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Papers by José Miguel Pérez

The purpose of this work is to shed light on the role of chemical equilibrium in the global insta... more The purpose of this work is to shed light on the role of chemical equilibrium in the global instabilities that arise in hypersonic non-parallel flows. For this end, the stability of temporal evolving disturbances on a hypersonic flow over a backstep are examined by the linearized Navier-Stokes equations. The flow conditions are unit Reynolds number equal to 6.6 x 10^6 1/m, boundary-layer edge temperature 350 K and freestream Mach number 10. The step height is equal to the local displacement thickness. For these conditions the two-dimensional laminar base flow is computed with the full Navier-Stokes solver TAU software. The results for a given wave number of the perturbations in the homogeneous direction shows that the leading linear mode located around the recirculation bubble is unstable in both cases. The real gas effects increase the temporal growth rate of the leading mode. This instability corresponds to a zero-frequency global linear instability. The spectrum and the structure...

Theoretical and Computational Fluid Dynamics, 2016

Modal global linear instability analysis is performed using, for the first time ever, the Lattice... more Modal global linear instability analysis is performed using, for the first time ever, the Lattice Boltzmann Method (LBM) to analyze incompressible flows with two and three inhomogeneous spatial directions. Four linearization models have been implemented in order to recover the linearized Navier-Stokes equations in the incompressible limit. Two of those models employ the single relaxation time and have been proposed previously in the literature as linearization of the collision operator of the lattice Boltzmann equation. Two additional models are derived herein for the first time by linearizing the local equilibrium probability distribution function. Instability analysis results are obtained in three benchmark problems, two in closed geometries and one in open flow, namely the square and cubic lid-driven cavity flow and flow in the wake of the circular cylinder. Comparisons with results delivered by classic spectral-element methods verifies the accuracy of the proposed new methodologies and points potential limitations particular to the LBM approach. The known issue of appearance of numerical instabilities when the SRT model is used in direct numerical simulations employing the LBM, is shown to be reflected in a spurious global eigenmode when the SRT model is used in the instability analysis. Although this mode is absent in the multiple relaxation times model, other spurious instabilities can also arise and are documented herein. Areas of potential improvements in order to make the proposed methodology competitive with established approaches for global instability analysis are discussed. Keywords Lattice Boltzmann methods • complex geometries • global instability analysis • flow control

Procedia IUTAM, 2015

Modal three-dimensional BiGlobal linear instability analysis is performed in steady, spanwise-hom... more Modal three-dimensional BiGlobal linear instability analysis is performed in steady, spanwise-homogeneous two-dimensional laminar compressible boundary-layer flow past a millimeter-tall hemispherical bump at transonic conditions. Starting with subsonic inlet flow, at the flow conditions considered a stationary shock is formed near the downstream end of the bump. The interplay of shock and adverse-pressure-gradient results in a steady spanwise homogeneous laminar two-dimensional laminar separation bubble being formed at the downstream end of the bump. The objective of the present analysis is to interrogate this basic flow with respect to its potential to sustain low-frequency unsteadiness arising from linear amplification of unstable traveling global flow eigenmodes. Such unsteadiness, coupled to eigenfrequencies of the structure, can lead to resonance phenomena that are detrimental for the performance and adversely affect the efficiency of systems on which the bump configuration is employed. Only damped global eigenmodes have been identified at the parameters examined, pointing to the possibility of the above mentioned unsteadiness being the result of algebraic instability.

42nd AIAA Fluid Dynamics Conference and Exhibit, 2012

A new time-stepping shift-invert algorithm for linear stability analysis of large-scale laminar f... more A new time-stepping shift-invert algorithm for linear stability analysis of large-scale laminar flows in complex geometries is presented. This method, based on a Krylov subspace iteration, enables the solution of complex non-symmetric eigenvalue problems in a matrixfree framework. Compared with the classical exponential method, the new approach has the advantage of converging to specific parts of the full global spectrum. Validations and comparisons to the exponential power method have been performed in three different cases: (i) the stenotic flow, (ii) the backward-facing step and (iii) the two-dimensional swirl flow. It is shown that, although the exponential method remains the method of choice if leading eigenvalues are sought, the present method can be competitive when access to specific parts of the full global spectrum is required. In addition, as opposed to other methods, this strategy can be directly applied to any time-stepper, regardless of the temporal or spatial discretization of the latter.

Revista de Calidad Asistencial, 2003

Aerospace Science and Technology, 2015

A novel time-stepping shift-invert algorithm for linear stability analysis of laminar flows in co... more A novel time-stepping shift-invert algorithm for linear stability analysis of laminar flows in complex geometries is presented. This method, based on a Krylov subspace iteration, enables the solution of complex non-symmetric eigenvalue problems in a matrix-free framework. Validations and comparisons to the classical exponential method have been performed in three different cases: (i) stenotic flow, (ii) backward-facing step and (iii) lid-driven swirling flow. Results show that this new approach speeds Keywords-U P tne re Q u i re d Krylov subspace iterations and has the capability of converging to specific parts of the Global linear instability analysis global spectrum. It is shown that, although the exponential method remains the method of choice if Large-scale eigenvalue problems leading eigenvalues are sought, the performance of the present method could be dramatically improved Krylov subspace with the use of a preconditioner. In addition, as opposed to other methods, this strategy can be directly Jacobian-free methods applied to any time-stepper, regardless of the temporal or spatial discretization of the latter.

ABSTRACT BiGlobal linear stability analysis has been shown to provide useful insight in flows ove... more ABSTRACT BiGlobal linear stability analysis has been shown to provide useful insight in flows over or through complex geometries and is a promising path in devising theoretically founded flow control strategies. The present work seeks the development of a computational code capable of performing BiGlobal linear stability analyses of compressible flows. The aim is to investigate the computational challenges associated with problems of the linear stability and propose alternative numerical methods. The ideas developed are applied to analyse the effect of compressibility in attachment-line boundary global flow instability.

Fluid Mechanics and Its Applications, 2015

Geometries with sudden expansion have been a subject of study for decades now, owing to its engin... more Geometries with sudden expansion have been a subject of study for decades now, owing to its engineering applications. While attention has been lavished on flow through symmetric channels with sudden expansion (SE) and backward-facing step (BFS), channels with other divergent angles are studied far less. Straight-diverging-straight (SDS) channels with finite angle of divergences have been studied here. Our focus is on the formation of the laminar separation bubble, typically in the diverging region, and its reattachment downstream. Computations have been carried out to estimate the effect of various parameters such as the angle of divergence \((\alpha )\), the outlet to intet height ratios \((D/d)\) and the Reynolds numbers \((Re)\) on the formation of the recirculation bubble. The extreme case with \(\alpha = 90^\circ \) can be compared to the flow through a symmetric sudden-expansion (SE) flow. The base flow obtained from the two open source codes is characterized for the formation of laminar separation bubble for very low Reynolds numbers \((Re)\) in the parametric space including the angle of divergence, \(\alpha \) and the expansion ratio, \(\kappa =D/d\) and \(Re\).

43rd Fluid Dynamics Conference, 2013

ABSTRACT Linear global modal instability analyses of flows in variable-angle diverging channels h... more ABSTRACT Linear global modal instability analyses of flows in variable-angle diverging channels have been performed and a connection is established between the instability results at finite divergence angles, 0° < α < 90°, and the well-known limiting cases of plane Poiseuille flow, α = 0°, and the backward-facing step, α = 90°. The numerical integrity of the results has been ensured by employing three independent codes, two based on spectral elements and one on a second-order finite element spatial discretization in the two directions defining the channel geometry, as well as a Fourier expansion along the third homogenous spatial direction. Amplification/damping rates have been computed in these analyses and also have been recovered from the numerical residuals obtained from transient direct numerical simulations (DNS), and compared with the eigenvalues of the leading eigenmode. A detailed parametric study is underway at representative values of the divergence angle in order to determine the critical parameters at each α value, and study the effect of this parameter on the known instability branches of the limiting case flows.

Journal of Fluid Mechanics, 2012

Flow instability in the non-orthogonal swept attachment-line boundary layer is addressed in a lin... more Flow instability in the non-orthogonal swept attachment-line boundary layer is addressed in a linear analysis framework via solution of the pertinent global (BiGlobal) partial differential equation (PDE)-based eigenvalue problem. Subsequently, a simple extension of the extended Görtler–Hämmerlin ordinary differential equation (ODE)-based polynomial model proposed by Theofilis et al. (2003) for orthogonal flow, which includes previous models as special cases and recovers global instability analysis results, is presented for non-orthogonal flow. Direct numerical simulations have been used to verify the analysis results and unravel the limits of validity of the basic flow model analysed. The effect of the angle of attack, mathitAoA\mathit{AoA}mathitAoA, on the critical conditions of the non-orthogonal problem has been documented; an increase of the angle of attack, from mathitAoA=0\mathit{AoA}= 0mathitAoA=0 (orthogonal flow) up to values close to lrmpi/2\lrm{\pi} / 2lrmpi/2 which make the assumptions under which the basic flow is de...