Showing papers in "Theoretical and Computational Fluid Dynamics in 2011"

Applications of the dynamic mode decomposition

Abstract: The decomposition of experimental data into dynamic modes using a data-based algorithm is applied to Schlieren snapshots of a helium jet and to time-resolved PIV-measurements of an unforced and harmonically forced jet. The algorithm relies on the reconstruction of a low-dimensional inter-snapshot map from the available flow field data. The spectral decomposition of this map results in an eigenvalue and eigenvector representation (referred to as dynamic modes) of the underlying fluid behavior contained in the processed flow fields. This dynamic mode decomposition allows the breakdown of a fluid process into dynamically revelant and coherent structures and thus aids in the characterization and quantification of physical mechanisms in fluid flow.

Reduced order models for control of fluids using the Eigensystem Realization Algorithm

Abstract: As sensors and flow control actuators become smaller, cheaper, and more pervasive, the use of feedback control to manipulate the details of fluid flows becomes increasingly attractive. One of the challenges is to develop mathematical models that describe the fluid physics relevant to the task at hand, while neglecting irrelevant details of the flow in order to remain computationally tractable. A number of techniques are presently used to develop such reduced-order models, such as proper orthogonal decomposition (POD), and approximate snapshot-based balanced truncation, also known as balanced POD. Each method has its strengths and weaknesses: for instance, POD models can behave unpredictably and perform poorly, but they can be computed directly from experimental data; approximate balanced truncation often produces vastly superior models to POD, but requires data from adjoint simulations, and thus cannot be applied to experimental data. In this article, we show that using the Eigensystem Realization Algorithm (ERA) (Juang and Pappa, J Guid Control Dyn 8(5):620–627, 1985) one can theoretically obtain exactly the same reduced-order models as by balanced POD. Moreover, the models can be obtained directly from experimental data, without the use of adjoint information. The algorithm can also substantially improve computational efficiency when forming reduced-order models from simulation data. If adjoint information is available, then balanced POD has some advantages over ERA: for instance, it produces modes that are useful for multiple purposes, and the method has been generalized to unstable systems. We also present a modified ERA procedure that produces modes without adjoint information, but for this procedure, the resulting models are not balanced, and do not perform as well in examples. We present a detailed comparison of the methods, and illustrate them on an example of the flow past an inclined flat plate at a low Reynolds number.

On the birth of stall cells on airfoils

Abstract: Critical 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.

Spatially developing secondary instabilities in compressible swept airfoil boundary layers

Abstract: Two-dimensional eigenvalue analysis is used on a massive scale to study the spatial instabilities of compressible shear flows with two inhomogeneous directions. The main focus of the study is crossflow dominated swept-wing boundary layers although the methodology can also be applied to study other types of flows, such as the attachment-line flow. Certain unique aspects of formulating a spatial, two-dimensional eigenvalue problem for the secondary instability of finite amplitude crossflow vortices are discussed, namely, fixing the spatial growth direction unambiguously through a non-orthogonal formulation of the linearized disturbance equations. A primary test case used for parameter study corresponds to Numerical results are presented for the low-speed, NLF-0415(b) airfoil configuration as tested in the ASU Unsteady Wind Tunnel, wherein a spanwise periodic array of roughness elements was placed near the leading edge in order to excite stationary crossflow modes with a specified fundamental wavelength. The two classes of flow conditions selected for this analysis include those for which the roughness array spacing corresponds to either the naturally dominant crossflow wavelength, or a subcritical wavelength that serves to reduce the growth of the naturally excited dominant crossflow modes. Numerical predictions are compared with the measured database, both as indirect validation for the spatial instability analysis and to provide a basis for comparison with a higher Reynolds number, supersonic swept-wing configuration. Application of the eigenvalue analysis to the supersonic configuration reveals that a broad spectrum of stationary crossflow modes can sustain sufficiently strong secondary instabilities as to potentially cause transition over this configuration. In particular, the control mode itself, if initiated with too large an amplitude, may lead to an earlier transition.

Self-sustained global oscillations in a jet in crossflow

Abstract: A jet in crossflow with an inflow ratio of 3, based on the maximum velocity of the parabolic jet profile, is studied numerically. The jet is modeled as an inhomogeneous boundary condition at the crossflow wall. We find two fundamental frequencies, pertaining to self-sustained oscillations in the flow, using full nonlinear direct numerical simulation (DNS) as well as a modal decomposition into global linear eigenmodes and proper orthogonal decomposition (POD) modes; a high frequency which is characteristic for the shear-layer vortices and the upright vortices in the jet wake, and a low frequency which is dominant in the region downstream of the jet orifice. Both frequencies can be related to a region of reversed flow downstream of the jet orifice. This region is observed to oscillate predominantly in the wall-normal direction with the high frequency, and in the spanwise direction with the low frequency. Moreover, the steady-state solution of the governing Navier–Stokes equations clearly shows the horseshoe vortices and the corresponding wall vortices further downstream, and the emergence of a distinct counter-rotating vortex pair high in the free stream. It is thus found that neither the inclusion of the jet pipe nor unsteadiness is necessary to generate the characteristic counter-rotating vortex pair.

Transient growth and bypass transition in stenotic flow with a physiological waveform

Abstract: A direct analysis method is applied to compute optimal transient growth initial conditions for physiologically relevant pulsatile flows in a smooth axisymmetric stenosis with 75% occlusion. The flow waveform employed represents phase-average measurements obtained in the human common carotid artery. Floquet analysis shows that the periodic flow is stable to infinitesimal eigenmodal-type perturbations that would grow from one cycle to the next at the Reynolds numbers considered. However, the same flows display explosive transient growth of optimal disturbances, with our analysis predicting disturbance energy growths of order 1025 within half a pulse period at a mean bulk flow Reynolds number Re = 300, which is significantly lower than the physiological value of Re = 450 at this location. Direct numerical simulation at Re = 300 shows that when the base flow is perturbed a small amount with the optimal growth initial condition, the disturbance grows rapidly in time in agreement with the linear analysis, and saturates to provide a locally turbulent state within half a pulse period. This transition resulting from non-normal growth mechanisms shows the flow exhibits bypass transition to turbulence. Our analysis suggests that this route to localized turbulent states could be relatively common in human arterial flows.

Global instabilities in diverging channel flows

Abstract: A global stability study of a divergent channel flow reveals features not obtained hitherto by making either the parallel or the weakly non-parallel (WNP) flow assumption. A divergent channel flow is chosen for this study since it is the simplest spatially developing flow: the Reynolds number is constant downstream, and for a theoretical Jeffery–Hamel flow, the velocity profile obeys similarity. Even in this simple flow, the global modes are shown to be qualitatively different from the parallel or WNP. In particular, the disturbance modes are often not wave-like, and the local scale, estimated from a wavelet analysis, can be a function of both streamwise and normal coordinates. The streamwise variation of the scales is often very different from the expected linear variation. Given recent global stability studies on boundary layers, such spatially extended modes which are not wave-like are unexpected. A scaling argument for why the critical Reynolds number is so sensitive to divergence is offered.

Hypersonic viscous flow over large roughness elements

Abstract: Viscous flow over discrete or distributed surface roughness has great implications for hypersonic flight due to aerothermodynamic considerations related to laminar–turbulent transition. Current prediction capability is greatly hampered by the limited knowledge base for such flows. To help fill that gap, numerical computations are used to investigate the intricate flow physics involved. An unstructured mesh, compressible Navier–Stokes code based on the space–time conservation element, solution element (CESE) method is used to perform time-accurate Navier–Stokes calculations for two roughness shapes investigated in wind tunnel experiments at NASA Langley Research Center. It was found through 2D parametric study that at subcritical Reynolds numbers, spontaneous absolute instability accompanying by sustained vortex shedding downstream of the roughness is likely to take place at subsonic free-stream conditions. On the other hand, convective instability may be the dominant mechanism for supersonic boundary layers. Three-dimensional calculations for both a rectangular and a cylindrical roughness element at post-shock Mach numbers of 4.1 and 6.5 also confirm that no self-sustained vortex generation from the top face of the roughness is observed, despite the presence of flow unsteadiness for the smaller post-shock Mach number case.

Global modes in a confined impinging jet: application to heat transfer and control

Abstract: We investigate the stability and control of a plane, laminar jet impinging on a flat plate in a channel, a geometry used to cool down a hot wall with a cold air jet in many industrial configurations. The global stability analysis indicates that, even for a strong confinement, the two-dimensional (2-D) steady flow is unstable to three-dimensional (3-D), steady perturbations. In the simplest limit case where dilatation effects are neglected, we show that the development of the instability induces a significant spanwise modulation of the heat flux at the impacted wall. To control the leading global mode, we propose adjoint-based 3-D harmonic and 2-D steady forcing in the bulk or at the wall. We show for instance that the unstable mode is controllable using a spanwise uniform blowing at the upper wall, in a specific domain corresponding to the footprint of the upper recirculating bubble. These techniques are applied to a novel open-loop control, in which we introduce into the flow a small airfoil, modelled by the lift force it exerts on the flow.

On modelling transitional turbulent flows using under-resolved direct numerical simulations: the case of plane Couette flow

Abstract: Direct numerical simulations have proven of inestimable help to our understanding of the transition to turbulence in wall-bounded flows. While the dynamics of the transition from laminar flow to turbulence via localised spots can be investigated with reasonable computing resources in the domains of limited extent, the study of the decay of turbulence in conditions approaching those in the laboratory requires the consideration of domains so wide as to exclude the recourse to fully resolved simulations. Using Gibson’s C++ code Channel-Flow, we scrutinise the effects of a controlled lowering of the numerical resolution on the decay of turbulence in-plane Couette flow at a quantitative level. We show that the number of Chebyshev polynomials describing the cross-stream dependence can be drastically decreased while preserving all the qualitative features of the solution. In particular, the oblique turbulent band regime experimentally observed in the upper part of the transitional range is extremely robust. In terms of Reynolds numbers, the resolution lowering is seen to yield a regular downward shift of the upper and lower thresholds R t and R g where the bands appear and break down. The study is illustrated with the results of two preliminary experiments.

Transient growth mechanisms of low Reynolds number flow over a low-pressure turbine blade

Abstract: A direct transient growth analysis for three-dimensional perturbations to flow past a periodic array of T-106/300 low-pressure turbine fan blades is presented. The methodology is based on a singular value decomposition of the flow evolution operator, linearised about a steady or periodic base flow. This analysis yields the optimal growth modes. Previous work on global mode stability analysis of this flow geometry showed the flow is asymptotically stable, indicating a non-modal explanation of transition may be more appropriate. The present work extends previous investigations into the transient growth around a steady base flow, to higher Reynolds numbers and periodic base flows. It is found that the notable transient growth of the optimal modes suggests a plausible route to transition in comparison to modal growth for this configuration. The spatial extent and localisation of the optimal modes is examined and possible physical triggering mechanisms are discussed. It is found that for longer times and longer spanwise wavelengths, a separation in the shear layer excites the wake mode. For shorter times and spanwise wavelengths, smaller growth associated with excitation of the near wake are observed.

Control of a separated boundary layer: reduced-order modeling using global modes revisited

Abstract: The possibility of model reduction using global modes is readdressed, aiming at the controlling of a globally unstable separation bubble induced by a bump geometry. A combined oblique and orthogonal projection approach is proposed to design an estimator and controller in a Riccati-type feedback setting. An input–output criterion is used to appropriately select the modes of the projection basis. The full-state linear instability dynamics is shown to be successfully controlled by the feedback coupling with controllers of moderate degrees of freedom.

Modeling of optimal perturbations in flat plate boundary layer using global modes: benefits and limits

Abstract: The ability of capturing the noise amplifier dynamics of a boundary layer on a flat plate subjected to an adverse pressure gradient by means of a global modes strategy is numerically investigated. After a brief description of the mechanism regarding the exact optimal perturbation fields, the system is rewritten into an input–output framework. In order to achieve this, the input and output are derived from a direct-optimal growth computation through the perturbation fields at times t = 0 and t = topt where the wave packet reaches a maximum energy growth. By expanding the flow disturbance variables as a summation of global modes, their observability, controllability, and truncation error are assessed. It is shown that the truncation error decreases by taking into account highly temporally damped global modes. Therefore, we propose the ability of a reduced-order model based on global modes to capture the full dynamics of the stable subspace, under the consideration of a large number of modes.

Control of Tollmien–Schlichting instabilities by finite distributed wall actuation

Abstract: Tollmien–Schlichting waves are one of the key mechanisms triggering the laminar-turbulent transition in a flat-plate boundary-layer flow. By damping these waves and thus delaying transition, skin friction drag can be significantly decreased. In this simulation study, a wall segment is actuated according to a control scheme based on a POD-Galerkin model driven extended Kalman filter for state estimation and a model predictive controller to dampen TS waves by negative superposition based on this information. The setup of the simulation is chosen to resemble actuation with a driven compliant wall, such as a membrane actuator. Most importantly, a method is proposed to integrate such a localized wall actuation into a Galerkin model.

Closed-loop bluff-body wake stabilization via fluidic excitation

Abstract: This article describes an experimental study aimed at stabilizing the wake of a shedding bluff-body by means of closed-loop active flow control at low Reynolds numbers. A D-shaped (6.5 mm thick) cylinder was used to allow a direct wake interaction rather than mixed wake-boundary-layer separation control. The fluidic actuators, installed inside the thin body, were ideally located at the separation locations, i.e., the trailing edges’ upper and lower corners. The wake unsteadiness was monitored by a pair of hot wires (HWs), while a single surface-mounted hot-film (HF) sensor was used as a frequency and phase reference for closed-loop control. The HF signal was contaminated by noise. Hence, a technique for real-time tracking of a low signal-to-noise ratio (SNR) signal was necessary. This was achieved by means of a Phase-Locked Loop (PLL), common in communications systems. The closed-loop scheme was based on real-time measurement of the wake-state, using the surface-mounted HF sensor, and control authority imposed by the fluidic actuators. By using opposition control at frequencies close to the natural vortex shedding frequency (VSF), it was possible to significantly reduce the wake unsteadiness. Applying the same approach, but sensing the wake HW signal, rather than the surface-mounted HF signal, as the controller input did not result in wake stabilization. On the contrary, the unsteadiness increased at all the tested conditions. It is expected that a similar approach would work at much higher Reynolds numbers as well, as long as a clearly identifiable and nominally 2D vortex shedding occurs, even when the background flow is fully turbulent.

Lyapunov analysis for fully developed homogeneous isotropic turbulence

Abstract: The present work studies the isotropic and homogeneous turbulence for incompressible fluids through a specific Lyapunov analysis. The analysis consists in the calculation of the velocity fluctuation through the Lyapunov theory applied to the local deformation using the Navier-Stokes equations, and in the study of the mechanism of energy cascade through the finite scale Lyapunov analysis of the relative motion between two particles. The analysis provides an explanation for the mechanism of energy cascade, leads to the closure of the von Karman-Howarth equation, and describes the statistics of the velocity difference. Several tests and numerical results are presented.

Feedback control of vortex shedding from an inclined flat plate

Abstract: Open- and closed-loop control of vortex shedding in two-dimensional flow over a flat plate at high angle of attack is numerically investigated at a Reynolds number of 300. Unsteady actuation is modeled as a body force near the leading or trailing edge and is directed either upstream or downstream. For moderate angles of attack, sinusoidal forcing at the natural shedding frequency results in phase locking, with a periodic variation of lift at the same frequency, leading to higher unsteady lift than the natural shedding. However, at sufficiently high angles of attack, a subharmonic of the forcing frequency is also excited and the average lift over the forcing period varies from cycle-to-cycle in a complex manner. It is observed that the periods with the highest averaged lift are associated with particular phase differences between the forcing and the lift, but that this highest-lift shedding cycle is not always stably maintained with open-loop forcing. We design a feedback algorithm to lock the forcing with the phase shift associated with the highest period-averaged lift. It is shown that the compensator results in a stable phase-locked limit cycle for a broader range of forcing frequencies than the open-loop control, and that it is able to stabilize otherwise unstable high-lift limit cycles that cannot be obtained with open-loop control. For example, at an angle of attack of 40°, the feedback controller can increase the averaged magnitude of force on the plate by 76% and increase the averaged lift coefficient from 1.33 to 2.43.

Classification of instability modes in a model of aluminium reduction cells with a uniform magnetic field

Abstract: A unified view on the interfacial instability in a model of aluminium reduction cells in the presence of a uniform, vertical, background magnetic field is presented. The classification of instability modes is based on the asymptotic theory for high values of parameter β, which characterises the ratio of the Lorentz force based on the disturbance current, and gravity. It is shown that the spectrum of the travelling waves consists of two parts independent of the horizontal cross-section of the cell: highly unstable wall modes and stable or weakly unstable centre, or Sele’s modes. The wall modes with the disturbance of the interface being localised at the sidewalls of the cell dominate the dynamics of instability. Sele’s modes are characterised by a distributed disturbance over the whole horizontal extent of the cell. As β increases these modes are stabilized by the field.

A new development of the dynamic procedure in large-eddy simulation based on a Finite Volume integral approach. Application to stratified turbulence

Abstract: A Finite Volume-based large-eddy simulation method is proposed along with a suitable extension of the dynamic modelling procedure that takes into account for the integral formulation of the governing filtered equations. Discussion about the misleading interpretation of FV in some literature is addressed. Then, the classical Germano identity is congruently rewritten in such a way that the determination of the modelling parameters does not require any arbitrary averaging procedure and thus retains a fully local character. The numerical modelling of stratified turbulence is the specific problem considered in this study, as an archetypal of simple geophysical flows. The original scaling formulation of the dynamic sub-grid scale model proposed by Wong and Lilly (Phys. Fluids 6(6), 1994) is suitably extended to the present integral formulation. This approach is preferred with respect to traditional ones since the eddy coefficients can be independently computed by avoiding the addition of unjustified buoyancy production terms in the constitutive equations. Simple scaling arguments allow us not to use the equilibrium hypothesis according to which the dissipation rate should equal the sub-grid scale energy production. A careful a priori analysis of the relevance of the test filter shape as well as the filter-to-grid ratio is reported. Large-eddy simulation results are a posteriori compared with a reference pseudo-spectral direct numerical solution that is suitably post-filtered in order to have a meaningful comparison. In particular, the spectral distribution of kinetic and thermal energy as well as the viscosity and diffusivity sub-grid scale profiles are illustrated. The good performances of the proposed method, in terms of both evolutions of global quantities and statistics, are very promising for the future development and application of the method.

On the Reynolds number scaling of vorticity production at no-slip walls during vortex-wall collisions

Abstract: Recently, numerical studies revealed two different scaling regimes of the peak enstrophy Z and palinstrophy P during the collision of a dipole with a no-slip wall [Clercx and van Heijst, Phys. Rev. E 65, 066305, 2002]: Z ∝ Re0.8 and P ∝ Re2.25 for 5 × 102 ≤ Re ≤ 2 × 104 and Z ∝ Re0.5 and P ∝ Re1.5 for Re ≥ 2 × 104 (with Re based on the velocity and size of the dipole). A critical Reynolds number Rec(here, Rec ≈ 2 × 104) is identified below which the interaction time of the dipole with the boundary layer depends on the kinematic viscosity ν. The oscillating plate as a boundary-layer problem can then be used to mimick the vortex-wall interaction and the following scaling relations are obtained: Z ∝ Re^3/4, P ∝ Re^9/4, and dP/dt ∝ Re11/4 in agreement with the numerically obtained scaling laws. For Re ≥ Rec the interaction time of the dipole with the boundary layer becomes independent of the kinematic viscosity and, applying flat-plate boundary-layer theory, this yields: Z ∝ Re1/2 and P ∝ Re3/2.

Signalling problem in absolutely unstable systems

Abstract: The dynamics of unstable systems crucially depends on the nature of the instability, either convective or absolute. The signalling problem, which is the study of the spatial response to a localized time-harmonic forcing, is generally believed to be relevant only for stable or convectively unstable systems and to be ill-posed for absolutely unstable systems, where the self-sustained perturbations grow faster than the forced harmonic response. The present investigation shows that the signalling problem may still be well posed for media displaying absolutely unstable regions. Considering weakly spatially inhomogenous systems, conditions are derived for the validity of the signalling problem. The complete spatial response to harmonic forcing is first analytically derived in terms of asymptotic approximations and then confirmed by direct numerical simulations.

Special issue on global flow instability and control

Abstract: This 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.

On the downstream development and breakup of systems of trailing-line vortices

Abstract: The downstream evolution of two configurations of trailing-line vortex systems is considered and analysed from the point of view of bi-global instability. The results lead to predictions for the breakup of the systems considered, based primarily on stability analysis. Throughout, the analysis is entirely rational from the theoretical (asymptotic, large Reynolds number) point of view, with a relatively long developmental lengthscale in the streamwise direction for the base flow, and a relatively short streamwise wavelength for the bi-global stability analysis. As such, the stability modes are inviscid in nature, and therefore likely to be one of the dominant instability mechanisms. The issue of adverse streamwise freestream pressure gradients is also addressed, and it is suggested that these can lead to a rapid breakdown/up of a vortex system, analogous to the axisymmetric case discussed by Hall (Ann Rev Fluid Mech 4:195–218, 1972).

Global stability of separated flows: subsonic flow past corners

Abstract: The triple-deck equations for the steady subsonic flow past a convex corner are solved numerically using a novel technique based on Chebychev collocation in the direction normal to the body combined with finite differences in the direction along the flow. The resulting set of nonlinear algebraic equations are solved with Newton linearization and using the GMRES method for the solution of the linear system of equations. The stability of the computed steady flows is then examined using global stability analysis. It is found that for small corner angles, the Tollmien–Schlichting modes are globally unstable and these persist to larger corner angles. Multiple steady state solutions also exist beyond a critical corner angle but these are globally unstable because of the presence of the Tollmien–Schlichting modes.

Stratified wakes, the high Froude number approximation, and potential flow

Abstract: Properties of a steady wake generated by a body moving uniformly at constant depth through a stratified fluid are studied as a function of two parameters inserted into the linearized equations of motion. The first parameter, μ, multiplies the along-track gradient term in the source equation. When formal solutions for an arbitrary buoyancy frequency profile are written as eigenfunction expansions, one finds that the limit μ → 0 corresponds to a high Froude number approximation accompanied by a substantial reduction in the complexity of the calculation. For μ = 1, upstream effects are present and the eigenvalues correspond to critical speeds above which transverse waves disappear for any given mode. For sufficiently high modes, the high Froude number approximation is valid. The second tracer multiplies the square of the buoyancy frequency term in the linearized conservation of mass equation and enables direct comparisons with the limit of potential flow. Detailed results are given for the simplest possible profile, in which the buoyancy frequency is independent of depth; emphasis is placed upon quantities that can, in principle, be experimentally measured in a laboratory experiment. The vertical displacement field is written in terms of a stratified wake form factor \({\mathbb{H}}\) , which is the sum of a wavelike contribution that is non-zero downstream and an evanescent contribution that appears symmetrically upstream and downstream. First- and second-order cross-track moments of \({\mathbb{H}}\) are analyzed. First-order results predict enhanced upstream vertical displacements. Second-order results expand upon previous predictions of wavelike resonances and also predict evanescent resonance effects.

Effects of non-uniform heating on a variable viscosity Rayleigh–Bénard problem

Abstract: This study presents a natural convection problem with a temperature-dependent viscosity fluid, driven by buoyancy and influenced by horizontal temperature gradients. A numerical linear stability analysis of the stationary solutions is studied. The horizontal temperature gradients tend to localize motion near the warmer zones and favour pattern formation in the direction perpendicular to the gradient. In fact, the problem is almost 2D in the uniform heating case, but becomes totally 3D in the non-uniform heating case.

Variable-density jet flows induced by concentrated sources of momentum and energy

Abstract: The planar and axisymmetric variable-density flows induced in a quiescent gas by a concentrated source of momentum that is simultaneously either a source or a sink of energy are investigated for application to the description of the velocity and temperature far fields in laminar gaseous jets with either large or small values of the initial jet-to-ambient temperature ratio. The source fluxes of momentum and heat are used to construct the characteristic scales of velocity and length in the region where the density differences are of the order of the ambient density, which is slender for the large values of the Reynolds number considered herein. The problem reduces to the integration of the dimensionless boundary-layer conservation equations, giving a solution that depends on the gas transport properties but is otherwise free of parameters. The boundary conditions at the jet exit for integration are obtained by analysing the self-similar flow that appears near the heat source in planar and axisymmetric configurations and also near the heat sink in the planar case. Numerical integrations of the boundary-layer equations with these conditions give solutions that describe accurately the velocity and temperature fields of very hot planar and round jets and also of very cold plane jets in the far field region where the density and temperature differences are comparable to the ambient values. Simple scaling arguments indicate that the point source description does not apply, however, to cold round jets, whose far field region is not large compared with the jet development region, as verified by numerical integrations.

Flow control using bifrequency motion

Abstract: We used a second-order approximation for the periodic lift coefficient of a circular cylinder under monofrequency and bifrequency cross-flow motions. Two lock-in modes exist under monofrequency fundamental (i.e., near the Strouhal number) motion. In the first mode, the work is done by the flow on the cylinder, whereas in the second mode the work is done by the cylinder on the flow. Under monofrequency superharmonic (i.e., near three times the Strouhal number) motion, the work is always done on the flow. We then replaced the monofrequency motions by a bifrequency one, consisting of a fundamental term combined with a small-magnitude superharmonic term. We examined the effect of the magnitude and phase of the superharmonic motion term on the two modes of lock-in which we obtained when only the fundamental motion term is applied, considering two different frequencies that belonged to the two lock-in modes. Under the bifrequency motion, the work can be done on the flow or on the cylinder. This can be controlled using the superharmonic motion term, even when its magnitude is 5% of magnitude of the fundamental motion term. Other flow variables, such as the magnification of the lift, can be remarkably altered through the added superharmonic motion term. The phase of the third superharmonic lift-coefficient component relative to the fundamental one is the most responsive variable to the phase of the superharmonic motion component relative to the fundamental one.