Project
Investigation of Fluid Structure Interaction (FSI) in abstracted canopies inspired by aquatic vegetation using Large Eddy Simulations
Figure 1: Visualization of an instantaneous solution, showing the streamwise velocity component
u in the center plane z = 0.5Lz, and the instantaneous shape of the canopy with each blade colored according to the vertical position y.
Figure reprinted from [1], license: Creative Commons CC BY 4.0 
Figure 2: Illustration of the three physical models investigated, showing snapshots of the numerical
solution. (a) Base configuration; (b) derived configuration with shorter blades; (c) derived
configuration with shorter, but also more densely placed blades. Unpublished, license: Creative Commons CC BY 4.0 Flows over aquatic plants have mostly been studied in experiments, often with artificial,
geometrically simple, model plants. With such experiments being tedious to set up, plant properties restricted by available materials, numerical simulations have recently gained momentum in the community. Existing studies cover almost exclusively configurations with rigid or mildly deforming canopy elements, where fluid-structure coupling is dominated by pressure drag. In contrast, the present study focuses on situations involving densely arranged, highly flexible plants, expressed by a high Cauchy number. Here drag-related friction becomes more important, and steady mechanical contact between blades is crucial. The situation is overall closer to actual seagrass meadows than in presently available studies.
Project Details
Project term
December 26, 2022–August 25, 2023
Affiliations
Technische Universität Dresden
Institute
Institute of Fluid Mechanics
Project Manager
Principal Investigator
Methods
Simulations were conducted using the multi-phase simulation code PRIME which was developed and is maintained by the work group of the reporting authors. It employs a spatially and temporally second order finite volume method solving the Navier Stokes equations for incompressible fluids. A specialized immersed boundary method (IBM) enables the coupling with solid objects or immersed surfaces. In the present project, the coupling with flexible strip-like elements (of vanishing thickness) was implemented, solving equations for the deformation of so-called Cosserat rods. This situation is numerically very challenging due to the strong coupling between the very light rods and the fluid, and necessitated a new coupling approach which improves upon existing methods for this problem. The fluid-structure coupling is numerically stable without any global iterations between the fluid part and the structure part, yielding low computational cost. A constraint-based collision model accounts for contact between rods, extending this well-established concept to deformable bodies. The resulting collision impulses account for the non-permeability of colliding objects, dissipation of energy in case of inelastic collisions, and frictional effects.
Results
Results outside report period
Simulations of an experimentally investigated reference case from the literature served as a proof of concept for the methodology employed in subsequent simulations. This case features the turbulent flow over a homogeneous canopy bed consisting of flexible blades, with flow conditions triggering an organized motion of the blades, the so-called monami phenomenon. Data analyses included the investigation of the three-dimensional nature of coherent vortex structures, with results published in [15, 10]. In preparation for greater realism, the numerical method was then extended to enable rods of non-constant widths. The flow around a single trapezoidal ribbon served as a validation case which was presented in [14, 9, 5, 4]. A case consisting of a canopy with spanwise gaps, which features hydrodynamic processes with an impact on patch growth, were reported in [11, 7]. Finally, a first set of canopies consisting of highly flexible slender rods was configured as part of the cooperation ESCaFlex. Figure 1 gives an impression of the flow which is characterized by a pronounced secondary current. The definition of a continuous hull was developed, enabling the systematic investigation of canopy movement in relation to fluid motion. First results are discussed in [6, 1, 2], but evaluations are still being carried out.
Results from report period
Additional simulations featuring wider domains were simulated in this project period, including sensitivity analyses, and the variation of different canopy properties. An illustration is given in figure 2. Characteristics of flow and canopy motion were extracted by means of time averages, including Reynolds stresses. Quadrant analyses give access to sweep and ejection events which are linked to low- and high-speed velocity streaks.
A continuous canopy envelope is constructed by projecting the Lagrangian information associated with the canopy blades onto a horizontal plane. In this framework, frequency and wave number spectra of the canopy envelope are readily computable, spatial and temporal correlations can be determined using the same tools as applied to the fluid data, and also cross-correlations between fluid motion and canopy motion are looked at.
Discussion
The investigations above follow the plan established in the ANR-DFG project ESCaFlex (ANR-16-CE92-0020, DFG grant 634058), with the unfinished high Cauchy-number case constituting the center piece of the present research project. Simulations of this case were set back by a number of unforeseen complications that necessitated, above all, a fundamental revision of the collision model. The revised model was presented in [3], and a manuscript is in preparation. In the meantime, a number of different cases at a lower Cauchy numbers were devised. With the collision model now fully functional, several production runs were devised in the past year, and are presently being completed as well as analyzed. First results suggests striking patterns in the movement of the highly flexible canopy cases investigated. Given the extraordinary flexibility of the blades, underlying processes are supposed to be different from those governing the monami phenomenon in cases with stiffer blades. A corresponding manuscript is in preparation.
Additional Project Information
DFG classification: 404-03 Fluid Mechanics
Software: GCC, PETSc library, HYPRE library, Python3, ParaView
Cluster: CLAIX