Renormalized Numerical Simulation of Flow over Planar and 3D Fractal Trees

Abstract

We review the fundamentals of a new numerical modeling technique called Renormalized Numerical Simulation (RNS). It is applied to the calculation of drag forces produced by high Reynolds-number turbulent flow over 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). RNS results are used to study the influence of the tree fractal dimension on the tree drag. The procedure is generalized from trees in which all branches lie in a plane, to the more general case of 3D trees. Results illustrate that RNS enables numerical modeling of physical processes associated with fractal geometries using affordable computational resolution.