scholarly journals Mean flow stability analysis of oscillating jet experiments

2014 ◽  
Vol 757 ◽  
pp. 1-32 ◽  
Author(s):  
Kilian Oberleithner ◽  
Lothar Rukes ◽  
Julio Soria
Keyword(s):  
Stability Analysis ◽  
Wave Model ◽  
Flow Stability ◽  
Mean Flow ◽  
Axisymmetric Mode ◽  
Wide Range ◽  
Flow Oscillations ◽  
The Mean ◽  
Wave Models ◽  
The Stability

AbstractLinear stability analysis (LSA) is applied to the mean flow of an oscillating round jet with the aim of investigating the robustness and accuracy of mean flow stability wave models. The jet’s axisymmetric mode is excited at the nozzle lip through a sinusoidal modulation of the flow rate at amplitudes ranging from 0.1 % to 100 %. The instantaneous flow field is measured via particle image velocimetry (PIV) and decomposed into a mean and periodic part utilizing proper orthogonal decomposition (POD). Local LSA is applied to the measured mean flow adopting a weakly non-parallel flow approach. The resulting global perturbation field is carefully compared with the measurements in terms of spatial growth rate, phase velocity, and phase and amplitude distribution. It is shown that the stability wave model accurately predicts the excited flow oscillations during their entire growth phase and during a large part of their decay phase. The stability wave model applies over a wide range of forcing amplitudes, showing no pronounced sensitivity to the strength of nonlinear saturation. The upstream displacement of the neutral point and the successive reduction of gain with increasing forcing amplitude is very well captured by the stability wave model. At very strong forcing ($\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}{>}40\, \%$), the flow becomes essentially stable to the axisymmetric mode. For these extreme cases, the prediction deteriorates from the measurements due to an interaction of the forced wave with the geometric confinement of the nozzle. Moreover, the model fails far downstream in a region where energy is transferred from the oscillation back to the mean flow. This study supports previously conducted mean flow stability analysis of self-excited flow oscillations in the cylinder wake and in the vortex breakdown bubble and extends the methodology to externally forced convectively unstable flows. The high accuracy of mean flow stability wave models as demonstrated here is of great importance for the analysis of coherent structures in turbulent shear flows.

The instability of the thin vortex ring of constant vorticity

1977 ◽  
Vol 287 (1344) ◽  
pp. 273-305 ◽  
Keyword(s):  
Stability Analysis ◽  
Vortex Ring ◽  
Mean Flow ◽  
Bending Waves ◽  
Constant Vorticity ◽  
Ring Radius ◽  
Amplification Rate ◽  
The Mean ◽  
The Stability ◽  
Good Agreement

A theoretical investigation of the instability of a vortex ring to short azimuthal bending waves is presented. The theory considers only the stability of a thin vortex ring with a core of constant vorticity (constant /r) in an ideal fluid. Both the mean flow and the disturbance flow are found as an asymptotic solution in e = a /R, the ratio of core radius to ring radius. Only terms linear in wave amplitude are retained in the stability analysis. The solution to 0 (e 2 ) is presented, although the details of the stability analysis are carried through completely only for a special class of bending waves that are known to be unstable on a line filament in the presence of strain (Tsai & Widnall 1976) and have been identified in the simple model of Widnall, Bliss & Tsai (1974) as a likely mode of instability for the vortex ring: these occur at certain critical wavenumbers for which waves on a line filament of the same vorticity distribution would not rotate (w 0 = 0). The ring is found to be always unstable for at least the lowest two critical wavenumbers ( ka = 2.5 and 4.35). The amplification rate and wavenumber predicted by the theory are found to be in good agreement with available experimental results.

Zonal approach to centrifugal, elliptic and hyperbolic instabilities in Stuart vortices with external rotation

2001 ◽  
Vol 449 ◽  
pp. 1-37 ◽  
Author(s):  
FABIEN S. GODEFERD ◽  
CLAUDE CAMBON ◽  
S. LEBLANC
Keyword(s):  
Stability Analysis ◽  
External Rotation ◽  
Short Wave ◽  
Rotating Flows ◽  
Mean Flow ◽  
Mode Decomposition ◽  
Centrifugal Instability ◽  
The Mean ◽  
The Stability ◽  
Stuart Vortices

The stability analysis of a street of Stuart vortices in a rotating frame is performed by integrating the Kelvin–Townsend equations along the mean flow trajectories, using the geometrical optics technique (Lifschitz & Hameiri 1991) for short-wave perturbations. A parallel is drawn between the formulations of this zonal approach and that of rapid distortion theory, better known to the turbulence community. The results presented confirm those obtained by the standard stability analysis based on normal-mode decomposition: depending on the rotation parameter and the oblique mode considered, three unstable zones are identified, related to the centrifugal, elliptic and hyperbolic instabilities, as observed for Taylor–Green cells (Sipp et al. 1999). Anticyclonic rotation is shown to destabilize Stuart vortices through a combination of the elliptical and centrifugal instability mechanisms, depending on the ratio of its rate to the structure core vorticity. Available stability criteria are discussed in the general case of two-dimensional rotating flows, in relation to their streamline topology and the values of the local Rossby number or vorticity.

scholarly journals Quantifying the Effects of Wave—Current Interactions on Tidal Energy Resource at Sites in the English Channel Using Coupled Numerical Simulations

Energies ◽  
2021 ◽  
Vol 14 (12) ◽  
pp. 3625
Author(s):  
Jon Hardwick ◽  
Ed B. L. Mackay ◽  
Ian G. C. Ashton ◽  
Helen C. M. Smith ◽  
Philipp R. Thies
Keyword(s):  
Wave Model ◽  
Tidal Energy ◽  
English Channel ◽  
Flow Conditions ◽  
Mean Flow ◽  
Radiation Stress ◽  
Large Wave ◽  
Stress Gradients ◽  
The Mean ◽  
Flow Power

Numerical modeling of currents and waves is used throughout the marine energy industry for resource assessment. This study compared the output of numerical flow simulations run both as a standalone model and as a two-way coupled wave–current simulation. A regional coupled flow-wave model was established covering the English Channel using the Delft D-Flow 2D model coupled with a SWAN spectral wave model. Outputs were analyzed at three tidal energy sites: Alderney Race, Big Roussel (Guernsey), and PTEC (Isle of Wight). The difference in the power in the tidal flow between coupled and standalone model runs was strongly correlated to the relative direction of the waves and currents. The net difference between the coupled and standalone runs was less than 2.5%. However, when wave and current directions were aligned, the mean flow power was increased by up to 7%, whereas, when the directions were opposed, the mean flow power was reduced by as much as 9.6%. The D-Flow Flexible Mesh model incorporates the effects of waves into the flow calculations in three areas: Stokes drift, forcing by radiation stress gradients, and enhancement of the bed shear stress. Each of these mechanisms is discussed. Forcing from radiation stress gradients is shown to be the dominant mechanism affecting the flow conditions at the sites considered, primarily caused by dissipation of wave energy due to white-capping. Wave action is an important consideration at tidal energy sites. Although the net impact on the flow power was found to be small for the present sites, the effect is site specific and may be significant at sites with large wave exposure or strong asymmetry in the flow conditions and should thus be considered for detailed resource and engineering assessments.

Effects of finite-rate chemistry and detailed transport on the instability of jet diffusion flames

2014 ◽  
Vol 745 ◽  
pp. 647-681 ◽  
Author(s):  
Yee Chee See ◽  
Matthias Ihme
Keyword(s):  
Transport Properties ◽  
Diffusion Flames ◽  
Diffusive Transport ◽  
Mean Flow ◽  
Stability Behaviour ◽  
Jet Diffusion Flames ◽  
One Step ◽  
The Mean ◽  
Modelling Assumptions ◽  
The Stability

AbstractLocal linear stability analysis has been shown to provide valuable information about the response of jet diffusion flames to flow-field perturbations. However, this analysis commonly relies on several modelling assumptions about the mean flow prescription, the thermo-viscous-diffusive transport properties, and the complexity and representation of the chemical reaction mechanisms. In this work, the effects of these modelling assumptions on the stability behaviour of a jet diffusion flame are systematically investigated. A flamelet formulation is combined with linear stability theory to fully account for the effects of complex transport properties and the detailed reaction chemistry on the perturbation dynamics. The model is applied to a methane–air jet diffusion flame that was experimentally investigated by Füriet al.(Proc. Combust. Inst., vol. 29, 2002, pp. 1653–1661). Detailed simulations are performed to obtain mean flow quantities, about which the stability analysis is performed. Simulation results show that the growth rate of the inviscid instability mode is insensitive to the representation of the transport properties at low frequencies, and exhibits a stronger dependence on the mean flow representation. The effects of the complexity of the reaction chemistry on the stability behaviour are investigated in the context of an adiabatic jet flame configuration. Comparisons with a detailed chemical-kinetics model show that the use of a one-step chemistry representation in combination with a simplified viscous-diffusive transport model can affect the mean flow representation and heat release location, thereby modifying the instability behaviour. This is attributed to the shift in the flame structure predicted by the one-step chemistry model, and is further exacerbated by the representation of the transport properties. A pinch-point analysis is performed to investigate the stability behaviour; it is shown that the shear-layer instability is convectively unstable, while the outer buoyancy-driven instability mode transitions from absolutely to convectively unstable in the nozzle near field, and this transition point is dependent on the Froude number.

scholarly journals On strongly nonlinear gravity waves in a vertically sheared atmosphere

2020 ◽  
Vol 6 (1) ◽  
pp. 63-74
Author(s):  
Mark Schlutow ◽  
Georg S. Voelker
Keyword(s):  
Gravity Waves ◽  
Lower Layer ◽  
Vertical Shear ◽  
Horizontal Wind ◽  
Necessary Condition ◽  
Mean Flow ◽  
Individual Layer ◽  
Strongly Nonlinear ◽  
The Mean ◽  
The Stability

Abstract We investigate strongly nonlinear stationary gravity waves which experience refraction due to a thin vertical shear layer of horizontal background wind. The velocity amplitude of the waves is of the same order of magnitude as the background flow and hence the self-induced mean flow alters the modulation properties to leading order. In this theoretical study, we show that the stability of such a refracted wave depends on the classical modulation stability criterion for each individual layer, above and below the shearing. Additionally, the stability is conditioned by novel instability criteria providing bounds on the mean-flow horizontal wind and the amplitude of the wave. A necessary condition for instability is that the mean-flow horizontal wind in the upper layer is stronger than the wind in the lower layer.

scholarly journals Dynamics of the Blade Channel of an Inducer Under Cavitation-Induced Instabilities

2018 ◽  
Vol 141 (4) ◽  
Author(s):  
Angelo Pasini ◽  
Ruzbeh Hadavandi ◽  
Dario Valentini ◽  
Giovanni Pace ◽  
Luca d'Agostino
Keyword(s):  
Experimental Data ◽  
Spectral Analysis ◽  
Main Flow ◽  
Operating Conditions ◽  
Flow Instabilities ◽  
Mean Flow ◽  
Flow Oscillations ◽  
Rotating Frames ◽  
The Mean ◽  
High Head

A high-head three-bladed inducer has been equipped with pressure taps on the hub along the blade channels with the aim of more closely investigating the dynamics of cavitation-induced instabilities developing in the impeller flow. Spectral analysis of the pressure signals obtained from two sets of transducers mounted both in the stationary and rotating frames has allowed to characterize the nature, intensity, and interactions of the main flow instabilities detected in the experiments: subsynchronous rotating cavitation (RC), cavitation surge (CS), and a high-order axial surge oscillation. A dynamic model of the unsteady flow in the blade channels has been developed based on experimental data and on suitable descriptions of the mean flow and the oscillations of the cavitating volume. The model has been used for estimating at the inducer operating conditions of interest the intensity of the flow oscillations associated with the occurrence of the CS mode generated by RC in the inducer inlet.

scholarly journals Inviscid spatial stability of a compressible mixing layer. Part 3. Effect of thermodynamics

1991 ◽  
Vol 224 ◽  
pp. 159-175 ◽  
Author(s):  
T. L. Jackson ◽  
C. E. Grosch
Keyword(s):  
Prandtl Number ◽  
Mixing Layer ◽  
Mean Flow ◽  
Temperature Relation ◽  
Compressible Mixing Layer ◽  
Spatial Stability ◽  
Mean Temperature ◽  
The Mean ◽  
The Difference ◽  
The Stability

We report the results of a comprehensive comparative study of the inviscid spatial stability of a parallel compressible mixing layer using various models for the mean flow. The models are (i) the hyperbolic tangent profile for the mean speed and the Crocco relation for the mean temperature, with the Chapman viscosity–temperature relation and a Prandtl number of one; (ii) the Lock profile for the mean speed and the Crocco relation for the mean temperature, with the Chapman viscosity-temperature relation and a Prandtl number of one; and (iii) the similarity solution for the coupled velocity and temperature equations using the Sutherland viscosity–temperature relation and arbitrary but constant Prandtl number. The purpose of this study was to determine the sensitivity of the stability characteristics of the compressible mixing layer to the assumed thermodynamic properties of the fluid. It is shown that the qualitative features of the stability characteristics are quite similar for all models but that there are quantitative differences resulting from the difference in the thermodynamic models. In particular, we show that the stability characteristics are sensitive to the value of the Prandtl number and to a particular value of the temperature ratio across the mixing layer.

On the realizability of pressure–strain closures

2014 ◽  
Vol 755 ◽  
pp. 535-560 ◽  
Author(s):  
Aashwin A. Mishra ◽  
Sharath S. Girimaji
Keyword(s):  
Statistical Models ◽  
Flow Stability ◽  
Mean Flow ◽  
Model Formulation ◽  
Closure Model ◽  
Two Component ◽  
The Mean ◽  
The Relationship ◽  
Rapid Pressure ◽  
Domain Of Validity

AbstractThe realizability condition for statistical models of turbulence is augmented to ensure that not only is the Reynolds stress tensor positive semi-definite, but the process of its evolution is physically attainable as well. The mathematical constraints due to this process realizability requirement on the rapid pressure strain correlation are derived. The resulting constraints reveal important limits on the inter-component energy transfer and the consequent flow stability characteristics, as a function of the mean flow. For planar mean flows, the realizability constraints are most stringent for the case of purely sheared flows rather than elliptic flows. The relationship between the constraints and flow stability is explained. Process realizability leads to closure model guidance not only at the two-component (2C) limit of turbulence (as in the classical realizability approach) but throughout the anisotropy space. Consequently, the domain of validity and applicability of current models can be clearly identified for different mean flows. A simple framework for incorporating these process realizability constraints in model formulation is outlined.

On the stability of an inviscid shear layer which is periodic in space and time

1967 ◽  
Vol 27 (4) ◽  
pp. 657-689 ◽  
Author(s):  
R. E. Kelly
Keyword(s):  
Growth Rate ◽  
Shear Layer ◽  
Finite Amplitude ◽  
Periodic Component ◽  
Periodic Flow ◽  
Flow Profile ◽  
Mean Flow ◽  
Mean Velocity ◽  
The Mean ◽  
The Stability

In experiments concerning the instability of free shear layers, oscillations have been observed in the downstream flow which have a frequency exactly half that of the dominant oscillation closer to the origin of the layer. The present analysis indicates that the phenomenon is due to a secondary instability associated with the nearly periodic flow which arises from the finite-amplitude growth of the fundamental disturbance.At first, however, the stability of inviscid shear flows, consisting of a non-zero mean component, together with a component periodic in the direction of flow and with time, is investigated fairly generally. It is found that the periodic component can serve as a means by which waves with twice the wavelength of the periodic component can be reinforced. The dependence of the growth rate of the subharmonic wave upon the amplitude of the periodic component is found for the case when the mean flow profile is of the hyperbolic-tangent type. In order that the subharmonic growth rate may exceed that of the most unstable disturbance associated with the mean flow, the amplitude of the streamwise component of the periodic flow is required to be about 12 % of the mean velocity difference across the shear layer. This represents order-of-magnitude agreement with experiment.Other possibilities of interaction between disturbances and the periodic flow are discussed, and the concluding section contains a discussion of the interactions on the basis of the energy equation.

Effect of an Azimuthal Mean Flow On the Structure and Stability of Thermoacoustic Modes in an Annular Combustor Model with Electroacoustic Feedback

2020 ◽  
Author(s):  
Sylvain C. Humbert ◽  
Jonas Moeck ◽  
Alessandro Orchini ◽  
Christian Oliver Paschereit
Keyword(s):  
Mach Number ◽  
Initial Conditions ◽  
Mean Flow ◽  
Final State ◽  
Mean Velocity ◽  
Acoustic Damping ◽  
Annular Combustor ◽  
The Mean ◽  
High Mach ◽  
The Stability

Abstract Thermoacoustic oscillations in axisymmetric annular combustors are generally coupled by degenerate azimuthal modes, which can be of standing or spinning nature. Symmetry breaking due to the presence of a mean azimuthal flow splits the degenerate thermoacoustic eigenvalues, resulting in pairs of counter-spinning modes with close but distinct frequencies and growth rates. In this study, experiments have been performed using an annular system where the thermoacoustic feedback due to the flames is mimicked by twelve identical electroacoustic feedback loops. The mean azimuthal flow is generated by fans. We investigate the standing/spinning nature of the oscillations as a function of the Mach number for two types of initial states, and how the stability of the system is affected by the mean azimuthal flow. It is found that spinning, standing or mixed modes can be encountered at very low Mach number, but increasing the mean velocity promotes one spinning direction. At sufficiently high Mach number, spinning modes are observed in the limit cycle oscillations. In some cases, the initial conditions have a significant impact on the final state of the system. It is found that the presence of a mean azimuthal flow increases the acoustic damping. This has a beneficial effect on stability: it often reduces the amplitude of the self-sustained oscillations, and can even suppress them in some cases. However, we observe that the suppression of a mode due to the mean flow may destabilize another one. We discuss our findings in relation with an existing low-order model.

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