Curvilinear Immersed Boundary Research Articles

Numerical Simulations of the NREL Phase VI Wind Turbine with Low-Amplitude Sinusoidal Pitch

Currently, most wind turbine performance analyses and simulations are performed assuming constant pitch and yaw angles during each rotation. Nevertheless, induced vibration or rotor imbalance can affect the pitch or yaw angle within each rotation. In this study, the effects of low-amplitude sinusoidal pitch angle oscillations of the blade on the performance of a wind turbine was investigated numerically by comparing it against the baseline (without pitch variations). Large eddy simulations were performed in which the motion of blades was handled by the curvilinear immersed boundary (CURVIB) method. The grid resolution was increased near the moving immersed boundaries using dynamic overset grids to resolve rotating blades. It was found that low-amplitude (up to 3 degrees) sinusoidal oscillations in the pitch angle negligibly affected the mean torque but increased its fluctuations and created distinct features in the wake of the turbine. In fact, the turbine’s mean torque at wind speed of 15 m/s decreases from 1245 N.m to 1223 N.m, while its fluctuation (standard deviation) increases from 2.85 N.m to 7.94 N.m, with a dynamic pitch of 0.5 degrees and frequency of 3.6 Hz.

The Effects of Implantation Orientation of a Bileaflet Mechanical Heart Valve in an Anatomic Left Ventricle-Aorta Configuration.

We have performed three-dimensional high-resolution numerical simulations of a bi-leaflet mechanical heart valve implanted at different orientations in an anatomic left ventricle-aorta obtained from magnetic resonance imaging of a volunteer. The thoroughly validated overset curvilinear-immersed boundary fluid-structure interaction flow solver is used in which the aorta and left ventricle (LV) are discretized with boundary-conforming and nonconforming curvilinear grids, respectively. The motion of the left ventricle wall is prescribed based on a lumped parameter model while the motion of the leaflets is calculated using a strongly coupled fluid-structure interaction algorithm enhanced with Aitken convergence technique. We carried out simulations for three valve orientations, which differ from each other by 45 deg, and compared the leaflet motion and flow field for multiple cycles. Our results show reproducible and relatively symmetrical opening for all valve orientations. The presence of small-scale vortical structures after peak systole causes significant cycle-to-cycle variations in valve kinematics during the closing phase for all valve orientations. Furthermore, our results show that valve orientation does not have a significant effect on the distribution of viscous shear stress in the ascending aorta. Additionally, two different mathematical activation models including linear level of activation and Soares model are used to quantify the platelet activation in the ascending aorta. The results show that the valve orientation does not significantly affect (less than 8%) the total platelet activation in the ascending aorta.

On the capability of the curvilinear immersed boundary method in predicting near-wall turbulence of turbulent channel flows

The immersed boundary method has been widely used for simulating flows over complex geometries. However, its accuracy in predicting the statistics of near-wall turbulence has not been fully tested. In this work, we evaluate the capability of the curvilinear immersed boundary (CURVIB) method in predicting near-wall velocity and pressure fluctuations in turbulent channel flows. Simulation results show that quantities including the time-averaged streamwise velocity, the rms (root-mean-square) of velocity fluctuations, the rms of vorticity fluctuations, the shear stresses, and the correlation coefficients of u′ and v′ computed from the CURVIB simulations are in good agreement with those from the body-fitted simulations. More importantly, it is found that the time-averaged pressure, the rms and wavenumber-frequency spectra of pressure fluctuations computed using the CURVIB method agree well with the body-fitted results.

The influence of inertia on the rheology of a periodic suspension of neutrally buoyant rigid ellipsoids

We investigate the rheological properties of a suspension of neutrally buoyant rigid ellipsoids by fluid–structure interaction simulations of a particle in a periodic domain under simple shear using the curvilinear immersed-boundary (CURVIB) method along with a quaternion–angular velocity technique to calculate the dynamics of the particle’s motion. We calculate all the different terms of particle stress for the first time for non-spherical particles, i.e. in addition to the stresslet, we calculate the acceleration and Reynolds stress, which are typically ignored in previous similar works. Furthermore, we derive analytical expressions for all these terms to verify the numerical results and deduce the effect of inertia by comparing our numerical results with the analytical solution. The effect of particle Reynolds number ($\mathit{Re}$), volume fraction (${\it\phi}$), and the shape of particles has been studied on all mechanisms of stress generation, the intrinsic viscosity, and normal stress differences of the suspension for the range$0.008\leqslant {\it\phi}\leqslant 0.112$and$0.01\leqslant \mathit{Re}\leqslant 10.0$. We found that inertia increases the shear and the second normal difference of the stresslet (dominant term of the particle stress), and decreases the first normal difference that is generated due to the strain field. The contribution of acceleration stress to the total stress is found to be important in the second normal stress difference, with a cycle-average comparable to the stresslet component. We also discovered that the contribution of Reynolds stress in the first normal stress difference becomes important even when inertia is as low as$\mathit{Re}\sim O(0.1)$, and its value can be even greater than the stresslet when inertia increases, i.e. Reynolds stresses cannot be ignored for non-spherical particles. For concentrations in the range from dilute to semi-dilute, the effect of inertia on the intrinsic viscosity of a suspension is found to be comparable to the volume fraction. Furthermore, our calculations show that for a dilute concentration and the low-inertia regime ($\mathit{Re}<1.0$), the intrinsic viscosity of a suspension consisting of ellipsoids with an aspect ratio of five can be 20 % higher than its Stokesian analytical value.

Large-Eddy Simulation of Three-Dimensional Turbulent Free Surface Flow Past a Complex Stream Restoration Structure

AbstractLarge-eddy simulation (LES) of a three-dimensional, turbulent free surface flow past a stream restoration structure with arbitrarily complex geometries is presented. The three-dimensional, incompressible, spatially filtered Navier-Stokes and continuity equations are solved in generalized curvilinear coordinates. For the solution of mixed air-water flows, the curvilinear immersed boundary (CURVIB)–level set method developed previously is used and extended to carry out LES. Complex solid geometries are handled by the sharp-interface CURVIB method, and the subgrid scale stress terms arising from the spatial filtering of the Navier-Stokes equations are closed by the dynamic Smagorinsky model. To demonstrate the potential of the CURVIB–LES–level set model for simulating real-life, turbulent free surface flows involving arbitrarily complex geometries, LES is carried out for the flow past a complex rock structure that is fully submerged in water in a laboratory flume. The simulations show that the method...

Flow structure interaction around an axial-flow hydrokinetic turbine: Experiments and CFD simulations

We carry out large-eddy simulation of turbulent flow past a complete hydrokinetic turbine mounted on the bed of a straight rectangular open channel. The complex turbine geometry, including the rotor and all stationary components, is handled by employing the curvilinear immersed boundary (CURVIB) method [1], and velocity boundary conditions near all solid surfaces are reconstructed using a wall model based on solving the simplified boundary layer equations [2]. In this study we attempt to directly resolve flow-blade interactions without introducing turbine parameterization methods. The computed wake profiles of velocities and turbulent stresses agree well with the experimentally measured values.

Numerical simulation of large dunes in meandering streams and rivers with in-stream rock structures

The evolution and migration of large dunes in a realistic intermediate-size experimental stream, the Saint Anthony Falls Laboratory (SAFL) Outdoor StreamLab (OSL), and two large-scale meandering rivers with in–stream rock structures are studied numerically using the SAFL Virtual StreamLab hydro-morphodynamic (VSL3D) model. Due to the challenges arising from mesh quality and large disparity in time-scales, coupled morpho- and hydro-dynamics simulations of bed forms has, for the most part, been restricted to sand wave amplitudes of few centimeters. In this work, we overcome such difficulties by employing the immersed boundary approach and a dual time–stepping technique of the VSL3D model [63]. The VSL3D employs the curvilinear immersed boundary (CURVIB) method along with a suspended sediment load module and is capable of simulating turbulent stratified flows coupled with bed morphodynamic evolution in realistic riverine environments with arbitrarily complex hydraulic structures. Turbulence is handled either via large-eddy simulation (LES) with the dynamic Smagorinski subgrid scale model or unsteady Reynolds-averaged Navier Stokes (URANS) equations closed with the k-ω turbulence model. Simulations in the intermediate-scale OSL channel, in which we also collected experimental morphodynamic data, show that LES can capture the evolution and migration of bed forms with characteristics that are in good agreement with experimental measurements. The URANS model, however, fails to excite the bed instability in the OSL channel but captures realistic dune evolution in the two large-scale meandering rivers. This finding is especially important as it demonstrates the potential of the VSL3D model as a powerful tool for simulating morphodynamic evolution under prototype conditions. To our knowledge, our work is the first attempt to simulate large-scale bed forms in waterways with an order of magnitude disparity in spatial scales, from the ∼2.7m wide OSL channel to the 27m wide rivers. Accordingly, the height of the simulated dunes ranges from ∼0.2m to 2.0m and the wavelength ranges from ∼0.1m to 50m for the OSL and large-scale rivers, respectively. For all cases the statistical properties of the simulated bed forms are shown to agree well with those of bed forms observed in nature.

Level set immersed boundary method for coupled simulation of air/water interaction with complex floating structures

We propose a new computational approach for simulating the coupled interaction between air–water flows and arbitrarily complex floating rigid bodies. The numerical method integrates the fluid–structure interaction (FSI) curvilinear immersed boundary (CURVIB) method of Borazjani et al. (2008) [21] with a level set approach for simulating free surface flows in arbitrarily complex domains. We show that when applying the CURVIB method to simulate two-phase flow FSI problems the approach used to calculate the force imparted on the body is critical for determining the overall accuracy of the method. We develop and demonstrate the accuracy of a new approach for calculating the force, namely the pressure projection boundary condition (PPBC), which is based on projecting the pressure on the surface of the body using the momentum equation along the local normal to the body direction. Extensive numerical tests show that the new approach greatly improves the ability of the method to correctly predict the dynamics of the floating structure motion. To demonstrate the predictive capabilities of the method and its ability to simulate non-linear free surface phenomena, such as breaking waves, we apply it to various two- and three-dimensional problems involving complex rigid bodies interacting with a free surface both with prescribed body motion and coupled FSI. We show that for all cases the proposed method yields results in very good accuracy with benchmark numerical data and available experiments. The simulations also reveal the onset of dynamically rich, energetic coherent structures in the air phase induced by the waves generated as the rigid body interacts with the free surface.

Coupled fluid-structure interaction simulation of floating offshore wind turbines and waves: a large eddy simulation approach

We develop a computational framework for simulating the coupled interaction of complex floating structures with large-scale ocean waves and atmospheric turbulent winds. The near-field approach features a partitioned fluid-structure interaction model (FSI) combining the curvilinear immersed boundary (CURVIB) method of Borazjani and Sotiropoulos (J. Comput. Phys. 2008) and the two-phase flow level set formulation of Kang and Sotiropoulos (Adv. in Water Res. 2012) and is capable of solving complex free-surface flows interacting non-linearly with complex real life floating structures. The near-field solver is coupled with a large-scale wave and wind model based on the two-fluid approach of Yang and Shen (J. Comput. Phys. 2011) which integrates a viscous Navier-Stokes solver with undulatory boundaries for the motion of the air and an efficient potential-flow based wave solver. The large-scale turbulent wind is incorporated from the far-field solver to the near-field solver by feeding into the latter inlet boundary conditions. The wave field is incorporated to the near-field solver by using the pressure-forcing method of Guo and Shen (J. Comput. Phys. 2009) which has been appropriately adapted to the level set method. The algorithm for coupling the two codes has been validated for a variety of wave cases including a broadband spectrum showing excellent agreement when compared to theoretical results. Finally, the capabilities of the numerical framework are demonstrated by carrying out large eddy simulation (LES) of a floating wind turbine interacting with realistic ocean wind and wave conditions.

Simulation-Based Approach for Stream Restoration Structure Design: Model Development and Validation

We develop, validate, and demonstrate the potential of Virtual StreamLab (VSL3D), a novel three-dimensional hydromorphodynamics computational model capable of simulating turbulent flow and sediment transport in natural waterways with embedded and arbitrarily complex hydraulic structures under live-bed conditions. The numerical model is based on the curvilinear immersed boundary (CURVIB) approach and can solve the unsteady Reynolds-averaged Navier-Stokes (URANS) equations closed with the k−ω turbulence model in arbitrarily complex waterways with mobile sediment beds. Bed material transport is simulated by solving the nonequilibrium Exner equation for the bed surface elevation coupled with a transport equation for suspended load. Field-scale measurements obtained from experiments carried out in the St. Anthony Falls Laboratory Outdoor StreamLab are employed to validate the predictive capabilities of the numerical model. The VSL3D is used to develop a virtual testing environment of unprecedented resolution and physical realism for designing and optimizing the arrangements and installation of stream restoration rock structures. To our knowledge, the present work is the first systematic attempt to employ unsteady, three-dimensional, hydro-morphodynamics numerical modeling coupled with high-performance computing to develop an engineering framework for designing hydraulic structures for stream restoration applications.

A parallel overset-curvilinear-immersed boundary framework for simulating complex 3D incompressible flows

We develop an overset-curvilinear immersed boundary (overset-CURVIB) method in a general non-inertial frame of reference to simulate a wide range of challenging biological flow problems. The method incorporates overset-curvilinear grids to efficiently handle multi-connected geometries and increase the resolution locally near immersed boundaries. Complex bodies undergoing arbitrarily large deformations may be embedded within the overset-curvilinear background grid and treated as sharp interfaces using the curvilinear immersed boundary (CURVIB) method (Ge and Sotiropoulos, J Comput Phys, 2007). The incompressible flow equations are formulated in a general non-inertial frame of reference to enhance the overall versatility and efficiency of the numerical approach. Efficient search algorithms to identify areas requiring blanking, donor cells, and interpolation coefficients for constructing the boundary conditions at grid interfaces of the overset grid are developed and implemented using efficient parallel computing communication strategies to transfer information among sub-domains. The governing equations are discretized using a second-order accurate finite-volume approach and integrated in time via an efficient fractional-step method. Various strategies for ensuring globally conservative interpolation at grid interfaces suitable for incompressible flow fractional step methods are implemented and evaluated. The method is verified and validated against experimental data, and its capabilities are demonstrated by simulating the flow past multiple aquatic swimmers and the systolic flow in an anatomic left ventricle with a mechanical heart valve implanted in the aortic position.

Computational and experimental investigation of scour past laboratory models of stream restoration rock structures

Local scour of the streambed around three models of stream restoration rock structures, including a rock vane, a cross vane, and a J-hook vane, is investigated via laboratory experiments and numerical simulations. In the experimental study, a physical model of each rock structure is constructed via an assembly of rocks and installed in a straight mobile sand bed flume. Continuous bed topography measurements provide insight into the time evolution of the scour patterns downstream of the structures and yield comprehensive data sets for validating the numerical simulations in terms of scour patterns, maximum scour depths, and bar migration dynamics. The numerical simulations are carried out using the coupled, hydro-morphodynamic Curvilinear Immersed Boundary (CURVIB) method of Khosronejad et al. (2011) [17]. The mobile channel bed and the individual rocks comprising a stream restoration structure are discretized with an unstructured triangular mesh and treated as sharp-interface immersed boundaries embedded in the background curvilinear mesh used to discretize the flow domain. For each case, simulations are carried out solving both the unsteady Reynolds-averaged Navier–Stokes (URANS) equations closed with the k–ω model and filtered Large-Eddy Simulation (LES) equations closed with the dynamic Smagorinski subgrid scale model. Both the URANS and LES models yield flow and scour patterns in reasonable agreement with the measurements with the LES results being consistently in better overall agreement with the measurements. To our knowledge, the present study is the first attempt to simulate local scour patterns around realistic model of stream restoration rock structures by taking into account and directly modeling their arbitrarily complex geometrical features.

Fluid–structure interaction of an aortic heart valve prosthesis driven by an animated anatomic left ventricle

We develop a novel large-scale kinematic model for animating the left ventricle (LV) wall and use this model to drive the fluid–structure interaction (FSI) between the ensuing blood flow and a mechanical heart valve prosthesis implanted in the aortic position of an anatomic LV/aorta configuration. The kinematic model is of lumped type and employs a cell-based, FitzHugh–Nagumo framework to simulate the motion of the LV wall in response to an excitation wavefront propagating along the heart wall. The emerging large-scale LV wall motion exhibits complex contractile mechanisms that include contraction (twist) and expansion (untwist). The kinematic model is shown to yield global LV motion parameters that are well within the physiologic range throughout the cardiac cycle. The FSI between the leaflets of the mechanical heart valve and the blood flow driven by the dynamic LV wall motion and mitral inflow is simulated using the curvilinear immersed boundary (CURVIB) method (Ge and Sotiropoulos, 2007; Borazjani et al., 2008) [1,2] implemented in conjunction with a domain decomposition approach. The computed results show that the simulated flow patterns are in good qualitative agreement with in vivo observations. The simulations also reveal complex kinematics of the valve leaflets, thus, underscoring the need for patient-specific simulations of heart valve prosthesis and other cardiac devices.

Numerical modeling of 3D turbulent free surface flow in natural waterways

We develop a numerical model capable of simulating three-dimensional, turbulent free surface flows in natural waterways. Free surface motion is captured by coupling the two-phase level set method and the sharp-interface curvilinear immersed boundary (CURVIB) method of Kang et al. [1]. The model solves the three-dimensional, incompressible, unsteady Reynolds-averaged Navier–Stokes (RANS) and continuity equations in generalized curvilinear coordinates using a fractional step method extended to handle multiphase flows. Turbulence is modeled by a two-equation RANS model implemented in the context of the CURVIB method. The accuracy of the level set method is verified by applying it to simulate two- and three-dimensional sloshing problems, and the potential of the model for simulating real life, turbulent free surface flows is demonstrated by applying it to carry out RANS simulation of flow past rock structures in a laboratory flume and flow in a field scale meandering channel. The simulations show that the method is able to accurately predict water surface elevation over complex hydraulic structures and bathymetry, and capture the transition between subcritical and supercritical flows without any special treatment.

Numerical simulation of 3D flow past a real-life marine hydrokinetic turbine

We simulate three-dimensional, turbulent flow past an axial-flow marine hydrokinetic (MHK) turbine mounted on the bed of a rectangular open channel by adapting a computational framework developed for carrying out high-resolution large-eddy simulation (LES) in arbitrarily complex domains involving moving or stationary boundaries. The complex turbine geometry, including the rotor and all stationary components, is handled by employing the curvilinear immersed boundary (CURVIB) method [1,2]. Velocity boundary conditions near all solid surfaces are reconstructed using a wall model based on solving the simplified boundary layer equations [2]. To demonstrate the capabilities of the model we apply it to simulate the flow past a Gen4 axial flow MHK turbine developed by Verdant Power for the Roosevelt Island Tidal Energy (RITE) project in the East River in New York City, USA. We carry out systematic grid refinement studies, using grids with up to 185 million nodes, for only the turbine rotor placed in an infinite free stream to show that the computed torque converges to a grid insensitive value, which is in good agreement with field measurements. We also carry out LES for the complete turbine configuration, including the pylon, nacelle and rotor, mounted on the bed of a straight rectangular open channel. The computed results illustrate the complexity of the flow and show that the power output of the complete turbine is primarily dependent on the rotor geometry and tip speed ratio, and is not affected by the stationary components of the turbine and the presence of the channel bed. The complete turbine simulation also reveals that the downstream wake of the turbine consists of three main regions: (1) the outer layer with the spiral blade tip vortices rotating in the same direction as the blades; (2) the counter-rotating inner layer surrounded by the spiral tip vortices; and (3) the core layer co-rotating with respect to the tip vortices. This study is the first to report the three-dimensional wake structure of MHK turbines.

The effect of implantation orientation of a bileaflet mechanical heart valve on kinematics and hemodynamics in an anatomic aorta.

We carry out three-dimensional high-resolution numerical simulations of a bileaflet mechanical heart valve under physiologic pulsatile flow conditions implanted at different orientations in an anatomic aorta obtained from magnetic resonance imaging (MRI) of a volunteer. We use the extensively validated for heart valve flow curvilinear-immersed boundary (CURVIB) fluid-structure interaction (FSI) solver in which the empty aorta is discretized with a curvilinear, aorta-conforming grid while the valve is handled as an immersed boundary. The motion of the valve leaflets are calculated through a strongly coupled FSI algorithm implemented in conjunction with the Aitken convergence acceleration technique. We perform simulations for three valve orientations, which differ from each other by 45 deg and compare the results in terms of leaflet motion and flow field. We show that the valve implanted symmetrically relative to the symmetry plane of the ascending aorta curvature exhibits the smallest overall asymmetry in the motion of its two leaflets and lowest rebound during closure. Consequently, we hypothesize that this orientation is beneficial to reduce the chance of intermittent regurgitation. Furthermore, we find that the valve orientation does not significantly affect the shear stress distribution in the aortic lumen, which is in agreement with previous studies.

High-resolution numerical simulation of turbulence in natural waterways

We develop an efficient and versatile numerical model for carrying out high-resolution simulations of turbulent flows in natural meandering streams with arbitrarily complex bathymetry. The numerical model solves the 3D, unsteady, incompressible Navier–Stokes and continuity equations in generalized curvilinear coordinates. The method can handle the arbitrary geometrical complexity of natural streams using the sharp-interface curvilinear immersed boundary (CURVIB) method of Ge and Sotiropoulos (2007) [1]. The governing equations are discretized with three-point, central, second-order accurate finite-difference formulas and integrated in time using an efficient, second-order accurate fractional step method. To enable efficient simulations on grids with tens of millions of grid nodes in long and shallow domains typical of natural streams, the algebraic multigrid (AMG) method is used to solve the Poisson equation for the pressure coupled with a matrix-free Krylov solver for the momentum equations. Depending on the desired level of resolution and available computational resources, the numerical model can either simulate, via direct numerical simulation (DNS), large-eddy simulation (LES), or unsteady Reynolds-averaged Navier–Stokes (URANS) modeling. The potential of the model as a powerful tool for simulating energetic coherent structures in turbulent flows in natural river reaches is demonstrated by applying it to carry out LES and URANS in a 50-m long natural meandering stream at resolution sufficiently fine to capture vortex shedding from centimeter-scale roughness elements on the bed. The accuracy of the simulations is demonstrated by comparisons with experimental data and the relative performance of the LES and URANS models is also discussed.