Computational Analysis of Active and Passive Flow Control for Backward Facing Step

The internal steady and unsteady flows with a frequency and amplitude are examined through a backward facing step (expansion ratio 2), for low Reynolds numbers (Re=400, Re=800), using the immersed boundary method. A lower part of the backward facing step is oscillating with the same frequency as the unsteady flow. The effect of the frequency, the amplitude, and the length of this oscillation is investigated. By suitable active control regulation, the recirculation lengths are reduced, and, for a percentage of the time period, no upper wall, negative velocity, region occurs. Moreover, substituting the prescriptively moving surface by a pressure responsive homogeneous membrane, the fluid–structure interaction is examined. We show that, by selecting proper values for the membrane parameters, such as membrane tension and applied external pressure, the upper wall flow separation bubble vanishes, while the lower one diminishes significantly in both the steady and the unsteady cases. Furthermore, for the time varying case, the length fluctuation of the lower wall reversed flow region is fairly contracted. The findings of the study have applications at the control of confined and external flows where separation occurs.

Numerical solutions of 2D Navier-Stokes equations based on generalized harmonic polynomial cell method with non-uniform grid

It is essential for a Navier-Stokes equations solver based on a projection method to be able to solve the resulting Poisson equation accurately and efficiently. In this paper, we present numerical solutions of the 2D Navier-Stokes equations using the fourth-order generalized harmonic polynomial cell (GHPC) method as the Poisson equation solver. Particular focus is on the local and global accuracy of the GHPC method on non-uniform grids. Our study reveals that the GHPC method enables use of more stretched grids than the original HPC method. Compared with a second-order central finite difference method (FDM), global accuracy analysis also demonstrates the advantage of applying the GHPC method on stretched non-uniform grids. An immersed boundary method is used to deal with general geometries involving the fluid-structure-interaction problems. The Taylor-Green vortex and flow around a smooth circular cylinder and square are studied for the purpose of verification and validation. Good agreement with reference results in the literature confirms the accuracy and efficiency of the new 2D Navier-Stokes equation solver based on the present immersed-boundary GHPC method utilizing non-uniform grids. The present Navier-Stokes equations solver uses second-order FDM for the discretization of the diffusion and advection terms, which may be replaced by other higher-order schemes to further improve the accuracy.

Passive concentration dynamics incorporated into the library IB2d, a two-dimensional implementation of the immersed boundary method

In this paper, we present an open-source software library that can be used to numerically simulate the advection and diffusion of a chemical concentration or heat density in a viscous fluid where a moving, elastic boundary drives the fluid and acts as a source or sink. The fully- coupled fluid-structure interaction problem of an elastic boundary in a viscous fluid is solved using Peskin’s immersed boundary method. The addition or removal of the concentration or heat density from the boundary is solved using an immersed boundary-like approach in which the concentration is spread from the immersed boundary to the fluid using a regularized delta function. The concentration or density over time is then described by the advection-diffusion equation and numerically solved. This functionality has been added to our software library, IB2d, which provides an easy-to-use immersed boundary method in two dimensions with full implementations in MATLAB and Python. We provide four examples that illustrate the usefulness of the method. A simple rubber band that resists stretching and absorbs and releases a chemical concentration is simulated as a first example. Complete convergence results are presented for this benchmark case. Three more biological examples are presented: (1) an oscillating row of cylinders, representative of an idealized appendage used for filter-feeding or sniffing, (2) an oscillating plate in a background flow is considered to study the case of heat dissipation in a vibrating leaf, and (3) a simplified model of a pulsing soft coral where carbon dioxide is taken up and oxygen is released as a byproduct from the moving tentacles. This method is applicable to a broad range of problems in the life sciences, including chemical sensing by antennae, heat dissipation in plants and other structures, the advection-diffusion of morphogens during development, filter-feeding by marine organisms, and the release of waste products from organisms in flows.