A.H. van Zuijlen

Higher-order time integration through smooth mesh deformation for 3D fluid-structure interaction simulations

In this paper, we present a higher-order accurate in time, partitioned integration scheme (IMEX) for fluid-structure interaction. The scheme is based on a combination of an implicit, L-stable, multi-stage Runge-Kutta scheme and an explicit Runge-Kutta scheme. Fluid and structure dynamics are integrated using the implicit scheme and only the pressure loads acting on the structure are integrated explicitly. For an academic problem we show that mesh optimization functions, which are often necessary in standard mesh deformation algorithms, can have a detrimental effect on the temporal order and accuracy. We use a radial basis function (RBF) interpolation with a thin plate spline to create a smooth displacement field for the whole fluid domain, which does not affect the order of the IMEX time integration scheme. For reasonable accuracies, the IMEX schemes outperform a second-order staggered scheme by a factor of 2-3. As an example for a three-dimensional, real-world problem, a simulation of a transonic wing flutter case, the AGARD 445.6 wing, is performed. For this test case, a clear third-order time accuracy is observed for IMEX3.

COMPARISON OF THE CONSERVATIVE AND A CONSISTENT APPROACH FOR THE COUPLING OF NON-MATCHING MESHES

In fluid-structure interaction simulations the meshes at the fluid-structure interface usually do not match, because of the different mesh requirements for the flow and structure. The exchange of data over the discrete interface becomes then far from trivial. In this paper we investigate the difference in accuracy and efficiency between a conservative and a consistent coupling approach. This is done for an analytical test problem as well as a quasi-1D FSI problem, for different coupling methods found in literature. It is found that when the coupling method is based on a weak formulation of the coupling conditions the conservative approach is the best choice. For other coupling methods the consistent approach provides the best accuracy and efficiency, because the conservative approach results in unphysical oscillations in the pressure received by the structure and is therefore not consistent.

Adaptive radial basis function mesh deformation using data reduction

Radial Basis Function (RBF) mesh deformation is one of the most robust mesh deformation methods available. Using the greedy (data reduction) method in combination with an explicit boundary correction, results in an efficient method as shown in literature. However, to ensure the method remains robust, two issues are addressed: 1) how to ensure that the set of control points remains an accurate representation of the geometry in time and 2) how to use/automate the explicit boundary correction, while ensuring a high mesh quality. In this paper, we propose an adaptive RBF mesh deformation method, which ensures the set of control points always represents the geometry/displacement up to a certain (user-specified) criteria, by keeping track of the boundary error throughout the simulation and re-selecting when needed. Opposed to the unit displacement and prescribed displacement selection methods, the adaptive method is more robust, user-independent and efficient, for the cases considered. Secondly, the analysis of a single high aspect ratio cell is used to formulate an equation for the correction radius needed, depending on the characteristics of the correction function used, maximum aspect ratio, minimum first cell height and boundary error. Based on the analysis two new radial basis correction functions are derived and proposed. This proposed automated procedure is verified while varying the correction function, Reynolds number (and thus first cell height and aspect ratio) and boundary error. Finally, the parallel efficiency is studied for the two adaptive methods, unit displacement and prescribed displacement for both the CPU as well as the memory formulation with a 2D oscillating and translating airfoil with oscillating flap, a 3D flexible locally deforming tube and deforming wind turbine blade. Generally, the memory formulation requires less work (due to the large amount of work required for evaluating RBFs), but the parallel efficiency reduces due to the limited bandwidth available between CPU and memory. In terms of parallel efficiency/scaling the different studied methods perform similarly, with the greedy algorithm being the bottleneck. In terms of absolute computational work the adaptive methods are better for the cases studied due to their more efficient selection of the control points. By automating most of the RBF mesh deformation, a robust, efficient and almost user-independent mesh deformation method is presented.

Analysis and application of high order implicit Runge–Kutta schemes for unsteady conjugate heat transfer: A strongly-coupled approach

Abstract Thermal interaction of fluids and solids, or conjugate heat transfer (CHT), is encountered in many engineering applications. Since time-accurate computations of unsteady CHT can be computationally demanding, we consider the use of high order implicit time integration schemes which have the potential to be more efficient relative to the commonly used second order implicit schemes. We present a strongly-coupled solution algorithm where the high order L-stable explicit first-stage singly diagonally implicit Runge–Kutta (ESDIRK) schemes are used to advance the solution in time within each separate fluid and solid subdomains. Furthermore, the stability and rate of convergence of performing (Gauss–Seidel) subiterations at each stage of the ESDIRK schemes are analyzed. The results from solving a numerical example (an unsteady conjugate natural convection in an enclosure) show good agreement with the performed analytical stability analysis. In addition, the (computational) work-(temporal) precision character of several schemes in solving a strongly coupled CHT problem is compared over a range of accuracy requirements. From the efficiency investigation, it is observed that performing subiterations with the strongly-coupled ESDIRK algorithm is more efficient than lowering time-step size using a high order loosely-coupled IMEX algorithm. In addition, by using the ESDIRK schemes, gain in computational efficiency relative to Crank–Nicolson is observed for time-accurate solutions (a factor of 1.4 using the fourth order ESDIRK). The computational gain is higher for smaller tolerances.

Experimental benchmark and code validation for airfoils equipped with passive vortex generators

Experimental results and complimentary computations for airfoils with vortex generators are compared in this paper, as part of an effort within the AVATAR project to develop tools for wind turbine blade control devices. Measurements from two airfoils equipped with passive vortex generators, a 30% thick DU97W300 and an 18% thick NTUA T18 have been used for benchmarking several simulation tools. These tools span low-to-high complexity, ranging from engineering-level integral boundary layer tools to fully-resolved computational fluid dynamics codes. Results indicate that with appropriate calibration, engineering-type tools can capture the effects of vortex generators and outperform more complex tools. Fully resolved CFD comes at a much higher computational cost and does not necessarily capture the increased lift due to the VGs. However, in lieu of the limited experimental data available for calibration, high fidelity tools are still required for assessing the effect of vortex generators on airfoil performance.

Radial Basis Functions for Interface Interpolation and Mesh Deformation

Many engineering applications involve fluid-structure interaction (FSI) phenomena. For instance light-weight airplanes, long span suspension bridges and modern wind turbines are susceptible to dynamic instability due to aeroelastic effects. FSI simulations are crucial for an efficient and safe design. Computers and numerical algorithms have significantly advanced over the last decade, such that the simulation of these problems has become feasible.

Active flap control on an aeroelastic wind turbine airfoil in gust conditions using both a CFD and an engineering model

In the past year, smart rotor technology has been studied significantly as solution to the ever growing turbines. Aeroservoelastic tools are used to asses and predict the behavior of rotors using trailing edge devices like flaps. In this paper an unsteady aerodynamic model (Beddoes-Leishman type) and an CFD model (URANS) are used to analyze the aeroservoelastic response of a 2D three degree of freedom rigid body wind turbine airfoil with a deforming trailing edge flap encountering deterministic gusts. Both uncontrolled and controlled simulations are used to asses the differences between the two models for 2D aerservoelastic simulations. Results show an increase in the difference between models for the y component if the deforming trailing edge flap is used as control device. Observed flap deflections are significantly larger in the URANS model in certain cases, while the same controller is used. The pitch angle and moment shows large differences in the uncontrolled case, which become smaller, but remain significant when the controller is applied. Both models show similar reductions in vertical displacement, with a penalty of a significant increase in pitch angle deflections.

Multi-Level Accelerated Sub-Iterations for Fluid-Structure Interaction

Computational fluid-structure interaction is most commonly performed using a partitioned approach. For strongly coupled problems sub-iterations are required, increasing computational time as flow and structure have to be resolved multiple times every time step. Many sub-iteration techniques exist that improve robustness and convergence, although still flow and structure problems have to be solved a number of times every time step. In this paper we apply a multilevel acceleration technique, which is based on the presumed existing multigrid solver for the flow domain, to a two-dimensional strongly coupled laminar and turbulent problem and investigate the combination of multilevel acceleration with the Aitken underrelaxtion technique. It is found that the value for the under-relaxation parameter is not significantly different when performing sub-iterations purely on the coarse level or purely on the fine level. Therefore coarse and fine level sub-iterations are used alternately, where it is found that performing 3 or 4 coarse level sub-iterations followed by 1 fine level sub-iteration resulted in the highest gain in efficiency. Although the total number of sub-iterations increases slightly by 30%, the number of fine grid iterations can be decreased by as much as 65–70%.

Acoustic simulation of a patient's obstructed airway

This research focuses on the numerical simulation of stridor; a high pitched, abnormal noise, resulting from turbulent airflow and vibrating tissue through a partially obstructed airway. Characteristics of stridor noise are used by medical doctors as indication for location and size of the obstruction. The relation between type of stridor and the various diseases associated with airway obstruction is unclear; therefore, simply listening to stridor is an unreliable diagnostic tool. The overall aim of the study is to better understand the relationship between characteristics of stridor noise and localization and size of the obstruction. Acoustic analysis of stridor may then in future simplify the diagnostic process, and reduce the need for more invasive procedures such as laryngoscopy under general anesthesia. In this paper, the feasibility of a coupled flow, acoustic and structural model is investigated to predict the noise generated by the obstruction as well as the propagation of the noise through the airways, taking into account a one-way coupled fluid, structure, and acoustic interaction components. The flow and acoustic solver are validated on a diaphragm and a simplified airway model. A realistic airway model of a patient suffering from a subglottic stenosis, derived from a real computed tomography scan, is further analyzed. Near the mouth, the broadband noise levels at higher frequencies increased with approximately 15–20 dB comparing the stridorous model with the healthy model, indicating stridorous sound.

Comparison of CFD simulations to non-rotating MEXICO blades experiment in the LTT wind tunnel of TUDelft

In this paper, three dimensional flow over non-rotating MEXICO blades is simulated by CFD methods. The numerical results are compared with the latest MEXICO wind turbine blades measurements obtained in the low speed low turbulence (LTT) wind tunnel of Delft University of Technology. This study aims to validate CFD codes by using these experimental data measured in well controlled conditions. In order to avoid use of wind tunnel corrections, both the blades and the wind tunnel test section are modelled in the simulations. The ability of Menters k-w shear stress transport (SST) turbulence model is investigated at both attached flow and massively separated flow cases. Steady state Reynolds averaged Navier Stokes (RANS) equations are solved in these computations. The pressure distribution at three measured sections are compared under the conditions of different in flow velocities and a range of angles of attack. The comparison shows that at attached flow condition, good agreement can be obtained for all three airfoil sections. Even with massively separated flow, still fairly good pressure distribution comparison can be found for the DU and NACA airfoil sections, although the RIS¬ section shows poor comparison. At the near stall case, considerable deviations exists on the forward half part of the upper surface for all three sections.