MEASUREMENT AND CFD ANALYSIS OF UNSTEADY THERMAL ENVIRONMENT IN GYMNASIUM ADOPTED DISPLACEMENT AIR CONDITION SYSTEM

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1 MEASUREMENT AND CFD ANALYSIS OF UNSTEADY THERMAL ENVIRONMENT IN GYMNASIUM ADOPTED DISPLACEMENT AIR CONDITION SYSTEM Koji Sakai 1, Yasutaka Murata 2, Ryutaro Kubo 3 Ryoichi Kajiya 1, and Osamu Ishihara 3 1 Department of Architecture, Meiji University, Kawasaki, Japan 2 Department of Architecture, Sojo University, Kumamoto, Japan 3 Department of Architecture, Kumamoto University, Kumamoto, Japan ABSTRACT It is necessary to unsteadily accurately estimate handling and time-related spatial distribution of the indoor environment element in respect of externality meteorological phenomenon and time-varying movement of the heating and cooling load in order to carry out the thermal environment design in detail. With the speedup of the recent computer, the unsteady CFD calculation was practically carried out and results fed back to the environmental design. However, time subtraction interval and convergence decision are appropriately set at the case of the unsteady analysis, and it is necessary to examine the calculation accuracy. Then, in this study, measurement and CFD analysis of unsteady thermal environment were carried out for the gymnasium that adopted displacement air-conditioning system, and following characteristic of CFD was examined. As a result of comparing the measurement with the analysis, it was confirmed that both LES and k-ε corresponded to actual phenomenon approximately on the temperature distribution. In k-ε with SIMPLEC analysis, it was cleared that calculation accuracy that is equivalent to MAC, if time subtraction interval is made to be less than 1sec. KEYWORDS CFD, Measurement, Unsteady State, Thermal Environment, Displacement HVAC INTRODUCTION To perform detailed thermal environmental design, it is necessary to handle variability that occurs over time (time variability) of the surrounding weather and the air-conditioning load for heating and cooling in an unsteady situation and to grasp or predict adequately the time-related spatial distribution of the indoor environmental elements: temperature, airflow, humidity, radiation, and cleanliness. With recent advances in computer technology, the following trend is apparent: unsteady Computation Fluid Dynamics (CFD) calculation is performed practically and fed back to the design (Sakai, et al. 2001). For performing analyses of unsteady conditions, however, it is necessary to specify the interval of the temporal subtraction and the convergence judgment adequately and to study the calculation accuracy. Therefore, for this study, actual measurements and CFD analyses of an unsteady thermal environment were performed for a gymnasium with installed displacement air-conditioning; then a follow-up study of CFD was performed. General features of the gymnasium under study The gymnasium in this study has a floor space of 600 m 2, a ceiling height of 10m, and mobile spectator seats collapsed against the wall surface can be extended to accommodate 0 persons for lectures and entertainment. Generally, the gymnasium is used for badminton, table tennis, basketball, and other Corresponding Author: Tel: , Fax: address: sakaik@isc.meiji.ac.jp

2 sports. The gymnasium is located in Kurume City, Kyushu area in south of Japan. The climate in Kyushu area becomes hot and high humidity in the summertime. Since the daytime summer temperature may reach 35 C with around 60% relative humidity. Therefore, it is necessary to introduce the air conditioning system for human health. On the other hand, consideration was required in the selection of an air-conditioning system for the sport of badminton, since the shuttle is affected if the indoor wind velocity exceeds 1.0m/s. Based on research during the design stage, a floor system was adopted because control of indoor wind velocity was possible. The building diagram and displacement air-conditioning system (ASHRAE 2005) are shown in Figure 1. By using a fan from the machine room, the cold air is blown out through the floor outlet from cold air chambers under the floor around the circumference of the gymnasium. The central ceiling is equipped with a suction opening and, using the attic as an exhaust chamber, circulates the air back to the machine room. The facility outline is shown in Table 1. N N c Air Outlet 2m e a W O E (a) Inside view of the gymnasium Lounge f b d S :Air temp. :Wind velo. : + :Surface temp, : +Globe temp.+humidity (b) Section (West-East) (c) Plan Figure 1. Diagram of gymnasium and measuring points Table 1. Specifications of the facility Application Gymnasium, Assembly, Conference Air Conditioning Unit Floor space 522m 2 (m x 18m) Heat Source Absorption cooling/heating (LiBr) Ceiling height Minimum 8 m, maximum 11m Cooling ability 352kW Outlet area m 2 (m x 70m) Heating ability 2kW Suction area m 2 (1m x m) Fan power 880 m 3 /h Audience 0 seats O.A. supply 6000 m 3 /h Table 2. Measurement schedule (July, 2001) Air-Conditioning, Setup Temp. C 14 Air-Conditioning, Setup Temp. C 15 Air-Conditioning, Setup Temp. 22 C, with Audience sheet 16 AC, S.T. C Natural Ventilation AC, S.T. C 17 AC, S.T. C AC, S.T.22 C S.T.20 C S.T.22 C AC, S.T. C S.T. C

3 Temperature[deg.C] roof inside Temp. Outdoor Solar Rad Figure 2. Weather condition 00 Solar Radiation[W/m2] Water Vapor Pressure[kPa] Outdoor Return Supply Figure 3. Humidity fluctuation Temperature[deg.C] 22 Return outlet 20 inlet Supply a b c d e f Figure 4. Supply, Return air temp. fluctuation Figure 5. Wind velocity of floor outlet MEASUREMENT Outline of measurement The measurement was important for understanding the thermal environment in the gymnasium and understanding the wind speed distribution in the playing area. Summary and measurements are shown in Figure 1. The measurement was conducted using hot wire anemometer for measuring wind velocity, and a T-CC thermocouple for measuring surface temperature and air temperature in intervals of 1 minute. The observation schedule is shown at Table 2. Measurement results The measurement was taken on July 13-17, Since the weather was not stable during the measurement period, there was a thermal load in comparison with the equipment ability. As a representative result, the discussion uses July 14th. The fluctuation of outdoor temperature and solar radiation is shown in Figure 3. The temperature in the daytime has exceeded 35 C, and it can be confirmed that the summer in Kyushu in which the gymnasium is located is hot. Air Conditioning System Taking air temperature and blowing vapor tension with suction opening as in Figure 3,4, the wind velocity of each outlet is shown in Figure 5. At the time of air-conditioning, supply temperature was about C, and return temperature was about C. Blowing humidity and suction humidity were almost equivalent. Since measurements were taken under conditions in which there was seldom a thermal load indoors, therefore the system retained reserve cooling ability. The blowing airflow differed greatly depending on the place it blew out from the chamber under the floor. Airflow was a maximum of about 1.2m/s in the east where the chamber airflow was straight, and a minimum of about m/s in the west. It seems the shape of the chamber controls the velocity of the blowing airflow. Thermal Performance The change in temperature and wind velocity in the central gymnasium is shown in Figure 6, 7. Figure 8 is the temperature change of the wall surface. The temperature 1m above the floor level was stable at about C and near the ceiling was about C at the time of air-conditioning.

4 Temperature[deg.C] h=4m h=1m Wind Velocity[m/s] h=0.5m h=1.5m h=2.5m h=3.5m Temperature[deg.C] Figure 6. Indoor air temp. fluctuation(point-o) ceiling north south east west floor Figure 8. Wall surface temp. fluctuation SET*[deg.C] Figure 7. Wind velocity fluctuation(point-o) h=3.5m h=2.5m h=1.5m Figure 9. Calculation result of SET*(point-O) Although when using the spectator seats, temperature control to about 4m was a problem, the temperature of the space as a whole was kept almost constant, and thus was considered satisfactory. Room temperature reached the lowest minutes after air-conditioning start and was stabilized about 1 hour afterwards. The time for room temperature to fall below the setting temperature was about 10 minutes, and operation according to gymnasium use was possible. The wind velocity near the floor surface was kept at 0.3m/s or less; velocity near the floor surface was the maximum. It was confirmed that this system was useful for games, which are influenced by wind velocity. For the purpose of evaluating comfort in the gymnasium, SET* (Gagge Fobelets 1986), which was one of the comfort indices, was calculated using measured values. Figure 9 shows the changes in SET*. SET* becomes about C during air-conditioning and the playing area (0-4m height) was comfortable. SIMULATION Unsteady CFD Analysys Large Eddy Simulation (LES) is anticipated as a model that can predict unsteady phenomena precisely (Sagaut 2002). Unfortunately, the calculation cost is generally high because it is necessary to use small units for space division and the time division. In contrast, a standard k-e model, which is a time average model, can be used for unsteady analysis at a business level of precision because comparatively rough division of units can provide a useful solution and a general-purpose code can be used. For solving k-e in unsteady conditions, it is thought that a solution method of the SIMPLE(Patanker 1980), with loose restrictions of the clock interval, is superior. For that solution method, however, although t can be set larger than the Marker and Cell (MAC) method, the iteration count of an inner loop is unsteady. The possibility also exists that a solution changes by the method of convergence judgment. The method for obtaining a solution stably is thought to vary according to the time-variability characteristics of an analysis object also. For that reason, a study by trial and error is necessary (Ferziger, Peric 2002). Outline of simulation The analysis was performed for 4 h from the start of air-conditioning (10:00). For this report, the main intentions were to perform a study of an airflow analysis area; only the airflow calculation was performed assuming that the outlet temperature and the wall surface temperature were already known.

5 Table 3. Simulation cases and results t model method CPU Error* Case [sec] [hour] [ % ] LES 01 LES MAC 4weeks MAC 01 k-ε MAC 4weeks SMP1 0.1 k-ε SIMPLEC SMP2 1 k-ε SIMPLEC SMP3 10 k-ε SIMPLEC SMP4 10 k-ε SIMPLEC SMP5 k-ε SIMPLEC SMP6 k-ε SIMPLEC SMP7 k-ε SIMPLEC SMP8 60 k-ε SIMPLEC * Error of heat balance= (Θout-Θin) CFD / (Θout-Θin) EXPx100 Simulation mesh:40(x) x 62(y) x (z) window top light lighting window 11m(z) inlet(m/s) inlet(0.6m/s) 18m(x) outlet window inlet(0.8m/s) Analysis section m(y) inlet(1.2m/s) inlet width:0.12m kin=05m 2/s2 Figure 10. Simulation model The actual data (1 min value) and the read values from the thermal image (image taken every min) were treated using linear interpolation and were used for the outlet and wall temperatures, and the lighting and window surface temperatures (Figure 8). Furthermore, to simplify the calculation, the object is modeled as shown in Figure 10. To elucidate the difference of turbulence models, analyses were performed using LES and k-ε models. Moreover, with the intention of studying differences between solution methods, analyses were performed using SIMPLEC(Doormaal, Raithby 1984) and MAC methods as k-ε solution methods. Study cases are shown in Table 3. In addition, all analysis ware carried out by own development CFD code. Study of calculation stability To study the calculation stability of SIMPLEC in addition to LES and k-ε (MAC method), the convergence conditions of t and the inner loop were varied; eight cases were studied. Results are shown in Table 3. The error of heat balance in the table was calculated from the difference between the intake temperature and the outlet temperature, which were actual measurements and calculation values. In the calculation, because both the outlet temperature and the wind rate correspond to actual measured values, evaluation of the heat balance error is performed solely using the temperature difference between the outlet and the intake. A positive value of the error indicates that the calculated intake temperature is higher than the actual measurement (percentage). For the k-ε analysis, a solution obtained using MAC with second-order accurate temporal subtraction can be regarded as an accurate solution in the conditions used for this study. Cases SMP1 and SMP2 in SIMPLEC corresponded approximately with MAC (Figures 11 and 12). When t was small in SIMPLEC, the calculation time lengthened because of iterative computation at every time and step, but the average iteration number of the inner loop was about one time. The error between the calculation and actual measurement is approximately 17%. The convergence was good, although t of SMP2 was 10 times that of SMP1. In addition, the calculation times of LES and MAC were approximately 4 weeks (calculated using Pentium IV 2 GHz). For SMP3, no solution was obtained in the first convergence condition, but a solution was obtained according to progress of the situation. For SMP4, convergence was attained by making the convergence judgment easy. The heat balance error was the smallest among the studied cases, but a remarkable difference from MAC was apparent in the result of temperature distribution and wind speed distribution. Therefore, the accidental error is thought to be negligible. Regarding SMP6 SMP8, for which t was made larger and convergence judgment was made loosely, the calculation time became short, but the heat balance error was large. In addition, results of temperature, wind velocity, etc., differed remarkably from those of MAC (data not shown). In SIMPLEC, the following were confirmed from these results: the obtained solution changed remarkably according to the change of t and convergence judgment.

6 Air Temperature [ ] h=5.5m h=4m h=8.5m Experiment(July,14) h=3,2m h=1m h=0.5m h=1.5m h=2.5m h=3.5m Expreriment (July,14) Air Temperature [ ] h=8.5m h=5.5m h=4m LES( t=01sec) h=3,2,1m h=0.5m h=1.5m h=2.5m h=3.5m LES( t=01sec) Air Temperature [ ] h=8.5m h=5.5m k-ε(mac, t=01sec) h=4,3,21m h=3.5m h=0.5m h=1.5m h=2.5m k-ε(mac, t=01sec) k-ε(simplec, t=1sec) h=8.5m h=5.5m h=4,3,21m Air Temperature [ ] Figure 11 Indoor air temp. fluctuation (A. section) h=0.5m h=3.5m h=1.5m h=2.5m k-ε(simplec, t=1sec) Figure 12 Wind velocity fluctuation (A. section) A solution was stably obtained by setting t to a certain small value, and a solution was obtained in a shorter calculation time than by the MAC method. In the study cases used this time, the case of t=1 sec was superior from the perspective of the calculation time and the calculation accuracy. Time variability characteristics The calculation results of LES, MAC and SMP1 were compared to actual measurements. The air temperature at the indoor center and the temporal sequence of the scalar wind speed at the room center are shown respectively with actual measurement results in Figures 11 and 12. Regarding temperature variability, tendencies such as the temperature decrease after the air-conditioning start (10:00 11:00) and the constant maintenance of the room temperature after 12:00 correspond well with actual measurements. However, the calculated temperature is approximately 1 2 C lower than the experimental value.

7 Θ Exp. 0sec Θ Exp. 1800sec Θ Exp. 3600sec LES 0sec LES 1800sec LES 3600sec Θ LES 0sec Θ LES 1800sec Θ LES 3600sec k-ε 0sec k-ε 1800sec k-ε 3600sec Θ k-ε 0sec Θ k-ε 1800sec Figure 13. Wind vector distribution and the temperature distribution (A. section) Θ k-ε 3600sec Furthermore, in the actual measurement, the temperature difference distribution between the upper area and the lower area was confirmed, but the temperature below the floor height 4 m in LES and below the floor height 5.5 m in k-ε were mostly equal. Regarding the temporal sequence change of wind speed, the indoor wind speeds for both the actual measurement and the calculation are less than 0.3 m/s. Although a tendency toward variability similar to the actual measurements was confirmed in LES, no correspondence was found in k-ε. Because the quantities of turbulence inflow in LES and k-ε were not identical, an accurate comparison was not performed; however, a tendency was apparent that LES was nearer the actual measurement. Modeling of a region, lattice division and boundary condition, etc. are considered as causes of the discrepancy in the temperature and wind speed behaviors. This matter will be examined further in later studies.

8 Space distribution The wind speed distribution and the temperature distribution are shown for 1 hour after the beginning of the calculation in Figure 13 (excerpt). The result by LES was obtained by time averaging at 1 min intervals. The air flow, blown from the floor surface (right end in the figure) rises along the wall surface and separates from the wall near the wall surface center; it then flows along the floor surface. The point of separation from the wall surface moves slightly upward over time. The airflow attached to the floor surface separates near the center, but it is confirmed that the separation point moves over time. The wind speed in areas other than the vicinity of the outlet was less than 0.3 m/s. The airflow at the center area of the space is turbulent in LES, which probably reflects the time-variability characteristics. For temperature distributions, in both cases of the actual measurement and the calculation, flow of the cool wind from the outlet onto the vicinity of the floor surface is confirmed. Furthermore, up to 1 hour after the beginning of calculation (corresponding to 11:00), temperature stratification resembling that of the actual measurements is apparent. The outlet temperature becomes approximately equal to the room temperature in 1.5 hour after the beginning of calculation (data not shown). Consequently, the temperature difference between the upper area and the lower area decreases; the temperature within the space becomes mostly constant at around C. Regarding the actual measurement result at min after the beginning of calculation, the cool air from the outlet is visible at a lower right area in the figure, but in the calculation, the cool air is distributed along the wall. Regarding the rough tendency of the temperature distribution, the actual measurement, LES, and k-ε were identical. CONCLUSIONS For this study, examination of the follow-up of the CFD analysis was performed in for a time variability problem. The obtained results are summarized below. In the problem examined for this study, the solution and convergence varied remarkably in accordance with the convergence conditions. A more detailed study is necessary. In the study cases reported herein, t = 1 sec was superior from the perspective of computing time and accuracy. Comparison between the analysis results and the actual measurements clarified that both LES and k-ε mostly corresponded with the actual phenomenon regarding the temperature distribution. The wind velocity distribution of k-ε showed a different result from both the actual measurement and LES. REFERENCES 1. ASHRAE HANDBOOK Fundamentals (2005), Chapter 33, SPACE AIR DIFFUSION, American Society of Heating, Refrigerating and Air-Conditioning Engineers, Inc. 2. Doormaal J P, Raithby G D (1984), Enhancements of the SIMPLE Method for Predicting Incompressible Fluid Flows, Numerical Heat Transfer, vol.7, Ferziger, J H, Peric M (2002), Computational Methods for Fluid Dynamics, Springer. 4. Gagge A P, Fobelets A P, Berglund L G (1986), A Standard Predictive Index of Human Response to the Thermal Environment, ASHRAE Transactions, vol.92, Part 2B, 709-7, 5. Sagaut P (2002), Large Eddy Simulation for Incompressible Flows, Springer. 6. Sakai K, Yamaguchi E, Ishihara O, Manabe M (2002), A Study on the Thermal Performance and Air Distribution of a Displacement Ventilation System Applied for Large Space, Proc. of the 9th Int. Conference on Indoor Air Quality and Climate, Vol.3, Patanker S V (1980), Numerical heat transfer and fluid flows, New York:McGraw-Hill.