Linear instability characteristics of incompressible coaxial jets

The present study deals with the local linear instability of axisymmetric coaxial jets with a duct wall separating the two streams. The flow is assumed to be locally parallel, inviscid and incompressible. The objective of the work is to understand how the various parameters describing this flow geometry (i.e. boundary layers thicknesses at the exit, velocity ratio, wall thickness) may influence the instability of the flow and, in particular, the convective/absolute instability transition. A specific family of profiles is chosen for the modelling of the mean undisturbed flow and a spatial stability analysis is performed in order to identify the unstable modes and to assess how they are affected by the wake region behind the wall. An absolutely unstable mode is found, and its characteristics, depending on the velocity ratio and shear layers thicknesses, are determined. Results show that the absolute unstable mode is present only for a limited range of velocity ratios and that the corresponding frequency is almost constant if normalized with the mean velocity and wake thickness. This frequency value and the extension of the range of velocity ratios is similar to those found in the experiments on a similar geometry. Finally, a specific velocity ratio is found that maximizes the region at the jet exit for which an absolute instability behind the wall is present. This may increase the possibility for the onset of a global mode that may sustain the instability of the whole jet, enhancing considerably the mixing and entrainment characteristics between the two streams.     

Spanwise effects on instabilities of compressible flow over a long rectangular cavity

The stability properties of two-dimensional (2D) and three-dimensional (3D) compressible flows over a rectangular cavity with length-to-depth ratio of \(L/D=6\) are analyzed at a free-stream Mach number of \(M_\infty =0.6\) and depth-based Reynolds number of \(Re_D=502\). In this study, we closely examine the influence of three-dimensionality on the wake mode that has been reported to exhibit high-amplitude fluctuations from the formation and ejection of large-scale spanwise vortices. Direct numerical simulation (DNS) and bi-global stability analysis are utilized to study the stability characteristics of the wake mode. Using the bi-global stability analysis with the time-averaged flow as the base state, we capture the global stability properties of the wake mode at a spanwise wavenumber of \(\beta =0\). To uncover spanwise effects on the 2D wake mode, 3D DNS are performed with cavity width-to-depth ratio of \(W/D=1\) and 2. We find that the 2D wake mode is not present in the 3D cavity flow with \(W/D=2\), in which spanwise structures are observed near the rear region of the cavity. These 3D instabilities are further investigated via bi-global stability analysis for spanwise wavelengths of \(\lambda /D=0.5{-}2.0\) to reveal the eigenspectra of the 3D eigenmodes. Based on the findings of 2D and 3D global stability analysis, we conclude that the absence of the wake mode in 3D rectangular cavity flows is due to the release of kinetic energy from the spanwise vortices to the streamwise vortical structures that develops from the spanwise instabilities.     

Direct numerical simulation and global stability analysis of three-dimensional instabilities in a lid-driven cavity

The first bifurcation in a lid-driven cavity characterized by three-dimensional Taylor–Görtler-Like instabilities is investigated for a cubical cavity with spanwise periodic boundary conditions at Re=1000. The modes predicted by a global linear stability analysis are compared to the results of a direct numerical simulation. The amplification rate, and the shape of the three-dimensional perturbation fields from the direct numerical simulation are in very good agreement with the characteristics of the steady S1 mode from the stability analysis, showing that this mode dominates the other unstable unsteady modes. To cite this article: J. Chicheportiche et al., C. R. Mecanique 336 (2008).     

Self-sustained global oscillations in a jet in crossflow

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?CStokes 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.     

A numerical investigation of wall effects in three‐dimensional,laminar flow over a backward facing step with a constant aspect and expansion ratio

The wall effects are investigated in the three‐dimensional laminar flow over a backward‐facing step. For this purpose, a numerical experiment is designed under actual laboratory conditions. The aspect ratio of the computational domain is 1:40 and the expansion ratio is 1:2. The Reynolds number ranges from 100 to 950. The governing equations are the steady state, isothermal and incompressible Navier–Stokes equations for Newtonian fluids. They are solved with a homemade Galerkin finite element code. The computations are validated with data from available laboratory and numerical experiments. The results focus on the variation of both velocity profiles and lengths of eddies along the lower and upper wall in the spanwise direction. Calculated streamlines in the streamwise and transverse direction show how the flow is distorted near the lateral wall and how it develops up to the plane of symmetry. The study of skin friction lines along the top and bottom wall of the domain reveals a flow that takes place in the spanwise direction. This spanwise component of the flow becomes more dominant with increasing Reynolds number and is impossible to be sustained at steady state for Reynolds numbers higher than 950 for this particular geometry. Copyright © 2012 John Wiley & Sons, Ltd.     

Control of a submerged jet in a thin rectangular cavity

An innovative method is presented for control of an oscillatory turbulent jet in a thin rectangular cavity with a thickness to width ratio of 0.16. Jet flow control is achieved by mass injection of a secondary jet into the region above the submerged primary jet nozzle exit and perpendicular to the primary nozzle axis. An experimental model, a 2-D and a 3-D computational fluid dynamics (CFD) model are used to investigate the flow characteristics under various secondary injection mass flow rates and injection positions. Two-dimensional laser Doppler anemometry (LDA) measurements are compared with results from the CFD models, which incorporate a standard k–ε turbulence model or a 2-D and 3-D realisable k–ε model. Experimental results show deflection angles up to 23.3° for 24.6% of relative secondary mass flow are possible. The key to high jet control sensitivity is found to be lateral jet momentum with the optimum injection position at 12% of cavity width (31.6% of the primary nozzle length) above the primary nozzle exit. CFD results also show that a standard k–ε turbulence closure with nonequilibrium wall functions provides the best predictions of the flow.     

Computational studies of inertia-gravity waves radiated from upper tropospheric jets

The generation and physical characteristics of inertia-gravity waves radiated from an unstable forced jet at the tropopause are investigated through high-resolution numerical simulations of the three-dimensional Navier–Stokes anelastic equations. Such waves are induced by Kelvin–Helmholtz instabilities on the flanks of the inhomogeneously stratified jet. From the evolution of the averaged momentum flux above the jet, it is found that gravity waves are continuously radiated after the shear-stratified flow reaches a quasi-equilibrium state. The time–vertical coordinate cross-sections of potential temperature show phase patterns indicating upward energy propagation. The sign of the momentum flux above and below the jet further confirms this, indicating that the group velocity of the generated waves is pointing away from the jet core region. Space–time spectral analysis at the upper flank level of the jet shows a broad spectral band, with different phase speeds. The spectra obtained in the stratosphere above the jet show a shift toward lower frequencies and larger spatial scales compared to the spectra found in the jet region. The three-dimensional character of the generated waves is confirmed by analysis of the co-spectra of the spanwise and vertical velocities. Imposing the background rotation modifies the polarization relation between the horizontal wind components. This out-of-phase relation is evidenced by the hodograph of the horizontal wind vector, further confirming the upward energy propagation. The background rotation also causes the co-spectra of the waves high above the jet core to be asymmetric in the spanwise modes, with contributions from modes with negative wavenumbers dominating the co-spectra. Dedicated to the memory of our colleague Dr. Binson Joseph     

Experimental investigation of the unsteady structure of a transitional plane wall jet

 A laminar wall jet undergoing transition is investigated using the particle image velocimetry (PIV) technique. The plane wall jet is issued from a rectangular channel, with the jet-exit velocity profile being parabolic. The Reynolds number, based on the exit mean velocity and the channel width, is 1450. To aid the understanding of the global flow features, laser-sheet/smoke flow visualizations are performed along streamwise, spanwise, and cross-stream directions. Surface pressure measurements are made to correlate the instantaneous vorticity distribution with the surface pressure fluctuations. The instantaneous velocity and vorticity field measurements provide the basis for understanding the formation of the inner-region vortex and the subsequent interactions between the outer-region (free-shear-layer region) and inner-region (boundary-layer region) vortical structures. Results show that under the influence of the free-shear-layer vortex, the local boundary layer becomes detached from the surface and inviscidly unstable, and a vortex is formed in the inner region. Once this vortex has formed, the free-shear-layer vortex and the inner-region vortex form a vortex couple and convect downstream. The mutual interactions between these inner- and outer-region vortical structures dominate the transition process. Farther downstream, the emergence of the three-dimensional structure in the free shear layer initiates complete breakdown of the flow. Received: 8 November 1995/Accepted: 6 November 1996     

On the stability of plane parallel viscoelastic shear flows in the limit of infinite Weissenberg and Reynolds numbers

Elastic effects on the hydrodynamic instability of inviscid parallel shear flows are investigated through a linear stability analysis. We focus on the upper convected Maxwell model in the limit of infinite Weissenberg and Reynolds numbers. We study the effects of elasticity on the instability of a few classes of simple parallel flows, specifically plane Poiseuille and Couette flows, the hyperbolic-tangent shear layer and the Bickley jet.The equation for stability is derived and solved numerically using the spectral Chebyshev collocation method. This algorithm is computationally efficient and accurate in reproducing the eigenvalues. We consider flows bounded by walls as well as flows bounded by free surfaces. In the inviscid, nonelastic case all the flows we study are unstable for free surfaces. In the case of wall bounded flow, there are instabilities in the shear layer and Bickley jet flows. In all cases, the effect of elasticity is to reduce and ultimately suppress the inviscid instability.     

Features of the supercritical transition in the wake of a circular cylinder

The features of the wake behind a uniform circular cylinder atRe=200, which is just beyond the critical Reynolds number of 3-D transition, are investigated in detail by direct numerical simulations by solving 3-D incompressible Navier-Stokes equations using mixed spectral-spectral-element method. The high-order splitting algorithm based on the mixed stiffly stable scheme is employed in the time discretization. Due to the nonlinear evolution of the secondary instability of the wake, the spanwise modes with different wavelengths emerge. The spanwise characteristic length determines the transition features and global properties of the wake. The existence of the spanwise phase difference of the primary vortices shedding is confirmed by Fourier analysis of the time series of the spanwise vorticity and attributed to the dominant spanwise mode. The spatial energy distributions of various modes and the velocity profiles in the near wake are obtained. The numerical results indicate that the near wake is in 3-D quasi-periodic laminar state with transitional behaviors at this supercritical Reynolds number. The project supported by the State Key Fundamental Research Project of “Large Scale Scientific Computation Research” (G199903281)     

Dielectric-barrier-discharge vortex generators: characterisation and optimisation for flow separation control

We investigated the use of dielectric-barrier-discharge plasma actuators as vortex generators for flow separation control applications. Plasma actuators were placed at a yaw angle to the oncoming flow, so that they produced a spanwise wall jet. Through interaction with the oncoming boundary layer, this created a streamwise longitudinal vortex. In this experimental investigation, the effect of yaw angle, actuator length and plasma-induced velocity ratio was studied. Particular attention was given to the vortex formation mechanism and its development downstream. The DBD plasma actuators were then applied in the form of co-rotating and counter-rotating vortex arrays to control flow separation over a trailing-edge ramp. It was found that the vortex generators were successful in reducing the separation region, even at plasma-to-free-stream velocity ratios of less than 10%.     

Receptivity mechanisms for Görtler vortex modes

The receptivity problem for Görtler vortices induced by wall roughness or freestream disturbances is reviewed. To date, receptivity studies for this problem have been exclusively linear in character and here we show how the roughness and freestream disturbance mechanisms can each play dominant or inconsequential roles as possible routes to transition. The importance of each process is dependent on the exact situation at hand. For example, distributed wall-roughness elements tend to be more important in the generation of O(1) wave-number vortices than are isolated roughness patches whilst variations in the freestream velocity can easily provoke high wave-number disturbances on which roughness distributions typically have negligible effect.It has only been in recent times that the influence a spanwise component of the underlying basic boundary-layer flow may have on the Görtler mechanism has come to be appreciated. In some new computations we show that the imposition of such a spanwise component can lead to an increase in the coupling coefficient (a measure of the efficiency of a generating process) for modes provoked by wall roughness. However, such crossflow tends to reduce the global amplification rate of the most unstable mode so has the overall effect of restricting vortex growth downstream of any roughness element. We also demonstrate how the nonparallelism of Görtler vortices implies that conclusions concerning vortex receptivity properties can only be drawn after taking full account of upstream conditions and the precise form of the generating mechanism but it appears that for a large class of flows distributed wall forcing is more important in the provocation of modes than are either isolated roughness or freestream disturbances.This work was completed whilst APB was on study leave at the School of Mathematics, University of New South Wales, Sydney. He is indebted to the Royal Society of London and the Australian Research Council without whose grants (the latter to Dr. Peter Blennerhassett) his visit would not have been possible. In addition he is grateful to the staff and students of New College, UNSW for their provision of a Visiting Fellowship and to the School of Mathematics for their hospitality.     

Absolute, convective, and global instability of a magnetic liquid jet

An infinite or semi-infinite jet of non-conductive magnetic liquid in a uniform longitudinal magnetic field can be absolutely or convectively unstable for different values of the flow parameters. Though the higher field inhibits the absolute instability, this inhibition is maximum at some field intensity. A critical value of the surface tension exists, above which the instability is absolute for any intensity of the field. If the jet has a large but finite length and proper boundary conditions are held at its beginning and end, it is always globally unstable. The unstable global mode is based on a pair of waves that propagate in opposite directions and reflect from one into the other at the flow boundaries.     

Three-dimensional numerical simulations of cross-flow around four cylinders in an in-line square configuration

This paper presents a numerical study of three-dimensional (3-D) laminar flow around four circular cylinders in an in-line square configuration. The investigation focuses on effects of spacing ratio (L/D) and aspect ratio (H/D) on 3-D flow characteristics, and the force and pressure coefficients of the cylinders. Extensive 3-D numerical simulations were performed at Reynolds number of 200 for L/D from 1.6 to 5.0 at H/D=16 and H/D from 6 to 20 at L/D=3.5. The results show that the 3-D numerical simulations have remedied the inadequacy of 2-D simulations and the results are in excellent agreement with the experimental results. The relation between 3-D flow patterns and pressure characteristics around the four cylinders is examined and discussed. The critical spacing ratio for flow pattern transformation was found to be L/D=3.5 for H/D=16, while a bistable wake pattern was observed at L/D=1.6 for the same aspect ratio. Moreover, a transformation of flow pattern from a stable shielding flow pattern to a vortex shedding flow pattern near the middle spanwise positions of the cylinders was observed and was found to be dependent on the aspect ratio, spacing ratio, and end wall conditions. Due to the highly 3-D nature of the flows, different flow patterns coexist over different spanwise positions of the cylinders even for the same aspect ratio. It is concluded that spacing ratio, aspect ratio, and the no-slip end wall condition have important combined effects on free shear layer development of the cylinders and hence have significant effects on the pressure field and force characteristics of the four cylinders with different spacing ratios and aspect ratios.     

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

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.     

Effect of the domain spanwise periodic length on the flow around a circular cylinder

We assess the effect of the choice of spanwise periodic length on simulations of the flow around a fixed circular cylinder. The Reynolds number is set to 400 because, at this value, both lift coefficient and shedding frequency show significant drop due to three-dimensional flow structures. From the analysis of the three-dimensionalities of the wake and of the integral quantities such as Strouhal number, RMS of lift coefficient and energy contained in the three-dimensional portion of the flow we obtain an estimate of the minimum spanwise length to satisfactorily represent the flow. Furthermore, we observe a distinct wake behavior when the spanwise length is approximately the mode B instability wavelength.     

The effect of a single vortex generator jet on the characteristics of a turbulent boundary layer

A flat plate experiment was performed in a water tunnel to determine the effects of a vortex generator jet on the characteristics of a turbulent boundary layer at various wall normal locations. The results show that the characteristic distributions of the turbulent fluctuation quantities are nearly unaffected by the induced vortex structures neither in the steady nor in the dynamic blowing case. The shear layer interaction between the turbulent main flow and the jet flow produces less turbulent fluctuations than it is expected from a turbulent free jet flow. Thus, the mixing process of this flow control strategy is based only on a large-scale momentum transport superimposed by the turbulent fluctuation quantities. This allows a separation of scales for physical interpretation and numerical simulations.     

Temporal stability of a particle-laden jet

The temporal instability of a particle-laden jet was investigated numerically which took into consideration the parametric effects of jet parameter, B, jet Reynolds number, Re_j, particle mass loading, Z and Stokes number, St. The linear stability theory was used to derive the instability equations of a viscous particle-laden jet flow. The single-phase instability of a top-hat jet was then calculated and compared with the available analytical theories. The numerical results agree well with the analytical results for both the axisymmetric (n = 0) and first azimuthal (n = 1) modes. The results show that the first azimuthal mode disturbance is usually more unstable than that of the axisymmetric mode. But the axisymmetric mode disturbance can be more unstable when Z is high enough (i.e., Z ? 0.1). The higher B and Re_j are, the more unstable the particle-laden jet will be. The existence of particles enhances the flow stability. With the increasing of Z, the jet flow will grow more stable. The inviscid single-phase jet is the most unstable. The wave amplification, c_i first decreases with the increasing of St and then increases afterwards. There exist certain values of St, at which the jet is the most stable.     

Transverse-roll global modes in a Rayleigh–Bénard–Poiseuille system with streamwise variable heating

The effect of a spatially inhomogeneous heating of the bottom wall in Rayleigh–Bénard–Poiseuille convection is studied for slow streamwise variations of the temperature profile. The problem is defined by the constant Reynolds number of the Poiseuille through flow, assumed to be low (typically 10), the constant Prandtl number, and the spatial evolution of the Rayleigh number , assumed to be subcritical everywhere except in a limited region around its single maximum . In this initial study, all spanwise inhomogeneities such as side walls or spanwise variable heating are neglected to obtain two-dimensional (transverse roll) global mode solutions by means of WKBJ asymptotics. The resulting frequency selection yields, at leading order, a global mode frequency equal to the local absolute frequency ω^t at the streamwise location where the Rayleigh number is maximum, with higher-order corrections for non-parallelism. These allow the determination of critical values of for global instability as a function of the profile of the local Rayleigh number and of Prandtl and Reynolds numbers.     

A computational analysis of the hydrodynamic instability of a liquid jet focused into a converging microchannel

The instability of a focused liquid jet is studied by semi-analytical methods and by methods of computational fluid dynamics. The semi-analytical approach relies on earlier work on the instability of an extending liquid thread and is based on the Stokes flow regime and small-amplitude perturbations. The evolution of different excitation modes is evaluated and compared. Through hydrodynamic focusing and the corresponding extensional flow an initially stable mode may become unstable and it depends on the position away from the inlet which mode is to be regarded as the most unstable one. When plotting a hypothetical jet decay length against the excitation wave number, a comparatively broad minimum is exhibited. The CFD simulations based on the volume-of-fluid method show that the jet may break up either in the conical focusing zone or in the attached capillary, depending on the flow velocity. When the deformation of the jet surface reaches a certain amplitude, the jet assumes a “beads-on-a-string” structure instead of a shape derived from a harmonic perturbation. A jet decay within the capillary produces elongated droplets with cusped ends. When comparing the results of the CFD and the semi-analytical model, it turns out that the CFD simulations predict more stable jets with a larger decay length. An analysis of the flow velocity field shows that the increased stability might be due to the interaction of the jet with the channel walls.