Abstract: The present paper investigates the high-order spectral finite volume method with emphasis on applicability aspects for compressible flows. The intent is to improve the understanding and implementation of numerical techniques related to high-order unstructured grid schemes. In that regard, a hierarchical moment limiter and high-order mesh capability are developed for a 2-dimensional Euler spectral finite volume solver. The limiter formulation and geometry interpreter for high-order mesh generation are new contributions for the spectral finite volume method. Literature test cases are evaluated to assess the interaction of curved mesh, limiter and spatial reconstruction features of the spectral finite volume scheme. An order-of-accuracy study is presented along with steady and unsteady problems with strong shock waves and other discontinuities typical of compressible flows. Moreover, second, third and fourth-order spatial resolution analyses are explored and the spectral finite volume results are compared with those from different numerical methods.

ABSTRACT: It is performed and presented an experimental and numerical investigation over the flow patterns around the fore-body section of a microsatellite launch vehicle in development at Instituto de Aeronáutica e Espaço. The experimental investigation with a VLM-1 model in 1:50 scale is carried out at the Brazilian Pilot Transonic Wind Tunnel, located in the Aerodynamics Division of the mentioned Institute, using the classical schlieren flow visualization technique. Schlieren images are obtained for nominal Mach number varying from 0.9 to 1.01. Numerical simulation using Stanford's SU2 code is conducted together with the experimental investigation in order to improve the understanding of the complex physical phenomena associated with the experimental results of this particular regime. The combination of the 2 techniques allowed the assessment of some important aspects on the flow field around the vehicle in the conditions considered in this study, such as shock wave/boundary-layer interaction. The numerical simulation is also very important, allowing the quantification of some important parameters and confirming the shock wave formation patterns observed in the simulation when compared with the schlieren images. A good agreement regarding the position of the shock wave, when compared with the schlieren images, with a maximum error of about 6%, is observed over the VLM model.

ABSTRACT: The work is a study of conservation on linearization techniques of time-marching schemes for the unstructured finite volume Reynolds-averaged Navier-Stokes formulation. The solver used in this work calculates the numerical flux applying an upwind discretization based on the flux vector splitting scheme. This numerical treatment results in a very large sparse linear system. The direct solution of this full implicit linear system is very expensive and, in most cases, impractical. There are several numerical approaches which are commonly used by the scientific community to treat sparse linear systems, and the point-implicit integration was selected in the present case. However, numerical approaches to solve implicit linear systems can be non-conservative in time, even for formulations which are conservative by construction, as the finite volume techniques. Moreover, there are physical problems which strongly demand conservative schemes in order to achieve the correct numerical solution. The work presents results of numerical simulations to evaluate the conservation of implicit and explicit time-marching methods and discusses numerical requirements that can help avoiding such non-conservation issues.

ABSTRACT: The present work addresses a sensitivity analysis investigation of the aeroelastic stability margins for the VSB-30 sounding rocket during the atmospheric flight phase. Parametric stability analyses are performed considering variations of the inertia properties of the modular payload. Such variations can be caused by different type and/or number of experiments (payload modules). The aerodynamic model is based on a supersonic unsteady potential aerodynamic method. Freestream conditions depend on the flight speed and atmosphere. An equivalent structural dynamic model of the rocket is represented by a beam-like structure. The objective of this investigation is to establish an aeroelastic model for aeroelastic stability and response analyses, as well as a procedure for the identification of stability margins for rockets. The resulting aeroelastic model should be further used in MDO processes for the improvement of the vehicle flight performance. The results of the present effort indicate that the flutter behavior of the VSB-30 sounding rocket is sufficiently robust inside the operational envelope, even considering the environmental and loading conditions. The spinning effect, in this case, does not play a significant role, because the flutter margins remain almost unaltered with and without VSB-30 body spin.

This paper presents the effects of some convective flux computation schemes on boundary layer and shocked flow solutions. Second-order accurate centered and upwind convective flux computation schemes are discussed. The centered Jameson scheme, plus explicitly added artificial dissipation terms are considered. Three artificial dissipation models, namely a scalar and a matrix version of a switched model, and the CUSP scheme are available. Some implementation options regarding these methods are proposed and addressed in the paper. For the upwind option, the Roe flux-difference splitting scheme is used. The CUSP and Roe schemes require property reconstructions to achieve second-order accuracy in space. A multidimensional limited MUSCL interpolation method is used to perform property reconstruction. Extended multidimensional limiter formulation and implementation are here proposed and verified. Theoretical flow solutions are used in order to provide a representative testbed for the current study. It is observed that explicitly added artificial dissipation terms of the centered scheme may nonphysically modify the numerical solution, whereas upwind schemes seem to better represent the flow structure.

Abstract The work reported in the present paper was performed to honor the centennial of the flight by Alberto Santos Dumont with his 14-Bis aircraft. The paper describes results for a computational fluid dynamics (CFD) analysis of the 14-Bis aircraft aerodynamics and flight stability. The 14-Bis aircraft geometry was generated from historical sources and observations. CFD computations were performed using well-established commercial codes for calculation of the historical flight conditions. Simulations considered a Reynolds-averaged Navier-Stokes formulation, in which turbulence closure was achieved by using Menter's model. The flight conditions investigated were primarily concerned with historical observations regarding flight speeds and the need for a more powerful engine, as well as flight stability characteristics of the 14-Bis airplane, which are unknown up to the present day. The results led to qualitative agreement with historical reports, although quite interesting conclusions could be drawn with regard to the actual aerodynamic flight speeds and the aircraft stability parameters.

Abstract: Aerodynamic flow simulations over a typical sounding rocket are presented in this paper. The work is inserted in the effort of developing computational tools necessary to simulate aerodynamic flows over configurations of interest for Instituto de Aeronáutica e Espaço of Departamento de Ciência e Tecnologia Aeroespacial. Sounding rocket configurations usually require fairly large fins and, quite frequently, have more than one set of fins. In order to be able to handle such configurations, the present paper presents a novel methodology which combines both Chimera and patched multiblock grids in the discretization of the computational domain. The flows of interest are modeled using the 3-D Euler equations and the work describes the details of discretization procedure, which uses a finite difference approach for structure, body-conforming, multiblock grids. The method is used to calculate the aerodynamics of a sounding rocket vehicle. The results indicate that the present approach can be a powerful aerodynamic analysis and design tool.

The present work implements the spectral finite volume scheme in a cell centered finite volume context for unstructured meshes. The 2-D Euler equations are considered to represent the flows of interest. The spatial discretization scheme is developed to achieve high resolution and computational efficiency for flow problems governed by hyperbolic conservation laws, including flow discontinuities. Such discontinuities are mainly shock waves in the aerodynamic studies of interest in the present paper. The entire reconstruction process is described in detail for the 2nd to 4th order schemes. Roe's flux difference splitting method is used as the numerical Riemann solver. Several applications are performed in order to assess the method capability compared to data available in the literature. The results obtained with the present method are also compared to those of essentially nonoscillatory and weighted essentially non-oscillatory high-order schemes. There is a good agreement with the comparison data and efficiency improvements have been observed.

Abstract: The present work is concerned with the numerical simulation of hypersonic blunt body flows with chemical non-equilibrium. New theoretical and numerical formulations for coupling the chemical reaction to the fluid dynamics are presented and validated. The fluid dynamics is defined for a stationary unstructured mesh and the chemical reaction process is defined for "finite quantities" moving through the stationary mesh. The fluid dynamics is modeled by the Euler equations and the chemical reaction rates by the Arrhenius law. Ideal gases are considered. The thermodynamical data are based on JANNAF tables and Burcat's database. The algorithm proposed by Liou, known as AUSM+, is implemented in a cell-centered based finite volume method and in an unstructured mesh context. Multidimensional limited MUSCL interpolation method is used to perform property reconstructions and to achieve second-order accuracy in space. The minmod limiter is used. The second order accuracy, five stage, Runge-Kutta time-stepping scheme is employed to perform the time march for the fluid dynamics. The numerical code VODE, which is part of the CHEMKIN-II package, is adopted to perform the time integration for the chemical reaction equations. The freestream reacting fluid is composed of H2 and air at the stoichiometric ratio. The emphasis of the present paper is on the description of the new methodology for handling the coupling of chemical and fluid mechanic processes, and its validation by comparison with the standard time-splitting procedure. The configurations considered are the hypersonic flow over a wedge, in which the oblique detonation wave is induced by an oblique shock wave, and the hypersonic flow over a blunt body. Differences between the solutions obtained with each formulation are presented and discussed, including the effects of grid refinement in each case. The primary objective of such comparisons is the validation of the proposed methodology. Moreover, for the hypersonic flow over a blunt body, solutions obtained for two meshes are shown, compared and analyzed. The numerical solutions are also compared with experimental data.

A detailed numerical study is presented of the order of accuracy of some proposed cell centered, finite volume schemes used for the solution of the 2-D gasdynamic equations on triangular unstructured grids. The schemes studied are based on a MUSCL-type linear reconstruction of interface properties, which seeks to achieve 2nd-order accuracy in space. They are also nominally flux-vector splitting-type schemes, and the results here presented use Liou's AUSM+ algorithm. The basic aspects effecting the scheme's order of accuracy are the form in which the reconstruction process is designed and the form in which the limiting process is performed. Two basic concepts are tested with regard to the reconstruction process, namely the use of 1-D-type and gradient-based reconstruction. The limiter can also be constructed as a 1-D-type limiter or as a truly multi-dimensional limiter. The schemes are tested on a linear convection-like model equation and the numerical solutions are compared to the analytical solution, for different mesh sizes, in order to assess the scheme's order of accuracy. For comparison purposes, the results obtained with a centered scheme are also presented. Second-order accuracy is shown to be only obtained for the centered scheme. The nominally 2nd-order upwind algorithms lead to actual orders of accuracy, which vary from 0.9 to 1.5.

Abstract: A comparison of five different spatial discretization schemes is performed considering a typical high speed flow application. Flowfields are simulated using the 2-D Euler equations, discretized in a cell-centered finite volume procedure on unstructured triangular meshes. The algorithms studied include a central difference-type scheme, and 1st- and 2nd-order van Leer and Liou flux-vector splitting schemes. These methods are implemented in an efficient, edge-based, unstructured grid procedure which allows for adaptive mesh refinement based on flow property gradients. Details of the unstructured grid implementation of the methods are presented together with a discussion of the data structure and of the adaptive refinement strategy. The application of interest is the cold gas flow through a typical hypersonic inlet. Results for different entrance Mach numbers and mesh topologies are discussed in order to assess the comparative performance of the various spatial discretization schemes.

The present work is part of an effort for developing a methodology for the aeroelastic analysis of two-dimensional lifting surfaces using an unsteady, Euler-based, CFD tool for the calculation of the aerodynamic operator. The CFD tool solves the flow problem with the finite-volume method applied to an unstructured grid context. The proposed methodology is based on the determination of the aerodynamic operator with the transfer function technique, which is given, in the frequency domain, by the analysis of the system response to an exponentially-shaped pulse in the time domain. The response in the frequency domain is achieved with the Fast Fourier Transform (FFT) technique available in any mathematical manipulation tool, such as Matlab©. Some numerical experiments are performed involving unsteady subsonic and transonic flows around a flat plate and a NACA 0012 airfoil, and the results are presented as curves of generalized aerodynamic forces. The unsteady simulations start from a converged steady state solution obtained by the same CFD tool. Some unsteady validation results are compared with available data in the literature and the initial steps of the methodology are tested. The frequency domain results obtained agree very well with other numerical solutions given in the literature, which validates the present approach for the evaluation of the generalized aerodynamic forces for use in efficient, frequency domain, aeroelastic analyses.

An unstructured grid Euler solver for reactive compressible flow applications is presented. The method is implemented in a cell centered, finite volume context for unstructured triangular grids. Three different schemes for spatial discretization are implemented and analyzed. Time march is implemented in a time-split fashion with independent integrators for the flow and chemistry equations. The capability implemented is tested for inert flows in a hypersonic inlet and for inert and reactive supersonic flows over a 2-D wedge. The results of the different schemes are compared with each other and with independent calculations using a structured grid code. The strengths and the possible weaknesses of the proposed methods are discussed.