAGE UNIT

Thesls Ior II): Degree oI ph. D.
MICHIGAN STATE UNIVERSITY
John Jett McDow
1957

 

515'

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3 1293 20081 8155

This is to certify that the

thesis entitled
FACTCES fiFI’EL'I'ILIG THE DEE) ION CF A
SOLAR ELERGY STORAGE UNIT

presented by

John Jett McDow

has been accepted towards fulfillment

of the requirements for

Ph. D. degree infigricultural Engineering

1' l I ‘

Date e

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FACTORS AFFECTING THE DESIGN OF

A SOLAR ENERGY STORAGE UNIT

By
John Jett McDow

AN ABSTRACT

Submitted to the School for Advanced Graduate Studies of
Michigan State University of Agriculture and
Applied Science in partial fulfillment of
the requirements fer the degree of

DOCTOR OF PHILOSOPHY
Department of Agricultural Engineering

Year 1957

a/jW/Héawz

John Jett McDow
1

ABSTRACT

The objectives of this project were to (l) statistically

analyze daily radiation data for East Lansing in the determination
for each “ontn, as would affect

‘4.

of fre e(uenc5 of various rate levels

.1-J

"torage of solar energy, (2) mathematical y uGS gn

utilization and so

P

".d construct a solar storag e unit, and (3) perform Operations

at

tests on the solar energy storage unit under laboratory conditions.

guantity of available solar ra ittL n at any locali y is the

determinin: criterion in the design of solar utilization e ui pxme t.

v
h)

Dailv solar—enelgy data for 14 years at F“‘t Lansing were analyzed.

Charts develoccd "ere monthly probas * curves and monthly co-

tit-A

o". ': P a 1‘ 1. r . .A\ 9"» ,— r- " ~ I'\ ‘1 . r. v - ,~‘ v“: ': r v r . v r
efficients oi variatio: i r n ‘nnl, Malinda, and minimum daily rate

The probability.fln~a given job is selected by balancing between the

Wnortance of consistent ener " rates and the allowable investment

r

in equipment. Once this selection has been made, the pioaaoiiit,

curves give quanti tative rates ex;>ected. The coefficients of varia-

tion aid in selecting a probability and adapting solar-energy efit i'

ment to other localities.

A study of heat storage methods :jrov ed that rocks JOUlC be the

best material for agricultural use. Analysis by heat transfer

principles indicated that the A—inch diazeter rock would provide the

maximum rate of heat storage at minimum pressure drop across the

Thenral con ductivit5, specific heat, and denSity of a special

concrete mixture were determined. The 4-inch diameter Spheres of

John Jet McDow
2

this mixture were used in a laboratory storage unit.

Copper-constantan thermocouples in 15 control Spheres provided
information on rate of heating, retention of heat, and rate of heat
recovery from the Spheres. Observations proved the spheres to react
very closely to theoretical solutions. Lower mass air velocities
of 320 lb per (hr)(sqft) provided the greatest heat transfer effec-
tiveness and the most economical Operation. This velocity provided a
surface conductance coefficient of two for the Spheres. The heating

and cooling of the spheres could be considered essentially Newtonian.
Tests showed that the effectiveness of the spheres in heat

absorption was reduced considerably after subjected to heated air for

three hours. About 68 percent of the available heat was absorbed

during this period, with the top layers heating rapidly at first and

then the lower layers.
Up to 78.6 percent of the stored energy was calculated to be re-
coverable, when using a l2-foot cube storage unit within the building

where the heat was utilized. It was also found that 68 percent of the

energy stored could be remaining in the storage unit after three days.

Faster heat losses at ends of storage unit during storage indicated

that convection currents must be reduced to conserve heat.

In a prototype unit, the storage material would be of well

Sized and selected A—inch diameter field rocks. Placement of the

storage unit within the building where the heat is utilized will

increase efficiencies. The shape should be cylindrical or cubical.

Calculations showed that a 7-ft cube storage unit with stones could
fUrnish a poultry house 25,700 Btu/hr for drying 16 hours a day.

This was based on an 80 percent probability in January.

FAC'IDRS AFFECTING THE DESIGN OF

A SOLAR ENERGY S'I'ORACE UNIT

By
John Jett HcDow

A THESIS

Submitted to the School for Advanced Graduate Studies of
Michigan State University of Agriculture and .
Applied Science in partial fulfillment of
the requirements for the degree of

DOCTOR OF PHILOSOPHY
Department of Agricultural Engineering

1957 w ' -

I; ’/y s‘-— I
r I (r
r" '/ / I '1' (J

A CKNOWLEDGLEI J TS

The author wishes to express his sincere gratitude to Dr. James
S. Boyd, under whose inspiring guidance, constant supervision, and
unfailing interest this investigation was undertaken.

He is also greatly indebted to the other members of the guidance
committee, Doctor James T. Anderson, Doctor Merle L. Esmay,
Professor Ernest H. Kidder, Doctor Heinrich Larcher, Doctor Donald
J. Montgomery, and Doctor Charles P. Wells, for their valuable
suggeStions. Special thanks is due to Dr. Anderson for his help
in the determination of the thermal conductivity and methods for
analysis of data.

Grateful acknowledgment is also due to Doctor Frederick H.
Buelow for his helpful suggestions, especially on instrumentation,
and to Doctor William D. Eaten for the valuable aid he gave on the
statistical analysis.

The writer is greatly indebted to Doctor Arthur W. Farrell,
Head of the Agricultural Engineering Department, in obtaining the
financial support for the project, and a research assistantship
during the first part of the work. Acknowledgment is also due to
The Southern Fellowships Fund for an advanced graduate study grant
during the latter period of the undertaking.

The investigator deeply appreciates the sabbatical leave of

absence granted by Louisiana Polytechnic Institute, making this

study possible.

 

The author also recognizes the valuable assistance from
Messrs. James B. Cawood, Anandrao Deshmukh, Joseph D. Hovanesian,
Edward A. Kazarian, Cornelius Snih, and Bill A.Stout during the
investigation.

The writer is grateful to his wife, Dorothy, for her constant

help in processing the data, and for the typing of this manuscript.

ii

"" VITA

John Jett McDow
candidate for the degree of

Doctor of PhilosOphy

Final examination: November 27, 1957, 3 P.M., Room 218,
Agricultural Engineering Building

Dissertation: Factors Affecting the Design of a Solar Energy
Storage Unit

Outline of Studies

Major Subject: Agricultural Engineering
Minor Subjects: Mathematics and Mechanical Engineering

Biographical Items
Born: January 6, 1925, Covington, Tennessee

Undergraduate Studies: University of Tennessee, 1942-43, 1946-48,
BS, 1948

Graduate Studies: Michigan State University, 1948-19, MS, 191.9,
1956-57

Experience: Active duty with the United States Navy, l9h3-h6
Graduate Teaching Assistant, Michigan State University,
19h8-49
Instructor, Michigan State University, l9h9
Instructor and Assistant Professor, Oklahoma State
University, 19A9-51
Associate Professor, Professor'and Head of
Agricultural Engineering Department,1£misiana
Polytechnic Institute, l951-present
Graduate Research Assistant, Michigan State Univ., 1956-57

Honorary Societies: Phi Kappa Phi
Pi Mb Epsilon

Professional Organizations: American Society of Agricultural
Engineers
Inuisiana Agricultural Engineering
Association, President, 1955-56,
Vice-President, 195A~55,
Secretary-Treasurer, 1953-51.

iii

Registered Professional Engineer,
Louisiana

Louisiana Engineers Council,
(served 1955-56)

American Men of Science-

Other Organizations: Kiwanis Club, Huston, Louisiana
Active in U. S. Naval Reserve DIS-present

iv

TABLE OF mNTENTS

PAGE

I. INTmDUCTION O O O 0 O O O O O O O O O O O O 0 O O O ‘ 1
Possible Use of Solar Energy in Agriculture . . 3

II 0 OB‘JECTIVES O O O O 0 O O O 0 O O O O O O O O O O O O 5
II I O mmv OF H mmmm O 0 O O O O O O O 0 O O O O O O 6
A. Availability of Solar Energy . . . . . . . . 6

B. Storage of Solar Energy . . . . . . . . . . 7

1. General historical review . . . . . . 7

2. Characteristics of Specific

mterials o o o o o e o o o o. o o o 9

a. water as storage material . . . 9

b.‘ Phase-change material . . . . . 11

c. Rocks as storage of sensible
heat 0 O O O O O O C ' O O O O O 12
d. Other storage methods . . . . . 13

IV. AVAILABILITY OF SOLAR ENERGY AT EAST LANSING . . . . . 14

A. source Of Data 0 o o o o e o o e o e o o o o 15
B. AnalySiS Of Data 0 o e e o e o o e e e o o o 16
C. Results . . . . . . . . . . . . . . . . . . 20

V. DESIGN OF A REGENERATIVE SOLAR STORAGE UNIT . . . . . 28

A. Selection of Storage medium . . . . . . . 28
B. Mathematical Study of Heat Transfer in

Spherical Bodies . . . . . . . . . . . . . 29
C. Determination of Thermal and Physical

Characteristics for Storage Material . . 35

D. Design of the Control Sphere . . . . . . . . 37

E. Design of Heat Storage Unit . . . . . . . . an

F. Plan of Tests and Measurements . . . . . . . 49

VI. RESULTS AND DISCUSSION . . . . . . . . ....... . 53
A. Determination of Surface conductance

Coefficient . . . . . . . . . . . . . . . . 53

B. Effectiveness during Heating . . . . . . . . 58

C. .Effectiveness as a Storage Unit . . . . . . 71

coco. 7“

D. Heat Recovery Characteristics . .

V

VII.

VIII.
IX.
X.
XI.

XII.

TABLE OF CONTENTS (cont.)

APPLICATION . . . . . . . . . . . . . . . . . . .'.

P1CJcsu3>>

Cost of’Operation . ....... . . . . .
Storage material Used . . . . . . . . . .
Container for Storage Material . . . . . . .
Shape . . . . . . . . . . . . . . . . . . .
Size . . . . . . . . . . . . . . . . . . . .

mNCIJUSI()PJS O O I O I O O O 0 O O O O O O O O O O O

a] LflfA-RY . O O O O O O O O 0 O O O O O O O O O O O O C

RECOMMENDATIONS FOR FUTURE RESEARCH ON STORAGE . . .

BIBLIOGRAPHY . . . . . . . . .‘. . . . . . . . . . .

APPENDIX

A.
B.
C.
D

O O O O O O O O O O O O O O O O O O O O O O

Nomenclature . . . . . . . . . . . . . . . .
Description of Instruments . . . . . . . . .
Summary of Pertinent Data . . . . .
Example Problem of Storage Unit Application.

PAGE
83
83
85

86
87

91.
9A
95
99
100
102

103
10h

'14
KO

LIST OF FIGURES

Cumulative probability curves for daily solar radiation
rates calculated about the mean for East Lansing,
12:1.— Chigan O O O O O I O 0 O O 0 O O O O O I O O O O O 0

Cumulative probability curves for daily solar radiation
rates summarized from 14 years of data taken at East
IflnSing, Bii Chigm O O 0 I O O O O O O 0 O O O O O O O

Coefficients of variation for daily solar energy rates
at East Lansing, Kichigan . . . . . . . . . . . . . .

Cumulative probability curves for minimum daily solar
radiation rates calculated about the means for East
Lansing, Lichigan . . . . . . . . . . . . . . . . . .

Cumulative probability curves for maximum daily solar
radiation rates calculated about the mean for East
Lansing, Michigan . . . . . . . . . . . . . . . . . .

Coefficients of variation for minimum and maximum daily
solar energy rates for East Lansing, Michigan . . . .

Theoretical cumulative heat storage in single rocks . .
A view of the eguipment used in determining the thermal

conductivity of the heat storage material by the
‘ded hot plate method . . . . . . . . . . . .

‘79
as

8%

Theoretical accumulated heat in a single Sphere . . . .
A photogra h rf Concrete Spheres used in tests . . . .

Positions of thennoccuples in 15 control Spheres . . .

Theoretical temperature history of points at the

then ocouple locations within 4—inch diameter concrete

nghCms O O O O O O O O o O O O O O O O O o a o o 0 0
Observed temper tare history of paints at the
1 '1 h 4 .- “ .. '-.' I v, q. ’ 10‘" q, o y"'_‘
thermocoupie lOCJtIuUS "Itnln a 4—-Lc» dii eter
O O O O 0 O O

ccruiretc, sgnexvz . . . . . . . . . . . .
b

Vil

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" - 4- r ‘7. “q -. . - “0 rv- “ ‘. r - .
vlgou-56CoiJCJl vie" kf tLe st.luoe unit in} its
supplerent; ry components . . . . . . . . . . . . .

Lrientuti n cf 8) e~(u in top layer of storage unit
with not"+.i on of control sshere placement . . . .

General view of the storage unit . . . . . . . . .

' w

toserved cumulated heat per degree temperature
jiffrJrenCe in a 5111018 8;:1‘31‘6 o o o o o o o o o o

Lanirum.te.perature differences observed within sphere

3, Test A, with 198°? incoming air temperature . .
Accumulated energy during heating, Test A . . . . .
Accumulated energy during heating, Test 3 . . . . .
Accumulated energy during heating, Test C . . . . .
Accunu late d energy during heating, Test D . . . . .
Accumulated energy during heating, Test E . . . . .

Heat released in Q'lindrical st rage unit during
15-minute period . . . . . . . . . . . . . . . .

Cumulative urrcexsu e of available heat released to

spheres . . . . . . . . . . . . . . . . . . . . .
Heat retention characteristics of storage unit . .
Heat level during storane and cooling, Test A . . .
Heat level during storage and cooling, Test 3 . . .
Heat level during storage and cooling, Test C . . .
Heat level during storage and cooling, Test D . . .
Heat level during cooling, Test E . . . . . . . . .

Cperation of storage unit . . . . . . . . . . . .

PAGE

A5

70

,7
l

TABLE

II.

III.

IV.

:3

LIST OF TABLES

Physical and thermal characteristics of heat storage
materials . . . . . . . . . . . . . . . . . . . . . .

Cumulative heat storage in one cubic foot of field
rocks for the specified heating periods and surface
resistances . . . . . . . . . . . . . . . . . . .

Placement of control spheres in system . . . . . . . .

Predicted values of the surface conductance coefficient
by known relationship . . . . . . . . . . . . . . .

Total energy level of storage unit during tests . . .

Summary of heat recovery characteristics . . . . . . .

PAGE

10'

33

55
80

82

I. INTRODUCTION

The energy from.the sun has in the past been the ultimate
source of all mania power. It is a continuing power which will be
available as long as life exists on the earth. Man has utilized this
energy in a multitude of ways, always selecting the means most easily
harnessed with his meager devices. Direct radiation for keeping
warm, animals and vegetables fer nourishment and comfort, and fossil
fuels have all been ways the solar energy provided man with the
necessities for existence.

Solar energy is being constantly furnished to man through photo-
synthesis in plants, direct heating of surroundings, wind power, and
water power. But the storage of surplus energy in fossil fuels or ‘v//»
any other fonm known to man is positively not taking place at the
rate energy is being utilized. The rapid depletion of these known
sources of stored power has stimulated man to capture energies in
other forms. Atomic energy will soon attain a respected position of
furnishing useful power over wide areas; but the sources of raw I
materials fer power generation by fission are limited and will
eventually become exhausted. The fusion process, when fully developed,
will not be limited by the lack of raw materials.

Throughout the mechanical age, man, being aware of the vastness

of the daily solar energy received on the earth, has devised many
ways of successfully capturing and utilizing it on a broad scale.

His incentive has been dampened by the availability and the abundance

of cheap fossil fuels in the form of coal, oil, and gas. The wide
scale use of solar energy as a direct power source is a very diffi-
cult problem, but is not impossible. ,The main difficulties lie in
pits wide scattering, variability, and low temperatures compared.with
those under which present day machines operate.# Daniels (19) indi—
cates that these restrictions are not impossible in the following

statement:

If a tiny fraction of the effort which has been given to

atomic energy were now to be invested in research on

utilization of solar energy, significant progress would

certainly be forthcoming. .

This can well be true when considering that the average daily supply
of solar energy in the more thickly populated areas of the world is
about 500 kilocalories per square foot (19) or 1985 Btu per square
foot.

Methods for accelerated use of solarienergy are of’a wide
variety. Some of the important energy-conversion means are as
follows: (1) Photosynthesis is used to store up energy in plants
such as algae fer a potential fuel. The tonnage of dry matter pro-
duction is about ten times that of common creps.‘ (2) Solar flat-
plate collectors are the most-common means of converting the radiant
energy into useful sensible heat in the low temperature ranges.

(3) Solar furnaces collect the radiant energy fer higher temperatures
up to 3000°C. (A) Photo-electric cells of the photovoltaic type are.
used to convert the energy into electrical power, a fonm of energy

readily utilized.

Possible Use of Solar Energy in Agriculture

_ The possibility of incorporating solar energy as a power source
is not limited to any one industry or area of work.) However, owing
to its availability over large geographical areas at comparatively
low energy concentrations (as compared with fossil fuels), utiliza-
tion of solar energy as a power source would conceivably beimore
readily adapted to the rural areas. A single farming unit presents
a diversified number of powerbrequiring activities scattered over a
wide area in contrast to the concentration of large power require-
ments in cities and industrial areas. Elimination of other uses of
this diapersed form of energy is not to be implied, but accentuation
is placed on the locations allowing immediate economical use of
solar energy.

Farm.operations and activities which could easily utilize the
low-temperature solar heat are too numerous to duscuss fully here.
However; the two outstanding ones which should be investigated first
are mentioned. Crop drying and processing are probably the foremost
functions which could well use solar energy. Although agricultural
people have used the sun in drying crops in fields for centuries,.
modern practices of placing the crop in protective shelter as
Quickly as feasible for'higher quantity and quality of production
make this practice out—dated. Concentrated energy is, therefore,
needed at the building site to finish the job of drying. This energy

can be provided with a solar collector, as proved by Buelow (12).

Improper ventilation oftanimal shelters is an outstanding hin-
drance to building preservation and sanitary conditions for the
occupants. Giese 03h) states that "... ventilation should not only.
improve the purity of stable air and eliminate odors, but, perhaps

primarily, remove moisture and prevent condensation which may have a

ldetrimental effect upon the structural elements." Additional heat

is necessary to help eliminate the moisture. Some of the other

possible uses of solar energy on the farm are airbconditioning (heat-

ing and cooling) houses, heating and pumping water, preventing frost,

and heating work areas.

 

II. OBJECTIVES

Satisfactory utilization of solar energy in agricultural work
can be accomplished only after careful study of the problems involved.

The boundaries of the problems studied in this work are set up in

the following objectives:

1. Statistical analysis of daily solar-radiation data
for East Lansing to determine frequency of various
rate levels for each month of the year, as would
affect utilization and storage of solar energy.

2. mathematical design and construction of a solar-
energy storage unit.

3. Operational tests of solarbenergy storage unit under
laboratory conditions.

 

III. REVIEW OF LITERATURE

A. Availability of Solar Energy

 

The basic consideration in solar energy utilization is that of
its availability. Only by having adequate knowledge of its intensity
and frequency of occurrence can a workable collector and storage
unit for a locality be properly designed. Much effort has been
exerted ‘to devising maps indicating the average amount of solar
_ energy received per square centimeter or per square foot in a hori-
zontal plane. Baum (7) states that this is a valuable tool for gross
planning, and its importance should not be minimized. But, still
more important for local use, variations in the intensity and fre-
quency due to atmospheric pollution, altitude, cloudiness, ground
reflectivity, season, orientation, and latitude must be incorporated
in the- planning. Becker (8) made a study of these factors for
several localities in the United States, and his results can be used
to predict the local variation.

Hand (25) has developed a system of isolines denoting the
average solar heat in Btu per square foot per average day for the
United States. Its limitations have been pointed out; however, this
should not overshadow its general benefits. These data have been
further amplified by Cmbb (18) in his solar radiation investigations
in Michigan, which relate the average radiation for am' one day of D

the year at East Lansing with that at other localities in the

United States.

 

B. Egg-gags, 9_f. Solar Energ

‘ 1. General Historical Review
Storage of solar energy for periods of cloudiness or night-
time is a pressing problem, Robinson (35) states:

The question oprower storage by cheap and simple
methods for the time of absence of solar radiation is
one of the most important problems in the exploitation
of solar energy. A good solution of this problem.would
enable the use of solar energy in places where this is
impossible now.

‘Telkes (39) emphasizes its importance in connection with house

heating:

The storage of solar heat is one of the major
problems to be solved; economically acceptable solu-
tions must use a relatively small heat-storage volume
'within the house, because the cost of space is at a
premium.

Concern for storage of solar heat has been evident in all pro-
jects leading up to utilization of this form oftenergy. Examination
of patent claims and descriptions bears this out in early devised
apparatus for handling solar energy. Calver (11.) in 1883 made claims
for his "Apparatus for Storing and Distributing Solar Heat," whose

actual realization would be welcomed today.

Claim.l. A solar—heat storage device comprising a
reservoir completely surrounded, except at the heat-
supplying orifice, when open, with non-conducting
material, and a non-conducting door, substantially

as specified. .
‘The same principles of storing the heat were advocated in the late

19th century as are today. However, this is not to imply that

 

 

 

improvements and progress have not been made over the models which
were used then. WestonLCAI) promoted the idea of storage by a ther-
mepile and storage cell in 1882. He was closely folIOwed by
Cottle (17) in 1897, who also advocated converting the heat to
electricity:

....a thermo-electric generator adapted and arranged

to convert heat fran said body into energy of elec-

tricity ... . ‘
Bit, Cottle proposed using a body of stones as a reservoir for the
heat. .Many of the early workers on solar energy did not specify the
exact storage material but only stated "a body of heat—retaining
bmaterial."

Examination of more recent'patents indicates the emphasis placed
on storage material having the heat of fusion taking.p1ace at rela-
tively low temperatures. Howe and Katuck (27) patented the follow-

ing heat-storage material in 19553

Claim 1. A storage material consisting essentially of
tetrahydrate of calcium nitrate containing a nucleating
agent selected from the group consisting of barium_ ‘
hydroxide octahydrate, cadmium.hydroxide, sodium hydroxide,
potassium hydroxide, and strontium hydroxide, the said
nucleating agent being present in sufficient quantity to
saturate said calcium nitrate tetrahydrate at a tempera-
ture above the melting point thereof.

Schaefer (36) defined the same year his patented heat storage material
more‘specifically:
A heat storage material consisting essentially of 5% to

15% by weight diphenyl ether and 30% to 50% by weight
oleic acid, the balance consisting of stearic acid.

2. Characteristics of Specific laterials

Application of heat-storage materials in recently constructed-
solar heating systems has been limited to three kinds, rocks, water,
and phase—change material. Each has shown distinct advantages and
disadvantages, which govern the selection of the proper storage
material for a specific application. In general, the final selection
will be determined by the type of solar collector in the system,
allowable space for storage, general design of system, and/or in
summary the over-all cost of utilization of each material. A brief
discussion is given for each material's use and, in addition,
table I summarizes the governing characteristics for these materials

along with some others for possible use.

a. later ag’storage material
water has been a popular solar-energy storage material in

several of the projects undertaken in recent years. It is to be the
storage material for the fourth solar-heated house sponsored by the
Massachusetts Institute of Technology. Whillier (hZ) expresses the

outstanding advantages of water in the statement:

water was selected as a storage medium for several
reasons, of which the most important are that the water k;
is also to be used for removing the solar energy that is
absorbed by the collector, and that the somewhat higher
heat-storage capacity per unit volume of phase-change
storage materials is not sufficient to justify their

higher costs. ‘
Data in Table I indicate that water is superior as a sensible-heat

type storage material over others listed except a phase—change

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material. However, the fact remains that a relatively expensive
heat exchanger is necessary to obtain a suitable configuration
pattern fer heat transfer from water to air in the final phase of
utilizing the heat. Recommendations for size of storage tank are
based on collector size, with the optimum of about three gallons of

water per square foot of collector (26).

b. Phase-ghgggg material. .
Materials having a large phase-change enthalpy within the normal

storage-temperature range (90°F to 120°F) are preferable to sensible—
heat type materials. On the surface Table I would seem to eliminate
other materials, with the phase-change substances having a relative
heat storage capacity of more than six times that of water and even
more over the others. The cost of the raw material, in the range

of SlO to $20 per ton, is not excessive. Telkes (39) reports several
limitations of this material as experienced in tests made in the
_Dover house. First, the process of recovering the stored heat is not
promptly reversible as the salts may not solidify upon cooling but
will undercool below their normal melting points. This delay, however,
can be overcome_by the use of crystallization catalysts, or nucleating
agents. A more important restriction in the use of Glaubers salts is
.the limited crystallization velocity ofabout "0.02 inch per hour per
°F temperature difference between the solid and liquid (39)."
Relatively thin, expensive containers would be necessary to obtain

a suitable geometrical configuration for sufficient heat transfer.

This obstacle casts a shadow on the immediate possibility of heat of

fusion materials in agricultural work.

12

c. mpg; storage of sensible h_e_a_t
Rocks and the other solid materials listed in Table I do not
offer highly desirable characteristics in heat storage. However,
'their low cost and other’physical characteristics constitute the
advantages for their use. The shape of small rocks and their normal
placement within a container produces adequate surfaceéto-volume
ratio for rapid heat transfer to the circulating fluid. Solareenergy
storage units have been constructed with stones in sizes from three-
feurths inch diameter [Lbf (30i3 to those having an approximate.
diameter of four inches Bliss (9i1.
15f (29) advocates the use of gravel about 15 inches in diameter
after having made investigations with B/hs, l-, and lfi-inch size '
material. This type of storage unit is usually constructed in fonn
of a column through which the air passes at a low velocity of about
1 to 2 feet per second. A heating front takes place at first at the
entrance and and continues moving toward the exit end. A sufficient
length of column enables the heat exchange to be very efficient since
the exit-air temperature is nearly the same as the rock temperature
until the heated front has reached that end. The air is usually
circulated back through the collector for higher efficiency. The
stratification of the heat is due mainly to a very low rate of heat
transfer from pebble to pebble.
Bliss (9) in a loo-percent solar-heated house near Tucson
selected fourbinch diameter field stones as optimmm. The channels

for air flow are larger in this case, and accordingly the

13

heat-transfer rate changes. This unit was 10 feet by 12 feet by L2 feet,
and held 65 tons of stones. It provides winter heating and summer
cooling of an average-size house. Bliss reports that under typical
winter conditions this rock pile was adequate for heating during four
cold cloudless days with its average temperature ranging from 90°F

to 140°F. Under normal conditions, it was believed that there was a

25 percent heat loss which could be reduced by placing the storage

unit directly under the house. '

Utilization of the heat in both cases was obtained by reversing
the direction of air flow. Both designers advocated dual use of the
storage unit by blowing cool air through the bed at night, and
.circulating house air through the unit for day-time cooling. Auxi-
liary heaters were recommended for standby condition during winter-

time Operation.

d. chgg storage methods

The door to other methods of solarbheat storage is certainly
not closed. Robinson (35) states that every energy—change process
for converting solar energy to potential energy is feasible. He
suggests the possibility of electrolysis of water,-if the storage
problem of hydrogen and oxygen were simplified. Conversion to
electrical energy would be a very deSirable means, but_the efficiency
is low andthe cost is high. Photosynthesis process will continue

to be explored for storage of fuel in some areas.

14

IV. AVAILABILITY OF SOLAR ENERGY AT

EAST LANSING

Effective utilization of solar energy in a given locality can be
accomplished only when adequate basic data are readily available in
usable form._ The quantity of available solar energy holds the top_‘
position ahnng data which should be known fbr design work. However,
variability of the solar energy available in any one locality limits
the use of average quantities for any given time. .Solar radiation
will vary by the hour, day, month, season, and even from year to year.

Of course, for any given date in the year, the probability of
not receiving the maximum.quantity of radiation will be because of
cloudiness. This phase of the weather is not predictable for long
periods of time, and, consequently, cannot be predicted from year
to year fbr a given date. Average values could be used, but only to
the extent that the average solar radiation rate for a specified
date will be reached on a future day 50 percent of the time. Acti-
vities utilizing solar energy may be required to Operate at an out-
put level higher than one specified for 50 percent of the time.

It may be necessary to Operate on a basis of 75 percent, 85 percent,
’ or some other probability.

Such needs indicate that a closer examination and analysis of
the solar energy are necessary. For’maximum.use of the data, it is
desired to know (1) rate of energy received for any probability,

(2) coefficients for the adjustment of solar energy equipment designs

'15

in various localities due to difference in variation, (3) minimum
and maximum rates of energy received for any probability, (A) varia-
bility of minimum.and maximum which can be expected from year to
year. A detailed statistical study of the solar energy data for'a

given locality is necessary in order to accomplish these purposes.
A. Source 2; Data

Solar radiation data,obtained from the Michigan Hydrologic
Research Station under the United States Department of Agriculture
and Michigan State University Agricultural Experiment Station,
covered the period from December 12, 191.2‘ to August 5, 1956. Failure
of the pyrheliometer and/or the recording equipment owing to various,
reasons, including damage by hail, prevented the maintaining of a
continuous record. However, absence of data during these few days
did not prevent making a statistical analysis; the results were.
affected only by a slight reduction in degrees of freedom for some
months. ,

There has been some question as to the validity Of the data
during some periods, owing to a change in pyrheliometers. Notes in
the records of raw data indicate that the data taken during the
period January 18, 1953 to November 5, 195h, were calculated with an
incorrect "factor," and the recorded data should be multiplied by a
factor of 1.2h. However, a footnote in-Climatological Data -'
Nations; §Eflflé£2 (LO) states with reference to the East Lansing

Station:

16

A study of available information about instmme ntal
equipment and radiation indicates that data pub—

lished prior to November 5, 1954, are systematically
low. This condition'has been corrected in data

published in CDNS_for that station beginning Nov. 5,

l95h. "

Assuming that the data were low only for the period January l8,
1953 to November A, 1954. the prOposed correction factor was applied.
to data taken in April during this period. A discrepancy in the
results to follow was in most cases well below 3 percent. At any
rate, the discrepancy is in the conservative direction of design
when using the data. '

All data published by the above station and other united States
Weather Bireau Stations are given in units of gram calories per
square centimeter (one gram calorie per square centimeter equals
one Langley). These data were converted to British Thermal units 3
by a multiplication factor of 3.69 to obtain units normally used in
engineering work.

B. Analysis 2; Da

SOlar energy at East Lansing and most localities is known to
vary widely from month to month. It was, therefore, desirable to
study the data for each individual month. Analysis of shorter
periods of time, such as bi-monthly or weekly, may prove profitable
in the future in order to increase the accuracy of prediction.
Calendar months were used in this analysis for simplification of
presentation and utilization of data. Periods with the beginning

and terminal dates in step with the vernal and autumnal equinox'

17

would slightly increase the accuracy of prediction. Analysis of
shorter periods would be advantageous with the latter system.

The mean,.i, and the standard deviation, s, from the lh.years
of data were calculated for each month.' By using the probabilities
determined from the Z—Tables in Dixon and Massey (21), calculations
were made to determine points for plotting the cumulative proba-
bility curves in Figure.l. These curves are classified as normal
curves calculated about their'means. Confidence in the validity of
these normal curves based on lh years of data was improved by
analyzing data by another method. The raw data for the 14 years were
tabulated in such a manner to enable construction of the cumulative
probability curves for expected daily solar radiation in Figure 2.

Comparisons of the radiationerate variability are possible by
comparing the magnitude of the cOefficients of variation, C, where
C 3 sfli. The coefficient unit is dimensionless and provides a means
of comparing the variance of radiation among months or between two
localities.

The minimum and maximum.radiation rates for a given geographical
location are someof the factors needed in the design of solar
radiation equipment. The lower rate expected for a given month in
some cases will be the determining criterion of design for an
activity utilizing solar heat‘ in which the incoming heat rate is of
a critical nature. However, an auxiliary heating system may be
required under such conditions. The upper extreme rate of incoming
solar heat will require an adequate air flow unit to reduce tempera-

tures below the point of danger of damage to component parts of the

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system. For example, Buelow (13) experienced breakage of collector

cover because of high temperatures reached. Also, some agricultural
products being dried by solar heat would be damaged by air which is

too hot.

The cumulative probability curves for monthly minimum.and.maxi-
mum.solar radiation rates were developed by a method similar to the
one used with the previous probability curves. Only normal curves
were deveIOped in these cases, as the variation within a given month
was small with the exception of the minimums for the summer months.
In like manner, the coefficients of variation for minimum and maximum

daily rates were computed by the method previously described.
0- Results

The primary results of this phase of work are presented in the
accompanying graphs. Figures 1 and 2 both represent cumulative
probability curves for daily radiation rates. The predicted normal
distributions about the means have been calculated for each month in
Figure 1. Whereas, the curves in Figure 2 were plotted directly
from tabulated daily rates for the 14 years of data. Close comparison
of the two sets of curves will indicate the closeness of the paths.
for the two methods. Differences will be found mainly at the two
extremes. The extreme values may be of importance in some engineer-
ing design work; therefore, more detailed treatment is given to the
minimum and maximum rates study.

Utilization of these curves is explained in the following

typical design problem. It is desired to use solar energy for the

drying of corn in October. By predetermining the needs of the system,
an estimation is made that the drying Operation by utilizing solar
energy could operate satisfactorily if a Specified rate of heat would
be available from a solar collector 75 percent of the days. From
Figure 1, it is indicated that approximately 575 Btu per horizontal
square foot could be obtained during the daylight hours. Knowing
thetotal quantity of heat necessary for this particular job, the
size, in square feet, of the solar collector can be calculated.
Tilting the collector so that the rays of the sun are perpendicular
to the collection plate will increase the amount of incoming heat.
Such angles of tilt are discussed by Becker and.Boyd (8).

Since the rate of solar energy.varies each hour, efficient
utilization of heat cannot be had by channeling all heated air
through the grain continuously. Near solar noon, the rate of’heat
received could boost the air temperature high enough to damage the
grain. During these periods of high intensity, part of the heated
air could be diverted to a heat storage unit. The cumulative
probability charts provide the total available-energy rates for one
square foot per day in a given month for these calculations.

The magnitude of the coefficients of variation for each month
may be canpared in Figure 3. The bar graphs show, as might be ex-
pected, that the solar radiation rates are much more variable about
.their means in winter months than in summer months. Hence, a lower
probability must be selected in design work fOr winter use as compared

With summer use.

22

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Cumulative probability curves for.minimum rates of solar energy
(Figure l.) have a large variation fr'an month to month, with December
having a minimum of less than 51 Btu per horizontal square foot
for 88.5 percent of the years. The steep slopes of the curves in
the colder months indicate that these low rates will be reached
nearly every year. However, a month such as July will have a wide
variation in minimum rates from year to year. The negative slopes
of the June and July curves are much less than those of_other months.

The cumulative probability curves about the means for monthly
maximum rates, shown in Figure 5, do not have the variation that is
found among the minimum curves. The slopes for all months are very
nearly the same, although the magnitude of the maximum value for a
given probability varies from month to month. The steepness of the
curves indicates that maximum.radiation expected for any one month
does not have a wide variation. For example, June's maximum.will
always stay within the range of 2290 to 2790 Btu per horizontal
square fect 80 percent of the years. Also, the December maximum
will vary only fran 580 to 850 Btu per horizontal square foot for
80 percent of the years.

TA study of the coefficients of variation for the minimum and
maximum.values in Figure 6 will indicate several obvious factors.
Minimum.expected rates for any one month vary widely fromtyear to
year. This is due to the wide variation of cloudiness that may
occur for any given month in one year. On the other hand, the

maximum rates have a very small coefficient of variation. The

24

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27

maximum daily rate of solar energy in a given month will probably
be reached each year, but the minimum rates for a given month will
vary widely from year to year.

The limitation of the probability curves lies in the ability
of the user to select a proper value of probability. If the need
of heat is of a critical nature, a higher probability would be
necessary. This will result in dependence on lower radiation rates,
but will have assurance of obtaining that particular rate or a
greater one a larger percentage of the time. The dependency upon,
lower rates directly requires larger and more expensive solar equip-
ment to handle the job. The selection of’a suitable probability
will, therefore, depend upon the Judgment of the designer.

The coefficient of variations can aid the user in the selection
of the probability. 'Higher coefficients indicate that the varia-
bility of the daily rates will be greater. For closer design work,
it would then be desirable to select a higher probability. If a
coefficient of variation for a given month in one locality is much
lower than in another area, the solar equipment in the former
location could be smaller and do the same job when comparing to the
latter place. The coefficients of variation can, therefore, help
project the experience gained in one place to other areas effectively.

This will become more important as more experience is had.

28

V. DESIGN OF A REGENERATIVE SOLAR STORAGE UNIT

 

A. Selection _f 3 Storage Medium

Wise selection of a storage means in a solar-energy utilization
system.requires careful study of the existing methods and some con-
sideration of new ones. The existing ways include (1) biochemical
conversion to vegetation by photosynthesis, (2) electrical conver- _
sion by thermopiles or semi-conductors and storage in batteries, and
(3) storage directly in form of sensible heat or phase.change. For
economic reasons, the third method appears more appropriate for_
application in and around farm structures. The wide choice of materials
listed in Table I for this purpose is not the limit of selection.
However, it does include those apparently known to be suitable at
the present time. Detailed discussion earlier has covered the
advantages and disadvantages. For the present study, rock was
selected for the storage material in this study for the following

reasons:

1. Configuration of material provides a self-contained
heat exchanger.

2. Heat loss reduced due to conduction because of point-
to—point contact between stones. '

3. .Large surface area between fluid and solid.allows
large heat transfer at low temperature differences.

is. Allows low initial cost.

5. Minimizes depreciation,costs of maintenance, and
repair of storage material.

6. Installation without skilled labor.

29

7. No maintenance when not in use.
8. Small energy consumption for forced air movement

through heat exchanger.

B. Mathematical M of. flea; Transfer in
Spherical'gggigg

Although neither field stone nor gravel is found consistently
in regular geometrical shapes, they normally approach more nearly
the shape of a sphere. This is in comparison to other common
geometries, such as the cylinder, plate, or cube, which have been
examined for heat transfer purposes. By considering the stones to
be spherical, calculation of heat storage ability for various values
of surface conductances, of periods of time, and of ranges of size
is possible for prediction of optimum requirements.

A spherical rock subjected to heating or cooling can be examined
for a variety of conditions. First, consider that it has a high
thermal conductivity, k, which would reduce the temperature gradient
within the sphere during any heating or cooling process. The heat
transfer process would be controlled mainly by the surface resistance
and would be called Newtonian heating (or cooling). The temperature
history of the sphere could then be expressed as

2 (l)
t _ tf e—(ArO/V )(NuVO/ro)

 

30

or, in reduced form

(2)
—( 3Nua< O/ri)
e

t - t:
as given by Schneider (37).. Definitions of symbols used in the
above equations and throughout the ex1t- re manuscript ar-; gi/:n in

upperdix A. The cumulative heat rate, Q, after time, 9, may be

expressed as

(3)

_ -(3Nuo(o/r§):'
Q - ch [2; - t;][:3 - e

The most likely situation that will be encountered in a tran-
sient heating and cooling system would be one with finite internal
and surface resiStances. Schneider (37) and Boelter et al. (10)

derive the temperature history of a Sphere for this condition,
(a)

y n 2‘ ~un2Eo‘9/I‘2
t - tfl _ 2 2e :1an -LinCoslan Sin(Mnr r
t. - tf - n 3 18 -SinMnCosMn Mhr r0

1

where mm are the roots of the transcendental equation

 

(5)

Schneider presents values of the first five roots which apparently
are an adequate number for solutions in normal engineering problems.‘
Boelter et al. go further and derive the cumulative heat, Q,

equation for a Sphere with finite internal and surface resistance.

31

(6)

 

:60
a): = 87rr3/pc(ti .. tr) )n2 2 .2.<-(lm «chit.
O n 3 1 Mn [Mn - SinMnCosMn]

The determination of an optimum size rock for a regenerative
storage system.was made by Equation 6, using the physical charac-
teristics given in Table I. Several reasonable values for the
surface resistance, h, and time of fluid flow, 0, were selected and
the results plotted in Figure 7. Note should be made that a tem-
perature difference, ti - tf, is not specified but would vary and
depend on the given condition. Values of the cumulative heat, Q,
will naturally vary for various sizes of rocks. Tb arrive at an
optimum rock size, data from Figure 7 were used to calculate the heat
stored in a cubic foot of.material, considering that the spheres
~are close packed. The summary of the results is presented in
Table II.

. Values of the upper limit of heat stored in a cubic foot of
rock vary. slightly around 25 Stg.» This small variation is owing
to the vast amount of calculations involved and the limitations of
slide rule accuracy. The significant point is that the size of rock
at which the heat stored drops off, for a film coefficient of six, is
0-5-, 4-, and 8-inch spheres for periods of 0.1, 1.0, and 10 hours,
reapectively. Collection periods of less than one hour may not
~prove feasible for storage. Therefore, the four—inch diameter
Sphere would have approximately the maximum cumulative heat storage
with the least amount of pressure drop of air flow through the
system. If higher film coefficients and in turn high velocities

of air flow are used, the optimum size rock for maximum heat

32

 

 

 

 

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transfer will, of course, increase. It was concluded, therefore, to

use a four-inch diameter rock for the heat-storage bed.

C. Determination 93 m and Physical
@aracteristics for Storage Material

A sufficient number of four-inch diameter field stones approach-
ing spheres would be difficult to accumulate for the test. Also,
the exact thermal concmctivity of these stones could not be measured
with available equipment. ‘Ihese variabilities in the storage system
were eliminated by molding the spheres from a very dry mixture of a
water: cement: sand ratio of l:l.92:6.68 by weigit. This enabled an
exact determination of the thermal conductivity to be made for this
material. he guarded hot plate modified and calibrated by Anderson .
(5) and operated under the specification of the American Society for
'lbsting Materials (3) was used to determine the thermal conductivity
of two l-inch by 1.2-inch by 1.2-inch mortar plates made of the same
mix as that of the Spheres. ‘Ihe value obtained was 0.372 Btu per
(hr)(sq. ft)(°F) per (ft). A picture of this testing equipment in
operation is shown in Figure 8.

Determination of the specific heat was made by use of a calori-
meter, with the resulting value of 0.210 (Btu) per (lb)(°F). An
average density of 123.3 pounds per cubic foot was determined by
taking the yaeight and dimensions of several geometrical shaped

fignites made of this mixture.

 

Fig. 8. A View of the equipmnt used in dete
the thermal conductivity of the heat storage
material by the guarded hot plate method.

1) Guarded hot plate Iith specimen

2) Water circulation pump

(3) Constant voltage transformer

(h) mutate

(5) Voltneter and meter

g6) Switches

7; Potentiometer

8 Ice bath (ref. thermocouple junction)
(9) Water source

37

With the necessary physical characteristics determined, the
cumulative heat in one sphere for one degree temperature difference
was calculated by Equation 6 for time periods of the range 0.1 to
2 hours and film coefficients of 6, 12, 18, and 21.. The resulting
data were plotted in Figure 9. Study of the curves in Figure 9
discloses that the rate of heating'is not increased in the same
proportion as the increase in the surface conductance value. Higher
velocities of air, with accompanying increased operational cost,
are not necessarily justified for obtaining high h-values. For
surface conductance values of 6 or more, 93 percent of the maximum
storable heat is already in the sphere after one hour's operation.
Again, note should be made that the difference between the initial
temperature of the sphere and that of the air or fluid does not
affect the rate of heating or cooling, but only the quantity of heat
stored. The apparent maximum heat which can be stored per °F tem-
perature difference is 0.5 Btu, which is approached asymptotically

for all values of the surface conductance coefficient.

 

D. Desng _o_f ___e Control Sphere

For actual study of the heat received by the sphere, four
thermocouples were placed in 16 control spheres. Placement of the
thermocouples was made at the boundary layers of three concentric,
equal-volume shells aboutithe center of the sphere during- the mold-
ing process. Exact positions are denoted in Figure 10 and a _

photographic cut-away view of the spheres in Figure 11. The

100

 

1.0

ITTT

l

. 22.9“”

 

 

 

 

0.1

6.f 0.2 0.3 0.5 0.5
(“ti- tr)

Theoretical accumulated heat in a single sphere.

 

 

89

 

 

e b c

Fig. 10. A hotograph of concrete spheres used in tests.
Ens, Control sphere with thermocouples
b) Oxb-away View of control sphere with
themocouple placement.
(c) Plain sphere

 

 

1'13. 11. Position- of thermocouples in 15 control spheres.

a0

The copper-constantan thermocouples were made of 30-gauge wire to
give a small junction point and reduce heat loss or gain through
the wire.

Theoretical calculations with Equation 1., were made to study the
temperature history of the thermocouple points within the sphere
and plotted in Figure 12. For these calculations, an h-value of
1.65 was used for comparison with oven conditions. However, an
h-value of 1.76 is produced by the following empirical equation

from Brown and fires (11) for natural convection about a sphere:

(7)
he 3 0.63 15 (8.131310%
r

Definitions of symbols are given in Appendix A.

A similar study was madeby placing the control spheres in an
oven of an average temps rature of 208°F. Tue recording potentio-
meters wereused to make the temperature history. Average values of
the corresponding points for the 16 spheres at specified times
were used to plot the actual temperature histories in Figure 13.

No distinct differences are to be noted between the actual and
the theoretical temperature histories. First, the temperature gra-
dient appears to be considerably maller under actual tests. Secondly,
the equilibrium temperatures are reached more quickly under the
actual situation than the equation predicts. Several factors could
be responsible for these discrepancies. First, it is apparent that
the film condictance chosen for natural convection was slightly low
in comparison with the one given by the formula. Other variables

entering the formula have been measured with reasonable accuracy;

 

1-0 TWTIFII‘] I IF__

Des ‘—

 

Ourve Radius, ft.
__ 1 0.0000
2 0.1158 “
3 0.11.51;
h 0.1667
’2.
0
a
y 001 r— .—
5 _. _
3" —— _
' L— —I
3 __
OeOS '— _.
>—- -—

 

 

 

 

0.0107 1 151.71 IJLILJr

line, 0, hours

Fig. 12. ‘lhecretical temperature history or points a the
thermocouple locations within Irinch diameter

concrete spheres.

(t - tam. ‘tfl

 

1.0

l

l

0.5

 

 

 

 

 

 

0e —
0.05 __
r. ._
1 1 l 1 14 11 ‘1 1
0010.2 0.5 - 1.0 5.0
thme, 0, hours

Fig. 13. Observed temperature history or point at the
thermocouple locations within a Lpinch
diameter concrete sphere.

AB

however, variations owing to time lag in.thermostat control of
heater, conduction from.plates supporting the spheres, and radiation
probably are the contributors to these discrepancies. Percentage
of error varies from.approximately zero within the first 12 mdnutes
to 53.9 percent of the theoretical at the time two hours. The high

percentage discrepancy at the later time is due to the sharp drOp

in the curves.

13- Pasisaeffisaimrassm

A storage unit for the initial investigations was designed to
be small and compact so that closer control could be had over the
variables. A cross-sectional view of the cylindrical-shaped container
and its supplementary components is shown in Figure la. The cylin-
drical container provides the minimum axposed.surfacs to volume
ratio of common geometrical shaped bodies with the exception of a
sphere. This allows a minimum heat loss for a defined amount of
insulation. The one-inch rock wool insulation covers both the out-
side and inside of the main body. Only one layer of insulation was
used on the approach and.sxhaust frustums and the pipe leading to
the fan. The three-layer sheet asbestos covering over the pipe
containing the heating element was primarily a safety feature to elimi-
nate exposure of a hot pipe to nearby surroundings in the building.

An electrical heating source was selected in order that constant
control over the incoming heat was obtained. Variation of solar 6
energy through a collector airing tests would make accurate measure-
ment of heat input to the storage unit more difficult. Input heat
was regulated by the carbon pile rheostat in series with the heating
element. A vane anemometer was used to measure the air velocities
in the sixpinch pipe on the exhaust. This anemometer was feund to

have a considerable error, owing to the fact that it was~calibratsd
in open air rather than on.a pipe. A 2é-inch orifice plate was later

constructed to fit in a nominal three-inch tube, according to

Radiation

Gap ‘ '
Slut
bestos Gsrbonpile
” ‘ “mm 4*

/

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

{Iolts n47;- -
flee
Element“
Power Analyser
Radiation .. ..
axields ‘__-

1 ° 1c

' O...
189 1.- 11; ..g...‘ 1' Rockwool
spa... ‘—°.-—~ ....‘ When. and Outside
O... 1 -

see-1 was» .1...
* ....
0......“

0....

T0 Beale: 3/1." 3 l'
0
Air Control
1
'\

 

 

Fan with Motor

Fig. lb. (rose-sections]. vi- of the stems unit and its
supplementary mounts.

1.6

specifications of Madison (33). The orifice plate with the micro-
manometer was used to calibrate the vane anemometer. Flow rate
values by the orifice were found to be 61.5 to 61. percent of those
recorded by the anemometer. The previously recorded readings of the
anemometer were corrected accordingly. 6

The unit was constructed so as to have the warm air directed
into the top layer of spheres, passing through the entire unit, and
exiting at the bottom after releasing the heat. The heating process
will. progress on through toward the bottom layers. While in storage,
any convection currents set up will have a tendency to move the heat
from'ths lower layers to the t0p ones. When the heat is recovered,
the air flow is reversed, bringing the cooler air over the lower
temperature'Spheres first and progressively heating as it moves to
the tap.

To reduce radiation losses from the heater as much as possible,
7a cap was placed over the six-inch diameter intake pipe. It was
necessary to install the radiation shields between the heating
elements and the top layer of spheres after preliminary tests indi-
cated that the top layer of spheres was heating to a higher tempera-
ture than that of the air passing over them. It was evident that
the spheres could "see" the higher. temperature heating element and
were receiving radiant energy from the element. The shields proved
to be valuable'also in that they provided sufficient turbulence of
the incoming air to give approximate even distribution of the

velocity and temperature pattern over the top layer of Spheres.

47

Pitot tube and thermocouple probes were made to determine this
distribution.

A A metal grate at the bottom.of'the unit provides support of
the Spheres and a minimum drop in static pressure. The static
pressure drop across the main body was found to range from

0.004 to 0.09 inches of water for the mass velocities used in the
tests. The spheres were placed in layers as shown in the photo-
graphic view of the top layer in Figure 15. There were nine layers
with 21 spheres per layer, making a total of 189 spheres in the
unit. Originally 16 control spheres with thermocouples were made.
However, No. 9 was damaged in the preliminary test and was not used
in the storage unit. Placement of the other control Spheres in

the unit was made according to Table III. Description of the

instruments used in the tests are listed in Appendix B.

 

Fig. 15. Orientation of spheres in top layer of storage
unit with notation of control sphere placement.

TABLE III
PLACEMENT OF CONTROL SPHERES IN SYSTEM

 

 

 

 

 

 

 

Layer A B C D E 1 F
1 1 2 3 I.
I. 5 6 7 8
7 10 11 12 13
9 15 k 11. 16

 

 

49

F. Plan of Tests and Measurements

*“w”

Basically, the desired infermation from the proposed tests was
the effectiveness of the stone Spheres as a heat storage unit.
Measurement of this effectiveness must be accomplished by measure-
.ment and calculation of several heat transfer characteristics. For
immediate application, optimum values or description of the follow-
ing characteristics would be desirable:

l. fiirfacs conductance, h.

2. Mess velocity, G.

3. Effectiveness of unit during heating period.

b. Effectiveness as a storage unit.

5. Quantity of recoverable heat.

6. Dimensional ratio of a prototype bed.

7. Economical aspects of heat storage.

To accomplish the above, tests were designed to have variations over
the range of the equipment. The surface condictance variation was
obtained by changing the mass velocity of the air within the limits
of the fan. Different temperature rises of the incoming air were
made possible through the variable heat input.

Measurements of air temperature by thermocouples were made at
the following points: (1) outside ambient, (2) approach to Spheres,
(3) exit from.spheres, (h) at anemometer. Temperatures were measured
in the control Spheres, which were placed according to Table III.

For heat-loss determination,.thermocouples were placed on the

50

surface of (l) heater cylinder, (2) tap fmstum, (3) storage cylinder,
(1.) bottom frustum. The wet and dry bulb temperatures of the out- -
side air were obtained from a sling psychrometer and the air velocity
with the anemometer every 30 minutes. Also, input electrical power
was measured at the same time interval.

The lZ—point recording potentiometer provided a reading on each
point every minute. Readings of the air outside, incoming to spheres,
exiting from spheres, and at the anemometer were made every minute.
All other temperature readings were taken every eight minutes
through the use of the switching mechanism shown in Figure 16.
Barometric pressures were obtained from a mercury barometer in a
nearby building.

The general procechre used involved (1) a heating period,

(2) aperiod for holding the heat or storage period, and (3) a cool—
ing or recovery period. The length of a heating and recovery periods
depended on the mass velocity of the air. At lower velocities, the
period was extended to as much as five hours, while higher velocities
reduced it to as little as one hour. The fan and heater were shut

off when the difference between the incoming and outgoing air tem-
peratures was 10 to 20°F during heating. The fan was stopped during
cooling or recovery when the air temperature difference was 5 to 10°F.

The main storage period curing the tests was 21., hours. During
this period, checks were made at intervals to determine the heat
retained. Shorter storage periods of A, 9, and 12 hours were used

to provide possible comparative studies with the longer duration.

0

51

 

Fig. 1.6. General view of the storage unit.

Storage unit

'memeouple switchee
Recording potentiometer

fining peyehrometer

Vane mmter and stop watch
Power analyzer

Gubon pile rheoetet

Fen

52

A total of nine tests was. completed. However, the first four
were eliminated from use, because the radiation shields were not
in place. The latter five tests provided data forra wide range of

air flow rates and quantities of heat stored.

53

VI. RESULTS AND DISCUSSION

A. Determination gt; the gztrfape
Conductance Coeffigcent
Several methods are available for determining the surface con-

ductance, h, under forced convection conditions. 15f and Hawley (31)

recommend the relation

0.7 (8)
h = 0.79 (go/d)

for the determination of the surface conchctance coefficient in
"builder's gravel." Application of Equation 8 to the proposed heat
storage system appeared impractical as extremely high surface con-
ductance values are obtained when calculating for the 4-inch
diameter. As the equation was, develOped for a small size rock, an
error for use with a larger rock is quite possible.

McAdsms (32) recommends for a single Sphere a relationship which

was derived from data of several investigators in the form of

0.6 (9)
E“ Da = 0.37 D8 G

kf Mf

 

that holds true in the range of D8 G/loLf from 17 to 70,000. However,
the spheres in the storage unit act more like a bank of staggered

tubes with an effective diameter being determined by
(10)

LzL'tL.
D6 D8 , DS

5A

The recommended formula for nine layers of Spheres then becomes

0.553 (11)

hm Di 2 0.1.92 De 0

“r . Mr

where De G ranges from 2,000 to [0,000.

Mr
The h—values predicted by Equations 9 and ll for the five tests are
presented in Table IV for both heating and cooling conditions. The
values given by the latter equation are ll. to 25 percent higher,
which would be expected for staggered banks of spheres as compared
to a Single. It is, therefore, expected that the surface conchctance
coefficients calculated by Equation 11 would best predict the con-
ditions actually occurring around the Spheres. The values ranged
from 2.51 to 6.09 for the heating phases of the tests. This range
approaches the one found by the subsequent method. .

An alternative method for determining the surface conductance
coefficients is by constructing curves similar to the theoretical ones
in Figure 9 from data obtained in tests. Data for No. 3 Sphere in
the top layer were used for this determination, as the temperature
of the incoming air was known and was approximately constant.
Resulting curves are presented in Figure 17.

Relative positions of these curves are according to the mass
velocity, with the higler velocities allowing the sphere to reach
maximum possible heat absorption first. Qualitative characteristics
of the curves are very such the same as the theoretical ones in
Figure 9. The curves plotted from observed data approach asympto-

tically a value of'0.55 Btu per 0? difference; whereas, the

TABLE IV

PREDICT'ED VALUES OF THE
SURFACE CONDUCTANCE COEFFICIENT
BY KNOWN RELATIONSHIPS ‘

 

 

 

Test Process ' lean tr I, G hm hm
°F #/hr Hewitt-.2) Eq. 9 liq-11

A Heat 122.5 1A7 320 1.87 2.51
0001 80.0 238 518 2.39 2.97

B Heat 120.1 309 67A 2.87 3.51.
Cool 73.1 532 ' 1160 3.83 b.56

C Heat 95-5 39h 859 3.h1 3.96
0001 79.0 h7h 1033 3.62 A.32

D Heat 100.8 559 1220 h.06 b.83
’ 0001 73.3 705 1538 h-83 5-36

E Heat 87.5 863 1883 5.22 6.09
0001 85.7 965 2105 5.55 6.41

 

 

 

 

 

 

 

Time, 0, hours

56

 

5.9

1.d_

TV!

 

0.1
.05

Fig. 17.

 

 

0J.2 J 01.1. I 4.6
Q/te

Observed emulated heat per degree temperature difference
in single sphere.

57

theoretical value approaches 0.5 in the same manner. Several
factors could be responsible for this discrepancy. (1) Radiation
from the heating coils could be reflected by the shields and
frustum. (2) heaSurement of the thermal and physical characteris-
tics, such as Specific heat, density, or thermal conchctivity, may
not be of sufficient accuracy, although the same corresponding
values appeared in both the observed and theoretical data.

By superimposing the observed results in Figure 17 over the
theoretical in Figure 9, it could be noted that the entire set of
observed data would fall approximately between the curves having
h-values of two to Slightly beyond six. This range of coefficients
fits very closely to the one obtained by Equation 11. Basically,
the two methods produced comparatively close results, which give
confidence in the validity of the data.

\The importance of these findings is that only a Slight advantage
is obtained by producing high surface conductance coefficients by
means of high air velocities. The lowest mass-velocity rate allowed
the spheres to receive 72.8 percent of the asymptotic value in one
hour. On the other hand, the highest velocity rate, 5.9 times
greater than that of the lowest rate, almost reached the asymptotic
value at the end of the same period. This vast increase in power
requirement for moving the air is not justified when considering that
the lower velocity system will have 92 percent of the maximum possi-
ble heat stored in one additional hour.

It Should be noted from these OJPVGS that the effectiveness as

a heat exchanger does not depend on the temperature difference between

\f‘
(T)

the incoming air and initial temperature of the sphere. The mean
temperature difference varied from 33°F at the highest velocity to
l230F for the lowest velocity. The time required for the Sphere

to reach asymptotic condition depends on the surface conductance

and notAt. Such characteristic would allow the solar collector to
operate at the lower air temperature rise which gives a higher
Operating efficiency (13). Compatibility between the storage unit

and the collector is obtained in this respect.

8. Effectiveness during Heating

Although the mass velocity and surface conductance study pro-
duced a qualitative view of the unit's effectiveness, the quantita-
tive sepect is of eQual importance. Ultimately, the quantity of
heat which is later recoverable for use is the primary objective.

Control spheres were placed in the unit at various locations
in order that reliable observations could be made on heat absorp-
tion and release throughout the unit and.within a Sphere. Tempera-
ture gradients within the spheres proved to be important only at the
beginning of a cooling or heating period. This gradient was as high
as 260F difference between the surface and center in top layer
spheres, but always less than 10°F difference in the lower layers.
However, the larger difference occurred only when higher incoming
air temperatures were used. hax'num temperature gradients observed
during all the five tests are plotted in Figure 18. This family of

gradients mes plotted from sphere 3 data during Test A when the

Temperature indicated by thermocouples, 0F

F:
o
T

I 1\\\\\\ x

200

 

 

 

120

 

9O

 

60

 

45

 

3O

 

 

 

 

 

 

15
80 L—
0 Minutes
1 1 l L l l I l J
50 1 2
Center Surface

Distance from center, inches

Fig. 18. Maximum temperature differences observed within sphere 3,
Test A, with 198°? incoming air temperature.

60

incoming air temperature was 198°F. Note should be made of the
gradient being maximum at lS-minutes and reducing on to practically
zero after 300 minutes.

A.mathematical check was made to determine the value of using
all four thermocouple readings within a sphere, as compared with
only the center and surface ones, for calculating the heat absorbed;
'At most, the error, when using only the two, was less than 5%. The
curves in Figure 18 Show that averaging will always give values too
high. The gradient within the Sphere when making oven tests was
generally larger; however, this was probably because of radiation
it received from the insulated walls.

Determination of total heat absorbed in the storage unit was.
made by projecting the quantity absorbed by control spheres into the
other spheres according to their location. Figure 15 shows that the
spheres can be thought of being arranged roughly in two concentric
circles around a central sphere. The outside ring has 13 Spheres,
while the inner circle is made of seven spheres. At least one
control sphere was located in the two rings and at the center for
Layers l, h, and 7. Layer 9 has three control spheres located in
the inner ring.

After calculating the quantity of heat each control Sphere ab-
sorbed for each 15-minute period of heating, heat absorbed by plain
Spheres in a given layer was found.by assuming that they receive
the same amount of heat as a control sphere in that corresponding
ring. Summation of individual heat quantities gives the total

energy received in one layer. Values for Layers l, h, 7, and 9

61

were plotted at 15-minute intervals in Figures 19 through 23 for
the five heating tests, respectively. Curves were then drawn
through the known points, which made it possible to pick off the
quantity of heat absorbed at other layers. It is noted that Layer 1
is the top section in the storage unit.

The initial temperatures on the graphs are for layers 1, A, 7,
and 9 in each case. Temperatures of the incoming air over the top
layer and the mass velocities are also listed on each of the five
graphs.

Operational characteristics, such as incoming air temperature,
mass velocity, and initial temperature of the spheres, are different
for each tests. Although this prevents making direct comparisons
between graphs to a certain extent, it provides a means of pre—
ldicting the reaction within a storage unit. Results of Test A are
presented in Figure 19. The mean incoming air temperature of 187OF
was the highest for all tests,and the mass velocity was the lowest.
Initial temperatures of the Spheres varied only 5°F from the top to
the bottom layer. The quantity of heat stored was higher for this
test because of high temperature of incoming air.

Qualitative results derived from Figure 19 are as follows:

(1) The top layers heated at the.most rapid rate during the first
part of the tests, with an increase of heating rate for the other
layers after about 90 minutes. The heating rate can be distinguished
by the spacing between the time lines, with the wider Spacing
representing higher heating rates. (2) Only a Small quantity

of heat was added during the last two hours (180 to 300 minutes)

62

 

1600 l I [

Increase in energy per layer, Btu's

 

1200 ~—

 

J
1 3

so '
3
2
800 _
0
h 90
—_' 75
so
1.00 —
as

I l l l ' I
REE?“ temperature 60° 59°

tin - 187°?
0 - 320#/(hr)(sqft)

15 Minute

1 l 1 l l l
5 7 9
Layer

Fig. 19. Accumulated energy during heating, Test A.

 

 

 

63

as compared to the quantity received during the first three hours.
This shows a marked drop in the efficiency of heat transfer which
will be explained more in detail later. (3) The low mass velocity
allowed the upper layers to continue to have an increase in heat
level even after five hours. This is demonstrated by the substan-
tial negative slope of the heat level line even after 300 minutes.

In Test E, Figure 20, the mean incoming temperature has been
reduced and the mass velocity increased. Initial temperature
variation.of'the spheres is somewhat reversed with the higher tem-
peratures in the lower layers. A similar type of heating process
was had as in Test A, with the exception that the heating rate drOps
off after only two hours. Only about 10 percent additional heat
was added during the third hour as compared with that which had been
absorbed during the first two hours. Note should be made also that
the heat level line began to approach more of a horizontal line than
did the curves in Figure 19. This is primarily because of the
higher'velocities.

The distinguishing change seen in the curves for Test C,
Figure 21, is the flattening of the heat level curves at a very
rapid rate. This characteristic is due to two factors. First, the
heat level line at any one layer is based on the initial temperature
as a reference point. Note that the initial temperature of the upper
layer is 10°F higher than the lower layer. It is evident that the
lower layers have more storage potential for a given incoming air

temperature as compared to the upper layers. This is the reason that

Increase in energy per layer, Btu's

1600

6h

 

-—-1
a
——
_

l l T l l

e— t1 - thOF
G - 67A#/(hr)(sqft)

Initial temperature
62° 63° 66° 65°

1200 _._

co

8

l
a

  

120
5
O
5
O

O

9

— 7
L00 _

— as

f— 30

 

.—

15 Minutes
0111111111

3 5 7
Layer

 

...:

Fig. 20. Accumulated energy during heating, Test B.

 

Increase in energy per layer, Btu's

65

 

I T I T l I I r f
tin - 109°?
G - 859#/(hr)(sqrt)
6oo __ __
Initial temperature
*— 73° 72° 6ao 63° —'

h00+——

 

/

105

 

 

 

75 \
60
L— ———J
45
20G-- \\\\\\\\\\\\\\\\\\\\\“‘~22———‘—-‘-~“‘~‘-. -‘
L— —.
15 Minutes _____‘fl_,
0 J 1 gr I i_lg l _fiLi l l
1 5 7 9
Layer
Fig. 21 Accumulated energy during heating, Tbst C.

 

66

heat level lines can be higher for the lower section after a period
of receiving heat.

The second reason for the lines flattening out Quickly is the
higher mass velocity, which gives the heated air a shorter'period of
time to release the heat in the upper layers. Air will remain at
a higher temperature while going through the storage unit. This
allows the lower spheres acceSs to higher temperature air and a
possibility of receiving more heat. Whereas, at lower velocities,
only lower temperature air reached the bottom Spheres.

Test D, Figure 22, had a very pronounced heat level increase
for Layers 6, 7, 8, and 9. This resulted from the high initial tem-
perature gradient of 15°F, which was greater than for any other
test. Test E in Figure 23 approached the same qualitative results
found in Test C. The initial temperature gradient was not as pro—
nounced,and the heat level lines had a tendency to become horizontal
after 90 minutes of operation.

The effectiveness of the regenerative storage unit during
heating periods was determined quantitatively on the basis of the
percent of available heat the air releases to spheres during the
progress of storage. The available heat was based on the difference
between the incoming air and initial Sphere temperatures, and the,
mass velocity of air. TWO sets of plots were made of this study:
(1) percent of available heat released during any 15-minute period,
and (2) the cumulative percentage of’available heat released up to
any time during the operation. These results are presented in

Figures 2A and 25, respectively.

Increase in energy per layer, Btu's

600

#00

200‘

6?

 

 

l‘T T l T 1 I I

tin - 115°?

C — 1220#/(hr)(sqft)
Initial temperature

690 670 580 no

 

15 Minutes

 

 

H
w
\R
“Q

\0

Layer

Fig. 22. Accumulated energy airing heating, Test D.

 

Increase in energy nor layer, Btu'a

 

111Tl‘l'l

t - 95°F
600 -— oi? 1833a’#/(hr)(sqft)

63 63° 61° 59°

 

\

zoo,—

 

_.
#—
....
....
h
h—-.
_
....

Initial temperature ""

 

 

H—
w
\n
x)
o

Layer

fig. 23. Accumulated energy during heating, Test E.

69

 

 

  

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70

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71

The points at the end of the first 15-minute period were erratic
because of the transient heating conditions. However, the succeed-
ing points plotted into relatively smooth curves. The most out—
standing feature these curves present is that higher efficiencies of
heat absorption were obtained with low mass velocities. The instan-
taneous efficiency (Figure 24) for the air mass velocity of 320 lb
per (hr)(sqft) was 70 percent at the end of 1% hours. For the
' velocity of 1883 lb per (hr)(sqft), it was only 13 percent at the end
of the same period. The values of efficiency for the intermediate
tests range accordingly between these two extremes.

Cumulative efficiencies of available heat released present a
similar picture in Figure 25, but the sharpness of drOp is not so
pronounced, as would be eXpected. The heat released after 1% hours
operation is 79 percent of available heat fer the lowest velocity,
as compared to 33 percent for the highest velocity. Lower velocities,
therefore, appear to be more suitable from the standpoint of higher
efficiency of heat release and lower cost for moving the air through

the system.

C. Effectiveness gg‘g Storage Unit

 

Heat retention of a storage unit during the holding period
will depend essentially on four factors: (1) temperature gradient
between the spheres and the surrounding medium, (2) the insulation
effectiveness of the material enclosing the storage unit, (3) the
length of holding period, and (h) the ratio of the storage material

bordering the sides of the container to the total volume.

72

In the storage tests presented in Figure 26, the temperature
gradient did not appear to have the effect on the heat retention
characteristics as might be expected. The gradient was much higher
in Test B; however, the percent of heat retained was slightly greater
during the same period of 12 hours. Length of holding period has a
considerable effect on the percent of heat retained in storage. For
this small unit, the percent retained dropped to 55 after 12 hours,
and then to 33 after 2h hours of storage. This low percentage of
retention after 2h hours lies to the fact that 81 percent of the
spheres in this small unit make up the outside boundary, which
allows heat loss to be at a relatively higher rate than in a larger
whit. This factor will be projected into the larger unit in the
section devoted to application.

Additional study of the storage was made of the layer profile
with regard to the heat retained in Figures 27 through 30. The
distinguishing change of layer profile during storage was a more
rapid cooling of top and bottom layers as compared with center layers.
A hump or higher heat level appears after about four hours of storage
as a result of convection cooling in the tOp and bottom of the unit.
In each of the four storage periods, heat loss was more pronounced
on the lower side. rmess curves indicate that convection at the
areas where air enters or exits must be kept at a minimum to reduce

storage losses.

73

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74

D. Heat Recovegy Characteristics

#3E9_99§EEEEX or heat recovered after storage is_the most im— .

portant factor governing justificatienmfpr.e.unit. The cooling or

.._‘,

 

 

heat recovering curves are given in Figures 27 through 31 for the
five tests. These curves present qualitative characteristics during
heat recovery. As the air flow has been reversed and cold air is
coming up through the bottom layers first, it is expected that this
section will cool at a faster rate. The disappearance of the storage
"hump" in the heat level curves takes place at a rapid rate. .The
curves then approach a straight line, which at the end of each test
has only a small slope.

Summation of heat levels for each layer at a Specified time in
Figures 27 through 31 will give the total Quantity of heat in the
system. These total energy levels are listed in Table V for the
beginning of the storage period, end of storage period, end of cool-
ing period, and total energy recovered.

Note should be made that the Btu level in the unit depends on
some reference. All calculations of the cumulative energy were made
on the basis of initial temperature of spheres, which had to be
adjusted to the incoming air temperature at time of cooling to give
a true picture of recovery. Comparisons between tests can more
easily be made by heat recovery characteristics which are summarized

in Table VI. On the basis of available heat in the unit at end of

Energy per layer, Btu's

75

 

 

    
 

 

 

1500
'lllll
__ 0 hr (storage)
1200 ——
9 hr (storage)
800 ___ 0 min (cooling)
A00 -—- ...
0 ~—- __
lllllllll
1 3 5 7 9
Layer

Fig. 27. Heat level during storage and cooling, Test A.

Energy per layer, Btu's

76

 

 

 

 

 

 

 

 

1200 -— __
— 0 hr (storage) "*
8m— _.
1.00— ._
0
Layer
Heat level during storage and cooling, Test B.

Fig. 28.

 

 

600

‘2;

Energy per layer, Btu'e

'e’

77

 

 

0 hr (storage)

\__/

14» hr (storage)
0 min (cooling)

15 min (cooling)

30

 

Fig. 29.

 

Layer

Heat level during storage and cooling, Test C.

 

 

 

 

 

 

 

800 .
600— x '
5
n L—
'5 __
5
I:
9. .
.3
1‘00— 12hr(storage) _
g. 0 min cooling)
s
a
0
L5.
15 )
zoo—- __
/\
A... “5 __‘
/\
o L L l 1 l 1 l 1 l
1 3 5 7 9
LBW

Fig. 30.

Heat level during storage and cooling, Test D.

 

79

 

600

 

 

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14
E
H
n
8‘ — .—
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Fig. 31. Heat level during cooling, Test E.

 

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81

storage period, the lower mass velocity will have a more efficient
rate recovery than at higher velocities.

Table VI shows that Tests A and E had an air temperature rise of
10°F or more. Thismeans that the system was turned off when the
temperature rise of air passing through the storage unit fell below
10°F. Fractions listed for recoverable heat should be representative
in both cases. The other three tests, B, C, and D,have temperature
rises of less than 10°F at the end of the tests. The fraction of
available heat recovered will be higher than if the operation had
been stopped when the 10°F temperature rise was reached. The values,
0.822, 0.660, and 0.787, are all too high in this reapect.

Comparison between Test A and E provesthat lower velocities are
most suitable in heat recovery. At the lower velocity, 78.6 percent

of the available heat was recovered, but only 46.2 percent was

recovered for the highest velocity.

82

 

 

 

 

 

 

 

 

 

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83

VII. APPLICATICN

A. Cost 3; Operation

Although the economical feasibility of the storage unit will

 

depend on a number of factors, comparisons will be made here of
operational cost, assuming that the equipment for heating with fuel
oil would cost approximately the same as the storage unit. It is
also considered that the collector will be available for other use
and is not primarily for the storage unit. Utilization of energy
from a storage system requires the movement of air one additional
time over normal direct use of heating with oil. The charge for
operation is based on the power required to move the air. Comparison
between cost of oil and storage of solar energy is to be made on the
following assumptions and calculations.

No. 1 Fuel Oil

Heat value, 136,000 Btu per gallon
Cost, 17 cents per gallon

Combustion efficiency, 70%

Unit cost, 1.785 cents per 10,000 Btu

Stored Solar Heat
Total heat input, 20 ,550 Btu
Incoming heated air, 50°F above initial sphere temperature
Air flow rate, 200 cfm [320 lb/(hr)(sqft)_j
Total fan pressure, 4 inches water
Total fan efficiency, 50%
Power requirement, 0.251 hp
Heating period, 2 hours (selected arbitrarily)
Heating efficiency, 76% (Fig. 25)
Storage period, 72 hours
Retention during storage, 67. 2% (calculated below)
Recovery efficiency, 78. 6% (Table VI)
Heat stored, 15, 600 Btu
Heat recovered, 8,240 Btu

8h

Total cost at 2.5 cents per Kwhr, 1.25 cents
Unit cost, 1.518 cents per 10,000 Btu

The fan horsepower requirement was calculated from formula by

Madison (33) :

hp 2 (Q.OOOl§7)(CHH)(Total_pressure in inches water) .
Total 8 fficien cy

Cost of operating the electric motor'was made on the basis oflOOO
watts required per horsepower. The retention of heat during storage
is based on the surface-volume ratio of a twelve-foot cube, in the
same relation that was had with the small laboratory unit.

This larger unit has a ratio of Spheres at the surface to total
number of Spheres of about 15 percent and has a heat loss of 67 percent
at end of 24 hours storage (Figure 26). Then the ratio between

this large unit and the laboratory model with a surface-to—volume

ratio of 81% is

or X Z 12.h%,
the loss of heat at the end of 24 hours. Projecting it to 72 hours,
the storage retention would be 67.2 percent.
The heating period is a critical factor in the economic balance.

The optimum operation period which will make the solar energy equal
to that of fuel oil under the assumptions above is about 3.1 hours.
Periods of heating longer than this will make the solar energy cost
more, and, in like manner, shorter periods will cost less than the

fuel oil as a heat source.

85

B. Storage Material Used

 

For a practical operation, the concrete Spheres would not be
used, but instead field stones for several reasons. (1) The process
of molding spheres is entirely unnecessary when field rocks of com-
parable size are available in many areas right on the farm. (2) The
field stones are superior in the quantity of heat retained for a given
temperature difference. Although the Specific heat is virtually
the same forrboth, the density is 37.2 percent higher for the stones.
This gives the field stones a heat retaining capacity of 1.38 times
that for the concrete spheres. (3) Thermal conductivity of the
natural occurring rock ranges from 1.0 to 1.5 Btu per (hr)(sqft)(°F)
per ft, as compared to 0.37 for the test spheres. This factor would
increase the speed of heating, making the theory of Newtonian heat—
ing or cooling. more pronounced. An advantage of the higher k-value
is the reduction of heating time. However, a disadvantageis the
possibility of higher heat loss rates. (A) The factor of roughness
of the field stones would have an effect on the surface conductance
coefficient. Increased roughness would. give higher h-values for

equal mass velocities.

C. Container $93; Storage Material

Maximum value can be derived from the solar storage unit only

when it is constructed withinthe structure utilizing its heat. It

is obvious that any heat loss from the unit would go directly into
the structure, thereby, increasing its effectiveness. Two possible
locations within the structure are (1) a compartment located on the
ground floor, or (2) an excavated hole.

The first type of structure would take up usable floor space
that would normally be used for production or storage of the farm
commodities. The side walls would require considerable bracing for
retaining the rocks. The second proposal would involve the expense
of excavation, but the only building material required, other than
the necessary duct work, would be a vapor barrier'to keep moisture
out of the system. In wetter areas, drain tile should be laid
around the perimeter to help reduce moisture troubles. Good vapor
barriers are aluminum foil with building paper padding to reduce

damage and protected plastic sheeting.

D. Shape

Basically, the most effective shape for storage is a container
with the greatest volume to surface ratio. The normal shapes in
order of decreasing value are the sphere, cylinder, and cube. For
ease of construction and air passage, the cylinder and cube are

referable. The longer air flow path will provide a more effect: c
heat exchanger. Within reasnnable pressure drops across the unit,

large L/d ratios would be desirable. The directional movement of

air in and out should follow the same paths as the laboratory unit.

87

E. Size

,The size of a storage unit will naturally depend upon the heat
load of the utilizing activity. For canparative purposes, an actual
problem of removing moisture from.a poultry house has been set up in
the Appendix.D, based on work of Esmay and Mbore (22). The sizes
of collector and storage units were calculated with the assumption
that the energy required would be obtained on the probabilities of
80, 60, and 40 percentages. From the data it can be noted that
higher probabilities of receiving a given amount of radiation
require the largest collector and the smallest storage unit. The
storage unit is smaller because of the higher air temperatures
obtained by the collector. The largest storage unit required to
store the 484,000 Btu at a 35.50F temperature rise would be about

541 cubic feet. This is equal to a cube 8.15 feet on a side.

 

P15. 32. Storage unit in operation.

89

VIII. CONCLUSIONS

Charts, deve10ped on the availability of daily solar radiation
rates at East Lansing, provide a designer of solar-energy equipment
‘with basic design information on quantities of heat cXpected
(Figures 1 throughtSL It was concluded that the cumulative probability
curves were highly reliable since the plots from 14 years of raw data
matched very closely norwal curves (Figu res 1 ani 2). Selection of
the probability, for finding the daily normal, maximum, and minimum
radiation rates, must he made by tile des igxer on the basis of ex-

perience and good Judgment. Balzuxce mus be Ira de between importance

of consistent energy rates and the allowable investxent. months

he. ing small coefficients of variation will have less variability

of available energy. These coefficients will aid the designer in
selecting the probability ands ' apting e uipnent to other localities.

v at ra ge w.is et~rmined

r‘

The optimum size rock for 0L lar wenel
to be four inches die or (Table II). This prc ovides maximum rate of

heat storage at minimum mpressure drog across the system. Lower mass
air velocities of 3 20 lb per (hr)(s qft) provide the grea,est heat
transfer effectiveness and most economical operation. This velocity
will produce a surface conductance coefficient of about two for the
spheres. Except at high temperature differences, the concrete Spheres
could be conside or} Newtonian he or cooling

The effectiveness of the spheres in halt absorption is reduced

consifernbly after receiving heat for three hours with a constant

90

incoming temperature. About 68 percent of the available heat will
be absorbed during this period (Figure 25). The top layers heat
rapidly at first and then the heat front moves on to the lower
layers.

If the storage unit is within the building where the heat is
utilized, up to 78.6 percent of the stored heat can be recovered.
Large units, such as a lZ—foot cube, will retain about 68 percent
of the stored heat after three days (page 8A). Smaller units will
lose the heat during storage at a higher rate because of a higher
percentage of the spheres bordering a surface. During storage the
center layers retain the largest percentage of heat. lbans should be
provided to prevent convection currents arcind the rocks during
storage (page 72).

When heating a given Quantity of air in a prototype unit, it
was found that the larger the collector used the ssaller the storage

unit necessary for storing a given amount of energy.

91

IX. SUMMARY

The objectives of this project were to (l) statistically
analyze daily radiation data for East Lansing in the determination
of frequency of various rate levels for each month, as would affect
utilization and storage of Solar energy, (2) mathematically design
and construct a solar storage unit, and (3) perform Operational
tests on the solar energy storage unit under laboratory conditions.

Quantity of available solar radiation at any locality is the
determining criterion in the design of solar utilization equipment.
Daily solar-energy data for 14 years at East Lansing were analyzed.
Charts developed were monthly probability curves and monthly co-
efficients of variation for normal, maximum, and minimum daily rates.
The probability of a given job is selected by balancing between the
importance of consistent energy rates and the allowable investment
in equipment. Once this selection has been made, the probability
curves give quantitative rates expected. The coefficients of varia-

tion aid in selecting a probability and adapting solar—energy equip-

ment to other localities.

A study of heat storage methods proved that rocks would be the
best material for agricultural use. Analysis by heat transfer
principles indicated that the 4—inch diaxeter rock would provide the
maximum rate of heat storage at minimum pressure drop across the

system. Thennal conductivity, specific heat, and density of a Special

92

concrete mixture were determined. The 4-inch diameter Spheres of
this mixture were used in a laboratory storage unit.

Copper-constantan thenmocouples in 15 control spheres provided
information on rate of heating, retention of heat, and rate of heat
recovery from the Spheres. Observations proved the Spheres to react
very closely to theoretical solutions. Lower mass air velocities
of 320 lb per (hr)(sqft) provided the greatest heat transfer effec-
tiveness and the most economical operation. This velocity provided a
surface conductance coefficient of two for the Spheres. The heating
and cooling of the spheres could be considered essentially Newtonian.

Tests showed that the effectiveness of the spheres in heat
absorption was reduced considerably after subjected to heated air for
three hours. About 68 percent of the available heat was absorbed
during this period, with the top layers heating rapidly at first and
then the lower layers.

Up to 78.6 percent of the stored heat was calculated to be re-
coverable, when using a lZ-foot cube storage unit within the building
‘where the heat was utilized. It was also found that 68 percent of the
heat stored could be remaining in the storage unit after three days.
Easter heat losses at ends of storage unit during storage indicated
that convection currents must be reduced to conserve heat.

In a prototype unit, the storage material would be of well
sized and selected 4-inch diameter field rocks. Placement of the
storage unit within the building where the heat is utilized will

increase efficiencies. The shape should be cylindrical or cubical.

Calculations showed that a 7—ft cube storage unit with stones could
furnish a poultry house 25,700 Btu/hr for drying 16 hours a day.

This was based on an 80 percent PPObability in January.

93

94

X. RECOMMENDATIONS FCR FUTURE RESEARCH

ON STORAGE

Storage means, other than sensible-heat methods, should con-

stantly be examined for possible use with solar energy in agricul-
tural work. Further study of sensible heat storage in rocks should

be carried out in a proto4type unit to determine the heating, storage,

and recovery characteristics. A larger unit in series with a solar

collector could determine the compatibility of the two under con-

ditions of maximum Operation efficiencies for each. Such study would

enable an accurate cost analysis and determination of the feasibility

of incorporating a unit in farm buildings for the purpose of reduction

of humidity, crop drying, and other uses.
In any further study with small laboratory units, it is suggested

that the container be square to enable perfect close packing of the

spheres. Also, it is recommended that the inside walls of the con-
The se factors

tainer have a smooth uniform surface, such as wood.

will favor more uniform air flow and heating across any one layer.

95

XI . BIBLIOGRAPHY

l. Abbot, C. 6., Weather and Solar Variation. The Journal of

 

 

Solar Energy and Science and Engneerigg, : 1, Jan. 1957.
pp. 3-5-

2. American Society of Agricultural Engineers. Agricultural
En ‘neers Yearbook, 1957 Edition. St. Joseph, Michu
American Society of Agricultural Engineers, 1957. p. 102.

3. American Society for Testing Materials. Standard Method of
the Test for Themal Conductivity of Materials by Means of
the Guarded Hot Plate. Philadelphia: American Society for
Testing Materials, 1945. pp. 1282-1290.

A. Anderson, Lawrence B., Hoyt C. Hottel, and Austin Whillier.
Solar Heating Design Problems. Daniels, F., and J. A. Duffie,
Editors, Solar Energy Research. Madison: The University of
Wisconsin Press, 1955. pp. til-56. -

5. Anderson, James T. The Design of a Guarded Ring Hot Plate
for Te sting the Thermal Conductivity of Homogeneous Materials.
Unpublished 1.1.8. thesis, Michigan State University, 191.8. 1.1 pp.

6. Barre, H. J., and L. L. Sammet. Farm Structures. New York:
John Wiley & Sons, Inc., 1950. pp. 103, 172, 612.

7. Baum, Werner A. Meteorology and the Utilization of Solar Energy.
Daniels, F. and J. A. Duffie, Editors, Solar Energy Research.
Madison: The University of Wisconsin Press, 1955. pp. 15-17.

8. Becker, Clarence F.,and J. S. Boyd. . Solar Radiation Availa-
bility on Shrfaces in the United States as Affected by Season,
Orientation, Latitude, Altitude, and Cloudiness. Jgirnal of
Applied Solar Energy Science and Engineering, 1: l,Jan. 1957.
pp. 13—21.

9. Bliss, R. W., Jr. Solar House Heating. The Association for
Applied Solar Energy, Proceedings of the World Symposimngn
Agglied Solar EnergyLPhoenix, Arizona, 1955. Menlo Park,
Ca1if.: Stanford Research Institute, 1956. pp. 151-158.

10. Boelter, L. M. K., V. H. Cherry, H. A. Johnson, and R. C.
Martinelli. 5341‘? Transfer Notes. Berkeley: University of
California Press, 1948. pp. V-18 to V—22.

96

Introduction to Heat Transfer,

11. Brown, A. I., and S. U. Marco.
267 pp.

2nd Ed. New York: McGraw—Hill Co., Inc., 1951.

12. Buelow, Frederick H. Utilization of Solar Energy in and
' around Farm Buildings. Unpublished iosoarch Report.
Michigan State University Agricultural Experiment Station,
Project 512, 1956-57.

Heating Air by Solar

13. Buelow, Frederick H., and J. s. Boyd.
pp. 28—30.”"

Energy, Agricultural Engineering, 38: 1, Jan. 1957.

14. Calver, W. Apparatus for Storing and Distributing Solar Heat,
U. 3. Pat. No. 290,851. The Official Gazette of the U. S.
Patent Office. 25: 13, Dec. 1883. p. 12A0.

Conduction of Heat in Solids.

 

15. Carslaw, H. 3., and J. C. Jaeger.
Oxford: At the Clarendon Press, 19h7. 386 pp.

16. Carter, Deane G. Challenges Awaiting Agricultural Engineers
in Farm Structures. AgriculturalLBngineering,34: l, -

Jan. 19530 pp. l7~20o

l7. Cottle, H. F. Apparatus for Storing and Using Solar Heat,
U. 8. Pat. No. 608,755. The Official Gazette of the U. 5.

Patent Office, 84: 6, Aug. 1898. p. as .

18. Crabb, George A., Jr. Solar Radiation Investigations in Hichigan.
Michigan State University Agricultural Experiment Station,
East Lansing, Tech. Bull. 222, 1950. 153 pp.

19. Daniels, Farrington. Introduction. Daniels, F., and J. A.
Duffie, Editors. Solar.Energngesearch. Madison: The
University of Wisconsin Press, 1955. pp. B-A.

The Sun’s Energy. The Association for

Proceedings of the world Symposi‘.

20. Daniels, Farrington.
lmnlo Park,

Applied Solar.Energy.
on Applied Solar Energy, Phoenix; Arizona, 1255.

Calif.: Stanford Research Institute, 1956. pp. 19-26.
Dixon, W. J., and F. J. Hassey., Jr. Introduction to Statistical
Analysis. New York: mcSraw—Hill Book Company, InC., 1951.

p. ms.

22. Esmay, morle L., and J. M. Moore.
for Here Densely Populated Laying Flocks.
Hichigan State University Agricultural Eerrinent Station.

21.

A Mechanized Poultry House
Unpublished paper,

Fritz, 8., and T. H. HacDonald. Average Solar Radiation in
61, July 1913.

the United States. Heating and Ventilating, 46:
pp. 61-640

230

24.

25.

26.

27.

28.

29.

30.

31.

32.

33.

34.

35.

36.

97

Giese, H., and A. A. Ibrahim. Ventilation of Animal Shelters
by the Use of Heat Exchangers. ,Agricultural Engineering, 31:
7, July 1950- pp. 329-33. .

Hand, I. F. Distribution of Solar Energy over the United
States. Heating and Ventilatingl 5 : 7, 1953. pp. 73-75.

Hottel, H. C. Residential Uses of Solar Energy. The
Association for Applied Solar Energy. Proceedings of the

World Symposigg_on Applied Solar Enerhy. PhoenigggArizona, 1955.
Menlo Park, Calif.: Stanford Research Institute, 1956.

pp. 103-112.

Howe, J. P., and R. R. Katuck. Heat Storage Material, U. S.
Pat. No. 2,706,716. The Official Gazette of the U. 3. Patent
Office, 693: 3, April 1955. p. 378. ‘

 

Kays, W. M., and A. L. London. Compact Heat Exchangers, Palo
Alto, Calif.: The National Press, 1955. 156 pp.

Lof, George O. G. House Heating and Cooling with Solar Energy.
Daniels, F., and J. A. Duffie, Editors. Solar Energy Research.
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Lof, George 0. G. Solar Housing Heating. The Association
for Applied Solar Energy. Proceedings of the World Symposium
on Applied Sola§_Energy,,Phoenix, Arigpna, 1955. Renlo Park,
Calif.: Stanford Research Institute, 1956. pp. 131—145.

Lbf, George 0. G., and R. W. Hawley. Unsteady State Heat
Transfer Between Air and Loose Solids. Industrial and En-

gineering Chemistgy, 59: 6, 1948. pp. 1061-1070.

McAdams, W. H. Heat Transmission, 3rd Ed. New York: McGraw-
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I

Madison, Richard D., Editor. Fan Engineering, Buffalo, N. Y.:
Buffalo Forage Co., 1949. p. 128.

Oliver, J. H. Poultry House Ventilation. Agricultural
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Robinson, Nathan. Solar machines. The Association for Applied
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Stanford Research Institute, 1956. p. 56.

Schaefer, Vincent. Heat Storage Material, U. 5. Pat
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37-

38.

39.

1+0.

1+3.

98

Schneider, P. J. Conduction Heat Transfer. Cambridge, Mass.:
Addison—Wesley Publishing Co., Inc., 1955. 386 pp.

Snedecor, George W. Statistical Methods, 4th Ed. Ames: The
Iowa State College Press, 1948. pp. 1-74.

Telkes, Maria. Solar Heat Storage. Daniels, F., and J. A.
Diffie, Editors. Solar Energg Research. Madison: The
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U. 3. Dept. of Commerce, Weather Bureau. Climatological
Data - NatiLonal Stunmam 6: 2, Feb. 1955. Washington: U. 3.
Government Printing Office. p. 50.

Weston, Edward. Apparatus for Utilizing Solar Radiant Energy,
U. S. Pat. No. 389,124-5. The Official Gazette of the U. 5.

Patent Office, 55: 10, Sept. 1888.

Whillier, Austin. Solar House Heating. The Association for
Applied Solar Energy. Proceedings of the World Symposium on
_APPJ.-.i§d Solar Energy, Phoenix, Arizona, 1955. Menlo Park,
Calif.: Stanford Research Institute, 1956. pp. 115-130.

Worthing, A. G., and David Halliday. Heat. New York: John
Wiley 8: Sons, Inc., 1948. pp. 111-128.

x11.

APPENDIX

.99

K‘EF'OD‘S‘

W

git"

100

APPENDIX A

Nomenclature
(gflflcxflx)
Surface area of heat transfer, sqft
Specific heat, Btu/(lb)(°F)
Coefficient of variation, dimensionless
Diameter, ft
Diameter of sphere, ft

Effective diameter of sphere when compared to tubes,

l/De : l/DS + l/DS

Base of Napierian 10garithms

Acceleration due to gravity; 4.17 x 108 ft/hr'2
Mass velocity, lbs/(hr)(sqft of cross-section)

Superficial mass velocity, lbs/(hr)(sqft of cross-section
without particles)

Surface resistance, Btu/(hr)(OF)(sqft)

Surface resistance in natural convection, Btu/(hr)(°F)(sqft)
Mean surface resistance

Thermal conductivity, Btu/(hr)(sqft)(OF per ft)

Thermal conductivity at film temperature, tf

Length of heat excaanger, ft

Roots of the transcendental equation, Nu 3 l - Uh Cot Mn
Nusselt number, (h hrh/k)

Instantaneous heat rate, Btu/hr, or Btu/day

Q ..
r ..
rh -
.1‘0-
3 -
t .-
tc -

101

APPENDIX A (Cont.)

Nomenclature
Cumulative heat, Btu
Radius of sphere or any point within, ft
Hydraulic radius, (4rh 3 hydraulic diameter)
Surface radius, ft
Standard deviation
Temperature at Specified time, OF
ti - tf
Film temperature, (ts + t)/(2), 0F
Initial temperature, oF‘

Surface temperature, 0?

Volume of sphere, cuft

Mean of a group of data
Themal diffusivity, (k/c/a ), sqft/hr

Coefficient of thermal expansion of a fluid; reciprocal
degrees Fahrenheit

Time of fluid flow, hr
Absolute viscosity, lb/(ft)(hr)
Viscosity at film temperature, tf, lb/(ft)(hr)

Density of material, lb/cuft (also denoted w)

1.

9.
10.

11.

102

APPENDIX B

Instruments Used in Tests

Ammeter, Simpson Electric Co., Chicago. Measurement:
Milliamperes.

Barometer, Central Scientific Co., Chicago. Mbasurement:
Inches of Mercury.

Guarded hot plate complete with constant voltage transformer,
coil rheostats, water pump, and thermocouples. Mechanical
Engineering Department, Michigan State University.
Measurement: Thermal Conductivity (by calculations).

Indlined Oil Micro—manometer. E. Vernon Hill & Co., Lake
Geneva, Wise. Measurement: Inches of water.

Industrial Analyzer, Model 639, Type 2, No. 4161. Weston
Electrical Instrument Corp., Newark, N. J. Measurement: Volts,

Amperes, and Kilowatts.

Orifice, 2.5 in. die. in 3 in. tube. special made.
measurement: Used with Inclined Manometer.

Potentiometer, No. 300083, A. E. No. 1776. Leeds & Northrup
Co., Philadelphia. Measurement: Millivolts.

Potentiometer, Recording, Serial No. 860990, 12 point,
Minneapolis-Honeywell. Measurement: 0F, Range 50 to 350°F.

Potentiometer, Recording, Serial No. 327582, 12 point,
Minneapolis-Honeywell. Measurement: oF, Range -1OO to 250°F.

Sling Psychrometer. Tycos, Rochester, N. Y. Measurement: 0F,
wet and dry bulbs.

Vane Anemometer, No. 5963, Serial No. 139L7, 6 in. dia.,
Keuffel & Esser. Measurement: Feet, with stopwatch feet

per minute.

Voltmeter, Type A025, fodel VAXBM. General Electric.
Measurement: Volts.

APPENDIX

C

Summary of Pertinent Data

103

 

 

 

 

 

 

 

 

 

Tbsts
A, B c D E
Heatigg:
Period, hrs. 5 3 2 3 1.5
Dry bulb temp., 0F 62.2 64.5 67.2 68.5 65
Wet bulb temp., 0F 50.6 54.4 55.0 56.1 52
Barometric pressure, in. Hg. 29.62 29.3 29.6 29.47 29.45
Wattage input 1,497 4 2,099 1,302 2,004 2,153
Total heat input, Btu 25,550 .21,500 8,900 20,500 11,020
Humidity, lb. H 0/1b.dry air 0.00514 0.00672 0.00642 0.00686 0.00543
Correction for ir (28):
Specific heat 1.004 1.005 1.005 1.005 1.004
Density 3 0.997 0.9965 0.9965 0.996 0.997
Sp. vol. at B.P. ft /1b 14.21 14.52 13.91 14.36 13.96
Sp. vol. at 29.92" Hg.rt3/1b 14.10 14.23 13.83 14.16 13.75
Flow rate, lbs/min 2.44 5.15 6.56 9.32 14.39
Flow rate, cfm 34.6 118.7 91.2 133.8 200.6
Mass velocity, lbs/(hr)(sqft) 320 674 859 1220 1883
Storage: Period, hrs. 9 24 4 12 0
Cooling:
Period, hrs. 2.5 1 l 1 0.367
Dry bulb temp., 0F 57.1. 63.3 63.0 61.8 65.0
wet bulb temp. 0F 47.6 54.0 51.7 51.7 52.0
Humidity, lbs H20/lb dry air 0.00486 0.00687 0.00543 0.00586 0.00543
Sp. vol. at B.P., rt2/13 13.19 13.59 13.21 13.33 13.57
Sp. v61 at 29.92" Hg.ft /1b 13.02 13.32 13.13 13.16 13.38
Flow rate, lb/min 3.96 8.85 7.90 11.65 16.08
Flow rate, cfm 52.0 103.8 103.8 155.5 218.0
Mass velocity, 1bs/(hr)(sqft) 518 1160 1033 1538 2105

 

 

104

APPENDIX D

Example Problem of Storage Unit Application
The following example is given to eXplain the use of the data
developed in the main body of the thesis. Data for the problem was
based on a mechanized poultry house designed and studied by Esmay
and Moore (22). Description of this building is as follows:

Location: Lapeer Co., Michigan

Size: 36 ft. by 108 ft.

Capacity: 2200 laying hens

Ventilation: Forced air

Lowest inside temperature allowable: 42°F

Heat production by hens: 72,600 Btu/hr

Moisture production by hens: 60.5 lb/hr

moisture removed by cleaner: 19.6 lb/hr

Moisture to be removed by fans: 40.9 lb/hr

Inside temperature: 42°F

Inside relative humidity: 80%

Outside temperature: 12°F

Outside relative humidity: 70%

Heat loss through side wallsand ceiling for 30°
temperature difference: 24,000 Btu/hr

Month: January

Calculations:

1. Pounds of air to move:

u : We Ref. (6)
(RHZ)(W§2) - (RH1)(V81)

M = air flow per hour, lb
we 3 mbisture to be exchanged per hour, lb.
RHl, RH2: relative humidity of incoming and outgoing
air respectively
W81, W52 3 water in saturated air vapor'mixtures at

temperature of incoming and outgoing
air, respectively, lb/lb dry air.

2.

105

n 2 90-9 = 11 700 lb r
(0.8)(0.00566) - (0.7)(0.001877 ’ 3/ r

Total heat required:

Q 2 ms (t2 — t1)

specific heat of air

t1, t2 - temperaturesof incoming and outgoing air,

3.

7.

respectively, °F
Q : (11,700)(0.24)(30)
84,300 Btu/hr

84,300 + 24,000 = 108,300 Btu/hr

Qt

Net heat required:

Qn 2 108,300 — 72,600 = 25,700 Btu/hr

Size of collector:

Area = 2 hr 2 00 Btu hr = 1908 sqft
0.85 Eff. 380 Btu.sqft)

Temperature rise of heated air from collector:

The temperature rises were calculated from
equation by Buelow and Boyd (l3) assuming collector
efficiency of 85%. Results are listed in table below.

Radiation rates expected in January:

Solar radiation rates were_taken from Figure 1
and corrected by a factor 1.9 LBecker and Boyd (8):
upon assumption that collector is at a 30° angle
with the horizontal. Rates for three
different probabilities are given to Show effect
on collector and storage sizes.

Size of Storage Unit:

It is assumed that U18 air will be blown through
the collector, storage unit (within building) and then ,

106

through the building. Assumption is made that one-third
of the heat is utilized during daytime and two-thirds
(for 16 hours operation) is stored for night-time use.
Sample calculations for storage capacity size are given
below making the following assumptions:

Rock density 3 170 lbs/cuft

Rock sp.ht. : 0.2 Btu/lbOF

Size 4~in. dia. rock 3 33.5 euin

Wt. 4-in. dia. rock 3 3.3 lbs

Rocks per cuft: 38.2

Wt. of rocks I 16 2 00 = 43,900 lbs
0.2 55.1 _

Volume Occupied Z - 348 cuft

SUMMARY OF DATA ON COLLECTOR AND STORAGE UNITS

 

Probability, Btu/day
%

Btu/day Collector Temp. Rise °F Size

 

80
6O

40

Hor. rt2 300 ft2 Size,ft2 Storage,ft3
200 7 380 1908 55.1 348
350 665 1090 41.6 452
A50 855 867 35.5 541

 

 

 

 

 

 

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