Collins, M.R., and Harrison, S.J., "Calorimetric Measurement of the Inward-Flowing Fraction of Absorbed Solar Radiation in Venetian Blinds", ASHRAE Transactions, pp. 1022-1030, Vol. 105 (2), 1999.

Copyright 1999, ©American Society of Heating, Refrigerating and Air-Conditioning Engineers, Inc.

(www.ashrae.org). Reprinted by permission from ASHRAE Transactions

1999, Volume 105, Part 2. This material may not be copied nor distributed in either

paper or digital form without ASHRAE’s permission.

CALORIMETRIC MEASUREMENT OF THE INWARD-FLOWING FRACTION OF ABSORBED SOLAR

RADIATION IN VENETIAN BLINDS

ABSTRACT

This paper presents the calorimetric measurement of the inward-flowing fraction of absorbed solar radiation for a venetian

blind at various blind slat angles. The general methodology used for this study followed that originally used by Klems and

Kelley (Klems and Kelley 1996). By conducting controlled experiments with an electrically heated blind (to simulate the

effects of absorbed solar radiation), the magnitude of the inward-flowing fraction can be directly determined, and

environmental effects can be evaluated (i.e., irradiance, interior/exterior temperature difference, and exterior air film

coefficient). For these tests, a calibration transfer standard (Bowen 1985) was used rather than a commercial sealed-glazing

unit. Furthermore, because irradiation of the specimen was unnecessary, the entire test was performed indoors. Results

indicate that the inward-flowing fraction is dependent on the interior/exterior temperature difference, and only slightly

dependent on the absorbed irradiance and exterior air film coefficient. Blind slat angle was also found to have an effect under

certain circumstances. Specifically, an open blind combined with an interior/exterior temperature difference had higher

inward-flowing fraction values than all other cases. Finally, a proposed test method for determining the inward-flowing

fraction is presented and examined. The application of this data is discussed.

INTRODUCTION

The determination of the Solar Heat Gain (SHG) through fenestrations is required for the evaluation of fenestration

energy performance, estimating building loads, and assessing occupant comfort levels. SHG is the product of the solar heat

gain coefficient (F) and the incident solar irradiance (I), i.e.,

SHG F I= ⋅ (1)

F is defined for a single layer as

F N= + ⋅τ α (2)

where τ and α are the transmitted and absorbed solar radiation, respectively, and N is the inward-flowing fraction of absorbed

solar radiation. The inward-flowing fraction can be further described as follows. When solar radiation passes through a

window, some of the energy is transmitted through each layer, some reflected (either into the room or back out of the

window), and some is absorbed. Absorbed energy causes the temperature of the layer to increase relative to its surroundings.

This in turn causes convection and radiation exchange to the room, and to other glazing layers (Jordan and Threlkeld 1959).

In the past, calculation of SHG was undertaken using tables contained in Chapter 27 of the ASHRAE – Handbook of

Fundamentals (ASHRAE 1997). While these tables handle many systems adequately, a method for the determination of SHG

for fenestrations with attachments, called complex fenestrations, needs to be developed. The complex geometry of these

systems, and the flow of room air between the inner glazing and shade layers, make analysis difficult when using

conventional techniques.

A number of methods have been proposed in the past to determine the SHG for complex fenestration. These methods

have been summarized in reports by Collins (Collins 1997) and Harrison et al. (Harrison et al. 1996a). Unfortunately, none of

these attempts produced a generalized model of SHG for complex fenestrations. The reason for this was twofold. First, model

applicability was limited, i.e., all previous models were incapable of being used for different blind positions and angles,

fenestration types, or for cases involving multiple glazings. Second, no analysis was performed to determine the nature of the

inward-flowing fraction for the shade layer. Consequently, the inward-flowing fraction was determined by experimental

correlation, or by the assumption that it was 100%.

Recently, Klems et al. (Klems and Warner 1992; Klems and Kelley 1996; Klems and Warner 1997) successfully

calculated solar heat gain for complex fenestration by a combination of calorimetric and optical methods. Using a two-band

radiation model, solar-optical transmission and absorption could be measured using a scanning radiometer, and N, a thermal

property, could be determined using a calorimetric test. This method, called solar-thermal separation, has shown great

potential over previous models. It is potentially applicable to all geometries, all shading devices, with all types and numbers

of glazings, in any combination or order.

To collect data for solar-thermal separation, calorimetric tests were performed on a limited number of shade and glazing

combinations (Klems and Kelley 1996). Two identical complex fenestration samples were placed in adjacent calorimetric

cells. In one, the blind was electrically heated to simulate an increased solar absorption, relative to the other “control” sample.

The increase in metered energy between the two cells was then attributed to

Q N P= ⋅ (3)

where Q was the increase in metered energy and P was the input power to the blind and is equivalent to the absorbed

irradiance, I⋅α⋅Af.

These tests provided valuable insight into the nature of the inward-flowing fraction. The authors observed that the solar

irradiance and the incident angle of irradiation did not seem to affect the inward-flowing fraction. As well, measurements

showed no significant change in the inward-flowing fraction between values taken early and late in the day. The authors

theorized that high afternoon wind speeds (and consequently, the high exterior air film coefficients) decreased N, but were

offset by an increase in exterior temperature relative to the room’s temperature. As a result of their studies, they concluded

that while N could be measured, its sensitivity to environmental factors required further investigation before a test method

could be verified and reliable data produced (Klems and Kelley 1996).

EXPERIMENT

As a result of the previous recommendation, and the need to refine the evaluation of the inward-flowing fraction, a test

program was initiated at Queen’s University in Kingston, Ontario, Canada. This study focused on the effects of what we

grouped together as "environmental" variables (i.e., solar irradiance, interior/exterior temperature difference, and exterior air

film coefficient), and blind slat angle, on the measured values of inward-flowing fraction. The general methodology used for

this study followed that originally used by Klems and Kelley (Klems and Kelley 1996). By conducting controlled

experiments with an electrically heated blind (to simulate the effects of absorbed solar radiation), the magnitude of the

inward-flowing fraction could be directly determined, and the environmental and slat angle effects can be gauged. Because

irradiation of the specimen was unnecessary, however, the entire test was performed indoors using a single calorimeter cell.

Queen’s Solar Calorimeter

Testing was performed using Queen’s Solar Calorimeter (Fig. 1), located at Queen’s University. The calorimeter

incorporated many important sub-systems of both traditional and innovative design. A full description of the calorimeter is

provided by Collins (Collins 1997).

An important feature of the calorimeter is its active thermal guard. The walls of the solar calorimeter were designed to

reduce heat loss using a series of five individually controlled heaters, placed inside the calorimeter walls. These heaters were

activated when a temperature difference was measured between the interior surface of the calorimeter and the heater. An

aluminum plate, located behind the heater, served the dual purpose of providing a rigid mounting surface for the heater and

ensured an even distribution of heat. In this way, heat loss through all of the calorimeter walls was reduced to less than 2 W

(6.82 Btu/h).

The calorimeter mask was constructed from polyisocyanurate foam insulation (R = 3.81 m2K/W, 21.63 h⋅ft2F/Btu), with

an interior facing of masonite and exterior facing of 6.4 mm (0.25 in) plywood. The total system has an R-factor of 3.88

m2K/W (22.03 h⋅ft2F/Btu). Samples up to 90 cm x 120 cm (35.4 in x 47.2 in) in size can be mounted in the mask wall.

A multiple-loop flow system of both air and water was used to remove energy from the calorimeter and conditions the

internal air. The first loop, called the liquid-conditioning loop, consisted of a temperature bath and chiller. It was located

external to the calorimeter, and provided a constant temperature supply to the calorimeter. A second loop, located entirely

within the calorimeter, circulated liquid through the solar absorber panel, and the air-to-liquid heat exchanger. A third,

metering loop, supplied water from the conditioning loop to the calorimeter at a constant rate, and returned an equal amount

of fluid in the opposite direction. Based on the flow rate and temperature difference in this loop, and the fluid properties,

energy removed from the calorimeter was determined. Finally, an air-circulation loop within the calorimeter aided in cooling

the air, and promoted a uniform air temperature within the test cell. Fans drew air from the bottom of the calorimeter, through

the air-to-liquid heat exchanger, and down across the specimen. An internal baffle ensured the desired direction of air flow

was maintained within the calorimeter.

The data acquisition (DA) and control system provided many functions. Thermopiles, and thermocouples were located

within the calorimeter walls, and the guard heaters were controlled based on this input. Thermocouples measured interior and

exterior air, and mask temperatures. As well, flow rate and temperature rise through the calorimeter were recorded, and a

voltage-divider circuit and current shunt were used to determine power input to the calorimeter for the internal pump and

fans.

The energy input to the calorimeter follows from an energy balance on the system. Energy removed by the flow loop

(Qflow), added through internal mechanisms, i.e., the internal fan (Qfan) and pump (Qpump), and lost through the walls (Qwalls)

and mask (Qmask) are known. Energy input, Qinput, is then determined by

Q Q Q Q Q Qinput flow fan pump walls mask= − − + + (4)

Procedure

A test method similar to that employed by Klems and Kelley (Klems and Kelley 1996) was used (i.e., a commercial

venetian blind was mounted adjacent to a window, in the mask wall of a calorimeter). The blind alone was then electrically

heated to simulate the absorption of solar energy. In contrast to the previous work, however, only a single calorimeter test

cell was used to perform steady-state indoor tests, in simulated wind. While testing indoors eliminated the effects of solar

absorption in the glazings, this was not expected to produce any significant difference in radiative or convective exchange

from the interior glazing. More importantly, indoor testing allowed steady-state conditions to be reached.

Rather than using a commercial sealed-glazing unit (SGU), a calibration transfer standard (CTS) (Bowen 1985) was used.

A CTS is a mock window in which the air cavity has been replaced with a foam core, across which thermocouples have been

placed. This allows the determination of the heat flux flowing through the CTS. The ability to measure heat flux through the

CTS was important for this experiment. In addition to providing a redundant outward-flowing fraction measurement, it aided

in the analysis of radiative and convective air-film coefficients, used in the development of a predictive inward-flowing

fraction model (Collins 1997). In defense of its use, the CTS had a thermal resistance similar to a double-glazed SGU

(R=0.397 m2K/W, 2.25 h⋅ft2F/Btu), and the interior glass surface would be identical to a normal SGU when considering long

wave radiative properties. Only the effects of convection in the glazing cavity are sacrificed by this substitution.

The test sample (61 mm x 61 mm, 2 ft x 2 ft) was installed in the mask wall as shown in Fig. 2, to be representative of an

actual window installation (Harrison and Van Wonderen 1996b). A simple plywood casing was put around the specimen,

both to protect the mask wall and to simulate the frame. A 25.4 mm (1 in) square block braced the window from the exterior

side. The entire unit was inserted into the mask wall, and shimmed to a tight fit. Any spaces were then filled with insulation,

and the inner and outer seams were taped.

An aluminum blind, with a typical slat geometry and white enamel surface, was then mounted at a nominal distance of 17

mm (0.67 in) from the window. The slats (2.54 cm wide and 60.96 cm long, 1 in x 24 in) were wired together in series to

provide the maximum electrical resistance for heating. This resulted in a total resistance of about 0.40 ohms, 10% of which

was due to the connecting wires. An adjustable AC power supply was then used to provide the desired power to the blind.

The calorimeter operated in the manner normally used for SHG testing except that all tests were conducted indoors. The

DA system was set to record all interior and exterior thermocouples, meter the power input to the pump and fans, meter the

temperature difference and flow rate into the calorimeter, and monitor and control the active thermal guard. Power dissipated

in the blind was set using a voltage controller and monitored by the DA system. To control the interior/exterior temperature

difference, the conditioning loop temperature was adjusted. Finally, two axial fans were situated 4 meters (13.1 ft) in front of

the mask wall, and provided wind perpendicular to the CTS. The fan speed was adjusted until the external air-film coefficient,

as measured using the CTS, was at the desired value.

Due to the relatively fast system response of the calorimeter (Collins 1997), the long test periods typically associated with

guarded hot box tests were not necessary. Thermal response tests showed that 5 time constants (or 99% of full response) were

achieved in approximately 40 minutes. Once the system was given time to respond to a new set of test conditions, steady-

state conditions were determined based on accepted calorimetric procedures (SCL 1993). In order to achieve steady-state

conditions, the heat transfer fluid was circulated through the absorber plate at the appropriate values for inlet temperature and

flow rate until they remained constant within ± 0.3 oC (0.17 F) and ± 1 W/oC (6.14 Btu/h⋅F), respectively, for 15 minutes

prior to each period in which the data were taken, and for the 15 minutes in which data were collected.

For an inward-flowing fraction test, the energy flows into and out of the calorimeter are shown in Fig 3. The electrical

energy input to the blind may be shown to equal

) (5) P Q Q Q Q Q Q Qflow fan pump walls mask CTS OFF= − − + + + +(

It is important to note that the total energy loss through the CTS, the terms contained in brackets in Eq. 5, is considered to be

the combination of losses driven by the air-to-air temperature difference (QCTS), and the outward-flowing fraction of power

dissipated in the blind (QOFF). Losses through the specimen were measured by the CTS in a separate test, using an equivalent

air to air temperature difference, when no power was dissipated in the blind. Thus letting P = N⋅P + (1-N)⋅P, and (1-N)⋅P =

QOFF , the inward-flowing fraction can be determined from

( )N

Q Q Q Q Q QP

flow fan pump lwalls mask CTS=

− − + + + (6)

An uncertainty analysis was performed on the experimental data based on the propagation of the estimated component

uncertainties according to the method of Kline and McClintock (Kline and McClintock 1953). Details of the method and the

uncertainty analysis can be found in (Collins 1997).

Test Series

The main objective of the experimental test sequence was to measure the inward-flowing fraction of a venetian blind with

respect to slat angle, and to quantify the effects of external variables such as the absorbed irradiance (I⋅α), internal/external

temperature difference (ΔT), and external wind speed or air film coefficient (ho). To achieve these goals, a statistical

experiment design, called a "face-centered central composite test sequence " (Montgomery 1984), was used to investigate the

level of interaction between these variables at each of the desired slat angles (θ) of -45, 0, 45, or 70o. Other geometric

considerations, such as nominal distance from the window, were not examined.

To test the effects of absorbed irradiance, data were collected for three input power levels, i.e., 50 , 125, 200 W (170.5,

426.3, 682.4 Btu/h). These power levels were expected to encompass the full range of anticipated solar absorption levels for a

shade the size of the test specimen. The low power level of 50 W (170 Btu/h) is representative of a reflective blind, whereas

the maximum value of 200 W (682.4 Btu/h) is representative of absorption in a darker blind. The power level of 200 W

(682.4 Btu/h) is representative of 800 W/m2 (253.6 Btu/ h⋅ft2) passing through two clear glazings of a 0.37 m2 (3.98 ft2)

window (the size of the test specimen).

The effect of the temperature difference across the window assembly was investigated by controlling the interior

temperature of the calorimeter to produce a temperature difference of 0, 5, and 10 oC (0, 2.8, 5.6 F), above the exterior

temperature. While it would have been preferable to maintain room conditions within the calorimeter and vary the

surroundings, this was not possible with the available equipment.

To test the effect of the exterior air film coefficient on the inward-flowing fraction, the wind speed was varied to provide

air film coefficients of 20, 25, and 30 W/m2K (3.5, 4.4, 5.3 Btu/h⋅ft2F). A single test sequence was also run for each slat angle

with the fan turned off. The low external heat transfer coefficient created in this test (~8 W/m2K, 1.4 Btu/h⋅ft2F), allowed the

effect of the exterior film resistance to become more pronounced.

RESULTS

Table 1 and Fig. 4 show the results of each test series in the context of the statistical experiment. Figure 5 shows the

results for all slat angles as a function of the four experimental input variables: ΔT, ho, P, and θ. The error bars shown

represent the experimental uncertainty associated with each measurement.

A stepwise regression analysis (Montgomery 1984) was performed on the test data to identify an equation that accounted

for the effects of the four independent variables. Starting with an equation containing all the independent variables and their

interactions, a term that does not contribute positively to the data fit could be statistically identified and removed. This

process is then repeated, using the reduced equation, until only significant terms remain. Using this method, an excellent fit

for the experimental data (standard error of 0.034) was obtained which contained 11 terms. Unfortunately, the complexity of

the fit made it unsuitable for any practical usage. Further stepwise regression identified a simpler equation with little change

in the quality of fit (standard error of 0.044). This relation, containing only 5 terms, is as follows

(7) PThTN o ⋅Δ⋅×+⋅×+⋅×−Δ⋅−= −−− 4222 1015.1)(cos1065.81036.0027.085.0 θ

This equation is valid within the test limits described in the previous section, for the blind used in this experiment. Figure 6

demonstrates the goodness of the fit. At a more practical level, an N value of 76% will have a standard error of ± 12% for the

venetian blind, slat angles and environmental conditions studied. This is drastically different, than the value of 100%

assumed in some previous investigations (Owens 1974; Van Dyck and Konen 1982).

Table 1. Summary of Inward-Flowing Fraction test results for all slat angles. Result uncertainties are as indicated.

N Test Conditions Slat Angle

P W (Btu/h)

ho W/m2K

(Btu/h⋅ft2F)

ΔT oC (F)

-45o 0o 45o 70o

50 (170.6) 20 (3.5) 0 (0) 0.87 ± 0.13 0.87 ± 0.14 0.87 ± 0.13 0.79 ± 0.15 50(170.6) 30 (5.3) 0 (0) 0.88 ± 0.18 0.87 ± 0.17 0.84 ± 0.12 0.76 ± 0.15

125 (426.3) 25 (4.4) 0 (0) 0.86 ± 0.07 0.86 ± 0.07 0.81 ± 0.07 0.82 ± 0.07 200 (682.4) 20 (3.5) 0 (0) 0.85 ± 0.04 0.84 ± 0.05 0.81 ± 0.03 0.82 ± 0.05 200 (682.4) 30 (5.3) 0 (0) 0.81 ± 0.04 0.83 ± 0.05 0.81 ± 0.03 0.81 ± 0.05 50(170.6) 25 (4.4) 5 (2.8) 0.68 ± 0.15 0.76 ± 0.10 0.64 ± 0.13 0.60 ± 0.14

125 (426.3) 20 (3.5) 5 (2.8) 0.78 ± 0.07 0.85 ± 0.07 0.75 ± 0.05 0.77 ± 0.07 125 (426.3) 25 (4.4) 5 (2.8) 0.73 ± 0.07 0.81 ± 0.07 0.72 ± 0.05 0.75 ± 0.07 125 (426.3) 30 (5.3) 5 (2.8) 0.74 ± 0.07 0.80 ± 0.07 0.71 ± 0.05 0.74 ± 0.07 200 (682.4) 25 (4.4) 5 (2.8) 0.78 ± 0.04 0.82 ± 0.04 0.75 ± 0.03 0.80 ± 0.05 50(170.6) 20 (3.5) 10 (5.6) 0.65 ± 0.17 0.73 ± 0.19 0.65 ± 0.14 0.65 ± 0.17 50(170.6) 30 (5.3) 10 (5.6) 0.51 ± 0.18 0.64 ± 0.18 0.54 ± 0.14 0.49 ± 0.16

125 (426.3) 25 (4.4) 10 (5.6) 0.74 ± 0.07 0.79 ± 0.07 0.73 ± 0.06 0.71 ± 0.07 200 (682.4) 20 (3.5) 10 (5.6) 0.80 ± 0.04 0.83 ± 0.05 0.77 ± 0.04 0.77 ± 0.05 200 (682.4) 30 (5.3) 10 (5.6) 0.71 ± 0.04 0.78 ± 0.04 0.74 ± 0.05 0.72 ± 0.05 125 (426.3) 8 (1.4) 5 (2.8) 0.78 ± 0.06 0.81 ± 0.06 0.78 ± 0.05 0.77 ± 0.06

DISCUSSION

The effects of the individual parameters are discussed in the following sections:

Slat Angle: In general, the results indicate that there is very little difference in the inward-flowing fraction between closed

and partially closed blinds. Measured values of N remained relatively constant for slat angles of -45o, 45o, and 70o. In the

context of inward-flowing fraction, there may only be a small difference between -45o or 70o slat angles. For a fixed

indoor/outdoor temperature difference, the results indicate the inward-flowing fraction is greater (N=0.80) for the case with

fully open blinds (i.e., θ = 0) as compared to 0.60 to 0.75 for the partially closed blinds. The increase in the inward-flowing

fraction for open blinds was primarily due to reduced radiative heat transfer between the blind and the inner surface of the

CTS.

Irradiance Level: With respect to irradiance, analysis of the data indicates that the inward-flowing fraction increased slightly

between low and high power inputs (72% at 50 W (170.6 Btu/h) to 79% at 200W (682.4 Btu/h)). This can be explained as

follows: Increased irradiance, and subsequent higher blind temperature, would increase convection from the blind to the room

air, while radiation from the blind to the interior of the calorimetric cell and window would increase proportionately. As a

result, more of the absorbed irradiance remains in the calorimeter cell. More importantly, the accuracy of measurements

taken at higher power levels is significantly better than those taken at low power levels.

Temperature Effects: When considering temperature effects, N reduced from 0.83 to 0.70 as the calorimeter interior

temperature was increased from 0 to 10 oC (0 to 5.6 F) above the ambient conditions. This confirms the previously stated

conclusions of Klems and Kelley (Klems and Kelley 1996). As the exterior temperature drops relative to the calorimeter

interior and blind temperatures, so too does the interior glass temperature. Increased radiation exchange from the blind to the

glass, would result in a decrease in the inward-flowing fraction.

Exterior Film Coefficient: While it was expected that as ho was increased (decreasing the overall R-factor for the window)

the inward-flowing fraction would drop, this was not evident in the experimental data. This is likely due to the fact that a

variation in ho from 20 to 30 W/m2K (3.5 to 5.3 Btu/h⋅ft2F), only changed the R-factor from 0.45 m2K/W (2.56 h⋅ft2F/Btu) for

ho=20 W/m2K (3.5 Btu/h⋅ft2F) to R=0.43 m2K/W (2.44 h⋅ft2F/Btu) for ho=30 W/m2K (3.5 Btu/h⋅ft2F). It is likely that N would

drop with increased ho if the window R-factor was low, e.g., in the case of a single glazing. This is an area for further

investigation.

CONCLUSIONS

An experimental apparatus and test method were developed for use in determining the inward-flowing fraction of

absorbed solar energy in interior venetian blinds. A properly installed window and blind combination, in which the blind is

electrically heated, can be used to determine N. The results of this study further indicate that:

1) The level of absorbed irradiance appears to have a minimal effect on the measured inward-flowing fraction other than to

increase measurement accuracy.

2) Increases in the interior/exterior temperature difference resulted in a modest reduction in the inward-flowing fraction for

all tests, i.e., N dropped by about 0.13 between 0 and 10 oC (0 to 5.6 F).

3) The range of naturally occurring values of ho had only a small effect on the overall U-factor of the double glazing system

studied, and therefore little effect on the inward-flowing fraction.

An equation has been presented which is suitable for the determination of the inward-flowing fraction for interior

venetian blind and double glazing combinations that are similar to the test sample. For quick estimates, a value of 76% would

be applicable to these systems for the range of the environmental conditions or blind angles studied.

The inward-flowing fraction was proven to depend on the interior/exterior temperature difference, the level of absorbed

irradiance, and the exterior film coefficient. To quantify the full impact of these results, however, values of the inward-

flowing fraction for a particular shade and glazing system must be combined with factors such as optical properties, usage

patterns, system orientation and location, and time of day. Such a combination would aid in refining SHG estimates when

shades are included as part of the system.

RECOMMENDATIONS

The variables examined by this experiment provided sufficient data to recommend calorimetric test conditions for the

measurement of inward-flowing fraction. Based on this study, it is suggested that the following conditions be applied:

1) a power level of about 250 W/m2 (79.2 Btu/h⋅ft2) of blind profile area is suggested, as power levels below this contribute

little to the SHG equation, and cause large uncertainties in calorimetric measurements;

2) testing should be conducted under realistic summer and winter conditions, depending on whether summer cooling or

winter heating is being evaluated;

3) standard ASHRAE exterior wind speeds of 3.4 m/s (11.2 ft/s) (summer) and 6.7 m/s (22.0 ft/s) (winter) would be

acceptable for testing (ASHRAE 1997).

FUTURE WORK

To fully examine the interaction between blind optical properties, the inward-flowing fraction, and usage patterns,

detailed theoretical modeling would be advantageous. This, used in conjunction with experimental data, is needed to refine

our understanding of the inward-flowing fraction interactions.

Analysis of tilted glazings would be also be useful as many solar calorimeters currently tilt in an effort to receive direct

normal solar irradiance. There is no proof that a tilted complex fenestration has the same inward-flowing fraction as a vertical

system. This testing is already underway at the Solar Calorimetry Laboratory.

Finally, future efforts should investigate multiple glazings, special films, and various blind geometries and optical

properties, under a wide range of environmental conditions.

ACKNOWLEDGEMENT

Funding for this project was provided by CANMET/NRCan, and the National Science and Engineering Research Council.

NOMENCLATURE

Af Area of fenestration, (m2, ft2)

F Solar Heat Gain Coefficient, dimensionless

hi,o Inside/outside film coefficient, (W/m2K, Btu/h⋅ft2F)

I Solar Irradiance, (W/m2, Btu/h⋅ft2)

N Inward-flowing fraction, dimensionless

P Blind Power, (W, Btu/h)

QCTS CTS heat loss, (W, Btu/h)

Qfan Fan input power, (W, Btu/h)

Qflow Metered energy in flow loop, (W, Btu/h)

QIFF Inward-flowing fraction of absorbed solar energy, (W, Btu/h)

Qmask Calorimeter mask losses, (W, Btu/h)

QOFF Outward-flowing fraction of absorbed solar energy, (W, Btu/h)

Qpump Pump input power, (W, Btu/h)

Qwalls Calorimeter wall losses, (W, Btu/h)

R Thermal resistance, (m2K/W, h⋅ft2F/Btu)

SHG Solar Heat Gain, (W/m2, Btu/h⋅ft2)

Ti,o Inside/outside temperature, (oC, F)

τ Transmissivity, dimensionless

α Absorptivity, dimensionless

θ Blind slat angle, (o)

REFERENCES

ASHRAE (1997). ASHRAE Handbook of Fundamentals. American Society of Heating, Refrigeration, and Air Conditioning Engineers, Inc., Atlanta. Bowen, R. P. (1985). “DBR’s Approach for Determining the Heat Transmission Characteristics of Windows.” Division of Building Research, National Research Council Canada. Collins, M. R. (1997). “Inward-Flowing Fraction of Absorbed Solar Radiation for Venetian Blinds.” M.Sc. Thesis, Queen’s University, Kingston, Ontario, Canada. Harrison, S. J., Van Wonderen, S. J., Wright, J. L., and McCluney, R. (1996a), “Evaluation of Solar Heat Gain Test Methods.” Final Report of ASHRAE Research Project 713, American Society of Heating, Refrigeration, and Air Conditioning Engineers, Inc., Atlanta. Harrison, S. J., and Van Wonderen, S. J. (1996b). “Solar Heat Gain Performance Evaluation of Commercial Solar-Control Glazings and Shading Devices.” Buildings Group, CANMET. Ottawa Jordan, R. C. and Threlkeld, J. L. (1959). “Determination of the Effectiveness of Window Shading Materials on the Reduction of Solar Radiation Heat Gain.” ASHRAE Trans. 65, 683-696.

Klems, J. H. and Warner, J. L. (1992). “A New Method for Predicting the Solar Heat Gain of Complex Fenestration Systems.“ Thermal Performance of the Exterior Envelope of Building Conference V, Clearwater Beach, FL. Klems, J. H. and Kelley, G. O. (1996). “Calorimetric Measurements of Inward-Flowing Fraction for Complex Glazing and Shading Systems.” ASHRAE Trans. 102 (1), 947-954. Klems, J. H., and Warner, J. L. (1997). “Solar Heat Gain Coefficient of Complex Fenestrations with a Venetian Blind for Differing Slat Tilt Angles.” ASHRAE Trans. 103 (1) Kline, S. J., and McClintock, F. A. (1953). “Describing Uncertainties in Single-Sample Experiments.” Mechanical Engineering Montgomery, D. C. (1984): Design and Analysis of Experiments – Second Edition. John Wiley and Sons Inc. Owens, P. G. T. (1974). “Solar Control Performance of Open and Translucent Louver Systems.” ASHRAE Trans. 80 (2), 324-336. Solar Calorimetry Laboratory (1993). “The Determination of Fenestration Thermal Performance Using Simulated Solar Irradiance.” Natural Resources Canada, Report DSS No. 06455-23440-0-9469. Van Dyck, R. L. and Konen, T. P. (1982). “Energy Conservation through Interior Shading of Windows: An Analysis, Test and Evaluation of Reflective Venetian Blinds.” Lawrence Berkeley Laboratory, University of California.

a)

SolarAbsorberPanel

TestSpecimen

MaskWall

Active Thermal Guard

Insulation

Circulating FansSupply WaterReturn Water

Air Flow

Baffle

Liquid to AirHeat Exchanger

b)

Figure 1: Queen’s Solar Calorimeter. a) Photo of the calorimeter and b) cross-sectional schematic (not to scale).

Blind

Nominal Distance

θ

Pine

Glass

Plywood

Neoprene Seal

Foam Core

Mask Wall

InteriorExterior

a)

b)

Figure 2: Blind installation details. a) Detail of installation (Harrison and Van Wonderen 1997b) and b) photo of CTS and blind assembly.

Qwalls

Qflow

Qpump

Qfan

P

QOFF

ControlVolume

QIFF

Qmask

QCTS

Figure 3: Calorimeter energy balance for inward-flowing fraction testing.

Blind Powerho

ΔT

20 W/m2K

30 W/m2K

50 W 200 W

0 oC

10 oC

0.86

0.76

0.87

0.87

0.84

0.83

0.80

0.81

0.85

0.82

0.73

0.64

0.79

0.78

0.83

0.818 W/m2K

b) 0o Slat Angle

Blind Powerho

ΔT

20 W/m2K

30 W/m2K

50 W 200 W

0 oC

10 oC

0.86

0.68

0.87

0.88

0.85

0.81

0.74

0.73

0.78

0.78

0.65

0.51

0.74

0.71

0.80

0.788 W/m2K

a) -45o Slat Angle

Blind Powerho

ΔT

20 W/m2K

30 W/m2K

50 W 200 W

0 oC

10 oC

0.82

0.60

0.79

0.76

0.82

0.81

0.74

0.75

0.77

0.80

0.65

0.49

0.71

0.72

0.77

0.778 W/m2K

d) 70o Slat Angle

Blind Powerho

ΔT

20 W/m2K

30 W/m2K

50 W 200 W

0 oC

10 oC

0.81

0.64

0.87

0.84

0.81

0.81

0.71

0.72

0.75

0.75

0.65

0.54

0.73

0.74

0.77

0.788 W/m2K

c) 45o Slat Angle

Figure 4: Values of measured N as represented in “face-centered cubic composite” experimental designs. Values next to nodes represent measured values of N at the corresponding values of ho, P and ΔT. Figures a) to d) are representative of the results obtained for the blind slat angles studied.

P (W)

20 40 60 80 100 120 140 160 180 200 220

N

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

ΔT (oC)

-2 0 2 4 6 8 10 12 14

N

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

ho (W/m2K)

0 5 10 15 20 25

N

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Figure 5: Inward-flowing fraction results plotted verses dependant variables for all slat angles. σ -45o slat angle, λ 0o slat angle, τ 45o slat angle, ν 70o slat angle.

0.5

0.6

0.7

0.8

0.9

1

0.5 0.6 0.7 0.8 0.9 1

Measured N

Cal

cula

ted

N (E

q. 7

)

Figure 6: Comparison of the inward-flowing fraction as measured and calculated using Eq. 7.