Session F12: Computational Fluid Dynamics: Immersed Boundary Methods (3:55pm - 4:40pm CST)

An Efficient Immersed Boundary Method and Multiphase Flow Framework for Simulating Wave Energy Converter Devices

Simulating marine engineering applications with moving bodies involve complex fluid-structure interactions (FSI). In such cases, the fictitious domain/immersed boundary methods are found to be computationally efficient than the body-conforming grid techniques. In the fictitious domain Brinkman penalization (FD/BP) technique, the fluid equations are extended into the solid domain along with an additional penalization force enforcing rigidity of the body. Two level-set functions are defined to track the solid, liquid, and gas phases. A robust and second-order accurate multiphase flow solver that preserves stability in the presence of high-density ratio flows is implemented. We demonstrate that the FD/BP technique can capture the complex wave-structure interaction (WSI) phenomena, which is not possible using linear potential flow theory when simulating wave energy converter (WEC) devices. Results include 2D and 3D simulations of an inertial sea wave energy converter (ISWEC) device. Obtained results conclude that the FD/BP technique, along with the multiphase flow framework discussed, efficiently captures the device physics. A strategy to include energy-maximizing control of WECs within the FD/BP framework is also presented.   

Flight modes and postural stability of wedge shapes

Recent experiments have shown that cones of intermediate apex angles display orientational stability with apex leading in flight. Here we show in experiments and simulations that analogous results hold in the two-dimensional setting of solid wedges or triangular shapes in planar flows at Reynolds numbers $\textrm{Re} \sim 10^2-10^4$. Slender wedges are statically unstable with apex leading and tend to flip over or tumble, and broad wedges oscillate or flutter due to dynamical instabilities, but those of apex half-angles between about $40^{\circ}$ and $55^{\circ}$ maintain stable posture during flight. The existence of these ``Goldilocks" shapes that possess the ``just right" angularity for flight stability is thus robust across dimensions. The stability is also robust to moderate changes in shape and Reynolds number.   

An immersed boundary-thin shell finite element framework for fluid-structure interaction simulation of non-linear material

A three-dimensional fluid-structure interaction (FSI) framework has been implemented for deformable tissues by coupling the sharp-interface curvilinear immersed boundary (CURVIB) incompressible Navier-Stokes flow solver with a large-deformation, rotation-free, Kirchhoff-Love thin shell finite element (FE) structure solver, which is based on Loop's subdivision surfaces. A set of Fung-elastic constitutive laws for in-plane and bending responses are implemented separately and is shown to be in good agreement with experimental results. A set of standard dynamic validation studies is performed to show the accuracy of the structure solver. The FSI solver uses a strongly-coupled approach which is stabilized using under-relaxation enhanced with Aitken acceleration technique. The coupled CURVIB-FE-FSI solver is validated by applying it to simulate an FSI problem. Finally, the capabilities of the framework is demonstrated by simulating the complex cardiovascular flow of a bio-prosthetic heart valve (BHV) and validating against experimental measurements. An efficient kinematic contact handling method is used to manage the closing phase of the leaflets.   

Closure of Distributed Element Roughness Modeling for Deterministic Roughness Morphologies Using DNS

Design for cooling effectiveness in internal flow systems relies on accurate models for dynamic losses and heat transfer. In these systems (e.g., gas turbine blades, intercoolers), thousands of individual passages of varying configuration and roughness morphology can be present, rendering resolved modeling of each passage using CFD methods impractical. Even RANS modeling requires sublayer resolution, due to the comparatively low Reynolds numbers present and the small geometric scales of the explicitly resolved deterministic roughness elements (e.g., turbulators, wavy fins, etc\textellipsis ), and this leads to mesh requirements O(10$^{\mathrm{4}}$-10$^{\mathrm{6}})$ degrees of freedom per passage. Accordingly, a volumetric roughness modeling approach, distributed element roughness modeling (DERM) is being developed to enable orders of magnitude lower computational resources in these systems. In this approach, which draws on Eulerian two-fluid modeling, and is akin to Immersed Boundary Methods, the detailed geometry of roughness elements is not resolved, but rather the morphology is represented by volume fraction and volume fraction gradient distributions. Attendant interfacial forces due to drag, turbulence dispersion and recently identified spatial dispersion forces are imparted on the flow. In this work we employ DNS modeling of a host of several different cube arrays and a classic V-shaped turbulator configuration. The DNS statistics are interpreted and applied to calibrate the DERM model for each of the morphologies studied.   

Large eddy simulation of high velocity compressible flows interacting with immersed objects

Large-eddy simulations (LES) of flows involving solid surfaces, shock waves, and turbulent flows are performed using a dynamic subgrid-scale model along with a sharp-interface immersed boundary method. The inviscid fluxes of compressible flow equations in curvilinear coordinates are discretized with a hybrid discretization comprising a fourth-order central scheme and a third-order weighted essentially non-oscillatory (WENO) scheme. The LES is validated by comparing the results for the decay of isotropic homogeneous turbulent flows with the results obtained from direct numerical simulations (DNS). Then, the method is validated against experimental measurements and shown to be second-order accurate in the presence of immersed boundaries. The numerical results capture all of shock features observed in the experiments and show great agreement with the measurements. Finally, the interaction of the shock and turbulent flow is studied by modeling transonic flow over a circular-arc bump. This work was partly supported by the National Science Foundation (NSF) CAREER Grant CBET 1453982, and the High Performance and Research Center (HPRC) of Texas A{\&}M University.   

Development of an algorithm for the fluid-structure interaction of bioinspired problems with multi-body systems

A non-monolithic algorithm for the fluid-structure interaction with multi-body systems is presented. The motivation behind is the analysis of biological motion, such as insect flight or fish swimming. For the modelling, the multi-body systems are composed by a collection of rigid bodies which are connected among them by kinematic joints which restrain certain degrees of freedom. The flow is assumed to be Newtonian, incompressible and is solved by means of direct numerical simulations, where the presence of the bodies in the flow is modelled using and Immersed boundary method. A recursive dynamic algorithm in reduced coordinates is employed to compute the dynamic equations of the multi-body systems, allowing for the computation of a large variety of different system with no code modification. The algorithm is validated against existing literature, showing very good agreement. Additionally, simulations of a flexible, self-propelled wing are presented, as an illustration of the capabilities of the algorithm. In particular, the kinematics and performance of a 2D self-propelled flexible wing are compared to those of a 3D flexible wing of aspect ratio, $AR = 0.5$.   

An explicit characteristic based immersed boundary method for compressible flows

In recent years, there has been increasing interest to develop improved models for particle-laden flows and simulate complex geometries in high-speed (compressible) flow regimes. Immersed boundary (IB) methods offer the benefits of simplicity and scalability inherent to structured grids with the flexibility to handle non-conforming geometries. While IB methods are now well established for incompressible flows, additional challenges exist for compressible flows, in particular in representing boundary conditions for scalar quantities and resolving strong discontinuities due to shocks. In this talk, the characteristic based volume penalization (CBVP) method is extended and combined with a direct forcing technique within a high-order energy stable finite difference framework for both the Navier--Stokes and Euler equations. CBVP techniques typically rely on tuning parameters that result in stiff equations that require implicit solvers. Here we propose a purely explicit CBVP approach, where the parameters are chosen based on the limits of the numerical discretization. Validation and verification are performed for one-, two-, and three-dimensional steady and unsteady flow configurations. Other complex geometries are considered to demonstrate the robust nature of the method.   

An immersed interface vortex method for internal and external 2D flows with moving boundaries

We present a novel Immersed Interface Method for 2D viscous incompressible flows. The vorticity-velocity form of the Navier-Stokes equations are discretized using second-order conservative finite differences and third-order explicit time integration. The discretization and interface treatment can handle both internal and external flows, and both stationary and moving boundaries. For external flows, the use of a vorticity-based formulation allows free-space boundary conditions while only discretizing the compact support of the vorticity field. We further show how the sharp treatment of the boundary provides a natural and accurate way to compute pressure and viscous force distributions on stationary and moving obstacles. Our method is ideal for unsteady aero- and hydrodynamic problems, and we demonstrate its utility through simulations of cylinder arrays, heaving/pitching foils, and kinematically-driven internal flows.   

A monolithic projection framework for constrained FSI problems with the immersed boundary method

Constrained fluid-structure interaction (CFSI) problems involving complex substructures and their shapes are commonly seen in daily life, e.g. a flying kite and a drifting parachute. Such a system may contain several substructures inter-linked by ropes or hinges, and may have high stiffness materials in certain parts. By treating all high stiffness constraints ideally, a monolithic projection framework for CFSI problems is proposed to solve multi-structure and multi-constraint problems. Immersed boundary method (IBM) in the continuous forcing form is used to evaluate the constraint force on the fluid-structure interface due to the no-slip condition. Besides, constraints from material properties and inter-structure dynamics are uniformly formulated, with both bilateral and unilateral types. All subsystems are assembled into a monolithic system and solved efficiently by decoupling with nested approximate LU decomposition. Error analysis based on general semi-discrete operators shows that the current framework has a second-order temporal accuracy for decomposition. Cases such as flags and parachutes are simulated and results show a nearly second-order overall temporal accuracy, along with significant efficiency improvement.   

Dimensionally-split provably stable cut-cell approach for flow calculations

Cartesian cut-cell approaches belong to a class of immersed boundary methods that allow sharp representation of solid boundaries in a fluid domain. A Cartesian discretization for the entire computational domain highly simplifies grid generation for fluid-flow simulations over complex geometries and improves computational efficiency by providing a structured framework. This talk will discuss a finite-difference cut-cell approach that, by construction, is dimensionally split and addresses the small-cell problem without compromising on global high-order accuracy. A framework to prove time-stability with strong (or exact) boundary conditions is employed to obtain boundary stencils for centered interior schemes to solve hyperbolic and parabolic systems on cut-cell grids. Characteristic boundary treatment is used to apply the developed approach to embedded boundaries in fluid-flow calculations. Various linear and non-linear numerical tests that verify the accuracy and stability of the method will be presented.   

Handling Flux Boundary Conditions in an Immersed Boundary Method

Immersed boundary (IB) or fictitious domain (FD) methods allow for efficient modeling of moving domain problems, without requiring the computational mesh to conform to the geometrically complex interfaces. The volume penalization (VP) method is one such FD approach to solve complex moving domain problems. Most of the IB/FD methods in the literature have considered Dirichlet boundary conditions on the interfaces. In this presentation, we present a flux-based VP method to impose inhomogeneous Neumann boundary conditions. Applications include flux-driven thermal convection in an irregular domain or sedimentation of particles in thermally stratified flows, among others. The proposed approach modifies the diffusion coefficient and includes an additional forcing term in the governing equations to enforce flux boundary conditions on the surface that may also be spatially varying. As such, the flux-based VP method can be easily incorporated in existing codes. We assess the accuracy of this technique using the method of manufactured solutions. Several test problems involving irregular domains are considered to assess the order of accuracy of the solution for the Poisson equation, as well as for the scalar transport equation coupled to incompressible Navier Stokes solver.   

Improving Pressure Simulations Driven by Immersed Dynamic Surfaces

Immersed boundary methods are extensively used for fluid-structure interaction problems involving large and complex deformations of the body such as a flapping fishtail, or a boat’s sail during tacking. When the body is thin and drives the flow, as in these examples, correctly capturing the unsteady pressure forces is extremely important. However, very few immersed boundary methods correctly impose the no-slip condition, leading to substantial errors in those forces. Part of the issue in the no-slip steams from the treatment of the pressure flux at the immersed boundary. We discuss the technical challenges in enforcing the correct pressure flux treatment on the immersed boundary and develop a simple 1D FSI system to illustrate these issues explicitly. We develop a method for quickly and accurately simulating pressure driven by immersed dynamic surfaces and present results for unsteady 2D and 3D test cases related to insect flight.   

Hybrid immersed boundary method for general purpose CFD simulation

We propose a novel direct forcing immersed boundary method, hybrid immersed boundary (HIB), that closely mimics conformal grid formulation. HIB is a hybrid of ghost-cell and cut-cell methods; boundary cells are split along immersed boundary (IB) in similar fashion to cut-cell method and a virtual ghost cell is created in which virtual force act to enforce desired boundary condition at the exact location of IB. HIB is interpolation free and is capable of simulating flow with complex geometries, massless IBs and high aspect ratio. It is especially attractive in flow with multiple IBs and internal flow. Benchmark results obtained from simulation of flow over massless flat plate normal to flow direction, flow over isolated cylinder and flow over a sphere are in close agreement (within 2{\%} margin) with established experimental results. HIB's prowess in handling flow with multiple immersed boundaries is tested by simulating an array of 284 cylinders evenly distributed in circular area. Capability of HIB to simulate turbulent flow with heat transfer has also been demonstrated.