an infrared sphere method to measure mean radiant temperature. - stainless steel ice balls
Average radiation temperature (MRT)
It is an important indicator to measure the thermal comfort of the thermal environment (Fanger et al. 1980; Fanger et al. 1985;
And Korsgaard 1949).
About a radiation heat transfer accountthird to two-
30 of the total heat transfer personal experience.
The remainder of the heat transfer is mainly convection, which is directly related to the air temperature.
The use of a single air temperature to indicate that the thermal environment may not be representative, as MRT may be significantly different from the air temperature, especially for spaces with large open windows.
Therefore, MRT is an important factor in assessing the thermal comfort of occupants, as it indicates a radio transfer to and from people.
There are two established methods in determining MRT: the black ball method and the surface temperature method.
Both methods are defective and cannot be used for HVACcontrol.
Researchers recognize that it is not feasible to measure, monitor and control MRT (
Jones and Chapman 1994)
Trying to simplify the determination of MRT.
The black ball method uses an air temperature sensor, a single black ball temperature sensor, and a speed meter.
The black temperature sensor measures the resulting temperature caused by radiation and convection heat transfer.
The air temperature and air speed measured by the anemometer allow the calculation of the convection heat transfer composition through the empirical equation.
Since the thermal mass of the sphere prevents the sensor from producing instantaneous data, the black ball method is not suitable for measuring dynamic MRT changes and usually takes 30 minutes of settling time to produce reliable results.
The black ball method must have three sensors deployed in the location to be exported by MRT in a tight configuration.
This usually means where the occupants are, and it is likely to interfere with them, and at the same time, it will expose sensitive sensors to the occupants and distort the results.
This is especially critical to the fragile heat.
The ball speedometer is easy to damage and easy to lose calibration.
Surface temperature method using surface-
Install a temperature sensor or an infrared camera to determine the average surface temperature and combine the field of view coefficient, the MRT can be calculated for a specific location.
The average value of the surface sensor reading may not represent the actual average temperature of the surface with a complex temperature gradient, such as a column wall structure with poor insulation.
Failure of the surface sensor to adhere properly will affect the accuracy of the data set, again, if the infrared camera is moved or shifted, the mapping will be out of date and cause insufficient temperature readings.
Determining the surface temperature method of emrt requires more preparation and deployment time than conventional sensor packages like the black ball method.
The view factor can be determined by three spatial integral, but usually by the view factor equation developed by Fanger for the rectangular room and referenced in the ASHRAE manual-Fundamentals (2009).
Another way to determine the perspective factor is through the nusseltandialog (Nusselt 1928).
The determination of these two view factors is limited inaccuracy and development time.
Since the sensor is located on the surface of the room, rather than determining the location of the MRT, the occupant's indication is limited.
However, indirect interference persists, such as wire wiring that results in an average temperature sensor on the surface.
To solve these problems while still being able to produce accurate MRT measurements, an infrared sphere method was developed.
The red ball method is proposed on the basis of the existing MRT definition. it does not include
Wave radiation enables the infrared sensor to be used, and the infrared sensor is only sensitive to the short wave radiation.
The definition of MRTis is based on the heat emitted by a hot object and therefore is similar to the heat transfer in the infrared spectrum.
Infrared radiation follows the law of reflection like other radiation such as light;
Therefore, Nusselt simulations that allow the use of photographic methods to determine the angle factor will also be applicable to infrared spectra.
This means that if the infrared camera replaces the camera in the photographic method, the infrared camera will read the temperature of the surrounding environment with the perspective factor-
Represents the MRT seen in the hemisphere, which is the view of the room. A back-to-
The two infrared sensors and the hemisphere are reset to a sphere, and the average value of the sensor readings therefore produces the MRT of the room.
More detailed theories will be discussed later in this paper.
The red ball method is used in two separate buildings together with the black ball method and surface temperature method for several weeks to measure MRT as part of a large research project.
This paper introduces the development of the method of red ball, the test device in two independent buildings, and the comparison and discussion of the results.
The existing definition of MRT and its significance to MRT measurement methods are discussed.
The traditional method of determining the average radiation temperature needs special attention because it is essentially difficult to determine.
The first MRT concept proposed by Korsgaard (1949)
ASHRAE passed by the United States (2010)
International Organization for (ISO)(2007)
As a thermal environment indicator of a room or space.
ASHRAE manual--Fundamentals (2009)
Define MRT as "the uniform temperature of the imaginary shell, where the radiation heat transfer from the human body is equal to the actual non-
"Radiation heat transfer in the thelongwave spectrum, the requirements of the human body mean that the radiation temperature is in a specific position.
There are two accepted methods to determine the actual average MRT.
The first is the black ball method and the second is the surface temperature method.
The interpretation of the MRT definition by these two accepted methods is inconsistent.
The black ball pair includes microwave, X-
Radiation and gamma radiation, therefore, will have a stronger reaction to solar radiation.
The surface temperature method is based entirely on Stefan-
Zimmerman's law, or rather, the law of radiation of mischief, excludes other radiation such as microwaves and gamma rays.
Therefore, the Association of Air Conditioning Engineers (2010)and ISO (2007)
It has been shown that the black ball method tends to overestimate MRT under direct solar radiation.
In climate chambers without direct solar radiation, most of the accepted thermal comfort and MRT studies have been completed (Fanger et al. 1980; Fanger et al. 1985; Korsgaard 1949);
The relationship between solar radiation and thermal comfort has not yet been well established and it seems that pure thermal radiation should be used to explain MRT.
A black ball thermometer method for the determination of MRT (T. Bedford & C. G. Warner 1934)
And quote in ASHRAEHandbook--Fundamentals (2009).
The black ball thermometer was originally a copper water Cabinet float, painted black and inserted in the middle with athermeter.
It is found that the black ball represents the visual factors of the human body.
The relationship between the global temperature and MRTis given (2009): [T. sub. MRT]= [[([T. sub. g]+ 273). sup. 4]+ [1. 10 x [10. sup. 8]x[V. sub. a. sup. 0. 6]]/[[[epsilon]. sub. globe]x [D. sub. 0. 4]]x ([T. sub. g]-[T. sub. a]). sup. 0. 25]](1a [SI])where [T. sub. MRT]
= Average radiation temperature, K [T. sub. g]
Global temperature ,[degrees]C [V. sub. a]
= Wind speed, m/s [[epsilon]. sub. globe]
= Immigration of black ball, 0. 95 [T. sub. a]
C d = diameter of sphere, m or [T. sub. MRT]= [[([T. sub. g]+ 459. 67). sup. 4]+ [4. 47 x [10. sup. 7]x[V. sub. a. sup. 0. 6]]/[[[epsilon]. sub. globe]x [D. sub. 0. 4]]x ([T. sub. g]-[T. sub. a]). sup. 0. 25]](1b [I-P])where [T. sub. MRT]
= Average radiation temperature, R [T. sub. g]
Global temperature ,[degrees]F [V. sub. a]
= Wind speed, m/s [[epsilon]. sub. globe]
= Immigration of black ball, 0. 95 [T. sub. a]
F d = the diameter of the globe, ft found that the globe temperature represents the operating temperature of the person sitting.
However, it was found that for a standing person, the radiation exposure of the ceiling and floor was too heavy, and again, for a tilted person, the floor and wall exposure should be excessively weighed (ISO 2007).
The MRT needs to determine the flight speed;
This is usually done by heat-
Calibrate to measure the spherical anemometer at low speed, such as free reflection. Hot-
The ball speedometer is a very sophisticated equipment with a very high purchase cost.
In order to eliminate the need to measure the airflow velocity, a double Globe method is developed (ISO, 2007).
This method takes advantage of a black sphere and a polished sphere, which is used as a representation of heat transfer due to convection.
Another method requires understanding of the surface temperature and calculating the observed factors on the human body.
MRT can be determined by: Equation in ASHRAE manual--Fundamentals(2009)[T. sub. MRT. sup. 4]= [[SIGMA]. sub. i=0. sup. n][T. sub. n. sup. 4]x[F. sub. n](2)where [T. sub. MRT]
= Average radiation temperature, K or R [T. sub. n]
= Wall Temperature, K or R [F. sub. n]= view factor -
Determined according to the layout of the site plan, the surface temperature method has been used to calibrate the black ball sensor in the climate chamber, which is considered the most accurate method due to its proximity to the actual definition of MRT.
The surface temperature can be determined by a series of surface temperature sensors.
A sufficient number of temperature sensors are required to construct an accurate description of the table.
Accuracy may be affected when the surface has an irregular temperature gradient.
An infrared camera can be used to map the surface temperature.
Although the infrared camera method can handle complex temperature distribution and has good graphical sensitivity, the accuracy of temperature measurement is usually within the [range]+ or -]2[degrees]C ([+ or-]3. 6[degrees]F)
Significantly affected by surface texture, specific radiation rate and background radiation.
In addition, infrared images provide only snapshots of temperature, while infrared cameras that can provide more accurate readings and perform background correction and calibration tend to be much more expensive.
The view factor is the geometric correlation between each surface and the human body, depending on the position of the person.
As a special function, the view factor can be described as the thermal personal reception ratio in the specific surface direction corresponding to the view factor.
The view factor can be developed by partial differential equations, but has been linear to the basic room shape via fanger (1970)
For those standing and sitting.
Alternatively, the view factor can be determined by the Nusselt sphere method (Nusselt 1928)
, Which is a simpler way to compare the projected surface area of a particular surface to the virtual ball on the subject objectsectional area.
Using the perspective factor theory of Nusselt, a simple polishing sphere photography method can be used to determine the perspective factor.
The development of the red ball method developed an alternative method to measure MRT, that is, the red ball method.
The theory of this method is based on the simulation method (Nusselt, 1928)
Where the view factor of the plane area and the small plane element is the ratio of the plane area projection on any hemisphere-
The dimension base area is divided by the base area of the hemisphere.
Proof is not the focus of this article.
Figure 1 is the description. As Farrell (1976)
It has been shown that the area ratio obtained by photography of the reflective hemisphere can estimate the angle factor between the radiation plane and the plane element, the main error is the circle degree of the sphere caused by optical reasons and the truncated angle of the hemisphere.
The infrared sphere method for MRT measurement consists of a highly polished low polished sphere
In order to determine the indoor radiation temperature of the reflection, the reflector and two opposite radiation temperature sensors are emitted.
Theoretically speaking, the radiation temperature reading of the reflection chamber is the actual MRT affected by the reflection ratio.
Reflector geometry infrared reflector has geometric requirements similar to the top reflector used in lighting equipment.
The launch reflector is not easy to buy on the market, but the perfect semi-spherical stainless steel, aluminum and copper balls are available.
The aim is to use a high reflective surface of a polished metal ball, allowing a commercial infrared sensor to view all the radiant surfaces of the room.
The two sensors are positioned to read the reflected heat from the polished sphere.
As shown in Figure 2, the task of each sensor is to read half of the room quadrant.
The view angle aspect ratio of the expected infrared sensor is 1:2, which means that the viewing angle cone is 14. 036[degrees](28. 072[degrees]
To do this, the sensor must be positioned so that the end of the cone receives the reflected energy orthogonal to the sensor.
This is calculated by Figure 3.
The construction of the equipment is based on the construction of the equipment ise I with a radius of 101 stainless steel sphere. 6 mm (4 in. ).
It is lifted to a base. 2 mm (3in. )
Form above the cantilever arm of the base.
The cantilever arm extends out from the center of the sphere and supports two extensions, which in turn support each infrared sensor.
The extended structure makes the position of the infrared sensor in relation to the atmosphere good-tuned.
Each sensor can be adjusted vertically;
The sensor's teeth can be tilted up and down, yawning left and right.
The slot allows the sensor to be closer or further away from the Earth.
There are four degrees of freedom in total, only one sideto-
Side displacement cannot be provided (Figure 4).
Where R = ball radius [beta]
= Perspective of infrared sensor [alpha]
= Reflection angle [theta]
= The law of reflection the thermal expansion of the wire angle, so the deformation of the sphere and the relative position of the sensor;
Effects of radiation paths, such as shadows caused by other equipment required when determining mrt;
Effects of temperature and humidity on absorption coefficient and conductivity
Inertia of the sensor, residual heat flow and residual signal, etc.
Table 2 lists the estimated uncertainty of each method using the mean value of the test period recorded in Test Site 2.
Relive the wording in MRT and ASHRAEHandbook defined by the definition of mean radiation temperature Fanger-Fundamentals (2009)
As: "The radiation heat transfer of the human body is equal to the uniform temperature of the binary shell of the actual non-radiation heat transfer
"The definition of radiation heat transfer can and has been considered to be radiation heat transfer through longwave radiation, which is reflected in the method of calculating MRT by surface temperature and angle factor.
This means that when measuring MRT, the short wave radiation from solarsource is usually omitted, which affects the accuracy of the device.
Essentially, MRT determined by a sufficiently distributed surface temperature sensor will be different from MRT determined by the black ball method if the black ball is in direct sunlight.
This difference is caused by the working mechanism of each method.
The working principle of the black ball method is to find a neutral temperature point in the position of the recipient, at this temperature point, global Radiation heat flux gain/loss matches global convection heat loss/gain when the surface temperature method works by measuring the surface temperature, these surface temperatures can be used to determine the langwa radiation heat flow towards the receiver.
Direct sunlight on several surface temperature sensors will only raise a portion of the heat flow to the recipient, while direct sunlight on the black ball will significantly increase the heat flow into the hemisphere direction of the solar event.
Like the surface temperature method, the red outer sphere method measures the short-wave infrared heat flow reflected on the polished sphere.
Since the infrared sensor is only sensitive to the short wave radiation, and the polished stainless steel is higher than the short wave radiation under the short wave radiation;
The red ball method does not represent the effect of direct sunlight.
MRT determined by the black ball method is one of the reasons for the other two methods at night, although in direct sunlight, MRT will increase significantly.
Meteorological data obtained from Environment Canada (2012)
It is shown that the precipitation on April 20, 25 and 26 did not have direct solar revenue, and Figure 9 shows that the MRT derived by the black ball method is similar to other methods, with no characteristic spikes at noon.
This is related to the ISO standard (ISO 2007)
In the performance of the black ball, it was found that the black ball overestimated the MRT when the sun was insufficient.
This raises the question, should MRT consider direct solar radiation heat transfer?
Or direct solar radiation should be removed from the definition of MRT.
Solar radiation is not traditionally controlled by HVACsystem, but it can be clearly controlled by occupants by drawing curtains.
While HVAC systems can affect surface temperature, air temperature, and speed, these items cannot be directly controlled by occupants.
In conclusion, the red-ball method for determining the mean radiation temperature in this study shows that it is consistent with other methods for determining the mean radiation temperature in two field test sites.
Some differences between the black ball method and the red ball method were recorded, and previous studies were also recorded (ISO 2007).
Further research is needed to verify it before adopting the red ball method.
This study also illustrates the importance of MRT definition to the method of determining MRT. An in-
It is recommended to conduct an in-depth review of its intended application.
Conclusion in two different site study sites, the infrared sphere method for determining MRT was tested with different heating systems and building shells.
In both locations, MRT determined by the red ball method is consistent with MRTs obtained by the traditional method.
It was found that the infrared sphere method is more resistant to direct sunlight than the black ball method and is very similar to the temperature estimated by the surface temperature method.
The success of the infrared ball method also shows that the reflector method is feasible and more practical for HVAC control.
For the purpose of HVAC control, a minimally invasive method for measuring emrt or AUST can be developed.
The law of reflection allows special reflector shapes to make the infrared MRT sensor more sensitive in some directions;
Therefore, the reflector can be designed to allow the infrared sensor to view the radiation heat at an equivalent position other than where the sensor is located.
This allows the sensor to be offset to the wall instead of focusing them in the position where the occupants are, like the black ball.
The infrared sphere is relatively simple, and it itself is more economical and sturdy than the black ball method, which requires expensive, sensitive and fragile wind speed meters to determine wind speed and temperature.
Table 3 summarizes the comparison of the three methods for determining MRT.
The costs and setup times listed in Table 3 are specific to the experiments performed in this article and may vary in different cases.
To sum up, the red ball method shows a promising prospect in the determination of thermal weight, which is worthy of further exploration.
More testing and comparison should be carried out, especially compared with other methods, before accepting the red ball method as an accurate method for determining MRT, the quasi-red ball method should be lieutenant-colonel in the controlled environment.
More importantly, the definition of MRT should be further refined.
The authors thank the University of Ryerson and the Canadian commission for natural science and engineering studies for their financial support (NSERC).
We would like to express our gratitude to the gentleman.
Fred Belusa kindly allowed us to conduct field studies at his home and at his PhD.
Liao Zaiyi and Dr.
Rent theirequest and negotiate at Meiliana Horvat.
Term R = sphere radius = angle of view of infrared sensor = reflection angle = law of reflection line angle x = distance from the front of the sensor to the center of the sphere T = temperature, k ,[degrees]C, [degrees]
F, r v = speed D = diameter F = angle of view coefficient = specific radiation rate subscript MRT = mean radiation temperature g = Earth a = Air n = Surface number reference ASHRAE. 2009.
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Christopher Leung, Peng huago, PhD, Peng member ASHRAE Christopher Leung is a graduate researcher in the Department of architectural science, University of Ryerson, Toronto, Ontario, Canada, andHua Ge is an assistant professor at the Department of Architecture, civilization and environmental engineering, Concordia University, Quebec, Canada.