A fast immersed boundary method for external incompressible viscous flows using lattice Green's functions

A new parallel, computationally efficient immersed boundary method for solving three-dimensional, viscous, incompressible flows on unbounded domains is presented. Immersed surfaces with prescribed motions are generated using the interpolation and regularization operators obtained from the discrete delta function approach of the original (Peskin's) immersed boundary method. Unlike Peskin's method, boundary forces are regarded as Lagrange multipliers that are used to satisfy the no-slip condition. The incompressible Navier-Stokes equations are discretized on an unbounded staggered Cartesian grid and are solved in a finite number of operations using lattice Green's function techniques. These techniques are used to automatically enforce the natural free-space boundary conditions and to implement a novel block-wise adaptive grid that significantly reduces the run-time cost of solutions by limiting operations to grid cells in the immediate vicinity and near-wake region of the immersed surface. These techniques also enable the construction of practical discrete viscous integrating factors that are used in combination with specialized half-explicit Runge-Kutta schemes to accurately and efficiently solve the differential algebraic equations describing the discrete momentum equation, incompressibility constraint, and no-slip constraint. Linear systems of equations resulting from the time integration scheme are efficiently solved using an approximation-free nested projection technique. The algebraic properties of the discrete operators are used to reduce projection steps to simple discrete elliptic problems, e.g. discrete Poisson problems, that are compatible with recent parallel fast multipole methods for difference equations. Numerical experiments on low-aspect-ratio flat plates and spheres at Reynolds numbers up to 3,700 are used to verify the accuracy and physical fidelity of the formulation.Comment: 32 pages, 9 figures; preprint submitted to Journal of Computational Physic

Numerical Investigation of Second Mode Attenuation over Carbon/Carbon Surfaces on a Sharp Slender Cone

We have carried out axisymmetric numerical simulations of a spatially developing hypersonic boundary layer over a sharp 7$^{\circ{}}$-half-angle cone at $M_\infty=7.5$ inspired by the experimental investigations by Wagner (2015). Simulations are first performed with impermeable (or solid) walls with a one-time broadband pulse excitation applied upstream to determine the most convectively-amplified frequencies resulting in the range 260kHz -- 400kHz, consistent with experimental observations of second-mode instability waves. Subsequently, we introduce harmonic disturbances via continuous periodic suction and blowing at 270kHz and 350kHz. For each of these forcing frequencies complex impedance boundary conditions (IBC), modeling the acoustic response of two different carbon/carbon (C/C) ultrasonically absorptive porous surfaces, are applied at the wall. The IBCs are derived as an output of a pore-scale aeroacoustic analysis -- the inverse Helmholtz Solver (iHS) -- which is able to return the broadband real and imaginary components of the surface-averaged impedance. The introduction of the IBCs in all cases leads to a significant attenuation of the harmonically-forced second-mode wave. In particular, we observe a higher attenuation rate of the introduced waves with frequency of 350kHz in comparison with 270kHz, and, along with the iHS impedance results, we establish that the C/C surfaces absorb acoustic energy more effectively at higher frequencies.Comment: AIAA-SciTech 201

Computational methods for internal flows with emphasis on turbomachinery

Current computational methods for analyzing flows in turbomachinery and other related internal propulsion components are presented. The methods are divided into two classes. The inviscid methods deal specifically with turbomachinery applications. Viscous methods, deal with generalized duct flows as well as flows in turbomachinery passages. Inviscid methods are categorized into the potential, stream function, and Euler aproaches. Viscous methods are treated in terms of parabolic, partially parabolic, and elliptic procedures. Various grids used in association with these procedures are also discussed

Numerical techniques for computational aeroacoustics

The problem of aerodynamic noise is considered following the Computational Aeroacoustics approach which is based on direct numerical simulation of the sound field. In the region of sound generation, the unsteady airflow is computed separately from the sound using Computational Fluid Dynamics (CFD) codes. Overlapping this region and extending further away is the acoustic domain where the linearised Euler equations governing the sound propagation in moving medium are solved numerically. After considering a finite volume technique of improved accuracy, preference is given to an optimised higher order finite difference scheme which is validated against analytical solutions of the governing equations. A coupling technique of two different CFD codes with the acoustic solver is demonstrated to capture the mechanism of sound generation by vortices hitting solid objects in the flow. Sub-grid turbulence and its effect 011sound generation has not been considered in this thesis. The contribution made to the knowledge of Computational Aeroacoustics can be summarised in the following: 1) Extending the order of accuracy of the staggered leap-frog method for the linearised Euler equations in both finite volume and finite difference formulations; 2) Heuristically determined optimal coefficients for the staggered dispersion relation preserving scheme; 3) A solution procedure for the linearised Euler equations involving mirroring at solid boundaries which combines the flexibility of the finite volume method with the higher accuracy of the finite difference schemes; 4) A method for identifying the sound sources in the CFD solution at solid walls and an expansion technique for sound sources inside the flow; 5) Better understanding of the three-level structure of the motions in air: mean flow, flow perturbations, and acoustic waves. It can be used, together with detailed simulation results, in the search for ways of reducing the aerodynamic noise generated by propellers, jets, wind turbines, tunnel exits, and wind-streamed buildings