Methodology for the Evaluation of Natural Ventilation in ... - Cham

Table 19. Summary of Values and Dimensionless Parameters for Full-Scale Building, Scaled Airand Scaled Water ModelsAir-Building Air-Model Water Model Water ModelScale 1 12 12 100g (m/s 2 ) 9.8 9.8 9.8 9.8β (1/°K) 0.0033 0.0034 0.0002 0.0002ΔT (°K) 5 30 6 6g'=gβΔT 0.1655 0.9800 0.0118 0.0118H=height of Atrium (m) 15 1.2 1.2 0.75α (m 2 /s) 2.16x10 -5 2.40 x10 -5 1.44 x10 -7 1.44x10 -7ν (m 2 /s) 1.477 x10 -5 1.60 x10 -5 1.01 x10 -6 1.01 x10 -6A CS (m 2 ) 6.32 0.522 0.559 0.037Pr 0.7 0.7 7.0 7.0Re 6.74x10 5 3.54 x10 4 1.10 x10 4 1.70 x10 4Pe=PrRe 4.72 x10 5 2.47 x10 4 7.68 x10 4 1.19 x10 5Gr 3.84 x10 13 7.94 x10 9 2.05 x10 8 3.65 x10 9Ra=PrGr 2.69 x10 13 5.56 x10 9 1.43 x10 9 2.55 x10 10For the reduced scale air model, the primary characteristic length used in evaluating the occupiedzones is the hydraulic diameter of the cross section of a single floor. This parameter accuratelydescribes the main flow through the model and provides a characteristic length of 0.52m.However, the height of the atrium is used in evaluating the buoyancy velocity, since it is theheight difference between the inlet and the outlet, at the top of the stack, which drives the airflow. The Reynolds number for the model was approximately 3.54x10 4 , using the hydraulicdiameter of a single heated zone. This falls in the turbulent regime. The Grashof number for thescale model is on the order of 1.2x10 8 . When comparing both the Reynolds number and Grashofnumber to those calculated for the prototype building for buoyancy-driven flow, the prototypebuilding is also in the turbulent regime (Re=7.1x10 5 ) and buoyancy dominated flow(Gr=9.1x10 10 ). Finally, for thermal similarity the temperature differences and heat flow mustremain proportional. The internal heat load per square meter (W/m 2 ) is scaled using the same12 th scale to provide the similar buoyancy effect. The temperatures recorded from the reducedscaleair model are non-dimensionalized using the ΔT ref to obtain the resulting full-scale buildingtemperatures for analysis.From Table 19, the critical Reynolds number, 2.3x10 3 is achieved for all models and the fullscaleprototype building. The air model achieves a slightly closer value of Reynolds number thaneither of the water models, but is still off by a factor of 10. When the Prandtl number isaccounted for using the Peclet number, Pe, the small-scale water model achieves a closer matchto the full-scale prototype than either of the other models. It is assumed that each of the models,as well as the prototype building, is operating in a turbulent regime for the airflow in the heatedzone. For the buoyancy-driven case, equality of Grashof number is required after meeting thecritical Reynolds number condition. The twelfth-scale air model and 100 th scale water modelmore closely match the Grashof number, but none of the models matches it exactly. Someresearch (Etheridge and Sandberg 1996) that indicates that for buoyancy-driven flow it issufficient to achieve critical values of Grashof number when using air as the working fluid.They propose a critical value of Grashof number in the range of 10 6 to 10 9 based on someexperimental work, and using the height of a room as the characteristic length. When the room90