Modal Decomposition and Linear Modeling of Swirl Fluctuations in the Mixing Section of a Model Combustor Based on PIV Data

2021 ◽  
Author(s):  
Jens Satria Müller ◽  
Finn Lückoff ◽  
Thomas Ludwig Kaiser ◽  
Christian Oliver Paschereit ◽  
Kilian Oberleithner
Keyword(s):  
Acoustic Waves ◽  
Stokes Equations ◽  
Flow Instability ◽  
Theoretical Work ◽  
Navier Stokes ◽  
Inertial Waves ◽  
Linear Modeling ◽  
Swirl Combustor ◽  
Time Resolved ◽  
Flow Response

Abstract In order to determine the flame transfer function of a combustion system only based on isothermal flow field data, three governing mechanisms have been identified which need to be modeled: swirl fluctuations, equivalence fluctuations and velocity fluctuations excited by planar acoustic waves. This study focuses on the generation and propagation of swirl fluctuations downstream of a radial swirl combustor under isothermal conditions. Swirl fluctuations are generated experimentally by imposing acoustic perturbations. Time-resolved longitudinal and crosswise PIV measurements are conducted inside the mixing tube and combustion chamber to quantify the evolution of the swirl fluctuations. The measured flow response is decomposed using spectral proper orthogonal decomposition to unravel the contributions of different dynamical modes. In addition a resolvent analysis is conducted based on the linearized Navier-Stokes equations to reveal the intrinsically most amplified flow structures. Both, the data-driven and analytic approach, show that inertial waves are indeed present in the flow response and an inherent flow instability downstream of the swirler, which confirms the recent theoretical work of Albayrak et al. (Journal of Fluid Mechanics, 879). However, the contribution of these inertial waves to the total swirl fluctuations turns out to be very small. This is suggested to be due to the very structured forcing at the swirler and the amplification of shear-driven modes which are expected to be much more influential for this type of swirler. Overall, this work confirms the presence of inertial waves in highly turbulent swirl combustors and evaluates its relevance for industry-related configurations. It further outlines a methodology to analyze and predict their characteristics based on mean fields only, which is applicable for complex geometries of industrial relevance.

Modal Decomposition and Linear Modeling of Swirl Fluctuations in the Mixing Section of a Model Combustor Based On PIV Data

2021 ◽  
Author(s):  
Jens S. Müller ◽  
Finn Lückoff ◽  
Thomas Ludwig Kaiser ◽  
Christian Oliver Paschereit ◽  
Kilian Oberleithner
Keyword(s):  
Stokes Equations ◽  
Flow Instability ◽  
Navier Stokes ◽  
Inertial Waves ◽  
Linear Modeling ◽  
Navier Stokes Equations ◽  
Swirl Combustor ◽  
Time Resolved ◽  
Flow Response ◽  
Measured Flow

Abstract In order to determine the flame transfer function of a combustion system, different mechanisms have been identified that need to be modeled. This study focuses on the generation and propagation of one of these mechanisms, namely the swirl fluctuations downstream of a radial swirl combustor under isothermal conditions. Swirl fluctuations are generated experimentally by imposing acoustic perturbations. Time-resolved longitudinal and crosswise PIV measurements are conducted inside the mixing tube and combustion chamber to quantify the evolution of the swirl fluctuations. The measured flow response is decomposed using spectral proper orthogonal decomposition to unravel the contributions of different dynamical modes. In addition a resolvent analysis is conducted based on the linearized Navier-Stokes equations to reveal the intrinsically most amplified flow structures. Both, the data-driven and analytic approach, show that inertial waves are indeed present in the flow response and an inherent flow instability downstream of the swirler, which confirms recent theoretical works on inertial waves. However, the contribution of the identified inertial waves to the total swirl fluctuations turns out to be very small. This is suggested to be due to the very structured forcing at the swirler and the additional amplification of shear-driven modes. Overall, this work confirms the presence of inertial waves in highly turbulent swirl combustors and evaluates its relevance for industry-related configurations. It further outlines a methodology to analyze and predict their characteristics based on mean fields only, which is applicable for complex geometries of industrial relevance.

Boundary layer leading-edge receptivity to sound at incidence angles

2001 ◽  
Vol 444 ◽  
pp. 383-407 ◽  
Author(s):  
ERCAN ERTURK ◽  
THOMAS C. CORKE
Keyword(s):  
Acoustic Waves ◽  
Stokes Equations ◽  
Incidence Angle ◽  
Leading Edge ◽  
Quantitative Agreement ◽  
Navier Stokes ◽  
Angle Of Incidence ◽  
Sound Waves ◽  
Nose Radius ◽  
Navier Stokes Equations

The leading-edge receptivity to acoustic waves of two-dimensional parabolic bodies was investigated using a spatial solution of the Navier–Stokes equations in vorticity/streamfunction form in parabolic coordinates. The free stream is composed of a uniform flow with a superposed periodic velocity fluctuation of small amplitude. The method follows that of Haddad & Corke (1998) in which the solution for the basic flow and linearized perturbation flow are solved separately. We primarily investigated the effect of frequency and angle of incidence (−180° [les ] α2 [les ] 180°) of the acoustic waves on the leading-edge receptivity. The results at α2 = 0° were found to be in quantitative agreement with those of Haddad & Corke (1998), and substantiated the Strouhal number scaling based on the nose radius. The results with sound waves at angles of incidence agreed qualitatively with the analysis of Hammerton & Kerschen (1996). These included a maximum receptivity at α2 = 90°, and an asymmetric variation in the receptivity with sound incidence angle, with minima at angles which were slightly less than α2 = 0° and α2 = 180°.

Unsteady Multicellular Natural Convection in a Narrow Horizontal Cylindrical Annulus

1990 ◽  
Vol 112 (2) ◽  
pp. 379-387 ◽  
Author(s):  
D. B. Fant ◽  
J. Prusa ◽  
A. P. Rothmayer
Keyword(s):  
Chaotic Systems ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Flow Instability ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Boundary Layer Equations ◽  
Cylindrical Annulus ◽  
Gap Spacing ◽  
Limiting Case

Numerical and analytical solutions are presented for multicellular flow instability and the subsequent nonlinear development in a horizontal cylindrical annulus. The Boussinesq approximated Navier–Stokes equations are simplified to Cartesian-like boundary layer equations by means of a high Rayleigh number small gap asymptotic expansion. The full numerical problem is explored for the limiting case of zero Prandtl number. At a finite scaled gap spacing, an instability sets in, which results in periodic multicellular flow. The numerical solutions are found to progress through an increasingly complex sequence of periodic solutions, culminating in a very complex unsteady solution that has features normally associated with chaotic systems.

scholarly journals The scattering of sound waves by a vortex: numerical simulations and analytical solutions

1994 ◽  
Vol 260 ◽  
pp. 271-298 ◽  
Author(s):  
Tim Colonius ◽  
Sanjiva K. Lele ◽  
Parviz Moin
Keyword(s):  
Boundary Conditions ◽  
Analytical Solutions ◽  
Acoustic Waves ◽  
Stokes Equations ◽  
Spatial Differentiation ◽  
Navier Stokes ◽  
Sound Waves ◽  
Navier Stokes Equations ◽  
Refraction Effect ◽  
Approximate Analytical Solutions

The scattering of plane sound waves by a vortex is investigated by solving the compressible Navier–-Stokes equations numerically, and analytically with asymptotic expansions. Numerical errors associated with discretization and boundary conditions are made small by using high-order-accurate spatial differentiation and time marching schemes along with accurate non-reflecting boundary conditions. The accuracy of computations of flow fields with acoustic waves of amplitude five orders of magnitude smaller than the hydrodynamic fluctuations is directly verified. The properties of the scattered field are examined in detail. The results reveal inadequacies in previous vortex scattering theories when the circulation of the vortex is non-zero and refraction by the slowly decaying vortex flow field is important. Approximate analytical solutions that account for the refraction effect are developed and found to be in good agreement with the computations and experiments.

scholarly journals Reynolds, Maxwell, and the Radiometer, Revisited

2010 ◽  
Author(s):  
Holger Martin
Keyword(s):  
Heat Transfer ◽  
Stokes Equations ◽  
Historical Review ◽  
Theoretical Work ◽  
Creeping Flow ◽  
Navier Stokes ◽  
Molecular Flow ◽  
Flow Equations ◽  
Thermal Transpiration ◽  
Crookes Radiometer

In 1969, S. G. Brush and C. W. F. Everitt published a historical review, that was reprinted as subchapter 5.5 Maxwell, Osborne Reynolds, and the radiometer, in Stephen G. Brush’s famous book The Kind of Motion We Call Heat. This review covers the history of the explanation of the forces acting on the vanes of Crookes radiometer up to the end of the 19th century. The forces moving the vanes in Crookes radiometer (which are not due to radiation pressure, as initially believed by Crookes and Maxwell) have been recognized as thermal effects of the remaining gas by Reynolds — from his experimental and theoretical work on Thermal Transpiration and Impulsion, in 1879 — and by the development of the differential equations describing Thermal Creeping Flow, induced by tangential stresses due to a temperature gradient on a solid surface by Maxwell, earlier in the same year, 1879. These fundamental physical laws have not yet made their way into the majority of textbooks of heat transfer and fluid mechanics so far. A literature research about the terms of Thermal Transpiration and Thermal Creeping Flow, in connection with the radiometer forces, resulted in a large number of interesting papers; not only the original ones as mentioned in subchapter 5.5 of Brush’s book, but many more in the earlier twentieth century, by Martin Knudsen, Wilhelm Westphal, Albert Einstein, Theodor Sexl, Paul Epstein and others. The forces as calculated from free molecular flow (by Knudsen), increase linearly with pressure, while the forces from Maxwell’s Thermal Creeping Flow decrease with pressure. In an intermediate range of pressures, depending on the characteristic geometrical dimensions of flow channels or radiometer vanes, an appropriate interpolation between these two kinds of forces, as suggested by Wilhelm Westphal and later by G. Hettner, goes through a maximum. Albert Einstein’s approximate solution of the problem happens to give the order of magnitude of the forces in the maximum range. A comprehensive formula and a graph of the these forces versus pressure combines all the relevant theories by Knudsen (1910), Einstein (1924), Maxwell (1879) (and Hettner (1926), Sexl (1928), and Epstein (1929) who found mathematical solutions for Maxwells creeping flow equations for non-isothermal spheres and circular discs, which are important for thermophoresis and for the radiometer). The mechanism of Thermal Creeping Flow will become of increasing interest in micro- and submicro-channels in various new applications, so it ought to be known to every graduate student of heat transfer in the future. That’s one of the reasons why some authors have recently questioned the validity of the classical Navier-Stokes, Fourier, and Fick equations: Dieter Straub (1996) published a book on an Alternative Mathematical Theory of Non-equilibrium Phenomena. Howard Brenner (since 2005) wrote a number of papers, like Navier-Stokes, revisited, and Bi-velocity hydrodynamics, explicitly pointing to the forces acting on the vanes of the lightmill, to thermophoresis and related phenomena. Franz Durst (since 2006) also developed modifications of the classical Navier-Stokes equations. So, Reynolds, Maxwell, and the radiometer may finally have initiated a revision of the fundamental equations of thermofluiddynamics and heat- and mass transfer.

Unsteady Vortices and Blade Loading in a High-Pressure Turbine

2009 ◽  
Author(s):  
Dongil Chang ◽  
Stavros Tavoularis
Keyword(s):  
High Pressure ◽  
Stokes Equations ◽  
Pressure Fluctuations ◽  
Rotor Blades ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Time Resolved ◽  
Blade Loading ◽  
Pressure Losses ◽  
Horseshoe Vortices

Unsteady flow in a transonic, single-stage, high-pressure, axial turbine has been investigated numerically by solving the URANS (Unsteady Reynolds-Averaged Navier-Stokes) equations with the SST (Shear Stress Transport) turbulence model. Interest has focused on the identification and effects of the quasi-stationary vane and blade horseshoe vortices, vane and blade passage vortices, vane and blade trailing edge vortices, and blade tip leakage vortices. Moreover, two types of unsteady vortices, not discussed explicitly in the previous literature, have been identified and termed “axial gap vortices” and “crown vortices”. All vortices have been clearly and distinctly identified using a modified form of the Q criterion, which is less sensitive to the set threshold than the original version. The use of pathlines and iso-contours of static pressure, axial vorticity and entropy has been further exploited to distinguish the different types of vortices from each other and to mark their senses of rotation and strengths. The influence of these vortices on the entropy distribution at the outlet has been investigated. The observed high total pressure losses in the turbine at blade midspan have been connected to the action of passage vortices. The formation and disappearance processes of unsteady vortices located in the spacing between the stator and the rotor have been time-resolved. These vortices are roughly aligned with the leading edges of the rotor blades and their existence depends on the position of the blade with respect to the upstream vanes. In addition, the present study focuses on the unsteady blade loading that influences vibratory stresses. Contours of the time-dependent surface pressure on the rotor blade have demonstrated the presence of large pressure fluctuations near the front of the blade suction sides; these pressure fluctuations have been associated with the periodic passages of shock waves originating at the vane trailing edges.

Study of 3D Mixing Processes by Numerical and Experimental Approaches

2002 ◽  
Author(s):  
Y. Zhao ◽  
R. S. Brodkey ◽  
S. Nakamura
Keyword(s):  
Stokes Equations ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Mixing Processes ◽  
Time Resolved ◽  
Simplified Approach ◽  
Eddy Simulation ◽  
Flow Mixing ◽  
Mixing Vessels ◽  
Simulation And Validation

Mixing vessels are widely used for blending and chemical reactions. Although much has been done on mixing processes, the complex, three-dimensional flow phenomena are still not well understood. The purpose of our first step in this research is the simulation and validation of time-resolved, three-dimensional velocity vector data. Such results are an essential part of the design of mixing systems, but are generally not available to the engineers. The computational work involves direct numerical simulation (DNS) and large eddy simulation (LES) of the Navier-Stokes equations. Later, modeling of the Reynolds averaged Navier-Stokes (RANS) equations will be undertaken as a simplified approach. Simulations and modeling are being validated by experiments. Two flow mixing systems are under investigation. First and most important for validation is an opposed jet flow system that offers some unique characteristics that can be used for validation of DNS/LES simulations. It also has applications in the injection molding of plastics. Second, simulations of impeller driven mixing vessels that are more commonly used in processing are under development. Here the moving mesh system adds complexity. In addition, visualization of both numerical and experimental results, 3-D particle tracking velocimetry (PTV) techniques have been developed. The proposed paper will address the problems in the modeling of chemical mixing and discuss the results of simulation and validation.

Navier–Stokes Simulation of Transonic Blade-Vortex Interactions

1990 ◽  
Vol 112 (4) ◽  
pp. 501-509 ◽  
Author(s):  
N.-S. Liu ◽  
F. Davoudzadeh ◽  
W. R. Briley ◽  
S. J. Shamroth
Keyword(s):  
Acoustic Waves ◽  
Stokes Equations ◽  
Leading Edge ◽  
Lower Surface ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Load Variations ◽  
Vortex Interactions ◽  
Blade Vortex Interaction ◽  
Order Scheme

Transonic strong blade-vortex interaction is numerically analyzed by solving the unsteady 2-D Navier–Stokes equations using an iterative implicit second order scheme. The dominant processes during the interaction are the development of large transverse pressure gradients in the upper leading edge region and the development of disturbances at the root of the lower surface shock wave. As a result of this interaction, high pressure pulses are emitted from the leading edge, and acoustic waves are radiated from the lower surface in a region originally occupied by a supersonic pocket. In addition, severe load variations occur when the vortex is within one chord length of the blade.

Deployable Vortex Generator Dynamic Stall Alleviation through Experimental and Numerical Investigations

2013 ◽  
Vol 58 (3) ◽  
pp. 1-13 ◽  
Author(s):  
G. Joubert ◽  
A. Le Pape ◽  
B. Heine ◽  
S. Huberson
Keyword(s):  
Stokes Equations ◽  
Decomposition Analysis ◽  
Vortex Generator ◽  
Detailed Comparison ◽  
Dynamic Stall ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Time Resolved ◽  
Stall Control ◽  
Point Detection

The flow over an OA209 airfoil subjected to a sinusoidal pitching motion under dynamic stall conditions and equipped with an innovative deployable vortex generator actuator inducing stall control is experimentally and numerically investigated. Pressure and time-resolved particle image velocimetry measurements allow a detailed comparison to be performed between clean and controlled cases, including separation point detection and proper orthogonal decomposition analysis. Along with wind tunnel testing, numerical simulations are performed by solving the unsteady Reynolds-averaged Navier–Stokes equations with the ONERA elsA code. Computations are successfully compared to the experimental reference and bring further understanding of the deployable vortex generator actuation.

scholarly journals New class of turbulence in active fluids

2015 ◽  
Vol 112 (49) ◽  
pp. 15048-15053 ◽  
Author(s):  
Vasil Bratanov ◽  
Frank Jenko ◽  
Erwin Frey
Keyword(s):  
Turbulent Flows ◽  
Stokes Equations ◽  
Spatial Scales ◽  
Finite Size ◽  
Power Laws ◽  
Theoretical Work ◽  
Navier Stokes ◽  
Physical Parameters ◽  
New Class ◽  
General Terms

Turbulence is a fundamental and ubiquitous phenomenon in nature, occurring from astrophysical to biophysical scales. At the same time, it is widely recognized as one of the key unsolved problems in modern physics, representing a paradigmatic example of nonlinear dynamics far from thermodynamic equilibrium. Whereas in the past, most theoretical work in this area has been devoted to Navier–Stokes flows, there is now a growing awareness of the need to extend the research focus to systems with more general patterns of energy injection and dissipation. These include various types of complex fluids and plasmas, as well as active systems consisting of self-propelled particles, like dense bacterial suspensions. Recently, a continuum model has been proposed for such “living fluids” that is based on the Navier–Stokes equations, but extends them to include some of the most general terms admitted by the symmetry of the problem [Wensink HH, et al. (2012) Proc Natl Acad Sci USA 109:14308–14313]. This introduces a cubic nonlinearity, related to the Toner–Tu theory of flocking, which can interact with the quadratic Navier–Stokes nonlinearity. We show that as a result of the subtle interaction between these two terms, the energy spectra at large spatial scales exhibit power laws that are not universal, but depend on both finite-size effects and physical parameters. Our combined numerical and analytical analysis reveals the origin of this effect and even provides a way to understand it quantitatively. Turbulence in active fluids, characterized by this kind of nonlinear self-organization, defines a new class of turbulent flows.

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