Linear modal instabilities of hypersonic flow over an elliptic cone

Steady laminar flow over a rounded-tip 2 : 1 elliptic cone of 0.86 m length at zero angle of attack and yaw has been computed at Mach number 7.45 and unit Reynolds number Re′ = 1.015 × 107 m−1. The flow conditions are selected to match the planned flight of the Hypersonic Flight Research Experimentation HIFiRE-5 test geometry at an altitude of 21.8 km. Spatial linear BiGlobal modal instability analysis of this flow has been performed at selected streamwise locations on planes normal to the cone symmetry axis, resolving the entire flow domain in a coupled manner while exploiting flow symmetries. Four amplified classes of linear eigenmodes have been unravelled. The shear layer formed near the cone minor-axis centreline gives rise to amplified symmetric and antisymmetric centreline instability modes, classified as shear-layer instabilities. At the attachment line formed along the major axis of the cone, both symmetric and antisymmetric instabilities are also discovered and identified as boundary-layer second Mack modes. In both cases of centreline and attachment-line modes, symmetric instabilities are found to be more unstable than their antisymmetric counterparts. Furthermore, spatial BiGlobal analysis is used for the first time to resolve oblique second modes and cross-flow instabilities in the boundary layer between the major- and minor-axis meridians. Contrary to predictions for the incompressible regime for swept infinite wing flow, the cross-flow instabilities are not found to be linked to the attachment-line instabilities. In fact, cross-flow modes peak along most of the surface of the cone, but vanish towards the attachment line. On the other hand, the leading oblique second modes peak near the leading edge and their associated frequencies are in the range of the attachment-line instability frequencies. Consequently, the attachment-line instabilities are observed to be related to oblique second modes at the major-axis meridian. The linear amplification of centreline and attachment-line instability modes is found to be strong enough to lead to laminar–turbulent flow transition within the length of the test object. The predictions of global linear theory are compared with those of local instability analysis, also performed here under the assumption of locally parallel flow, where use of this assumption is permissible. Fair agreement is obtained for symmetric centreline and symmetric attachment-line modes, while for all other classes of linear disturbances use of the proposed global analysis methodology is warranted for accurate linear instability predictions

Investigation of the Global Mode in Swirling Combustor Flows: Experimental Observations and Local and Global Stability Analysis

Self-excited helical flow oscillations are frequently observed in gas turbine combustors. In the present work a new approach is presented tackling this phenomenon with stability concepts. Three reacting swirling flows are investigated. All of them undergo vortex breakdown, but only two of them show self-excited global flow oscillations at well-defined frequencies. The oscillations feature a precession of the vortex core and synchronized Kelvin-Helmholtz instabilities in the shear layers. Based on the mean flow fields, local and global linear hydrodynamic stability analyses are carried out. The dampening effect of the Reynolds stresses is accounted for by an eddy viscosity estimated from the experimental results. Both the local and the global analysis successfully identify linear global modes as being responsible for the large-scale flow oscillations and successfully predict their frequency. However, only the global analysis accurately predicts a globally stable flow field for the case without the oscillation, while the local analysis overpredicts the global growth rate. The predicted spatial distribution of the amplitude functions agree very well to the experimentally identified global mode. This successful application of global and local stability concepts to a complex and practically relevant flow configuration paves the way for the application of theoretically-founded passive and active control strategies

On the Origins of Three-Dimensionality And Unsteadiness in the Laminar Separation Bubble

We 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

Biglobal linear stability analysis for the flow in eccentric annular channels and a related geometry

Recently, 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

Spatial Stability of Incompressible Attachment-Line Flow

Linear 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

Transient growth analysis of the flow past a circular cylinder

We 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

On the Resolution of Critical Flow Regions in Inviscid Linear And Nonlinear Instability Calculations

Numerical 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

Monitoring, Awareness and Reflection in Blended Technology Enhanced Learning: a Systematic Review

Education is experiencing a paradigm shift towards blended learning models in technology-enhanced learning (TEL). Despite the potential benefits of blended learning, it also entails additional complexity in terms of monitoring, awareness and reflection, as learning happens across different spaces and modalities. In recent years, literature on Learning Analytics (LA) and Educational Data Mining (EDM) has gained momentum and started to address the issue. To provide a clear picture of the current state of the research on the topic and to outline open research gaps, this paper presents a systematic literature review of the state-of-the-art of research in LA and EDM on monitoring, awareness and reflection in blended TEL scenarios. The search included six main academic databases in TEL that were enriched with the proceedings of the workshop on ’Awareness and Reflection in TEL’ (ARTEL), resulting in 1089 papers out of which 40 papers were included in the final analysis