Cartesian Mesh Linearized Euler Equations Solver for Aeroacoustic Problems around Full Aircraft

The linearized Euler equations (LEEs) solver for aeroacoustic problems has been developed on block-structured Cartesian mesh to address complex geometry. Taking advantage of the benefits of Cartesian mesh, we employ high-order schemes for spatial derivatives and for time integration. On the other hand, the difficulty of accommodating curved wall boundaries is addressed by the immersed boundary method. The resulting LEEs solver is robust to complex geometry and numerically efficient in a parallel environment. The accuracy and effectiveness of the present solver are validated by one-dimensional and three-dimensional test cases. Acoustic scattering around a sphere and noise propagation from the JT15D nacelle are computed. The results show good agreement with analytical, computational, and experimental results. Finally, noise propagation around fuselage-wing-nacelle configurations is computed as a practical example. The results show that the sound pressure level below the over-the-wing nacelle (OWN) configuration is much lower than that of the conventional DLR-F6 aircraft configuration due to the shielding effect of the OWN configuration.

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A DISSIPATION-FREE TIME-DOMAIN DISCONTINUOUS GALERKIN METHOD APPLIED TO THREE-DIMENSIONAL LINEARIZED EULER EQUATIONS AROUND A STEADY-STATE NON-UNIFORM INVISCID FLOW

Journal of Computational Acoustics ◽

10.1142/s0218396x0600313x ◽

2006 ◽

Vol 14 (04) ◽

pp. 445-467 ◽

Cited By ~ 6

Author(s):

MARC BERNACKI ◽

SERGE PIPERNO

Keyword(s):

Steady State ◽

Euler Equations ◽

Discontinuous Galerkin ◽

Time Domain ◽

Balance Equation ◽

Message Passing ◽

Parallel Implementation ◽

Three Dimensional ◽

General Context ◽

Linearized Euler Equations

We present in this paper a time-domain discontinuous Galerkin dissipation-free method for the transient solution of the three-dimensional linearized Euler equations around a steady-state solution. In the general context of a nonuniform supporting flow, we prove, using the well-known symmetrization of Euler equations, that some aeroacoustic energy satisfies a balance equation with source term at the continuous level, and that our numerical framework satisfies an equivalent balance equation at the discrete level and is genuinely dissipation-free. In the case of ℙ1 Lagrange basis functions and tetrahedral unstructured meshes, a parallel implementation of the method has been developed, based on message passing and mesh partitioning. Three-dimensional numerical results confirm the theoretical properties of the method. They include test-cases where Kelvin–Helmholtz instabilities appear.

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Application of Combination of Local Domain Free Discretization and Immersed Boundary Method (LDFD-IBM) to Numerical Simulation of 3D Flows Over a Circular Cylinder

Volume 2: CFD and VIV ◽

10.1115/omae2014-23725 ◽

2014 ◽

Author(s):

Yanling Wu ◽

Chang Shu ◽

Johan Gullman-Strand

Keyword(s):

Circular Cylinder ◽

Immersed Boundary Method ◽

Adaptive Mesh Refinement ◽

Solid Wall ◽

Three Dimensional ◽

Immersed Boundary ◽

Local Domain ◽

Cartesian Mesh ◽

Boundary Method ◽

Dimensional Version

In this paper, the recent developed Local Domain Free Discretization method combined with Immersed Boundary Method (called LDFD-IBM) is extended from two-dimensional version to three-dimensional version. LDFD-IBM is a new member in the family of Cartesian mesh methods. The advantages of LDFD-IBM over other Cartesian mesh solvers includes: no cutting cell, easy to adaptive mesh refinement, easy to implement for moving boundary problems, truly second order accuracy over whole domain, no flow penetration into the solid wall. LDFD-IBM three-dimensional solver is then used to simulate three-dimensional flow past a circular cylinder. Both oblique mode and parallel mode of vortex shedding of the cylinder in three-dimensional configuration are reproduced according to different end-conditions. Oblique shedding is one of the important three-dimensional features that could influence the amplitude, frequency and phase of the flow-induced forces.

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Mathematical and Numerical Modeling of Turbulent Flows

Anais da Academia Brasileira de Ciências ◽

10.1590/0001-3765201520140510 ◽

2015 ◽

Vol 87 (2) ◽

pp. 1195-1232 ◽

Cited By ~ 5

Author(s):

João M. Vedovoto ◽

Ricardo Serfaty ◽

Aristeu Da Silveira Neto

Keyword(s):

Turbulent Flows ◽

Complex Geometry ◽

Time Integration ◽

Immersed Boundary ◽

Integration Scheme ◽

Computational Framework ◽

Wide Range ◽

Time Integration Scheme ◽

Sphere Covering ◽

Predictor Corrector

The present work is devoted to the development and implementation of a computational framework to perform numerical simulations of low Mach number turbulent flows over complex geometries. The algorithm under consideration is based on a classical predictor-corrector time integration scheme that employs a projection method for the momentum equations. The domain decomposition strategy is adopted for distributed computing, displaying very satisfactory levels of speed-up and efficiency. The Immersed Boundary Methodology is used to characterize the presence of a complex geometry. Such method demands two separate grids: An Eulerian, where the transport equations are solved with a Finite Volume, second order discretization and a Lagrangian domain, represented by a non-structured shell grid representing the immersed geometry. The in-house code developed was fully verified by the Method of Manufactured Solu- tions, in both Eulerian and Lagrangian domains. The capabilities of the resulting computational framework are illustrated on four distinct cases: a turbulent jet, the Poiseuille flow, as a matter of validation of the implemented Immersed Boundary methodology, the flow over a sphere covering a wide range of Reynolds numbers, and finally, with the intention of demonstrating the applicability of Large Eddy Simulations - LES - in an industrial problem, the turbulent flow inside an industrial fan.

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A Study of Three-Dimensional Acoustic Scattering by Arbitrary Distribution Multibodies Using Extended Immersed Boundary Method

Journal of Vibration and Acoustics ◽

10.1115/1.4026672 ◽

2014 ◽

Vol 136 (3) ◽

Cited By ~ 4

Author(s):

Yongsong Jiang ◽

Xiaoyu Wang ◽

Xiaodong Jing ◽

Xiaofeng Sun

Keyword(s):

Boundary Condition ◽

Computational Model ◽

Acoustic Field ◽

Three Dimensional ◽

Acoustic Scattering ◽

Impedance Boundary Condition ◽

Immersed Boundary ◽

Complex Geometries ◽

Impedance Boundary ◽

Wall Boundary Conditions

A three-dimensional computational model for acoustic scattering with complex geometries is presented, which employs the immersed boundary technique to deal with the effect of both hard and soft wall boundary conditions on the acoustic fields. In this numerical model, the acoustic field is solved on uniform Cartesian grids, together with simple triangle meshes to partition the immersed body surface. A direct force at the Lagrangian points is calculated from an influence matrix system, and then spreads to the neighboring Cartesian grid points to make the acoustic field satisfy the required boundary condition. This method applies a uniform stencil on the whole domain except at the computational boundary, which has the benefit of low dispersion and dissipation errors of the used scheme. The method has been used to simulate two benchmark problems to validate its effectiveness and good agreements with the analytical solutions are achieved. No matter how complex the geometries are, single body or multibodies, complex geometries do not pose any difficulty in this model. Furthermore, a simple implementation of time-domain impedance boundary condition is reported and demonstrates the versatility of the computational model.

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Preconditioned gridless methods for solving three-dimensional Euler equations at low Mach numbers

International Journal of Modeling Simulation and Scientific Computing ◽

10.1142/s1793962320500555 ◽

2020 ◽

pp. 2050055

Author(s):

Cheng Cao ◽

Hongquan Chen ◽

Jiale Zhang

Keyword(s):

Euler Equations ◽

Incompressible Flows ◽

Time Derivative ◽

Time Integration ◽

Three Dimensional ◽

Numerical Results ◽

Computational Domain ◽

Flow Simulations ◽

Pressure Distributions ◽

Mach Numbers

In this paper, preconditioned gridless methods are developed for solving the three-dimensional (3D) Euler equations at low Mach numbers. The preconditioned system is obtained by multiplying a preconditioning matrix of the type of Weiss and Smith to the time derivative of the 3D Euler equations, which are discretized under the clouds of points distributed in the computational domain by using a gridless technique. The implementations of the preconditioned gridless methods are mainly based on the frame of the traditional gridless method without preconditioning, which may fail to have convergence for flow simulations at low Mach numbers, therefore the modifications corresponding to the affected terms of preconditioning are mainly addressed in the paper. An explicit four-stage Runge–Kutta scheme is first applied for time integration, and the lower-upper symmetric Gauss-Seidel (LU-SGS) algorithm is then introduced to form the implicit counterpart to have the further speed up of the convergence. Both the resulting explicit and implicit preconditioned gridless methods are validated by simulating flows over two academic bodies like sphere or hemispherical headform, and transonic and nearly incompressible flows over one aerodynamic ONERA M6 wing. The gridless clouds of both regular and irregular points are used in the simulations, which demonstrates the ability of the method presented for coping with flows over complicated aerodynamic geometries. Numerical results of surface pressure distributions agree well with available experimental data or simulated solutions in the literature. The numerical results also show that the preconditioned gridless methods presented still functions for compressible transonic flow simulations and additionally, for nearly incompressible flow simulations at low Mach numbers as well. The convergence of the implicit preconditioned gridless method, as expected, is much faster than its explicit counterpart.

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Towards a Parallel Implementation of an Immersed Boundary Method on Non-Uniform Cartesian Mesh Coupled With a Fluid Structure Interaction Model

Volume 1A, Symposia: Advances in Fluids Engineering Education; Turbomachinery Flow Predictions and Optimization; Applications in CFD; Bio-Inspired Fluid Mechanics; Droplet-Surface Interactions; CFD Verification and Validation; Development and Applications of Immersed Boundary Methods; DNS, LES, and Hybrid RANS/LES Methods ◽

10.1115/fedsm2014-22085 ◽

2014 ◽

Author(s):

Z. Wei ◽

Z. C. Zheng

Keyword(s):

Immersed Boundary Method ◽

Parallel Implementation ◽

Fluid Structure Interaction ◽

Three Dimensional ◽

Interaction Model ◽

Immersed Boundary ◽

Fluid Structure ◽

Structure Interaction ◽

Cartesian Mesh ◽

Boundary Method

The immersed boundary methods are well known as an efficient flow solver for engineering problems involving fluid structure interactions. However, in order to obtain better results, higher resolutions near the immersed boundary points are desired. Non-uniform Cartesian mesh can easily fulfill this task without introducing a dramatic increase on the cost of computation and coding. In the current paper, an immersed boundary method with non-uniform Cartesian mesh is demonstrated. The Poisson problem is solved with assistance of a scientific parallel computational library PETSc. The code is validated with a three-dimensional flow over a stationary sphere. Then, a fluid-structure interaction model is coupled and validated with two-dimensional vortex induced vibration problems. Comparisons with previous studies are presented. The ultimate goal is to couple the fluid-structure interaction model with the three-dimensional immersed boundary method.

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