Structural sensitivity of spiral vortex breakdown

2013 ◽  
Vol 720 ◽  
pp. 558-581 ◽  
Author(s):  
Ubaid Ali Qadri ◽  
Dhiren Mistry ◽  
Matthew P. Juniper
Keyword(s):  
Stability Analysis ◽  
Passive Control ◽  
Stokes Equations ◽  
Vortex Breakdown ◽  
Control Strategies ◽  
Axial Component ◽  
Azimuthal Mode ◽  
Global Mode ◽  
Structural Sensitivity ◽  
Spiral Vortex

AbstractPrevious numerical simulations have shown that vortex breakdown starts with the formation of a steady axisymmetric bubble and that an unsteady spiralling mode then develops on top of this. We investigate this spiral mode with a linear global stability analysis around the steady bubble and its wake. We obtain the linear direct and adjoint global modes of the linearized Navier–Stokes equations and overlap these to obtain the structural sensitivity of the spiral mode, which identifies the wavemaker region. We also identify regions of absolute instability with a local stability analysis. At moderate swirls, we find that the $m= - 1$ azimuthal mode is the most unstable and that the wavemaker regions of the $m= - 1$ mode lie around the bubble, which is absolutely unstable. The mode is most sensitive to feedback involving the radial and azimuthal components of momentum in the region just upstream of the bubble. To a lesser extent, the mode is also sensitive to feedback involving the axial component of momentum in regions of high shear around the bubble. At an intermediate swirl, in which the bubble and wake have similar absolute growth rates, other researchers have found that the wavemaker of the nonlinear global mode lies in the wake. We agree with their analysis but find that the regions around the bubble are more influential than the wake in determining the growth rate and frequency of the linear global mode. The results from this paper provide the first steps towards passive control strategies for spiral vortex breakdown.

Linear three-dimensional global and asymptotic stability analysis of incompressible open cavity flow

2015 ◽  
Vol 768 ◽  
pp. 113-140 ◽  
Author(s):  
Vincenzo Citro ◽  
Flavio Giannetti ◽  
Luca Brandt ◽  
Paolo Luchini
Keyword(s):  
Growth Rate ◽  
Reynolds Number ◽  
Stability Analysis ◽  
Closed Orbit ◽  
Three Dimensional ◽  
Base Flow ◽  
Open Cavity ◽  
Critical Conditions ◽  
Global Mode ◽  
Structural Sensitivity

The viscous and inviscid linear stability of the incompressible flow past a square open cavity is studied numerically. The analysis shows that the flow first undergoes a steady three-dimensional bifurcation at a critical Reynolds number of 1370. The critical mode is localized inside the cavity and has a flat roll structure with a spanwise wavelength of about 0.47 cavity depths. The adjoint global mode reveals that the instability is most efficiently triggered in the thin region close to the upstream tip of the cavity. The structural sensitivity analysis identifies the wavemaker as the region located inside the cavity and spatially concentrated around a closed orbit. As the flow outside the cavity plays no role in the generation mechanisms leading to the bifurcation, we confirm that an appropriate parameter to describe the critical conditions in open cavity flows is the Reynolds number based on the average velocity between the two upper edges. Stabilization is achieved by a decrease of the total momentum inside the shear layer that drives the core vortex within the cavity. The mechanism of instability is then studied by means of a short-wavelength approximation considering pressureless inviscid modes. The closed streamline related to the maximum inviscid growth rate is found to be the same as that around which the global wavemaker is concentrated. The structural sensitivity field based on direct and adjoint eigenmodes, computed at a Reynolds number far higher than that of the base flow, can predict the critical orbit on which the main instabilities inside the cavity arise. Further, we show that the sub-leading unstable time-dependent modes emerging at supercritical conditions are characterized by a period that is a multiple of the revolution time of Lagrangian particles along the orbit of maximum growth rate. The eigenfrequencies of these modes, computed by global stability analysis, are in very good agreement with the asymptotic results.

Three-dimensional coherent structures in a swirling jet undergoing vortex breakdown: stability analysis and empirical mode construction

2011 ◽  
Vol 679 ◽  
pp. 383-414 ◽  
Author(s):  
K. OBERLEITHNER ◽  
M. SIEBER ◽  
C. N. NAYERI ◽  
C. O. PASCHEREIT ◽  
C. PETZ ◽  
...  
Keyword(s):  
Stability Analysis ◽  
Coherent Structures ◽  
Vortex Breakdown ◽  
Particle Image Velocimetry Data ◽  
Turbulent Shear ◽  
Mean Flow ◽  
Helical Structures ◽  
Global Mode ◽  
Swirling Jet ◽  
Time Periodic

The spatio-temporal evolution of a turbulent swirling jet undergoing vortex breakdown has been investigated. Experiments suggest the existence of a self-excited global mode having a single dominant frequency. This oscillatory mode is shown to be absolutely unstable and leads to a rotating counter-winding helical structure that is located at the periphery of the recirculation zone. The resulting time-periodic 3D velocity field is predicted theoretically as being the most unstable mode determined by parabolized stability analysis employing the mean flow data from experiments. The 3D oscillatory flow is constructed from uncorrelated 2D snapshots of particle image velocimetry data, using proper orthogonal decomposition, a phase-averaging technique and an azimuthal symmetry associated with helical structures. Stability-derived modes and empirically derived modes correspond remarkably well, yielding prototypical coherent structures that dominate the investigated flow region. The proposed method of constructing 3D time-periodic velocity fields from uncorrelated 2D data is applicable to a large class of turbulent shear flows.

Methods for the Extraction and Analysis of the Global Mode in Swirling Jets Undergoing Vortex Breakdown

2016 ◽  
Author(s):  
Lothar Rukes ◽  
Moritz Sieber ◽  
C. Oliver Paschereit ◽  
Kilian Oberleithner
Keyword(s):  
Vortex Breakdown ◽  
Control Strategies ◽  
Combustion Process ◽  
Flame Stabilization ◽  
Global Mode ◽  
Swirling Jets ◽  
Precessing Vortex Core ◽  
Finite Time Lyapunov Exponent ◽  
Image Velocimetry ◽  
The Impact

Swirling jets undergoing vortex breakdown are widely used in combustion applications, due to their ability to provide aerodynamic flame stabilization. It is well known that vortex breakdown is accompanied by a dominant coherent structure, the so called precessing vortex core (PVC). Reports on the impact of the PVC on the combustion process range from beneficial to detrimental. In any event, efficient methods for the analysis of the PVC help to increase the benefit or reduce the penalty resulting from it. This study uses Particle Image Velocimetry (PIV) measurements of a generic non-isothermal swirling jet to demonstrate the use of advanced data analysis techniques. In particular, the Finite Time Lyapunov Exponent (FTLE) and local linear stability analysis (LSA) are shown to reveal deep insight into the physical mechanisms that drive the PVC. Particularly, it is demonstrated that the PVC amplitude is strongly reduced, if heating is applied at the wavemaker of the flow. These techniques are complemented by the traditionally used Proper Orthogonal Decomposition (POD) and spatial correlation techniques. It is demonstrated how these methods complement each other and lead to a comprehensive understanding of the PVC that lays out the path to efficient control strategies.

scholarly journals Spiral vortex breakdown as a global mode

2006 ◽  
Vol 549 (-1) ◽  
pp. 71 ◽  
Author(s):  
FRANÇOIS GALLAIRE ◽  
MICHAEL RUITH ◽  
ECKART MEIBURG ◽  
JEAN-MARC CHOMAZ ◽  
PATRICK HUERRE
Keyword(s):  
Vortex Breakdown ◽  
Global Mode ◽  
Spiral Vortex

Methods for the Extraction and Analysis of the Global Mode in Swirling Jets Undergoing Vortex Breakdown

2016 ◽  
Vol 139 (2) ◽  
Author(s):  
Lothar Rukes ◽  
Moritz Sieber ◽  
C. Oliver Pashereit ◽  
Kilian Oberleithner
Keyword(s):  
Vortex Breakdown ◽  
Control Strategies ◽  
Combustion Process ◽  
Flame Stabilization ◽  
Global Mode ◽  
Swirling Jets ◽  
Precessing Vortex Core ◽  
Finite Time Lyapunov Exponent ◽  
Image Velocimetry ◽  
The Impact

Swirling jets undergoing vortex breakdown are widely used in combustion applications, due to their ability to provide aerodynamic flame stabilization. It is well known that vortex breakdown is accompanied by a dominant coherent structure, the so-called precessing vortex core (PVC). Reports on the impact of the PVC on the combustion process range from beneficial to detrimental. In any event, efficient methods for the analysis of the PVC help to increase the benefit or reduce the penalty resulting from it. This study uses particle image velocimetry (PIV) measurements of a generic nonisothermal swirling jet to demonstrate the use of advanced data analysis techniques. In particular, the finite time Lyapunov exponent (FTLE) and the local linear stability analysis (LSA) are shown to reveal deep insight into the physical mechanisms that drive the PVC. Particularly, it is demonstrated that the PVC amplitude is strongly reduced, if heating is applied at the wavemaker of the flow. These techniques are complemented by the traditionally used proper orthogonal decomposition (POD) and spatial correlation techniques. It is demonstrated how these methods complement each other and lead to a comprehensive understanding of the PVC that lays out the path to efficient control strategies.

Effect of Heat Transfer on Pipe Flow Stability

2017 ◽  
Author(s):  
Ce Zhang ◽  
Wei Ma ◽  
Wensheng Yu ◽  
Jinfang Teng
Keyword(s):  
Heat Transfer ◽  
Stability Analysis ◽  
Flow Field ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Pipe Flow ◽  
Cfd Simulation ◽  
Stokes Equations ◽  
Flow Stability ◽  
Global Mode

The compressibility of flow field has an important effect on flow stability. However, when the compressibility is considered, the effect of Mach number is often considered while the effect of heat transfer is always neglected in the existing flow stability studies. Linear stability analysis tools based on compressible Orr-Sommerfeld (O-S) equations and linearized Navier-Stokes equations in cylindrical coordinate system are established in this paper. These equations are numerically solved by using Chebyshev spectral collocation method and pseudo-modes are eliminated. Linear stability analysis of pipe flow with heat transfer whose average flow field is obtained by CFD simulation is carried out. The results show that for spatial modes, the heating effect of the wall makes pipe flow more unstable, while cooling effect of the wall makes pipe flow more stable. For global modes of pipe flow, the frequency of global mode decreases when the wall cools the flow and the decrease of mean temperature of pipe flow leads to the improvement of global mode stability.

Predictive control of spiral vortex breakdown

2018 ◽  
Vol 842 ◽  
pp. 58-86 ◽  
Author(s):  
S. Pasche ◽  
F. Gallaire ◽  
F. Avellan
Keyword(s):  
Objective Function ◽  
Predictive Control ◽  
Vortex Breakdown ◽  
Control Strategies ◽  
Three Dimensional ◽  
The Self ◽  
Mean Flow ◽  
Volume Force ◽  
Spiral Vortex ◽  
The Mean

The predictive control of the self-sustained single spiral vortex breakdown mode is addressed in the three-dimensional flow geometry of Ruithet al.(2003) for a constant swirl number$S=1.095$. Based on adjoint optimization algorithms, two different control strategies have been designed. First, a quadratic objective function minimizing the radial velocity intensity, taking advantage of the physical mechanism underpinning spiral vortex breakdown. The second strategy focuses on the hydrodynamic instability properties using as objective function the growth rate of the most unstable global eigenmode. These minimization algorithms seek for an optimal volume force in an axisymmetric domain avoiding therefore expensive three-dimensional computations. In addition to considering eigenvalues around the base flow, we also investigate the stability around the mean flow and we find that it correctly predicts the frequency of the self-sustained single spiral vortex breakdown mode for Reynolds numbers up to$Re=500$. Close to the instability threshold, at a Reynolds value of$Re=180$, all these control strategies successfully quench the spiral vortex breakdown. The related volume force is found identical for the base and mean flow eigenvalue control even if the uncontrolled growth rates differ significantly. The control of the least unstable eigenvalue of the mean flow is not only found optimal at$Re=180$, it also stabilizes the flow at a Reynolds value as large as$Re=300$, which opens promising extensions to industrial applications.

Part Load Vortex Rope as a Global Unstable Mode

2017 ◽  
Vol 139 (5) ◽  
Author(s):  
Simon Pasche ◽  
François Avellan ◽  
François Gallaire
Keyword(s):  
Flow Field ◽  
Large Scale ◽  
Vortex Breakdown ◽  
Control Strategies ◽  
Renewable Energy Sources ◽  
Vortex Rope ◽  
Part Load ◽  
Spiral Vortex ◽  
Electrical Generation ◽  
Operation Flexibility

Renewable energy sources (RES) have reached 23.7% of the worldwide electrical generation production in 2015. The hydraulic energy contribution amounts to 16.6% and comes mainly form large-scale hydropower plants, where Francis turbines represents 60% of the generating units. However, the future massive development of RES will require more advanced grid regulation strategies that may be achieved by increasing the operation flexibility of the Francis generating units. Part load operating condition of these turbines is hindered by pressure fluctuations in the draft tube of the machine. A precessing helical vortex rope develops in this condition, which imperils the mechanical structure and limits the operation flexibility of these turbines. A thorough description of the physical mechanism leading to the vortex rope is a prerequisite to develop relevant flow control strategies. This work, based on a linear global stability analysis of the time-averaged flow field, including a turbulent eddy viscosity, interprets the vortex rope as a global unstable eigenmode. In close resemblance to spiral vortex breakdown, a single-helix disturbance develops around the time-averaged flow field and growths in time to finally form the vortex rope. The frequency and the structure of this unstable linear disturbance are found in good agreement with respect to the three-dimensional (3D) numerical flow simulations.

scholarly journals The Stability Analysis of a Multi-Port Single-Phase Solid-State Transformer in the Electromagnetic Timescale

Energies ◽  
2018 ◽  
Vol 11 (9) ◽  
pp. 2250 ◽  
Author(s):  
Rui Wang ◽  
Qiuye Sun ◽  
Qifu Cheng ◽  
Dazhong Ma
Keyword(s):  
Stability Analysis ◽  
Solid State ◽  
Single Phase ◽  
Control Strategies ◽  
Current Source ◽  
Practical Stability ◽  
Stability Assessment ◽  
Solid State Transformer ◽  
The Stability ◽  
Signal Sinusoïdal

This paper proposes an overall practical stability assessment for a multi-port single-phase solid-state transformer (MS3T) in the electromagnetic timescale. When multiple stable subsystems are combined into one MS3T, the newly formed MS3T has a certain possibility to be unstable. Thus, this paper discusses the stability assessment of the MS3T in detail. First and foremost, the structure of the MS3T and its three stage control strategies are proposed. Furthermore, the stability analysis of each of the MS3T’s subsystems is achieved through the closed loop transfer function of each subsystem, respectively, including an AC-DC front-end side converter, dual active bridge (DAB) with a high-frequency (HF) or medium-frequency (MF) transformer, and back-end side incorporating DC-AC and dc-dc converters. Furthermore, the practical impedance stability criterion in the electromagnetic timescale, which only requires two current sensors and one external high-bandwidth small-signal sinusoidal perturbation current source, is proposed by the Gershgorin theorem and Kirchhoff laws. Finally, the overall stability assessment, based on a modified impedance criterion for the MS3T is investigated. The overall practical stability assessment of the MS3T can be validated through extensive simulation and hardware results.

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