ROOM AVERAGE VELOCITY EQUATION A TOOL TO IMPROVE DESIGN OF THERMAL COMFORT CONDITIONS K Hagström *, O Hakkola and T Moilanen Halton Solutions, Kausala, Finland ABSTRACT For a long time PPD index defined in international ISO7730 standard has been a practical tool for evaluation of measured thermal comfort conditions in existing buildings. However, its usage has not yet been realized in design phase. One of the reasons is that there has not been any practical tool available to estimate average velocity conditions within the occupied zone. A kinetic energy model for calculation of the average room velocity has been presented in earlier paper. Current paper reports additional verification results of the kinetic energy model with different types of diffusers. The verified kinetic energy method has been applied together with other appropriate theories in development of design procedure and a software tool for designing of thermal comfort conditions according to ISO7730. Additionally, the design tool enables designer to evaluate maximum draft velocity conditions from the supply jet. INDEX TERMS Thermal Conditions, Room Velocity, Human Activities, Velocity, Laboratory Experiments INTRODUCTION For a long time PPD index defined in international (ISO7730 993) standard has been a practical tool for evaluation of measured thermal comfort conditions in existing buildings. However, its usage has not yet been realized in design phase. One of the main reasons is that there has not been any practical tool available to estimate room velocity, more accurately average velocity conditions, within the occupied zone. For the most the designer has been able to estimate jet maximum velocity at the edge of the occupied zone utilizing diffuser manufacturers product information. However, this information is valid only for evaluation of maximum draft conditions due to supply jet not for PPD evaluation. A kinetic energy model for calculation of the average room velocity has been presented in (Hagström 2000). The model takes into account, except the supply air jet, also the influence of the other kinetic energy sources, such as thermal plumes, on the room velocity. Current paper reports additional verification results of the kinetic energy model with different types of diffusers. With the aid of method for average velocity evaluation together with supporting thermal model such as one presented by (Fanger, 970) one would be able to design for optimal thermal comfort defined in (ISO7730, 993). * Contact author email: kim.hagstrom@haltongroup.com 760
METHODS Method for room average velocity calculation A thorough analysis of the room kinetic energy balance was conducted by (Hagström 2000). Typically, the main sources of kinetic energy to be considered are supply airflow and room heat sources. The introduced kinetic energy flux can be calculated from equation: 3 3 2 q e= ρ u A= ρ u q = ρ, 2 2 2 2 A where A (m 2 ) is the outlet area and, u (m/s) is an initial velocity and, q (m 3 /s) is volume flow rate from the source. Application of the equation to different sources is presented in (/Hagström 2002). Based on the analysis and experimental validation, a method for the room average velocity calculation was presented. The average velocity quantifies the velocity level in the room bulk flow, thus, excluding areas of primary flows of air jets or plumes. An equation developed for the average velocity calculation is (Hagström 2000): =( C x ur ρ einput + e 0.664 A /2 /2 sources s ) ( V A r s Proceedings: Indoor Air 2002 ) 6, where C x =.40 [m /3 /s 5/3 ] is an empirical coefficient, ρ is air density, [kg/m 3 ], e input and e sources [W], are kinetic energy fluxes from external and internal sources, A s,[ m 2 ], is an area of the room surfaces and V r, [m 3 ], is a room volume. The ratio C x /2 /ρ can be neglected in the normal range of room temperatures because the influence on the result is only ±2 %. A design approach for thermal comfort The average velocity equation can be used together with existing methods for thermal environment to a thermal comfort oriented design approach. Application of the approach is a straightforward process for evaluation of comfort conditions in which a little input information is needed. The design algorithm consists of following steps: () A collection of the input data from external and internal kinetic energy sources and room dimensions; (2) Calculation of the kinetic energy supplied into the room, the room volume and the area of the room surfaces; (3) Calculation of the resulting room average velocity. (4) Together with information on room temperature conditions the average velocity can be used to estimate thermal comfort conditions of the room using PPD or PMV index. (ISO7730, 993) (5) Additionally, the local maximum draft velocity conditions from the primary airflows can be evaluated at the edge of the occupied zone using traditional design methods. RESULTS OF THE FURTHER VERIFICATION OF KINETIC ENERGY MODEL Additional experience of the applicability of equation (2) for different air supply methods and room set-ups was collected through verification with the experimental results collected from the litterature. Measurement results from five different technical papers were compareded with predicted occupied zone average velocities. (Zhang 99, Chow 998, Heikkinen 99, Li 995, Skovgaard 99) The overall correlation was found good and encouraging for the practical use. However, it must be noted that lacking information of of boundary conditions created some source of inaccuracy into the calculations(heat sources, diffuser details). Also the limited amount of measurement points as well as possible measurement errors in the reference datas influenced on the comparison results of single cases. (Zhang 99). A two dimensional flow from a continuous slot diffuser was studied by Zhang in full and /4-scale environmental chambers in a laboratory. The size of the full-scale room 76 () (2)
was 7.3x5.5x2.4 m and the small-scale chamber was.4x2.4x0.6 m. Both isothermal and nonisothermal situations were measured. The cooling load was supplied into the room by heating panels on the floor. The correlation of predicted velocities with eleven measured set-ups, six in full scale and five in small scale is presented in Figure. The overall correlation was found excellent. Only in non-isothermal scale model tests the calculated results were found smaller than measured. The probable reason for this is that in those cases the cooled air jet turned down to the occupied zone, thus incorporating surplus kinetic energy into the zone. (Chow 998). The comparison of predicted average velocities to measured results from air flow chamber tests with wall jet and wall mounted air grille and field surveys of three different waiting halls with ceiling diffusers are presented in Figure 2. The size of the airflow chamber was 4.x2.6x2. m and waiting halls were 56.3x23x4.3 m, 49x28.6x3.6 m and 7.4x0.7x2.9m..2 0.8 0.6 0.4 0.2 0 - AVERAGE: 0.02 y =.039x - STDEV: R 2 = 0.9745 Upred =.04 * Umeas R 2 = 0.97 0 0.2 0.4 0.6 0.8 Figure. Correlation of measured and predicted velocities, Continuous Slot diffuser, 2 Scales, Laboratory (Zhang99) 0.5 0.0 - AVERAGE: -5 y =.063x - STDEV: 0.02 R 2 = 0.7899 Upred =.02 * Umeas R 2 = 0.79 0 0. 0.5 0.2 Figure 2. Correlation of measured and predicted velocities, three different diffuser types, laboratory and field studies (Chow998) (Skovgaard 99). Isothermal laboratory tests with commercial multi-nozzle, 84 nozzles, each with the diameter,8 mm, wall diffuser were carried in situation using different air change rates. The test room was 4.2x3.6x2.4 m. The correlation of predicted and measured occupied zone velocities are presented in Figure 3. During prediction the reported initial supply velocities that were calculated based on the free opening of the nozzle were corrected with nozzle coefficient 0.8 to get actual kinetic energy output. The nozzle coefficient was derived utilizing technical handbook. (Niskanen 965) (Heikkinen 99). Altogether four laboratory tests with a similar multi-nozzle wall diffuser as Skovgaard were carried in isothermal and non-isothermal situations using two different air change rates. The test room was 4.2x3.6x2.5 m and the cooling load was imported in nonisothermal situations through a cold window on the opposite wall from the diffuser. The correlation of predicted and measured occupied zone velocities are presented in Figure 4. 762
0.40 0.35 0.5 0.5 0.0 - AVERAGE: y =.027x - STDEV: R 2 = 0.986 0.0 Upred =.02 * Umeas R 2 = 0.99 0.0 - AVERAGE: 0.03 - STDEV: 0.02 Upred = 0.87 y = 0.8733x * Umeas R 2 = 0.9R 2 = 0.9056 0 0. 0.5 0.2 0.3 0.35 0.4 0.0 0.5 Figure 3. Correlation of measured and predicted velocities, Multinozzle diffuser, laboratory studies (Skovgaard 99) Figure 4. Correlation of measured and predicted velocities, Multinozzle diffuser, laboratory studies (Heikkinen 99) (Li 995). Four different types of commercial diffusers were measured in non-isothermal situations in empty room. The diffuser types were, linear ceiling diffusers, square ceiling diffusers, swirl ceiling diffusers and nozzles. The size of the test room was 7.3x4.9x2.4 m and the non-uniform cooling load was supplied into the room by heating panels with on-off control on the floor. Test parameters were varied in very large ranges, supply air velocity from 0.4 m/s to 30 m/s and supply air temperature difference from C to 23 C. The comparison between predicted and measured occupied zone velocities is shown in Figure 5. Though the overall concentration was good, some differences existed between the results especially in cases, where the kinetic energy input from heat sources was several times the jet kinetic energy. Also some differences were founded with the high-speed nozzles. The reason for this is probably that part of the measurement points were actually inside the primary jet flow. Following assumptions and simplifications were made during prediction because of the lacking background information: Kinetic energy supply for ceiling diffusers was calculated based on the connection duct size and for linear diffusers based on the free opening. The heat input was considered to be all convective heat, which was the assumption by Li in his own model. Though this did not seem to be realistic, no data on heat sources was available to make better judgement. 0.60 0.50 0.40 0.0 - AVERAGE: 0.02 - STDEV: y = 0.9663x R 2 = 0.7744 Upred = 0.97 * Umeas 0.0 0.40 0.50 0.60 Um, [m/s] R 2 = 0.77 Figure 5. Correlation of measured and predicted velocities, six different diffusers, Laboratory (Li 995) DISCUSSION The applicability of the kinetic energy model for the average velocity calculation was verified with additional experimental data. Generally the calculated velocities correlated well with the measurements. Thus, it can be utilized for evaluation of occupied zone average velocity in 763
mixing air diffusion. For zonal air diffusion situations the method is not directly applicable, which has been discussed in (Hagström 2000). The weaknesses of the method lie in the quality of the boundary conditions of the kinetic energy sources. For thermal sources it seems to be appropriate to utilize plume equations, but for the supply air devices the details of the device can have a great impact on the kinetic energy supplied into the room. CONCLUSION AND IMPLICATIONS The proposed method has been utilized in development of a software tool for designing of thermal comfort conditions according to ISO 7730. Additionally, the design tool enables designer to evaluate maximum draft velocity conditions from the supply jet. An example of the screen view of the design software is shown in Figure 6. The manikin in the room presents current observation point. PMV, mean radiant temperature and sound pressure level of the current position as well as occupied zone average velocity can be read from the bar below the room picture. Proceedings: Indoor Air 2002 Figure 6. Screen view of the design software utilizing thermal comfort approach. REFERENCES Chow W K, Wong L T, Air diffusion terminal devices: Macroscopic numbers describing jet momentum, Proceedings of CIBSE A: Building Serv. Eng. Res. Technol. 9() 49-54(998). Hagström K, Sirén K, Calculation of the Room Velocity Using Kinetic Energy Balance, ASHRAE Transactions, (2) 2000, 3-2. Heikkinen J, Measurement of test cases B2, B3, E2 and E3 (Isothermal and summer cooling cases), A non published report within IEA Annex 20, Airflow Patterns Within Buildings, Subtask : Room air and contaminant flow, 99. ISO 7730, 993, Moderate thermal environments - Determination of the PMV and PPD indices and specification of the conditions for thermal comfort. International Standards Organization. Li, Z H, Fundamental Studies on Ventilation for improving Thermal Comfort and IAQ, Ph.D. Thesis, University of Illinois, Urbana, 995. Niskanen E, Hydromechanics, Technology Handbook, Part, 8th edition, Gummerrus 965. (In Finnish) Skovgaard M, Turbulent flow in rooms ventilated by the mixing principle - Comparisons between computational fluid dynamics and full scale experiments, PhD Thesis, The University of Aalborg, Denmark, December 99. Zhang J, A fundamental Study of two dimensional room ventilation flows under isothermal and non-isothermal conditions, Ph.D. Thesis, University of Illinois, Urbana, 99. Fanger PO. 970. Thermal Comfort. Copenhagen: Danish Technical Press. 764