Archivo Digital UPM: No conditions. Results ordered -Date Deposited. 2020-01-29T03:49:44ZEPrintshttp://oa.upm.es/style/images/logo-archivo-digital.pnghttp://oa.upm.es/2016-11-22T12:44:04Z2016-11-22T12:44:04Zhttp://oa.upm.es/id/eprint/40207This item is in the repository with the URL: http://oa.upm.es/id/eprint/402072016-11-22T12:44:04ZNumerical studies of non-linear intrinsic streaks in the flat plate boundary layerThe development of streaky perturbations near the leading edge of a flat plate boundary layer was analyzed by Luchini (1996) using a description of the flow linearized around the Blaius solution. He found that there is just one single streaky mode (periodic in the spanwise direction) that grows downstream from the leading edge. The presence of this mode in the linear approximation indicates that, for the complete non-linear problem, there is an one parameter family of streak solutions that grow from the leading edge of the boundary layer. This family of steady 3D non-linear intrinsic streaks (intrinsic because they appear in the complete absence of any free stream perturbation) was recently non-linearly computed, using the Reduced Navier-Stokes formulation to describe its downstream evolution far away from the linear region. In this work, we enlarge the analysis of the transversal structure of the streaks. Furthermore, the stability characteristics of the streaky boundary layer flow is presented using the three-dimensional Parabolized Stability Equations (PSE-3D) and spatial BiGlobal analysis formulations, which have been successfully employed in flows that are inhomogeneous in two directions and weakly dependent along the third spatial direction. The stability analysis results show that the intrinsic streaks damp Tollmien-Schlichting waves. This effect is increased as the amplitude of the streak grows. At a certain limit, as observed in linear optimal streaks, shear-layer modes become unstable, potentially producing bypass transition.Juan Angel Martin BautistaCarlos Martel EscobarPedro Paredes GonzalezVassilios Theofilis2016-02-19T08:24:30Z2016-06-06T08:24:30Zhttp://oa.upm.es/id/eprint/36574This item is in the repository with the URL: http://oa.upm.es/id/eprint/365742016-02-19T08:24:30ZWind tunnel experiments to teach physicsInnovative teaching experimental activities for secondary school students have been developed in order to introduce some aerodynamic concepts, with the aim of making science subjects such as mathematics and physics more attractive. Post-graduate students of Universidad Politécnica de Madrid (UPM) and teachers of Deutsche Schule Madrid (DSM) have constructed a small wind tunnel. The main goal has been to provide a tool for secondary school students to become familiar with the scientific method developing curiosity, imagination, initiative, critical thinking and problem-solving skills. Students of DSM have performed wind tunnel experiments, resulting in a successful and amusing experience. The students were able to relate the experimental results obtained with the physic principle of flight, previously explained in class. Evaluations reveal that both, the teacher and the students, considered the experience as interesting and helpful to lead with teaching physics, mathematics and engineering sciences. The teacher observed the strong motivation factor developed for the students to continue learning engineering sciences. Some of the students expressed that this experience had changed their prejudices about physics and mathematics, based only on theoretical approaches.Soledad Le Clainche MartinezVassilios TheofilisWei HeJuan Angel Tendero VentanasQiong LiuJose Miguel Perez PerezM. Schlapkohl2016-02-18T09:20:45Z2016-02-18T09:20:46Zhttp://oa.upm.es/id/eprint/37657This item is in the repository with the URL: http://oa.upm.es/id/eprint/376572016-02-18T09:20:45ZLinear instability analysis of incompressible flow over a cuboid cavityDirect numerical simulations are performed to analyze the three-dimensional instability of flows over three-dimensional cavities. The flow structures at different Reynolds numbers are investigated by using the spectral-element solver nek5000. As the Reynolds number increasing, the lateral wall effects become more important, the recirculation zone shrinks, the front vortex increases and the flow structure inside of the cavity becomes more complex. Results show that the flow bifurcates from a steady state to an oscillatory regime beyond a value of Reynolds number Re = 1100.Qiong LiuFrancisco Sierra GomezVassilios Theofilis2016-02-11T12:21:42Z2016-02-11T12:21:42Zhttp://oa.upm.es/id/eprint/37656This item is in the repository with the URL: http://oa.upm.es/id/eprint/376562016-02-11T12:21:42ZNumerical simulation of a synthetic jet with OpenFoamNumerical simulations of flow surrounding a synthetic jet actuating device are presented. By modifying a dynamic mesh technique available in OpenFoam-a well-documented open-source solver for fluid dynamics, detailed computations of the sinusoidal motion of the synthetic jet diaphragm were possible. Numerical solutions were obtained by solving the two dimensional incompressible viscous N-S equations, with the use of a second order implicit time marching scheme and a central finite volume method for spatial discretization in both streamwise and crossflow directions. A systematic parametric study is reported here, in which the external Reynolds number, the diaphragm amplitude and frequency, and the slot dimensions are varied.Qiong LiuAsimina KazakidiMarcello A. F. MedeirosVassilios Theofilis2016-01-29T11:11:29Z2016-01-29T11:11:29Zhttp://oa.upm.es/id/eprint/36590This item is in the repository with the URL: http://oa.upm.es/id/eprint/365902016-01-29T11:11:29ZOn the role of global flow instability analysis in closed loop flow controlControl of linear flow instabilities has been demonstrated to be an effective theoretical flow control methodology, capable of modifying transitional flows on canonical geometries such as the plane channel and the flat-plate boundary layer. Extending the well-developed theoretical flow control techniques to flows over or through complex geometries requires addressing the issue of efficient capturing of the leading members of the global eigenspectrum pertinent to such flows. The present contribution describes state-of-the-art modal global instability analysis methodologies recently developed in our group, based on matrix formation and time-stepping, respectively. The relative performance of these algorithms is assessed on the recovery of BiGlobal and TriGlobal eigenspectra in the spanwise periodic and the cubic lid-driven cavity, respectively; the adjoint eigenspectrum in the latter flow is recovered for the first time. For three-dimensional flows without any homogeneous spatial direction, the time-stepping methodology was found to outperform the matrix-forming approach and permit recovering the leading TriGlobal eigenmodes in an three-dimensional open cavity of aspect ratio L : D : W = 5 : 1 : 1; theoretical flow control of this configuration is underway.Francisco Sierra GomezVassilios TheofilisPedro Paredes GonzalezQiong LiuWei He2015-07-27T17:14:19Z2019-05-31T16:44:40Zhttp://oa.upm.es/id/eprint/36553This item is in the repository with the URL: http://oa.upm.es/id/eprint/365532015-07-27T17:14:19ZOn the Use of Matrix-Free Shift-Invert Strategies For Global Flow Instability AnalysisA 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 up the required Krylov subspace iterations and has the capability of converging to specific parts of the global spectrum. It is shown that, although the exponential method remains the method of choice if leading eigenvalues are sought, the performance of the present method could be dramatically improved with the use of a preconditioner. 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.Francisco Gómez CarrascoJosé Miguel Pérez PérezHugh M. BlackburnVassilios Theofilis2015-04-09T12:05:12Z2017-11-10T15:02:52Zhttp://oa.upm.es/id/eprint/30030This item is in the repository with the URL: http://oa.upm.es/id/eprint/300302015-04-09T12:05:12ZBiGlobal and point vortex methods for the instability analysis of wakesTo better understand destruction mechanisms of wake-vortices behind aircraft, the point vortex method for stability (inviscid) used by Crow is here compared with viscous modal global stability analysis of the linearized Navier-Stokes equations acting on a two-dimensional basic flow, i.e. BiGlobal stability analysis.
The fact that the BiGlobal method is viscous, and uses a flnite área vortex model, gives rise to results somewhat different from the point vortex model. It adds more parameters to the problem, but is more realistic.Juan Angel Tendero VentanasPedro Paredes GonzalezVassilios TheofilisMiquel RouraRama Govindarajan2014-11-07T16:30:05Z2014-11-07T16:30:05Zhttp://oa.upm.es/id/eprint/16146This item is in the repository with the URL: http://oa.upm.es/id/eprint/161462014-11-07T16:30:05ZFour Decades of Studying Global Linear Instability: Progress and ChallengesGlobal linear instability theory is concerned with the temporal or spatial development of small-amplitude
perturbations superposed upon laminar steady or time-periodic three-dimensional flows, which are inhomogeneous in two(and periodic in one)or all three spatial directions.After a brief exposition of the theory,some recent advances are reported. First, results are presented on the implementation of a Jacobian-free Newton–Krylov time-stepping method into a standard
finite-volume aerodynamic code to obtain global linear instability results in flows of industrial interest. Second, connections are sought between established and more-modern approaches for structure identification in
flows, such as proper orthogonal decomposition and Koopman modes analysis (dynamic mode decomposition), and the possibility to connect solutions of the eigenvalue problem obtained by matrix formation or time-stepping with those delivered by dynamic mode decomposition, residual algorithm, and proper orthogonal decomposition analysis is highlighted in the laminar regime; turbulent and three-dimensional flows are identified as open areas for future research. Finally, a new stable very-high-order finite-difference method is implemented for the
spatial discretization of the operators describing the spatial biglobal eigenvalue problem, parabolized stability
equation three-dimensional analysis, and the triglobal eigenvalue problem; it is shown that, combined with sparse
matrix treatment, all these problems may now be solved on standard desktop computersF. GómezSoledad Le Clainche MartínezPedro Paredes GarciaMiguel Hermanns NavarroVassilios Theofilis2014-11-04T18:02:54Z2016-04-27T07:52:38Zhttp://oa.upm.es/id/eprint/30168This item is in the repository with the URL: http://oa.upm.es/id/eprint/301682014-11-04T18:02:54ZSpatial linear global instability analysis of the HIFiRE-5 elliptic cone model flowThe linear instability of the three-dimensional boundary-layer over the HIFiRE-5 flight test geometry, i.e. a rounded-tip 2:1 elliptic cone, at Mach 7, has been analyzed through spatial BiGlobal analysis, in a effort to understand transition and accurately predict local
heat loads on next-generation ight vehicles. The results at an intermediate axial section of the cone, Re x = 8x10 5, show three different families of spatially amplied linear global modes, the attachment-line and cross- ow modes known from earlier analyses, and a new global mode, peaking in the vicinity of the minor axis of the cone, termed \center-line mode". We discover that a sequence of symmetric and anti-symmetric centerline modes exist and, for the basic ow at hand, are maximally amplied around F* = 130kHz. The wavenumbers and spatial distribution of amplitude functions of the centerline modes are documentedPedro Paredes GonzalezVassilios Theofilis2014-11-03T18:13:00Z2016-04-27T07:31:11Zhttp://oa.upm.es/id/eprint/30169This item is in the repository with the URL: http://oa.upm.es/id/eprint/301692014-11-03T18:13:00ZAccurate Parabolic Navier-Stokes solutions of the supersonic flow around and elliptic coneFlows of relevance to new generation aerospace vehicles exist, which are weakly dependent on the streamwise direction and strongly dependent on the other two spatial
directions, such as the flow around the (flattened) nose of the vehicle and the associated elliptic cone model. Exploiting these characteristics, a parabolic integration of the Navier-Stokes equations is more appropriate than solution of the full equations, resulting in the so-called Parabolic Navier-Stokes (PNS). This approach not only is the best candidate, in terms of computational efficiency and accuracy, for the computation of steady base flows with the appointed properties, but also permits performing instability analysis and laminar-turbulent transition studies a-posteriori to the base flow computation. This
is to be contrasted with the alternative approach of using order-of-magnitude more expensive spatial Direct Numerical Simulations (DNS) for the description of the transition
process. The PNS equations used here have been formulated for an arbitrary coordinate transformation and the spatial discretization is performed using a novel stable high-order
finite-difference-based numerical scheme, ensuring the recovery of highly accurate solutions using modest computing resources. For verification purposes, the boundary layer solution around a circular cone at zero angle of attack is compared in the incompressible limit with
theoretical profiles. Also, the recovered shock wave angle at supersonic conditions is compared with theoretical predictions in the same circular-base cone geometry. Finally, the entire flow field, including shock position and compressible boundary layer around a 2:1 elliptic cone is recovered at Mach numbers 3 and 4Pedro Paredes GonzalezVassilios Theofilis2014-08-07T16:59:00Z2016-04-21T23:57:25Zhttp://oa.upm.es/id/eprint/29557This item is in the repository with the URL: http://oa.upm.es/id/eprint/295572014-08-07T16:59:00ZLaminar-turbulent transition induced by a discrete roughness element in a supersonic boundary layerThe linear instability and breakdown to turbulence induced by an isolated roughness element in a boundary layer at Mach 2:5, over an isothermal flat plate with laminar adiabatic wall temperature, have been analysed by means of direct numerical simulations, aided by spatial BiGlobal and three-dimensional parabolized (PSE-3D) stability analyses. It is important to understand transition in this flow regime since the process can be slower than in incompressible flow and is crucial to prediction
of local heat loads on next-generation flight vehicles. The results show that the roughness element, with a height of the order of the boundary layer displacement
thickness, generates a highly unstable wake, which is composed of a low-velocity streak surrounded by a three-dimensional high-shear layer and is able to sustain the
rapid growth of a number of instability modes. The most unstable of these modes are associated with varicose or sinuous deformations of the low-velocity streak; they are
a consequence of the instability developing in the three-dimensional shear layer as a whole (the varicose mode) or in the lateral shear layers (the sinuous mode). The most
unstable wake mode is of the varicose type and grows on average 17% faster tan the most unstable sinuous mode and 30 times faster than the most unstable boundary
layer mode occurring in the absence of a roughness element. Due to the high growthrates registered in the presence of the roughness element, an amplification factor of
N D 9 is reached within 50 roughness heights from the roughness trailing edge. The independently performed Navier–Stokes, spatial BiGlobal and PSE-3D stability results
are in excellent agreement with each other, validating the use of simplified theories for roughness-induced transition involving wake instabilities. Following the linear stages
of the laminar–turbulent transition process, the roll-up of the three-dimensional shear layer leads to the formation of a wedge of turbulence, which spreads laterally at a rate
similar to that observed in the case of compressible turbulent spots for the same Mach number.N. De TullioPedro Paredes GonzalezN. D. SandhamVassilios Theofilis2014-08-05T16:38:51Z2016-04-22T00:17:18Zhttp://oa.upm.es/id/eprint/29950This item is in the repository with the URL: http://oa.upm.es/id/eprint/299502014-08-05T16:38:51ZMolecular Dynamics Simulations of Couette flowThe first steps towards developing a continuum-molecular coupled simulations techniques are presented, for the purpose of computing macroscopic systems of confined fluids. The idea is to compute the interface wall-fluid by Molecular Dynamics simulations, where Lennard-Jones potential (and others) have been employed for the molecular interactions, so the usual non slip boundary condition is not specified. Instead, a shear rate can be imposed at the wall, which allows to obtain the properties of the wall material by means of an iterative method. The remaining fluid region will be computed by a spectral hp method. We present MD simulations of a Couette flow, and the results of the developed boundary conditions from the wall fluid interaction.Juan A. Martín BautistaJulio MeneghiniVassilios Theofilis2014-04-07T16:45:17Z2016-04-21T17:21:04Zhttp://oa.upm.es/id/eprint/19104This item is in the repository with the URL: http://oa.upm.es/id/eprint/191042014-04-07T16:45:17ZOrder 10 4 speedup in global linear instability analysis using matrix formationA unified solution framework is presented for one-, two- or three-dimensional complex non-symmetric eigenvalue problems, respectively governing linear modal instability of incompressible fluid flows in rectangular domains having two, one or no homogeneous spatial directions. The solution algorithm is based on subspace iteration in which the spatial discretization matrix is formed, stored and inverted serially. Results delivered by spectral collocation based on the Chebyshev-Gauss-Lobatto (CGL) points and a suite of high-order finite-difference methods comprising the previously employed for this type of work Dispersion-Relation-Preserving (DRP) and Padé finite-difference schemes, as well as the Summationby- parts (SBP) and the new high-order finite-difference scheme of order q (FD-q) have been compared from the point of view of accuracy and efficiency in standard validation cases of temporal local and BiGlobal linear instability. The FD-q method has been found to significantly outperform all other finite difference schemes in solving classic linear local, BiGlobal, and TriGlobal eigenvalue problems, as regards both memory and CPU time requirements. Results shown in the present study disprove the paradigm that spectral methods are superior to finite difference methods in terms of computational cost, at equal accuracy, FD-q spatial discretization delivering a speedup of ð (10 4). Consequently, accurate solutions of the three-dimensional (TriGlobal) eigenvalue problems may be solved on typical desktop computers with modest computational effort.Pedro Paredes GonzalezMiguel Hermanns NavarroSoledad Le Clainche MartínezVassilios Theofilis2013-02-27T09:54:34Z2014-09-22T10:55:05Zhttp://oa.upm.es/id/eprint/12517This item is in the repository with the URL: http://oa.upm.es/id/eprint/125172013-02-27T09:54:34ZLinear global instability of non-orthogonal incompressible swept attachment-line boundary layer flowInstability of the orthogonal swept attachment line boundary layer has received attention by local1, 2 and global3–5 analysis methods over several decades, owing to the significance of this model to transition to turbulence on the surface of swept wings. However, substantially less attention has been paid to the problem of laminar flow instability in the non-orthogonal swept attachment-line boundary layer; only a local analysis framework has been employed to-date.6 The present contribution addresses this issue from a linear global (BiGlobal) instability analysis point of view in the incompressible regime. Direct numerical simulations have also been performed in order to verify the analysis results and unravel the limits of validity of the Dorrepaal basic flow7 model analyzed. Cross-validated results document the effect of the angle _ on the critical conditions identified by Hall et al.1 and show linear destabilization of the flow with decreasing AoA, up to a limit at which the assumptions of the Dorrepaal model become questionable. Finally, a simple extension of the extended G¨ortler-H¨ammerlin ODE-based polynomial model proposed by Theofilis et al.4 is presented for the non-orthogonal flow. In this model, the symmetries of the three-dimensional disturbances are broken by the non-orthogonal flow conditions. Temporal and spatial one-dimensional linear eigenvalue codes were developed, obtaining consistent results with BiGlobal stability analysis and DNS. Beyond the computational advantages presented by the ODE-based model, it allows us to understand the functional dependence of the three-dimensional disturbances in the non-orthogonal case as well as their connections with the disturbances of the orthogonal stability problem.José Miguel Pérez PérezDaniel Rodríguez ÁlvarezVassilios Theofilis2013-02-26T08:03:10Z2014-09-22T10:57:19Zhttp://oa.upm.es/id/eprint/13075This item is in the repository with the URL: http://oa.upm.es/id/eprint/130752013-02-26T08:03:10ZTowards the foundation of a global modes conceptA contribution is presented, intended to provide theoretical foundations for the ongoing efforts to employ global instability theory for the analysis of the classic boundary-layer flow, and address the associated issue of appropriate inflow/outflow boundary conditions to close the PDE-based global eigenvalue problem in open flows. Starting from a theoretically clean and numerically simple application, in which results are also known analytically and thus serve as a guidance for the assessment of the performance of the numerical methods employed herein, a sequence of issues is systematically built into the target application, until we arrive at one representative of open systems whose instability is presently addressed by global linear theory applied to open flows, the latter application being neither tractable theoretically nor straightforward to solve by numerical means. Experience gained along the way is documented. It regards quantification of the depar- ture of the numerical solution from the analytical one in the simple problem, the generation of numerical boundary layers at artificially truncated boundaries, no matter how far the latter are placed from the region of highest flow gradients and, ultimately the impracti- cally large number of (direct and adjoint) modes necessary to project an arbitrary initial perturbation and follow its temporal evolution by a global analysis approach, a finding which may question the purported robustness reported in the literature of the recovery of optimal perturbations as part of global analyses yielding under-resolved eigenspectra.Daniel Rodríguez ÁlvarezA. TuminVassilios Theofilis2013-02-25T15:37:37Z2014-09-22T10:57:44Zhttp://oa.upm.es/id/eprint/13172This item is in the repository with the URL: http://oa.upm.es/id/eprint/131722013-02-25T15:37:37ZGlobal Linear Instability at the Dawn of its 4th Decade: A List of Challenges (A Practical Guide on how to Contain the Euphoria and Avoid the Oversell)Global linear instability theory is concerned with the temporal or spatial development of small-amplitude perturbations superposed upon laminar steady or time-periodic threedimensional flows, which are inhomogeneous in two (and periodic in one) or all three spatial directions.1 The theory addresses flows developing in complex geometries, in which the parallel or weakly nonparallel basic flow approximation invoked by classic linear stability theory does not hold. As such, global linear theory is called to fill the gap in research into stability and transition in flows over or through complex geometries. Historically, global linear instability has been (and still is) concerned with solution of multi-dimensional eigenvalue problems; the maturing of non-modal linear instability ideas in simple parallel flows during the last decade of last century2–4 has given rise to investigation of transient growth scenarios in an ever increasing variety of complex flows. After a brief exposition of the theory, connections are sought with established approaches for structure identification in flows, such as the proper orthogonal decomposition and topology theory in the laminar regime and the open areas for future research, mainly concerning turbulent and three-dimensional flows, are highlighted. Recent results obtained in our group are reported in both the time-stepping and the matrix-forming approaches to global linear theory. In the first context, progress has been made in implementing a Jacobian-Free Newton Krylov method into a standard finite-volume aerodynamic code, such that global linear instability results may now be obtained in compressible flows of aeronautical interest. In the second context a new stable very high-order finite difference method is implemented for the spatial discretization of the operators describing the spatial BiGlobal EVP, PSE-3D and the TriGlobal EVP; combined with sparse matrix treatment, all these problems may now be solved on standard desktop computers.Vassilios TheofilisF. GómezPedro Paredes GonzalezSoledad Le Clainche MartínezMiguel Hermanns Navarro2012-12-04T10:43:09Z2014-09-22T10:57:19Zhttp://oa.upm.es/id/eprint/13077This item is in the repository with the URL: http://oa.upm.es/id/eprint/130772012-12-04T10:43:09ZEffect of Aspect Ratio on the Three-Dimensional Global Instability Analysis of Incompressible Open Cavity FlowsThe stability analysis of open cavity ﬂows is a problem of great interest in the aeronautical industry. This type of ﬂow can appear, for example, in landing gears or auxiliary power unit conﬁgurations. Open cavity ﬂows is very sensitive to any change in the conﬁguration, either physical (incoming boundary layer, Reynolds or Mach numbers) or geometrical (length to depth and length to width ratio). In this work, we have focused on the eﬀect of geometry and of the Reynolds number on the stability properties of a threedimensional spanwise periodic cavity ﬂow in the incompressible limit. To that end, BiGlobal analysis is used to investigate the instabilities in this conﬁguration. The basic ﬂow is obtained by the numerical integration of the Navier-Stokes equations with laminar boundary layers imposed upstream. The 3D perturbation, assumed to be periodic in the spanwise direction, is obtained as the solution of the global eigenvalue problem. A parametric study has been performed, analyzing the stability of the ﬂow under variation of the Reynolds number, the L/D ratio of the cavity, and the spanwise wavenumber β. For consistency, multidomain high order numerical schemes have been used in all the computations, either basic ﬂow or eigenvalue problems. The results allow to deﬁne the neutral curves in the range of L/D = 1 to L/D = 3. A scaling relating the frequency of the eigenmodes and the length to depth ratio is provided, based on the analysis results.Fernando Meseguer GarridoJavier de Vicente BuendiaEusebio Valero SánchezVassilios Theofilis2012-12-04T09:58:24Z2016-04-21T12:23:07Zhttp://oa.upm.es/id/eprint/13080This item is in the repository with the URL: http://oa.upm.es/id/eprint/130802012-12-04T09:58:24ZLinear instability of orthogonal compressible leading-edge boundary layer flowInstability analysis of compressible orthogonal swept leading-edge boundary layer ﬂow was performed in the context of BiGlobal linear theory. 1, 2 An algorithm was developed exploiting the sparsity characteristics of the matrix discretizing the PDE-based eigenvalue problem. This allowed use of the MUMPS sparse linear algebra package 3 to obtain a direct solution of the linear systems associated with the Arnoldi iteration. The developed algorithm was then applied to eﬃciently analyze the eﬀect of compressibility on the stability of the swept leading-edge boundary layer and obtain neutral curves of this ﬂow as a function of the Mach number in the range 0 ≤ Ma ≤ 1. The present numerical results fully conﬁrmed the asymptotic theory results of Theoﬁlis et al. 4 Up to the maximum Mach number value studied, it was found that an increase of this parameter reduces the critical Reynolds number and the range of the unstable spanwise wavenumbers.Elmer GennaroDaniel Rodríguez ÁlvarezM. MedeirosVassilios Theofilis2012-12-04T09:49:03Z2016-04-21T12:23:17Zhttp://oa.upm.es/id/eprint/13082This item is in the repository with the URL: http://oa.upm.es/id/eprint/130822012-12-04T09:49:03ZThe PSE-3D instability analysis methodology for flows depending strongly on two and weakly on the third spatial dimensionThe present contribution discusses the development of a PSE-3D instability analysis algorithm, in which a matrix forming and storing approach is followed. Alternatively to the typically used in stability calculations spectral methods, new stable high-order ﬁnitediﬀerence-based numerical schemes for spatial discretization 1 are employed. Attention is paid to the issue of eﬃciency, which is critical for the success of the overall algorithm. To this end, use is made of a parallelizable sparse matrix linear algebra package which takes advantage of the sparsity oﬀered by the ﬁnite-diﬀerence scheme and, as expected, is shown to perform substantially more eﬃciently than when spectral collocation methods are used. The building blocks of the algorithm have been implemented and extensively validated, focusing on classic PSE analysis of instability on the ﬂow-plate boundary layer, temporal and spatial BiGlobal EVP solutions (the latter necessary for the initialization of the PSE-3D), as well as standard PSE in a cylindrical coordinates using the nonparallel Batchelor vortex basic ﬂow model, such that comparisons between PSE and PSE-3D be possible; excellent agreement is shown in all aforementioned comparisons. Finally, the linear PSE-3D instability analysis is applied to a fully three-dimensional ﬂow composed of a counter-rotating pair of nonparallel Batchelor vortices.Pedro Paredes GonzalezVassilios TheofilisDaniel Rodríguez ÁlvarezJuan Angel Tendero Ventanas2012-12-04T09:45:32Z2016-04-21T12:23:28Zhttp://oa.upm.es/id/eprint/13084This item is in the repository with the URL: http://oa.upm.es/id/eprint/130842012-12-04T09:45:32ZCoupling time-stepping numerical methods and standard aerodynamics codes for instability analysis of flows in complex geometriesThe development of a global instability analysis code coupling a time-stepping approach, as applied to the solution of BiGlobal and TriGlobal instability analysis 1, 2 and ﬁnite-volume-based spatial discretization, as used in standard aerodynamics codes is presented. The key advantage of the time-stepping method over matrix-formulation approaches is that the former provides a solution to the computer-storage issues associated with the latter methodology. To-date both approaches are successfully in use to analyze instability in complex geometries, although their relative advantages have never been quantiﬁed. The ultimate goal of the present work is to address this issue in the context of spatial discretization schemes typically used in industry. The time-stepping approach of Chiba 3 has been implemented in conjunction with two direct numerical simulation algorithms, one based on the typically-used in this context high-order method and another based on low-order methods representative of those in common use in industry. The two codes have been validated with solutions of the BiGlobal EVP and it has been showed that small errors in the base ﬂow do not have aﬀect signiﬁcantly the results. As a result, a three-dimensional compressible unsteady second-order code for global linear stability has been successfully developed based on ﬁnite-volume spatial discretization and time-stepping method with the ability to study complex geometries by means of unstructured and hybrid meshesFrancisco Gómez CarrascoRaquel GómezVassilios Theofilis2012-12-04T09:05:08Z2014-09-22T10:57:24Zhttp://oa.upm.es/id/eprint/13092This item is in the repository with the URL: http://oa.upm.es/id/eprint/130922012-12-04T09:05:08ZWave-like Disturbances on the Downstream Wall of an Open CavityThis contribution presents results of an incompressible two-dimensional ﬂow over an open cavity of ﬁxed aspect ratio (length/depth) L/D = 2 and the coupling between the three dimensional low frequency oscillation mode conﬁned in the cavity and the wave-like disturbances evolving on the downstream wall of the cavity in the form of Tollmien-Schlichting waves. BiGlobal instability analysis is conducted to search the global disturbances superimposed upon a two-dimensional steady basic ﬂow. The base solution is computed by the integration of the laminar Navier-Stokes equations in primitive variable formulation, while the eigenvalue problem (EVP) derived from the discretization of the linearized equations of motion in the BiGlobal framework is solved using an iterative procedure. The formulation of the BiGlobal EVP for the unbounded ﬂow in the open cavity problem introduces additional diﬃculties regarding the ﬂow-through boundaries. Local analysis has been utilized for the determination of the proper boundary conditions in the upper limit of the downstream regionJavier de Vicente BuendiaPedro Paredes GonzalezEusebio Valero SánchezVassilios Theofilis2012-09-11T12:53:33Z2016-04-21T11:17:59Zhttp://oa.upm.es/id/eprint/12112This item is in the repository with the URL: http://oa.upm.es/id/eprint/121122012-09-11T12:53:33ZThree-dimensional flow instability in a lid-driven isosceles triangular cavityLinear three-dimensional modal instability of steady laminar two-dimensional states developing in a lid-driven cavity of isosceles triangular cross-section is investigated theoretically and experimentally for the case in which the equal sides form a rectangular corner. An asymmetric steady two-dimensional motion is driven by the steady motion of one of the equal sides. If the side moves away from the rectangular corner, a stationary three-dimensional instability is found. If the motion is directed towards the corner, the instability is oscillatory. The respective critical Reynolds numbers are identified both theoretically and experimentally. The neutral curves pertinent to the two configurations and the properties of the respective leading eigenmodes are documented and analogies to instabilities in rectangular lid-driven cavities are discussed.Leo Miguel González GutierrezJ. KuhnenVassilios TheofilisH. C. Kuhlmann2012-03-06T09:03:19Z2016-04-20T18:39:28Zhttp://oa.upm.es/id/eprint/10443This item is in the repository with the URL: http://oa.upm.es/id/eprint/104432012-03-06T09:03:19ZOn the Spatial Structure of Global Linear Instabilities And Their Experimental IdentificationThe purpose of the present paper is to discuss the spatial structure of global instabilities, solutions of the partial derivative eigenvalue problem resulting from a nonparallel linear instability analysis of the incompressible Navier–Stokes and continuity equations, as developing upon four prototype essentially two-dimensional steady laminar flows. Theoretical knowledge of these eigendisturbances is instrumental to devising measurement techniques appropriate for their experimental recovery and ultimate control of laminar-turbulent transition mechanisms. Raising the awareness of the global linear flow eigenmodes contributes to redefining the boundaries between experimental observations which may be attributed to linear global as opposed to nonlinear mechanismsVassilios Theofilis2012-03-05T12:27:50Z2016-04-20T18:39:26Zhttp://oa.upm.es/id/eprint/10442This item is in the repository with the URL: http://oa.upm.es/id/eprint/104422012-03-05T12:27:50ZOn the Origins of Three-Dimensionality And Unsteadiness in the Laminar Separation BubbleWe analyse the three-dimensional non-parallel instability mechanisms responsible for transition to turbulence in regions of recirculating steady laminar two-dimensional incompressible separation bubble ®ow in a twofold manner. First, we revisit the problem of Tollmien{Schlichting (TS)-like disturbances and we demonstrate, for the rst time for this type of ®ow, excellent agreement between the parabolized stabil- ity equation results and those of independently performed direct numerical simula- tions. Second, we perform a partial-derivative eigenvalue problem stability analysis by discretizing the two spatial directions on which the basic ®ow depends, precluding TS-like waves from entering the calculation domain. A new two-dimensional set of global ampli ed instability modes is thus discovered. In order to prove earlier topo- logical conjectures about the ®ow structural changes occurring prior to the onset of bubble unsteadiness, we reconstruct the total ®ow eld by linear superposition of the steady two-dimensional basic ®ow and the new most-ampli ed global eigenmodes. In the parameter range investigated, the result is a bifurcation into a three-dimensional ®ow eld in which the separation line remains una¬ected while the primary reattach- ment line becomes three dimensional, in line with the analogous result of a multitude of experimental observations.Vassilios TheofilisStefan HeinUwe Ch. Dallmann2012-03-05T12:16:23Z2016-04-20T18:39:34Zhttp://oa.upm.es/id/eprint/10446This item is in the repository with the URL: http://oa.upm.es/id/eprint/104462012-03-05T12:16:23ZThe Extended Görtler-Hämmerlin Model For Linear Instability of Three-Dimensional Incompressible Swept Attachment-Line Boundary Layer FlowA simple extension of the classic Görtler–Hämmerlin (1955) (GH) model, essential for three-dimensional linear instability analysis, is presented. The extended Görtler–Hämmerlin model classifies all three-dimensional disturbances in this flow by means of symmetric and antisymmetric polynomials of the chordwise coordinate. It results in one-dimensional linear eigenvalue problems, a temporal or spatial solution of which, presented herein, is demonstrated to recover results otherwise only accessible to the temporal or spatial partial-derivative eigenvalue problem (the former also solved here) or to spatial direct numerical simulation (DNS). From a numerical point of view, the significance of the extended GH model is that it delivers the three-dimensional linear instability characteristics of this flow, discovered by solution of the partial-derivative eigenvalue problem by Lin & Malik (1996a), at a negligible fraction of the computing effort required by either of the aforementioned alternative numerical methodologies. More significant, however, is the physical insight which the model offers into the stability of this technologically interesting flow. On the one hand, the dependence of three-dimensional linear disturbances on the chordwise spatial direction is unravelled analytically. On the other hand, numerical results obtained demonstrate that all linear three-dimensional instability modes possess the same (scaled) dependence on the wall-normal coordinate, that of the well-known GH mode. The latter result may explain why the three-dimensional linear modes have not been detected in past experiments; criteria for experimental identification of three-dimensional disturbances are discussed. Asymptotic analysis based on a multiple-scales method confirms the results of the extended GH model and provides an alternative algorithm for the recovery of three-dimensional linear instability characteristics, also based on solution of one-dimensional eigenvalue problems. Finally, the polynomial structure of individual three-dimensional extended GH eigenmodes is demonstrated using three-dimensional DNS, performed here under linear conditions.Vassilios TheofilisAlexander FedorovDominik ObristUwe Ch. Dallmann2012-03-05T12:09:27Z2016-04-20T18:39:31Zhttp://oa.upm.es/id/eprint/10445This item is in the repository with the URL: http://oa.upm.es/id/eprint/104452012-03-05T12:09:27ZComplex-Grid Spectral Algorithms For Inviscid Linear Instability of Boundary-Layer FlowsWe present a suite of algorithms designed to obtain accurate numerical solutions of the generalised eigenvalue problem governing inviscid linear instability of boundary-layer type of flow in both the incompressible and compressible regimes on planar and axisymmetric curved geometries. The large gradient problems which occur in the governing equations at critical layers are treated by diverting the integration path into the complex plane, making use of complex mappings. The need for expansion of the basic flow profiles in truncated Taylor series is circumvented by solving the boundary-layer equations directly on the same (complex) grid used for the instability calculations. Iterative and direct solution algorithms are employed and the performance of the resulting algorithms using nonlinear radiation or homogeneous Dirichlet far-field boundary conditions is examined. The dependence of the solution on the parameters of the complex mappings is discussed. Results of incompressible and supersonic flow examples are presented; their excellent agreement with established works demonstrates the accuracy and robustness of the new methods presented. Means of improving the efficiency of the proposed spectral algorithms are suggested.Vassilios TheofilisA. KarabisS. J. Shaw2012-03-05T11:49:50Z2016-04-20T18:39:23Zhttp://oa.upm.es/id/eprint/10441This item is in the repository with the URL: http://oa.upm.es/id/eprint/104412012-03-05T11:49:50ZOn the Resolution of Critical Flow Regions in Inviscid Linear And Nonlinear Instability CalculationsNumerical methods for tackling the inviscid instability problem are discussed. Convergence is demon- strated to be a necessary, but not a sufficient condition for accuracy. Inviscid flow physics set requirements regarding grid-point distribution in order for physically accurate results to be obtained. These requirements are relevant to the viscous problem also and are shown to be related to the resolution of the critical layers. In this respect, high-resolution nonlinear calculations based on the inviscid initial-boundary-value problem are presented for a model shear-layer flow, aiming at identification of the regions that require attention in the course of high-Reynolds-number viscous calculations. The results bear a remarkable resemblance with those pertinent to viscous flow, with a cascade of high-shear regions being shed towards the vortex-core centre as time progresses. In parallel, numerical instability related to the finite-time singularity of the nonlinear equations solved globally contaminates and eventually destroys the simulations, irrespective of resolution.Vassilios Theofilis2012-03-05T11:36:11Z2016-04-20T18:39:37Zhttp://oa.upm.es/id/eprint/10447This item is in the repository with the URL: http://oa.upm.es/id/eprint/104472012-03-05T11:36:11ZBiglobal Stability Analysis of Steady Flow in Constricted Channel GeometriesIn this paper we apply a BiGlobal stability analysis technique to measure the stability of two-dimensional constricted channel flows to three-dimensional perturbations. Critical Reynolds numbers and spanwise perturbation wavelengths are presented for three instabilities of steady flow in constricted channels.R.E. PittSpencer SherwinVassilios Theofilis2012-03-05T11:27:22Z2016-04-20T18:39:20Zhttp://oa.upm.es/id/eprint/10440This item is in the repository with the URL: http://oa.upm.es/id/eprint/104402012-03-05T11:27:22ZOn Linear And Nonlinear Instability in the Infinte Swept Attachment-Line Boundary LayerOn linear and nonlinear instability of the incompressible swept attachment-line boundary layer
VASSILIOS THEOFILIS a1
a1 DLR, Institute for Fluid Mechanics, Division Transition and Turbulence, Bunsenstraße 10, D-37073 Göttingen, Germany
Abstract
The stability of an incompressible swept attachment-line boundary layer flow is studied numerically, within the Görtler–Hämmerlin framework, in both the linear and nonlinear two-dimensional regimes in a self-consistent manner. The initial-boundary-value problem resulting from substitution of small-amplitude excitation into the incompressible Navier–Stokes equations and linearization about the generalized Hiemenz profile is solved. A comprehensive comparison of all linear approaches utilized to date is presented and it is demonstrated that the linear initial-boundary-value problem formulation delivers results in excellent agreement with those obtained by solution of either the temporal or the spatial linear stability theory eigenvalue problem for both zero suction and a layer in which blowing is applied. In the latter boundary layer recent experiments have documented the growth of instability waves with frequencies in a range encompassed by that of the unstable Görtler–Hämmerlin linear modes found in our simulations. In order to enable further comparisons with experiment and, thus, assess the validity of the Görtler–Hämmerlin theoretical model, we make available the spatial structure of the eigenfunctions at maximum growth conditions.
The condition on smallness of the imposed excitation is subsequently relaxed and the resulting nonlinear initial-boundary-value problem is solved. Extensive numerical experimentation has been performed which has verified theoretical predictions on the way in which the solution is expected to bifurcate from the linear neutral loop. However, it is demonstrated that the two-dimensional model equations considered do not deliver subcritical instability of this flow; this strengthens the conjecture that three-dimensionality is, at least partly, responsible for the observed discrepancy between the linear theory critical Reynolds number and the subcritical turbulence observed either experimentally or in three-dimensional numerical simulations. Further, the present nonlinear computations demonstrate that the unstable flow has its line of maximum amplification in the neighbourhood of the experimentally observed instability waves, in a manner analogous to the Blasius boundary layer. In line with previous eigenvalue problem and direct simulation work, suction is observed to be a powerful stabilization mechanism for naturally occurring instabilities of small amplitude.Vassilios Theofilis2012-03-05T11:18:40Z2016-04-20T18:39:18Zhttp://oa.upm.es/id/eprint/10439This item is in the repository with the URL: http://oa.upm.es/id/eprint/104392012-03-05T11:18:40ZSpatial Stability of Incompressible Attachment-Line FlowLinear stability analysis of incompressible attachment-line flow is presented within the spatial framework. The system of perturbation equations is solved using spectral collocation. This system has been solved in the past using the temporal approach and the current results are shown to be in excellent agreement with neutral temporal calculations. Results amenable to direct comparison with experiments are then presented for the case of zero suction. The global solution method utilized for solving the eigenproblem yields, aside from the well-understood primary mode, the full spectrum of least-damped waves. Of those, a new mode, well separated from the continuous spectrum is singled out and discussed. Further, relaxation of the condition of decaying perturbations in the far-field results in the appearance of sinusoidal modes akin to those found in the classical Orr-Sommerfeld problem. Finally, the continuous spectrum is demonstrated to be amenable to asymptotic analysis. Expressions are derived for the location, in parameter space, of the continuous spectrum, as well as for the limiting cases of practical interest. In the large Reynolds number limit the continuous spectrum is demonstrated to be identical to that of the Orr-Sommerfeld equation.Vassilios Theofilis2012-03-05T10:58:07Z2016-04-20T18:39:15Zhttp://oa.upm.es/id/eprint/10438This item is in the repository with the URL: http://oa.upm.es/id/eprint/104382012-03-05T10:58:07ZThe Discrete Temporal Eigenvalue Spectrum of the Generalised Hiemenz Boundary Layer Flow As Solution of the Orr-Sommerfeld EquationA spectral collocation method is used to obtain the solution to the Orr-Sommerfeld stability equation. The accuracy of the method is established by comparing against well documented flows, such as the plane Poiseuille and the Blasius Boundary layers. The focus is then placed on the generalised Hiemenz flow, an exact solution to the Navier-Stokes equations constituting the base flow at the leading edge of swept cylinders and aerofoils. The spanwise profile of this flow is very similar to that of Blasius but, unlike the latter case, there is no rational approximation leading to the Orr-Sommerfeld equation. We will show that if, based on experimentally obtained intuition, a nonrational reduction of the full system of linear stability equations is attempted and the resulting Orr-Sommerfeld equation is solved, the linear stability critical Reynolds number is overestimated, as has indeed been done in the past. However, as shown by recent Direct Numerical Simulation results, the frequency eigenspectrum of instability waves may still be obtained through solution of the Orr-Sommerfeld equation. This fact lends some credibility to the assumption under which the Orr-Sommerfeld equation is obtained insofar as the identification of the frequency regime responsible for linear growth is concerned. Finally, an argument is presented pointing towards potential directions in the ongoing research for explanation of subcriticality in the leading edge boundary layer.Vassilios Theofilis2012-03-05T10:42:19Z2016-04-20T18:39:39Zhttp://oa.upm.es/id/eprint/10448This item is in the repository with the URL: http://oa.upm.es/id/eprint/104482012-03-05T10:42:19ZOn the Birth of Stall Cells on AirfoilsCritical point theory asserts that two-dimensional topologies are defined as degeneracies and any three-dimensional disturbance of a two-dimensional flow will lead to a new three-dimensional flowfield topology, regardless of the disturbance amplitude. Here, the topology of the composite flowfields reconstructed by linear superposition of the two-dimensional flow around a stalled airfoil and the leading stationary three-dimensional global eigenmode has been studied. In the conditions monitored the two-dimensional flow is steady and laminar and is separated over a fraction of the suction side, while the amplitudes considered in the linear superposition are small enough for the linearization assumption to be valid. The multiple topological bifurcations resulting have been analysed in detail; the surface streamlines generated by the leading stationary global mode of the separated flow have been found to be strongly reminiscent of the characteristic stall cells, observed experimentally on airfoils just beyond stall in both laminar and turbulent flow.Daniel Rodríguez ÁlvarezVassilios Theofilis2012-03-05T10:27:44Z2016-04-20T18:39:12Zhttp://oa.upm.es/id/eprint/10437This item is in the repository with the URL: http://oa.upm.es/id/eprint/104372012-03-05T10:27:44ZA Finite-Volume Approach to Compressible Large-Eddy SimulationsWe present Large Eddy Simulations of compressible turbulent flow within a finite volume approach with central spatial differencing. Different spatial discretisations yield quite different predictions of fluctuating flow properties although mean and integral flow properties appeared less sensitive. In the case of homogeneous, isotropic, decaying turbulence the Kolmogorov -(5/3) law is reproduced if the convective and viscous fluxes are treated with Simpson's cell vertex method. For the temporal flat plate exponentially growing unstable modes are recovered in the linear regime. Moreover, a scheme in which the viscous fluxes are treated with a vertex based method is required in order to properly capture the saturation of growing fluctuations, due to nonlinear interactions.B.J. GeurtsJ.G.M. KuertenA.W. VremanVassilios TheofilisP.J. Zandbergen2012-03-05T10:05:59Z2016-04-20T18:39:10Zhttp://oa.upm.es/id/eprint/10436This item is in the repository with the URL: http://oa.upm.es/id/eprint/104362012-03-05T10:05:59ZNumerical Experiments on the Stability of Leading Edge Boundary Layer FlowA numerical study is performed in order to gain insight to the stability of the infinite swept attachment line boundary layer. The basic flow is taken to be of the Hiemenz class with an added cross-flow giving rise to a constant thickness boundary layer along the attachment line. The full Navier-Stokes equations are solved using an initial value problem approach after two-dimensional perturbations of varying amplitude are introduced into the basic flow. A second-order-accurate finite difference scheme is used in the normal-to-the-wall direction, while a pseudospectral approach is employed in the other directions; temporally, an implicit Crank-Nicolson scheme is used. Extensive use of the efficient fast Fourier transform (FFT) algorithm has been made, resulting in substantial savings in computing cost. Results for the two-dimensional linear regime of perturbations are in very good agreement with past numerical and theoretical investigations, without the need for specific assumptions used by the latter, thus establishing the generality of our method.Vassilios Theofilis2012-03-05T10:02:13Z2016-04-20T18:39:07Zhttp://oa.upm.es/id/eprint/10435This item is in the repository with the URL: http://oa.upm.es/id/eprint/104352012-03-05T10:02:13ZBoundary Layer Growth on a Rotating And Accelerating SphereBoundary-layer growth on a sphere is studied when it is set into motion with constant acceleration and constant angular velocity, the latter being normal to the former. Analytic expressions are derived for the velocity components of the incompressible fluid in terms of a power series of the time of motion as well as for the skin frictionG.T. KarahaliosVassilios Theofilis2012-03-05T09:32:16Z2016-04-20T18:39:42Zhttp://oa.upm.es/id/eprint/10449This item is in the repository with the URL: http://oa.upm.es/id/eprint/104492012-03-05T09:32:16ZSpecial Issue on Global Flow Instability And ControlThis special issue is intended to provide a snapshot of current research in the area of “Global Flow Instability and Control”. The original papers, and to a certain extent the topic itself, are intimately linked with the series of symposia by the same name that were held in Crete, Greece, between 2001 and 2009. As members of the organizing committees of the Crete symposia, we invited all past participants to contribute, and all papers were reviewed following the strict standards of the journal. This preface gives a brief historical account of events that have shaped ideas in the field over the past decade, followed by a synopsis of the papers published herein.Vassilios TheofilisTim Colonius2012-03-05T09:00:03Z2016-04-20T18:39:45Zhttp://oa.upm.es/id/eprint/10450This item is in the repository with the URL: http://oa.upm.es/id/eprint/104502012-03-05T09:00:03ZStability Analysis in Spanwise-Periodic Double-Sided Lid-Driven Cavity Flows With Complex Cross-Sectional ProfilesThree-dimensional linear instability analyses are presented of steady two-dimensional laminar flows in the lid-driven cavity defined by [15] and further analyzed in the present volume [1], as well as in a derivative of the same geometry. It is shown that in both of the geometries considered three-dimensional BiGlobal instability leads to deviation of the flow from the two-dimensional solution; the analysis results are used to define low- and high-Reynolds number solutions by reference to the flow physics. Critical conditions for linear global instability and neutral loops are presented in both geometries.Javier de Vicente BuendiaDaniel Rodríguez ÁlvarezVassilios TheofilisEusebio Valero Sánchez2011-06-21T12:06:14Z2016-04-20T16:45:04Zhttp://oa.upm.es/id/eprint/7671This item is in the repository with the URL: http://oa.upm.es/id/eprint/76712011-06-21T12:06:14ZStructural changes of laminar separation bubbles induced by global linear instabilityThe topology of the composite flow fields reconstructed by linear superposition of a two-dimensional boundary layer flow with an embedded laminar separation bubble and its leading three-dimensional global eigenmodes has been studied. According to critical point theory, the basic flow is structurally unstable; it is shown that in the presence of three-dimensional disturbances the degenerate basic flow topology is replaced by a fully three-dimensional pattern, regardless of the amplitude of the superposed linear perturbations. Attention has been focused on the leading stationary eigenmode of the laminar separation bubble discovered by Theofilis; the composite flow fields have been fully characterized with respect to the generation and evolution of their critical points. The stationary global mode is shown to give rise to a three-dimensional flow field which is equivalent to the classical U-shaped separation, defined by Hornung & Perry, and induces topologies on the surface streamlines that are resemblant to the characteristic stall cells observed experimentally.Daniel Rodríguez ÁlvarezVassilios Theofilis2011-04-27T13:44:09Z2016-04-20T15:55:27Zhttp://oa.upm.es/id/eprint/6740This item is in the repository with the URL: http://oa.upm.es/id/eprint/67402011-04-27T13:44:09ZHigh-order methods for the numerical solution of the BiGlobal linear stability eigenvalue problem in complex geometries.A high-order computational tool based on spectral and spectral/hp elements (J. Fluid. Mech. 2009; to appear) discretizations is employed for the analysis of BiGlobal fluid instability problems. Unlike other implementations of this type, which use a time-stepping-based formulation (J. Comput. Phys. 1994; 110(1):82–102; J. Fluid Mech. 1996; 322:215–241), a formulation is considered here in which the discretized matrix is constructed and stored prior to applying an iterative shift-and-invert Arnoldi algorithm for the solution of the generalized eigenvalue problem. In contrast to the time-stepping-based formulations, the matrix-based approach permits searching anywhere in the eigenspace using shifting. Hybrid and fully unstructured meshes are used in conjunction with the spatial discretization. This permits analysis of flow instability on arbitrarily complex 2-D geometries, homogeneous in the third spatial direction and allows both mesh (h)-refinement as well as polynomial (p)-refinement. A series of validation cases has been defined, using well-known stability results in confined geometries. In addition new results are presented for ducts of curvilinear cross-sections with rounded corners.Leo Miguel González GutierrezVassilios TheofilisSpencer Sherwin2011-01-13T10:26:14Z2014-09-22T10:21:24Zhttp://oa.upm.es/id/eprint/5692This item is in the repository with the URL: http://oa.upm.es/id/eprint/56922011-01-13T10:26:14ZOn Multidimensional Global Eigenvalue Problems for Hydrodynamic and Aeroacoustic instabilitiesThe present effort discusses multi-dimensional eigenvalue problems as applied to the solution of hydro- dynamic and aeroacoustic instability problems on complex geometries. As a demonstrator, global linear instability analyses of steady lamina flows on an elliptic cone in compressible ¿¿ows are monitored; one such flow, obtained using a standard aerodynamics solver, is presented figure 1. Flows on this geometry are intrinsically three-dimensional; as a matter of fact the three-dimensionality of the geometry of the elliptic cone accounts for the departure of the laminar-turbulent transition process from the fairly well-understood scenarios on circular cones and other axisymmetric bodies of revolution. Shedding light on the essentially three-dimensional transition process on the elliptic cone provides motivation for several recent experimental and numerical efforts, as well as for the theoretical/numerical methodology described herein.Vassilios Theofilis2010-12-02T09:59:54Z2016-04-20T14:09:41Zhttp://oa.upm.es/id/eprint/5319This item is in the repository with the URL: http://oa.upm.es/id/eprint/53192010-12-02T09:59:54ZMassively Parallel Solution of the BiGlobal Eigenvalue Problem Using Dense Linear AlgebraLinear instability of complex flows may be analyzed by numerical solutions of partial-derivative-based eigenvalue problems; the concepts are, respectively, referred to as BiGlobal or TriGlobal instability, depending on whether two or three spatial directions are resolved simultaneously. Numerical solutions of the BiGlobal eigenvalue problems in flows of engineering significance, such as the laminar separation bubble in which global eigenmodes have been identified, reveal that recovery of (two-dimensional) amplitude functions of globally stable but convectively unstable flows (i.e., flows which sustain spatially amplifying disturbances in a local instability analysis context) requires resolutions well beyond the capabilities of serial, in-core solutions of the BiGlobal eigenvalue problems. The present contribution presents a methodology capable of overcoming this bottleneck via massive parallel solution of the problem at hand; the approach discussed is especially useful when a large window of the eigenspectrum is sought. Two separated flow applications, one in the boundary-layer on a flat plate and one in the wake of a stalled airfoil, are briefly discussed as demonstrators of the class of problems in which the present enabling technology permits the study of global instability in an accurate manner.Vassilios TheofilisDaniel Rodriguez2010-12-01T12:51:17Z2016-04-20T14:09:33Zhttp://oa.upm.es/id/eprint/5316This item is in the repository with the URL: http://oa.upm.es/id/eprint/53162010-12-01T12:51:17ZLinear instability analysis of low-pressure turbine flowsThree-dimensional linear BiGlobal instability of two-dimensional states over a periodic array of T-106/300 low-pressure turbine (LPT) blades is investigated for Reynolds numbers below 5000. The analyses are based on a high-order spectral/hp element discretization using a hybrid mesh. Steady basic states are investigated by solution of the partial-derivative eigenvalue problem, while Floquet theory is used to analyse time-periodic flow set-up past the first bifurcation. The leading mode is associated with the wake and long-wavelength perturbations, while a second short-wavelength mode can be associated with the separation bubble at the tralling edge. The leading eigenvalues and Floquet multipliers of the LPT flow have been obtained in a range of spanwise wavenumbers. For the most general configuration all secondary modes were observed to be stable in the Reynolds number regime considered. When a single LPT blade with top to bottom periodicity is considered as a base flow, the imposed periodicity forces the wakes of adjacent blades to be synchronized. This enforced synchronization can produce a linear instability due to long-wavelength disturbances. However, relaxing the periodic restrictions is shown to remove this instability. A pseudo-spectrum analysis shows that the eigenvalues can become unstable due to the non-orthogonal properties of the eigenmodes. Three-dimensional direct numerical simulations confirm all perturbations identified herein, All optimum growth analysis based on singular-value decomposition identifies perturbations with energy growths O(10(5)).Nadir AbdessemedSpencer SherwinVassilios Theofilis2010-12-01T12:23:16Z2016-04-20T14:09:35Zhttp://oa.upm.es/id/eprint/5317This item is in the repository with the URL: http://oa.upm.es/id/eprint/53172010-12-01T12:23:16ZTransient growth analysis of the flow past a circular cylinderWe apply direct transient growth analysis in complex geometries to investigate its role in the primary and secondary bifurcation/transition process of the flow past a circular cylinder. The methodology is based on the singular value decomposition of the Navier-Stokes evolution operator linearized about a two-dimensional steady or periodic state which leads to the optimal growth modes. Linearly stable and unstable steady flow at Re=45 and 50 is considered first, where the analysis demonstrates that strong two-dimensional transient growth is observed with energy amplifications of order of 10(3) at U-infinity tau/D approximate to 30. Transient growth at Re=50 promotes the linear instability which ultimately saturates into the well known von-Kaacutermaacuten street. Subsequently we consider the transient growth upon the time-periodic base state corresponding to the von-Kaacutermaacuten street at Re=200 and 300. Depending upon the spanwise wavenumber the flow at these Reynolds numbers are linearly unstable due to the so-called mode A and B instabilities. Once again energy amplifications of order of 10(3) are observed over a time interval of tau/T=2, where T is the time period of the base flow shedding. In all cases the maximum energy of the optimal initial conditions are located within a diameter of the cylinder in contrast to the spatial distribution of the unstable eigenmodes which extend far into the downstream wake. It is therefore reasonable to consider the analysis as presenting an accelerator to the existing modal mechanism. The rapid amplification of the optimal growth modes highlights their importance in the transition process for flow past circular cylinder, particularly when comparing with experimental results where these types of convective instability mechanisms are likely to be activated. The spatial localization, close to the cylinder, of the optimal initial condition may be significant when considering strategies to promote or control shedding.Nadir AbdessemedAtul S. SharmaVassilios TheofilisSpencer Sherwin2010-12-01T11:51:33Z2016-04-20T14:09:38Zhttp://oa.upm.es/id/eprint/5318This item is in the repository with the URL: http://oa.upm.es/id/eprint/53182010-12-01T11:51:33ZBiGlobal stability analysis in curvilinear coordinates of massively separated lifting bodiesA methodology based on spectral collocation numerical methods for global flow stability analysis of incompressible external flows is presented. A potential shortcoming of spectral methods, namely the handling of the complex geometries encountered in global stability analysis, has been dealt with successfully in past works by the development of spectral-element methods on unstructured meshes. The present contribution shows that a certain degree of regularity of the geometry may be exploited in order to build a global stability analysis approach based on a regular spectral rectangular grid in curvilinear coordinates and conformal mappings. The derivation of the stability linear operator in curvilinear coordinates is presented along with the discretisation method. Unlike common practice to the solution of the same problem, the matrix discretising the eigenvalue problem is formed and stored. Subspace iteration and massive parallelisation are used in order to recover a wide window of its leading Ritz system. The method is applied to two external flows, both of which are lifting bodies with separation occurring just downstream of the leading edge. Specifically the flow configurations are a NACA 0015 airfoil, and an ellipse of aspect ratio 8 chosen to closely approximate the geometry of the airfoil. Both flow configurations are at an angle of attack of 18, with a Reynolds number based on the chord length of 200. The results of the stability analysis for both geometries are presented and illustrate analogous features.Vassili KitsiosDaniel RodriguezVassilios TheofilisAndrew OoiJulio Soria2010-10-28T08:29:47Z2016-04-20T13:49:29Zhttp://oa.upm.es/id/eprint/4714This item is in the repository with the URL: http://oa.upm.es/id/eprint/47142010-10-28T08:29:47ZOptimal growth of linear perturbations in low pressure turbine flowsThis paper presents a numerical algorithm for the linearized flow initial value problem involving complex geometries where analytical solution is impossible. The method centres around the calculation of an eigenvalue problem involving the linearised flow and its spatial adjoint, and yields the flow perturbations that grow the most in a prescribed time, the magnitude of that growth and the perturbations after the growth has occurred. Previous work has shown that classical stability analysis of flow past a low-pressure turbine blade gives only stable eigenvalues, which cannot explain transition to turbulence in this flow. The inital value problem for this fan blade is presented and demonstrates significant perturbation growth, indicating that this growth may be the facilitator for transition in this case.Atul S. SharmaNadir AbdessemedSpencer SherwinVassilios Theofilis2010-10-28T08:20:18Z2016-04-20T13:49:32Zhttp://oa.upm.es/id/eprint/4715This item is in the repository with the URL: http://oa.upm.es/id/eprint/47152010-10-28T08:20:18ZMinisymposium "Global Flow Instability"Linear stability theory is concerned with the evolution of small-amplitude disturbances superimposed upon a steady- or time-periodic so-called basic flow. The vast majority of investigations during the second half of the last century has dealt with the analysis of one-dimensional (“parallel”) basic flows. On the other hand, Global flow instability deals with essentially non-parallel (as well as with weakly non-parallel) flows [1] and is an emerging and highly active area of research, to which a Minisymposium has been dedicated. Four invited contributions from three countries were presented, one summarizing experimental work and the rest presenting alternative numerical methodologies to solve the large eigenvalue problem resulting in the context of BiGlobal instability analysis. Applications addressed ranged from laminar and turbulent separation control (Avi Seifert, Tel-Aviv University), vortex instabilities (Michael Broadhurst, Imperial College London), and cavity flow hydrodynamic (Leo González, School of Naval Engineering, UP Madrid) and aeroacoustic (Javier de Vicente, School of Aeronautics, UP Madrid) instabilities. With the exception of the first author, whose contribution is outlined below, papers were submitted describing in detail the contents of the talks delivered.Vassilios Theofilis2010-10-28T08:16:05Z2016-04-20T13:49:34Zhttp://oa.upm.es/id/eprint/4716This item is in the repository with the URL: http://oa.upm.es/id/eprint/47162010-10-28T08:16:05ZNumerical considerations in spectral multidomain methods for BiGlobal instability analysis of open cavity configurationsA 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.Javier de Vicente BuendiaEusebio Valero SánchezVassilios Theofilis2010-09-27T08:23:59Z2014-09-22T10:14:45Zhttp://oa.upm.es/id/eprint/4265This item is in the repository with the URL: http://oa.upm.es/id/eprint/42652010-09-27T08:23:59ZOn instability and structural sensitivity of incompressible laminar separation bubbles in a flat-plate boundary layerThe separation of the laminar boundary layer under an adverse pressure gradient and its subsequent turbulent re-attachment, forming what is known as a "laminar separation bubble", is a technological problem of primary significance, with applications in aircraft wings, turbine blades and wind turbines. Despite extensive studies during the last century, many questions related to the appearance, structure and instability properties of laminar separation bubbles, still remain open. Some of these questions are first referred to in the works of Gault,1 and McCullough and Gault,2, 3 in which separation bubbles are classified according to their stream wise extension as \short" or \long". Tani4 indicated classification conditions but it was not until Gaster5 that a universal classification criterion was proposed, based on the free stream velocity, Us, the momentum thickness at separation, Os, and the ensuing momentum-thickness Reynolds number, Res .Following this classification, several investigators have proposed analogous criteria;6{8 however, the physical origin of a classification is not fully understood, and a generally accepted threshold for the change from one kind of bubble to the other does not exist presently.Daniel RodriguezVassilios Theofilis2010-05-20T08:59:11Z2016-04-20T12:02:35Zhttp://oa.upm.es/id/eprint/2293This item is in the repository with the URL: http://oa.upm.es/id/eprint/22932010-05-20T08:59:11ZBiglobal linear stability analysis for the flow in eccentric annular channels and a related geometryRecently, it has been observed that simple geometry characterized by a low level of symmetry present interesting peculiarities in the process of transition from laminar Poiseuille flow to turbulent flow. Examples of this type of geometry are eccentric channels and, more generally, parallel channels containing a narrow gap. In the present work, a global linear stability analysis for the flow in this class of geometry has been performed. The problem is discretized through spectral collocation and the eigenvalue problem has been solved with the Arnoldi-method based algorithms and the QZ algorithm. Since no numerical studies of this type have yet been performed to address the issue of transition in this geometry, the codes have been validated toward results obtained in simplified geometries _e.g., concentric annular channel and square channel_. The eigenvalue spectra of the Poiseuille flow in eccentric channels and a U-shaped channel have then been computed and analyzed for a wide range of geometric parameters. After comparison with spectra typical of channel flow and pipe flow it is shown that an additional linear mechanism of instability is present, related to the spanwise variation of the laminar velocity profile.Elia MerzariSheng WangHisashi NinokataVassilios Theofilis