English

Computational fluid dynamics (CFD) is increasingly becoming the tool of choice for researchers and engineers facing complex fluid flow problems. One area of CFD that has attracted significant attention in recent years is the development of meshless or mesh-free methods[1]. These methods have so far been used in many applications like fracture mechanics, astrophysics and fluid flow. The key advantage of meshless methods over mesh-based methods like finite volume (FV) and finite element (FE) methods is its non-requirement of pre-specified connectivity between nodes in order to derive approximation and interpolation. This leads to the ability of finite difference (FD) methods to treat irregular domains and boundaries. A direct result of this is another advantage of mesh-free methods having the adaptability for problems involving large movement or wholesale motion of boundaries or embedded bodies. In this area, it has the edge over composite or overset grid methods in being able to use only one coordinate frame.A convecting meshless scheme for boundary driven fluid flow is described. This scheme can be applied to self-propulsion problems, or, in general, flows involving motion of rigid or deformable bodies embedded within the flow.The generalized finite difference method[2] (GFD) was chosen this scheme. A meshless cloud of nodes is embedded around the body surface along with the structured Cartesian background nodes for the entire flow field. By incorporating a subdomain for each node and its neighbours, the use of Taylor series expansion enables the derivatives to be found. Two forms of incompressible momentum equations are used: the standard Eulerian form in primitive variables for the structured nodes and the Arbitrary Lagrangian-Eulerian (ALE) form for the meshless cloud of nodes. GFD with moving least squares approximation is used for spatial discretization of the convecting meshless nodes. The projection method with Crank-Nicolson discretization is used to achieve second order accurate time discretization. Following prescribed body motion or fluid structure interaction, the meshless cloud acquire new locations in the next time step and the momentum equations in ALE form can then be solved.Test cases were performed to verify code usability and method accuracy and convergence. The simulation of the decaying vortex has been a popular benchmark for the gauging of accuracy. Basically the exact solutions of the time-dependent function values are known and both residues and absolute errors were calculated. Solving using different grid sizes proved the present method to be of second order spatial accuracy. The meshless method was then tried on the driven cavity flow at Reynolds number 1000. The results were well-compared with popular benchmark results[4]. In considering the effects of implementing the convecting meshless nodes across a normal flow field, the decaying vortex was again simulated, with a moving patch of nodes within the Cartesian field. The residues were well controlled and the errors were not significantly increased. Finally, a couple of external flows cases were simulated, basically on a flow past a stationary bluff body and a flapping ellipse inside an enclosed body of fluid.Future works in the pipeline include writing a parallel code for larger scale simulation and simulating oscillating cylinders and flapping of elliptic aerofoil(s).

The conventional no-slip boundary condition does not always hold in several fluid flow applications and must be replaced with appropriate slip conditions according to the wall and fluid properties. However, not only slip boundary conditions are still a subject of discussion among fluid dynamicists, but also their numerical treatment is far from being well-developed, particularly in the context of very high-order accurate methods. The complexity of these conditions significantly increases when the boundary is not aligned with the chosen coordinate system and, even more challenging, when the fluid slips along a curved boundary. The present work proposes a simple and efficient numerical treatment of general slip boundary conditions on arbitrary curved boundaries for three-dimensional fluid flow problems governed by the incompressible Navier–Stokes equations. In that regard, two critical challenges arise: (i) achieving very high-order of convergence with arbitrary curved boundaries for the classical no-slip boundary conditions and (ii) extending the developed numerical techniques to impose general slip boundary conditions. The conventional treatment of curved boundaries relies on generating curved meshes to eliminate the geometrical mismatch between the physical and computational boundaries and achieve high-order of convergence. However, such an approach requires sophisticated meshing algorithms, cumbersome quadrature rules on curved elements, and complex non-linear transformations. In contrast, the reconstruction for off-site data (ROD) method handles arbitrary curved boundaries approximated with linear piecewise elements while employing polynomial reconstructions with specific linear constraints to fulfil the prescribed boundary conditions. For that purpose, the general slip boundary conditions are reformulated on a local orthonormal basis to allow a straightforward application of the ROD method with scalar boundary conditions. The Navier–Stokes equations are discretised with a staggered finite volume method, and the numerical fluxes are computed solely on the polygonal mesh elements. Several benchmark test cases of fluid flow problems in non-trivial three-dimensional curved domains are addressed and confirm that the proposed method effectively achieves up to the eighth-order of convergence.

Computational fluid dynamics (CFD) has been widely used to predict and understand cardiovascular flows. However, the accuracy of CFD predictions depends on faithful reconstruction of patient vascular anatomy and accurate patient-specific inlet and outlet boundary conditions. 4-Dimensional magnetic resonance imaging (4D MRI) can provide patient-specific data to obtain the required geometry and time-dependent flow boundary conditions for CFD simulations, and can further be used to validate CFD predictions. This work presents a framework to combine both spatiotemporal 4D MRI data and patient monitoring data with CFD simulation workflows. To assist practitioners, all aspects of the modeling workflow, from geometry reconstruction to results postprocessing, are illustrated and compared using three software packages (ansys, comsol, SimVascular) to predict hemodynamics in the thoracic aorta. A sensitivity analysis with respect to inlet boundary condition is presented. Results highlight the importance of 4D MRI data for improving the accuracy of flow predictions on the ascending aorta and the aortic arch. In contrast, simulation results for the descending aorta are less sensitive to the patient-specific inlet boundary conditions.

The paper focus on mathematical modelling of incompressible fluid flow interacting with vibrations of an elastic vocal fold. The flow in moving domain is modelled by the incompressible Navier-Stokes equations written in the Arbitrary Lagrangian-Eulerian (ALE) form. The channel geometry is an approximation of the human glottal region. The flow model is coupled with a simplified structure model. The problem is mathematically described and the resulting fluid-structure interaction problem is discretized by a stabilized finite element method. A strong coupling algorithm is applied for solution of the coupled fluid-structure problem. The choice of boundary conditions is discussed, particularly the choice of different artificial inlet/outlet boundary conditions is described in details. The numerical results are shown.

Multiphysics numerical modelling of backward flow forming process of AISI 5140 steel

Understanding fluid flow in fractured porous media is of great importance in the fields of civil engineering in general or in soil science particular. This study is devoted to the development and validation of a numerical tool based on the use of the finite element method. To this aim, the problem of fluid flow in fractured porous media is considered as a problem of coupling free fluid and fluid flow in porous media or coupling of the Stokes and Darcy equations. The strong formulation of the problem is constructed, highlighting the condition at the free surface between the Stokes and Darcy regions, following by the variational formulation and numerical integration using the finite element method. Besides, the analytical solutions of the problem are constructed and compared with the numerical solutions given by the finite element approach. Both local properties and macroscopic responses of the two solutions are in excellent agreement, on condition that the porous media are sufficiently discretized by a certain level of finesse. The developed finite element tool of this study could pave the way to investigate many interesting flow problems in the field of soil science.

There are numerous electromagnetic accelerator concepts which require plasma expansion through a magnetic nozzle. If the inlet flow is slower than one or all of the outgoing characteristics, namely, the Alfven, slow and fast magnetosonic speeds, then the number of inlet conditions which could be arbitrarily specified are reduced by the number of outgoing characteristics (up to three). We derive the axisymmetric compatibility equations using the method of projected characteristics for the inlet conditions in the z-plane to assure the boundary conditions being consistent with flow properties. We make simplifications to the equations assuming that the inlet Alfven speed is much faster than the sonic and slow magnetosonic speeds. We compare results for various inlet boundary conditions, including a modified Lax–Wendroff implementation of the compatibility equations, first order extrapolation and arbitrarily specifying the inlet conditions, in order to assess the stability and accuracy of various approaches.

Patient-specific fluid-structure interaction modeling of cerebral aneurysm: influence of wall compliance, tissue prestress, and blood rheology.

Very high-order accurate finite volume scheme for the steady-state incompressible Navier–Stokes equations with polygonal meshes on arbitrary curved boundaries

A computational framework for fluid–rigid body interaction: Finite element formulation and applications

The current paper presents a cold flow simulation study of a low Mach number air-air ejector with a four ring entraining diffuser that is used in a variety of applications including infrared (IR) suppression of exhaust from helicopters and fixed wing aircraft. The main objectives of this investigation were to identify key issues that must be addressed in successful CFD modelling of such devices, and recognize opportunities to improve the performance of these devices. Two-dimensional CFD simulations were carried out using commercial software, Ansys14. Studies of mesh and domain size sensitivity were made to ensure the CFD results were independent of both factors. A turbulence model independence study using k-ε, k-ω and RSM turbulence models was performed to figure out the appropriate turbulence model that produced the best agreement with the experimental data for several of ejector performance criteria. The measured flow properties in the annulus were used as input boundary conditions for the CFD simulations. However, in the comprehensive turbulence model study, the measured flow parameters at the nozzle exit were also applied as inlet boundary conditions for the CFD simulations. The measured flow velocity at the nozzle exit, at one centerline section inside the mixing tube and at the diffuser exit and the system pressure recovery were compared with the CFD predictions. The ejector pumping ratios, back pressure coefficient and diffuser gap velocities were also compared. It was found that the RANS-based CFD predictions were sensitive to the changes in the ejector domain size, mesh refinement and inlet boundary condition locations. With the annulus inlet boundary conditions, the tested turbulence models under predicted the size of the core separation downstream of the system, back pressure, pumping ratio and pressure recovery in the mixing tube and diffuser. However, the ability of the RNG turbulence model to predict the ejector performance parameters was better than that of the other turbulence models at all inlet flow conditions. Nevertheless, applying the inlet boundary conditions at the nozzle exit enhanced the capability of the RANS-based turbulence model particularly in predicting the ejector pumping ratios, pressure recovery and the size of the core separation. Finally, the acceptable agreement between the experimental data and the CFD predictions provides a valid tool to continue improving these devices using CFD techniques.

Aiming at the problem that it is difficult to model and analyze the thermal effect of large motors as a whole, a method based on fluid network decoupling is proposed to solve the global thermal effect of large motors. Taking YJKK500-4 2500-kW compact medium-sized high-voltage motor as an example, combined with the internal structure and the actual size of the motor, and using the flow-heat coordination mechanism and the fluid network, the whole internal ventilated paths of motor are divided into four equal pressure regions: end, stator-rotor, end, and internal fan according to the magnitude of pressure. The reasonable basic assumptions and boundary conditions are selected to link each region, which can avoid the problem that the inlet boundary condition is difficult to give. After that, the internally ventilated paths are modeled and analyzed, and the fluid flow and temperature in each region of the internally ventilated paths are obtained. Combined with the experimental data, the calculation results are all within the error. The rationality and correctness of the method used in the paper are confirmed, which solves the problem that the ordinary computer cannot calculate the huge model of large motor and provides a basis for the calculation of similar motor in the future.

This paper reports a follow-up feasibility study on different approaches for numerical modeling of blast loads, implemented recently in a few commercial programs based on finite element method and explicit time integration. Four approaches have been considered including: explicit blast wave representation using fluid-structure interaction (FSI) with 2D and 3D multi-material arbitrary Lagrangian-Eulerian (ALE) formulations, direct application of empirical explosive blast loads on structures, and the most recent, combined method, in which direct empirical loading is applied to a reduced ALE domain. Each of these approaches has its own strengths and weaknesses, although the last one seems to be the most universal. Based on the published experimental data, a benchmark problem was selected, which considers a pressure loading exerted by explosion of near field hemispherical charges on a rigid steel plate. The comparison is done in terms of pressure peaks (overpressure) and time histories of reflected pressure, and reflected specific impulses.

Evaluation of the influence of inlet boundary conditions on computational fluid dynamics for intracranial aneurysms: A virtual experiment

The coupling between different components of a turbomachinery is becoming more widely studied especially by use of computational fluid dynamics. Such simulations are of particular interest especially at the interface between a combustion chamber and a turbine, for which the prediction of the migration of hotspots generated in the chamber is of paramount importance for performance and life-duration issues. Despite this need for fully integrated simulations, typical turbomachinery simulations however often only consider isolated components with either time-averaged constant value, radial profile or least frequently two-dimensional maps imposed at their inlet boundaries preventing any accurate two-way coupling. The objective of this study is to investigate available solutions to perform isolated simulations while taking into account the effect of multicomponent coupling. Investigations presented in the paper focus on the full aero-thermal combustor-turbine interaction research (FACTOR) configuration. The first step of the proposed method is to record conservative variables solved by the large-eddy simulation (LES) code at the interface plane between the chamber and the turbine of a reference simulation. Then, using the spectral proper orthogonal decomposition (SPOD) method, the recorded data is analyzed and can be partially reconstructed using different numbers of frequencies. Using the partial reconstructions, it is then possible to replicate a realistic inlet boundary condition for isolated turbine simulations with both velocity and temperature fluctuations, while reducing the storage cost compared to the initial database. The integrated simulation is then compared to the isolated simulations as well as against simulations making use of averaged quantities with or without synthetic turbulence injection at their inlet. The isolated simulations for which the inlet condition is reconstructed with a large number of frequencies show very good agreement with the fully integrated simulation compared to the typical isolated simulation using average quantities at the inlet. As expected, decreasing the number of frequencies in the reconstructed signal deteriorates the accuracy of the resulting signal compared to the full recorded database. However, isolated simulations with a low number of frequencies still perform better than standard boundary conditions, especially from an aero-thermal point of view.