Modeling turbulent flow over fractal trees with renormalized numerical simulation

Abstract

High-Reynolds number flow over tree-like fractals is considered, with emphasis on the drag forces produced. Fractal objects display large scale-disparity and complexity while being amenable to a simple and standardized description. Hence, they offer an elegant idealization of the actual boundaries in practical applications where turbulence interacts with boundaries that are characterized by multiple length-scales. First, using large-eddy-simulation of flow over prefractal shapes with increasing numbers of branch generations, the dependence of the tree drag on the inner cutoff-scale of the fractal is studied. It is found that the convergence of the drag coefficient towards a value that is independent of inner cutoff-scale is very slow. In order to address this fundamental difficulty and avoid the need to resolve all the small-scale branches of the fractal, a new numerical modeling technique called renormalized numerical simulation (RNS) is introduced. RNS models the drag of the unresolved branches using drag coefficients measured from both resolved branches and unresolved branches as modeled in previous iterations of the procedure. The RNS technique and its convergence properties are tested by means of a series of simulations using different levels of resolution. Then, RNS is used to investigate the influence of the tree fractal dimension on the drag coefficient. The increase of the drag with fractal dimension is quantified for two types of tree geometry, in two flow configurations. Results illustrate that RNS enables numerical modeling of physical processes associated with fractal geometries using affordable computational resolution.

Spatial Characteristics of Roughness Sublayer Mean Flow and Turbulence Over a Realistic Urban Surface

“…Theφ(x, y, z) function is initialized adopting an iterative projection technique on the triangulated (urban) surface, which has been specifically developed for the current study. The immersed boundary algorithm is a minor modification of the one proposed in Chester et al (2007). The velocity field is fixed to zero in Ω b through a penalty method and the law-of-the-wall is enforced at all the collocation nodes that fall in the region −1.1Δ ≤φ ≤ 1.1Δ.…”

“…The argument of the logarithmic function in Eq. 1 has been regularized by adding a unity constant (Chester et al 2007). …”

Detached Eddy Simulation for Turbulent Flows in a Pipe with a Snowflake Fractal Orifice

“…The former is much easier than the later and there is need for methods aiming at the modeling of fractal flows. Apart from DNS, there is one paper [2] on a high-Reynolds number flow over a tree-like fractal using large eddy simulation (LES). A renormalized numerical simulation (RNS) was needed to model the drag of the unresolved branches of the fractal tree.…”

Towards oscillation-free implementation of the immersed boundary method with spectral-like methods

“…A significant reduction of the oscillations was reported. Laplacian smoothing has also been tried [20,21], in which the velocity field inside the body is set by applying the Laplace operator iteratively. Nevertheless, the final smoothing effect strongly depends on the initial guess of the velocity and the number of iterations, for which a proper choice is often difficult to make.…”