Actual Performance Assessment and Validation of Solar Kiln ...

Actual Performance Assessment and Validation of Solar Kiln Model Chapter 5

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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


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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

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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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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

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T (o C

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H (%

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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.


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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.

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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

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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


267

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


268

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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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.


271

Figure 5.10: Actual and set point temperatures and relative humidities and moisturecontents as function of time for the fifth run.


5.4.2 Heat Exchanger Input and Moisture Content Measurement

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272

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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273

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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274

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


275

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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Sample 1 Sample 2 Sample 3 Sample 4 Sample 5Sample 6 Sample 7 Sample 8 Average Variation

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Variation


276

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


277

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.


278

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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279

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


280

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.


281

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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282

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


283

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).


284

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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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


286

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.


287

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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288

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.


289

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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Actual


290

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


291

(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

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Boa

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No condensate accumulation Basecase


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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


293

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

-10

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0 10 20 30 40 50 60 70 80

Time (days)

Ener

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Convection Radiation


294

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.


295

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.


296

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


297

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


298

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


299

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):


300

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)


301

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.


302

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

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Tem

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Sky

Ambient

Roof

Wall


303

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.


304

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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T (o C

) & R

H (%

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Moi

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)



305

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

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40

60

80

100

0 20 40 60 80Time (days)

T (o C

) & R

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)

0.00

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306

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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40

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Time (days)

Tem

pera

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(o C)

Ambient

Swinbank

BlissWhillier


307

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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Time (days)

Tem

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(o C)

Ambient

Daguenet's eq 2 Elasser

Clark & Allen Berger et al .Melchor

Melchor's eq 2


308

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


309

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


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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).


311

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.


312

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)


313

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.


314

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

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40

60

80

100

0 20 40 60 80Time (days)

T (o C

) & R

H (%

)

0.00

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0.20

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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


315

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


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

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0.6

0.7

0 10 20 30 40 50 60 70 80Time (days)

Moi

stur

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t (kg

/kg)

Actual

Floor thermal mass increased

Floor thermal mass reduced

Basecase


317

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

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30

40

50

0 20 40 60 80Time (days)

Pred

icte

d flo

or te

mpe

ratu

re (o C

)


Basecase



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

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30

40

50

0 20 40 60 80Time (days)

Pred

icte

d bo

ard

tem

pera

ture

(o C)


Basecase



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.


320

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

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60

0 20 40 60 80Time (days)

Inte

rnal

air

T (o C

)

Basecase


0

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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


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


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


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.


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


325

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


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).


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%


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


329

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


330

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


331

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


332

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


333

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


334

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


335

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.


336

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


337

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.


338

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.


339

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).


340

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