Propagation of unsteady disturbances in a slowly varying duct with mean swirling flow

2001 ◽  
Vol 445 ◽  
pp. 207-234 ◽  
Author(s):  
A. J. COOPER ◽  
N. PEAKE
Keyword(s):  
Turning Point ◽  
Multiple Scales ◽  
Swirling Flow ◽  
Coupled System ◽  
Mean Flow ◽  
Amplitude Variation ◽  
Small Shift ◽  
Swirl Velocity ◽  
Vorticity Equations ◽  
Multiple Scales Solution

The propagation of unsteady disturbances in a slowly varying cylindrical duct carrying mean swirling flow is described. A consistent multiple-scales solution for the mean flow and disturbance is derived, and the effect of finite-impedance boundaries on the propagation of disturbances in mean swirling flow is also addressed.Two degrees of mean swirl are considered: first the case when the swirl velocity is of the same order as the axial velocity, which is applicable to turbomachinery flow behind a rotor stage; secondly a small swirl approximation, where the swirl velocity is of the same order as the axial slope of the duct walls, which is relevant to the flow downstream of the stator in a turbofan engine duct.The presence of mean vorticity couples the acoustic and vorticity equations and the associated eigenvalue problem is not self-adjoint as it is for irrotational mean flow. In order to obtain a secularity condition, which determines the amplitude variation along the duct, an adjoint solution for the coupled system of equations is derived. The solution breaks down at a turning point where a mode changes from cut on to cut off. Analysis in this region shows that the amplitude here is governed by a form of Airy's equation, and that the effect of swirl is to introduce a small shift in the location of the turning point. The reflection coefficient at this corrected turning point is shown to be exp (iπ/2).The evolution of axial wavenumbers and cross-sectionally averaged amplitudes along the duct are calculated and comparisons made between the cases of zero mean swirl, small mean swirl and O(1) mean swirl. In a hard-walled duct it is found that small mean swirl only affects the phase of the amplitude, but O(1) mean swirl produces a much larger amplitude variation along the duct compared with a non-swirling mean flow. In a duct with finite-impedance walls, mean swirl has a large damping effect when the modes are co-rotating with the swirl. If the modes are counter-rotating then an upstream-propagating mode can be amplified compared to the no-swirl case, but a downstream-propagating mode remains more damped.

The stability of a slowly diverging swirling jet

2002 ◽  
Vol 473 ◽  
pp. 389-411 ◽  
Author(s):  
A. J. COOPER ◽  
N. PEAKE
Keyword(s):  
Turning Point ◽  
Multiple Scales ◽  
Radial Distance ◽  
Shear Instability ◽  
Parabolic Cylinder ◽  
Leading Order ◽  
Mean Flow ◽  
Envelope Amplitude ◽  
Swirling Jet ◽  
Consistent Solution

The spatial evolution of small-amplitude unsteady disturbances of an axisymmetric swirling jet is examined theoretically. The slow axial divergence of the jet mean flow is accounted for by using the method of multiple scales and a consistent solution for both the mean flow and unsteady disturbance is derived. Previous work by Lu & Lele (1999) has considered the leading-order analysis, in which the modal eigenvalues are determined from locally parallel theory, but the key feature of our analysis is the solution of the next-order secularity condition for the axial variation of the wave-envelope amplitude.The swirling jet profile sustains two types of instability waves: the Kelvin–Helmholtz instability associated with axial shear, and a centrifugal instability which arises due to a decrease in circulation with radial distance. The evolution of the disturbance axial wavenumber and envelope amplitude with downstream distance is calculated. Numerical results show that the growth of the centrifugal mode is significantly curtailed as a result of a rapidly decaying envelope amplitude. The shear instability is significantly more amplified by the addition of swirl.The general solution for the disturbance envelope amplitude breaks down at so-called turning points. This is found to occur for a series of neutral propagating modes. A rescaling in the vicinity of the turning point shows that the amplitude in this region is governed by a parabolic cylinder equation. The modal amplitude is seen to decay very significantly through this turning point, even though the mode is neutral to leading order.

scholarly journals Sound transmission in slowly varying circular and annular lined ducts with flow

1999 ◽  
Vol 380 ◽  
pp. 279-296 ◽  
Author(s):  
S. W. RIENSTRA
Keyword(s):  
Multiple Scales ◽  
Natural Extension ◽  
Sound Transmission ◽  
Attractive Alternative ◽  
Mean Flow ◽  
Modal Expansion ◽  
Present Solution ◽  
Impedance Wall ◽  
Lined Ducts ◽  
Multiple Scales Solution

Sound transmission through straight circular ducts with a uniform inviscid mean flow and a constant acoustic lining (impedance wall) is classically described by a modal expansion. A natural extension for ducts with axially slowly varying properties (diameter and mean flow, wall impedance) is a multiple-scales solution. It is shown in the present paper that a consistent approximation of boundary condition and isentropic mean flow allows the multiple-scales problem to have an exact solution. Since the calculational complexities are no greater than for the classical straight duct model, the present solution provides an attractive alternative to a full numerical solution if diameter variation is relevant. A unique feature of the present solution is that it provides a systematic approximation to the hollow-to-annular cylinder transition problem in the turbofan engine inlet duct.

Analysis of Turbulence in the Tip Region of a Waterjet Pump Rotor

2010 ◽  
Author(s):  
Huixuan Wu ◽  
Rinaldo L. Miorini ◽  
Joseph Katz
Keyword(s):  
Energy Flux ◽  
Large Scale ◽  
Multiple Scales ◽  
Tip Clearance ◽  
Mean Flow ◽  
Production Characteristic ◽  
Pump Rotor ◽  
The Mean ◽  
Turbulence Production ◽  
Waterjet Pump

A series of high resolution planar particle image velocimetry measurements performed in a waterjet pump rotor reveal the inner structure of the tip leakage vortex (TLV) which dominates the entire flow field in the tip region. Turbulence generated by interactions among the TLV, the shear layer that develops as the backward leakage flow emerges from the tip clearance as a “wall jet”, the passage flow, and the endwall is highly inhomogeneous and anisotropic. We examine this turbulence in both RANS and LES modelling contexts. Spatially non-uniform distributions of Reynolds stress components are explained in terms of the local mean strain field and associated turbulence production. Characteristic length scales are also inferred from spectral analysis. Spatial filtering of instantaneous data enables the calculation of subgrid scale (SGS) stresses, along with the SGS energy flux (dissipation). The data show that the SGS energy flux differs from the turbulence production rate both in trends and magnitude. The latter is dominated by energy flux from the mean flow to the large scale turbulence, which is resolved in LES, whereas the former is dominated by energy flux from the mean flow to the SGS turbulence. The SGS dissipation rate is also used for calculating the static and dynamic Smagorinsky coefficients, the latter involving filtering at multiple scales; both vary substantially in the tip region, and neither is equal to values obtained in isotropic turbulence.

Effects of the Interaction Point of Multi-Passage Swirlers on the Swirling Flow Field

2019 ◽  
Vol 141 (6) ◽  
Author(s):  
Foad Vashahi ◽  
Jeekeun Lee
Keyword(s):  
Geometrical Parameter ◽  
Swirling Flow ◽  
Energy Levels ◽  
Fuel Mixture ◽  
Mean Flow ◽  
Interaction Point ◽  
Stagnation Points ◽  
Image Velocimetry ◽  
The Mean ◽  
Proper Orthogonal

An experimental study is conducted to understand the mean and instantaneous behavior of the swirling flow issued from a triple swirler influenced by a single critical geometrical parameter, termed as the passage length. The investigated geometrical parameter defines the interaction point of the inner axial swirlers with the outer radial swirler, which consequently defines the primary air–fuel mixture characteristics and the resultant combustion state. Experiments were performed under cold flow conditions, and planar particle image velocimetry was employed to measure the velocity field. The mean flow pattern exhibited significant differences in terms of the swirl-jet width and angle and altered the number of stagnation points on the swirler axis. When the passage length was reduced to half, two stagnation points appeared on the swirler axis due to an initially developed smaller recirculation zone at the swirler mouth. Also, the turbulent activity at the vicinity of the swirler increased with as the passage length reduced. Investigations on the relocation of the second stagnation point on the axis through an arbitrary window revealed identical standard deviation in x and y directions. The energetic coherent structures extracted from the proper orthogonal decomposition also identified major differences in terms of the spatial distribution of the modes and their corresponding energy levels. The experimental results indicated that if the passage length is altered, the number of stagnation points on the swirler axis increases, and a breakdown of both the bubble and cone vortex may appear at the same time as different energy levels.

The wave modes in ducted swirling flows

1998 ◽  
Vol 371 ◽  
pp. 1-20 ◽  
Author(s):  
CHRISTOPHER K. W. TAM ◽  
LAURENT AURIAULT
Keyword(s):  
Swirling Flow ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Inviscid Flow ◽  
Mean Flow ◽  
Compressibility Effect ◽  
Propagating Waves ◽  
The Mean ◽  
Initial Boundary Value ◽  
Wave Modes

The small-amplitude wave modes inside a ducted inviscid compressible swirling flow are investigated. In order to avoid possible mathematical ambiguities arising from the use of an inviscid flow model, the wave modes are cast as the solution of an initial boundary value problem. Two families of propagating waves are found. The acoustic modes are supported by the compressibility effect of the flow. The rotational modes are sustained by the centrifugal force field associated with the mean flow rotation. Two cases, one with a free-vortex swirl and the other with a rigid-body swirl, are investigated in some depth. Numerical results are provided.

Analysis of Turbulent Swirling Flow in an Isothermal Gas Turbine Combustor Model

2014 ◽  
Author(s):  
A. C. Benim ◽  
S. Iqbal ◽  
A. Nahavandi ◽  
W. Meier ◽  
A. Wiedermann ◽  
...  
Keyword(s):  
Swirling Flow ◽  
Turbulence Models ◽  
Scale Model ◽  
Gas Turbine Combustor ◽  
Wall Functions ◽  
Swirl Velocity ◽  
Subgrid Scale Model ◽  
German Aerospace ◽  
Isothermal Gas ◽  
Upstream Flow

Isothermal turbulent swirling flow in a model combustor is computationally and experimentally investigated. The main purpose was the validation of turbulence models for this flow type. The experiments were carried out at the German Aerospace Centre (DLR), Stuttgart. For the modeling, the validation of the LES approach, applying the Smagorinsky subgrid-scale model, using wall-functions, takes a central role in the present study. URANS calculations based on SST and RSM were also performed. An analysis for LES showed that a sufficient resolution is indeed obtained for grid index values proposed in the literature. It was also observed that coarser grids can still deliver useful results. LES results were observed to be quite accurate, except the swirl velocity in the outer parts of the jet, which was under-predicted. URANS results were not that good, whereas the RSM performed better than the SST, especially in predicting the swirl velocity in the outer parts. An investigation performed on different domain sizes indicated that the outlet boundary formulation has some influence on the prediction of the upstream flow. The influence of the differencing scheme on LES was also investigated.

scholarly journals Evaluation of the Autoparametric Pendulum Vibration Absorber for a Duffing System

2008 ◽  
Vol 15 (3-4) ◽  
pp. 355-368 ◽  
Author(s):  
Benjamın Vazquez-Gonzalez ◽  
Gerardo Silva-Navarro
Keyword(s):  
Frequency Response ◽  
Fixed Points ◽  
Multiple Scales ◽  
Coupled System ◽  
Vibration Absorber ◽  
Primary System ◽  
Duffing System ◽  
Approximate Frequency ◽  
The Stability ◽  
Cubic Stiffness

In this work we study the frequency and dynamic response of a damped Duffing system attached to a parametrically excited pendulum vibration absorber. The multiple scales method is applied to get the autoparametric resonance conditions and the results are compared with a similar application of a pendulum absorber for a linear primary system. The approximate frequency analysis reveals that the nonlinear dynamics of the externally excited system are suppressed by the pendulum absorber and, under this condition, the primary Duffing system yields a time response almost equivalent to that obtained for a linear primary system, although the absorber frequency response is drastically modified and affected by the cubic stiffness, thus modifying the jumps defined by the fixed points. In the absorber frequency response can be appreciated a good absorption capability for certain ranges of nonlinear stiffness and the internal coupling is maintained by the existing damping between the pendulum and the primary system. Moreover, the stability of the coupled system is also affected by some extra fixed points introduced by the cubic stiffness, which is illustrated with several amplitude-force responses. Some numerical simulations of the approximate frequency responses and dynamic behavior are performed to show the steady-state and transient responses.

The generation of sound by vorticity waves in swirling duct flows

1977 ◽  
Vol 81 (2) ◽  
pp. 369-383 ◽  
Author(s):  
M. S. Howe ◽  
J. T. C. Liu
Keyword(s):  
Acoustic Pressure ◽  
Swirling Flow ◽  
Sound Waves ◽  
Cross Sectional ◽  
Aerodynamic Sound ◽  
Swirl Velocity ◽  
Perturbation Velocity ◽  
Linearized Model ◽  
Axisymmetric Duct ◽  
Turbine Blading

Swirling flow in an axisymmetric duct can support vorticity waves propagating parallel to the axis of the duct. When the cross-sectional area of the duct changes a portion of the wave energy is scattered into secondary vorticity and sound waves. Thus the swirling flow in the jet pipe of an aeroengine provides a mechanism whereby disturbances produced by unsteady combustion or turbine blading can be propagated along the pipe and subsequently scattered into aerodynamic sound. In this paper a linearized model of this process is examined for low Mach number swirling flow in a duct of infinite extent. It is shown that the amplitude of the scattered acoustic pressure waves is proportional to the product of the characteristic swirl velocity and the perturbation velocity of the vorticity wave. The sound produced in this way may therefore be of more significance than that generated by vorticity fluctuations in the absence of swirl, for which the acoustic pressure is proportional to the square of the perturbation velocity. The results of the analysis are discussed in relation to the problem of excess jet noise.

The Vibration Reduction Analysis of a Rotating Mechanism Deck System

2008 ◽  
Vol 24 (3) ◽  
pp. 253-266 ◽  
Author(s):  
Y.-R. Wang ◽  
T.-H. Chen
Keyword(s):  
Multiple Scales ◽  
Vibration Reduction ◽  
Coupled System ◽  
Cost Effective ◽  
Disk Drive ◽  
Theoretical Background ◽  
Vibration Absorber ◽  
Aeroelastic System ◽  
Lagrange’S Equation ◽  
Optical Disk Drive

AbstractIn this paper, an optimized position of a mass-spring-damper vibration absorber is proposed for a rotating mechanism device (such as optical disk drive or rotary-wing and deck coupled system). A nonlinear 3-D theoretical model for a deck is established by Lagrange's equation. A 2-bladed rotor and deck (foundation) coupled aeroelastic system with vibration reduction device is presented and studied as well. The analytical solution is obtained by the Multiple-scales method for the case of no vibration absorber. The numerical results in time and frequency domain and with/no absorber are acquired. This research provides a theoretical background for the preliminary vibration reduction design for industries. It is found that the existing disk drives vibration can be reduced by simply adding the absorber at the end corner isolator of the deck, but without changing the main configurations. This will not only save costs but also increase testing efficiency, achieving the most cost-effective vibration reduction result.

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