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CHAPTER 5: ACTUAL PERFORMANCE ASSESSMENT AND VALIDATIONOF SOLAR KILN MODEL
5.1 INTRODUCTION
An overall system (distributed-parameter) model for solar kilns has been
developed in the previous chapter (Chapter 4). This model is a combination of an
equipment model and a product model. The equipment model is a set of first-order
ordinary differential equations, developed from unsteady-state energy balances for
each element of the solar kiln. Possible heat-transfer mechanisms present here, such
as convection and radiation, are considered in this model. The product model consists
of a wood drying model and a stress model. The wood drying model is based on
Fickian diffusion and predicts the drying time (which is a measure of the
productivity), as well as supplying the temperature and moisture content profiles that
are inputs for the stress model. The stress model is based on the mechanical properties
of timber and predicts a product quality measure, i.e. the output is the stress and strain
developed in the timber boards during drying. The stress and strain can exceed the
limiting failure strain if the drying rate is too fast for a particular timber species,
causing the timber to crack.
The aim of this chapter is to report the actual performance of an industrial solar
kiln and to describe the validation of this overall system model for a solar kiln. Key
parameters in the system model have been measured experimentally. The predicted
outputs for this model have been compared with the measured outputs. The drying
conditions and the data collection procedures for these experiments are described, and
the results are discussed, in the following sections.
Preliminary explorations with the solar kiln model suggested that the solar energy
input is a key variable, and the measurement of this parameter is described in section
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5.2.1. The external wind speed affects convective energy losses significantly, and its
measurement is presented in section 5.2.2. Section 5.2.3 outlines the measurement of
air temperature and humidity, which are boundary conditions for the drying of timber
boards in these kilns. The data logging and acquisition system is described in section
5.2.4. The measurement procedures for the energy release rate from the auxiliary heat
exchanger, the amount of water spray and venting are explained in section 5.2.5.
Then, the important results from the kiln control system are discussed, followed by a
comparison of the model predictions and the actual measurements. Finally an
assessment of the impact of uncertainties in the solar kiln model on the predicted
drying performance has been undertaken. The uncertainties included the steam heat
exchanger output; the estimation of the initial moisture contents; the accumulation of
condensate on the floor; energy losses and the impact of various correlations for the
estimation of the sky temperature; operating variables such as heat exchanger, water
spray and venting rates; kiln design variables, thermal mass of the floor, glazing
properties; and timber properties, reference diffusion coefficient and thickness. The
effects have been assessed of some aspects of the input data quantity and quality,
specifically the boundary conditions (solar radiation, wind velocity, ambient
temperatures and humidity) averaged at different time intervals (half hour, one hour,
one day, one week) on the predicted results. These effects govern how easily the
model can be applied to predicting the kiln performance in different locations.
5.2 MATERIALS AND METHODS
The model inputs and outputs have been measured using sensors and an electronic
data acquisition and logging system during the process of timber drying in a solar kiln
at Boral Timber's Herons Creek site, NSW. Various sensors were used to measure the
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input and output variables and boundary conditions for this integrated solar kiln
model.
5.2.1 Pyranometer Selection and Installation for Solar Radiation Measurement
A pyranometer or solarimeter measures total hemispherical solar (beam and
diffuse) radiation. A secondary standard pyranometer is used for precise engineering,
research or industrial applications (Duffie and Beckman, 1991). Hence, for this
project, a secondary standard pyranometer was chosen to measure the total global
solar radiation on a flat surface. The model was a EP09 Pyranometer, Middleton Solar
Instruments, manufactured by Carter-Scott Design, Victoria, Australia. The
Middleton EP09 is a high-specification pyranometer for the measurement of solar
radiation on a plane surface (certified under the ISO 9060 Secondary Standard). The
range of irradiance measurable is 0-2000 W/m2 within the spectral range of 300-3000
nm, which covers 98% of the solar radiation spectrum (Duffie and Beckmann, 1991).
This sensor has a fast, stable and linear platinum resistance thermal sensor. The
instrument has an upward facing black receiver disk with a radial heat conduction
path for rapid signal response (less than 10 seconds for 95% signal response). An
identical (reference) disk faces into the instrument body. The temperature difference
between the disks is a direct function of the intensity of radiation absorbed by the
receiver disk. The disk temperature is determined with miniature thin-film platinum
resistance elements, which give the instrument good linearity (less than ± 0.25% non-
linearity) and stability (less than -0.6% drift each year). The sensor consists of a
cylindrical thermopile. Solar radiation is absorbed by the blackened sensor disc,
resulting in its temperature increasing. This, in turn, causes a temperature gradient
between the hot and cold junctions of the thermopile, resulting in a linear voltage
Actual Performance Assessment and Validation of Solar Kiln Model Chapter 5
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output that is proportional to the magnitude of irradiance. The voltage output signal
can be recorded using automatic data loggers or similar measuring devices. Silica gel
desiccant is used to keep the inside of the instrument moisture free.
This pyranometer was installed on a flat rigid level surface (a plywood block with
legs) using supplied nylon studs, screws, washers, nuts and springs. The legs of the
plywood block were screwed on the roof top of the control room for the solar kiln.
The heights of the feet of the pyranometer were adjusted after installation until the
bubble level was centered, to make the sensor plate perfectly horizontal. The terminal
ends of the output cable were connected to a power source and the data logger to
measure the solar radiation. The solar radiation was measured at one minute intervals
for the period of drying for each batch of timber.
5.2.2 Anemometer Selection and Installation
The anemometer for wind speed measurement was a Model AN2 (Long Arm),
manufactured by Monitor Sensors, Australia and supplied by ESIS Pty Ltd, NSW,
Australia. This model is for applications where sensitivity is important and has a
starting wind speed threshold level of 0.1 metres per second. The accuracy of the
reading was ± 2.5% of full scale, according to the manual for this sensor. This sensor
uses three conical aluminium cups and gives an approximately linear relationship
between rotational speed and actual wind speed. An internal electronic gear-box
provides a digital output as a measure of windrun. For example, one pulse represents
10 meters of windrun. The range of wind speeds that can be measured by this sensor
is 0.2 m s-1 to 40 m s-1. This cup anemometer was installed in a clear area on a two-
meter long steel pipe fixed on the ground (2 m above the ground) adjacent to the solar
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kiln. The terminal ends of the output cable were connected to the power source and
the data logger.
5.2.3 Temperature and Humidity Sensor Selection and Placement
Two stand-alone type data loggers were selected for the measurements of
temperature and humidity. The model was Tinytag Plus TGP-1500, manufactured by
Gemini Data Loggers, UK and supplied by Hastings Data Loggers, NSW, Australia.
The range for temperature and relative humidity for this type of logger is -30 to 50oC
and 0 to 100%, respectively. This small data logger has a memory for 16000 readings.
Logging is started and the data are retrieved by means of the management software,
called Gemini Logger Manager version 2.1 (OTLM). One of these Tinytag data
loggers was placed outside, to measure the ambient temperature and relative
humidity. The other Tinytag data logger was placed inside the solar kiln, to measure
the internal air temperature and relative humidity in the kiln. Both these data loggers
were set to measure the data at two or four minute intervals continuously throughout
the drying period of a particular batch of timber.
5.2.4 Electronic Data Logging and Acquisition System
A Datataker Data Logger model DT505, manufactured by the Data Electronics Pty
Ltd, Australia and supplied by ESIS Pty Ltd, NSW, Australia, was used with the De-
Terminal for Windows software system. Once programmed, this datalogger can be
left alone to acquire and log data from various sensors connected to it. Ten differential
channels and thirty single-ended channels can be used for ten or thirty sensors,
respectively. This datalogger was powered from a main power source in the solar kiln
control room. The data were logged into the internal memory and 1MB PC Card
(PCMCIA) and later sent to a laptop computer for further analysis. Up to 360,000
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readings can be stored in the 1 MB PC Card. The sensor types and the functions of
those sensors are shown in Table 5.1.
Table 5.1: Sensor names and channel numbers for the data loggers.
Channel numbersof Datataker
datalogger andother dataloggers
Sensor type Function/componentname
Unit
Analog - 1 Thermocouple Heat exchangertemperature
oC
Analog - 2 Anemometer Wind speed m/sAnalog - 3 Solarimeter Solar radiation W/m2
Digital - 1 Digital output Heat exchangerstatus
1 and 0
Digital - 2 Digital output Venting status 1 and 0Digital - 3 Digital output Water spray status 1 and 0Tinytag 1 Temperature and
relative humidityInternal air in the
solar kilnoC and %
Tinytag 2 Temperature andrelative humidity
External air(ambient)
oC and %
The type of thermocouple sensor used for measuring the heat exchanger
temperature in the solar kiln, was a Type 'K', General Purpose Sensor (GPA) with
mineral insulated cable, sheathed with 310 SS (stainless steel), with extension leads
made of fibreglass, manufactured and supplied by Pyrosales Pty Ltd, Australia. The
thermocouple tip was placed and attached to the surface of the steam inlet pipe of the
heat exchanger. A calibration was performed using ice and boiling water. This
calibration indicated a zero offset of 2oC, i.e. 2oC for ice and 102oC for boiling water.
This offset was corrected for the data used here.
The blackbutt (Eucalyptus pilularis) timber species was selected for this study
since the species represents 90% of the total processing throughput from Boral
Timber's Heron's Creek operation (industrial observation). Physical and mechanical
properties of this species have been measured in Chapter 2, and an optimised drying
schedule for this species has also been produced in Chapter 3. Thus this choice of
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material is consistent with earlier work in this thesis. The moisture contents of timber
were determined based on oven drying of small biscuit samples and the weight
reduction of kiln samples compared with the estimated oven-dry weight of the kiln
samples. The sample preparation procedure for the determination and monitoring of
the moisture content is explained in section 5.3.1.
5.2.5 Measurements of the Heat Exchanger, Water Spray and VentingPerformance
The determination of the total energy input is required for the solar kiln model
simulation. The energy input consists of solar energy and additional auxiliary heat
energy. The auxiliary heat energy is supplied from a wood-waste fired boiler and
steam system. The amount of steam that is used in the solar kiln has been determined
by measuring the amount of condensate collected from the outlet of the heat
exchanger for a particular time period. The status of the heat exchanger, which was
controlled by a solenoid valve, was recorded as "on" or "off" through a data logging
and control system. Thus it is possible to estimate the amount of heat energy entering
the solar kiln from the auxiliary heating system.
There is a primary vent with a 0.2 kW fan in the solar kiln, which is used to
control the relative humidity of the internal air. It was necessary to measure the
velocity of the air through the primary vent opening and the size of the vent to
determine the flow rate of air leaving the kiln. There is also a secondary vent (without
any fan) in the solar kiln to draw fresh air from outside. In addition, the air velocity
and the size for the secondary vent were measured for determining the flow rate of air
for this secondary vent opening. The water spray is used to control the humidity of the
internal air of the kiln, and the amount of water spray was measured.
Procedure
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Steam was passed through the heat exchanger for the solar kiln, and the heat
exchanger was manually switched "on" for the measurement. This steam condensed
and passed through a steam trap to the condensate water line. The outlet of the steam
trap was disconnected from the condensate water line and put in a bucket. A stop-
watch was used to measure the time. A graduated cylinder was used to measure the
amount of condensate after collecting it in a bucket for particular time intervals. The
steam pressure was recorded from the pressure gauge placed just before the inlet of
the solar kiln heat exchanger. The results are shown in Table 5.2. The status of the
heat exchanger, whether it is "on" or "off", can be recorded every minute through the
data logging and control system.
Table 5.2: Measurement of condensate water from the heat exchanger.
Readingnumber
Time (minutes) Amount ofcondensatewater (litre)
Volumetric rateof condensate
(l/s)
Steampressure
(kPa)1 5 12.4 0.041 1002 4 13.85 0.057 2003 1 3.3 0.055 5004 1 4.1 0.068 5005 1 4.5 0.075 500
The volumetric flow rate of condensate in l/s is equivalent to the mass flow rate in
kg/s for this case, assuming that the density of condensate water is around 1000
kg/m3.
The boiler was started in the early morning before the experiment. Initially the
pressure was low, and it was easy to collect the amount of condensate water for five
minutes. However, later the steam pressure reached its maximum value for the system
and it was very difficult and unsafe to collect the very hot condensate for more than a
minute. That is why, after the second reading, the amount of condensate was collected
for one minute. Since the pressure increased after the third reading, the first two
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readings have been ignored. Thus the average volumetric flow rate for the condensate
from the heat exchanger over the last three readings was 0.066 l/s, equivalent to 0.066
kg/s. The steam pressure was 500 kPa. At 500 kPa pressure, the latent heat of
condensation is 2107.4 kJ/kg from Felder and Rousseau (1986). Based on these data,
the rate of energy released from the heat exchanger is 139 kW if the heat exchanger is
"on". This rate has been calculated by multiplying the flow rate of condensate water
by the latent heat of condensation. However, there may be significant uncertainties,
since there would have been substantial energy losses from about 150 m of the
unlagged steam pipes between the boiler and the kiln.
A hand-held vane anemometer was used to measure the air velocity near the
primary vent. The primary vent is fitted with a 0.2 kW fan. This vent is electronically
controlled to regulate the humidity in the solar kiln. The anemometer was held at a
number of positions at this vent opening, and the results are shown in Table 5.3.
Table 5.3: Air velocity for the primary vent (opening size 30×30 cm) with a 0.2 kWfan.
Reading number Air velocity (m/s)1 4.362 5.933 6.314 4.495 5.766 5.61
Average 5.41
The volumetric flow rate has been estimated by multiplying the velocity by the
size of the vent opening. The mass flow rate of air has then been estimated by
multiplying the volumetric flow rate by the density of air. The average air velocity for
the primary vent was 5.4 m/s. This velocity has been used to determine the mass flow
rate of air, which is 0.486 kg/s assuming that the density of air is 1 kg/m3. Damp air
left the solar kiln through this vent. The primary vent opens automatically when the
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relative humidity of the internal air is above the set point and closes when the relative
humidity of the internal air is below the set point.
The secondary vent is the same size as the primary vent but has no fan. This vent
should open only for the intake of fresh air from the outside when there is a suction
effect due to the forced expulsion of damp air by the primary vent. However, in
reality this vent is open continuously because of corrosion in the bearings. The air
velocity was measured for two conditions. For the first two readings, the primary vent
was kept open and the outside air entered at a relatively high velocity through the
secondary vent in the solar kiln. For the second condition, the primary vent was
closed and the outside air entered at a lower velocity through the secondary vent. The
results are shown in Table 5.4. Air still enters through the secondary vent when the
primary vent is closed because leakage occurs from the kiln, particularly in front of
the fans.
Table 5.4: Air velocity for the secondary vent (opening size 30×30 cm) (without anyfan).
Velocity (m/s) Velocity (m/s) Mass flow rate (kg/s)Number ofreadings Primary vent
openPrimary vent
closedPrimary vent
openPrimary vent
closed1 2.82 0.67 0.25 0.062 2.98 0.83 0.27 0.07
Average 2.9 0.75 0.26 0.067
The mass flow rate has been calculated for the secondary vent opening size of 0.09
m2 and an air density of 1 kg/m3. The average mass flow rates of air entering through
the secondary vent were 0.26 kg/s and 0.075 kg/s when the primary vent was in the
open and the closed positions, respectively. Since the secondary vent is open all the
time due to a mechanical fault, some energy may be lost due to this vent, when the
outside air is wetter than the inside air. However, this condition is rare. The primary
vent only expels air outside, since it is fitted with a fan. Thus the overall venting
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amount (primary vent open) is the difference between the primary and the secondary
vents, (0.48-0.26), or 0.22 kg/s.
The flow rate for the water spray has been determined. There are four small
diameter nozzles in the solar kiln to spray water in order to control the humidity. The
amount of water sprayed for three-minute time intervals through one nozzle was
collected and measured for two runs, which gave exactly the same results (0.26 litres
in 3 minutes).
Hence, the average water spray rate for one nozzle is 0.0014 kg/s, assuming that
the density of water is 1000 kg/m3. Since there are four nozzles in the solar kiln, the
average water spray rate (total) is 0.0056 kg/s.
5.2.6 Drying Runs
Four complete drying runs were studied for general performance assessment. Data
were collected on temperatures and humidities of internal air and the moisture content
of the timber batch based on the kiln samples. The drying runs were used to test
various parts of the data-logging system.
The fifth experiment was conducted to collect all the key inputs and outputs of the
simulation for validation purposes. The key inputs to the simulation were the solar
radiation intensity, the wind velocity, the status and the surface temperature of the
heat exchanger, the status of the water sprays and the vents, and the external boundary
conditions (ambient temperatures and humidities). The key outputs from the
simulation were the temperatures and humidity of the internal air of the kiln and the
moisture contents of the timber as functions of time. These data have been used to
validate the complete solar kiln model.
5.3 ACTUAL PERFORMANCE: RESULTS AND DISCUSSION
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The actual performance of this solar kiln is presented first, followed by the model
validation and the assessment of uncertainties.
5.3.1 Actual Performance
The actual temperatures and relative humidities of the internal air, and the timber
moisture contents, at various time intervals for the first, second, third and fourth
drying batches are shown in Figures 5.1, 5.3, 5.4 and 5.5, respectively.
Figure 5.1: The actual performance of the solar kiln for drying run 1.
The first batch of timber was dried in the solar kiln from 5 May 2000 to 29 June
2000. The actual temperature 'T' and relative humidity 'RH', compared with their set
points 'Tset' and 'RHset', respectively, are shown in Figure 5.1. The initial average
moisture content 'X' was about 55% with a standard deviation of 7.9%. The
coefficient of variation for the moisture contents from the oven-dried biscuit samples
(the standard deviation is divided by the average) was initially 0.14. This moisture
content was determined using small biscuit samples of 20 mm long from two sides of
0
20
40
60
80
100
0 10 20 30 40 50 60Time (days)
T (o C
) & R
H (%
)
0
10
20
30
40
50
60
Moi
stur
e co
nten
t (%
)
T RH Tset RHset X
Actual Performance Assessment and Validation of Solar Kiln Model Chapter 5
259
a kiln sample of 300 mm long, taken from a representative board of the timber stack,
as shown in Figure 5.2.
Biscuits
30 cm
Kilnsample
2 cm
Figure 5.2: Sample preparation for biscuit samples in the solar kiln experiments.
Eight such samples were collected from eight boards taken from the whole batch
of timber. These biscuit samples were weighed on a top pan balance and then dried in
an oven set at 105oC for 24 hours. The moisture content was estimated based on the
dry weight and the initial green weight.
The kiln samples were also weighed on a top pan balance. The dry weight of the
kiln samples were estimated based on the moisture contents of the biscuit samples
assuming that these represent the kiln samples, so the initial moisture contents of the
kiln samples were assumed to be the same as those of the biscuit samples. Eight kiln
samples were placed at strategic locations in the solar kiln (three samples at both the
front and rear ends, and two samples in the middle of the kiln; about two metres
above the kiln floor). Each kiln sample was regularly weighed during the drying test,
and the moisture contents were calculated based on the estimated dry weights. This
location of kiln samples is the standard industrial practice in many timber companies.
The moisture content reported here is the average of eight samples, which are taken to
represent the whole batch of timber. The final average moisture content of this batch
of timber after 55 days of drying was about 16%.
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The actual temperatures and relative humidities cycled up or down due to day-
night variations in weather conditions. The actual temperature of the air was close to
the set point temperature during the first two weeks but later deviated much more
from the set points. The heat exchanger was used to provide additional heat input
when there was no solar energy available. However, during nights, weekends and
holidays, the boiler was shut down, and no additional heating was available.
The kiln control was poor for both relative humidities and temperatures (in this
first run) if the actual relative humidities and temperatures are compared with set
point relative humidities and temperatures. The quantification of control quality is
carried out and shown in the next section. The integrals of absolute errors for the
temperatures and relative humidities were 9.7oC and 11.8%, respectively, which were
the highest of all the five runs. The drying curve suggests the drying rate was
reasonably fast (55 days for 40% reduction in moisture content), compared with open-
air drying (55 days for 20% reduction in moisture content, from an initial moisture
content of 60% to a final one of 40%). The drying times for all five runs are shown in
Table 5.5.
Table 5.5: Drying time comparisons for various runs.
Drying run number Average initialmoisture content
(%)
Average finalmoisture content
(%)
Drying time (days)
1 55 16 552 62 22 553 50 20 424 43 12 1195 53 19 74
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Figure 5.3: The actual performance of the solar kiln for drying run 2.
The second batch of timber (Figure 5.3) was dried from 5 July 2000 to 29 August
2000. The kiln control was not very good for temperature, because the temperature
was almost always significantly below the set points, 10 to 20oC lower, particularly at
night. The integrals of absolute errors for both the temperatures and relative
humidities were 7.5oC and 6.4%, respectively, lower than run 1. The drying time was
55 days from an initial moisture content of 62% to a final moisture content of 22%.
The third batch of timber (Figure 5.4) was dried from 1 September 2000 to 20
October 2000. The qualities of control for the temperature and humidity were both
poor, since the maximum difference between the actual and set point temperatures
was about 20oC, and between actual and set point humidities the maximum difference
was about 30%. The temperatures were 10oC to 15oC above the set points during the
day for the first few weeks. A more aggressive drying schedule was tested for drying
this batch of timber. The schedule was more aggressive in the sense that the set points
0
20
40
60
80
100
0 10 20 30 40 50 60Time (days)
T (o C
) & R
H (%
)
0
10
20
30
40
50
60
70
Moi
stur
e co
nten
t (%
)
T RH Tset RHset X
Actual Performance Assessment and Validation of Solar Kiln Model Chapter 5
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for temperatures and relative humidities for this time-based schedule were higher and
lower, respectively, than other schedules. For example, after the second week, the set-
point temperature was increased to 35oC compared with 30oC for the previous drying
schedules. The ambient conditions were also harsher compared with the ambient
conditions for other runs. For example, the highest ambient temperature was recorded
as 46oC on October 20, 2000 at 12:22 pm. At this time, the highest solar energy was
recorded (1217 W/m2) for this run. This highest temperature is comparable with the
reported annual maximum of 44oC for Wauchope State Forest's weather station in
NSW (18 km away from the test site) during the month of November (Bureau of
Meteorology, 2000). The internal air conditions of the kiln are influenced by the
ambient ones, so the ambient temperature is relevant here. The drying rate was faster,
i.e. after 42 days, the moisture content reduced from 50% to 20%, compared with the
first and the second batches, which took 55 days for a similar reduction in moisture
content.
Actual Performance Assessment and Validation of Solar Kiln Model Chapter 5
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Figure 5.4: The actual performance of the solar kiln for drying run 3.
The drying of the fourth batch of timber (Figure 5.5) was performed from 9
November 2000 to 7 March 2001. The timber was left in the solar kiln during the
yearly close down during the months of December to January. No steam heating was
available at those times. For about eight weeks (the time from the fourth to the twelfth
week), the kiln was set at a temperature of 35oC and 80% relative humidity. That is
why the drying time was 119 days for a 31% reduction in moisture content, for an
initial moisture content of 43% to a final one of 12% (Table 5.5). The control quality
was better than for other batches because the kiln was run with a lower dry-bulb
temperature of 35oC for about eight weeks, when the ambient temperature was also
relatively higher (a maximum of about 35oC in Figure 5.9) compared with other
batches. The integrals of the absolute errors for temperatures and relative humidities
were 5.1oC and 7.9%, respectively, lower than all other runs.
0
20
40
60
80
100
0 10 20 30 40 50 60Time (days)
T (o C
) & R
H (%
)
0
10
20
30
40
50
60
Moi
stur
e co
nten
t (%
)
T RH Tset RHset X
Actual Performance Assessment and Validation of Solar Kiln Model Chapter 5
264
Figure 5.5: The actual performance of the solar kiln for drying run 4.
In summary, the kiln control was not very good for every batch of timber studied.
However, the solar kiln reduced the drying time from six months to three months for
predrying compared with open-air drying (as practiced conventionally). The drying
quality was judged to be better than open-air drying because of the protection from
direct sun and rain. The recovery was about 2% higher, which is equivalent to 320 m3
per year of dry timber assuming the board mill capacity is 16000 m3 per year, since
the exposed top layer in open-air drying is generally damaged due to direct sun and
rain. This recovery is equivalent to an annual monetary value (not selling value) of
AUS $480,000 for the processing of 960 m3 of green logs (which produce 320 m3 of
dry timber), assuming that the log purchase and conversion costs are about $500 per
m3. However, some improvements in the kiln design (e.g. better kiln control, more
appropriate water spraying design and venting amounts, the use of an appropriate heat
exchanger) may be desirable for better operation and control. Appropriate operating
0
20
40
60
80
100
0 20 40 60 80 100 120 140Time (days)
T (o C
) & R
H (%
)
0
10
20
30
40
50
Moi
stur
e co
nten
t (%
)
T RH Tset RHset X
Actual Performance Assessment and Validation of Solar Kiln Model Chapter 5
265
procedures (e.g. an optimised drying schedule, fan operation strategies etc) are also
necessary for the solar kiln.
5.3.2 Assessment of Control Systems
The performance of the kiln control system was assessed after calculation of the
integral of absolute errors and the integral of the root mean square errors. These errors
quantify control performance (Stephanopoulos, 1984). The errors were calculated for
the deviations between the actual values and the set points for temperature and
relative humidity of the internal air, using the following equations. The integral of the
absolute value of the errors (IAE) is given by:
IAE =
∫
∫ ∈
T
0
T
0
dt
dt)t( (5.1)
Where T is the total time. The integral of the squared errors (ISE) is calculated by:
ISE =
∫
∫∈
T
0
T
0
2
dt
dt)t( (5.2)
The error function ∈(t) is defined as:
∈(t) = ysp(t) - y(t) (5.3)
Here ysp is the set point, y is the actual values of the variable, and t is the time. The
calculated errors are shown in Table 5.6.
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Table 5.6: Integrals of the errors for the control system.
Run number Integral ofabsolute errors
for T (oC)
Integral of rootmean square
error for T (oC)
Integral ofabsolute errors
for RH (%)
Integral of rootmean squareerror for RH
(%)1 9.7 12.5 11.8 14.32 7.5 9.4 6.4 8.03 6.2 7.8 8.1 9.774 5.1 6.4 10.1 12.25 4.7 6.9 7.9 11.2
Generally the smaller these errors are (the closer to zero), the better the quality of
the control. The temperature control was best for run 5, having the lowest value of the
integral of absolute errors. The integral of absolute errors decreased from run 1 to run
5. The integrals of the root mean square errors showed a similar trend except for run
5, which gave a slightly higher root mean square error than that for run 4. This means
that the temperature control was better for the later runs. This improvement is likely
to be due mainly to seasonal variations, in the following sense. Runs 1 to 3 were
carried out over the winter months, whereas runs 4 and 5 were carried out over the
summer months. The lower ambient temperatures over the winter months affected the
internal conditions. The temperature of the internal air was much lower than the set
points many times during the winter months. Another reason for the poor control
quality for runs 1, 2 and 3 may be that these batches were dried with a schedule that
changed the lower starting temperature (i.e. 25oC) to a higher temperature after only a
week or two. In comparison, runs 4 and 5 used a drying schedule that had a lower
starting temperature for a longer time (i.e. 3 to 7 weeks). The temperature control is
better for lower temperatures, since this low temperature control can be achieved
without additional heat input. There was no additional heating during weekends, at
night and in the holidays. The control of relative humidity was better for runs 2 and 3
compared with runs 1, 4 and 5 since both absolute errors and root mean square errors
Actual Performance Assessment and Validation of Solar Kiln Model Chapter 5
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were higher for run 1, 4 and 5 than that for runs 2 and 3. The measured ambient
temperatures and relative humidities for runs 1 to 4 are shown in Figures 5.6 to 5.9.
The ambient temperatures were relatively low for run 1 compared with run 4 because
run 1 was carried out over typical winter months, and run 4 was performed over
typical summer months.
It is possible that the poor quality of control, particularly in the beginning of
drying (too high temperatures and too low humidities compared with the set points)
may affect the drying quality. However, there was no significant correlation found
between the drying quality (for structural grade timber) and the quality of control.
This implies that improving control quality is not, in this case, such a high priority as
improving the set points for control, which are the drying schedules. In other words,
set-point tracking is not a critical issue.
These figures (5.6 to 5.9) for the ambient conditions may be compared with
Figures 5.1 to 5.5, which show the conditions inside the kilns. The average increases
in air temperatures for the kiln (compared with ambient conditions) were 17.3oC,
13.8oC, 10 oC, and 8.2oC (for runs 1 to 4), respectively, while the average decreases
for relative humidities (kiln - ambient) were 21.8%, 15%, 21.9%, and 23.9% for runs
1 to 4, respectively. These figures show the overall enhancement in the severity of
drying conditions inside solar kilns. Run 4 is particularly significant, since very little
steam heating was used in this experiment, so the 8oC increase in air temperature
cannot be attributed to the use of steam, but is due to solar input alone.
The significance of the temperature differences in terms of drying times can be
assessed approximately in the following way. The activation energy in the drying
model was found to be 3730 K in section 2.5, and this parameter quantifies the
temperature dependency of the diffusion coefficient. For example, the diffusion
Actual Performance Assessment and Validation of Solar Kiln Model Chapter 5
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coefficient at 30oC is likely to be 5.1×10-11 m/s2, about 1.5 times greater than that at
20oC (3.3×10-11 m/s2) according to equation (2.3) in Chapter 2. This difference in
diffusion coefficient is then likely to be reflected in a corresponding reduction in
drying time at 30oC compared with 20oC, since the constant-coefficient solution of the
diffusion equation (McCabe and Smith, 1976) indicates that the drying time is
inversely proportional to the diffusion coefficient. Hence the (kiln - ambient)
temperature differences of around 10oC are likely to enhance drying throughputs by
approximately 50%. The reduction of predrying time from about six to eight months
by air drying to two months by solar kiln drying for 25 mm thick boards is also
consistent with this explanation, since this increase in productivity is over 50%.
Figure 5.6: The ambient temperatures and relative humidities for run 1.
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Figure 5.7: The ambient temperatures and relative humidities for run 2.
Figure 5.8: The ambient temperatures and relative humidities for run 3.
Figure 5.9: The ambient temperatures and relative humidities for run 4.
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5.4 MODEL VALIDATION: RESULTS AND DISCUSSION
From a production viewpoint, the drying time is the key output of this model and
needs to be compared with the experimental data. The drying rate and time are
strongly influenced by the air temperature and humidity, so these variables are also
key points of comparison.
5.4.1 Actual Data and Base Case Comparison
The actual temperatures 'T', the set-point temperatures 'T Set', the actual relative
humidities 'RH', and the set point relative humidities 'RH Set' of the internal air and
the moisture contents for the whole drying regime of a batch of timber in a solar kiln
are shown in Figure 5.10 for the fifth run. The actual ambient conditions
(temperatures and relative humidities) are shown in Figure 5.11. These data were
collected from March 14 to May 25, 2001. The average increase in air temperatures
for the kiln (compared with ambient conditions) was 7.4oC for run 5, while the
average decrease in relative humidities (kiln - ambient) was 22% for this run. It is
necessary to distinguish between the initial period, when no heating was used (until
30 days) and the final period, when the heat exchanger was used heavily, since the use
of the heat exchanger increases the kiln temperature and decreases the relative
humidity in the kiln air compared with the ambient air. The average differences in the
temperature and relative humidity were 5oC (increase) and 19% (decrease),
respectively, for the initial period until 30 days when there was no additional heat
input. In comparison, these averages were 9oC and 24% for the later period when the
heat exchanger was used heavily.
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Figure 5.10: Actual and set point temperatures and relative humidities and moisturecontents as function of time for the fifth run.
Figure 5.11: The ambient temperatures and relative humidities for run 5.
5.4.2 Heat Exchanger Input and Moisture Content Measurement
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The energy release rate of 139 kW from the heat exchanger was measured by
collecting the condensate from the outlet of the heat exchanger. Simulated internal air
temperatures, relative humidities and timber moisture contents for 139 kW heat input
and the corresponding actual measurements are shown in Figure 5.12. However, this
condensate also included heat losses in the 150 m of piping up to the kiln, so 139 kW
is an upper estimate for the heat release rate. It therefore seems reasonable to assess
the impact of decreasing the estimated heat release rate on the agreement between the
simulation predictions and the measurements. Figure 5.13 shows the effect of halving
the estimated energy release rate to 69 kW, with better agreements between simulated
and measured air temperatures, humidities and between simulated and measured
moisture contents. The agreements between simulations and experiments for moisture
contents, air temperatures and relative humidities will now be reviewed. The model-
experiment mismatch will be reviewed in subsequent sections.
Figure 5.12: Simulated internal air temperatures, relative humidities and timbermoisture contents with actual measurements (139 kW heat exchanger output).
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Actual TPredicted T
Actual XPredicted X
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Figure 5.13: The effect of a reduced energy release rate from the heat exchanger (69kW) on the agreement between the simulation predictions and the measurements.
In terms of the time required for a complete simulation, the computational time
was about 48 hours for 74 days real time simulation on a PC (500 MHz clock speed
with a Pentium III processor and 192 MB RAM) (the base case). However, this
computational time may be lower on a workstation, depending on the clock speed of
the computer. For example, the speed is double on a DEC Alphastation 500/333.
Moisture Content
There is little difference between Figures 5.12 (139 kW) and 5.13 (69 kW) until 40
days in terms of drying, because the heat exchanger was used very little until that
point in time. After 40 days, Figure 5.12 (139 kW) shows that the predicted drying
rate (the slope of the moisture content against time curve) is much greater than that in
reality. The overall result is a much lower predicted final moisture content (0.12
kg/kg) than that actually measured (0.20 kg/kg). The predicted air temperatures for
this case (139 kW) are much higher than those measured, particularly during the
period when the heat exchanger is on, by a maximum of 40oC.
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Actual T Actual RH Predicted T Predicted RH Actual X Predicted X
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Reviewing Figure 5.13 now, there is still a difference between the actual and the
predicted moisture contents. The maximum difference between the actual and
predicted moisture contents for this case of a lower heat exchanger output was 0.05
kg/kg. The consequence of lower predicted air temperatures in the initial stages of
drying (than the measurements), as seen in Figure 5.13, is that the predicted drying
rates should be lower than in reality, whereas higher predicted air temperatures than
measured at the end of drying (also in Figure 5.13) should mean higher drying rates
than in reality. Reviewing the slopes of the actual and predicted moisture contents as a
function of time, in Figure 5.13, shows that there is some evidence of this situation.
Initially, the slope of the moisture content against time curve, which is the drying rate,
is lower than the actual slope (or drying rate), so this situation is consistent with the
lower predicted air temperatures (than in reality). Again, at the end of drying, the
higher predicted air temperatures (than in reality) are consistent with the higher
predicted slope of the moisture content against time curve than the actual slope of the
measured moisture content against time curve.
The halved energy release rate gives much better agreement between simulated
and measured moisture contents. The agreement between the simulated and the
measured air temperatures is also more reasonable than for the 139 kW heat
exchanger output. The remaining disagreements for moisture contents and air
temperatures between the simulations and the experiments are self consistent, in the
sense that when the predicted drying rate is lower than the actual one, the predicted
air temperature is higher than the actual temperature. Since there are uncertainties in
the measurement of moisture contents, this measurement is now explained.
Uncertainties in Moisture Content Measurement
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There may be some uncertainties in the measurement of the moisture content. The
procedure for moisture content measurement has been explained in section 5.3.1. The
sampling preparation technique for biscuit samples for oven-drying and kiln samples
for kiln monitoring is shown in Figure 5.2. The range of moisture contents for eight
samples and their average for the fifth run are shown in Figure 5.14.
Figure 5.14: Actual moisture contents of eight samples for the fifth run. The variationis the coefficient of variation (standard deviation/mean) in percent.
The moisture contents at the beginning of drying are the results of averaging eight
biscuit samples that have been oven-dried at 105oC for 24 hours. These values ranged
from 43 to 72%. After the start of drying, the moisture contents are the loss of water
from eight larger kiln samples based on their estimated oven-dry weights. This oven-
dry weight was estimated based on the moisture content of the biscuit samples, which
are assumed to be representative of the kiln samples. These biscuit samples were
taken from the same board from which the kiln samples were taken. There may be
some uncertainty from the third week in the moisture content measurements because
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Moi
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)
Sample 1 Sample 2 Sample 3 Sample 4 Sample 5Sample 6 Sample 7 Sample 8 Average Variation
Biscuit samples
Kiln sample boards
Variation
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of this change in the estimation process from biscuit samples to kiln ones. However,
this is accepted practice in the timber drying industry to represent the average
moisture content of a whole batch of timber. Hardwood drying kilns are often
controlled based on this method of moisture content measurement. In this case, the
average moisture contents were calculated based on the kiln samples after drying for
three, four, seven, nine, ten and eleven weeks. The standard deviation ranged from 2
to 9% for eight samples, and the coefficient of variation (standard deviation/mean)
was 6 to 19%. The variation among eight biscuit samples was very high in the
beginning, since there was a mixture of boards with various apparent initial moisture
contents from 43 to 72%. These measurements in the beginning were the actual
measurements of biscuit samples by the oven-drying method, whereas the rest of the
measurements from the third week are the estimated moisture contents of the kiln
samples. The variation reduced over time to 7%, since various boards dried
differently (e.g. sample 2 dried faster than sample 6). The variations are shown as
error bars in Figure 5.13.
Now looking at Figure 5.13 again, the mismatch between the model predictions
and measurements at different times may be reviewed. For example, the model
predictions are consistently higher than the measurements, but only slightly outside
the error bars at 20 days and 60 days, and very close to the error bars at 70 days.
There is a significant difference at 27 days and 48 days.
The uncertainty (relatively large) in the initial moisture content may be
responsible for the consistently higher predicted moisture contents than in reality.
This means that the assumed initial moisture content (in the predictions) could have
been lower than the assumed value, resulting in much better agreement between
model predictions and experimental measurements. This can explain a large part of
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the mismatch. Even if the uncertainty in the initial moisture content were half of the
estimated value used, then such a halved uncertainty would still mean that the model
predictions would agree much better with the measurements. The effect of different
initial moisture contents on the predicted final moisture contents is shown below.
Initial Moisture Content
During the simulation shown in Figure 5.13, an average initial moisture content of
53% for eight biscuit samples (using oven-drying method) was used. However, the
actual range of moisture contents was 43 to 72% and the standard deviation was 9%.
This simulation aimed to investigate the effect of a lower initial moisture content on
the final moisture content achieved.
An initial moisture content of 44% was assumed in this simulation, representing
the likely lowest (within the standard deviation) green moisture content for some
boards of this batch of timber. The effect of this change in initial moisture content on
the drying behaviour can be seen in Figure 5.15, which shows the agreement between
the model predictions and the measured moisture contents is much better for this
simulation compared with the base case prediction. The predicted final average
content was 0.1844 kg/kg for this simulation compared with the base case prediction
of 0.2101 kg/kg and the actual value of 0.20 kg/kg.
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Figure 5.15: The effect of the initial moisture content of the board on the drying rate.The overall drying rate of the timber decreases from an average of 0.004 kg/kg per
day (when starting from an initial moisture content of 53%) to 0.0032 kg/kg per day
when starting from 44%. When an initial moisture content of 44% is used, the timber
moisture content reduced to 19%, slightly below the actual moisture content (20%).
At a lower moisture content inside the timber (above the fibre saturation point), the
humidity just above the surface of the timber is further from the saturation value than
at lower moisture contents. Hence the difference between the absolute humidity
directly above the surface of the timber (which is a function of the temperature and
moisture content at the surface) and the bulk air is smaller for the lower initial
moisture content compared with the base case simulation. Therefore a smaller driving
force for drying occurs with an initial moisture content of 44%, resulting in a lower
drying rate for a lower initial moisture content until the fibre saturation point. If there
was no difference in drying between these cases, then the drying curves for the lower
initial moisture content and the base case in Figure 5.15 would be expected to be
exactly parallel.
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The difference between the energy requirement between chemically and
physically bound water and free water is the heat of sorption, which is a maximum of
100 kJ/kg for drying from an initial moisture content of 30% to a final moisture
content of 21% (Keey et al., 2000). The higher energy requirements for drying timber
with an initial moisture content of 44% is another reason for the slower drying rate of
this timber compared with the base case prediction.
Since halving the heat exchanger output gives much better agreement for the
trends as shown in Figure 5.13, the halved energy release rate (69 kW) will be
referred to as the base case from here onwards. There is still a mismatch between the
model prediction and the actual measurements for the temperatures and the relative
humidities of the internal air and also the moisture contents. This discrepancy for the
initial moisture content can be largely explained due to the significant variation in the
measurement of initial moisture content. The predicted temperatures and the
humidities of the internal air are compared with the measurements in the following
sections.
Air Temperature Comparisons
The agreement between the predicted and measured temperatures of the internal
air is reasonable, and both the predictions and measurements have a similar cyclical
pattern, with the predicted temperatures being lower in the beginning than the
measured ones. The predicted temperatures were lower initially, with a maximum
difference of about 10oC between the predicted and measured temperatures until 27
days after the start of drying. During this time, there was no additional heat input,
because the boiler was shut down during the April holidays. After 27 days, there was
an additional heat input from the steam for a few days. The heat exchanger was again
"on" only during the day from 40 days until the end of drying. During workdays, the
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boiler is shut down around 10:00 pm. The predicted temperatures were higher than the
actual temperatures when the heat exchanger was used for additional heat input. The
maximum difference between the predicted and the measured temperatures was 5oC
(better than with 139 kW assumed output from the heat exchanger).
Relative Humidity Comparisons
The agreement between the predicted and measured relative humidities was better
at the beginning of the drying run (until 43 days) than the later period of drying when
the heat exchanger was continuously used for additional heat input. The predicted
relative humidities were a little higher than the actual ones in the beginning. Initially,
the maximum difference was between 10 to 15%. However, after about 44 days, the
predicted relative humidities were much higher than the actual relative humidities.
The maximum difference during this period was 20 to 25%. The actual status of the
heat exchanger is shown in Figure 5.16. It is evident from the graph (Figure 5.16) that
the heat exchanger was not "on" until 43 days, except for brief period around the 27th
day.
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Figure 5.16: The actual status of the heat exchanger.
Quality Prediction
Heat Exchanger Input
There is a stress-strain model integrated within the solar kiln model, which
predicts the instantaneous stress and strain experienced by the timber boards during
drying. The developed stresses and strains in timber boards during drying indicate a
measure of product quality. The strain model has been explained in section 2.2.3.
Figure 5.17 shows the predicted instantaneous strain (according to equation (2.13)) in
timber for both higher (139 kW) and lower (69.5 kW) energy outputs from the heat
exchanger.
Figure 5.17: The predicted instantaneous strains for two heat inputs.
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There is no difference between two strains until 27 days because the heat
exchanger was not used until that point in time. The strain was predicted to develop
after four days of drying (in both cases) because the predicted moisture content of the
board surface was 0.298 kg/kg and started to reduce below the fibre saturation point
(0.30 kg/kg). However, the average board moisture content at that point in time was
0.5041 kg/kg. There is a cyclical trend in the strains and stresses due to variations in
the diurnal temperatures and humidities, which resulted in variations in internal air
temperatures and humidities, i.e. variations in drying conditions. The maximum
instantaneous strain developed for the higher energy input was 0.0217 m/m, and it
was a little lower (0.0215 m/m) for the lower energy input. The reason for the
development of the different strains is because of the different drying rates. The
drying rate was higher when the heat exchanger was assumed to release 139 kW of
energy, which increased internal air temperatures by 25oC compared with the lower
heat input of 69.5 kW. The drying rate and the diffusion coefficient increase with an
increase in temperature, since the diffusion coefficient is a temperature-dependent
parameter. The predicted maximum instantaneous stresses were 6.0 MPa and 5.9 MPa
for 139 kW and 69.5 kW heat exchanger outputs, respectively. The average failure
strain for three samples was 0.015 m/m from the mechanical test described in Chapter
2 but analysis in Chapter 3 (section 3.5) indicates that strains up to 0.04 m/m may not
damage the timber too severely. The limiting instantaneous strain was 0.018 m/m for
ironbark timber when an optimised drying schedule was developed by Langrish et al.
(1997). The failure strain for green radiata pine samples at room temperature was
0.049 m/m as reported by Keep (1998). The predicted maximum strain here compared
with the limiting strain values from the analysis in Chapter 3 (section 3.5) indicates
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that the drying quality from this solar kiln is likely to be good (e.g. largely free from
surface checks). It was observed for a drying run that the number of surface checks
was about 40% lower on the dried timber in solar kilns compared with the air-dried
boards (for few sample boards).
Initial Moisture Contents
The effect of the initial moisture content on the predicted instantaneous strain
levels (Figure 5.18) is that above the fibre saturation point, no bound water is
removed from the timber, and hence no shrinkage occurs within the timber. Since the
drying rate was lower for the lower initial moisture content as explained earlier, the
maximum instantaneous strain was lower (0.0202 m/m) for the lower initial moisture
content compared to the base case prediction (0.0215 m/m). The instantaneous strain
was predicted to start about two days earlier for the lower initial moisture content
compared with the base case. The reason for this is that the predicted surface moisture
content started to reduce below the fibre saturation point two days earlier compared
with the base case prediction, as shown in Figure 5.19. The predicted final moisture
contents for the board surface were similar (0.086 kg/kg) for this simulation and the
base case prediction (0.091 kg/kg).
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Figure 5.18: The effect of initial moisture content on the predicted instantaneousstrain.
Figure 5.19: The predicted moisture content of the board surface as a function oftime.
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Basecase 53% initial mc 44% Initial mc
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Further analysis has been carried out to assess the effect of other major
uncertainties on the agreement between the model predictions and the measurements
for the temperatures and the humidities of internal air and the moisture contents of
timber. The basic approach has been, firstly, to assess the effect of condensate
accumulation on the floor, and to identify which energy flows are the largest. Then,
the assessment has been carried out of the uncertainties in the sky temperature,
structural variables such as the thermal mass of the floor, and operating variables such
as the amount of water spray and leakage. The effects of uncertainties in the thermal
and solar radiation properties of the plastic cover have also been assessed, together
with the effect of timber properties.
5.4.3 Analysis of Uncertainties in Condensate Accumulation
Condensation is a phenomenon that occurs in the kiln when the temperature of any
surface in the kiln falls below the estimated dew point temperature of the air. The
condensation rate on the internal surfaces of the solar kiln is calculated based on the
estimated dew point temperature and the temperatures of the internal surfaces, as
shown in section 4.4.3. A significant amount of additional energy is required to
evaporate this additional water from the kiln floor, if condensate accumulates there.
This estimated internal condensation rate has some uncertainties associated with it.
Condensation decreases the humidity of the air, since moisture is removed from the
air. Thus if no condensation is assumed, the predicted humidity is likely to increase.
Though the assumption that no condensation ever occurs is unphysical, the
assumption that the condensate drains from the kiln floor by some means, instead of
evaporation, may affect the drying rate significantly, since such drainage means that
evaporation from the floor is very limited for this case. The effect of assuming no
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condensate accumulation (on the kiln floor) on the model predictions is shown in this
section.
The model predicted that this internal accumulation of condensate may be up to 22
tons in the solar kiln for the base case simulation, which assumes that condensate
accumulates on the kiln floor and evaporated into the internal air. Energy is required
to evaporate condensate on the floor. It is probable (and observed in practice) that
majority of this condensate leaves the floor through the two drains (each of 0.04 m
width × 0.04 m deep × 1.5 m long) constructed in the rear of the kiln. This sensitivity
study was undertaken in order to examine the effect of this assumption (no condensate
accumulates on kiln floor), by setting the rate of condensate accumulation to zero. At
the same time, the evaporation from the floor is set to zero because there is very little
condensate available to evaporate from the floor for this situation.
Figure 5.20 shows the impact of no condensate accumulation on the agreement
between the model predictions and the actual measurements for the temperatures,
relative humidities and timber moisture contents. Although the final moisture content
was 0.189 kg/kg compared with the base case (0.2101 kg/kg) and the actual value of
0.20 kg/kg, the agreement did not improve significantly for most of the time. The
predicted temperatures, relative humidities and timber moisture contents for this
simulation and the base case are shown in Figure 5.21. Since no condensate
accumulation was observed in practice, this situation might be considered to be a
more realistic base case. Also, both with and without condensate accumulation, the
predicted final moisture contents are within error bars of the final measured values.
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Figure 5.20: Effect of no condensate accumulation on the predicted internal airtemperatures, relative humidities and timber moisture contents (actual, base case
(accumulation), and predicted (no accumulation).
Figure 5.21: The predicted temperatures, relative humidities and timber moisturecontents for no condensate accumulation and the base case.
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Condensation within the kiln affects the energy balances for the air and floor, as
shown in section 4.4.3. The absence of condensate accumulation results in no
evaporation of water from the kiln floor. The temperature of the floor decreased due
to evaporation, since the heat of vaporisation must be supplied when the water is
transferred to the air. Figure 5.22 shows the increase in floor temperature as a result of
the absence of condensate accumulation on the kiln floor. The measured floor
temperature is also shown in this figure, and this agrees more closely with the base
case (condensate accumulation). However, it must be noted that the measured floor
temperature was not accurate and reliable, particularly for the early period (at least the
first five weeks), because the floor was flooded with unevaporated water from the
water sprays and the thermocouple sensor measured the water temperature.
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Figure 5.22: The effect of no condensation on the predicted floor temperature withthe actual measurements.
The average increase of 8oC in floor temperature for this simulation over the base
case increases the air and other kiln component temperatures. Since the kiln
component temperatures increase, the amount of condensate forming on these
components decreases, and hence the various components of the kiln do not act as
efficiently as condensers as they do for the base case. The lesser amount of
condensation on other surfaces is expected to increase the air humidity, since less
moisture is taken from the internal air, as shown in Figure 5.21. The effect on the
external driving force for mass transfer is greater than that on the internal resistance to
mass transfer in timber, even though the internal resistance to mass transfer is the
main moisture transfer resistance, resulting in an initial decrease in the predicted
drying rate (no accumulation) as shown in Figure 5.21. The average increase in air
temperature for this simulation during the first 40 days, when the heat exchanger was
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Floo
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No condensate accumulation
Basecase
Actual
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not used, was 4oC, but after 40 days, when the heat exchanger was heavily used, the
increase was 11oC compared with the base case. That is why the final moisture
content was 0.0211 kg/kg lower compared with the base case. The drying rate
increased significantly after 53 days.
The temperature of the air increases for no condensate accumulation because of
the increased floor temperature, as explained before. The agreement between the
predicted air temperature and the actual measurement at the beginning of drying
(when the heat exchanger was not on for the first five weeks) was better compared
with the agreement for the (original) base case. However, this predicted temperature
increase did not increase the overall drying rate (particularly for the period when the
heat exchanger was not heavily used), possibly because of the increase in relative
humidity. The predicted relative humidity did not decrease below 80% for most of the
time (no accumulation), whereas the predicted relative humidity was 68% many times
for the base case.
When no condensate accumulates on the kiln floor and nothing evaporates from
the floor into the air, the predicted average board temperature increases about 6 to 7oC
above the base case level (Figure 5.23) because of the higher air temperature. In this
case, there are two competing effects. While the increase in relative humidity lowers
the humidity driving force (or strictly speaking the partial pressure driving force)
between the surface of board and the bulk of the air, higher board temperatures
increase the moisture diffusion rates within the timber. The impact on the drying rate
of the timber depends on the magnitudes of each of these forces. The rate of drying of
the timber is predicted to decrease until 40 days with a difference of 0.02 kg/kg
between this simulation and the base case. Hence the higher board temperatures lead
to higher drying rates at the end of drying, but the initially higher relative humidities
Actual Performance Assessment and Validation of Solar Kiln Model Chapter 5
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(no accumulation) lead to lower initial drying rates. These situations might be
expected from the consideration that the internal resistance to moisture movement is
initially small (since the timber is wet), so the higher relative humidity should lead to
lower initial drying rates, as predicted. In the final stages of drying, the timber is dry,
the internal resistance to moisture movement is large. The increase in board
temperature then decreases the large internal resistance significantly. Thus the drying
rate increases, as predicted.
Figure 5.23: The effect of no condensation on the predicted board temperature.
Since the energy losses are important underlying aspects of the solar kiln model,
uncertainties in the energy losses are explored in the next section.
5.4.4 Uncertainties in the Model Outputs (Predicted Energy Losses)
Solar radiation forms the primary energy input to the kiln. Through the interaction
of the various components of the kiln and the ambient conditions, both convection and
0
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Boa
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(o C)
No condensate accumulation Basecase
Actual Performance Assessment and Validation of Solar Kiln Model Chapter 5
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radiation heat-transfer losses occur. The convective losses from the kiln are given by
the following expression:
Convection Losses = Convection from Walls to Ambient +Convection from Roof to Ambient
The radiation losses from the kiln are given by the following expression:
Radiation Losses = Radiation from Stack to Ambient +Radiation from Stack to Floor +Radiation from North Absorber to Sky +Radiation from South Absorber to Sky +Radiation from Roof Absorber to Sky +Radiation from North Absorber to Ambient +Radiation from South Absorber to Ambient –Radiation from Roof to Sky –Radiation from Walls to Sky –Radiation from Walls to Ambient
The pathways for these energy loss terms were shown in the description of the
model development (section 4.4.3) of Chapter 4 (Figures 4.9 and 4.10).
5.4.5 Convection and Radiation Losses
Figure 5.24 shows the convection and radiation losses as functions of time for the
base case simulation. The cyclical nature of the energy losses over a day can be seen.
The radiation losses are always positive, because most surfaces (including the walls)
radiate to an effective sky temperature that is at least 10 to 20oC less than the ambient
temperature. A detailed discussion of the sky temperature, and its impact on the
predictions, will be given in section 5.4.6. At night, the surface temperatures are
predicted to be less than the ambient ones, so heat is convected into the kiln at night
when solar input is not available, particularly in the early stages of drying (the first
five weeks). When heat is convected into the kiln, the convection energy losses are
negative. In the later stages of drying (after the first five weeks), convection energy
losses are predicted to be higher than before, due to the higher temperatures of kiln
Actual Performance Assessment and Validation of Solar Kiln Model Chapter 5
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surfaces. These higher surface temperatures are predicted to occur because of the
energy gained from the heated internal air due to the use of the heat exchanger after
five weeks from the start of drying. The use of the heat exchanger, and the consequent
rise in the temperatures of kiln surfaces, is also the reason for the significant rise in
radiation energy losses after five weeks (35 days).
Figure 5.24: Predicted energy loss terms for radiation and convection, base case.
The magnitude of the energy loss terms is also consistent with the magnitude of the
energy inputs. The absorbers for solar energy have a total area of 108 m2. With a
maximum solar energy intensity of around 1 kWm-2 (Duffie and Beckmann, 1991), a
typical maximum value for the solar energy falling on a horizontal surface, an
approximate maximum value for the solar energy intensity would be 108 kW. The
measured maximum solar energy intensity was 1226 W m-2 for this run, which was
recorded at 11:54 am, on 29 March 2001. Using this solar intensity, the maximum
solar energy on the absorber surfaces for the kiln was up to 132 kW. In addition, the
heat exchanger contributed up to 139 kW (the actual figure may be somewhat less
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0 10 20 30 40 50 60 70 80
Time (days)
Ener
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Convection Radiation
Actual Performance Assessment and Validation of Solar Kiln Model Chapter 5
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than this value, as discussed before). Hence the magnitudes of the energy losses
shown in Figure 5.24, of up to 73 kW, are consistent with the magnitudes of the
energy inputs, suggesting that the values of the energy losses shown in Figure 5.24
are a reasonable basis for further discussion.
The radiation losses are predicted to be substantially higher than the convection
ones throughout the simulation, a result that may be considered unusual given that all
the temperatures are close to ambient ones. Temperatures of over 200oC are not
involved, a situation where Hewitt et al. (1994) indicates that radiation heat transfer
becomes very significant. However, these results are also consistent with the
experimental study of Langrish et al. (1993) and Prins (1981), even though many
studies in the literature have not generally distinguished between radiation and
convection losses (Keey et al., 2000). Langrish et al. (1993) found that radiation
losses from the walls and the roof of the kiln were 59% of the incoming solar energy,
compared with convection losses, which accounted for 32% of the incoming solar
energy. Hence the predicted dominance of radiation over convection losses here is
consistent with the dominance measured by Langrish et al. (1993), although the ratio
of radiation to convection losses here is over 20:1, compared with 2:1 by Langrish et
al. (1993). Prins (1981) found about 18% of the incoming solar energy is used by the
kiln to dry timber. The losses due to the reflected and transmitted radiation were 58%
of the incoming solar energy compared with the combined conduction and convection
losses of 19.5%, and the conduction through the floor was 16% of the incoming
energy. Kyi (1984) found the ratio of radiation to convection losses to be 10:1. Keey
et al. (2000) compiled and reported heat loss results from these studies, as shown in
Table 5.7.
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However Wengert (1971) found slightly different results. He identified major
energy losses for a greenhouse type solar dryer at Colorado State University and
found that five energy losses accounted for about 84% of the incoming solar energy.
Those losses were by convection (sensible heat loss from walls and roof) 29%,
outgoing solar energy 17%, net long wave radiation 13%, ventilation 14% and
conduction through the floor 11%. The remaining 16% of solar energy was utilised
for drying the wood and for minor losses. The energy losses due to combined
radiation and outgoing solar energy were 31%, a little higher than the convection
losses of 29%, so he is the exception to the other findings here, which found much
higher radiation losses than convection ones. Prins (1981) explained that these
different results (Wengert's (1971) results relative to the others) are due to the
differences in kiln design, capacity and materials used in construction, and
geographical location in terms of latitude and altitude. The glazing material of the
solar kiln used by Wengert (1971) was translucent fibreglass (with very low thermal
radiation transmissivity) and the north wall was a plywood sheet, whereas the glazing
material of Oxford kiln (Prins, 1981) and the solar kiln used for the research in this
thesis was polythene. This difference would have reduced the radiation losses in
Wengert's study significantly. The underlying reason for the dominance of radiation
over convection losses in this study and those by others may be connected with the
importance of the sky temperature, as will be discussed in the next section.
Table 5.7: Heat losses from three solar kilns.
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Energy losses and uses(%)
Wengert (1971) Prins (1981) Kyi (1984)
Solar kiln designersand location
Troxell andMueller (1968);Colorado, USA
Plumptre(1979); Oxford,
UK
Tschernitz andSimson (1979);Madison, USA
Evaporation of waterfrom wood
4.9 21.3
Hygroscopic water(water of sorption)
15.0 0.2 0.3
Energy to heat lumberload and kiln structure
0.5 2.0
Ventilation loss 14.0 9.0 35.7Conduction
/convection loss40.0 (floor loss
11.0)33.5 13.5 (floor loss
11.0)Radiation losses 31.0 51.9 27.2
Total 100.0 100.0 100.0
Some qualitative implications for the design of solar kilns follow immediately
from the dominance of radiation over convection energy losses. The amount of
thermal radiation leaving the kiln depends on a number of factors, including the
transmissivity of the walls and the roof to thermal radiation. Hence a material with a
lower transmissivity to thermal radiation may effectively lower radiation losses,
improving the kiln performance, so searching for such materials is a high priority. The
dominance of radiation over convection energy losses also means that parameters
mainly affecting convection losses, such as wind speed, are probably not very critical
in terms of either measuring them or designing kilns. This in turn implies that locating
kilns in low wind areas is not the most important factor in maximizing their
effectiveness.
The individual components of the predicted radiation loss are given in Figure 5.25.
The largest three losses are the radiation from the roof to the sky, the radiation from
the walls to the sky, and the radiation from the walls to the ambient environment. It is
significant that two out of the three major radiation loss terms include the sky
temperature. Together with the high predicted radiation losses compared with
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convection ones, both predicted here and measured by Prins (1981), Kyi (1984) and
Langrish et al. (1993), this situation means that the impact of the predicted sky
temperature on the energy losses needs to be explored.
Figure 5.25: Predicted values for various components of radiation losses, base case.
5.4.6 Analysis of Sky Temperature
The kiln and its surroundings irradiate each other at thermal wavelengths. The
surroundings include the ground, other structures and vegetation, all of which are
commonly assumed to be at the ambient temperature, whereas the atmosphere above
the kiln is at the 'sky' temperature. The sky temperature is different to the ambient
temperature because the atmosphere absorbs and emits radiation only in certain
wavelength bands. The atmosphere is essentially transparent in the wavelength region
from 8 to 14 µm, but outside this "window" the atmosphere has absorption bands
covering much of the infrared spectrum (Duffie and Beckmann, 1991). Therefore an
estimation of the sky temperature is required, which is often problematic, since it is
difficult to measure cloudiness as a continuous quantitative variable. The cloudiness
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Rad
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Radiation from walls to ambientRadiation from stack to floor
Radiation from roof to sky Radiation from walls to sky
Radiation from top panel to sky
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has some influence on the estimation of sky temperature because clouds are made up
of water droplets, which have strong absorption and emission energy bands for
thermal (mainly infrared and visible) radiation, compared with the "blue" sky, which
has a lower water vapour content than clouds. There has commonly been found to be
a correlation between cloudiness (which is difficult to measure) and ambient air
humidity and temperature (which are easier to measure) (Bliss, 1961; Swinbank,
1963). Several equations are available in the literature and can be used to assess the
estimation of sky temperature as functions of the ambient air temperature and
humidity.
During the day, the radiation impinging on a surface is equal to the sum of the net
solar and thermal radiation falling on it. Typically, this results in the surface
temperature being greater than that of the ambient environment, and hence convection
and radiation losses are positive. However, during the night, there is no energy input
to each surface from solar energy. This can lead to the temperature of the surface
decreasing (due to radiation losses to the sky temperatures, which are typically lower
than the ambient ones) to levels below that of the ambient temperature, leading to
negative convection losses (or energy gains) by the kiln. This situation is also
observed in the freezing of water into ice at night, even when the air temperatures are
above zero, since pools of water lose energy by radiation to the sky temperature,
which may be less than the freezing point of water at low ambient temperatures and
cooler than the air.
Equations for the Estimation of Sky Temperature
Langrish (1991) quoted expressions by Swinbank (1963) and Bliss (1961).
Thompson et al. (1999) quoted two more expressions; one is 10oC less than the
ambient temperature, given by Simonson (1984), and the other is 6oC less than the
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ambient temperature given by Whillier (1953). Berger et al. (1984) reported that the
sky temperature Ts is generally estimated using two parameters; one is the sky
emissivity ∈ and the other is the ground level air temperature Ta.
Ts = Ta ∈0.25 (5.4)
where the emissivity is given by:
∈ = 0.770 + 0.0038 Tdw (5.5)
and Tdw is the dew point temperatures, which is a unique function of the humidity
(here assumed to be the ambient humidity).
They also quoted another expression for emissivity from Kondratyev (1969):
∈ = 0.66 + 0.04 √Pv (5.6)
Pandey et al. (1995) also quoted several equations given by other workers to
estimate the emissivity. For example, Elasser (1942) gave:
∈ = 0.21 + 0.22 ln Pv (5.7)
Clark and Allen (1978) gave:
∈ = 0.787 + 0.0028 Tdw (5.8)
Berdahl and Fromberg (1982) gave:
∈ = 0.734 + 0.006 Tdw (5.9)
Martin and Berdahl (1984) gave:
∈ = 0.711 + 0.0056 Tdw (5.10)
Here Ta and Ts are in Kelvin, the dew point temperature Tdw, is in degrees Celsius
and the vapour pressure Pv is in millibars.
A more recent study by Adelard et al. (1998) has reviewed previous works and
reported a few more expressions for estimating the sky temperature. They quoted an
expression given by Garde (1997):
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Ts = Ta - K (where K = 6) (5.11)
Adelard et al. (1998) found that equation (5.11) gave the best fit to their
experimental data. They also mentioned Daguenet's (1985) two expressions; one is
that the sky temperature is simply dependent on the dry-bulb air temperature:
Ts4 = Ta
4 (1-0.261 exp((-7.77×10-4) (Ta-273)2 )) (5.12)
while another one of his equations takes into account the water vapour pressure in
addition to the air temperature:
Ts = Ta (0.55 + 3.85×10-2 Pv0.5)0.25 (5.13)
Adelard et al. (1998) also quoted the expression by Melchor (1982):
Ts = Ta (0.56 + 0.08 Pv0.5)0.25 (5.14)
The ambient temperature Ta and the sky temperature Ts are in Kelvin, whereas Pv
is in millibars in the above equations. It is worth noting that the vapour pressure, Pv,
like the dew point temperature, Tdw, is a function of the humidity.
The original literature by Melchor (1982) gave the following correlation:
Ts = Ta (5.7723+0.9555(0.6107)Z Ta1.893 RH0.0665×10-4)0.25 (5.15)
Here Ta and Ts are in Kelvins, Pv is the water vapour pressure (millibars), Z is the
altitude (km) and RH is the relative humidity (%). Melchor's (1982) equation (5.15) is
valid for 263 K < Ta < 303 K; 40% < RH < 100%; and 0 km < Z < 3 km and only for
clear skies.
Bliss (1961) related the effective sky temperature to the water vapour content of
the air (through the dew-point temperature, Tdw) and the air temperature (Ta, in K), as
follows:
Ts = Ta (0.8 + 250Tdw )0.25 (5.16)
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Here all the temperatures are in Kelvins except Tdw, which is in degrees Celsius. It is
likely that clouds will tend to increase the effective sky temperature over that for a
clear day because their larger amount of water vapour is likely to absorb more infra-
red radiation. This suggests that the relation of Bliss (1961) should be more
appropriate than others that only depend on the air temperature, because high
humidities are often associated with cloudy days, and equation (5.16) will predict
higher sky temperatures on humid days, which are often cloudy. A sample calculation
shows that for a dry-bulb temperature of 30oC and a relative humidity of 68%
(absolute humidity of 0.0181 kg/kg, dew-point temperature 23.0oC), this equation
estimates a sky temperature of 21.5oC. This condition is the maximum ambient
temperature recorded, with the corresponding humidity, for run 5.
The model for the base case uses the relationship proposed by Swinbank (1963),
which relates the sky temperature (Ts) to the ambient air temperature (Ta), both in
Kelvins, via the following power law expression:
1.5as T0.0552T = (5.17)
For example, when the ambient air temperature is 303 K (or 30oC) the sky
temperature is predicted to be 291 K (or 18oC).
Among all the equations reviewed above, Swinbank (1963) and Daguenet (1985)
gave the simplest expressions for the estimation of the sky temperature (only
dependent on the air temperature). All other equations considered the absolute or
relative humidity of the ambient air or the dew point temperature in addition to the
ambient air temperature for estimating the sky temperature. These latter equations are
probably the most reliable, because including the humidity recognises cloudiness
implicitly by allowing for the relationship between cloudiness and high ambient
relative humidities.
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In terms of using these equations for the estimation of the sky temperature to
calculate the radiation losses and for the simulation of the solar kiln model, the
Swinbank (1963) equation was used for the base case. This estimated sky
temperatures as shown in Figure 5.26, together with the predicted wall, roof and the
measured ambient temperatures. The estimated sky temperature from Swinbank
(1963) is at least 5oC less than all the other temperatures in the kiln.
Figure 5.26: Estimated sky temperature (Swinbank, 1963), predicted wall and rooftemperatures, base case, and the measured ambient temperature.
The likely ranking of different correlations to estimate the sky temperature is
shown in Table 5.8. The approximate difference was estimated at a point (for example
around 55 days), where the differences were more clearly distinguishable and which
represented the trend for most of the data points for a given correlation. Whillier's
(1953) correlation (which is same as equation (5.11) given by Garde (1997)) gave the
highest estimate of the sky temperature. The sky temperatures were predicted to be
the lowest using Elasser's (1942) correlation and Daguenet's (1985) two equations
relative to ambient temperatures compared with the other correlations. The correlation
0
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Tem
pera
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(o C)
Sky
Ambient
Roof
Wall
Actual Performance Assessment and Validation of Solar Kiln Model Chapter 5
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by Swinbank (1963) for the sky temperature was between the two extremes. The
model predictions for the temperatures, relative humidities and moisture contents
using the highest (Whillier (1953)) and the lowest (Daguenet's equation (5.13))
correlations are presented in Figures 5.27 and 5.28, respectively. The estimation of
sky temperatures is also shown afterwards using all the other correlations.
Table 5.8: Ranking of correlations for estimating sky temperature.
Authors Equationnumber
Approximate differencebetween sky and ambient air
temperature (oC)Whillier (1953); Garde (1977) 5.11 6
Clark and Allen (1978) 5.8 10Berger et al. (1984) 5.4, 5.5 12
Berdahl and Fromberg (1982) 5.9 14Bliss (1961) 5.16 15
Martin and Berdahl (1984) 5.10 16Melchor (1982) eq 2 5.15 16
Swinbank (1963) 5.17 18Kondratyev (1969) 5.6 20
Melchor (1982) eq 1 5.14 26Elasser (1942) 5.7 30
Daguenet (1985) eq 1 & 2 5.12, 5.13 30
The agreement between the model predictions and the actual measurement
improved only slightly when the correlation by Whillier (1953) or Garde's (1997)
equation (5.11) (Ts is 6oC less than Ta) was used (the highest estimated sky
temperature). The simulated results for Whiller's correlation are shown in Figure 5.27.
The final moisture content was 0.207 kg/kg for this simulation using the correlation of
Whillier (1953), compared with 0.2101 kg/kg for the base case (Swinbank's (1963)
correlation for sky temperature). Whillier's correlation gives the highest value for the
sky temperature, so the radiation losses from the roof to the sky and the walls to the
sky will be the lowest when using this correlation compared with the other
correlations.
Actual Performance Assessment and Validation of Solar Kiln Model Chapter 5
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Figure 5.27: The effect of Whiller's correlation for sky temperature on the agreementbetween the simulation predictions and the measurements.
The agreement between the model predictions and the actual measurements for
temperatures, humidities and moisture contents for the other extreme correlation (the
lowest estimated sky temperature by Daguenet's (1985) equation (5.13)) is shown in
Figure 5.28. The final moisture content was 0.2145 kg/kg, compared with 0.207 kg/kg
simulated by Whilllier's correlation for the highest estimated sky temperature, 0.2101
kg/kg for the base case, and the actual final moisture content of 0.20 kg/kg. Figures
5.27 and 5.28 show the likely range of predictions of internal air temperatures,
humidities and timber moisture contents for two extreme (both the highest and lowest)
correlations for estimating the sky temperature.
0
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60
80
100
0 20 40 60 80Time (days)
T (o C
) & R
H (%
)
0.00
0.10
0.20
0.30
0.40
0.50
0.60
0.70
Moi
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Actual T Actual RH Predicted T Predicted RHActual X Predicted X Basecase X
Actual Performance Assessment and Validation of Solar Kiln Model Chapter 5
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Figure 5.28: The effect of Daguenet's (1985) correlation for sky temperature on theagreement between the simulation predictions and the measurements.
Bliss's (1961) equation may be a better estimate since it includes the effect of the
ambient air humidity in addition to the air temperature on the sky temperature, and so
makes some attempt (implicitly) to account for cloudiness. Bliss (1961) predicted the
sky temperature to be somewhat higher than that given by the correlation of Swinbank
(1963). For clarity, the estimated sky temperatures by Swinbank (1963), Bliss (1961)
and Whillier (1953) with the ambient temperatures are shown in Figure 5.29.
Swinbank's (1963) correlation estimated the sky temperature to be a maximum of
12oC lower compared with the correlation by Bliss (1961). The correlation by Bliss
(1961) gave the lowest estimate of the sky temperature among these three correlations
(Whillier (1953); Bliss (1961) and Swinbank (1963)). Duffie and Beckmann (1991)
quoted the result of Berdahl and Martin (1984) that the range of the differences
between sky and air temperatures is from 5oC in a hot, moist climate to 30oC in a
cold, dry climate. The range of the differences between sky and air temperatures was
8 to 23oC for the correlation by Swinbank (1961) and 12 to 20oC for the correlation
0
20
40
60
80
100
0 20 40 60 80Time (days)
T (o C
) & R
H (%
)
0.00
0.10
0.20
0.30
0.40
0.50
0.60
0.70
Moi
stur
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t (k
g/kg
)
Actual T Actual RH Predicted T Predicted RHActual X Predicted X Basecase X
Actual Performance Assessment and Validation of Solar Kiln Model Chapter 5
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by Bliss (1961). Berger et al. (1984) reported that the variation between the
correlations proposed by different authors may be more than 15oC.
Figure 5.29: Estimated sky temperature for three correlations and the measuredambient temperature.
The estimated sky temperatures for all other correlations are shown in Figure 5.30.
All these correlations estimated reasonable sky temperatures when appropriate units
were used, in the sense that the sky temperature was always below the ambient
temperature. The correlation by Melchor's (1982) equation (5.15) estimated sky
temperatures that were a little higher compared with the other correlations for the
majority of the time. The simulation with this correlation is likely to predict results
that are similar to that using the correlation by Whillier (1953) because the estimated
sky temperature by this correlation was similar to that of Whillier (1953).
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10
20
30
40
0 20 40 60 80
Time (days)
Tem
pera
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(o C)
Ambient
Swinbank
BlissWhillier
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Figure 5.30: Estimated sky temperatures and the measured ambient temperature.
In conclusion, it is unlikely that any other correlation will improve the agreement
further since all the other estimated sky temperatures are below Whillier's correlation.
Much of the disagreement between the final moisture content predicted by the model
(0.2101 kg/kg) and that measured (0.20 kg/kg) can be explained by the uncertainties
in the sky temperature. Uncertainties in this temperature may explain a difference of
0.018 kg/kg between the observed and predicted final moisture contents, based on the
difference between the final moisture contents predicted by the two extreme
correlations for estimating the sky temperature, those of Whillier (1953) and
Daguenet (1985). The difference that can be explained by the uncertainty in the sky
temperature (0.018 kg/kg) is greater than the difference between the base case
prediction and the measurement (0.01 kg/kg), so the uncertainty in the sky
temperature may explain some the mismatch, together with the uncertainty in the
initial moisture content (section 5.4.2).
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0
10
20
30
0 20 40 60 80
Time (days)
Tem
pera
ture
(o C)
Ambient
Daguenet's eq 2 Elasser
Clark & Allen Berger et al .Melchor
Melchor's eq 2
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5.4.7 Analysis of Other Uncertainties
There are number of other uncertainties in the solar kiln model. These uncertainties
have been identified, and their effects have been assessed and ranked. This assessment
is described in the following section.
The uncertainties in the construction categories of the solar kiln simulation are
shown in Tables 5.9 to 5.14. They can be subdivided into a number of categories;
those connected with the kiln design and simulation development, those connected
with kiln operation, and those connected with model inputs and boundary conditions.
The impact of these uncertainties has been assessed. The effects of uncertainties in the
estimation of convective energy losses from the walls and the roof to the ambient
environment have not been assessed, because section 5.4.4 has shown that convective
losses are only a small component of the total energy losses. Hence, uncertainties in
the convective energy losses are unlikely to have a large effect on the model
predictions.
The ranking, as shown in Table 5.9, was done based on these uncertainties being
likely to be important in terms of their impact on improving the agreement between
the model predictions and the actual measurements for temperatures and humidities
and timber moisture contents. The ranking is somewhat subjective at this point, and
the purpose of this section is to quantify the impact of these uncertainties.
There is a connection between the predicted radiation from the timber stack to the
ambient environment and in the calculation of net heat transfer from the stack. This is
one of the radiation loss terms, which has some uncertainty. Changing this may
possibly affect the drying rate of timber significantly.
Some leakage is probably unavoidable, since there are small gaps between the
large front doors for loading and unloading the kiln. This will have some impact on
Actual Performance Assessment and Validation of Solar Kiln Model Chapter 5
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the drying rate in the sense that the internal air leaves the kiln continuously, which
may reduce the temperature, so it may decrease the drying rate. The thermal mass of
the floor is calculated based on the estimated skin depth of the floor, which needs
assessment.
Table 5.9: Uncertainties in the kiln design and simulation development variables.
Uncertainties Preli-minaryrankingorder
Assessment method
Radiation fromstack to ambient
1 Set this term in the model to zero.
Leakage 2 Set the leakage term to zero for no leakage, and forthe maximum to be the same as venting, becauseleakage is unlikely to be greater than venting.
Thermal mass offloor
3 Reduce to a very low value, considering a very thinlayer for the skin depth (one third of the valuedetermined using the skin depth). The verticalconduction may not affect or pass through thewhole thickness of the floor for the low andmedium temperature conditions in a solar kiln, soan equivalent skin depth is used as described inThompson et al. (1999).
The ranking in Table 5.10 has been done based on their likely impact on the model
and the measurement uncertainties. It is possible that the water spray and venting
rates may have a lower impact compared with the heat exchanger, because the
magnitudes of the water spray and venting rates are relatively small for the large kiln
volume, and these are used to control the internal air humidity. Hence the preliminary
ranking is shown in Table 5.10, although (again) the purpose of this sensitivity study
is to assess the ranking quantitatively.
Table 5.10: Uncertainties in the operating variables.
Uncertainties PreliminaryRanking order
Assessment method
Actual Performance Assessment and Validation of Solar Kiln Model Chapter 5
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Heat exchanger 1 Half of the calculated value. Not ON forfirst 30 days out of 74 days.
Water spray 2 Half of the calculated value.Venting 3 Half of the calculated value.
Table 5.11: Uncertainties in the model inputs and boundary conditions.
Input variables Uncertainties in measurementSolar radiation This is a high-specification precision pyranometer, calibration
accuracy ± 2% (Pyranometer Manual, 1998).Wind velocity 9 data points out of 36026 data points are beyond the possible
range, one data point was 206 km/hour value, 5 data points werejust above 50 but below 60 km/hour, 3 data points are near to 50km/hour at Herons Creek during 14 March to 28 May 2001, sowind velocity data are probably a reasonable estimate since mostof these measurements are physically realistic. The accuracy of thesensor is ± 2.5 %. Note: from the earlier assessment, theconvection energy loss terms are very small compared with theradiation terms, so uncertainties in the wind velocity are unlikelyto have a large impact on the model predictions.
Heat exchangerstatus
Status is accurate, but when it is "on", it does not necessarily meanthat it releases heat. If the air temperature is below the set-pointtemperature, and if the kiln is in auto mode, then the status is "on".During the night and holidays the boiler is off, so no additionalheat supply occurs. Also, during startup in the morning, it takestime to build up adequate pressure in the boiler and to supply thesteam to the solar kiln at a distance of about 150 metres, so thisreduces the energy input due to energy losses from the unlaggedpipe.
Heat exchangertemperature
This gives a reasonable status for heat release, because if the heatexchanger is really releasing heat, then the heat exchangertemperature is much higher than the air temperature. It is easilydistinguishable that if the heat exchanger temperature is in therange of above 60oC and a maximum of over 200oC, it releasesheat to the air.
Heatexchanger'senergy releaserate
Measured indirectly from collecting condensate as accurately aspossible. 50% error possible because the uncertainty in the energylosses due to the unlagged pipe distance between the kiln and theboiler could result in an overestimation of the heat exchangeroutput (i.e. the 139 kW estimated output is probably too high).
Actual Performance Assessment and Validation of Solar Kiln Model Chapter 5
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Table 5.11: Uncertainties in the model inputs and boundary conditions (continued).
Input variables Uncertainties in measurementWater spraystatus and rate
Status recording is accurate, but whenever it is "on", there is atime delay. The valve takes some time to open (5-10 minutesbased on observation). Also, there were six nozzles: the first few(three) nozzles start spraying, and then the other nozzles startafter a few minutes. There may be up to a 50% error in the rate,because of the awkward measurement position. Measureddirectly by collecting from a single nozzle for certain amount oftime. Again, because of the awkward position in the kiln, only afew measurements were possible (explained in section 5.2.5).
Venting statusand rate
Electronic digital output is recorded, and whenever the venting is"on" it opens up. Up to 50% error possible because of theawkward measurement position. Measured directly usinghandheld anemometer but because of the awkward position nearthe vent in the kiln, several measurements were made (explainedin section 5.2.5).
Ambienttemperature
± 0.2oC error possible according to the manual. The data do notshow any anomalous data points at all.
Ambienthumidity
± 3% error possible according to the manual. Some problemsdetected when the air was close to being fully saturated (relativehumidity close to 100%). At those times, the instrument recordedsome values that were less than 10% relative humidity, which arenot physically reasonable. If the sensor tip is protected fromdirect sun or water droplets, then the relative humidity is likely tobe within a range of 40 to 100%; ± 3% error (manufacturer). Forthe ambient humidity measurement, the data logger may havecontacted water droplets when the air was completely saturated.
Table 5.12: Uncertainties in the model outputs.
Output variables Uncertainties in measurementInternal airtemperature andhumidity
These data were recorded by the Tinytag data logger. The datalogger sensor was protected from the direct sun or waterdroplets. The quoted sensor accuracy is ± 0.2oC for temperatureand ± 3% for relative humidity.
Moisturecontent
This is an average of eight kiln samples based on ovendriedbiscuit samples; the average moisture content was 52.7% with astandard deviation of 9.8%. The coefficient of variation is 0.18.The kiln samples were measured every week but with longerintervals during holiday periods.
Actual Performance Assessment and Validation of Solar Kiln Model Chapter 5
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Table 5.13: Uncertainties in the timber properties.
Parameters Uncertainties in measurementsReference diffusioncoefficient
30% uncertainty because it is a property that varieswithin timber species and even within samples.However, the value used here was fitted to resultsfrom carefully controlled drying runs in a laboratorydrying tunnel for this timber species, for which thevariability was 10%. Keey et al. (2000) indicated thatthe coefficient of variation for many timberproperties is ± 30%.
Table 5.14: Uncertainties in the thermal and the solar radiation properties.
Properties Original value (base case) Proposed value foruncertainty assessment
Transmissivity of plasticcover for thermalradiation
0.06 0.01 (very little thermalradiation leaves the kilnthrough the plastic cover).
Emissivity of solarabsorber for thermalradiation
1.0 0.95 (for matt blacksurfaces, Duffie andBeckmann, 1991)
Transmissivity of plasticcover for solar radiation
0.84 0.98 (it was assumed thatmost of the solar radiationpasses through plasticcover into the kiln).
Uncertainties in Kiln Design Variables: Results and Discussion
Radiation from the Stack to the Ambient Environment
Radiation is absorbed by the exposed area of the stack, which affects the net heat
transfer rate to the ambient environment. The east and west face of the stack (front
and rear end of the solar kiln) can see the ambient environment through the plastic
cover with an equivalent area of 32.07 m2, as shown in Table 4.11. The radiation from
the stack to the ambient environment is predicted according to equation (4.22). For
the stack:
)1()TT(AQ
cp
ambstackstackambpcstack
44
ββ−−εστ
= (5.18)
Actual Performance Assessment and Validation of Solar Kiln Model Chapter 5
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Here, Qstack is the radiation from the stack to ambient, σ is the Stefan-Boltzmann
constant (5.67 × 10-11 W m-2 K-4), εp is the emissivity of the absorber panel, Astackamb is
the area of timber stack exposed to the ambient environment through the plastic
(32.07 m2), T is the temperature (in K) for the stack and the ambient environment, and
βp and βc are the reflectivities of the absorber panel and the plastic cover,
respectively.
Since this term predicts energy loss from the kiln when the stack is heated up, the
effects of this term on the model predictions for the humidities and moisture content
were assessed. This term was removed from the prediction term for the net energy
transfer from the kiln. Figure 5.31 shows that the drying rate predicted to increase
slightly due to the removal of this term. The final moisture content for this simulation
was 0.201 kg/kg compared with the base case prediction (0.2101 kg/kg) and the actual
final moisture content of 0.20 kg/kg. There was no significant change in terms of the
predicted internal temperatures and relative humidities between the base case and this
sensitivity test. The predicted and the actual final moisture contents are almost the
same, suggesting that this term might also be important in explaining the moisture
content discrepancies. However, it is unlikely that this term is negligible, so ignoring
it completely is not realistic. This simulation does emphasize the need to measure
variables such as the area between the stack and the ambient environment carefully.
Actual Performance Assessment and Validation of Solar Kiln Model Chapter 5
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Figure 5.31: The effect of neglecting the radiation from the stack to the ambientenvironment compared with the base case.
Thermal Mass of the Floor
The thermal mass of any element of the kiln is the product of the mass (in kg) and
the specific heat capacity (J kg-1 K-1) of that element, as described in section 4.4.6.
The value for the floor thermal mass in the base case was 2.02×107 J K-1. This value
has been reduced by one third (to a value of 1.34×107 J K-1) to assess the effect of this
thermal mass on the model predictions of moisture content and air temperature and
relative humidity.
Another calculation (as follows) shows that the thermal mass of the floor may be
about two and a half times higher than the base case, using a procedure given by
Thompson et al. (1999). The floor dimensions of the Boral solar kiln are 11.5 m×11.2
m×0.34 m, and the floor is constructed from concrete. The density ρ, thermal
conductivity k and specific heat capacity Cp of concrete are 1.5 W m-1 K-1, 2400
kg m-3 and 3350 J kg-1 K-1, respectively (Desch and Dinwoodie, 1996). Thompson et
0
20
40
60
80
100
0 20 40 60 80Time (days)
T (o C
) & R
H (%
)
0.00
0.10
0.20
0.30
0.40
0.50
0.60
0.70
Moi
stur
e co
nten
t (kg
/kg)
Basecase T Basecase RH Predicted T Predicted RHActual X Basecase X Predicted X
Actual Performance Assessment and Validation of Solar Kiln Model Chapter 5
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al. (1999) used an equation to determine the skin depth for calculating the thermal
mass of the floor. This skin depth is the depth through a material that is affected by
cyclical temperature variations, and it is affected by the frequency of such variations.
Vertical conduction may not effectively pass through the whole thickness of the floor
for the low and medium temperature conditions in a solar kiln. For a homogeneous
semi-infinite solid of uniform and constant material properties (in this case concrete is
assumed to be such a material, for the sake of simplicity), the skin depth δ (in metres)
is given by:
ωα
=δ (5.19)
Here, α is the thermal diffusivity of concrete (m2 s-1) is:
pCk
ρ=α (5.20)
where ω = frequency of (the daily) thermal cycle (radian s-1). ω is 2π day-1 for a daily
thermal cycle, which is 2π/(24×3600) s-1 (Thompson et al., 1999). For concrete, the
thermal diffusivity is:
113
11
KJkgkgmKWm
335024005.1
−−−
−−
×=α = 1.866×10-7 (m2 s-1); and
ω = 36002428.6
×= 7.272×10-5 (s-1).
∴Skin depth δ =
××
−
−
5
7
10272.710866.1 = 0.0506 m
Therefore the effective thermal volume of the floor is 11.5 m×11.2 m×0.0506 m or
6.52 m3. The mass of this volume is 6.52 m3 × 2400 kg m-3 or 15.65 tons. The thermal
mass of the floor is then 15.65×103 kg × 3350 J kg-1 K-1 or 5.24×107 J K-1. The impact
of the increased (5.24×107 J K-1) and decreased (1.34×107 J K-1) thermal masses of the
Actual Performance Assessment and Validation of Solar Kiln Model Chapter 5
316
floor on the predicted board moisture content, with the base case predictions and the
actual moisture contents, is shown in Figure 5.32.
Figure 5.32: The effect of reduced thermal mass of the floor on the drying rate.
The reduction of the thermal mass of the floor by one third from the value for the
base case was predicted to increase the drying rate very slightly. The final moisture
content for this simulation was 0.2096 kg/kg, compared with 0.2101 kg/kg for the
base case (actual value 0.20 kg/kg). The increase in thermal mass of the floor by two
and a half times compared with the base case was predicted to decrease the drying
rate slightly compared with the base case. The final moisture content was 0.2159
kg/kg, higher than the base case (0.2101 kg/kg). This simulation has implications for
assessing the effectiveness of heat storage by increasing the floor weight. Taylor and
Weir (1985) and Gough (1977) both attempted to use a rock pile as a heat storage
medium during the day for use at night.
To explain the increase in drying rate due to the reduction in the thermal mass of
the floor, it is necessary to examine the impact of this mass on the predicted floor
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0 10 20 30 40 50 60 70 80Time (days)
Moi
stur
e co
nten
t (kg
/kg)
Actual
Floor thermal mass increased
Floor thermal mass reduced
Basecase
Actual Performance Assessment and Validation of Solar Kiln Model Chapter 5
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temperatures. The effect of different thermal masses of the floor on the predicted floor
temperatures and the base case is shown in Figure 5.33. The variation in predicted
floor temperatures, both for the base case and the increased floor thermal mass,
indicates that the higher the thermal mass, the longer the time to cool down or heat up
during the day and night and vice versa. The higher thermal mass of the floor means
that this mass acts as an effective buffer to temperature changes.
Figure 5.33: The effect of reduced thermal mass of the floor on the predicted floortemperature.
The decrease or increase in thermal mass of the floor also affects the temperatures
of other components in the kiln, most importantly the timber temperature, since the
timber exchanges energy with a number of the various components of the kiln (by
convection and radiation), including the floor. Figure 5.34 shows how the temperature
of timber board was predicted to increase or decrease due to the reduction or increase
in the floor thermal mass compared with the base case. The effect was more
pronounced during the latter part of drying (after five weeks) when the heat exchanger
was "on", since the internal air temperature was higher at this time. Since the
0
10
20
30
40
50
0 20 40 60 80Time (days)
Pred
icte
d flo
or te
mpe
ratu
re (o C
)
Floor thermal mass reduced
Basecase
Floor thermal mass increased
Actual Performance Assessment and Validation of Solar Kiln Model Chapter 5
318
diffusion coefficient is dependent on the timber temperature (as explained in section
5.2.6), with a higher timber temperature, a higher drying rate is expected. The drying
rate was predicted to increase or decrease only slightly due to a modest increase (two
and a half times) or decrease (three times) in the thermal mass of the floor compared
with the prediction for the base case.
Figure 5.34: The effect of reduced thermal mass of the floor on the predicted timbertemperature.
By increasing the thermal mass of these components, an increase in the average
night temperature within the kiln was possible, but a decrease in the daily
temperatures was also found. Systems using rock piles as heat storage media were not
found to be successful by Taylor and Weir (1985) and Gough (1977), because they
stated that it is better to minimise thermal mass to gain a higher air temperature during
the day. The non-linear dependence of the diffusion coefficients on the temperature
(equation (2.3)) gives faster drying overall when the peak daily temperature is higher.
Here, the effect of the increase in the floor thermal mass on the predicted internal air
temperature compared with the base case also showed this effect (Figure 5.35), so this
0
10
20
30
40
50
0 20 40 60 80Time (days)
Pred
icte
d bo
ard
tem
pera
ture
(o C)
Floor thermal mass reduced
Basecase
Floor thermal mass increased
Actual Performance Assessment and Validation of Solar Kiln Model Chapter 5
319
simulation is consistent with results in the literature. The night-time air temperature
for the increased floor thermal mass was slightly higher, whereas the day-time air
temperature was slightly lower, compared with the base case. However, this effect
was not very significant for the small increase (i.e. two and a half times increase) in
the floor thermal mass, particularly when the heat exchanger was on. The lower air
temperature results in a lower timber temperature. Drying time is proportional to the
inverse of the diffusion coefficient, and the diffusion coefficient is proportional to the
temperature to the power of some exponent greater than one (Hildebrand, 1989).
Hence higher timber temperatures increase the drying rate more than lower
temperatures decrease it, so making the temperature more even decreases the average
drying rate. However, more even temperatures mean more even predicted strains, with
lower maximum strains, so the timber quality (with increased thermal mass) may be
better. Thus the predicted maximum strain (0.0204 m/m) for the increased thermal
mass is lower compared with the base case (0.0215 m/m), as can be seen in Figure
5.36.
Actual Performance Assessment and Validation of Solar Kiln Model Chapter 5
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Figure 5.35: The effect of increased floor thermal mass on the predicted internal airtemperature.
Figure 5.36: The effect of increased floor thermal mass on the predicted strain, andthe basecase predicted strains.
0
10
20
30
40
50
60
0 20 40 60 80Time (days)
Inte
rnal
air
T (o C
)
Basecase
Floor thermal mass increased
0
0.005
0.01
0.015
0.02
0.025
0 20 40 60 80Time (days)
Inst
anta
neou
s st
rain
(m/m
)
Basecase Floor thermal mass increased
Actual Performance Assessment and Validation of Solar Kiln Model Chapter 5
321
Uncertainties in Operating Variables: Results and Discussion
The effects of changes in the operating variables (water spray and venting; and
undesirable leakage) on the predictions showed that the improvement in the
agreement between the actual and the predicted internal air temperatures, humidities
and moisture contents was only marginal. The effects of these variables on the
moisture contents are chosen for discussion here. The flow rate for air venting was 0.2
kg/s, and the rate of water spray was 0.0056 kg/s for the base case. The leakage rate
was assumed to be zero for the base case. The assessed values for venting and water
spray rates were 0.41 kg/s air and 0.0028 kg/s water, respectively. The likely range of
leakage rates is between zero and a value equal to the maximum amount of venting. In
this analysis, the leakage was assumed to be 0.2 kg/s air, compared with the base case
for which the leakage was assumed to be zero.
The effects of the different amount of venting, water spray and leakage rate on the
drying rate are shown in Figure 5.37.
Figure 5.37: The effect of different operating variables on the drying rate.
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0 10 20 30 40 50 60 70 80Time (days)
Moi
stur
e co
nten
t (kg
/kg)
Actual
Leakage Basecase
VentingWater spray
Actual Performance Assessment and Validation of Solar Kiln Model Chapter 5
322
It was found from this analysis that changes in these operating variables changed
the prediction of the drying rate, air temperature and humidity only slightly. The final
moisture contents for these operating conditions, including other uncertainties, are
shown in Table 5.15.
Table 5.15: Final moisture contents for different simulations.
Simulation runs Final moisture content (kg/kg)Base case 0.2101
Radiation from stack to ambientneglected
0.201
Thermal mass of the floor is decreased byone third of the base case value
0.2096
Thermal mass of the floor is increased bytwo and a half times the base case value
0.2159
Water spray halved 0.2005Venting doubled 0.2117
Leakage increased to 0.2 kg/s 0.2121Transmissivity of the plastic cover for
solar radiation is increased0.2065
Transmissivity of the plastic cover forthermal radiation is decreased
0.2078
Emissivity of the plastic cover forthermal radiation is decreased
0.2133
Percentage of solar energy decreased to98% of measured value
0.2117
Actual final moisture content 0.20
Water Spray
The reduction in water spray rate by half the amount of the base case was
predicted to increase the drying rate a little (from 0.2101 kg/kg to 0.2005 kg/kg), so
the final moisture content was predicted to be a little lower compared with the base
case. A lower amount of water spray means a generally lower predicted humidity in
the kiln and higher drying rate, hence giving a lower final moisture content, as
predicted.
Venting
Actual Performance Assessment and Validation of Solar Kiln Model Chapter 5
323
The effect of venting is more complex than that of the water spray because the
damp air is expelled outside, and fresh air (with a varying humidity) is drawn into the
kiln by this effect. Since the vents remove wet air from the kiln, it should decrease the
air absolute humidity and also decrease the air temperature (although the change was
small), as shown in Figures 5.38 and 5.39, respectively. Even when the venting rate
was increased further to 0.6 kg/s, the change in predicted air temperature and
humidity was not large. An increase in the venting rate decreased the drying rate
slightly, i.e. the final moisture content was predicted to be 0.2117 kg/kg compared
with the base case prediction of 0.2101 kg/kg. The reason is likely to be the decrease
in temperature by venting, although a decrease in air humidity is expected to increase
the drying rate. Thus it may not be the case that the higher venting rate necessarily
will increase the drying rate, because some energy may be lost with the hot air,
decreasing the air and hence timber temperatures. It should also be noted that an
increase in the drying rate is not always desirable, because the associated stresses and
strains tend to be higher with increasing drying rates, which can damage the timber.
The predicted maximum instantaneous strain was 0.0202 m/m for increased venting
compared with the base case prediction of 0.0215 m/m, as shown in Figure 5.40. Thus
the control of venting is important in the effective operation of these kilns.
Actual Performance Assessment and Validation of Solar Kiln Model Chapter 5
324
Figure 5.38: The measured ambient absolute humidity and the predicted effect ofventing on the internal air absolute humidity.
Figure 5.39: The measured ambient temperature and the predicted effect of ventingon the internal air temperatures.
0
0.01
0.02
0.03
0.04
0.05
0 20 40 60 80Time (days)
Abs
olut
e hu
mid
ity (k
g/kg
)
Ambient
Increased venting
Basecase
0
10
20
30
40
50
60
0 20 40 60 80Time (days)
Tem
pera
ture
(o C)
Ambient T
Increased venting
Basecase
Actual Performance Assessment and Validation of Solar Kiln Model Chapter 5
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Figure 5.40: The effect of increased venting rate on the predicted instantaneous strainand the base case.
Leakage
The final moisture content was predicted to be 0.2121 kg/kg if the leakage was 0.2
kg/s, compared with the base case prediction of 0.2101 kg/kg (no leakage). Since 720
kg of internal air was assumed to leave the kiln per hour continuously due to this
leakage, a substantial amount of energy was lost with the air. If the internal air
relative humidity was above the set-point relative humidity, the venting was switched
"on" (both in the simulation and experiment), so the effect of venting was time-
specific. However, leakage is assumed to be continuous and not dependent on time. It
is important to note that venting and leakage have similar effects - air leaves the kiln,
ambient air is drawn in. Hence many of the same explanations (e.g. loss of energy
with the vented or leaked air) still apply in this case.
0
0.005
0.01
0.015
0.02
0.025
0 20 40 60 80Time (days)
Inst
anta
neou
s st
rain
(m/m
)Basecase Increased venting
Actual Performance Assessment and Validation of Solar Kiln Model Chapter 5
326
Overall effect
In summary, operating variables such as venting and water spray have less impact
compared with the use of heat exchanger on the drying rate in a solar kiln. Leakage
should have a larger predicted impact than venting on the drying rate because leakage
is assumed to occur continuously, whereas venting only has an effect when the vents
are on. However, the predicted differences in drying rate for the larger amount of
venting and leakage rates compared with the base case were small. It is important to
note that the air temperature, relative humidity and the air velocity through the timber
stack are generally regarded as the most significant variables in controlling timber
drying kilns (Keey et al., 2000). In this case of a solar kiln, it has been found here that
the heat exchanger and its energy release rate had a very large effect on drying rates
compared with the effects of the water spray, venting and leakage.
Uncertainties in Solar and Thermal Radiation Properties: Results and Discussion
The model predicted incoming and outgoing solar and thermal radiation according
to the equations (4.22 and 4.23) described in Chapter 4. The impacts of the
uncertainties in the solar and thermal properties of the glazing material (in this case,
the plastic) have been assessed (Figure 5.41).
Actual Performance Assessment and Validation of Solar Kiln Model Chapter 5
327
Figure 5.41: The effect of thermal and solar radiation properties on the drying rate.
Transmissivity of the Plastic Cover for Thermal Radiation
The value for the transmissivity of the plastic cover to thermal radiation is
assumed to be 0.06 for the base case, which means that only 6% of the thermal
radiation energy is assumed to leave the kiln through the plastic cover. This
sensitivity study set the transmissivity of plastic cover for thermal radiation to 0.01.
This assessment showed that the predicted drying rate increased very slightly
compared with the base case prediction. The final moisture content was predicted to
be 0.2078 kg/kg compared with the base case of 0.2101 kg/kg. The reason for the
increase in drying rate is that more thermal energy is retained in the kiln and used for
drying in this situation (less energy is lost due to thermal radiation through the
plastic). Thus the lower final moisture content compared with the base case is
expected.
Transmissivity of Plastic Cover for Solar Radiation
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0 10 20 30 40 50 60 70 80Time (days)
Moi
stur
e co
nten
t (kg
/kg)
Actual
Cover transmissivity for thermal radiation 0.01
Absorber emissivity for thermal radiation is 0.95
Cover transmissivity for solar radiation 98%
Basecase
Solar energy 98%
Actual Performance Assessment and Validation of Solar Kiln Model Chapter 5
328
Kyi (1984) reported and Thompson et al. (1999) quoted the transmissivity of
polythene plastic covers to be 0.84. This means that the 84% of the solar radiation is
assumed to pass through the plastic cover. This value was changed to 98% to assess
the effect of this property on the model predictions. This higher value was chosen
because the base case simulation predicted higher moisture contents compared with
the actual ones, so the increase in drying rate would improve the agreement between
the actual and predicted moisture contents. The physical reason why such an increase
in transmissivity is reasonable is that some plastics (polyvinyl fluoride or "Tedlar")
have higher transmissivities (98%) than polythene (Duffie and Beckmann, 1991).
The simulation results predicted that the final moisture content to be 0.2065 kg/kg,
compared with the base case of 0.2101 kg/kg. A very slight increase in the drying rate
is observed, as expected, since more solar energy passes through the plastic cover.
Emissivity of the Absorber Panel for Thermal Radiation
The emissivity of the absorber panel for the base case simulation was unity, which
is the value for an ideal blackbody. Duffie and Beckmann (1991) reported that
emissivity for the matt black surface to be 0.95. The lower emissivity value means
that the radiation energy loss from the panel surfaces to the sky or ambient should be
lower, although the amount of solar energy absorbed by the panels is also less by 5%.
The difference in drying curves for the decreased emissivity and the base case was
small, and the final moisture content for this simulation was predicted to be 0.2133
kg/kg, compared with 0.2101 kg/kg for the base case prediction.
Percentage of Solar Energy Input
For the base case simulation it was assumed that the 100% of the measured solar
energy fell on the kiln. This value was decreased to 98% considering that the
measured solar energy has 2% error (according to the manual). This simulation was
Actual Performance Assessment and Validation of Solar Kiln Model Chapter 5
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predicted to decrease the drying rate, as expected for a lower solar energy input. The
final moisture content was predicted to be 0.2117 kg/kg, compared with the base case
prediction of 0.2101 kg/kg. The impact of this change in solar energy input (2%) is
significant (0.0017 kg/kg for 2% change in solar energy input), emphasizing the need
to measure this parameter accurately, as has been done here with the use of a
precision pyranometer.
5.4.8 Analysis of Timber Properties
Timber properties have significant influence on the predicted moisture contents of
the timber boards using this simulation model. These properties, i.e. diffusion
coefficient, timber board thickness and the initial moisture content of timber, were
identified to be the key ones as described in section 3.6. The predicted simulation
results are shown and described in the following section.
Diffusion Coefficient
The rate of change of moisture content of the timber depends on the diffusion
coefficient of the timber species according to the Fickian diffusion model as explained
in section 2.2.3. The diffusion coefficient dictates the ease and rate at which moisture
moves within the timber according to equation (2.2). This equation uses a reference
diffusion coefficient that is species dependent, and this simulation was undertaken to
examine the impact of this parameter on the agreement between the predicted
moisture contents by this simulation and the base case prediction. For this simulation,
the reference diffusion coefficient was increased by 30% (1.445×10-5 m2/s) of the
base case (1.145×10-5 m2/s for blackbutt). This increase in the diffusion coefficient of
the timber was predicted to increase the rate of change of moisture content resulting
in a lower final moisture content (0.2039 kg/kg) compared with the base case
Actual Performance Assessment and Validation of Solar Kiln Model Chapter 5
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prediction (0.2101 kg/kg) and actual moisture content of 0.20 kg/kg. Figure 5.42
shows the predicted drying rates associated with a higher reference diffusion
coefficient compared with the base case.
Figure 5.42: The effect of diffusion coefficient on the predicted drying rate.
A higher rate of moisture diffusion is experienced within the timber, and hence a
higher drying rate is achieved, for a higher diffusion coefficient. For most of the
simulations above, an increase in drying rate has been reflected in an increase in the
instantaneous strain throughout the simulation and vice versa. This is not predicted to
be the case for increasing the reference diffusion coefficient. Figure 5.43 shows the
predicted instantaneous strain on the timber as a function of time.
A slight decrease in the maximum instantaneous strain (0.0207 m/m) on the timber
is predicted, despite a predicted increase in drying rate, compared with 0.0215 m/m
for the base case prediction. The reference diffusion coefficient, and hence by
definition the diffusion coefficient, dictates the rate at which moisture moves from the
centre to the surface of the timber where evaporation then occurs. At a higher value of
0
0.1
0.2
0.3
0.4
0.5
0.6
0 10 20 30 40 50 60 70 80Time (days)
Moi
stur
e co
nten
t (kg
/kg)
Basecase Dmref 30% up
Actual Performance Assessment and Validation of Solar Kiln Model Chapter 5
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the diffusion coefficient, the moisture within the timber distributes more quickly and
hence lower moisture content gradients are predicted to develop within the timber.
These lower gradients lead to smaller differences in shrinkage throughout the various
layers of the timber, and hence lower levels of instantaneous strain are predicted.
Figure 5.43: The effect of diffusion coefficient on the predicted instantaneous strain.
Timber Thickness
The board thickness was 43 mm for the base case. During this assessment, two
other thicknesses of 30 mm and 54 mm have been assessed because these are within
the common production range. This simulation was undertaken in order to determine
the effect of board thickness on the predicted moisture contents. Changing the
thickness of the timber affects both the timber temperature and drying rate. An
increase in the thickness of the timber causes an increase in the thermal mass of both
the boards and the stack (because there are fewer sticker spaces between boards, and
the size of the sticker spaces is the same, 25%), and hence the magnitude of the
0
0.005
0.01
0.015
0.02
0.025
0 20 40 60 80Time (days)
Inst
anta
neou
s st
rain
(m/m
)
Basecase Reference diffusion coeffcient 30% up
Actual Performance Assessment and Validation of Solar Kiln Model Chapter 5
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variations in the timber temperature would be expected to decrease with increasing
board thickness and vice versa. This effect is predicted, as shown in Figure 5.44.
Figure 5.44: The effect of timber board thickness on the predicted board temperature.
The average board temperature during the day decreases while the average board
temperature during the night increases for a higher thickness, compared with the
lower thickness. Since the rate of drying during the day is of greater importance to the
overall drying rate of the timber, this reduction in average timber temperature would
be expected to translate into a lower drying rate. In addition, the greater thickness of
the timber means that the resistance to internal moisture movement is much greater
than for the smaller thickness. Pordage and Langrish (1999) have shown that the Biot
number for mass transfer (the ratio of internal to external resistance to moisture
movement) is large, so this increase in internal resistance to moisture movement has a
large impact on the increase in overall resistance, slowing drying. This is why a
significant decrease in drying rate was predicted for 54 mm boards (with a final
moisture content of 0.2751 kg/kg), and a significant increase in drying rate was
10
20
30
40
50
0 20 40 60 80Time (days)
Pred
icte
d bo
ard
tem
pera
ture
(o C)
54 mm
Basecase 43 mm
30 mm
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predicted for 30 mm boards (with a final moisture content of 0.1325 kg/kg), compared
with the base case prediction for 43 mm boards (with a final moisture content of
0.2101 kg/kg), as shown in Figure 5.45. The drying rate is predicted to be the slowest
for 54 mm boards (a reduction in moisture content of 0.00329 kg/kg per day), and the
drying rate is highest for 30 mm boards (a reduction in moisture content of 0.00525
kg/kg per day), compared with the base case prediction (a reduction in moisture
content of 0.00416 kg/kg per day for 43 mm boards). This means that the drying times
were 60% and 30% higher for 54 mm and 43 mm thick boards, respectively,
compared with the drying rate of 30 mm thick boards. These results are similar to
those shown in the sensitivity analysis for the optimised schedule in section 3.6.2.
Figure 5.45: The effect of timber board thickness on the predicted drying rate.
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0 10 20 30 40 50 60 70 80Time (days)
Moi
stur
e co
nten
t (kg
/kg)
Basecase 43 mm 30 mm 54 mm Actual
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The effect of timber thickness on the predicted instantaneous strain levels in the
timber also can be seen in Figure 5.46. Though the maximum instantaneous strain was
slightly lower (0.021 m/m) for 54 mm boards compared with 0.0215 m/m for the base
case (43 mm), the instantaneous strains were higher for most of the time despite the
overall reduction in drying rate. Since the timber thickness increases, the moisture
content gradient within the timber is also expected to increase. Therefore the
difference in shrinkage associated with the various layers of the timber increases. This
is then translated into a higher level of predicted instantaneous strain for a timber of
greater thickness. Similarly, the maximum instantaneous strain was predicted to be
0.019 m/m for 34 mm boards, compared with 0.0215 m/m for the base case (43 mm)
prediction.
Figure 5.46: The effect of thickness on the predicted instantaneous strain.
In conclusion, the increase in the thickness of timber is predicted to decrease the
overall drying rate, and vice versa, as expected. The quality of the timber is also
0
0.005
0.01
0.015
0.02
0.025
0 20 40 60 80Time (days)
Inst
anta
neou
s st
rain
(m/m
)
Basecase 43 mm 30 mm 50 mm
Actual Performance Assessment and Validation of Solar Kiln Model Chapter 5
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affected, with a predicted increase in the instantaneous stain levels experienced for
thicker boards.
5.4.9 Assessment of the Utility of the Model as a Prediction Tool
For the base case simulation, the boundary conditions, i.e. solar energy, wind
velocity, ambient temperatures and humidities, are used in the model as they were
recorded, which have been explained in section 5.2. For the solar energy and wind
velocity, the data were recorded every minute and for the ambient temperature and
humidities, the data were recorded at eight minute intervals over 74 days. The effect
of the data for the boundary conditions averaged at different time intervals (half hour,
one hour, one day, one week) on the predicted moisture contents was assessed,
because it governs how easy it is to use this simulation model when applied to other
possible kiln locations. This assessment shows that the predicted drying curves were
almost the same for the data averaged for every half hour, one hour and the base case
predictions (Figure 5.47). However, the data averaged every day and every week
predicted significantly different results compared with the base case. This simulation
is not intended to examine the effect of these boundary conditions on the agreement
between the predicted and measured outputs, rather than to assess how easily the
model can be simulated using data for the boundary conditions recorded at different
time intervals. The final moisture content was the same (0.17 kg/kg) for data averaged
at one day and at one week compared with the base case prediction of 0.2101 kg/kg.
The drying rate was 13% higher (the final moisture content was 0.17 kg/kg) for the
data averaged at one day and at one week time intervals, compared with the base case.
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Figure 5.47: The effect of data for the boundary conditions averaged at different timeintervals.
5.5 CONCLUSIONS
The actual performance of an industrial solar kiln used for drying timber has been
assessed to test the effectiveness of the sensors and the data logging system used for
the measurements. The kiln control system was not very good, when the actual
internal air temperatures and relative humidities are compared with their set points.
The calculated ranges of the integral of the absolute errors for internal air temperature
and relative humidity were 4.7 to 9.7oC and 6.4 to 11.5%, respectively. The ranges of
the integral of the root mean square errors were 6.4 to 12.5oC and 8 to 14.3%, for
temperature and relative humidity, respectively. The differences in control quality
(and variations in it) appeared to have little effect on the timber quality.
0
0.1
0.2
0.3
0.4
0.5
0.6
0 20 40 60 80Time (days)
Moi
stur
e co
nten
t (kg
/kg)
One week
One day
One hourHalf hour
Basecase
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A complete system model for solar kiln has successfully been simulated and
validated based on comparisons of the predicted and the measured internal air
temperatures, relative humidities and the moisture contents.
Firstly, a reduced energy release rate (69.5 kW) from the measured heat exchanger
output (139 kW) improved the agreement significantly between the simulation
predictions and the measurements. There is a significant uncertainty in the
measurement of the heat exchanger output since there would have been substantial
energy losses from about 150 m of the unlagged steam pipes between the boiler and
the solar kiln. Since halving the heat exchanger output gave a much better agreement
between the simulation predictions and the measurements, this simulation has been
regarded as the base case.
The maximum difference between the actual and predicted moisture contents was
0.05 kg/kg. To explain this mismatch, further analysis has been carried out to assess
the uncertainties, which included the impact of uncertainties in the estimation of the
initial moisture content, the sky temperature, kiln design variables and operating
variables. The uncertainty in the initial moisture content could explain most of the
differences in moisture contents throughout the drying period.
Convection and radiation energy losses were predicted to be up to 17 kW and 73
kW, respectively, from the simulation. The largest three radiation loss terms were the
radiation from the roof to the sky, the radiation from the walls to the sky, and the
radiation from the walls to the ambient environment. Thus the uncertainty in several
correlations for the estimation of the sky temperature was analysed. The uncertainties
in the sky temperature could explain a mismatch of 0.02 kg/kg between the model
predictions and the actual measurements for moisture contents.
Actual Performance Assessment and Validation of Solar Kiln Model Chapter 5
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Among the other uncertainties and kiln operating variables, the energy release rate
from the heat exchanger had the greatest effect. This effect was only significant after
27 days, when the heat exchanger was used. The agreement between the predicted and
measured temperatures of the internal air is reasonable and both the predictions and
the measurements have a similar cyclical pattern. There was a maximum difference of
about 10oC between the predicted and measured temperatures until 27 days after the
start of drying. The maximum difference between the predicted and the measured
temperatures was 5oC for the later period of drying when there was an additional heat
input from steam heat exchanger. The agreement between the predicted and measured
relative humidities was better at the beginning of the drying run (until 43 days) than
the later period of drying when the heat exchanger was continuously used. Initially
the maximum difference was between 10 to 15%. The maximum difference after 44
days was 20 to 25%.
Neglecting the radiation loss term from the stack to the ambient environment is
also predicted to affect the discrepancy between the predicted and observed final
moisture contents, suggesting that the area involved in this heat transfer term needs to
be measured very carefully (as was done here).
Regarding the operation of the solar kiln, the following lessons may be learnt from
the sensitivity study carried out using the overall model. In terms of operating
variables, the water spray rate may be halved, which is predicted to increase the
drying rate slightly without having any large effect on internal air temperature and
humidity and stress/strain levels. The current venting amount is suggested to be
maintained at the current level based on the simulation results, which showed that
more venting did not increase the drying rate and stress/strains levels significantly.
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Regarding design aspects of solar kilns, the sensitivity study suggested the
following points. The simulation showed that the radiation loss is dominant in the
solar kiln and that the amount of thermal radiation leaving the kiln depends on a
number of factors, including the transmissivity of the walls and the roof to thermal
radiation. Hence a material with a lower transmissivity to thermal radiation may
effectively lower radiation losses, improving the kiln performance, so searching for
such materials is a high priority. The simulation showed that a slight reduction in the
transmissivity of the plastic cover to solar radiation had a significant effect on the
drying rate. Thus using more transparent polycarbonate sheets (to solar radiation) as
glazing compared with polythene is likely to be more effective for improving the heat
input rate to the solar kiln.
The simulation results showed that the data for the boundary conditions, i.e. solar
radiation, wind velocity, ambient temperatures and relative humidities, averaged
every hour predicted almost the same drying curves compared with the base case
prediction. The final moisture content was the same (0.17 kg/kg) for data averaged at
one day and at one week intervals, compared with the base case prediction of 0.2101
kg/kg. The final moisture content was 4% lower for the data averaged over one day
and over one week intervals than the base case.
The generally good agreement between the model prediction of the final moisture
content and its measurement may be due to the careful measurement of the boundary
conditions such as the solar energy input. Some of these conditions (e.g. solar energy
input) have a significant impact on the model predictions and have been measured
here very carefully (e.g. ± 2% for solar energy).
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