Unstructured Dynamic Meshes Research Articles

Nonlinear aerodynamic forces on thin flat plate: Numerical study

This paper first presents a numerical simulation of nonlinear aerodynamic forces on a thin flat plate through an integration of the computational fluid dynamics (CFD) method and the forced asymptotic oscillation method. The thin flat plate is forced to have either asymptotic torsional oscillation or asymptotic vertical oscillation of increasing amplitude. A multiple-domain mesh technique together with unstructured dynamic meshes is used in the CFD simulation to accommodate large amplitude oscillations of the plate. The instantaneous frequencies and amplitudes of the aerodynamic forces are then identified from the simulated asymptotic aerodynamic force time histories using the continuous wavelet transform (CWT) in terms of the CWT ridges. Extensive numerical studies are finally performed to examine the feasibility of the proposed approach. The results show that the CFD method used in this study can properly simulate nonlinear aerodynamic forces on the plate. The amplitude of the aerodynamic force depends on the amplitude of the forced oscillation and there are high-order harmonic aerodynamic forces of higher frequency than the forced oscillation frequency, both indicating the nonlinearity of aerodynamic forces. The results also show the flutter derivatives associated with self-excited aerodynamic forces depend on the amplitude of forced oscillation in addition to reduced velocity.

A parallel radial basis function interpolation method for unstructured dynamic meshes

In this paper a radial basis function (RBF) interpolation method is implemented to be applied in computational fluid dynamics (CFDs) problems with dynamic meshes. The method has been tested with two challenging examples of dynamic meshing, the deformation of a pitching airfoil and a three-dimensional movement of a sphere, both discretized over viscous grids of around 5M control volumes. The work also includes a qualitative comparison of the RBF interpolation and the classical spring analogy formulations, which asserts that the new approach is far less costly and, besides, can achieve a good performance in preserving the mesh quality. In addition, the dynamic mesh adaptation has been coupled with a CFD solver, what has been validated on a benchmark problem consisting on a duct with a moving indentation. Finally, it is analyzed the parallel performance of the algorithm for the case of the deformable sphere, pointing out some key aspects that must be considered in order to improve the parallelization.

NUMERICAL SIMULATION OF HIGH REYNOLDS NUMBER TURBULENT FLOW IN A VANE PASSAGE

The numerical simulations of two-dimensional high Reynolds number turbulent flow in a guide vane passage of a Francis hydro turbine are performed successfully by using the unstructured dynamic mesh model for moving body. The standard K – ε turbulence model is employed for the simulation of turbulence. The pressure-velocity coupling method is realized with the SIMPLEC algorithm. The temporal distributions of the pressure and turbulent viscosity in a passage were obtained in the closing of wicket gate on a platform of the software ANSYS FLUENT. The results show that the evolution of the flow field is unsteady with decrease of the geometrical opening of the gate. The details of the flow changes are obtained in the moving rigid body domain. The method can be used to simulate the high Reynolds number incompressible turbulent flow with moving boundary. The calculation provides some references for vortex-induced vibration of the structure in a complex turbulent flow.

Using the Unstructured Dynamic Mesh to Simulate Multi-Store Separating from Aircraft

Using Computational Fluid Dynamics (CFD), unsteady flow-field related to multi-store separating from aircraft was researched. The unsteady flow-field's change and multi-store's movement were interacted and interdepended. Unstructured dynamic mesh, Euler equation, 6-DOF kinematics, dynamics Equations of rigid body were solved and updated at the same physics time step with loosing coupling. AEDC wind tunnel test model is computed in this paper, the result of solution is in very good agreement with the wind tunnel test result. Last, multi-store separating from aircraft are modeled and simulated. The simulated results indicate that the movement of border upon stores has severe aerodynamic interfere action. The sequence and distance of multi-store have determinant influence for safe separation.

Numerical modeling of underwater rockfalls

A marine environment presents various settings where talus slopes are formed via gravity-driven rockfall processes similar to those existing on land. This is the case along fjords or submarine canyons, where submarine installations or natural sanctuaries, such as coral reefs, need to be protected. In submarine rockfall analysis, the effect of the ambient fluid, in addition to hydrodynamic constraints and water currents, must be considered. A finite volume model has been developed to model two-dimensional rockfall behaviour in a Newtonian fluid, such as water or air. Turbulent and incompressible flow around the moving rock is described with a pressure–velocity iterative method on a dynamic three-dimensional unstructured mesh of polyhedral cells. Pressure, shear, and turbulent forces are then applied to the moving rock. In this paper, we compare underwater rockfall behaviour with air rockfall behaviour in three different situations: free fall, bouncing on a horizontal plane, and bouncing on an inclined plane. A true-scale experiment has been conducted to validate the model. The results of various modeling suggest that, contrary to the air case, the speed of the blocks will be strongly influenced by the block density and volume.

Multiple levels of cell by cell Adaptive Mesh Refinement in the Lagrangian step of the ALE code CORVUS

A multi-level cell by cell Adaptive Mesh Refinement (AMR) hydrodynamics capability has been developed for the Lagrangian step of the 2D Arbitrary Lagrangian Eulerian (ALE) code CORVUS. Connectivity arrays are used rather than a hierarchical data structure. We solve only on the dynamic unstructured mesh rather than on every level of a refinement hierarchy. The strength, artificial viscosity, slide and programmed burn methods have been generalised to work with AMR. Results are presented for a range of Lagrangian test problems.

Runaway transient simulation of a model Kaplan turbine

The runaway transient is a typical transient process of a hydro power unit, where the rotational speed of a turbine runner rapidly increases up to the runaway speed under a working head as the guide vanes cannot be closed due to some reason at the load rejection. In the present paper, the characteristics of the runaway transient of a model Kaplan turbine having ns = 479(m-kW) is simulated by using a time-dependent CFD technique where equation of rotational motion of runner, continuity equation and unsteady RANS equations with RNG k-ϵ turbulence model are solved iteratively. In the calculation, unstructured mesh is used to the whole flow passage, which consists of several sub-domains: entrance, casing, stay vanes + guide vanes, guide section, runner and draft tube. And variable speed sliding mesh technique is used to exchange interface flow information between moving part and stationary part, and three-dimensional unstructured dynamic mesh technique is also adopted to ensure mesh quality. Two cases were treated in the simulation of runaway transient characteristics after load rejection: one is the rated operating condition as the initial condition, and the other is the condition at the maximum head. Regarding the runaway speed, the experimental speed is 1.45 times the initial speed and the calculation is 1.47 times the initial for the former case. In the latter case, the experiment and the calculation are 1.67 times and 1.69 times respectively. From these results, it is recognized that satisfactorily prediction will be possible by using the present numerical method. Further, numerical results show that the swirl in the draft-tube flow becomes stronger in the latter part of the transient process so that a vortex rope will occur in the draft tube and its precession will cause the pressure fluctuations which sometimes affect the stability of hydro power system considerably.

Scalable parallel methods for monolithic coupling in fluid–structure interaction with application to blood flow modeling

We introduce and study numerically a scalable parallel finite element solver for the simulation of blood flow in compliant arteries. The incompressible Navier–Stokes equations are used to model the fluid and coupled to an incompressible linear elastic model for the blood vessel walls. Our method features an unstructured dynamic mesh capable of modeling complicated geometries, an arbitrary Lagrangian–Eulerian framework that allows for large displacements of the moving fluid domain, monolithic coupling between the fluid and structure equations, and fully implicit time discretization. Simulations based on blood vessel geometries derived from patient-specific clinical data are performed on large supercomputers using scalable Newton–Krylov algorithms preconditioned with an overlapping restricted additive Schwarz method that preconditions the entire fluid–structure system together. The algorithm is shown to be robust and scalable for a variety of physical parameters, scaling to hundreds of processors and millions of unknowns.

Numerical Study of Turbulent Flows Over Vibrating Blades with Positive Interblade Phase Angle

AbstractIn this paper, a locally implicit scheme on unstructured dynamic meshes is presented to study transonic turbulent flows over vibrating blades with positive interblade phase angle. The unsteady Favre-averaged Navier-Stokes equations with moving domain effects and a low- Reynolds-number k-ε turbulence model are solved in the Cartesian coordinate system. To treat the viscous flux on quadrilateral-triangular meshes, the first-order derivatives of velocity components and temperature are calculated by constructing auxiliary cells and Green's theorem for surface integration is applied. The assessment of accuracy of the present scheme on quadrilateral-triangular meshes is conducted through the calculation of the turbulent flow around an NACA 0012 airfoil. Based on the comparison with the experimental data, the accuracy of the present approach is confirmed. From the distributions of magnitude of the first harmonic dynamic pressure difference coefficient which include the present solution and the related experimental and numerical results, it is found that the present solution approach is reliable and acceptable. The unsteady pressure wave, shock wave and vortex-shedding phenomena are demonstrated and discussed.

A preconditioned dual time-stepping procedure coupled with matrix-free LU-SGS scheme for unsteady low speed viscous flows with moving objects

In this paper an effective method is developed to solve unsteady low speed viscous flow problems with moving objects by using the governing equations of compressible fluids. The method is based on a dual time-stepping scheme, combined with low Mach number preconditioning and an implicit matrix-free Lower-Upper Symmetric Gauss-Seidel iteration on unstructured dynamic meshes. Because preconditioning modifies the governing equations, that induces the change of system's eigenvalues and eigenvectors, characteristic boundary conditions are also modified to suit the preconditioned characteristic system. Several test cases are simulated, including an in-line oscillating cylinder in a fluid at rest, flow over a flapping NACA0014 airfoil and low speed flow past a flapping-wing micro-air vehicle. Compared with experimental results whenever possible, the computed results indicate that this algorithm shows satisfactory improvement of solution efficiency and accuracy for low speed flow problems.

Viscous flow computations of aircraft with changing control surface deflection using unstructured dynamic meshes

AbstractA three‐dimensional unstructured dynamic mesh method for viscous flow computations is presented to simulate aircraft performance when control surface deflection is changed. The method includes an efficient surface mesh movement algorithm for unstructured hybrid meshes comprised of tetrahedra, prisms and pyramids. The method is applied to numerical simulations of the static longitudinal stability control of an experimental supersonic airplane designed at the Japan Aerospace Exploration Agency (previously known as the National Aerospace Laboratory of Japan). The deflection angles of the horizontal tail wings are changed at freestream Mach numbers of 2.0 and 0.95. The results are validated by comparison with experimental results, and the differences in the flow characteristics at the given flow conditions are estimated. Copyright © 2006 John Wiley & Sons, Ltd.

Construction of the discrete geometric conservation law for high-order time-accurate simulations on dynamic meshes

The formulation and implementation of higher-order accurate temporal schemes for dynamic unstructured mesh problems which satisfy the discrete conservation law are presented. The general approach consists of writing the spatially-discretized equations for an arbitrary-Lagrange–Eulerian system (ALE) as a non-homogeneous coupled set of ODE’s where the dependent variables consist of the product of the flow variables with the control volume. Standard application of backwards difference (BDF) and implicit Runge–Kutta (IRK) schemes to these ODE’s, when grid coordinates and velocities are known smooth functions of time, results in the design temporal accuracy of these schemes. However, in general, these schemes do not satisfy the GCL and are therefore not conservative. Using a suitable approximation of the grid velocities evaluated at the locations in time prescribed by the specific ODE time integrator, a GCL compliant scheme can be constructed which retains the design temporal accuracy of the underlying ODE time integrator. This constitutes a practical approach, since the grid velocities are seldom known as continuous functions in time. Numerical examples demonstrating design accuracy and conservation are given for one, two, and three-dimensional inviscid flow problems.

Simulation of Aircraft Response to Control Surface Deflection Using Unstructured Dynamic Grids

The computational techniques required for flight-test simulation in which the deflection angle of a tail wing is changed are discussed. To treat the computational grid for a moving control surface, an unstructured dynamic mesh method with surface-grid movement is used. This method is applied to the numerical simulation of the control-surface response for an experimental supersonic airplane at the National Aerospace Laboratory of Japan. Its high capability is demonstrated in both steady and unsteady simulations.

A parallel unstructured dynamic mesh adaptation algorithm for 3-D unsteady flows

An unstructured dynamic mesh adaptation and load balancing algorithm has been developed for the efficient simulation of three-dimensional unsteady inviscid flows on parallel machines. The numerical scheme was based on a cell-centred finite-volume method and the Roe's flux-difference splitting. Second-order accuracy was achieved in time by using an implicit Jacobi/Gauss–Seidel iteration. The resolution of time-dependent solutions was enhanced by adopting an h-refinement/coarsening algorithm. Parallelization and load balancing were concurrently achieved on the adaptive dynamic meshes for computational speed-up and efficient memory redistribution. A new tree data structure for boundary faces was developed for the continuous transfer of the communication data across the parallel subdomain boundary. The parallel efficiency was validated by applying the present method to an unsteady shock-tube problem. The flows around oscillating NACA0012 wing and F-5 wing were also calculated for the numerical verification of the present dynamic mesh adaptation and load balancing algorithm. Copyright © 2005 John Wiley & Sons, Ltd.

A Locality-conscious load-balancer based on negotiations in dynamic unstructured mesh computations

Recently hybrid/multi-level parallel programming models are gaining lots of momentum basically because they have proven to provide better scalability, speedup and utilization than any single parallel programming model alone. In such models, load balancing should not only mean balancing the computational loads (as it has always been perceived), but should also mean balancing I/O imbalance as well as synchronization imbalance. In this paper, we propose a broader generic application/language/model independent multi-agent framework for dynamic load balancing. It takes most of the load-balancing burden away from programmers. It is not a library but a runtime support system that is not hardwired to the parallel applications. The framework is intended to handle varying levels of load changes in computations, I/O and/or synchronization throughout the application run and it is an open-architecture that currently supports four multi-level parallel programming models. It has a clean interface to the application, runs in parallel and provides additional functionality such as determination of when to balance load and provide interface to end users. The proposed open-architecture multi-agent load-balancing capability currently makes use of a leading geometric partitioner engine (Chaco) at runtime. A mesh solver may initially create hundreds of lightweight threads, each handling a small submesh by calling Chaco partitioning engine in a pre-processing stage. This partitioner engine might be called again by these light-weight threads if a divide-and-conquer process is deemed necessary when the sub-domain (submesh) served by this thread grows out beyond certain threshold limits and thus creates an imbalance. In the proposed framework, the multi-agent is a set of SMP-based load balancers (agents) that do not have to share any data structure with the parallel application threads. They just monitor and collect system and application data frequently from the outside of the multi-threaded parallel application solver and send adjustments and negotiation plans to the SMP-load balancers and the application threads whenever a need for load balancing arises. The proposed framework has been deployed in four hybrid/multi-level parallel programming models and its capabilities of issuing corrective actions against emerging imbalances were tested in the context of an adaptive mesh refinement application. Experimental results show that the framework is effective in monitoring, tuning and rebalancing emerging computational, I/O and synchronization sources of load imbalance.

A Robust Method for Unstructured Volume/Surface Mesh Movement

In this paper, a simple and robust method of unstructured dynamic mesh with surface mesh movement method for unstructured triangle/tetrahedral meshes is proposed. The method is developed to avoid the generation of squashed invalid elements by considering each elemental shape. With several three-dimensional applications, it is demonstrated that the present method significantly improves robustness for problems concerning large body motion without much penalty in CPU time. The use of the present method for mesh movements on curved surfaces is also discussed. Its capability is demonstrated for the surface mesh movement in the tail-fuselage juncture region of an airplane.

고속 병렬처리 기법을 이용한 전기체 항공기 형상의 천음속/초음속 비선형 공탄성 해석

A nonlinear aeroelastic analysis system in transonic and supersonic flows has been developed using high speed parallel processing technique on the network based PC-clustered machines. This paper includes the coupling of advanced numerical techniques such as computational structural dynamics (CSD), finite element method (FEM) and computational fluid dynamics (CFD). The unsteady Euler solver on dynamic unstructured meshes is employed and coupled with computational aeroelastic solvers. Thus it can give very accurate engineering data in the structural and aeroelastic design of flight vehicles. To show the great potential of useful application, transonic and supersonic flutter analyses have been conducted for a complete aircraft model under developing in Korea.

Time-accurate Navier–Stokes simulation of vortex convection using an unstructured dynamic mesh procedure

A two-dimensional Navier–Stokes flow solver is developed for the simulation of unsteady flows on unstructured adaptive meshes. The solver is based on a second-order accurate implicit time integration using a point Gauss–Seidel relaxation scheme and a dual time-step subiteration. A vertex-centered, finite-volume discretization is used in conjunction with Roe’s flux-difference splitting. The Spalart–Allmaras one equation model is employed for the simulation of turbulence. An unsteady solution-adaptive dynamic mesh scheme is used by adding and deleting mesh points to take account of spatial and temporal variations of the flowfield. Unsteady viscous flow for a traveling vortex in a free stream is simulated to validate the accuracy of the dynamic mesh adaptation procedure. Flow around a circular cylinder and two blade–vortex interaction problems are investigated for demonstration of the present method. Computed results show good agreement with existing experimental and computational results. It was found that unsteady time-accurate viscous flows can be accurately simulated using the present unstructured dynamic mesh adaptation procedure.

Numerical Simulation of Two-Dimensional Blade-Vortex Interactions Using Unstructured Adaptive Meshes

Atwo-dimensionalEulere owsolver hasbeen developedforthesimulationofunsteady,blade ‐vortexinteraction problems on unstructured meshes. The Euler solver is based on a second-order-accurate implicit time integration using a point Gauss ‐Seidel relaxation scheme and a dual time-step subiteration. A vertex-centered, e nite volume discretizationisusedinconjunctionwiththeRoe’ se ux-differencesplitting.Anunsteadysolution-adaptivedynamic mesh schemeis used by adding and deleting mesh pointsat every adaptation step to takeaccountofnot only spatial butalsooftemporalvariationsofthee owe eld.Unsteadye owaroundaharmonicallyoscillatingairfoilandtraveling vortex in a freestream were simulated to validate the accuracy of the dynamic mesh adaptation procedure. Three blade‐vortex interaction problems, two at transonic freestream speeds and one with vortex ‐airfoil collision, were investigated. Computedresultsshowgood agreementswith existingexperimentalandcomputationalresultswithin the accuracy of the present inviscid solver. It is found that the evolution of vorticies and propagation of acoustic waves can be accurately simulated using the present unstructured dynamic mesh adaptation procedure.

A three-dimensional torsional spring analogy method for unstructured dynamic meshes

We present a three-dimensional spring analogy method for updating the position of unstructured dynamic meshes that features torsional springs for controlling the arbitrary motion of the grid points. We show that these torsional springs can be designed to prohibit the interpenetration of neighboring tetrahedra, and therefore to provide the method of spring analogy with the robustness needed for enlarging its range of applications. We illustrate the proposed spring analogy method with the solution of three-dimensional flow problems with complex moving boundaries, and where the unstructured meshes undergo significant deformations. We highlight the advantages of this method with respect to robustness and mesh quality, and address its computational performance.