Numerical considerations in spectral multidomain methods for BiGlobal instability analysis of open cavity configurations

A novel approach for the solution of the viscous incompresible and/or compressible BiGlobal eigenvalue problems (EVP) in complex open cavity domains is discussed. The algorithm is based on spectral multidomain spatial discretization, decomposing space into rectangular subdomains which are resolved by spectral collocation based on Chebyshev polynomials. The eigenvalue problem is solved by Krylov subspace iteration. Here particular emphasis is placed on aspects of the parallel developments that have been necessary, on account of the high computing demands placed on the solver, as ever more complex “T-store” configurations are addressed

Análisis del proceso de descarga de fluidos sometidos a altas presiones y temperaturas

En esta Tesis Doctoral se ha estudiado el proceso de descarga de fluidos sometidos a altas presiones y temperaturas. El fluido se encuentra confinado en un depósito o vasija herméticamente cerrado, y descarga a una presión exterior a través de un tubo o tobera. Este problema presenta una gran utilidad en problemas de pérdida de refrigerante dentro del campo de seguridad nuclear. Uno de los aspectos importantes que se presentan en un problema de este tipo, constituye la estimación del valor del flujo másico de salida. Debido a la existencia de un proceso de cambio de fase durante la despresu-rización, la teoría de fluidos monofásicos no es aplicable. El primer problema que surge consiste en definir el modelo matemático adecuado, dado que las ecuaciones que rigen el comportamiento de un fluido bifásico no están aún bien definidas. Se aplican diferentes modelos dependiendo de los regímenes fluidos que pueden aparecer, todos ellos función de la cantidad de vapor y líquido presentes en la mezcla. En la presente Tesis se han elegido dos de ellos: el modelo homogéneo, el cual considera una mezcla uniforme y en equilibrio de líquido y vapor, y el modelo EVUT (igual velocidad pero distinta temperatura entre las fases), que intenta conservar la simplicidad del modelo homogéneo al tiempo que incorpora los fenómenos de no-equilibrio que aparecen durante el proceso de cambio de fase. El primero de ellos es útil debido a su simplicidad y a que los resultados que se obtienen de él son cualitativa y en muchas ocasiones cuantitativamente muy buenos. Por otra parte el modelo EVUT utiliza teoría de nucleación para resolver los problemas de no-equilibrio, lo que permitirá explicar muchos de los fenómenos inherentes al cambio de fase, así como modificar las teorías de flujo crítico sin el coste excesivo de cálculo de otros modelos más complejos (modelo de flujos separados). Ambos modelos son aplicados al desarrollo de un problema de descarga de un fluido a través de un tubo o tobera, obteniendo como principal resultado el valor del flujo másico de salida, así como, en el modelo EVUT, la estimación de la metaesta-bilidad alcanzable por el líquido. Por ultimo, con objeto de comprobar el rango de validez de los modelos, se realiza una comparación con experimentos. Se elige para ello los Test de Marviken, realizados en el contexto de seguridad nuclear y que constituyen una referencia básica para trabajos en temas de flujos críticos en dos fases

Computational Fluid Dynamics Expert System using Artificial Neural Networks

The design of a modern aircraft is based on three pillars: theoretical results, experimental test and computational simulations. As a results of this, Computational Fluid Dynamic (CFD) solvers are widely used in the aeronautical field. These solvers require the correct selection of many parameters in order to obtain successful results. Besides, the computational time spent in the simulation depends on the proper choice of these parameters. In this paper we create an expert system capable of making an accurate prediction of the number of iterations and time required for the convergence of a computational fluid dynamic (CFD) solver. Artificial neural network (ANN) has been used to design the expert system. It is shown that the developed expert system is capable of making an accurate prediction the number of iterations and time required for the convergence of a CFD solver

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

The estimation of truncation error by tau-estimation revisited

The aim of this paper was to accurately estimate the local truncation error of partial differential equations, that are numerically solved using a finite difference or finite volume approach on structured and unstructured meshes. In this work, we approximated the local truncation error using the @t-estimation procedure, which aims to compare the residuals on a sequence of grids with different spacing. First, we focused the analysis on one-dimensional scalar linear and non-linear test cases to examine the accuracy of the estimation of the truncation error for both finite difference and finite volume approaches on different grid topologies. Then, we extended the analysis to two-dimensional problems: first on linear and non-linear scalar equations and finally on the Euler equations. We demonstrated that this approach yields a highly accurate estimation of the truncation error if some conditions are fulfilled. These conditions are related to the accuracy of the restriction operators, the choice of the boundary conditions, the distortion of the grids and the magnitude of the iteration error

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

An interpolation tool for aerodynamic mesh deformation problems based on octree decomposition

Desarrollo de algoritmo de interpolación basado en descomposición octree y funciones radiales de soporte compacto para movimiento de mallas en problemas aerolástico

Unsteady residual distribution schemes for transition prediction

In this work, the unsteady simulation of the Navier–Stokes equations is carried out by using a Residual Distribution Schemes (RDS) methodology. This algorithm has a compact stencil (cell-based computations) and uses a finite element like method to compute the residual over the cell. The RDS method has been successfully proven in steady Navier–Stokes computation but its application to fully unsteady configurations is still not closed, because some of the properties of the steady counterpart can be lost. Here, we proposed a numerical solution for unsteady problems that is fully compatible with the original approach. In order to check the method, we chose a very demanding test case, namely the numerical simulation of a Tollmien–Schlichting (TS) wave in a 2D boundary layer. The evolution of this numerical perturbation is accurately computed and checked against theoretical results

An interpolation tool for aeroelastic data transfer problems

In the loosely-coupled aeroelastic methodology, the aerodynamic and structural models are computed on different meshes. CFD tools are applied over the aerodynamic grid whereas CSM tools over the structural one. Depending on the model, the meshes can or not share an interface. In stick models, for example, there is no real interface. A common problem consists on transfering structural deformations to the aerodynamic mesh and aerodynamic loads to the structural one. In this work we have developed an interpolation tool based on Radial Basis Functions (RBF) to transfer information between loosely-coupled meshes, independent of their topologies. The problem arises when we have to deal with large meshes. In these cases, a domain decomposition is necessary to create more simplyfied fields that can be more easily handle by the interpolator. As the interpolation process is driven separately between each pair of associated blocks, the displacements at the junction nodes could be different. This fact could cause the ripping of the mesh along the junctions. A solution for this situation is also provided. The general methodology has been tested successfully in a whole aircraft configuration

Low cost 3D global instability analysis and flow sensitivity based on dynamic mode decomposition and high-order numerical tools

We explore the recently developed snapshot-based dynamic mode decomposition (DMD) technique, a matrix-free Arnoldi type method, to predict 3D linear global flow instabilities. We apply the DMD technique to flows confined in an L-shaped cavity and compare the resulting modes to their counterparts issued from classic, matrix forming, linear instability analysis (i.e. BiGlobal approach) and direct numerical simulations. Results show that the DMD technique, which uses snapshots generated by a 3D non-linear incompressible discontinuous Galerkin Navier?Stokes solver, provides very similar results to classical linear instability analysis techniques. In addition, we compare DMD results issued from non-linear and linearised Navier?Stokes solvers, showing that linearisation is not necessary (i.e. base flow not required) to obtain linear modes, as long as the analysis is restricted to the exponential growth regime, that is, flow regime governed by the linearised Navier?Stokes equations, and showing the potential of this type of analysis based on snapshots to general purpose CFD codes, without need of modifications. Finally, this work shows that the DMD technique can provide three-dimensional direct and adjoint modes through snapshots provided by the linearised and adjoint linearised Navier?Stokes equations advanced in time. Subsequently, these modes are used to provide structural sensitivity maps and sensitivity to base flow modification information for 3D flows and complex geometries, at an affordable computational cost. The information provided by the sensitivity study is used to modify the L-shaped geometry and control the most unstable 3D mode