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University

 

 

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This is to certify that the

thesis entitled

A Rockbed Regenerator for a
Farrowing Room

presented by
Yi Chen

has been accepted towards fulfillment V I
of the requirements for

M,S. degree in Agricultural Engineering ;

 

WMX

Major professor

Date 12-13-82

0-7639 MS U i: an Affirmative Action/Equal Opportunity Institution

 

 

 

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A ROCKBED REGENERATOR FOR A FARROWING ROOM

BY
Yi Chen

A THESIS

Submitted to
Michigan State University
in partial fulfillment of the requirement
for the degree of

MASTER OF SCIENCE

Department of Agricultural Engineering

1982

ABSTRACT
A ROCKBED REGENERATOR FOR A FARROWING ROOM
By ’
Yi Chen

Two rockbeds of 0.64 m2 were constructed for a
farrowing room to recover heat from exhaust air and preheat
incoming air during winter days. Rockbed depth, cycle time
and air flow rates were tested to evaluate their effects on
performance of the regenerative ventilation system. An
orthogonal design was used to form a half-fraction factorial
experiment.

On an average a heat effectiveness of 0.60 and a
moisture removal factor of 0.43 were achieved. Cycle time
affected the heat recovery effectiveness and the moisture
removal factor significantly. Rockbed depth was of little
importance. Interaction between two air flow rates was
strong. Essentially equal mass flow rates of the room
' exhaust and make-up air, 0.4 m rockbed ldepth and a heat
recovery effectiveness about 0.5 were recommended.

Balance equations of air mass, moisture and energy in
animal housing and design criteria for regenerative

ventilation systems were proposed.

ACKNOWLEDGEMENTS

The author wishes to express sincere gratitude to

Dr. Merle L. Esmay ( Agricultural Engineering ) for
his advice, encouragement and suggestions as the major
professor;

Dr. Howard L. Person ( Agricultural Engineering ) for
his guidance, suggestions and support as the project
director;

Dr. Maynard Hogburg ( Animal Science ) for his advice
and help as a committee member.

The author is also grateful to Professor Yi-Yuan Jiang,
Mr. Zai-Chun Yang, staff and students in the Department of
Agricultural Engineering, and Swine Research Center of
Michigan State University for their helpful support during
the course of this study.

The author wishes to express his deep appreciation to
his motherland - China for her love, education and support.

The author with all his heart thanks his wife Ping Yang
and his son Huan for their love, wishes, encouragement and

patience.

ii

TABLE OF CONTENTS

LISTOF TABLESOO0.0..OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOVi
LIST OF FIGURES...0..0..000......OOOOOOOOO‘OOOOOOOOOOOOOOOVii

1. INTRODUCTIONOOOOOOOOOOOOOOOOOOOOOOO0.00.00.00.0000000001
1.1 BaCkgroundOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO0.0.0.0000001

1.2 ObjeCti-ves.eeee00000000000000.0000...ooeooeeeeeeeeoe4

2. LITERATURE REVIEW AND ANALYTICAL APPROACHES............5
2.1 Previous Studies in Fields and Laboratories.........5
2.2 Analytical Approaches...............................8

2.2.1 Fundamental Assumptions.........:.............9
2.2.2 Biot Number..................................10
2.2.3 Heat Transfer in the Rockbed.................12
2.2.4 Pressure Drop through Rockbeds...............13
2.3 “Heat Effectiveness and Moisture Removal Factor.....15
2.3.1 Heat Recovery Factor and Effectiveness.......15

2.3.2 Moisture Removal Factor......................19

iii

3.

4.

5.

EXPERIMENTOOOOOOOOOOOOOOOOO..0.0.000000000000000000000ZO

3.1
3.2
3.3
3.4

Conditions and Environment.........................20
Experimental Facility..............................22
Method of Study....................................30
Measurement and Instrumentation....................31
3.4.1 Dry Bulb Temperature Measurement.............32
3.4.2 Humidity Measurement.........................33
3.4.3 Air Flow Measurement.........................36

3.4.4 Static Pressure Measurement..................36

ORTHOGONAL EXPERIMENT DESIGN...OOOOOOOOOOOOOOOOOO0.00.37

4.1
4.2

IntrOdUCtionee;eoeeeeeeoeeeeeeeeeeeeoeoeeeeeeeoeeee37

Orthogonal Table - OAas( 6 x 3 x 22 )..............39

RESULTS AND DISCUSSIONOOOOOOOOOOOOOOOOOOO0.0.0.0.0....41

5.1

5.2

5.3

Basic Character of This Study......................41
5.1.1 Rock Equivalent Diameter and Void Ratio......41
5.1.2 Air FLow Rates...............................41
5.1.3 Static Pressure Drop.........................43
5.1.4 Reynold's Number and Diet Number.............44

Results of the Orthogonal Table....................44
5.2.1 Main Effects.................................46
5.2.2 Interactions.................................49

RelationShip between” and RfOOO0.0.0.0.0000000000053

iv

5.4 Correlation of n with B ..........................54
5.5 Correlation between Enthalpy and Flow Rates........57
5.6 Correlation between Humidity and Flow rates........57
5.7 Air Temperature Profiles...........................58
5.7.1 Temperature Profiles within the Rockbed......58

5.7.2 Average Temperature from Rockbed Bottom
Upwards......................................65

5.7.3 Temperature Profiles in the Ventilation
System.......................................70

5.7.4 Overnight Performance of the Ventilation
‘System.......................................76
5.8 Other Results......................................80
5.8.1 Frost........................................80

5.8.2 DUSt ACCUmUlationO0.0..0...OOOOOOOOOOOOOOOOOOBO

6. BALANCE EQUATIONS AND DESIGN CRITERIA.................84
6.1 Air Mass Balance in Animal Housing.................84
6.2 Moisture Balance in Animal Housing.................85
6.3 Energy Balance in Animal Housing...................87

6.4 Design Criteria of Ventilation Systems.............87

7. CONCLUSIONS AND SUGGESTIONS...........................94
7.1 COnC1USi°nSCOOOOOOOOOOOOOOOOOOOOO...0.0.0.00000000094

7.2 suggestionSOOOOOO...O..0..0.0.00.0.000000000000000096

BIBLIOGRAPHYOO...OOOOOOOOOOOOOO.0......0.00.00.00.0000000097

LIST OF TABLES

Channel Allocation on Digistrip II Recorder...........34
Channel Number Allocation within the Rockbed..........34
Orthogonal Table OA35( 6'x 3 x 22 ).....w............40
Air Flow Rates ( m3/s )...............................42-
Comparison of Static Pressure Drop....................42
Orthogonal Table Results..............................45

AnaIYSis Of variance.OOOOOOOOOOOOOOOIOOOO0.0.00.00000048

vi

2.1

5.2

LIST OF FIGURES

Block Diagram of an Animal Building System

with Rockbeds ........................................16
Farrowing Unit of M.S.U. Swine Research Center........21
Ventilation System with Rockbed Regenerator...........23
West Side View of North Rockbed Chamber...............24
Schematic Plan View of West Farrowing Room

with Rockbed Regenerator..............................26
Flexible Hose Connecting Inlet and Air Distributor....27
Damper and Motor....{................:................28
Timer and Fan Speed Switches in Control Box...........29
Data Logger and Psychrometer..........................35
Main Effects of Factors...............................47
(a) Rockbed Depth.....................................47
(b) Cycle Time......... ...... .........................47
(c) Exhaust Fan Speed.................................47
(d) Make-up Fan speed.................................47
Two-Variable Interactions.............................50
(a) Interactions of Cycle time (min)

with ROCkbed Depth (m)OOOOOOOOOOOOOOOOO0.00.00.00.50

vii

5.3

5.4

5.5

(b)-Interactions
with Make-up
(c) Interactions
with Exhaust
(d) Interactions
with Make-up
(e) Interactions
with Exhaust
(f) Interactions

with Make-up

of Exhaust Fan Speed A (rpm)

Fan Speed B (rpm)....................50
of Cycle Time (min)

Fan speed A (rpm)....................51
of Cycle Time (min)

Fan Speed B (rpm)....................51
of Rockbed Depth (m)

Fan Speed (rpm)......................52
of Rockbed Depth (m)

Fan Speed (rpm)......................52

Correlation of Heat Effectiveness and

Moisture Removal

FaCtoreeeeeeoeeeeeooeeeoeee000000000056

Temperature Profiles within the Rockbed Layers........59

(a) 4min Cycle,

0.51m Depth, .159m3/s Exhaust and

Olssma/s Make-up Flow Rates...OOOOOOOOOOOOOOOOOO..59

(b) 12min Cycle,

0.51m Depth, .159m3/s Exhaust and

Olssma/s Make-up Flow Rates.OOOOOOOOOOOOOOOOOOOOOOSO

(c) 2min Cycle,

0.41m Depth, .110m3/s Exhaust and

.llea/s Make-up Flow Rates.......................61

(d) 6min Cycle,

0.51m Depth, .159m3/s Exhaust and

olleS/s Make-up Flow RateSOOOOOOOOOOOOOOOOO ...... 62

(e) 10min Cycle,

0.51m Depth, .108m3/s Exhaust and

.165m3/S Make-Up Flow Rates.00.000000000000000000063

Temperature Profiles along Rockbed Depth..............66

(a) 4min Cycle,

0.30m Depth, .167m3/s Exhaust and

viii

.184m3/s Make-up Flow Rates.......................66

(b) 10min Cycle, 0.51m Depth, .159m3/s Exhaust and
.113m3/s Make-up Flow Rates.......................67

(c) 8min Cycle, 0.41m Depth, .110m3/s Exhaust and
.172m3/s Make-up Flow Rates.......................68

(d) 12min Cycle, 0.51m Depth, .159m3/s Exhaust and
.165m3/s Make-up Flow Rates.......................69
5.6 Temperature Profiles in the Ventilation System........71

(a) 12min Cycle, 0.51m Depth, .159m3/s Exhaust and
.165m3/s Make-up Flow Rates.......................71

(b) 6min Cycle, 0.30m Depth, .111m3/s Exhaust and
.184m3/s Make-up Flow Rates.......................72

(c) 2min Cycle, 0.41m Depth, .110m3/s Exhaust and
.118m3/s Make-up Flow Rates.......................73

(d) 10min Cycle, 0.51m Depth, .159m3/s Exhaust and
.113m3/s Make-up Flow Rates.......................74
5.7 Overnight Performance of the Ventilation System.......77

(a) 12min Cycle, 0.51m Depth, .159m3/s Exhaust and
.165m3/s Make-up Flow Rates.......................77

(b) 8min Cycle, 0.41m Depth, .162m3/s Exhaust and
.1l8m3/s Make-up Flow Rates............... ........ 78,

(c) 4min Cycle, 0.30m Depth, .167m3/s Exhaust and
.184m3/s Make-up Flow Rates.......................79
5.8 Frosting on the Frame.................................81

5.9 Dust ACCUmUIation on surfaceSOOOOOOOOOOIOOO0.0.0.0....82

ix

l I N TRODUCTI ON

1.1 Background

A controlled environment for confined animal housing is
necessary not only to protect livestock or poultry from cold
and hot weather but also to provide them with nearly optimum
conditions for high production ( Esmay, 1978 ).
Temperature, humidity and fresh air in confined animal
structures are the most important environmental factors.
Continuous mechanical ventilation is a common, effective
means to remove water vapor, carbon dioxide, ammonia, odors,
dust and air-borne disease organisms, as well as sensible
heat, and to supply fresh air for confined animal houses.
However, under cold weather conditions, supplemental heat
may be required to maintain an appropriate indoor air
temperature. This is especially important for baby animals
and young stock, because they can not produce sufficient
heat to regulate their body temperatures in cold buildings.
The heat required depends on climate degree days, density
and size of animals housed, building insulation, and the
ventilation rate used.

Various types of heating devices, such as gas, oil or
water heaters, electric heaters, brooder lamps, electric

pads and so on, are used to provide supplemental heat in

animal houses through winter months. Most of them consume
fossil fuel ( gas, oil, or coal ) directly or indirectly.
Since both the uncertainty of supply and the increasing cost
of conventional fossil fuel have risen in recent years,
there has been an increasing interest in searching for
alternative heat energy sources.

The use of heat exchangers to recover a portion of the
heat from the exhaust ventilation air of livestock or
poultry buildings to preheat the cold incoming air is an
energy saving concept. It can reduce or, even, eliminate
the need for supplemental heat. Early research work on
shell-and-multitube exchangers of parallel-flow and
counterflow was reported by Giese and Downing ( 1950 ), and
Giese and Ibrahim ( 1950 ). Giese and Bond ( 1952 ). and
Ogilvie ( 1966 ) reported their counterflow plate-type
exchangers. Turnbull ( 1965 ) tested a perpendicular flow
plate-type exchanger. Larkin et a1. ( 1975 and 1977 )
operated thermosiphon heat exchangers. All those above have
the common problem of complexity, corrosion, cost and
maintenance.

In agriculture, rockbed regenerators have been studied
since 1970's. Witz et a1. ( 1974 and 1979 ) reported their
work on a rock sink system with rotation reversible fans.
Bon et a1. ( 1981 ) developed a computer program to simulate
the performance of the rock sink system above. Lampman (
1978 ) constructed a rockbed system with multiduct-dampers.

Moysey et al. ( 1980 ) examined an experimental rockbed unit

in laboratory conditions. Parker et al. ( 1978 and 1981 )
studied pressure drop and heat transfer in crushed limestone
and developed a finite difference algorithm to predict the
temperature distribution in the rockbed. Chandra et al. (
1977 ) applied dimensional analyses in their study of
pressure drop in an experimental rock chamber. Due to the
advantages of simple design and construction, high heat
capacity, low cost and long life, the rockbed heat exchanger
has interested many agricultural engineers, researchers and
farmers.

Freezing and dust clogging are common problems dealing
with rockbed regenerators. Due to lake influence East
Lansing seldom experiences prolonged periods of extreme cold
during the winter. From 1940 through 1969 there were an
average of only 6 days, on which the daily minimum
temperature was -17.8°C or below. The recorded lowest
temperature was -27.2°C in February of 1959 ( NCAA, 1973 ).
Therefore, ice clogging might not be a serious problem when
a rockbed regenerator is operated in this area.

Since the existing design procedure associated with
balance equations of moisture and sensible heat for
conventional ventilation systems is not applicable for
regenerative ventilation systems, new design criteria based
on new balance equations of mass, moisture and energy are

needed.

1.2 Objectives

The objectives of this thesis study were to:

1. Investigate extensively the effects of rockbed
design parameters on heat recovery and moisture removal
under conditions in a swine farrowing house,

2. Investigate air temperature profiles at various
locations within the rockbed and in the ventilation system,

3. Formulate balance equations of mass, moisture and
energy and propose criteria for design and evaluation of

ventilation systems with heat exchangers.

2 LITERATURE REVIEW AND ANALYTICAL APPROACHES

2.1 Previous Studies in Fields and Laboratories

Rockbeds are alternate-type heat exchangers, through
which two working gases do not pass simultaneously. During
a charge period while warm gas is flowing through a rockbed,
some heat is transferred from the gas to the rocks. During
a consequent. discharge period when cold gas passes through
the precharged rockbed, some heat stored in the rocks is
transferred to the gas. Phase changes and mass transfer may
also occur associated with the heat transfer.

A rockbed regenerator may consist of two identical’
rockbeds installed vertically into a ventilation system.
One rockbed is charged by downward warm air while the other
is discharged by upward cold air. After a time interval the
air flow directions are reversed so that the precharged
rockbed is discharged whereas the predischarged one is
charged. A cycle time includes two half cycles, charge and
discharge for each rockbed. There are many ways to reverse
the flow directions, such as reversing two fan rotation
directions, switching damper systems to change air flow
paths and so on.

Witz et a1. ( 1974 and 1979 ) developed a double rock

sink system for a beef barn since 1971. Two insulated rock

sinks were located separately at different sides out of the
building to prevent short circuiting between the exhaust and
incoming air. The ceiling and attic space of the barn was
divided into two sections. Each air path made up of one
sink, one fan and one section of the ceiling and attic
space. The ceiling was perforated. The rotation directions
of two fans were reversed at l to 15 minute intervals.
Reversing the fan rotation caused extra dynamic stress on
the motors and fans, and required special blade design to
get similar air flow rates in both directions. The area of.
each sink was approximately 1.04 m2. The depth of the sinks
increased from 223 mm up, as the rock size increaéed from 19
to 107 mm in diameter. An efficiency of 33 % was calculated
on the basis of temperature differences. The room
temperature was maintained at about 4.4°C without
supplemental heat when the outside temperature was -28.8°C.
The use of salt controlled the frost problem when the
outside temperature was down to -25°C for 4 to 5 days. For
longer periods of one week or more with the outside
temperature below -26°C, operating the fans in the exhaust
direction for about three hours removed the ice accumulation
from the rockbeds. They suggested using small rock size and
increasing the cross section area to improve rockbed
performance and reduce freezing problems, associated with
the use of salt. A cycle time of 10 to 15 min was
.
suggested. They also recommended locating both the inlet

and outlet vents on the same side of the building. This was

to prevent cold air flowing across the building due to wind
when both fans were off.

Lampman ( 1978 ) studied a rockbed system in a swine
barni Two rockbeds of 1.22 m square were filled to 0.305 m
deep with rocks of 50 to 100 mm of size. The rockbeds were
located separately on the same side out of the barn. Both
the exhaust fan and the make-up fan were connected to each
rockbed through two-way ducts. A single damper motor,
controlled by a timer, drove four dampers. Each damper
controlled one branch duct, respectively. The shutter
system was switched every 10 minutes to exchange the air
flow directions through the rockbeds. The room temperature
could be maintained above 10°C when holding 300 pigs in the
coldest weather of -40°C. To minimize freezing, the exhaust
flow rate was 0.85 to 1.4 m3/s whereas the make-up flow rate
was 0.47 to 0.59 m3/s. Skirts around the bottom of the
rockbeds were thought to reduce the effect of windchill.
Dust fouling became a severe problem when there was no water
condensation on the rocks during periods of low dew point
temperatures and warm weather, since condensed water flushed
out accumulated dust. Metal mesh filters were used.
However,. daily maintenance was required. The freezing
problem was overcome by combined efforts of adding salt and
applying an unidirectional warm air flow for over 1 hour. A
heat effectiveness of 28 to 34 % was obtained based on mass

flow rates and enthalpy.

Moysey et al. ( 1980 ) tested an experimental rockbed

regenerator of 0.3 m square in an environmentally controlled
room consisting of two compartments. They stated that
increasing the superficial flow velocity from 0.31 to
0.58 m/s or the bed thickness from 0.2 to 0.4 m, or reducing
the cycle time from 12 to 8 min had significant effect on
increasing the system efficiency. The effects of relative
humidity in the range of 33 to 78 % and rock size from 35 to
50 mm were of less importance. They mentioned that reducing
both the air flow rate and the cycle time resulted in
increasing the efficiency. This implied some interaction
between these two factors. They computed the heat exchanger
efficiency as 21.9 to 50.9 % based on the enthalpy
differences or 27.3 to 61.2 % based on the sensible heat
differences. Dust clogging and ice accumulation were alSo
observed. They recommended the cycle time of less than
10 min and the superficial airflow velocity of 0.42 m/s or
less. They pointed out that using small rocks and deep beds
could achieve better efficiencies. However, selecting rock
size and bed' depth should deal with reducing problems of

high pressUre drop and dust accumulation.

2.2 Analytical Approaches
The theoretical analysis for rockbed heat exchangers
lags behind' the accumulation of experimental results. Some

mathematical correlations are empirical and semiempirical.

2.2.1 Fundamental Assumptions

Parker et a1. ( 1978 ) summarized the following basic
assumptions in studying the characteristics of both heat
transfer and pressure drop in rockbeds:

1. Air temperature, rock temperature and static
pressure are uniform at any specific cross section of the
rockbed.

2. Thermal and fluid-mechanical properties are constant
for both air and the stone.

3. Rocks are uniform in size and shape, and are
uniformly but randomly packed in the rockbeds.

4. There is no temperature or pressure gradient
perpendicular to the air flow direction, i.e. a "plug flow”.

5. There is no edge effect on either the flow or the
temperature.

6. There is no temperature gradient within individual
stones.

7. There is no heat conduction parallel to the flow
direction in either the air or the stone.

8. There is no heat or mass transfer to the surrounding
environment.

Carefully screening stones could reduce the error due
to non-uniform size, shape and properties. Turbulent flow
provides quite uniform air conditions. Good insulation and
water proof around the rockbed reduce the losses of heat and
water.

Parker et a1. ( 1978 ) stated that for a larger rockbed

10

randomly packed with uniform rocks, a reasonable
approximation of plug flow could be achieved on a
statistical basis. Therefore, no heat or mass flow normal
to the air flow direction was considered.

Rose ( 1949 ) reported that the wall effect might be
neglected if the ratios of the diameter and the depth of the
rockbed to the particle diameter were at least 50:1 and
20:1, respectively. Close ( 1965 ) concluded that the rock
pile conductivity in the flow direction was negligible

during charging and discharging.

2.2.2 Biot Number

With high rock conductivity, low heat transfer
coefficient between air and rock surface, and small rock
size, the real temperature gradient within rocks may be
ignored. Whether the lumped system approach is reasonable
for a given rock size could be estimated by calculating the
Biot number ( Moyers, 1970 ):

Bi = 0.53 * d / k ( 2.1 )

where H - area heat transfer coefficient of the flow to

the rock, w/mz-x,

k rock conductivity, W/m-K,

d equivalent spherical diameter of the rock, m.
Moyers ( 1971 ) showed that an error of less than 5 %

resulted from the lumped system assumption if Bi was less

than 0.1. Parker et al. ( 1980 ) estimated the Bi value for

crushed stone of 25.4 mm in diameter would be at most 0.02

11

under the condition of normal rockbed flow rates.

The area heat transfer coefficient, H, can be

calculated with the following equatiion ( Duffie, 1980 ):
H = 108.3a( d/a )( G/d )°°7/( l - e ) ( 2.2 )
for 60 < Re < 480
where d - equivalent spherical diameter, m,
e - void fraction of the rockbed, decimal,
a - shape factor of the rocks, decimal.
G - mass velocity of the fluid, kg/ma-s.
G = D * v ( 2.3 )
where D - fluid mass density, kg/m3,
v - flow velocity, m/s.
Re is the particle Reynold's number

' Re a G * d/u ' . ' ( 2.4 )
where u - fluid absolute viscosity, kg/m-s. .

The void fraction 6, also known as 'porosity', is
defined as the ratio of the void volume Voi to the container
volome Vo filled with the sample rock pebbles. ‘

e = Voi / Vo ( 2.5 )
The void volume is measured with the water replacement
method, i.e. filling water into the sample rock container to
replace the air in the void.

The equivalent spherical diameter ( Duffie, 1980 ) is
the diameter of a sphere particle having the same volume as
the average particle volume in the rock sample. It can be
calculated from

d = [ 1.9lVo( 1 - e )/ n 11/3 ( 2.6 )

12

where n is the number of rocks in the sample.

The shape factor a is the ratio of the surface area of
the pebble in the sample to the surface area of the
equivalent sphere._ It is difficult to evaluate. Duffie
( 1980 ) recommended that for crushed gravel a varies
linearly from about 2.5 to about 1.5 as the pebble diameter
increases from 5 to 50 mm, and for smooth river gravel a is
approximately equal to 1.5 independent of the rock size.
McCorquodale et al. ( 1977 ) measured an a value of 1.92 for
crushed dolomite of 15.6 mm. No information was found for

crushed limestone.

2.2.3 Heat Transfer in the Rockbed

Schumann ( 1929 ) developed the'first analytical model
to describe the temperature change rates for an
incompressible fluid and a solid with respect to time and
the location in a packed bed. Furnas ( 1932 ) expanded the

fluid to gases.

aTg/ax

H(Tr-Tg)/(Cg*vg)

( 2.7 )
arr/at = -H( T - T )/[ c ( 1 - e ) l
r g r
where X - distance along the flow direction, m,
H - area heat transfer coefficient, W/mZ-k,
v - flow velocity, m/s,
t - time, s,
T - temperature, K,

e - void fraction,

13

C - volumetric heat capacity, J/m3.K,

g - subscript for gases,

r - subscript for rock.
The negative sign in equation ( 2.7 ) indicates that the
rock temperature decreases while discharging. Schumann
presented a series of analytical solution curves, which,
however, were of limited applications. Furnas ( 1932 )
observed that the area heat transfer coeffecient H is
affected'by fluid velocity, temperature, rock size and void
fraction. It is somewhat difficult to prove Schumann's
correlations by measuring the continuously changing
temperature of both the fluid and the solid within a porous
bed directly and simultaneously. In recent years computer
programs with applied numerical methods have been developed
to simulate the complicated transient thermal response of
the rock storage. These, however, are very time-consuming.
Due to the complexity of the heat transfer process and lack
of exact knowledge of the this mechanism, the accuracy and
adequacy of the analytical equations and numerical

approaches are still being examined by many investigators.

2.2.4 Pressure Drop through Rockbeds

The pressure drop through a packed bed is due to both
viscous and inertia drag ( Ergun, 1952 ). Many researchers
have worked on this problem.

Dunkle et al. ( 1976 ) recommended the following

relationship:

14

AP = ( 21 + 1750/Re )[ L*Gz/( p*d ) 1 ( 2.8 )
Parker et a1. ( 1978 ) stated that Dunkle's equation
agreed closely with the behavior of compacted beds of
crushed limestone, however, a loosely-filled rockbed
exhibited a lower pressure drop than predicted from ( 2.8 ).

Duffie ( 1980 ) quoted Shewen's equation:

AP = ( 4.24 + 166B/Re )[ L*Gz*B/( p*d ) ] ( 2.9 )
where B is a coefficient dealing with the void fraction
and the shape factor a.

B = a( 1 - e )/ e1-5 ’ ( 2.10 )

Brownell et al. ( 1947 ) introduced another correlation
between a modified Reynolds' number and a modified friction
coefficient

Re 8 G*d*e_m/u

{ ( 2.11 )'

-£ a 2d*p*AP*en/( L*02 )
where the exponents of both m and n depend upon the
porosity e and the shape factor a-

Leva ( 1959 ) proposed a pressure drop correlation.

AP = [ 2L*02*£m/( p*d ) ][ ( 1 - e )/a 13-ne-3( 2.12 )
where fm was a modified friction coefficient, and a
function of the particle Reynold's number. The
exponent n in ( 2.12 ) referred to the fluid state factor,
which varied from 1 for the laminar flow to 2 for the
turbulent flow. In most turbulent flow cases an
average n value of 1.9 was assumed.

These correlations above, as well as others not

presented in this thesis, have respective limited
applications. Each of them is a compromise leading to a

final generalized correlation.
2.3 Heat Effectiveness and Moisture Removal Factor

2.3.1 Heat Recovery Factor and Effectiveness

In the previous sections the study of the micrOScopic
process and mechanism of heat, momentum and mass transfer in
the porous rockbed was reviewed. Besides that, the rockbeds.
as well as other heat exchangers have been studied from a
macro viewpoint by examining their overall efficiency.

The term - "efficiency" - has different definitions in
the literature reviewed. Some confusion arises when various
results are compared. It is, therefore, desirable to define
the efficiency in an appropriate way.

'Since the air flows alternate in rockbeds, the air
state parameters at various locations within the rockbed
system fluctuate with respect to time. For analysis of long
term operation, it is convenient to describe the states of
the exhaust air, the incoming air, the outside air, etc. by
their mean values over the given time period.

Fig. 2.1 shows a block diagram of an animal building
with a rockbed regenerator. Consider the building
subsystem. The building exhaust air is indicated with mass
flow rate Me, enthalpy Ee and humidity ratio h;. The

building incoming air - Mi, Bi and hi. The possible leakage

16

._...._. SUBSYSTEM BOUNDARY .. .. _. MOISTURE

.. - ° .. SHORT CIRCUITING ENERGY
—--'AIR MASS

 

 
   
 
  
 
   

ANIMALS

HEATERS

SUPPLEMENTAL. HEAT

 

 

 

 

 

BUILDING -! LEAKEAGE AIR
HEAT LOSS I
qb h.

 

 

 

 

 

 

 

 

 

 

 

OUTSIDE AIR .. ._ ..

 

 

FIGURE 2.1 BLOCK DIAGRAM OF AN ANIMAL BUILDING SYSTEM WITH ROCKBEDS

17

air is represented with M E and hl' Both the exhaust and

l' l

the incoming air are mechanically-forced while the air
leakage is natural due to mass and pressure difference
betwwen the building and the atmosphere. The building
conductive heat loss is qb. The building supplemental heat
rate - qsp. The total heat production rate by animals - qa,
which includes both sensible and latent heat. The vapor
production rate in the building - Wa, which is the sum of
the rate of vapor released by animals and the rate of
evaporation from urine, feces and other wet surfaces ( Bond
et al., 1959 ).

Within the rockbed subsystem boundary, including ducts,
there are two pairs of inputs and outputs. The building
exhaust air is an input. The cooled exhaust air leaving the
rockbed bottom is its corresponding output, indicated with
Me, Eb and hb. The outside cold air, represented with "1'
Eo and ho' is the other input. The building incoming air is
its corresponding output.

The product of the incoming mass flow rate and the
enthalpy difference between the incoming air and the outside
air represents the actually recovered energy rate.
Likewise, the recoverable energy rate is the product of the
exhaust mass flow rate and the enthalpy difference between
the exhaust air and the outside air. The "heat recovery
factor" Rf for the rockbed subsystem is here defined as the

ratio of the recovered energy rate to the recoverable energy

rate for a given time period.

18

Rf =Mi( Ei-EO)/[Me(Ee-EO)] (2.13)
where M - mass rate of the air flow, kg dry air/s,
E - air enthalpy, kJ/kg dry air,
1 - subscript for the building incoming air,
e - subscript for the building exhaust air,
0 - subscript for the air outside the building.

Enthalpy is used here because there is some transfer
between sensible heat and latent heat when condensation and
evaporation of water occur on the rock surfaces.

A mass flow rate M is the product of the volumetric
flow rate and its density. The building incoming mass rate
My is not equal to the exhaust mass rate Me, when volumetric
rates, 91 and Qe, are assumed equal due to temperature
difference. If "1 is larger than Me, there should be air
leakage outgoing to preserve a mass balance. The leakage
air carries unrecoverable heat.

In order to reflect the inherant heat recovery
efficiency of the building subsystem, the "heat recovery
effectiveness" n is defined as the ratio of the actual
recovered energy rate to the maximum recoverable energy rate
for the system. On the mean value basis, the maximum
recoverable energy rate is the product of the total mass
flow rate leaving the building and the enthalpy difference
between the outgoing air and the outside air. The total
outgoing flow mass rate equals either Me or Mi, whichever is
larger. It is denoted by Mmax. Then, n is described as

n = Mi( Ei - so )/[ Mmax( Ee - so) ] (2.14)

19

Heat exchanger effectiveness has been introduced in
many heat transfer textbooks. In these textbooks, only the
simultaneous-type heat exchangers, such as plate-type,
shell-and-tube type and so on, have generally been
discussed. Sokhansanj et a1. ( 1980 ) introduced the term
of the heat recovery factor for a simultaneous-type heat
regenerator based on the sensible heat differences. If
there are some phase changes in fluids, e.g. evaporation or
condensation water in air, occuring in these exchangers,
latent heat should be taken into consideration. The
enthalpy term seems quite appropriate to calculate

efficiency for these cases.

2.3.2 Moisture Removal Factor

As a portion of energy is recovered and sent back to
the building, an amount of water vapor may also return back
to the building. To evaluate the moisture removal from the
building subsystem due to the effect of the heat exchanger
the ”moisture removal factor" is defined here as

e = 1 - i Mi( hi - hO )/[ Mmax( he - hO ) l I ( 2.15 )
where Mi( hi‘ho ) - rate of moisture retured to the building
Mmax‘ he-hO ) - maximum removable moisture rate.

If short circuiting occurs between adjacent rockbed
chambers, the cooled exhaust air leaves one rockbed bottom
and, then, enters the other bed bottom. Thus, the air state
at the bottom of rockbeds should be used instead of the

outside air state in calculation.

3 EXPERI MENT

3.1 Conditions and Environment

A field study on a rockbed heat exchanger was carried
out in the west room of the farrowing unit at Michigan State
University Swine Research Center.

The farrowing unit of M. S. U. Swine Research Center
consisted of two rooms of 14.5 x 7.6 x 1.7 m with a shed
roof of an 1:5 slope ( Fig. 3.1 ). Sixteen farrowing crates
were linked into two rows in the west room. As a whole,
75 % of the floor is slotted. An underfloor deep pit
accumulates manure before it is pumped out about every two
months. The farrowing unit was not well insulated. Its
exposure factor, EF, was 13.2 W/C per animal unit for 16
sows and litters. This EF value was much higher than that
of 0.5 to 2.6 W/C per animal unit recommended in ASAE D270.4
( 1979 ). A perforated duct channel was constructed as an
air distributor for a solar collector. However, the solar
heating system was inoperative during this study, due to
most cloud days. A conventional ventilation system,
consisting of winter, spring-fall and summer fans, was not
used during this study. A gas heater was the main heating
device in the room.

Baby pigs should be kept in a warm, dry and draft-free

20

21

 

mthwo Iom<wwmm m2:$m .D.m._z ".0 .52: GZ=$OEE<L pd mEDOE

.1. 1’}...

m. I
,. Amman... .14.”-

 

22

environment ( MWPS-l, 1980 ). In practice, the indoor air
temperature is maintained between 18 to 27°C ( Curtis, 1978
), plus zone heating in the piglet creep areas ( MWPS-l,
1980 ). Indoor air relative humidity of 40 to 80 % (
Sainsbury, 1974 ), and air. movement velocities below

0.25 m/s ( Sainsbury, 1979 ) are desired.

3.2 Experimental Facility

A regenerative ventilation system was. constructed on
the north side out of the west farrowing room ( Fig. 3.2 ).
Two rockbed chambers were adjacent to each other under a
common frame of 1.9 x 1.7 x 2.4 m with a 1:4 gable roof.
The structure illustrated in Fig. 3.3 was of 9.5 mm plywood
sheathing applied over 100 mm square post framing. The
inner side-wall and ceiling were of 12.7 mm plywood. The
two chambers were insulated with styrofoam of 1.8 mz-C/W
thermoresistance over the attic and the four side walls.
Two layers of 0.1 mm polyethylene film was used over the
insulation material to provide a vapor barrier. Frames,
made of 25.4 x 25.4 x 4.8 mm angle steel and 25.4 x 3.2 mm
flat iron with 25.4 mm. flattened expanded sheet metals,
supported the rockbeds. The rockbed bottom was 0.9 m above
the ground. Plywood skirts of 0.3 m wide were around the
bottom of the support frames. A 254 mm square opening was
on the upper west side of each chamber as an entrance for
the building exhaust air into the rockbed chamber.

Likewise, an opening of the same size was on the upper east

23

 

m0h<mm2m0wm Dmmvao: :._.:s Ewhm>m ZO..F<.=._.2m> Nd mZDGE

r earn-snags};

.

24

MAKE—UP AIR EXIT

 

 

 

 

 

 

 

 

 

CHECK
WINDOW
, EXPANDED
SHEET METAL
WITH .
TH ERMOCOUPLES
SUPPORT N
FRAME \
SKIRT
MAIN FRAME

 

 

 

 

FIGURE 3.3 WEST SIDE VIEW OF NORTH ROCKBED CHAMBER

25

side of each chamber as an exit for the warmed building
make-up air out the chamber.

Limestone rocks with an average size of 16 mm were
screened with a #4 mesh. The pebbles, not passing through
the screen, were packed into the rockbed randomly.

Fig. 3.4 shows the schematic plan view of the
regenerative ventilation system. Both the exhaust and the
make-up fans were blowers directly driven by
totally-enclosed 0.186 kW motors with double speeds of
1140/1725 rpm. Two switches were used to change fan speeds
manually. A '254 mm square two-way duct and the exhaust
blower connected a 152 mm room outlet pipe and the air
entrances of the chambers. Likewise, the make-up blower and
a 254 mm square two-way duct linked with the air exits of
two chambers and a room inlet pipe of 254 mm diameter. In'
the farrowing room, a 254 mm vinyl coated flexible hose
along the east wall transported the incoming air from the
room inlet to the solar collector distributor ( Fig. 3.5 ).

There were four shutters in the 254 mm square ducts.
Every shutter was controlled by a damper motor ( Fig. 3.6 ).
Opening and closing these dampers were arranged so that the
building exhaust air flowed downwards through one rockbed
while the make-up air flowed upwards through the other
rockbed. A clock-operated timer switched on and off these
four dampers to alternate cycles. Fan speed switches and

the timer were mounted in a control box ( Fig. 3.7 ).

26

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mOthEhma EOHUMAJOQ I<JOm

       

 
 

   

52m: med /

            
        

m>>Om mh<mo 200m 02_>>Omm<u_ hwwg

w..m.Xm..u_

  

EMF—.30

 

$32.
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24.1 25. ozEem
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mamas—<0

 
      

z<1 53.sz :02. R5225;

#030
Aslmxsz p.030 PmD<IXm

mommxoOm mmmezd .

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¢w>oo 3002.3 vamzu

27

  
    

. ; . _ “E. l..-
' _1' e . I ‘ l :35
-I. ‘ ,1—‘1 '3

"l 'l‘qu

    

 

 

.v 1.1.2.,
Ulyiyw...
>1-fL‘EIB_——

     

FIGURE 3.5 FLEXIBLE HOSE CONNECTING INLET AND AIR DISTRIBUTOR

28

a
I
e

. Afi“

-( *Nrfll‘hsceulr .
r . 1,,“ g»-

' w. ”ex—rm
, _, 11...“... wry-”m" .
. “WNW.

Ylf‘Eeu‘ «55“
5 .M

 

FIGURE 3.6 DAMPER AND MOTOR

r
w

29

XOm AOEFZOU Z. mmmIUPE—w Dummm Z<u_ QZ< mus—Z. Em NEED—u.

 

30

3.3 Method of Study

The rockbed regeneraor was continuously operated while
the farrowing room was full with 16 sows and litters from
February through April in 1982. Measurements were taken
from February 10th through March 4th.

Four design parameters of the rockbed regenerator were
tested to evaluate their effects on heat recovery and
moisture removal for the building subsystem. The ranges of
the four parameters studied were

1. Rockbed depth: 0.30, 0.41 and 0.51 m,

2. Cycle time: 2, 4, 6, 8, 10 and 12 min,

3. Exhaust fan speed: 1140 and 1725 rpm,

4. Make-up fan speed: 1140 and 1725 rpm.

It is desired to test flow rates of both the exhaust
and the make-up air. However, these flow rates were
dependent, affected by the fan speeds, the rockbed depth and
the resistance in the ducts. So the two independent factors
- the fan speeds - were used. This was a factorial
experiment of four factors.

The following data were measured in this study :

1. Dry- and wet-bulb temperatures at the farrowing room
outlet,

2. Dry- and wet-bulb temperatures at the farrowing room
inlet,

3. Dry- and wet-bulb temperatures at the bottom of the

north sample rockbed chamber,

31

4. Dry- and wet-bulb temperatures of the outside air,

5. Dry-bulb temperatures at the exhaust air entrance
and the make-up air exit in the sample rockbed chamber,

6. Temperatures at each 100 mm depth level within the
sample rockbed,

7. Static air pressure above and below the sample
rockbed,

8. Air flow velocity in the farrowing room outlet and
inlet pipes.

The experiment was scheduled according to an orthogonal
table. For each treatment combination of four factors, the
rockbed system was first operated about 2 hours to obtain a
steady state. During this period, only air temperatures at
various locations were recorded at an interval of several
minutes depending on the cycle time used. Then, during a
second period about 40 min the recording interval was set to
10 sec and measurements of humidity, velocities and static
pressure were taken. During the night, the temperatures

were monitored at 5 to 15 min interval.

3.4 Measurement and Instrumentation

The following instruments were used to carry out
measurements, data acquisition and calibration:

1. WEATHERtronics Hot Wire Anemometer Model 2440,

2. Copper-Constantan Thermocouple Wires TQAN #24,

3. ATKINS Thermocouple Psychrometer Model 90023,

4. DWYER Manometer Model 25,

32

5. KAYE Digistrip II Multipoint Recorder,

6. DIGI-CAL AN6520 Calibrator.

3.4.1 Dry Bulb Temperature Measurement

Dry-bulb temperatures were sensed by thermocouples at
16 locations. The thermal electromotive forces. in
microvolts from these sensors were converted to temperatures
and printed out on chart papers in digital form by the
multichannel recorder. Table 3.1 shows the recorder channel
allocatiOn.

Three or five pairs of thermocouple wires were mounted
separately on each piece of 12.7 mm flattened expanded sheet
metals. The Ithermojunction of these PVCfcoated wires did
not touch the metal material. One thermocouple was at the.
center of each sheet. Others were placed 100 to 380 mm away
around the center. Thermocouples were also mounted on the
expanded sheet metal at the bottom of the sample rockbed in
th same way. One metal sheet with mounted thermocouples was
placed in the center of the rockbed plane at each 100 mm
thickness of stones. The sheet on the rockbed top was
covered with an approximately 20 mm thick layer of rocks.
Eleven recording channels were allocated to these
thermocouples. At least, the center thermocouple of each
sheet was connected to a recording channel. Table 3.2 shows
the channel allocation among layers.

The Digistrip II recorder had an accuracy of +( 0.003 %

33

reading + 0.3°C ) with Copper-Constantan thermocouples for
temperature monitoring between ~219 to 402°C. Its scanning
speed was 8 channels ‘per second. It required an ambient
environment of 0 to 50°C and 0 to 95 % RH with no
condensation. The recorder was installed in a small cabin (
Fig. 3.8 ) next to the farrowing room and about 15 m away
from the rockbed. The recorder was calibrated with a

DIGI-CAL AN6520 calibrator.‘

3.4.2 Humidity Measurement

Air humidity can be determined by measuring the dry-
and wet-bulb temperatures of the air steam. Wet-bulb
depression is the temperature difference between the
dry-bulb and the wet-bulb. The ATKINS psychrometer used was
a handzheld microvolt thermometer with LCD digital display.
Two fine-wire K-type thermocouples sensed the dry-bulb and
wet-bulb temperature, respectively. The readout was the
dry-bulb temperature and the wet-bulb depression. Its
pistol-shape made it easy to measure air humidity in a duct
through a small hole.

The ATKINS psychrometer was accurate to within
0.5 % reading for the range of 0 to 100°C and 0 to
100 % RH. It was calibrated with the DIGI-CAL AN6520
calibrator. Incorrect readout of the wet-bulb depressions
occurred when the wet-bulb temperature dropped below -5°C.
The measured data were compared with current local daily

climate data on three-hour basis as a check.

34

-Table 3.1 Channel Allocation on Digistrip II Recorder

 

Channel Number

Thermocouple Locations

 

1 - 11

12

13

14
15
16

Bottom to Top in Rockbed
Rockbed Chamber Entrance
Rockbed Chamber Exit
Room Outlet Pipe

Room Inlet Pipe

Room Outside

 

Table 3.2 Channel Number Allocation within the Rockbed

 

Layer Level

Rockbed Depth ( m )

 

 

.30 .41 .51
0 # l - 2 # l - 2 # 1 - 2
1 # 3 - 4 # 3 - 4 # 3 - 4
2 # 5 - 7 # 5 - 6 # 5 - 6
3 # 8 - 11 # 7 - 8 # 7'- 8
4 # 9 - 11 # 9 - 10
5 # 11

Note : Level 0 - Rockbed Bottom.

(SIM Ji‘fl

35

 

REFER":

'I-H

 

FIGURE 3.8 DATA LOGGER AND PSYCHROMETER

36

3.4.3 Air Flow Measurement

The volumetric rate of an air flow in a pipe is the
product of the inside section area of the pipe and the mean
normal velocity of the air flow through the area. The mean
normal velocity of air flow was taken as an average of 10
velocities measured in 5 concentric ring sections of equal
area. The velocity measurements were taken several times
for each combination of rockbed depth and fan speeds.

The hot wire anemometer had an accuracy of 3 % full

scale for both 0 to 5 m/s and 0 to 40 m/s.

3.4.4 -Static Pressure Measurement

A simple DWYER inclined manometer was used in this
study. The manometer could handle 0 to 0.75kPa.

There was a tubular hole on the check window cover of
the sample rockbed chamber. One of two tubular probes of
the manometer was injected into the upper space above the
rockbed with the other probe open to the atmosphere. The
reading on the manometer scale was the static pressure
difference between the atmosphere and the space above the
sample chamber. When the air flow direction was reversed
the two probes were also exchanged in order to read positive
pressure differences. Measured static pressure data were
grouped and averaged for 12 combinations of rockbed depth

and two fan speeds.

4 ORTHOGONAL EXPERIMENT DESIGN .

4.1 Introduction

The major analysis of this study was through a
factorial experiment of 6 x 3 x 22 . A full factorial would
call for 72 treatment combinations, and the complete
analysis of the experiment would ideally require several
replicates of the full factorial. It would be very
time-consuming, costy and, even, inpractical. An orthogonal
design was, therefore, applied in this study. It involved a
half-fractional factorial experiment to estimate the main
effects of the four factors. According to its results one
or more of the following analysis could be performed :

1. Determining the main effects and significance of
these factors tested.

2. Identifying the factors which have appreciable
_effects for further close study; and releasing the
remaining factors with little effects, or replacing them
with new factors.

3. Selecting the optimum combination of design
parameters within the ranges tested, if all interactions of
factors, suppressed in residual with errors, were
negligible.

4. Predicting the necessity of replicating a full

37

38

factorial experiment in further study, if interactions were
competitive with main effects of these factors tested.

Orthogonal designs are based on orthogonal arrays of
strength two, which form orthogonal main effect plains
( John, 1971 ). Orthogonal designs can be expressed in
matrix form, which are named for "orthogonal tables” ( Wang
et al., 1979 ). In an orthogonal table the rows identify
the treatment combinations; the columns - the factors: and
the elements - the levels of the respective factor at the
respective run.

, The major properties of the orthogonal tables are
summarized as follows ( CAAMS, 1978 ) :

1. Every level of any individual factor appears for the
same number of times in its column.

2. Every treatment combination of any factor pair
appears for the same number of times in respective column
pair.

3. Permutation of rows, columns or level notations in a
column does not affect the orthogonality of the table.

4. If an orthogonal design is a fraction of a factorial
experiment, the remaining fractional factorial also forms an
orthogonal array.

5. Many orthogonal tables can handle some low-order
interactions while some can not handle any interactions.

6. Total number of factors and interactions tested
should not exceed the number of columns in an orthogonal

table.

39

4.2 Orthogonal Table - OA35( 6 x 3 x 22 )

Table 4.1 shows the orthogonal table constructed for
this study. The table is designated by OA36( 6 x 3 x 22 ),
where the subscript of 36 indicates the row dimension, the
expression of 6 x 3 x 2 - the number 'of levels for
individual factors and the superscript of 2 - the number
of factors having the same respective number of levels.

It is noticed that :

1. This orthogonal table was one-half fraction of the
full factorial experiment. A

2. All of four factors in this table were independent
and controllable.'

3. All levels of each factor were equally spaced over
its respective range.

4. This table could not estimate any interactions. All
interactions suppressed each other in the residual.

5. It was desired to conduct these runs in a randomized
order, although the table was organized in standard order
form. In this study other factors varied in random ways,
except the factor of rockbed depth changed in an increasing

order for some convenience.

40

Table 4.1 Orthogonal Table OA36( 6 x 3 x 22 )

 

Run Factors

 

 

Rockbed Cycle Exhaust Make-up
' Depth Time Fan Fan .
Speed Speed
(m) (min) (rpm) (rpm)
01 0.30 2 1725 1140
02 0.30 2 1140 1725
03 0.30 4 1725 1725
04 0.30 4 1140 1140
05 0.30 6 1725 1140
06 0.30 6 1140 1725
07 0.30 8 1725 1725
08 0.30 8 1140 1140
09 0.30 10 1725 1140
10 0.30 10 1140 1725
11 0.30 12 1725 1725
12 0.30 12 1140 1140
13 ' 0.41 2 1725 1725
14 0.41 2 1140 1140
15 0.41 4 1725 1140
16 0.41 4 1140 1725
17 0.41 6 1725 1725
18 0.41 6 1140 1140
19 0.41 8 1725 1140
20 0.41 8 1140 1725
21 0.41 10 1725 1725
22 0.41 10 1140 1140
23 0.41 12 1725 1140
24 0.41 12 1140 1725
25 0.51 2 1725 1140
26 0.51 2 1140 1725
27 0.51 4 1725 1725
28 0.51 4 1140 1140
29 0.51 6 1725 '1140
30 0.51 6 1140 1725
31 0.51 8 1725 1725
32 0.51 8 1140 1140
33 0.51 10 1725 1140
34 0.51 10 1140 1725
35 0.51 12 1725 1725
36 0.51 12 1140 1140

 

5 RESULTS AND DISCUSSION

During the test period the outside climate temperature
averaged -5.8°C and fluctuated between -19.7 and 6.1°C.
The atmospheric relative humidity varied from 56 to 100 %
with an average .of 82 %. The room temperature was
maintained between 17 and 26°C. The room relative humidity

averaged 47 % with a range of 29 to 57 %.

5.1 Basic Character of This Study

5.1.1 Rock Equivalent Diameter and Void Ratio

The equivalent spherical diameter of rocks was 15.8 mm
and the void ratio a was 0.507. The values were obtained
with 3 samples by using the water replacement method. The
ratio of the rockbed depth and the side length to the rock
equivalent spherical diameter were from 19 to 32, and 51,
respectively. Therefore, no edge effect was assumed in this

study, based on Rose's results mentioned in Section 2.2.1.

5.1.2 Air FLow Rates

The volumetric flow rates ( Table 5.1 ) varied as the
rockbed depth and the fan speeds changed, and were also
subject to the resistance in the exhaust and the make-up

ducts. The flow rates at low speed for both fans provided

41

42

Table 5.1 Air Flow Rates ( m3/s )

 

 

Rockbed Exhaust Fan Speed Make-up Fan Speed
Depth ----------------------------------------------
(m) 1725 rpm 1140 rpm 1725 rpm 1140 rpm
.30 .167 .111 .184 .125
.41 .162 .110 .172 .118
.51 .159 .108 .165 .113

 

Table 5.2 Comparison of Static Pressure Drop

 

 

 

 

Rockbed Air Flow Pressure Drop Pressure Drop
Depth Rate Measured Calculated
(m) (m3/s) (Pa) (Pa)
.184 37 53
.30 .167 35 44
.125 17 26
.111 16 22
.172 .50 63
.41 .162 45 56
.118 19 32
.110 17 28
.165 60 73
.51 .159 55 67
.113 24 38

.108 21 35

 

43

ventilation below the minimum winter ventilation rate of
0.142 m3/s for 16 sows and litters, suggested in MWPS-l (
1980 ). However, some air leaked out from the west
farrowing room through the underfloor channel due to a
pressure difference between the two farrowing rooms when a
fan was operated at a high speed in the east farrowing room.

The superficial velocity of the air flow was from 0.17
to 0.28 m/s with respect to the rockbed cross section of
0.64 m2. These values were below 0.42 m/s as suggested by
Moysey ( 1980 ). The mass flow rate of the exhaust air
varied from 0.12 to 0.19 kg/s while that of the make-up air
was between 0.13 and 0.22 kg/s. These measurements showed
that the mass flow rate of the room make-up air was slightly
higher than that of the exhaust air with both fans at the

same speed, either 1725 or 1140 rpm.

5.1.3 Static Pressure Drop

Table 5.2 shows a comparison between the meassured
static pressure drop and the calculated values from Shewen's
equation ( 2.10 ). In the calculation, a shape factor a of
2.0, the void ratio a of 0.507 and the equivalent diameter
of 0.0158 m were used. It was seen that the measured static
pressure drop was lower .than that calculated. Flattened
expanded metal sheets put into the rockbed might be a reason
for this pressure drop reduction, since these metal sheets
modified the bulk rockbed structure and air flow was

redistributed within the sample rockbed. These tested

44'

values were in the range of 50 to 100 Pa recommended by

Parker et al. ( 1981 ).

5.1.4 Reynold's Number and Biot Number

The particle Reynold's number was between 168 and 310
in this study, which was in the range of 60 to 480. When a
shape factor a of 2.0 was assumed, the convection heat
transfer coefficient H was of 10 to 15 W/mZoK, calculated
with equation ( 2.2 ). The specific heat of limestone is
2.15 W/m-K. The resulting Biot number was from 0.037 to
0.055, which was less than 0.1. Hence, a lumped system

approach was appropriate ( Section 2.2.2 ).

5.2 Results of the Orthogonal Table

Data processing was carried out at Albert H. Case
Computer Center, College of Engineering, M. S. U. Recorded
data were processed with a Fortran program, which also
formed graphs 'from analyzed data. A Fortran computer model
by Lerew ( 1972 ) was used to find psychrometric properties
of the moist air. The air properties were applied to
calculate the heat recovery effectiveness n, the moisture
removal factor B and the heat recovery factor Rf. Some
short circuiting‘ occurred in the study, since two adjacent
rockbeds were not blocked up well from their bottom.

Resultant values of n, 3 and Rf are listed in Table 5.3.

45

Table 5.3 Orthogonal Table Results

 

 

 

 

Run Factors Results
Rockbed Cycle Exhaust Make-up
Depth Time Fan Fan n 3 Rf
Speed Speed
(m) (min) (rpm) (rpm)

01 0.30 2 1725 1140 .36 .67 .36
02 0.30 2 1140 1725 .43 .60 .73
03 0.30 4 1725 1725 .65 .40 .73
04 0.30 4 1140 1140 .63 .43 .72
05 0.30 6 1725 1140 .56 .49 .56
06 0.30 6 1140 1725 .53 .51 .90
07 0.30 8 1725 1725 .72 .34 .81
08 0.30 8 1140 1140 .68 .40 .77
09 0.30 10 1725 1140 .52 .51 .52
10 0.30 10 1140 1725 .59 .47 1.0
11 0.30 12 1725 1725 .76 .31 .84
12 *0.30 12 1140 1140 .74 .31 .84
13 0.41 2 1725 1725 .65 .41 .72
14 0.41 2 1140 1140 .66 .39 .73
15 0.41 4 1725 1140 .50 .53 .50
16 0.41 4 1140 1725 .60 .46 .97
17 0.41 6 1725 1725 .69 .39 .75
18 0.41 6 1140 1140 .63 .49 .70
19 0.41 8 1725 1140 .57 .47 .57
20 0.41 8 1140 1725 .50 .54 .81
21 0.41 10 1725 1725 .78 .26 .84
22 0.41 10 1140 1140 .81 .24 .88
23 0.41 12 1725 1140 .58 .46 .58
24 0.41 12 1140 1725 .63 .42 1.0
25 0.51 2 1725 1140 .50 .52 .50
26 0.51 2 1140 1725 .59 .46 .93
27 0.51 4 1725 1725 .74 .31 .79
28 0.51 4 1140 1140 .76 .29 .81
29 0.51 6 1725 1140 .54 .49 .54
30 0.51 6 1140 1725 .58 .46 .92
31 0.51 8 1725 1725 .71 .34 .76
32 0.51 8 1140 1140 .74 .30 .79
33 0.51 10 1725 1140 .47 .57 .47
34 0.51 10 1140 1725 .56 .50 .88
35 0.51 12 1725 1725 .71 .34 .76
36 0.51 12 1140 1140 .70 .36 .76
Average : .60 .43 .74-

46

5.2.1 Main Effects

The main effects of each factor are shown graphically
in Fig. 5.1. Analysis of variance is tabulated in
Table 5.4. All interactions aliased each other with random
errors in the residual.

The F-test in Table 5.4 showed that the cycle time was
most significant for both the heat recovery effectiveness n
and the moisture removal factor 8, however, only with 75 %
confidence of significance because the interactions were
strong. Rockbed depth was of little importance
for n, B or Rf within the tested range. Fan speeds had
little effect on n or ‘8, but significantly effect on Rf.
Cycle time was the third important factor for Rf.

Fig. 5.1 (b) shows a tendency for . an increase
in n and Rf as the cycle time increased. Large values
of n observed were with 10 to 12 min cycle time in this
study. This agreed with the range of 10 to 15 min suggested
by Witz et al. ( 1979 ). In Moyseys' study ( 1980 ) both
increase and decrease in the efficiency were observed when
_the cycle time reduced from 12 to 8 min. Results of this
study were based on the statistical analysis rather than »a
single comparison. Fig. 5.1 (a) shows that from 0.4 m up
the influence of the rockbed depth on n and B was

negligible.

47

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Table 5.4 Analysis of Variance

 

 

 

 

Term Source SS 4 d.f. MS F-Ratio
Rockbed Depth .01119 2 .00559 .49
Cycle Time .09174 5 .01825 1.61

n Exhaust Fan Speed .00314. 1 .00314 .28
Make-up Fan Speed .00593 1 .00593 .52
Residual .29467 26 .01133

Total .40616 35 .01160
Rockbed Depth .01150 2 .00575 .57
Cycle Time ’ .08054 5 .01611 ‘1.50

8 Exhaust Fan Speed .00116 1 .00116 .11
Make-up Fan Speed .00401 1 .00401. .40
Residual .26248 26 .01010

Total .35968 35 .01028
Rockbed Depth .00340 2 .00170 .36
Cycle Time .06526 5 .01305 2.78

Rf Exhaust Fan Speed .35106 1 .35106 74.69
Make-up Fan Speed .35264 1 .35264 75.03
Residual .12209 26 .00470

Total .89445 35 .02556

 

Note : 1. SS - Sum of Square of deviations about a mean
d.f. - Degrees of Freedom,
MS - Mean of Sum of Square of Deviations

2. F0 os(1,25) = 4.22, F0 05(2,26) = 3.37, -
Fo'05(5,26) = 2.59. '

3. F0:05(1,26) = 1.38, F0 05(2,26) = 1.45,
F0.05(5,26) = 1.42. '

49

5.2.2 Interactions

Fig. 5.2 illustrates six two-factor interactions,
though it was impossible to study them mathematically.

There was a strong interaction of two fan speeds,
i.e. two air flow rates. When two fan speeds differed very
much from each other, the heat recovery effectiveness n
averaged 0.5 to 0.55 ( Fig. 5.2 (b) ). When the room
exhaust fan was at 1725 rpm and the room make-up fan was at
1140 rpm, the high exhaust flow rate gave much heat to the
rocks, however, the low make-up flow rate recovered less
heat from the rocks. This lowerred n down to 0.36 through
0.61. In this case, some cold outside air leaked into the
room, which required more supplemental heat. When the
exhaust fan was at 1140 rpm but the make-up fan was at
1725 rpm, less heat was transferred to the rocks by the low
exhaust flow rate, and some warm indoor air leaked out the
room. In this case, n dropped to 0.43 through 0.63. When
both fans were at 1725 rpm, 0 was from 0.65 to 0.78.
Likewise, in the case of 1140 rpm speed for both fans, the
heat recovery effectiveness was from 0.63 to 0.81. This
strong negative interaction of the two fan speeds was the
major source causing fluctuations in response curves of
cycle time in Fig. 5.2 (b) and Fig. 5 (a), (c) and (d).'

The interactions of rockbed depth with either the
exhaust fan or the make-up speed were negligible
on n and s ( FIg. 5 (e) and (f) ). So. was the

interaction of the cycle time with either the exhaust fan or

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53

the make-up fan speed on Rf. The interaction of cycle time
with rockbed depth had little effect on n, B and Rf if
response curves at 0.3 and 0.51 m were compared with each

.other.

5.3 Relationship between n and Rf

By definition, the heat recovery effectiveness n had
a direct relationship with the heat recovery factor Rf :

n = ( Me/Mmax )Rf ( 5.1 )

This depended merely upon two mass flow rates, Me and Mi, as
Mmax was either Me or ”1 whichever was larger. Rf was never
less than 0, because Me was always less than or equal to
Mmax' When both fans were at the same speed, either 1140 or
1725 rpm, the make-up mass flow rate "1 was a little larger
than the exhaust mass flow rate Me, so n was not much less
than Rf. The resulting values were of 0.65 to 0.78 for n,
0.72 to 0.84 for Rf in the case of 1725 rpm for both fans,
and of 0.63 to 0.81 for n, 0.70 to 0.88 for Rf in the case
of 1140 rpm for both fans.

When the exhaust fan was at 1725 rpm and the make-up

fan was at 1140 rpm, Me became M so n equaled Rf. The

max'
low resultant values of 0.36 to 0.61 for both n and Rf were
due to insufficient make-up air capable of carrying less
heat. Lampman ( 1978 ) concluded an exhaust air flow rate
of 2 or 2.5 times the make-up flow rate to minimize freezing

problems in his investigation. Somehow, it reduced the heat

recovery effectiveness. When the exhaust fan was at

54

1140 rpm and the make-up fan was at 1725 rpm, Rf was from
0.73 to 1.0. This meant that most, even approximately
total, heat, given up by the low exhaust flow rate to the
rockbed, was reclaimed by the high make-up flow rate. But,
in this case n was from 0.43 to 0.63, which was lower than '
Rf very much. This was because some heat was lost with the

leakage air.

5.4 Correlation of n with B

Physically, in this system the more heat was recovered,
the less moisture was removed from the room, since more
moisture was returned back to the room. In the extreme, if
entire mass of the exhaust air was recirculated back to the
room, all recoverable heat) would be "regenerated” if duct
losses were neglected. This case would be undesirable as
ventilation must remove moisture, toxic gases and so on from
the room. At the other extreme, if the exhaust air was
released_directly to the atmosphere without passing through
the rockbeds, no heat would be recovered, but all removable
moisture would be removed. This is the case for

conventional ventilation systems. Mathematically, these two

circumstances may be expressed as the following,
respectively:
80 = 0 for no = l ( 5.2 )
81 = 1 for HI = 0 ( 5.3 )

A third-order polynomial was expected as the

correlation of n with B-

55

B=a*n°+b*n2+c*n+d (5.4)
Transform ( 5.4 ) by applying two given conditions in

( 5.2 ) and ( 5.3 ). A linear model came out.

2 = u * n + s ( 5.5 )
where
z=<8+n-l)/(n2+n)
u=a

s - a * no + b

A single linear regression was conducted. The resultant
regressive equation was :

z a -0.51 * n + 0.1 ( 5.6 )
with r = -0.667 and d.f. = 34
A t-test showed that for 0.1 % significance level with 34
d.f. the absolute value of the correlation coefficient R
should be larger than 0.53 ( BIAM, 1980 ). Finally

8 = -0.51 * n3 + 0.61 * n2 - 1.1 * n + l ( 5.7 )
Fig. 5.3 shows the close relationship between the regression
curve with the tested data.

Since the moisture removal factor B was less 1.0, for
the renegerative ventilation system a larger exhaust flow
rate than that for a conventional ventilation system is
required. The performance of both heat recovery and
moisture removal should be considered during the design of a
regenerative ventilation system. A heat recovery
effectiveness about 0.5 would lead to a moisture removal

factor about 0.54, which may be desirable for the system.

56

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57

5.5 Correlation between Enthalpy and Flow Rates

The make-up air enthalpy Ei was a function of the
indoor air enthalpy Be, the outdoor air enthalpy E0, and the
exhaust and make-up air flow rates, Qe and Qi' for the given
rockbed regenerator structure. A multiregression model was
obtained:

Ei = 0.958e + 0.3EO + 86.5Qe - 74.30i - 15.8 I 5.8 )
where Es were in kJ/kg dry air and Qs in m3/s. This
regression model had a coefficient of determination of 0.95.

The mean values for Ee, Ei' E0, Qe and Qi were 60.13,
49.78, 21.9 kJ/kg dry air and 0.136 and 0.145 m°/s,

respectively, in this study. So, E was i the most

e
significant factor, Ei - the second, and both Qe and Qi - of
less importance in the ranges tested. A simplified
regression model was as follows :

E1 = 1.382Ee + 0.143Eo - 30.8 ( 5.9 )
with a coefficient of determination of 0.71 and d.f. of 33.

A F-test indicated this regression model had 95.5 %

confidence of significance.

5.6 Correlation between Humidity and Flow rates

Likewise, a multiregression equation shows the incoming
air humidity ratio hi had a functional relationship with the
exhaust and outside air humidity ratioes, he and ho, and
flow rates of Qe and Qi. .

hi = .83he + .34hO + .0110e - .010i - .0013 ( 5.10 )

58

where hs were in kg water/kg dry air and Qs - m3/s.

This model had R2 of 0.98 and d.f. of 33. Mean values
of he, hi and ho were 0.0079, 0.0062 and
0.0027 kg water/kg dry air, respectively. The first and the

second important factors affecting hi were h and ho,

e
respectively. A simplified regression equation is shown
below.

with R2.= 0.90 and d.f. = 33.
5.7 Air Temperature Profiles

5.7.1 Temperature Profiles within the Rockbed

‘ Fig. 5.4 (a), (b), (c), (d) and (e) present 5 typical
air temperature profiles at each 0.1 m depth level within
the sample rockbed.

Fig. 5.4 (a) and (b) show the influence of the cycle
time on the temperature profiles. In these two trials the
0.51 m depth and 1725 rpm of the two fan speeds were the
same, the cycle time was different, 4 and 12 min,
respectively, besides the exhaust and the outside
temperatures. It is seen that

l. The rockbed was charged and, discharged more
thoroughly for the 12 min cycle time than 4 min. For
example, consider the temperature profiles at the rockbed
bottom in FIg. 5.4 (a) and (b). _ Though the outside

temperature was about 6.0°C lower in the 12 min trial than

9
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64

that in the 4 min trial, the temperature increases during
the warming half cycle were approximately equal in the two
trials. During the cooling half cycles, the temperature
dropped closer to the outside temperature for the 12 min
cycle time. This was due to the larger heat capacity,
i.e. thermal inertia, of the rockbed. .

2. When the outside cold air or the room exhaust warm
air was first introduced, 'there was an abrupt drop or
increase in temperature within the rockbed. This abrupt
drop was obviously observed at the rockbed bottom and at the
12 min cycle time.

3. The upward and downward segments, corresponding to
warming and cooling half cycles, of these profiles were
closer to straight lines as the cycle time was above 10 min.
This indicated that the rockbed thermal response to the
temperature change was not constant with respect to the
cycle time. Similar results were seen in other trials
regardless of the two fan speeds.

4. The temperature gradient throughout the rockbed
depth was more uniform for the longer cycle time. This was
because during the longer cycles heat was distributed more
uniformly. Similar phenomena were observed for other trials
when the two fans were at the same speed, either 1140 or
1725 rpm. Fig. 5.4 (c) shows an example for the two fans at
1140 rpm speed. On the other hand, when the exhaust fan was
at 1725 rpm and the make-up fan - 1140 rpm ( Fig. 5.4 (d) ),

the temperature gradient differed very much along the

65

vertical direction. Since the warm exhaust flow rate was
higher than the cool make-up flow rate, the temperatures
throughout the rockbed were high. Especially, the mean
temperatures at the upper several depth levels were very
close to each other, and near to the exhaust air
temperature. When the exhaust fan was at 1140 rpm and the
make-up fan was at 1725 rpm, the profiles were just opposite
to the case above. In the lower depth levels the
temperatures were close to the outside cold temperature, and
the temperature at the rockbed top was much lower than the
exhaust air temperature ( Fig. 5.4 (e) ). This was caused
by the larger make-up flow carrying most stored heat from
the rockbed. In Fig. 5.4 ( e ) the mean temperature at the
rockbed bottom was little "lower" than the "outside"
temperature was due to wind chilling and position difference

between two points monitored.

5.7.2 Average Temperature from the Rockbed Bottom Upwards
Fig. 5.5 presentes 4 graphs, which illustrates the
average temperature varied at various depth levels.
Fig. 5.5 (a) shows that a positive temperature gradient
decreased from the rockbed bottom upwards for both fans at
1725 rpm. 'Similar results were seen for both fans at
1140 rpm, which is not repeatedly shown here. Fig. 5.5 (b)
shows an example of the 1725 rpm exhaust fan speed and the
1146 rpm make-up fan speed. Above 0.1 m the temperature

increased very little. From 0.3 m upwards, there was almost

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no temperature change. Fig. 5.5 (c) presents an example for
the 1140 rpm exhaust fan speed and the 1725 rpm make-up fan
speed. In the lower 0.1 m thickness the average temperature
was nearly a constant. Then, the temperature gradient
increased at the high depth levels. Fig. 5.5 (d)
illustrated an uniform temperature gradient throughout the
rockbed depth for the 12 min cycle time and the 1725 rpm

speed of both fans.

5.7.3 Temperature Profiles in the Ventilation System

Fig. 5.6 shows temperature profiles measured at the
entrance and the exit of the sample rockbed, at the room
inlet and outlet, and at the rockbed bottom and the outside.
,The upward segments on the temperature curve for the make-up
,air correspond to the discharge half cycles in the sample
chamber. The downward segments on the curve represent the
discharge half cycles in the other chamber. An interesting
phenomenon was observed that the make-up air temperature
from the sample chamber was higher than that from the other.
These two chambers had the same »size ‘and insulation, and
were packed with the same rocks in the same way. A
noticeable difference between them was with or without the
expanded metal sheets. These metal sheets divided the
sample rockbed into several blocks. They disturbed air flow
paths within the sample chamber and air was redistributed
while the air passed across each sheet. This might improve

the heat transfer process within the rockbed. Moreover, the

71

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sheets were good conductors, which made temperature more
even on the plains themselves. The phenomenon of different
temperature gains in make-up air flow became severe when the
exhaust fan was at 1140 rpm and the make-up fan - 1725 rpm,
see Fig. 5.6 (b). This was due to the high make-up flow
could easilier recover most heat in the sample rockbed with
screen sheets. When the cycle time was short ( Fig. 5.6 (c)
), the heat was not transferred thoroughly due to the
thermal inertia of the rockbed. In this case, the influence
of the metal sheets became significant, which also led to
high temperature gains in the make-up air from the sample
rockbed. On the other hand, when the exhaust fan was at
1725 rpm and the make-up fan - 1140 rpm, associated with a
long cycle time, this phenomenon. became slightly (
Fig. 5.6 (d) ). This was because the high exhaust flow rate
provided much heat to the rockbed during long cycles.

Some small peaks on the temperature curves of the
make-up air occurred at each turning point of the discharge
half cycle to the charge cycle. This was due to a time
delay between closing and opening dampers. As claimed by
the manufacturer, it took 40 to 56 sec or 64 to 80 sec for
the control timer to open or close a circuit, respectively.
As long as the entrance damper was opening, the warm air
flowed into the chamber immediately. However, the exit
damper was still closing.at the same time. Thus, an amount
of warm air flowed through the exit directly and mixed with

the make-up air. This resulted in a peak temperature of the

76

make-up air until the exit damper closed tightly.

The temperature drop between the chamber exit and the
room inlet indicated some heat loss in the duct. So did the
temperature drop between the room outlet and the chamber
entrance. In Fig. 5.6 (b) it was observed that the make-up
air temperature was,~ even, higher than that at the chamber
exit during the discharge half cycle. This was caused by
the warm room 'air, which influenced on the incoming air at
the room inlet. When the exhaust fan was at 1140 rpm and
the make-up fan - 1725 rpm, the air temperature at the
chamber entrance dropped very much during the cooling half

cycle, so this phenomenon was recognized.

5.7.4 Overnight Performance

Fig. 5.7 shows the overnight performance of the rockbed
regenerator system during 3 test runs. The shape of these
proflies depend on the combination of the cycle time and the
recording interval used. Therefore, they do not reflect the
actual performance in cycles.

It took about 2 hours for the system to approach a
steady state after adjusting some parameters, such as cycle
time, fan speed and so on, see Fig. 5.7 (a). The
temperature fluctuation of the exhaust air indicated that
the room gas heater was turned on once about each hour,
then, off ( Fig. 5.7 (a) and (b) ). It seems that the
thermostat was not sensible enough to maintain a stable room

temperature. Fig. 5.7 (b) illustrats an overnight

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performance of the ventilation system. This also shows the
poor performance of the thermostat. Fig. 5.7 (c) shows the
ventilation system performance over the coldest night during
the test period. It was seen that the room temperature
dropped when the outside was the lowest as the gas heater
did not work.’ The rockbed, however, maintained the room

temperature at a reasonable level between 17 to 23°C.
5.8 Other Results

5.8.1 Frost

During the whole experiment period, frosting was
observed only once. Several small frost spots were found on
the bottom frame of the rockbed in the coldest morning of .
February 11th, when outside temperature was -l7°C, see
Fig. 5.8. The frost disappeared soon as outside temperature
increased in the daytime. Relatively low humidity in the
farrowing room associated with moderate climate temperature

eliminated most frosting and freezing.

5.8.2 Dust Accumulation

Dust accumulation was observed on the surfaces of the
rockbeds, dampers and ducts in the ventilation system. The
dust accumulated heavier in the exhaust duct ( Fig. 5.9 ).
than in the make-up duct ( Fig. 3.6 ), since much dust
settled on various surfaceS‘while the exhaust air flowed

through bending corners and dampers in the exhaust duct.

b
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FIGURE 5.8 FROSTING ON THE FRAME

82

 

FIGURE 5.9 DUST ACCUMULATION ON SURFACES

83

Also, dust components were filtered out of the air when it
moved through the rockbed as the air velocity was very low
in the rockbed chambers. The dust settled on the rockbed
top and the make-up air could not lift the dust. The system
was not cleaned for the whole test period. No significant
effect of the dust problem on the static pressure drop or on
other system performance was observed.

Low room air humidity along with dry feed supply caused
undesirable dust. Since the size of dust, mostly feed
powder, was so small, using fine screen was not a practical

way to filter it out.

6 BALANCE EQUATIONS AND DESIGN CRITERIA

Regenerative ventilation systems, in which a part of
heat and, perhaps, moisture is returned back to animal
buildings, differ from conventional ventilation systems.
Mass, moisture and energy balances in the building subsystem
should, thus, be studied. New balance equations and design
criteria for ventilation systems with regenerators are

proposed.

6.1 Air Mass Balance in Animal Housing

An air mass balance must be maintained in the building
subsystem. The incoming air mass should equal the outgoing
air mass per unit of time. When these two mass rates are
not the same, some air, i.e. the difference between the two
mass rates, either gets into or escapes out through some
leakage or gaps of the room. In the former case, i.e. the
room exhaust mass flow rateMe is greater than the room
make-up mass flow rate Mir cold outside air leaks into the
room due to a negative air pressure in the room. More
supplemental heat is needed to warm the cold air. 'In the
latter case, i.e. Me < Mi, some indoor air leaks out of the

room caused by a positive indoor air pressure. Some heat is

lost since it does not pass through the rockbed. The mass

84

85

balance between the outgoing and the incoming air in an
animal building is written as:

Mi = Me + M1 ( 6.1 )
where M1 is the mean leakage mass rate, kg dry air/s. A
positive ”1 value means leaking out whereas a negative Ml
indicates leaking in. When air is leaking out, it is the
same as the exhaust air. If some air leaks in, it is the
same as the outside air.

In conventional ventilation systems, there is no
make-up fan. So Mi = 0 and Ml - -Me, which means that the
"leaking-in" air mass through inlets or gaps is
automatically balanced with the exhaust air mass. Hence,

the expression ( 6.1 ) does not lose its generality.

6.2 Moisture Balance in Animal Housing

A primary principle of ventilation is to maintain a
desirable humidity level for the animal environment (
MWPS-l, 1980 ). The moisture added to an enclosure by
animals and the incoming air must equal the moisture
removed. Then, the indoor humidity remains stable at a
certain level of he. Otherwise, he and others would change
until reaching a new moisture balance. The moisture balance
in an aniamal building is of the form:

Mehe + Mlhl = Mihi + wa ( 6.2 )
where h denotes the air humidity ratio at the given state
and Wa is the total vapor production rate in the room due to

animals. Rewrite ( 6.2 )

86

wa = Mehe + Mlhl - Mihi ( 6.3 )
The right side is the net moisture removal rate from the
building. It equals the maximum removable moisture rate
minus the real moisture return rate into the building, so

Waammax(he-hO)-Mi(hi-ho) (6.4)
It can be written with the moisture removal factor B

wa = Mmax( he - ho )8 (6.5)
Therefore, 8 can be computed as

B = Wa/I Mmax( he — ho ) 1 ( 6.6 )
Since 8 is never larger than I, “max should be larger than
Wa/( he - ho ).

In conventional‘ ventilation systems with no heat
exchanger, 8 becomes unity and "max equals Me. Therefore,

WaaMe(he-ho)   (6.7)

In the case with the heat exchanger, the make-up air
state and, consequently, B, are dependent not only on the
indoor and outdoor conditions, the animals and the

ventilation rates, Oe and 91' but also on the heat

exchanger. Consider a special case that Me is assumed to be

the same as “1' Thus
8 = ( he - hi )/( he - ho )
g ( 6.8 )
Wa ‘3 Me( he - hi )

87

6.3 Energy Balance in Animal Housing

Another principle function of ventilation is to control
the room temperature within a suitable range. The heat
supplied to an animal environment must~ equal the heat
removed from the room. Otherwise, the room temperature
and/or others would. adjust themselves until a new energy
balance is reached. ASAE D270.4 ( 1979 ) states that a
portion of sensible heat produced by animals evaporates some
water from various wetted surfaces in the room. Therefore,
enthalpy should be used in the energy balance equation
instead of sensible heat. The indoor temperature is
implicitly represented in the exhaust air enthalpy. The
energy balance in animal housing with heat recovery is

written as

qa+qi+qsp=qe+ql+qb (6.9)
where qa - total animal heat production rate, kW,
qi - energy rate in the incomimg air, kW,
qSp - supplemental and mechanical heat rate, kW,’
qe - energy ratein the exhaust air, kW,
ql - energy rate in the leaking air, kW,
qb - building conductive heat loss rate, kW.

Rearrange ( 6.9 )

(qa-qb)+qsp=qe+ql-qi (6.10)
The right side of ( 6.10 ) is the net energy loss due to
ventilation and leakage. Similar to the moisture balance
case, it can also be expressed as the remainder of the

maximum recoverable energy rate for the heat exchanger minus

88

the actual recovered portion:
qe + ql - qi = Mmax( Ee - so )(1 - n) ( 6.11 )
So
( qa - qb ) + qSp s Mmax( Be - EC )( 1 - n ) ( 6.12 )
It can be shown that starting with the mass balance ( 6.1 ),
one can derive the same results as ( 6.6 ) and ( 6.12 ). In
other words, both ( 6.6 ) and ( 6.12 ) satisfy ( 6.1 ).
If no heat exchanger is used, i.e. n a 0 and Mmax s M

e

in conventional ventilation, the energy balance becomes
(qa-qb)+qsp

On the other hand, when the heat exchanger is applied,

- Me( Be - so ) ( 6.13 )

if the exhaust and the incoming flow mass rates, Me and Mi'
are assumed equal, it leads to
n =(Ei-Eo)/(Ee-Eo)
{ ( 6.14 )
(qa-qb)+qu-Me(Ee-Ei)
So far, it is seen that ( 6.2 ) or ( 6.5 ), and ( 6.9 ) or

( 6.12 ) are the general expressions of the moisture and

energy balances in animal housing, respectively.

6.4 Design Criteria of Ventilation Systems

ASAE D270.4 ( 1979 ) states that ventilation systems
should maintain temperature and relative humidity in the
animal shelter within desired limits and provide a desired
amount of fresh air, without draft, to all parts of the
shelter. In confined animal housing the minimum winter

ventilation rate' Qw is to remove toxic gases, odors and

89

dust, and to bring in‘ fresh air ( MWPS-l, 1980 ).
Maintaining desirable temperature and humidity means
satisfactory management of the energy and moisture balances
discussed in previous sections. The general criteria for
ventilation design and evaluation could be mathematically

described as follows:

O
n

max( Qw, Qt' Qm )
{ ( 6.15 )
qSp = max{ qb-qa+Wa( Ee-EO )( l-n )/[B( he-ho )],0 }
where Q - Qe or Qi correspnoding to Me or Mi whichever is
larger, m3/s,
Qw - minimum winter ventilation rate, m3/s,
Qt - temperature control flow rate, m3/s,
Qm'- moisture control flow rate, m3/s.
The recommended Qw values for various species and size of
animals can be found in MWPS-l ( 1980 ). The temperature
and moisture control rates, Qt and Qm, can be computed.
Consider the conventional case without the heat
exchanger. From ( 6.7 ) and ( 6.13 ), it yields
Qt. Ve(qa-qb )/(Ee—Eo)
{ ( 6.16 )
Qm' ve * wa/( he - ho)

Qt' and Qm' are readily found if the design conditions of

the indoor and outdoor air, the animals and the building are
known. Then, the design ventilation rate Qe can be selected
based on ( 6.15 ).

Once the actual ventilation rate Qe is greater than

90

Qm', the indoor humidity he decreases until a new moisture
balance is reached, consequently, a new Qt' can be
calculated, with which Qe may be recompared. The real
humidity ratio in the building is
he = ho + ve * Wa/Qe ( 6.17 )
ASAE D271.2 ( 1979 ) recommends the following correlations:
h = 0.6219PV/( PO - PV )
{ ' ( 6.18 )
v‘= 287T/( Po - PV )
where P

O - atmospheric pressure, Pa,

).

PV - vapor pressure in Pa, ( Pv < Po
T - dry bulb temperature in Kelvin,
( 255.38 < T < 533.16 )
Applying ( 6:17 ),othe following is derived
he a ( Perho + 287Tewa )/( POQe - 461Tewa )

{ - ( 6.19 )
‘ve = ( 287 + 461hO )TeQe/( Per — 461TeWa )

It is observed that any increases in Qe will causes
decreases in both he and Ve.

When Qe is above Qt', more sensible heat is removed,
consequently, it is necessary to supply additional heat in
the building.

qsp = qb - qa + Qe( Ee - 36 )/ve ( 6.20 )
Notice that the actual Be and Ve from ( 6.19 ) should be

used in ( 6.20 ). In this case, i.e. conventional

ventilation, the criteria ( 6.15 ) becomes

91

Qe = max( Qw , Qt', Qm' )

[ ' ( 6.21 )

qSp = max[ qb " qa + Qe( Ee - Eo )/Ve, 0]

Turn to the case of the application of the heat
exchanger. When Me and ”1 are assumed equal, and qSp is
zero, it yields from ( 6.8 ) and ( 6.14 )

Qt" 3 Ve( qa ' qb )/( E:e - Ei )

{ ‘( 6.22 )

Qm" ' ve * wa/( he - hi )
Compared with ( 6.16 ), it is evident that both Qt" and Qm"
are greater than Qt' and Qm', respectively, because a part
of moisture and energy returns back into the building.

' If the correlations of Be, E1 and 80' and of he, hi and
hO are known for a given type of regenerator, Bi and hi
could be estimated. For example, for the rockbed-type like
that in this study the extrapolations of the regressing
equations ( 5.9 ) in Section 5.5 and ( 5.11 )‘in Section 5.6
may be used. Therfore, Qt” and Qm" can be estimated. The
design flow rate Qe can be determined with the first
criterion in ( 6.15 ). Then Qi can also be found since
Me = Mi .

If the actual ventilation rate Qe exceeds the moisture
control rate Qm", the following equation could be derived
( he - hi )/( .6219 + he ) = 461WaTe/PO*Qe ( 6.23 )
Applying the correlations of both enthalpy and moisture,
e.g. ( 5.9 ) and ( 5.11 ), the actual indoor humidity he

could be determined.

92

The supplemental heat qsp, when Qe > Qtf, is
qu = qb - qa + Qe( Be - Ei )/Ve ( 5.24 )
Also, Ei, Be and Ve should be their actual values based on

( 6.23 ). In this special situation, i.e. M a "1 with the

e
exchanger, the criteria in ( 6.15 ) can be replaced by

Q6 = max( Qw , Qt", Qm” )

{ ( 6.25 )

qsp ’ max[ qb ' qa + Qe( Ee --Ei )/ve' O 1

If Mi is not equal to Me, but qSp is zero, it leads to

Qt-v(qa-qb)/[(Ee‘-Eo)(1-n)l

{ ( 6.26 )

Qm=V*Wa/[ 8( lie—110)]
where the air specific volume V and the expected flow rate Q
are either Ve and Qe or Vi and Qi corresponding to the mass
flow rate Me or "1 whichever is larger. In this case, a
moisture removal factor B and a heat recovery effectiveness
n need to be estimated first. The estimation of B may be
made from correlation ( 5.6 ) if n is estimated. Values
of n may be chosen within a reasonable range if sufficient
experimental results are available for various types of heat
regenerators under various real conditions. If expected Q
used is larger than either Qm or Qt' the actual indoor
humidity he and supplemental heat qSp can be estimated based
on ( 6.5 ) and ( 6.12 ) in a way similar to those discussed
above.

In ventilation systems with exchangers, some estimation

needs to be made for design purposes. Therefore, more

93

experimental and analytical investigations are required to
obtain comprehensive knowledge about the heat exchanger
performance.

Finally, as to the design information, the local
historical climatological data should be used to determine
the outside design conditions. ASAE D270.4 ( 1979 ) and
MWPS-l ( 1980 ) recommend the use of:

l. the local low temperature exceeded more than 97.5 %
of the winter time to determine the minimum continuous air
change rate,

2. the local average daily temperature for January to
estimate the maximum winter ventilation for preventing any
net accumulation of vaporized moisture in the building,

3. the local hot weather data to calculate the maximum
design ventilation capacity for keeping the indoor
temperature the same or slightly warmer by l to 2°C than the
outdoor temperature.

It is noticed that the atmospheric humidity varies as
the climate temperature changes in accordance with seasons.
Therefore, both the outdoor temperature data and the
corresponding data of the outside relative humidity should
be selected and used in order to obtain more precise design
parameters and predict more realistic indoor environment
conditions. ASAE D309 ( 1976 ) provides the information
dealing with the monthly maps of the mean wet-bulb
temperature and the mean wet-bulb depressions over the

United States.

7 CONCLUSIONS AND SUGGESTIONS

7.1 Conclusions

The following conclusions were reached in this study:

1. The regenerative system was applicable. The heat
recovery effectiveness varied from 0.36 to 0.81, and the
moisture removal factor was of 0.24 to 0.67 during these
test days.

2. Cycle time affected the heat recovery effectiveness
and the moisture removal factor significantly. Increasing
the cycle time from 2 to 12 min resulted in a 13 2 increase
of the heat recovery effectiVeness, but a 9 % decrease of
the moisture removal factor.

3. The rockbed depth was not important in the tested
range for the heat recovery effectiveness and the moisture
removal factor. For the rockbed depth of 0.4 m or more, the
heat recovery effectiveness and the moisture removal factor
were appoximately constant.

4. Flow rates of the room exhaust and make-up air had
strong interaction on the system performance. Essentially
equal mass flow rates for both the exhaust and the make-up
air led to high heat recovery effectiveness.

5. Flattened expanded metal sheets divided the sample

rockbed into 0.1 m thick blocks, which caused a high

94

95

temperature gain up to 7°C in the make-up air, compared with
that in the other rockbed.

6. The correlation of the heat recovery effectiveness
and the moisture removal factor was found as:

8 = -0.51 * n3 + 0.61 * n2 - 1.1 * n + l
where B - moisture removal factor, decimal,

n - heat effectivenes, decimal.

Increasing the heat recovery effectiveness reduced the
moisture removal. factor significantly. In the design of a
rockbed regenerative ventilation system, both the heat
effectiveness and the moisture removal factor should be
considered. A heat recovery effectiveness about 0.5 would
be desirable.

7. Generalized balance equations of moisture and energy

in animal housing are the following :

{

where Wa - vapor production rate in housing, kg water/s,

wa = Mmax( he - n0 )8

(qa-qb)+qsp=Mmax(Ee-Eo)(l-n)

“max - either exhaust or make-up flow mass rate

whichever is larger, kg dry air/s,

qa - total animal heat production rate, kw,
qb - housing conductive heat loss, kw,
qSp - supplemental heat rate, kW.

8. Design criteria for animal housing ventilation could

be mathematically expressed :

Q

{

qsp

max( le Qt: Qm )

maxi qb-qa+wa( Ee-EO )( l-n )/[B( he-hO )],0 }

96

where Q - either Qe or Qi corresponding to Me or Mi

whichever is larger, ma/s

Qw - minimum winter control rate, ms/S.
Qt - temperature control rate, ma/S.
Qm - moisture control rate, ma/S-

7.2 Suggestions

The following suggestions were made for further study:

1. Further investigation on the effects of the” cycle
time, air flow rates and their interactions on the heat
recovery effectiveness and the moisture removal factor under
a constant rockbed depth.

2. Increasing both exhaust and make-up air flow rates
and managing mass rates of exhaust and make-up air as
similar as possible in further study.

3. Further study on the effect of mesh screen materials
on the rockbed performance.

4. Blocking up two rock bed from their bottom to avoid
short circuiting.

5. Development of effective dust filter devices for the
room exhaust air path.

6. Analysis of energy efficiency of the whole
building-ventilation system, including supplemental heaters,
solar collector, rockbed regenerator and so on, as well as
economic analysis of the system operation.

7. Study on new regenerators which recover heat but do

not recirculate moisture from the exhaust air to the room.

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