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.

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.

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.

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.

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.

On the wave excitation and the formation of recirculation eddies in an axisymmetric flow of uniformly rotating fluids

1996 ◽  
Vol 322 ◽  
pp. 165-200 ◽  
Author(s):  
Hideshi Hanazaki
Keyword(s):  
Stokes Equations ◽  
Vortex Breakdown ◽  
Axial Flow ◽  
Navier Stokes ◽  
Straight Tube ◽  
Inertial Waves ◽  
Rotating Fluids ◽  
Navier Stokes Equations ◽  
Numerical Studies ◽  
Uniform Tube

The inertial waves excited in a uniformly rotating fluid passing through a long circular tube are studied numerically. The waves are excited either by a local deformation of the tube wall or by an obstacle located on the tube axis. When the flow is subcritical, i.e. when the phase and group velocity of the fastest wave mode in their long-wave limit are larger than the incoming axial flow velocity, the excited waves propagate upstream of the excited position. The non-resonant waves have many linear aspects, including the upstream-advancing speed of the wave and the coexisting lee wavelength. When the flow is critical (resonant), i.e. when the long-wave velocity is nearly equal to the axial flow velocity, the large-amplitude waves are resonantly excited. The time development of these waves is described well by the equation derived by Grimshaw & Yi (1993). The integro-differential equation, which describes the strongly nonlinear waves until the axial flow reversal occurs, can predict the onset time and position of the recirculation eddies observed in the solutions of the Navier-Stokes equations. The numerical results and the theory both show that the flow reversal most probably occurs on the tube axis and also when the waves are excited by a contraction of the tube wall. The structure of the recirculation eddies obtained in the solutions of the Navier-Stokes equations at Re = 105 is similar to the axisymmetric or ‘bubble-type’ breakdown observed in the experiments of the vortex-breakdown which used a different non-uniform (Burgers-type) rotation. In uniformly rotating fluids the formation of the recirculation eddies has not been observed in the previous numerical studies of vortex breakdown where a straight tube was used and thus the inertial waves were not excited. This shows that the generation of the recirculation eddies in this study is genuinely explained by the topographically excited large-amplitude inertial ‘waves’ and not by other ‘instability’ mechanisms. Since the wave cannot be excited in a straight tube even in the non-uniformly rotating flows, the generation mechanism of the recirculation eddies in this study is different from the previous numerical studies for the vortex breakdown. The occurrence of the recirculation eddies depends not only on the Froude number and the strength of the excitation source but also on the Reynolds number since the wave amplitude generally decreases by the viscous effects. Some relations to the experiments of vortex breakdown, which have been exclusively done for non-uniformly rotating fluids but done in a ‘non-uniform tube’, are discussed. The flow states, which are classified as supercritical, subcritical or critical in hydraulic terminology, changes along the flow when the upstream flow is near resonant conditions and a non-uniform tube is used.

A resonant wave theory

1999 ◽  
Vol 395 ◽  
pp. 237-251 ◽  
Author(s):  
LUN-SHIN YAO
Keyword(s):  
Stokes Equations ◽  
Flow Instability ◽  
Initial Conditions ◽  
Laminar Flows ◽  
Navier Stokes ◽  
Real Interval ◽  
Mean Flow ◽  
Navier Stokes Equations ◽  
The Mean ◽  
The Waves

Analysis is used to show that a solution of the Navier–Stokes equations can be computed in terms of wave-like series, which are referred to as waves below. The mean flow is a wave of infinitely long wavelength and period; laminar flows contain only one wave, i.e. the mean flow. With a supercritical instability, there are a mean flow, a dominant wave and its harmonics. Under this scenario, the amplitude of the waves is determined by linear and nonlinear terms. The linear case is the target of flow-instability studies. The nonlinear case involves energy transfer among the waves satisfying resonance conditions so that the wavenumbers are discrete, form a denumerable set, and are homeomorphic to Cantor's set of rational numbers. Since an infinite number of these sets can exist over a finite real interval, nonlinear Navier–Stokes equations have multiple solutions and the initial conditions determine which particular set will be excited. Consequently, the influence of initial conditions can persist forever. This phenomenon has been observed for Couette–Taylor instability, turbulent mixing layers, wakes, jets, pipe flows, etc. This is a commonly known property of chaos.

Instabilities and inertial waves generated in a librating cylinder

2011 ◽  
Vol 687 ◽  
pp. 171-193 ◽  
Author(s):  
J. M. Lopez ◽  
F. Marques
Keyword(s):  
Boundary Layer ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Inertial Waves ◽  
Boundary Layer Flows ◽  
Viscous Boundary Layer ◽  
Navier Stokes Equations ◽  
Damping Rate ◽  
Layer Flow ◽  
Viscous Boundary

AbstractA librating cylinder consists of a rotating cylinder whose rate of rotation is modulated. When the mean rotation rate is large compared with the viscous damping rate, the flow may support inertial waves, depending on the frequency of the modulation. The modulation also produces time-dependent boundary layers on the cylinder endwalls and sidewall, and the sidewall boundary layer flow in particular is susceptible to instabilities which can introduce additional forcing on the interior flow with time scales different from the modulation period. These instabilities may also drive and/or modify the inertial waves. In this paper, we explore such flows numerically using a spectral-collocation code solving the Navier–Stokes equations in order to capture the dynamics involved in the interactions between the inertial waves and the viscous boundary layer flows.

scholarly journals The light/dark cycle of microalgae in a thin-layer photobioreactor

2020 ◽  
Author(s):  
Alessandro Chiarini ◽  
Maurizio Quadrio
Keyword(s):  
Thin Layer ◽  
Time Scale ◽  
Stokes Equations ◽  
Numerical Study ◽  
Numerical Approach ◽  
Navier Stokes ◽  
Dark Cycle ◽  
Navier Stokes Equations ◽  
Time Resolved ◽  
Typical Time

AbstractA numerical study of the motion of algal cells in a representative thin-layer-cascade (TLC) photobioreactor is presented. The goal is to determine the time scale associated with the light/dark (L/D) cycle seen by the cells during their turbulent motion in the liquid culture. Owing to the limited reliability of the available numerical results which deal with time-averaged quantities and thus lack time-resolved information, the present study is based upon the Direct Numerical Simulation of the Navier-Stokes equations, a reliable but consequently expensive numerical approach which does not incur in turbulence modelling errors. Indeed, the simulation is successfully validated in terms of averaged velocity with experimental data. The availability of full temporal information allows algae cells to be followed in time along their trajectories. A large number (up to a million) of tracers is placed in the flow to mimic the algae cell. Their trajectories are statistically studied and linked to the turbulent mixing. Results indicate that, in a typical TLC reactor designed to mimic an experimental setup, cells undergo an L/D cycle with a time scale in the range 0.1–2 s. Such time scale, albeit much longer than the typical time scale of the photosynthesis, significantly benefits the productivity of the algae compared to a steady illumination.

scholarly journals Error reduction for time-resolved PIV data based on Navier–Stokes equations

2018 ◽  
Vol 59 (10) ◽  
Author(s):  
Hong-Ping Wang ◽  
Qi Gao ◽  
Shi-Zhao Wang ◽  
Yu-Hang Li ◽  
Zhong-Yi Wang ◽  
...  
Keyword(s):  
Stokes Equations ◽  
Error Reduction ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Time Resolved
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