256 The UMAP Journal 23.3(2002) Figure 4. Streamlines for wind flow entering the plaza; decreased wind speed at the plaza level is apparent. Note the highly increased wind speed near the edge of the building The horizontal velocity profile for a streamline that passes about 3 m above the building roof (corresponding to c=0.6)is plotted in Figure 5; 3 m is reasonable height for an anemometer mounting. From these graphs, one can see that the wind speed through the plaza center(at a distance of 30 to 40 m from edge) is approximately half of the rooftop wind speed 0 0.05 102030 Figure 5. Horizontal velocity profile for the streamline corresponding to c=0.6. This streamline passes above the building s roof at a height of 3 m, a reasonable anemometer mounting height This calculation is validated by its excellent agreement with the findings of Santamouris and Dascalaki [2000], who report that in flows perpendicular to a street the ground-level speeds are between zero and 55% of the free-stream Results We conclude from this flow model
256 The UMAP Journal 23.3 (2002) Figure 4. Streamlines for wind flow entering the plaza; decreased wind speed at the plaza level is apparent. Note the highly increased wind speed near the edge of the building. The horizontal velocity profile for a streamline that passes about 3 m above the building roof (corresponding to c = 0.6) is plotted in Figure 5; 3 m is a reasonable height for an anemometer mounting. From these graphs, one can see that the wind speed through the plaza center (at a distance of 30 to 40 m from edge) is approximately half of the rooftop wind speed. Figure 5. Horizontal velocity profile for the streamline corresponding to c = 0.6. This streamline passes above the building’s roof at a height of 3 m, a reasonable anemometer mounting height. This calculation is validated by its excellent agreement with the findings of Santamouris and Dascalaki [2000], who report that in flows perpendicular to a street the ground-level speeds are between zero and 55% of the free-stream speeds. Results We conclude from this flow model:
A Foul-Weather Fountain 257 Placement of the anemometer is important! It should be mounted near the center of the rooftop to minimize disturbances from the roofs edge The anemometer reports a wind speed that is highly biased! Ground-level wind moves approximately half as fast as the roof-level wind Wind speeds are fairly independent of height. If the fountain is not signif- seems to icantly higher than the surrounding buildings, then it is safe to assume that contradict the wind is spatially constant precious laim Modeling wind variation Over Time The control system must be able to handle a range of weather conditions, from calm up to strongly gusty. We abstract the wind patterns into three gen- eralized types of increasing complexity: algorithms ability to judge the proper height for a given wind spee st the Type 1: A low intensity constant breeze of a few m/s, meant to te Type 2: a breeze varying smoothly over a timescale of a couple of minutes. We use a sinusoidal oscillation in magnitude and direction, with a constant term to reflect the prevailing wind direction of the hour. This type tests the algorithm's ability to adapt to slowly changing conditions Type 3: Sudden unexpected wind gusts, with a few seconds duration and very high intensity. We model the occurrence of a gust as a Poisson process and distribute the gust durations and intensities normally. The mean and variance are chosen to produce reasonable results. This is perhaps the most important test, since the gusty scenario can easily fool a naive algorithm Generating a realistic wind signal We parametrize the wind profile of a location by four numbers The mean steady wind steady The mean gust strength gust, where a gust is defined to be variation on the sub-15 s timescale The mean gust duration gust The gust deviation ogust From Webmet data [2001], we estimate these characteristic numbers for ome major U.S. cities(Table 2) le construct realistic wind signals from these characteristic numbers to correspond to our types
A Foul-Weather Fountain 257 • Placement of the anemometer is important! It should be mounted near the center of the rooftop to minimize disturbances from the roof’s edge. • The anemometer reports a wind speed that is highly biased! Ground-level wind moves approximately half as fast as the roof-level wind. • Wind speeds are fairly independent of height. If the fountain is not signif- seems to contradict previous claim!! icantly higher than the surrounding buildings, then it is safe to assume that the wind is spatially constant. Modeling Wind Variation Over Time The control system must be able to handle a range of weather conditions, from calm up to strongly gusty. We abstract the wind patterns into three generalized types of increasing complexity: • Type 1: A low intensity constant breeze of a few m/s, meant to test the algorithm’s ability to judge the proper height for a given wind speed. • Type 2: A breeze varying smoothly over a timescale of a couple of minutes. We use a sinusoidal oscillation in magnitude and direction, with a constant term to reflect the prevailing wind direction of the hour. This type tests the algorithm’s ability to adapt to slowly changing conditions. • Type 3: Sudden unexpected wind gusts, with a few seconds duration and very high intensity. We model the occurrence of a gust as a Poisson process and distribute the gust durations and intensities normally. The mean and variance are chosen to produce reasonable results. This is perhaps the most important test, since the gusty scenario can easily fool a naive algorithm. Generating a Realistic Wind Signal We parametrize the wind profile of a location by four numbers: • The mean steady wind µsteady. • The mean gust strength µgust, where a gust is defined to be variation on the sub-15 s timescale. • The mean gust duration tgust. • The gust deviation σgust. From WebMET data [2001], we estimate these characteristic numbers for some major U.S. cities (Table 2). We construct realistic wind signals from these characteristic numbers to correspond to our types: