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Measurements of air temperatures close to a low-velocity diffuser in displacement ventilation using an infrared camera
Energy and Buildings 34 (2002) 687–698
Measurements of air temperatures close to a low-velocity diffuser in displacement ventilation using an infrared camera M. Cehlina,b, B. Moshfegha,*, M. Sandbergb a
Division of Energy and Mechanical Engineering, Department of Technology, University of Ga¨vle, S-801 76 Ga¨vle, Sweden Center for Built Environment, Division of Indoor Environment and Ventilation, Laboratory of Ventilation and Air Quality, University of Ga¨vle, S-801 02 Ga¨vle, Sweden
b
Received 14 January 2001; accepted 11 February 2001
Abstract The near zone of supply air diffusers is very critical for the indoor climate. Complaints of draft are often associated with low-velocity diffusers in displacement ventilation because the air is discharged directly into the occupied zone. Today, the knowledge of the near zone of these air supply diffusers is insufficient, causing an increased need for better measuring methods and representation of the occupied zone. A whole-field measuring technique has been developed by the authors for visualization of air temperatures and airflow patterns over a large cross-section. In this particular whole-field method, air temperatures are measured with an infrared camera and a measuring screen placed in the airflow. The technique is applicable to most laboratory and field test environments. It offers several advantages over traditional techniques; for example, it can record real-time images within large areas and capture transient events. The purpose of this study was to conduct a parameter and error analysis of the proposed whole-field measuring method applied to a flow from a low-velocity diffuser in displacement ventilation. A model of the energy balance, for a solid measuring screen, was used for analyzing the influence of different parameters on the accuracy of the method. The analysis was performed with respect to the convective heat transfer coefficient, emissivity, screen temperature and surrounding surface temperatures. Theoretically, the temperature difference between the screen and the ambient air was found to be 0.2–2.4 8C for the specific delimitation in the investigation. However, after applying correction the maximum uncertainty of the predicted air temperature was found to vary between 0.62 and 0.98 8C, due to uncertainties in estimating parameters used in the correction. The maximum uncertainty can be reduced to a great extent by estimating the convective heat transfer coefficient more accurately and using a screen with rather low emissivity. # 2002 Elsevier Science B.V. All rights reserved. Keywords: Thermography; Whole-field measurement; Infrared camera; Visualization; Air temperature; Airflow pattern
1. Introduction It is well known that the indoor climate is important for our well-being, productivity and quality of life [1–4]. The sensation of the thermal indoor climate is a complex function of a number of physical variables, such as air temperature, air velocity, turbulence intensity and concentration of pollutants [4–6]. The values of these variables can vary strongly in a room or enclosure. It is, therefore, important to determine the spatial distribution of thermal parameters in the occupation zone. With good knowledge it is possible to evaluate a good comfort level. There is great dissatisfaction with today’s heating, cooling and ventilation technology and it is far from uncommon that mistakes are repeated. The basic reason for the situation is * Corresponding author. Tel.: þ46-2664-8804; fax: þ46-2664-8828. E-mail address: [email protected] (B. Moshfegh).
that the indoor climate is practically invisible, thus it is: difficult to conduct a specific dialogue about the indoor climate, difficult to set up a specification of requirements, difficult for manufacturers to show differences in the function of different systems and there is no learning process established about the indoor climate which would give experience feedback. The consequences are that it is difficult to implement quality control and to purchase a specified indoor climate. Since the price and not the quality and function will be decisive and customers more often buy the cheapest system, mistakes are repeated. An example of such dissatisfaction is the complaints of draft associated with low-velocity diffusers in displacement ventilation [7]. This kind of ventilation system is often used in industrial areas with high thermal load but also in offices. The system has several potential advantages, i.e. better air quality and efficient cooling of rooms [8]. It allows an efficient use of energy because the inlet temperature can
0378-7788/02/$ – see front matter # 2002 Elsevier Science B.V. All rights reserved. PII: S 0 3 7 8 - 7 7 8 8 ( 0 1 ) 0 0 1 3 3 - 5
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Nomenclature As Ar Fs–i h hd Ji l q Ta Ta DTa Ti Ti Tin Ts Troom DTs Tw uin y
area of the measuring screen (m2) gðTroom Tin Þhd =ðTroom u2in Þ view factor between screen and surface i height of the screen (m) height of the diffuser (m) radiosity (W/m2) length of the screen (m) heat flow (W/m2) ambient air temperature (K), (8C) Ta/Ts accuracy of the predicted air temperature (8C) temperature of surface i (K), (8C) Ti/Ts inlet temperature (8C) temperature of the screen (K), (8C) average room temperature (K) accuracy of the screen temperature (8C) weighted mean surrounding temperature (K), (8C), see Eq. (4) inlet velocity (m/s) distance from floor (mm)
Greek letters a convective heat transfer coefficient (W/(m2 K)) Da accuracy of the convective heat transfer coefficient (W/(m2 K)) e emissivity De accuracy of the emissivity s Stefan–Boltzman constant (5:67 108 W/ (m2 K4)) be higher than for mixing ventilation systems. For these types of diffusers the airflow is supplied direct into the occupied zone and the flow accelerates towards the floor due to the gravity effect on the cold air. The near zone (defined as the area close to the diffuser where the air velocities are higher than 0.2 m/s) is, therefore, very critical. Today, the knowledge of this near zone is insufficient. It is difficult for designers to estimate the extent of the near zone for arbitrary airflow rates, supply air temperature and arbitrary supply diffuser size and shape. Because the indoor climate is invisible, it is often overlooked at the design stage. Therefore, there is a need to develop better measuring methods and flow models, especially for low-velocity air supply in displacement ventilation. However, Ska˚ aret [9] has recently developed a semi-empirical flow model for displacement ventilation, which yields improved test standards and design methods for displacement ventilation. But, there is still much more work to do in order to fully achieve understanding and knowledge among clients and professionals, about the functions and performance of different air diffusers, especially low-velocity diffusers. This lack of understanding makes planning a displacement ventilation system
become a trial and error process, which leads to many malfunctioning systems. Therefore, it is hard to evaluate a good occupant comfort level and the industry gets a low reputation. One important aim of the present ongoing research is to improve the present situation by making the indoor climate visible in the early stages of the design process. To measure air temperatures over large areas in a ventilated room is today very time consuming and impractical with traditional technology and it yields insufficient information with low resolution. It takes either many sensors or the translation of a single sensor to cover the temperature distribution over a large area. Measuring instruments also give rise to airflow and temperature disturbances in the tested region. Therefore, careful and detailed field studies with the help of point measuring techniques are quite impossible. To overcome the problems and limitations with traditional techniques and invisible indoor climate, a measuring technique has been developed by the authors based on infrared thermography [10]. Infrared thermography is now commonly used in the industry and in research activities [11– 13]. It has become a qualitative tool that can be widely used in research. The measuring technique developed by Cehlin et al. [10] is a whole-field method making it possible to rapidly visualize both air temperatures and airflow patterns over a large cross section. A whole-field method is a measuring technique in which physical quantities are recorded simultaneously over a whole field in contrast to traditional point-measuring methods. In this particular whole-field method, air temperatures are measured with an infrared camera in conjunction with a measuring screen acting as a radiation target sheet, placed parallel with the airflow stream (Fig. 1). The proposed technique is very useful for checking the performance of ventilation systems in different environments. It is applicable to both laboratory and field test environments, such as in industries and workplaces. Because the technique records real-time images, correction and improvement of the performance of diffusers can be made instantaneously on site (Fig. 2). The temperature measurements can be carried out in several planes around the supply device (Fig. 3). In each
Fig. 1. Setup for measuring air temperatures in the near zone of an air supply diffuser using infrared thermography.
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Fig. 2. Thermal images taken by infrared thermography. The left thermal image shows a bad-functioning low-velocity diffuser for displacement ventilation system taken in a factory hall in Sweden. The right thermal image was taken in the near-zone of the same low-velocity diffuser after improvements, see [18] for more information.
Fig. 3. Measurement planes around a supply device.
plane, the temperatures are recorded with an infrared camera perpendicular to the measuring screen. For an ordinary infrared camera, the number of pixels in each image is 320 240 ¼ 76,800. From the two-dimensional measurements one can make a three-dimensional representation by means of modern three-dimensional programs (Fig. 4), that can also be implemented in computer-aided design (CAD) programs. This type of presentation enables a direct comparison between computational fluid dynamics (CFD) and the measurements. One difficulty with CFD is to define the boundary conditions accurately. However, infrared camera measurements can easily and quickly provide boundary conditions on surface temperatures of the walls as well as
Fig. 4. A typical three-dimensional reconstruction of the temperature distribution achieved by infrared camera measurements.
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the diffuser for CFD. Thermal images achieved by infrared camera measurements can also be combined with images from other whole-field techniques, yielding a very powerful representation of the indoor climate [14]. The intention of this study was to perform a parameter and error analysis of the proposed whole-field measuring method in a flow from a low-velocity diffuser in displacement ventilation. A model of the energy balance for a solid measuring screen is used for analyzing the influence of different parameters on the accuracy of the method.
2. Theory When a screen is placed in an airflow it might disturb the flow pattern and also the temperature distribution. However, it has been showed and reported by Cehlin et al. [10] that a screen placed parallel to the air stream from a low-velocity diffuser in displacement ventilation has negligible effect on both the velocity and the air temperature distribution. Remaining sources of error are then incorrect screen surface temperature compared to the ambient air temperature and infrared camera measurement errors. Recent experiments by Cehlin et al. [10] showed that a modern high-resolution infrared camera measures the surface temperature of a high emissivity paper screen with very good accuracy. An infrared camera measures the emitted infrared radiation from the measuring screen. However, the radiation detected by the camera also includes radiation from surroundings reflected in the screen. In order to eliminate this reflected radiation the screen must have a high emissivity. This is a cameraimposed limitation. Because the surrounding medium is air, the detected radiation is more or less uninfluenced by absorption in the medium with the camera working around a wavelength of 7–13 mm. However, air with very high moisture can absorb a fraction of the emitted radiation from an object and cause small errors at long distances between the object and the camera. Ideally, the air exchanges heat with the measuring screen by convective heat transfer, making the screen adopt the same temperature as the local air temperature. However, in displacement ventilation air is supplied at low velocities, yielding rather low values for the convective heat transfer coefficient, which means that there will be high thermal resistance for heat transfer between the screen and the local air. As a result, the measuring screen will not achieve exactly the right temperature, due to radiative heat transfer between the surroundings and the measuring screen. Experiments have showed that all tested screen materials exhibit slightly higher temperatures than the ambient air when exposed to cold air from the diffuser. Screens with high emissivity were about 1–2 8C warmer than the ambient air temperature in the cold airflow region [10]. Because the measuring screen has a low thermal mass it will reach steady-state condition quickly. The result will be that energy leaving the screen will be of the same magnitude
Fig. 5. Energy balance over screen.
as energy going in to the screen. Theoretically, the incoming radiation energy absorbed by the screen will undergo some lateral heat conduction inside through the screen and then leave the screen by convective heat flow. Due to the thinness and rather low conductivity, it is assume that lateral conduction has a negligible effect. Assuming steady-state condition and that lateral conduction does not influence the temperature distribution of the screen, an energy balance over the measuring screen can be carried out. The energy balance over the screen is shown in Fig. 5. It leads to a relationship between the air temperature and the screen temperature, as follows: se X Ts Ta ¼ Fsi ðTi 4 Ts 4 Þ (1) a or in dimensionless form Ta ¼ 1 RAD;
(2)
where RAD ¼
seTs 3 X Fsi ðTi 4 1Þ a
(3)
The radiation number (RAD) can be interpreted as a measure of the quality of the screen temperature. For best performance, RAD should, of course, be close to zero yielding a low heat transfer resistance between the screen and the ambient air. To attain a screen in equilibrium with the ambient air, its material should have an emissivity very close to zero. However, it has been shown that it is impossible to use a measuring screen with low emissivity due to infrared camera measurement errors [10]. It is a tradeoff in the emissivity of the screen. In order to drive the screen temperature toward the temperature of the ambient air, it should have a low emissivity, so that its temperature depends more on convection with the ambient air and less on radiation to the surrounding walls. However, low emissivity introduces errors into the measurement of the screen temperature by the infrared camera. In addition to the emissivity of the screen, the screen error depends highly on the convective heat transfer coefficient and the temperature of the ambient air and surrounding surfaces, as well as the view factors between these surfaces and the screen. Given knowledge of these parameters, the difference between the screen temperature and the ambient air can be accounted for mathematically using Eq. (1). The bigger the difference between the ambient air temperature and the surrounding surface temperatures, the higher the screen temperature
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Fig. 6. The layout of the room used in the measurements.
error. Locally very warm or cold surfaces can cause large screen errors if the view factor is high. One possible way to reduce the measurement error is to use a two-material screen. The emissivity of the screen material facing the camera must still be high (around 0.9), but a lowemissivity material, such as glossy aluminum with an emissivity around 0.05 can cover the opposite side. The effective emissivity will then be reduced by almost 50 %.
3. Measurements and analysis procedures The purpose is to investigate the accuracy of the present whole-field method for a typical office room, sized 4:1 m 3:4 m 2:7 m, under normal thermal indoor conditions. The design of the room used in the investigation is shown in Fig. 6. The air was supplied through a semicircular low-velocity diffuser of height 0.6 m with a free area of 0.0075 m2, located at the center of one of the walls. In order to be able to analyze the influence of the different parameters on the accuracy of the method, the view factors between the measuring screen and surrounding surfaces had to be calculated. The range of variation for the convective heat transfer coefficient, along a thin homogenous screen exposed to an airflow pattern from a low-velocity diffuser in displacement ventilation, also needed to be estimated.
Thereafter, an analysis of the method could be performed, under different supply air and indoor conditions. 3.1. View factors Mathematical calculations and non-linear estimation were applied to estimate the view factors between the screen and the surrounding surfaces. It is worth noting that the supply diffuser itself can have some influence on the screen temperature, especially if the diffuser is large. However, in this analysis the supply diffuser was not included in the calculations. Three-dimensional analysis was performed for three different positions of the supply diffuser (Fig. 7): (a) centrally at the left wall, (b) centrally at the back wall and (c) in the corner between the left wall and front wall. The view factor between the screen and surrounding surfaces was calculated by the finite element program FIDAP. Complete details of the view factor algorithm employed can be found in [15]. Without access to FIDAP, radiation view factors can be determined by a variety of other methods, for example the Monte Carlo method. For more information about this method, see [16]. Different screen sizes and aspect ratios between screen height and length were applied. The height of the screen was between 0.6 and 1.0 m while the length was between 1.0 and
Fig. 7. Placements of diffuser and measuring screen.
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1.5 m. Also, the influence of angular position of the screen was studied. 3.2. Approximation of the convective heat transfer coefficient The purpose of the experiments described in this section was to approximate a range of variation for the convective heat transfer coefficient (a) between a measuring screen and ambient airflow. This coefficient was calculated using the model of the energy balance over a solid screen expressed by Eq. (1). The experiments were carried out at the Laboratory of Ventilation and Air Quality at the Center for Built Environment, Ga¨ vle, Sweden. The experiments were performed in a full-scale test room, built inside a larger chamber acting as an operating room, making it possible to control all measurements in the test room and disturbing the indoor condition as little as possible. All experiments were carried out with a homogeneous measuring screen, made of paper with an emissivity of 0.91, placed parallel to the airflow. The measuring screen was held parallel to the airflow stream by means of a frame, mounted perpendicular to the diffuser placed centrally at the left wall. The exact emissivity of the screen was determined with a single-beam FTIR Bomem– Michelson 110 spectrophotometer with an accuracy up to 0.01, at the Department of Materials Science, University of Uppsala. The paper screen used in the investigation was 1.0 m long and 0.6 m high. Air temperatures in the room, as well as surface temperatures of walls, floor, ceiling and measuring screen were all measured with copper–constantan thermocouples. The temperatures were measured at five points along the screen. All measuring points were positioned in the cold airflow near the diffuser. The surroundings were measured in the middle of each surface. Parallel to the thermocouple measurements, the screen temperature was also measured with an infrared camera (Agema 570) shown to have an accuracy of 0.3 8C for a high emissivity surface. To maintain the air temperature in the test room at the decided level, an electrical air convector was placed centrally at the wall opposite the diffuser. Under these circumstances the heat-load in the room had minimal radiation exchange with the measuring screen, thereby causing minimal method errors. All experiments were carried out under steady-state conditions. The temperatures measured by each thermocouple were registered for 100 values and an average of these was calculated. To eliminate possible radiation effects causing thermocouple measurement errors, the thermocouples on the walls, floor, ceiling and measuring screen were covered with an adhesive tape of similar color and emissivity as the measured surface. Air temperatures were measured with the sensor covered with glossy aluminum as a radiation shield. However, several tests with and without a radiation shield on the sensor indicated negligible temperature differences. All thermocouples were calibrated individually. The calibration was intended for temperatures of 15–30 8C. Thermocouple
measurements within this interval showed an accuracy of about 0.1 8C. All thermocouples were connected to a Datascan data logger for conversion from voltage to degrees. In the experiments, the supply air temperature varied between 2.5 and 7 8C below mean room temperature. The relatively high temperature difference between inlet and room was established in order to achieve better accuracy in the calculation of the convective heat transfer coefficient. Because the thermocouples had an accuracy of 0.1 8C, there would be inappropriately large calculation errors at small registered temperature difference. The experiments were carried out with an inlet velocity that varied between 0.1 and 0.4 m/s. 3.3. Theoretical estimation of the difference between the screen and ambient air temperature using infrared camera A theoretical analysis has been performed to estimate the difference between the screen and ambient air temperature for the proposed method. The model stating the energy balance over a measuring screen was used in the evaluation of the temperature difference between the screen and the ambient air. This difference one can say is the theoretical error of the method; there is no consideration of measuring device errors or uncertainties in parameters. The temperature of the screen (Ts) was calculated for different conditions. In this investigation the ambient air temperature (Ta) was taken to 17 and 18 8C, respectively. The effect from each different surrounding surface on the screen temperature was not considered. Instead, a weighted mean surrounding temperature (Tw) was used (see Eq. (4)). X 1=4 Tw ¼ Fsi Ti 4 (4) Rewriting Eq. (1), yields se 4 T Ts4 Ts Ta ¼ (5) a w In the investigation, Tw varied between 20 and 24 8C. The weighted mean temperature was, thus, assumed to be higher then the ambient temperature. The effective emissivity of the screen was assumed to be between 0.5 and 1.0. Based on the measurement results, a range of variation for the convective heat transfer coefficient will be proposed, which will be used in the error analysis. The calculated screen surface temperature has been compared to the presumed ambient air temperature. The temperature difference between the screen and ambient air has been plotted against the parameters included in this error analysis. 3.4. Analysis of the measurement uncertainty using an infrared camera In the proposed whole-field method, air temperatures can be predicted from the screen temperature provided that all parameters in Eq. (5) are known. The errors in estimation of the parameters used in the prediction can heavily affect the
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quality of the predicted air temperature. Therefore, correction of the screen temperature is only suitable when the parameters are known with relatively good precision. In general, the uncertainty in a measured or calculated quantity is given by the sum of the individual components in the measurements/calculations. The uncertainty in the predicted air temperature for the proposed technique is given by the sum of the uncertainties for each individual parameter in Eq. (5). Since the view factors can be known with a rather high degree of accuracy, only the following data are needed to predict the air temperature correctly with an infrared camera in conjunction with a measuring screen: the emissivity of the measuring screen (e), the convective heat transfer coefficient (a) and the temperature of the screen (Ts) and the surrounding surfaces (Tw). The error in estimation of Ts, Tw, e and a can affect the quality of Ta and the maximum error (DTa) have been analyzed by the following equation @Ta @Ta @Ta @Ta (6) DTa ¼ DTs þ DTw þ De þ Da @Ts @Tw @e @a
4. Results and discussion 4.1. View factors When the diffuser is placed at the middle of the left wall, the floor and left wall have the largest influence on the screen (Fig. 8). The temperatures of these two surfaces are, therefore, critical for the method. The size and aspect ratio of the screen have a rather low influence on the view factors for most of the surfaces, except for those closest to the screen. The view factor between screen and right wall is very small, suggesting that the right wall has negligible effect on the
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screen energy balance. This implies that heat-sinks or heatloads placed on the opposite side of the diffuser have no appreciable effect on the performance of the method. When the diffuser is placed in a corner instead, for example, between the left wall and front wall, both the two walls closest to the corner plus the floor are of great importance to the energy balance over the screen (Fig. 9). As can be seen clearly in Figs. 8 and 9, for all three positions of the diffuser angular placing of the screen is also of some importance on the view factors between the screen and the surfaces closest to the screen. However, the surfaces furthest away from the screen, opposite wall and ceiling, have quite constant view factors for all angles. This emphasizes the fact that the screen temperature will be affected very little by these two surfaces and therefore, also little by heat-sinks or heat-loads placed near these surfaces. A regular office room can often be assumed to have the same mean temperatures on all the surrounding walls (not floor and ceiling). Under these circumstances, the walls have a dominating effect on the screen surface temperature. The view factor between a screen sized 0:6 m 1:0 m, placed low at the left wall and uniform surrounding walls is about 0.58– 0.65. With the help of non-linear estimation, the view factor as a function of area, screen aspect ratio and angle have been evaluated for the three different placements of the diffuser (Appendix A). 4.2. Estimation of convective heat transfer coefficient Using Eq. (5), the convective heat transfer coefficient was calculated at five points along the screens for different indoor conditions. The convective heat transfer coefficient (a) depends on a number of parameters such as inlet velocity, inlet temperature, screen temperature, position, etc. However, at the present time it is difficult for the authors to
Fig. 8. The view factors between measuring screen and surrounding walls when the diffuser is placed centrally at the left wall.
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Fig. 9. The view factors between measuring screen and surrounding walls when the diffuser is placed at the corner between left wall and front wall.
discern any clear relation between a and any of these parameters. Instead, all calculated values of a were plotted against Archimedes number in order to determine the variation of a in the cold airflow region (Fig. 10). In the investigation the Archimedes number was varying between 0.8 and 5.5. For supply air conditions within that magnitude, the calculated convective heat transfer coefficient along a smooth paper screen in the cold airflow stream varies between 10 and 20 W/(m2 K). Naturally, outside the cold airflow region the convective heat transfer coefficient is much lower. However, this region is of no importance because radiation heat transfer between this area of the screen and surroundings is negligible, due to the rather low temperature difference. It is worth to mention that the predicted convective heat transfer coefficient is an estimated value and more detailed experimental investiga-
tions are desirable to analyze accurately the variation of a in the cold airflow region. For uncertainty analysis the convective heat transfer coefficient between the screen and the ambient air was assumed to be a ¼ 15 5 W/(m2 K). The screen surface structure can influence the magnitude of the convective heat transfer coefficient, as presented by Hassani and Stetz [17]. He showed that in the air stream of a jet, the boundary layer is far thicker for a porous fiberglass screen than for a homogeneous acrylic sheet. 4.3. Theoretical estimation of the difference between the screen and ambient air temperature using an infrared camera In this section, the results from the theoretical analysis described in the Section 4.2 are presented. Figs. 11 and 12
Fig. 10. The convective heat transfer coefficient (a) for different Archimedes numbers and locations along the measuring screen.
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Fig. 11. Difference between screen temperature (Ts) and assumed ambient air (Ta) for different weighted mean surrounding temperatures (Tw) and convective heat transfer coefficients (a). The ambient air temperature was assumed to be 17 8C and the emissivity of the screen was set to 0.5.
show the difference, for different mean weighted temperatures and convective heat transfer coefficients, between the screen temperature and the presumed air temperature of 17 and 18 8C, respectively. For the specific delimitation in this investigation, the screen temperature is shown to be
between 0.2 and 2.4 8C warmer than the ambient air temperature. The figures indicate quite acceptable errors for a screen with an effective emissivity of 0.5, when Tw is between 20 and 21 8C. When the ambient air temperature rises from 17 to 18 8C, the difference is reduced by
Fig. 12. Difference between screen temperature (Ts) and assumed ambient air (Ta) for different weighted mean surrounding temperatures (Tw) and convective heat transfer coefficients (a). The ambient air temperature was assumed to be 18 8C and the emissivity of the screen was set to 0.5.
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Fig. 13. Difference between screen temperature (Ts) and assumed ambient air (Ta) for different weighted mean surrounding temperatures (Tw) and convective heat transfer coefficients (a). The ambient air temperature was assumed to be 18 8C and the emissivity of the screen was set to 1.0.
Fig. 14. Difference between screen temperature (Ts) and assumed ambient air (Ta) for different weighted mean surrounding temperatures (Tw) and convective heat transfer coefficients (a). The ambient air temperature was assumed to be 18 8C and the emissivity of the screen was set to 0.5.
approximately 0.2 8C for a screen with an effective emissivity of 0.5. For screens with high emissivity, the result shows that Tw has a very large effect on the temperature difference. However, for a screen with low emissivity the convective heat transfer coefficient can have as much influence as Tw on the temperature difference (Figs. 13 and 14). Measurements and the above analysis show that if infrared thermography is used in conjunction with a measuring screen,
correction is needed when measurements are performed around a low-velocity diffuser in displacement ventilation. 4.4. Analysis of the measurement uncertainty using an infrared camera In four different cases, the effects of the effective emissivity of the screen and different screen temperatures on the predicted air temperature are investigated. The result of the
Fig. 15. Predicted temperature compared with measured value by thermocouple.
M. Cehlin et al. / Energy and Buildings 34 (2002) 687–698 Table 1 Shows the uncertainty of each parameter and how much they contribute to the total maximum uncertainty of the estimated air temperature (DTa)
Ts (8C) DTs (8C) (@Ta/@Ts)DTs (8C) Tw (8C) DTw (8C) (@Ta/@Tw)DTw (8C) a (W/(m2 K)) Da (W/(m2 K)) (@Ta/@a)Da (8C) e De (@Ta/@e)De (8C) Ta (8C) DTa (8C)
Case 1
Case 2
Case 3
Case 4
18 0.3 0.36 22 0.3 0.06 15 5 0.25 0.5 0.01 0.02 17.24 0.68
19 0.3 0.36 22 0.3 0.06 15 5 0.19 0.5 0.01 0.02 18.43 0.62
18 0.3 0.40 22 0.3 0.11 15 5 0.46 0.91 0.01 0.02 16.62 0.98
19 0.3 0.40 22 0.3 0.11 15 5 0.35 0.91 0.01 0.02 17.96 0.87
analysis is shown in Table 1. According to Table 1, the maximum difference is found to vary between 0.6 and 1.0 8C for the above mentioned cases. The quality of the predicted air temperature more or less completely depends on the uncertainties in estimating the screen temperature and the convective heat transfer coefficient. The quality increases when the effective screen emissivity is lowered. This implies that the effect of uncertainty of the convective heat transfer coefficient can significantly be reduced when emissivity is low. The analysis clearly shows that it is important to use equipment of very high accuracy and a screen with low effective emissivity in order to keep uncertainty at an acceptable level. The main tradeoff in choosing an appropriate screen material is to use a screen with low enough emissivity to minimize the error introduced by uncertainty in the convective heat transfer coefficient, but high enough to not introduce errors into the infrared camera measurement. Due to the cameraimposed limitation, when using a solid screen it is optimal to use a two-material screen with an effective emissivity of 0.5. Fig. 15 shows the accuracy of the proposed technique by comparing the predicted air temperature based on Eq. (5) with the measured air temperature by thermocouple. As is shown in Fig. 15, rather good agreement has been found between the predicted air temperature and the measured value.
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the specific delimitation in this investigation, the screen temperature is shown to be theoretically between 0.2 and 2.4 8C warmer than the ambient air temperature. View factor calculations show that heat-sinks or heatloads placed on the opposite side of the diffuser and the measuring screen or in the ceiling have very small impact. The agreement between screen temperature and ambient air temperature is quite acceptable, for a screen with an effective emissivity of 0.5, when the ambient air temperature is between 17 and 18 8C and the weighted mean surrounding temperature is between 20 and 21 8C. A high screen emissivity, on other hand, can give poor agreement due to high radiation heat exchange with the surrounding. The maximum uncertainty of the predicted air temperature is found to vary between 0.6 and 1.0 8C for the four presented cases. The maximum uncertainty can be reduced to a great extent by estimating the convective heat transfer coefficient more accurately and using an infrared camera with very high accuracy. In order to minimize errors introduced by uncertainty in the convective coefficient and also control errors in the infrared camera measurement, a twomaterial screen should be used.
Acknowledgements The authors are thankful for the financial support from KK-Foundation (Stockholm, Sweden), University of Ga¨ vle (Ga¨ vle, Sweden) and FLIR systems AB. The authors gratefully acknowledge the support received from personnel at the Department of Indoor Environment and Ventilation, Center for Built Environment and faculty at the Department of Materials Science, Solid State Physics, Uppsala University.
Appendix A A.1. View factor function In order to summarize the calculations for future research, view factors were evaluated as a function of area, screen aspect ratio and angle with help of non-linear estimation. Estimations were performed for all three positions of the supply diffuser. The quasi-Newton method has been used to minimize the least squares loss function (L), L ¼ ðObs PredÞ2 . All view factor functions were first assumed to be in the form:
5. Conclusions
Fij ¼ la hb bc
The technique described here is applicable to any laboratory and field test environment. It is suitable for visualization and control of air temperatures and airflow pattern around a low-velocity diffuser in displacement ventilation. However, for absolute measurements of the air temperatures the described method can give rise to incorrect values. For
where b is the angle between screen and wall. However, in some cases, the assumed function was not suitable due to bad agreement between calculated and predicted values. When the assumed form of view factor function did not work, then it was slightly modified to find the ultimate function.
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R2 Placement A Fscreen–wall ¼ 0.821l0.067j0.126 ln b0.192 Fscreen–floor ¼ 0.161l0.116h0.332b0.142 Fscreen–ceiling ¼ 0.098l0.166h0.283 sinh b2.89E03
0.986 0.974 0.962
Placement B Fscreen–wall ¼ 0.815l0.077h0.125b0.069 Fscreen–floor ¼ 0.172l0.106h0.299b0.134 Fscreen–ceiling ¼ 0.094l0.115h0.258 sinh b6.78E04
0.988 0.973 0.959
Placement C Fscreen–wall ¼ l0.178h0.12645((1.60E05)b2 (1.31E03)b þ 0.779) Fscreen–floor ¼ l0.452h0.457((2.50E05)b2 (2.19E03)b þ 0.153) Fscreen–ceiling ¼ l0.438h0.209((1.10E05)b2 (1.036E03)b þ 0.073)
0.957 0.969 0.966
References [1] P.O. Fanger, Thermal Comfort, McGraw-Hill, New York, 1973. [2] G. Landskilde, K. Alexandersen, D. Wyon, P.O. Fanger, Mental performance during slight cool or warm discomfort, Archives of Science and Physiology 27 (4) (1973) A511–A518. [3] P. Wargocki, Human perception, productivity and symptoms related to indoor air quality, Ph.D. thesis, International Center for Indoor Environment and Energy, Copenhagen, 1998. [4] D.P. Wyon, B. Asgeirsdottir, P. Kjerulf-Jensen, P.O. Fanger, The effect of ambient temperature swings on comfort, performance and behavior, Archives of Science and Physiology 27 (4) (1973) A441– A458. [5] P.O. Fanger, C.J.K. Pedersen, Discomfort due to air velocities in spaces, in: Proceedings of the Meeting of B1, B2, E1 Commission of the International Institute of Refrigeration, Vol. 4, 1977, pp. 289–296. [6] L. Fang, G. Clausen, P.O. Fanger, Impact of temperature and humidity on perception of indoor air quality during immediate and longer whole-body exposures, Indoor Air 8 (4) (1998) 276–284. [7] D. Wyon, M. Sandberg, Thermal manikin prediction of discomfort due to displacement ventilation, ASHRAE Transactions 95 (1) (1989). [8] P.V. Nielsen, Displacement ventilation—theory and design, Department of Building Technology and Structural Engineering, Aalborg University, 1993. [9] E. Ska˚ aret, A semi-empirical flow model for low-velocity air supply in displacement ventilation, in: Proceedings of the ROOMVENT, Part 1, Pricor, Stockholm, 1998, pp. 85–92.
[10] M. Cehlin, B. Moshfegh, M. Sandberg, Visualization and measuring of air temperatures using infrared thermography, in: Proceedings of the ROOMVENT, Vol. 1, Elsevier, Oxford, 2000, pp. 339–347. [11] W. Rinehart, P. Pawlikowski, Applying predictive maintenance technologies to wire industry machinery, Wire Journal International 32 (7) (1999) 128–133. [12] E. Meinders, K. Hanjalic, R. Martinuzzi, Experimental study of the local convection heat transfer from a wall-mounted cube in turbulent channel flow, Journal of Heat Transfer 121 (3) (1999) 564–573. [13] A. Schulz, Infrared thermography as applied to film cooling of gas turbine components, Measurement Science and Technology 11 (7) (2000) 948–956. [14] E. Linden, M. Cehlin, M. Sandberg, Temperature and velocity measurements of a diffuser for displacement ventilation with wholefield methods, in: Proceedings of the ROOMVENT, Vol. 1, Elsevier, Oxford, 2000, pp. 491–496. [15] A.B. Shapiro, FACET: a radiation view factor computer code for axisymmetric, 2D planar and 3D geometries with shadowing, Lawrence Livermore National Laboratory, 1983. [16] M. Modest, Determination of radiative exchange factors for threedimensional geometries with non-ideal surface properties, Numerical Heat Transfer 1 (1978) 403–416. [17] V. Hassani, M. Stetz, Application of infrared thermography to room air temperature measurements, in: Proceedings of the ASHRAE Transactions, Part 2, 1994, pp. 1238–1247. [18] M. Cehlin, B. Moshfegh, H. Stymne, Mapping of indoor climate parameters in Volvo, Eskilstuna, Working Paper no. 10, University of Ga¨ vle, 2000 (in Swedish).
Measurements of air temperatures close to a low-velocity diffuser in displacement ventilation using an infrared camera M. Cehlina,b, B. Moshfegha,*, M. Sandbergb a
Division of Energy and Mechanical Engineering, Department of Technology, University of Ga¨vle, S-801 76 Ga¨vle, Sweden Center for Built Environment, Division of Indoor Environment and Ventilation, Laboratory of Ventilation and Air Quality, University of Ga¨vle, S-801 02 Ga¨vle, Sweden
b
Received 14 January 2001; accepted 11 February 2001
Abstract The near zone of supply air diffusers is very critical for the indoor climate. Complaints of draft are often associated with low-velocity diffusers in displacement ventilation because the air is discharged directly into the occupied zone. Today, the knowledge of the near zone of these air supply diffusers is insufficient, causing an increased need for better measuring methods and representation of the occupied zone. A whole-field measuring technique has been developed by the authors for visualization of air temperatures and airflow patterns over a large cross-section. In this particular whole-field method, air temperatures are measured with an infrared camera and a measuring screen placed in the airflow. The technique is applicable to most laboratory and field test environments. It offers several advantages over traditional techniques; for example, it can record real-time images within large areas and capture transient events. The purpose of this study was to conduct a parameter and error analysis of the proposed whole-field measuring method applied to a flow from a low-velocity diffuser in displacement ventilation. A model of the energy balance, for a solid measuring screen, was used for analyzing the influence of different parameters on the accuracy of the method. The analysis was performed with respect to the convective heat transfer coefficient, emissivity, screen temperature and surrounding surface temperatures. Theoretically, the temperature difference between the screen and the ambient air was found to be 0.2–2.4 8C for the specific delimitation in the investigation. However, after applying correction the maximum uncertainty of the predicted air temperature was found to vary between 0.62 and 0.98 8C, due to uncertainties in estimating parameters used in the correction. The maximum uncertainty can be reduced to a great extent by estimating the convective heat transfer coefficient more accurately and using a screen with rather low emissivity. # 2002 Elsevier Science B.V. All rights reserved. Keywords: Thermography; Whole-field measurement; Infrared camera; Visualization; Air temperature; Airflow pattern
1. Introduction It is well known that the indoor climate is important for our well-being, productivity and quality of life [1–4]. The sensation of the thermal indoor climate is a complex function of a number of physical variables, such as air temperature, air velocity, turbulence intensity and concentration of pollutants [4–6]. The values of these variables can vary strongly in a room or enclosure. It is, therefore, important to determine the spatial distribution of thermal parameters in the occupation zone. With good knowledge it is possible to evaluate a good comfort level. There is great dissatisfaction with today’s heating, cooling and ventilation technology and it is far from uncommon that mistakes are repeated. The basic reason for the situation is * Corresponding author. Tel.: þ46-2664-8804; fax: þ46-2664-8828. E-mail address: [email protected] (B. Moshfegh).
that the indoor climate is practically invisible, thus it is: difficult to conduct a specific dialogue about the indoor climate, difficult to set up a specification of requirements, difficult for manufacturers to show differences in the function of different systems and there is no learning process established about the indoor climate which would give experience feedback. The consequences are that it is difficult to implement quality control and to purchase a specified indoor climate. Since the price and not the quality and function will be decisive and customers more often buy the cheapest system, mistakes are repeated. An example of such dissatisfaction is the complaints of draft associated with low-velocity diffusers in displacement ventilation [7]. This kind of ventilation system is often used in industrial areas with high thermal load but also in offices. The system has several potential advantages, i.e. better air quality and efficient cooling of rooms [8]. It allows an efficient use of energy because the inlet temperature can
0378-7788/02/$ – see front matter # 2002 Elsevier Science B.V. All rights reserved. PII: S 0 3 7 8 - 7 7 8 8 ( 0 1 ) 0 0 1 3 3 - 5
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Nomenclature As Ar Fs–i h hd Ji l q Ta Ta DTa Ti Ti Tin Ts Troom DTs Tw uin y
area of the measuring screen (m2) gðTroom Tin Þhd =ðTroom u2in Þ view factor between screen and surface i height of the screen (m) height of the diffuser (m) radiosity (W/m2) length of the screen (m) heat flow (W/m2) ambient air temperature (K), (8C) Ta/Ts accuracy of the predicted air temperature (8C) temperature of surface i (K), (8C) Ti/Ts inlet temperature (8C) temperature of the screen (K), (8C) average room temperature (K) accuracy of the screen temperature (8C) weighted mean surrounding temperature (K), (8C), see Eq. (4) inlet velocity (m/s) distance from floor (mm)
Greek letters a convective heat transfer coefficient (W/(m2 K)) Da accuracy of the convective heat transfer coefficient (W/(m2 K)) e emissivity De accuracy of the emissivity s Stefan–Boltzman constant (5:67 108 W/ (m2 K4)) be higher than for mixing ventilation systems. For these types of diffusers the airflow is supplied direct into the occupied zone and the flow accelerates towards the floor due to the gravity effect on the cold air. The near zone (defined as the area close to the diffuser where the air velocities are higher than 0.2 m/s) is, therefore, very critical. Today, the knowledge of this near zone is insufficient. It is difficult for designers to estimate the extent of the near zone for arbitrary airflow rates, supply air temperature and arbitrary supply diffuser size and shape. Because the indoor climate is invisible, it is often overlooked at the design stage. Therefore, there is a need to develop better measuring methods and flow models, especially for low-velocity air supply in displacement ventilation. However, Ska˚ aret [9] has recently developed a semi-empirical flow model for displacement ventilation, which yields improved test standards and design methods for displacement ventilation. But, there is still much more work to do in order to fully achieve understanding and knowledge among clients and professionals, about the functions and performance of different air diffusers, especially low-velocity diffusers. This lack of understanding makes planning a displacement ventilation system
become a trial and error process, which leads to many malfunctioning systems. Therefore, it is hard to evaluate a good occupant comfort level and the industry gets a low reputation. One important aim of the present ongoing research is to improve the present situation by making the indoor climate visible in the early stages of the design process. To measure air temperatures over large areas in a ventilated room is today very time consuming and impractical with traditional technology and it yields insufficient information with low resolution. It takes either many sensors or the translation of a single sensor to cover the temperature distribution over a large area. Measuring instruments also give rise to airflow and temperature disturbances in the tested region. Therefore, careful and detailed field studies with the help of point measuring techniques are quite impossible. To overcome the problems and limitations with traditional techniques and invisible indoor climate, a measuring technique has been developed by the authors based on infrared thermography [10]. Infrared thermography is now commonly used in the industry and in research activities [11– 13]. It has become a qualitative tool that can be widely used in research. The measuring technique developed by Cehlin et al. [10] is a whole-field method making it possible to rapidly visualize both air temperatures and airflow patterns over a large cross section. A whole-field method is a measuring technique in which physical quantities are recorded simultaneously over a whole field in contrast to traditional point-measuring methods. In this particular whole-field method, air temperatures are measured with an infrared camera in conjunction with a measuring screen acting as a radiation target sheet, placed parallel with the airflow stream (Fig. 1). The proposed technique is very useful for checking the performance of ventilation systems in different environments. It is applicable to both laboratory and field test environments, such as in industries and workplaces. Because the technique records real-time images, correction and improvement of the performance of diffusers can be made instantaneously on site (Fig. 2). The temperature measurements can be carried out in several planes around the supply device (Fig. 3). In each
Fig. 1. Setup for measuring air temperatures in the near zone of an air supply diffuser using infrared thermography.
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Fig. 2. Thermal images taken by infrared thermography. The left thermal image shows a bad-functioning low-velocity diffuser for displacement ventilation system taken in a factory hall in Sweden. The right thermal image was taken in the near-zone of the same low-velocity diffuser after improvements, see [18] for more information.
Fig. 3. Measurement planes around a supply device.
plane, the temperatures are recorded with an infrared camera perpendicular to the measuring screen. For an ordinary infrared camera, the number of pixels in each image is 320 240 ¼ 76,800. From the two-dimensional measurements one can make a three-dimensional representation by means of modern three-dimensional programs (Fig. 4), that can also be implemented in computer-aided design (CAD) programs. This type of presentation enables a direct comparison between computational fluid dynamics (CFD) and the measurements. One difficulty with CFD is to define the boundary conditions accurately. However, infrared camera measurements can easily and quickly provide boundary conditions on surface temperatures of the walls as well as
Fig. 4. A typical three-dimensional reconstruction of the temperature distribution achieved by infrared camera measurements.
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the diffuser for CFD. Thermal images achieved by infrared camera measurements can also be combined with images from other whole-field techniques, yielding a very powerful representation of the indoor climate [14]. The intention of this study was to perform a parameter and error analysis of the proposed whole-field measuring method in a flow from a low-velocity diffuser in displacement ventilation. A model of the energy balance for a solid measuring screen is used for analyzing the influence of different parameters on the accuracy of the method.
2. Theory When a screen is placed in an airflow it might disturb the flow pattern and also the temperature distribution. However, it has been showed and reported by Cehlin et al. [10] that a screen placed parallel to the air stream from a low-velocity diffuser in displacement ventilation has negligible effect on both the velocity and the air temperature distribution. Remaining sources of error are then incorrect screen surface temperature compared to the ambient air temperature and infrared camera measurement errors. Recent experiments by Cehlin et al. [10] showed that a modern high-resolution infrared camera measures the surface temperature of a high emissivity paper screen with very good accuracy. An infrared camera measures the emitted infrared radiation from the measuring screen. However, the radiation detected by the camera also includes radiation from surroundings reflected in the screen. In order to eliminate this reflected radiation the screen must have a high emissivity. This is a cameraimposed limitation. Because the surrounding medium is air, the detected radiation is more or less uninfluenced by absorption in the medium with the camera working around a wavelength of 7–13 mm. However, air with very high moisture can absorb a fraction of the emitted radiation from an object and cause small errors at long distances between the object and the camera. Ideally, the air exchanges heat with the measuring screen by convective heat transfer, making the screen adopt the same temperature as the local air temperature. However, in displacement ventilation air is supplied at low velocities, yielding rather low values for the convective heat transfer coefficient, which means that there will be high thermal resistance for heat transfer between the screen and the local air. As a result, the measuring screen will not achieve exactly the right temperature, due to radiative heat transfer between the surroundings and the measuring screen. Experiments have showed that all tested screen materials exhibit slightly higher temperatures than the ambient air when exposed to cold air from the diffuser. Screens with high emissivity were about 1–2 8C warmer than the ambient air temperature in the cold airflow region [10]. Because the measuring screen has a low thermal mass it will reach steady-state condition quickly. The result will be that energy leaving the screen will be of the same magnitude
Fig. 5. Energy balance over screen.
as energy going in to the screen. Theoretically, the incoming radiation energy absorbed by the screen will undergo some lateral heat conduction inside through the screen and then leave the screen by convective heat flow. Due to the thinness and rather low conductivity, it is assume that lateral conduction has a negligible effect. Assuming steady-state condition and that lateral conduction does not influence the temperature distribution of the screen, an energy balance over the measuring screen can be carried out. The energy balance over the screen is shown in Fig. 5. It leads to a relationship between the air temperature and the screen temperature, as follows: se X Ts Ta ¼ Fsi ðTi 4 Ts 4 Þ (1) a or in dimensionless form Ta ¼ 1 RAD;
(2)
where RAD ¼
seTs 3 X Fsi ðTi 4 1Þ a
(3)
The radiation number (RAD) can be interpreted as a measure of the quality of the screen temperature. For best performance, RAD should, of course, be close to zero yielding a low heat transfer resistance between the screen and the ambient air. To attain a screen in equilibrium with the ambient air, its material should have an emissivity very close to zero. However, it has been shown that it is impossible to use a measuring screen with low emissivity due to infrared camera measurement errors [10]. It is a tradeoff in the emissivity of the screen. In order to drive the screen temperature toward the temperature of the ambient air, it should have a low emissivity, so that its temperature depends more on convection with the ambient air and less on radiation to the surrounding walls. However, low emissivity introduces errors into the measurement of the screen temperature by the infrared camera. In addition to the emissivity of the screen, the screen error depends highly on the convective heat transfer coefficient and the temperature of the ambient air and surrounding surfaces, as well as the view factors between these surfaces and the screen. Given knowledge of these parameters, the difference between the screen temperature and the ambient air can be accounted for mathematically using Eq. (1). The bigger the difference between the ambient air temperature and the surrounding surface temperatures, the higher the screen temperature
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Fig. 6. The layout of the room used in the measurements.
error. Locally very warm or cold surfaces can cause large screen errors if the view factor is high. One possible way to reduce the measurement error is to use a two-material screen. The emissivity of the screen material facing the camera must still be high (around 0.9), but a lowemissivity material, such as glossy aluminum with an emissivity around 0.05 can cover the opposite side. The effective emissivity will then be reduced by almost 50 %.
3. Measurements and analysis procedures The purpose is to investigate the accuracy of the present whole-field method for a typical office room, sized 4:1 m 3:4 m 2:7 m, under normal thermal indoor conditions. The design of the room used in the investigation is shown in Fig. 6. The air was supplied through a semicircular low-velocity diffuser of height 0.6 m with a free area of 0.0075 m2, located at the center of one of the walls. In order to be able to analyze the influence of the different parameters on the accuracy of the method, the view factors between the measuring screen and surrounding surfaces had to be calculated. The range of variation for the convective heat transfer coefficient, along a thin homogenous screen exposed to an airflow pattern from a low-velocity diffuser in displacement ventilation, also needed to be estimated.
Thereafter, an analysis of the method could be performed, under different supply air and indoor conditions. 3.1. View factors Mathematical calculations and non-linear estimation were applied to estimate the view factors between the screen and the surrounding surfaces. It is worth noting that the supply diffuser itself can have some influence on the screen temperature, especially if the diffuser is large. However, in this analysis the supply diffuser was not included in the calculations. Three-dimensional analysis was performed for three different positions of the supply diffuser (Fig. 7): (a) centrally at the left wall, (b) centrally at the back wall and (c) in the corner between the left wall and front wall. The view factor between the screen and surrounding surfaces was calculated by the finite element program FIDAP. Complete details of the view factor algorithm employed can be found in [15]. Without access to FIDAP, radiation view factors can be determined by a variety of other methods, for example the Monte Carlo method. For more information about this method, see [16]. Different screen sizes and aspect ratios between screen height and length were applied. The height of the screen was between 0.6 and 1.0 m while the length was between 1.0 and
Fig. 7. Placements of diffuser and measuring screen.
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1.5 m. Also, the influence of angular position of the screen was studied. 3.2. Approximation of the convective heat transfer coefficient The purpose of the experiments described in this section was to approximate a range of variation for the convective heat transfer coefficient (a) between a measuring screen and ambient airflow. This coefficient was calculated using the model of the energy balance over a solid screen expressed by Eq. (1). The experiments were carried out at the Laboratory of Ventilation and Air Quality at the Center for Built Environment, Ga¨ vle, Sweden. The experiments were performed in a full-scale test room, built inside a larger chamber acting as an operating room, making it possible to control all measurements in the test room and disturbing the indoor condition as little as possible. All experiments were carried out with a homogeneous measuring screen, made of paper with an emissivity of 0.91, placed parallel to the airflow. The measuring screen was held parallel to the airflow stream by means of a frame, mounted perpendicular to the diffuser placed centrally at the left wall. The exact emissivity of the screen was determined with a single-beam FTIR Bomem– Michelson 110 spectrophotometer with an accuracy up to 0.01, at the Department of Materials Science, University of Uppsala. The paper screen used in the investigation was 1.0 m long and 0.6 m high. Air temperatures in the room, as well as surface temperatures of walls, floor, ceiling and measuring screen were all measured with copper–constantan thermocouples. The temperatures were measured at five points along the screen. All measuring points were positioned in the cold airflow near the diffuser. The surroundings were measured in the middle of each surface. Parallel to the thermocouple measurements, the screen temperature was also measured with an infrared camera (Agema 570) shown to have an accuracy of 0.3 8C for a high emissivity surface. To maintain the air temperature in the test room at the decided level, an electrical air convector was placed centrally at the wall opposite the diffuser. Under these circumstances the heat-load in the room had minimal radiation exchange with the measuring screen, thereby causing minimal method errors. All experiments were carried out under steady-state conditions. The temperatures measured by each thermocouple were registered for 100 values and an average of these was calculated. To eliminate possible radiation effects causing thermocouple measurement errors, the thermocouples on the walls, floor, ceiling and measuring screen were covered with an adhesive tape of similar color and emissivity as the measured surface. Air temperatures were measured with the sensor covered with glossy aluminum as a radiation shield. However, several tests with and without a radiation shield on the sensor indicated negligible temperature differences. All thermocouples were calibrated individually. The calibration was intended for temperatures of 15–30 8C. Thermocouple
measurements within this interval showed an accuracy of about 0.1 8C. All thermocouples were connected to a Datascan data logger for conversion from voltage to degrees. In the experiments, the supply air temperature varied between 2.5 and 7 8C below mean room temperature. The relatively high temperature difference between inlet and room was established in order to achieve better accuracy in the calculation of the convective heat transfer coefficient. Because the thermocouples had an accuracy of 0.1 8C, there would be inappropriately large calculation errors at small registered temperature difference. The experiments were carried out with an inlet velocity that varied between 0.1 and 0.4 m/s. 3.3. Theoretical estimation of the difference between the screen and ambient air temperature using infrared camera A theoretical analysis has been performed to estimate the difference between the screen and ambient air temperature for the proposed method. The model stating the energy balance over a measuring screen was used in the evaluation of the temperature difference between the screen and the ambient air. This difference one can say is the theoretical error of the method; there is no consideration of measuring device errors or uncertainties in parameters. The temperature of the screen (Ts) was calculated for different conditions. In this investigation the ambient air temperature (Ta) was taken to 17 and 18 8C, respectively. The effect from each different surrounding surface on the screen temperature was not considered. Instead, a weighted mean surrounding temperature (Tw) was used (see Eq. (4)). X 1=4 Tw ¼ Fsi Ti 4 (4) Rewriting Eq. (1), yields se 4 T Ts4 Ts Ta ¼ (5) a w In the investigation, Tw varied between 20 and 24 8C. The weighted mean temperature was, thus, assumed to be higher then the ambient temperature. The effective emissivity of the screen was assumed to be between 0.5 and 1.0. Based on the measurement results, a range of variation for the convective heat transfer coefficient will be proposed, which will be used in the error analysis. The calculated screen surface temperature has been compared to the presumed ambient air temperature. The temperature difference between the screen and ambient air has been plotted against the parameters included in this error analysis. 3.4. Analysis of the measurement uncertainty using an infrared camera In the proposed whole-field method, air temperatures can be predicted from the screen temperature provided that all parameters in Eq. (5) are known. The errors in estimation of the parameters used in the prediction can heavily affect the
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quality of the predicted air temperature. Therefore, correction of the screen temperature is only suitable when the parameters are known with relatively good precision. In general, the uncertainty in a measured or calculated quantity is given by the sum of the individual components in the measurements/calculations. The uncertainty in the predicted air temperature for the proposed technique is given by the sum of the uncertainties for each individual parameter in Eq. (5). Since the view factors can be known with a rather high degree of accuracy, only the following data are needed to predict the air temperature correctly with an infrared camera in conjunction with a measuring screen: the emissivity of the measuring screen (e), the convective heat transfer coefficient (a) and the temperature of the screen (Ts) and the surrounding surfaces (Tw). The error in estimation of Ts, Tw, e and a can affect the quality of Ta and the maximum error (DTa) have been analyzed by the following equation @Ta @Ta @Ta @Ta (6) DTa ¼ DTs þ DTw þ De þ Da @Ts @Tw @e @a
4. Results and discussion 4.1. View factors When the diffuser is placed at the middle of the left wall, the floor and left wall have the largest influence on the screen (Fig. 8). The temperatures of these two surfaces are, therefore, critical for the method. The size and aspect ratio of the screen have a rather low influence on the view factors for most of the surfaces, except for those closest to the screen. The view factor between screen and right wall is very small, suggesting that the right wall has negligible effect on the
693
screen energy balance. This implies that heat-sinks or heatloads placed on the opposite side of the diffuser have no appreciable effect on the performance of the method. When the diffuser is placed in a corner instead, for example, between the left wall and front wall, both the two walls closest to the corner plus the floor are of great importance to the energy balance over the screen (Fig. 9). As can be seen clearly in Figs. 8 and 9, for all three positions of the diffuser angular placing of the screen is also of some importance on the view factors between the screen and the surfaces closest to the screen. However, the surfaces furthest away from the screen, opposite wall and ceiling, have quite constant view factors for all angles. This emphasizes the fact that the screen temperature will be affected very little by these two surfaces and therefore, also little by heat-sinks or heat-loads placed near these surfaces. A regular office room can often be assumed to have the same mean temperatures on all the surrounding walls (not floor and ceiling). Under these circumstances, the walls have a dominating effect on the screen surface temperature. The view factor between a screen sized 0:6 m 1:0 m, placed low at the left wall and uniform surrounding walls is about 0.58– 0.65. With the help of non-linear estimation, the view factor as a function of area, screen aspect ratio and angle have been evaluated for the three different placements of the diffuser (Appendix A). 4.2. Estimation of convective heat transfer coefficient Using Eq. (5), the convective heat transfer coefficient was calculated at five points along the screens for different indoor conditions. The convective heat transfer coefficient (a) depends on a number of parameters such as inlet velocity, inlet temperature, screen temperature, position, etc. However, at the present time it is difficult for the authors to
Fig. 8. The view factors between measuring screen and surrounding walls when the diffuser is placed centrally at the left wall.
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Fig. 9. The view factors between measuring screen and surrounding walls when the diffuser is placed at the corner between left wall and front wall.
discern any clear relation between a and any of these parameters. Instead, all calculated values of a were plotted against Archimedes number in order to determine the variation of a in the cold airflow region (Fig. 10). In the investigation the Archimedes number was varying between 0.8 and 5.5. For supply air conditions within that magnitude, the calculated convective heat transfer coefficient along a smooth paper screen in the cold airflow stream varies between 10 and 20 W/(m2 K). Naturally, outside the cold airflow region the convective heat transfer coefficient is much lower. However, this region is of no importance because radiation heat transfer between this area of the screen and surroundings is negligible, due to the rather low temperature difference. It is worth to mention that the predicted convective heat transfer coefficient is an estimated value and more detailed experimental investiga-
tions are desirable to analyze accurately the variation of a in the cold airflow region. For uncertainty analysis the convective heat transfer coefficient between the screen and the ambient air was assumed to be a ¼ 15 5 W/(m2 K). The screen surface structure can influence the magnitude of the convective heat transfer coefficient, as presented by Hassani and Stetz [17]. He showed that in the air stream of a jet, the boundary layer is far thicker for a porous fiberglass screen than for a homogeneous acrylic sheet. 4.3. Theoretical estimation of the difference between the screen and ambient air temperature using an infrared camera In this section, the results from the theoretical analysis described in the Section 4.2 are presented. Figs. 11 and 12
Fig. 10. The convective heat transfer coefficient (a) for different Archimedes numbers and locations along the measuring screen.
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Fig. 11. Difference between screen temperature (Ts) and assumed ambient air (Ta) for different weighted mean surrounding temperatures (Tw) and convective heat transfer coefficients (a). The ambient air temperature was assumed to be 17 8C and the emissivity of the screen was set to 0.5.
show the difference, for different mean weighted temperatures and convective heat transfer coefficients, between the screen temperature and the presumed air temperature of 17 and 18 8C, respectively. For the specific delimitation in this investigation, the screen temperature is shown to be
between 0.2 and 2.4 8C warmer than the ambient air temperature. The figures indicate quite acceptable errors for a screen with an effective emissivity of 0.5, when Tw is between 20 and 21 8C. When the ambient air temperature rises from 17 to 18 8C, the difference is reduced by
Fig. 12. Difference between screen temperature (Ts) and assumed ambient air (Ta) for different weighted mean surrounding temperatures (Tw) and convective heat transfer coefficients (a). The ambient air temperature was assumed to be 18 8C and the emissivity of the screen was set to 0.5.
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Fig. 13. Difference between screen temperature (Ts) and assumed ambient air (Ta) for different weighted mean surrounding temperatures (Tw) and convective heat transfer coefficients (a). The ambient air temperature was assumed to be 18 8C and the emissivity of the screen was set to 1.0.
Fig. 14. Difference between screen temperature (Ts) and assumed ambient air (Ta) for different weighted mean surrounding temperatures (Tw) and convective heat transfer coefficients (a). The ambient air temperature was assumed to be 18 8C and the emissivity of the screen was set to 0.5.
approximately 0.2 8C for a screen with an effective emissivity of 0.5. For screens with high emissivity, the result shows that Tw has a very large effect on the temperature difference. However, for a screen with low emissivity the convective heat transfer coefficient can have as much influence as Tw on the temperature difference (Figs. 13 and 14). Measurements and the above analysis show that if infrared thermography is used in conjunction with a measuring screen,
correction is needed when measurements are performed around a low-velocity diffuser in displacement ventilation. 4.4. Analysis of the measurement uncertainty using an infrared camera In four different cases, the effects of the effective emissivity of the screen and different screen temperatures on the predicted air temperature are investigated. The result of the
Fig. 15. Predicted temperature compared with measured value by thermocouple.
M. Cehlin et al. / Energy and Buildings 34 (2002) 687–698 Table 1 Shows the uncertainty of each parameter and how much they contribute to the total maximum uncertainty of the estimated air temperature (DTa)
Ts (8C) DTs (8C) (@Ta/@Ts)DTs (8C) Tw (8C) DTw (8C) (@Ta/@Tw)DTw (8C) a (W/(m2 K)) Da (W/(m2 K)) (@Ta/@a)Da (8C) e De (@Ta/@e)De (8C) Ta (8C) DTa (8C)
Case 1
Case 2
Case 3
Case 4
18 0.3 0.36 22 0.3 0.06 15 5 0.25 0.5 0.01 0.02 17.24 0.68
19 0.3 0.36 22 0.3 0.06 15 5 0.19 0.5 0.01 0.02 18.43 0.62
18 0.3 0.40 22 0.3 0.11 15 5 0.46 0.91 0.01 0.02 16.62 0.98
19 0.3 0.40 22 0.3 0.11 15 5 0.35 0.91 0.01 0.02 17.96 0.87
analysis is shown in Table 1. According to Table 1, the maximum difference is found to vary between 0.6 and 1.0 8C for the above mentioned cases. The quality of the predicted air temperature more or less completely depends on the uncertainties in estimating the screen temperature and the convective heat transfer coefficient. The quality increases when the effective screen emissivity is lowered. This implies that the effect of uncertainty of the convective heat transfer coefficient can significantly be reduced when emissivity is low. The analysis clearly shows that it is important to use equipment of very high accuracy and a screen with low effective emissivity in order to keep uncertainty at an acceptable level. The main tradeoff in choosing an appropriate screen material is to use a screen with low enough emissivity to minimize the error introduced by uncertainty in the convective heat transfer coefficient, but high enough to not introduce errors into the infrared camera measurement. Due to the cameraimposed limitation, when using a solid screen it is optimal to use a two-material screen with an effective emissivity of 0.5. Fig. 15 shows the accuracy of the proposed technique by comparing the predicted air temperature based on Eq. (5) with the measured air temperature by thermocouple. As is shown in Fig. 15, rather good agreement has been found between the predicted air temperature and the measured value.
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the specific delimitation in this investigation, the screen temperature is shown to be theoretically between 0.2 and 2.4 8C warmer than the ambient air temperature. View factor calculations show that heat-sinks or heatloads placed on the opposite side of the diffuser and the measuring screen or in the ceiling have very small impact. The agreement between screen temperature and ambient air temperature is quite acceptable, for a screen with an effective emissivity of 0.5, when the ambient air temperature is between 17 and 18 8C and the weighted mean surrounding temperature is between 20 and 21 8C. A high screen emissivity, on other hand, can give poor agreement due to high radiation heat exchange with the surrounding. The maximum uncertainty of the predicted air temperature is found to vary between 0.6 and 1.0 8C for the four presented cases. The maximum uncertainty can be reduced to a great extent by estimating the convective heat transfer coefficient more accurately and using an infrared camera with very high accuracy. In order to minimize errors introduced by uncertainty in the convective coefficient and also control errors in the infrared camera measurement, a twomaterial screen should be used.
Acknowledgements The authors are thankful for the financial support from KK-Foundation (Stockholm, Sweden), University of Ga¨ vle (Ga¨ vle, Sweden) and FLIR systems AB. The authors gratefully acknowledge the support received from personnel at the Department of Indoor Environment and Ventilation, Center for Built Environment and faculty at the Department of Materials Science, Solid State Physics, Uppsala University.
Appendix A A.1. View factor function In order to summarize the calculations for future research, view factors were evaluated as a function of area, screen aspect ratio and angle with help of non-linear estimation. Estimations were performed for all three positions of the supply diffuser. The quasi-Newton method has been used to minimize the least squares loss function (L), L ¼ ðObs PredÞ2 . All view factor functions were first assumed to be in the form:
5. Conclusions
Fij ¼ la hb bc
The technique described here is applicable to any laboratory and field test environment. It is suitable for visualization and control of air temperatures and airflow pattern around a low-velocity diffuser in displacement ventilation. However, for absolute measurements of the air temperatures the described method can give rise to incorrect values. For
where b is the angle between screen and wall. However, in some cases, the assumed function was not suitable due to bad agreement between calculated and predicted values. When the assumed form of view factor function did not work, then it was slightly modified to find the ultimate function.
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R2 Placement A Fscreen–wall ¼ 0.821l0.067j0.126 ln b0.192 Fscreen–floor ¼ 0.161l0.116h0.332b0.142 Fscreen–ceiling ¼ 0.098l0.166h0.283 sinh b2.89E03
0.986 0.974 0.962
Placement B Fscreen–wall ¼ 0.815l0.077h0.125b0.069 Fscreen–floor ¼ 0.172l0.106h0.299b0.134 Fscreen–ceiling ¼ 0.094l0.115h0.258 sinh b6.78E04
0.988 0.973 0.959
Placement C Fscreen–wall ¼ l0.178h0.12645((1.60E05)b2 (1.31E03)b þ 0.779) Fscreen–floor ¼ l0.452h0.457((2.50E05)b2 (2.19E03)b þ 0.153) Fscreen–ceiling ¼ l0.438h0.209((1.10E05)b2 (1.036E03)b þ 0.073)
0.957 0.969 0.966
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