Numerical Investigation of the Interaction of Counterflowing Jets and Supersonic Capsule Flows

Use of counterflowing jets ejected into supersonic freestreams as a flow control concept to modify the external flowfield has gained renewed interest with regards to potential retropropulsion applications pertinent to entry, descent, and landing investigations. This study describes numerical computations of such a concept for a scaled wind-tunnel capsule model by employing the space-time conservation element solution element viscous flow solver with unstructured meshes. Both steady-state and time-accurate computations are performed for several configurations with different counterflowing jet Mach numbers. Axisymmetric computations exploring the effect of the jet flow rate and jet Mach number on the flow stability, jet interaction with the bow shock and its subsequent impact on the aerodynamic and aerothermal loads on the capsule body are carried out. Similar to previous experimental findings, both long and short penetration modes exist at a windtunnel Mach number of 3.48. It was found that both modes exhibit non-stationary behavior and the former is much more unstable than the latter. It was also found that the unstable long penetration mode only exists in a relatively small range of the jet mass flow rate. Solution-based mesh refinement procedures are used to improve solution accuracy and provide guidelines for a more effective mesh generation procedure for parametric studies. Details of the computed flowfields also serve as a means to broaden the knowledge base for future retropropulsion design studies

TIME-CONSERVATIVE FINITE-VOLUME METHOD WITH LARGE-EDDY SIMULATION FOR COMPUTATIONAL AEROACOUSTICS

This thesis presents a time-conservative finite-volume method based on a modern flow simulation technique developed by the author. Its applicability to technically relevant aeroacoustic applications is demonstrated. The time-conservative finite-volume method has unique features and advantages in comparison to traditional methods. The main objectives of this study are to develop an advanced, high-resolution, low dissipation second-order scheme and to simulate the near acoustic field with similar accuracy as higher-order (e.g., 4th-order, 6th-order, etc.) numerical schemes. Other aims are to use a large-eddy simulation (LES) technique to directly predict the near-field aerodynamic noise and to simulate the turbulent flow field with high-fidelity. A three-dimensional parallel LES solver is developed in order to investigate the near acoustic field. Several cases with wide ranges of flow regimes have been computed to validate and verify the accuracy of the method as well as to demonstrate its effectiveness. The time-conservative finite-volume method is efficient and yields high-resolution results with low dissipation similar to higher-order conventional schemes. The time-conservative finite-volume approach offers an accurate way to compute the most relevant frequencies and acoustic modes for aeroacoustic calculations. Its accuracy was checked by solving demonstrative test cases including the prediction of narrowband and broadband cavity acoustics as well as the screech tones and the broadband shock-associated noise of a planar supersonic jet. The second-order time-conservative finite-volume method can solve practically relevant aeroacoustic problems with high-fidelity which is an exception to the conventional second-order schemes commonly regarded as inadequate for computational aeroacoustic (CAA) applications

Método dos elementos de conservação espacial-temporal de alta ordem e alta resolução para a solução de problemas hiperbólicos

Orientadora : Profª. Drª. Liliana Madalena GramaniCoorientadora : Profª. Drª. Eloy KaviskiTese (doutorado) - Universidade Federal do Paraná, Setor de Tecnologia, Programa de Pós-Graduação em Métodos Numéricos em Engenharia. Defesa: Curitiba, 03/08/2017Inclui referências : p. 113-121Resumo: Esta tese aborda o desenvolvimento de esquemas numéricos explícitos por meio do método dos elementos de conservação espacial-temporal aplicados em problemas hiperbólicos. O método, desenvolvido originalmente para leis de conservação de primeira ordem no tempo, é estendido a equações com derivadas de segunda ordem temporal e aplicado à equação da onda. Para o caso da onda elástica unidimensional sob condições de contorno naturais ou essenciais, um esquema numérico com resposta analítica foi obtido. Uma classe de problemas de ondas não-lineares unidimensionais foi estudada e soluções do tipo D'Alembert foram construídas. No sentido de ampliar a estratégia ao caso bidimensional, uma formulação híbrida foi construída ao utilizar-se, conjuntamente, a Transformada de Fourier. Desenvolveu-se, também, esquemas de alta ordem para a solução numérica das equações hiperbólicas de Saint-Venant em uma e duas dimensões. A estratégia para o aumento de ordem consiste em aumentar o grau dos polinômios presentes nas funções de base, o que resultou em um esquema com precisão de terceira ordem. Os vários experimentos numéricos realizados demonstram a eficiência dos esquemas desenvolvidos, sobretudo no que tange a problemas com descontinuidades e formação de choque, como o caso não-linear. Palavras-chaves: Método de Conservação Espacial-Temporal. Equações Hiperbólicas. Esquema de Alta Ordem e Alta Resolução. Volumes de Controle.Abstract: This thesis addresses the development of explicit numerical schemes using the space-time conservation element and solution element method applied to hyperbolic problems. The method, developed for first-order conservation laws, is extended to equations with second-order temporal derivatives and applied to the wave equation. For the one-dimensional elastic wave under natural or essential boundary conditions, a numerical scheme with analytical properties was obtained. A class of one-dimensional nonlinear wave problems was studied and D'Alembert type solutions were constructed. In order to extend the strategy to the two-dimensional case, a hybrid formulation was constructed using the Fourier Transform. High-order schemes are also developed for the numerical solution of the one- and two-dimensional Saint-Venant equations. The strategy to increase order consists of considering polynomials of higher degrees in the base functions, which resulted in a third order accuracy scheme. The numerical experiments performed demonstrate the efficiency of the developed schemes, especially with regard to problems with discontinuities and shock formation, such as the nonlinear case. Key-words: Space-Time Conservation Element and Solution Element Method. Hyperbolic Equations. High Order and High Resolution Numerical Schemes. Control Volumes