Wake Characterization of Building Clusters Immersed in Deep Boundary Layers
Abhishek Mishra, Marco Placidi, Matteo Carpentieri, Alan Robins
Abstract
Abstract Wind tunnel experiments were conducted to understand the effect of building array size ( N ), aspect ratio ( AR ), and the spacing between buildings ( $$W_S$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>W</mml:mi> <mml:mi>S</mml:mi> </mml:msub> </mml:math> ) on the mean structure and decay of their wakes. Arrays of size 3 $$\times $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mo>×</mml:mo> </mml:math> 3, 4 $$\times $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mo>×</mml:mo> </mml:math> 4,and 5 $$\times $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mo>×</mml:mo> </mml:math> 5, AR = 4, 6, and 8, and $$W_S$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>W</mml:mi> <mml:mi>S</mml:mi> </mml:msub> </mml:math> = 0.5 $$W_B$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>W</mml:mi> <mml:mi>B</mml:mi> </mml:msub> </mml:math> , 1 $$W_B$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>W</mml:mi> <mml:mi>B</mml:mi> </mml:msub> </mml:math> , 2 $$W_B$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>W</mml:mi> <mml:mi>B</mml:mi> </mml:msub> </mml:math> and 4 $$W_B$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>W</mml:mi> <mml:mi>B</mml:mi> </mml:msub> </mml:math> (where $$W_B$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>W</mml:mi> <mml:mi>B</mml:mi> </mml:msub> </mml:math> is the building width) were considered. Three different wake regimes behind the building clusters were identified: near-, transition-, and far-wake regimes. The results suggest that the spatial extent of these wake regimes is governed by the overall array width ( $$W_A$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>W</mml:mi> <mml:mi>A</mml:mi> </mml:msub> </mml:math> ). The effects of individual buildings are observed to be dominant in the near-wake regime ( $$0<x/W_A< {0.45}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>0</mml:mn> <mml:mo><</mml:mo> <mml:mi>x</mml:mi> <mml:mo>/</mml:mo> <mml:msub> <mml:mi>W</mml:mi> <mml:mi>A</mml:mi> </mml:msub> <mml:mo><</mml:mo> <mml:mrow> <mml:mn>0.45</mml:mn> </mml:mrow> </mml:mrow> </mml:math> ) where individual wakes appear behind each building. These wakes are observed to merge in the transition-wake region ( $${0.45}< x/W_A < 1.5$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mrow> <mml:mn>0.45</mml:mn> </mml:mrow> <mml:mo><</mml:mo> <mml:mi>x</mml:mi> <mml:mo>/</mml:mo> <mml:msub> <mml:mi>W</mml:mi> <mml:mi>A</mml:mi> </mml:msub> <mml:mo><</mml:mo> <mml:mn>1.5</mml:mn> </mml:mrow> </mml:math> ), forming a combined wake in which the individual contributions are no longer apparent. In the far-wake regime ( $$x/W_A > 1.5$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>x</mml:mi> <mml:mo>/</mml:mo> <mml:msub> <mml:mi>W</mml:mi> <mml:mi>A</mml:mi> </mml:msub> <mml:mo>></mml:mo> <mml:mn>1.5</mml:mn> </mml:mrow> </mml:math> ), clusters’ wakes are akin to those developing downwind of a single isolated building. Accordingly, new local and global scaling parameters in the near- and far-wake regimes are introduced. The decay of the centreline velocity deficit is then modelled as a function of the three parameters considered in the experiment.