Pressure Bifurcation Phenomenon on Supersonic Blowing Trailing Edges

Turbine blades operating in transonic-supersonic regime develop a complex shock wave system at the trailing edge, a phenomenon that leads to unfavorable pressure perturbations downstream and can interact with other turbine stages. Understanding the fluid behavior of the area adjacent to the trailing edge is essential in order to determine the parameters that have influence on these pressure fluctuations. Colder flow, bled from the high-pressure compressor, is often purged at the trailing edge to cool the thin blade edges, affecting the flow behavior and modulating the intensity and angle of the shock waves system. However, this purge flow can sometimes generate non-symmetrical configurations due to a pressure difference that is provoked by the injected flow. In this work, a combination of RANS simulations and global stability analysis is employed to explain the physical reasons of this flow bifurcation. Analyzing the features that naturally appear in the flow and become dominant for some value of the parameters involved in the problem, an anti-symmetrical global mode, related to the sudden geometrical expansion of the trailing edge slot, is identified as the main mechanism that forces the changes in the flow topology.Comment: Submitted to AIAA Journa

Comparison of Mesh Adaptation Using the Adjoint Methodology and Truncation Error Estimates

Mesh adaptation based on error estimation has become a key technique to improve th eaccuracy o fcomputational-fluid-dynamics computations. The adjoint-based approach for error estimation is one of the most promising techniques for computational-fluid-dynamics applications. Nevertheless, the level of implementation of this technique in the aeronautical industrial environment is still low because it is a computationally expensive method. In the present investigation, a new mesh refinement method based on estimation of truncation error is presented in the context of finite-volume discretization. The estimation method uses auxiliary coarser meshes to estimate the local truncation error, which can be used for driving an adaptation algorithm. The method is demonstrated in the context of two-dimensional NACA0012 and three-dimensional ONERA M6 wing inviscid flows, and the results are compared against the adjoint-based approach and physical sensors based on features of the flow field

Adaptation strategies for high order discontinuous Galerkin methods based on Tau-estimation

In this paper three p-adaptation strategies based on the minimization of the truncation error are presented for high order discontinuous Galerkin methods. The truncation error is approximated by means of a ? -estimation procedure and enables the identification of mesh regions that require adaptation. Three adaptation strategies are developed and termed a posteriori, quasi-a priori and quasi-a priori corrected. All strategies require fine solutions, which are obtained by enriching the polynomial order, but while the former needs time converged solutions, the last two rely on non-converged solutions, which lead to faster computations. In addition, the high order method permits the spatial decoupling for the estimated errors and enables anisotropic p-adaptation. These strategies are verified and compared in terms of accuracy and computational cost for the Euler and the compressible Navier?Stokes equations. It is shown that the two quasi- a priori methods achieve a significant reduction in computational cost when compared to a uniform polynomial enrichment. Namely, for a viscous boundary layer flow, we obtain a speedup of 6.6 and 7.6 for the quasi-a priori and quasi-a priori corrected approaches, respectively

Quasi-a priori truncation error estimation in the DGSEM

In this paper we show how to accurately perform a quasi-a priori estimation of the truncation error of steady-state solutions computed by a discontinuous Galerkin spectral element method. We estimate the spatial truncation error using the ?-estimation procedure. While most works in the literature rely on fully time-converged solutions on grids with different spacing to perform the estimation, we use non time-converged solutions on one grid with different polynomial orders. The quasi-a priori approach estimates the error while the residual of the time-iterative method is not negligible. Furthermore, the method permits one to decouple the surface and the volume contributions of the truncation error, and provides information about the anisotropy of the solution as well as its rate of convergence in polynomial order. First, we focus on the analysis of one dimensional scalar conservation laws to examine the accuracy of the estimate. Then, we extend the analysis to two dimensional problems. We demonstrate that this quasi-a priori approach yields a spectrally accurate estimate of the truncation error

h-Adaptive finite element method: extension of the isotropic error density recovery remeshing strategy of quadratic order

Orientador: Prof. Dr. Jucélio Tomás PereiraDissertação (mestrado) - Universidade Federal do Paraná, Setor de Tecnologia, Programa de Pós-Graduação em Engenharia Mecânica. Defesa : Curitiba, 05/07/2018Inclui referências: p.86-90Área de concentração: Mecânica dos Sólidos e VibraçõesResumo: O Método de Elementos Finitos (MEF) é uma técnica para resolver numericamente problemas físicos comumente utilizada na engenheria. Um fator importante na obtenção de uma solução precisa e eficiente decorre da utilização adequada da malha de discretização. Tipicamente, técnicas h-adaptativas são empregadas para projeção de uma malha ótima, onde o erro estimado em cada elemento é distribuído e minimizado de acordo com um critério de malha ótima. Neste contexto, o presente trabalho estende e avalia o método de refino hadaptativo denominado de Recuperação da Densidade do Erro Isotrópica (IEDR) para elementos triangulares quadráticos. Inicialmente desenvolvida para elementos lineares, esta técnica baseia-se na recuperação de uma função densidade do erro em energia em conjunto com a solução de um problema de otimização que busca o tamanho do novo elemento. Dessa maneira, a metodologia IEDR aborda os erros provenientes do MEF de maneira que contenha informações locais com maior abrangência, já que, nesta metodologia, uma função densidade do erro é recuperada. Os parâmetros de qualidade de malha, obtidos através desta técnica, são comparados à tradicionais técnicas de projeto de malha denominada de Chp e à técnica Li- Bettess (LB). A estimativa dos erros de discretização é realizada através do estimador de erro a posteriori baseado em recuperação, onde os gradientes recuperados são obtidos pelo método Superconvergente de Recuperação de Padrões (Superconvergent Patch Recovery - SPR). A implementação computacional é elaborada no software Matlab®, sendo a geração de malha realizada pelo gerador Bidimensional Anisotropic Mesh Generator (BAMG). Resultados numéricos demonstram que o processo h-adaptativo baseado na técnica IEDR obtém malhas convergentes para problemas com e sem singularidade, as quais apresentam, em geral, vantagens em relação ao número de graus de liberdade, à convergência e aos parâmetros de malha em comparação à tradicional técnica Chp e vantagens comparada à técnica LB para elementos quadráticos. Palavras-chave: Elemento Triangular de Deformações Lineares. h-adaptividade. Método dos Elementos Finitos. Estimadores de erro a posteriori. Recuperação da Densidade do Erro Isotrópica.Abstract: The finite element method (FEM) is a technique used to numerically solve physics problems which is often used in engineering. One factor in obtaining a solution that has acceptable accuracy is using adequate mesh discretization. Typically, h-adaptive techniques are used to determine new element sizes based on errors distributed among each element following an optimum mesh criterion. In this context, the current work proposes to extend and analyze the Isotropic Error Density Recovery (IEDR) h-refinement method for quadratic triangular finite elements. Initially developed for linear triangular finite elements, the extended technique is based on the recovery of an error density function, such that an optimization technique is used to search for the new element sizes. Hence, the IEDR technique utilizes more information of the local errors to design element sizes due to the recovery of an element error density function. The h-adaptive finite element method process based on the IEDR technique is compared to the traditionally used Chp and Li-Bettess mesh design techniques found in the literature. The discretization error estimates are achieved via a recovery based a posteriori error estimator, whereas the recovered gradients are obtained using the Superconvergent Patch Recovery Method. The algorithm is implemented using Matlab®, while the mesh generation is done by the Bidimensional Anisotropic Mesh Generator (BAMG). Results show, overall, that the meshes designed through the proposed methodology obtain superior mesh quality parameters, less degrees of freedom and better convergence in comparison with the traditional Chp remeshing methodology and advantages compared to the Li-Bettess element size estimation technique for quadratic elements. Keywords: Linear Strain Triangle. h-adaptativity. Finite Element Method. a posteriori Error Estimates. Isotropic Error Density Recovery