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Renormalized numerical simulation of flow over planar and non-planar fractal trees

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Abstract

We review the fundamentals of a new numerical modeling technique called Renormalized Numerical Simulation (RNS). The goal of RNS is to model the drag force produced by high Reynolds-number turbulent flow over objects that display scale-invariant properties, objects such as tree-like fractals. The hallmark of RNS in this application is that the drag of the unresolved tree branches is modeled using drag coefficients measured from the resolved branches and unresolved branches (as modeled in previous iterations of the procedure). In the present paper, RNS is used to study the effects of branch orientation on the drag force generated by highly idealized trees in which trunk and branches have square cross-section, and the branches all lie in a plane perpendicular to the incoming flow. Then, the procedure is generalized to the more general case of non-planar branch arrangements. Results illustrate that RNS may enable numerical modeling of environmental flow processes associated with fractal geometries using affordable computational resolution.

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Authors and Affiliations

  1. Department of Mechanical Engineering and Center for Environmental and Applied Fluid Mechanics, Johns Hopkins University, 223 Latrobe Hall, 3400 N. Charles St., Baltimore, MD, 21218-2681, USA

    Stuart Chester & Charles Meneveau

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  1. Stuart Chester
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  2. Charles Meneveau
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Correspondence to Charles Meneveau.

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Chester, S., Meneveau, C. Renormalized numerical simulation of flow over planar and non-planar fractal trees. Environ Fluid Mech 7, 289–301 (2007). https://doi.org/10.1007/s10652-007-9026-7

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  • DOI: https://doi.org/10.1007/s10652-007-9026-7

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