Sound radiation from a cylindrical duct. Part 2. Source modelling, nil-shielding directions, and the open-to-ducted transfer function

1996 ◽  
Vol 313 ◽  
pp. 367-380 ◽  
Author(s):  
C. J. Chapman
Keyword(s):  
Transfer Function ◽  
Good Accuracy ◽  
Shielding Effect ◽  
Front Face ◽  
Main Beam ◽  
Mean Flow ◽  
Sound Fields ◽  
Ducted Fan ◽  
Noise Shielding ◽  
Cylindrical Duct

This paper analyses the sound radiated from the front face of a hard-walled circular cylindrical duct in a subsonic mean flow when the duct contains acoustic sources typical of those in a ducted-fan aeroengine. Two main results are established for modes of any given frequency and circumferential order. The first result is that in certain easily calculated directions, called here the nil-shielding directions, the sound radiated by ducted sources is the same as the sound radiated by the corresponding open sources, i.e. by unducted sources of the same distribution and strength radiating into free space. Thus in these special directions the duct has no noise-shielding effect. The second result is that, in the Kirchhoff approximation, the sound radiated by the open sources in the nil-shielding directions determines the sound radiated by the ducted sources in all directions; i.e. the sound fields radiated by open and ducted sources are related by an open-to-ducted transfer function. This function is such that the sound radiated by the ducted sources is a linear combination of certain diffraction functions, in which the coefficients are given by the sound radiated by the open sources in the nil-shielding directions. The diffraction functions do not depend on the sources and are here calculated explicitly in terms of Bessel functions. The method used in the paper is Kirchhoff's approximation; within linear theory this gives the nil-shielding directions exactly, i.e. in agreement with the Wiener—Hopf solution, and gives the main beam of the radiated field, including the major side-lobes, to good accuracy. The results are relevant to the sound radiated into the forward arc by a ducted turbofan aeroengine.

Dynamic modulation of cerebrovascular resistance as an index of autoregulation under tilt and controlled Pet CO2

2002 ◽  
Vol 283 (3) ◽  
pp. R653-R662 ◽  
Author(s):  
Michael R. Edwards ◽  
J. Kevin Shoemaker ◽  
Richard L. Hughson
Keyword(s):  
Transfer Function ◽  
Function Analysis ◽  
Low Frequency ◽  
Mean Flow ◽  
Low Frequencies ◽  
Cerebrovascular Autoregulation ◽  
Cerebrovascular Resistance ◽  
Arterial Blood ◽  
Transfer Function Analysis ◽  
Frequency Changes

Transfer function analysis of the arterial blood pressure (BP)-mean flow velocity (MFV) relationship describes an aspect of cerebrovascular autoregulation. We hypothesized that the transfer function relating BP to cerebrovascular resistance (CVRi) would be sensitive to low-frequency changes in autoregulation induced by head-up tilt (HUT) and altered arterial Pco 2. Nine subjects were studied in supine and HUT positions with end-tidal Pco 2(Pet CO2 ) kept constant at normal levels: +5 and −5 mmHg. The BP-MFV relationship had low coherence at low frequencies, and there were significant effects of HUT on gain only at high frequencies and of Pco 2 on phase only at low frequencies. BP → CVRi had coherence >0.5 from very low to low frequencies. There was a significant reduction of gain with increased Pco 2 in the very low and low frequencies and with HUT at the low frequency. Phase was affected by Pco 2 in the very low frequencies. Transfer function analysis of BP → CVRi provides direct evidence of altered cerebrovascular autoregulation under HUT and higher levels of Pco 2.

scholarly journals Front-Face Fluorimeter for the Determination of Cutting Time of Cheese Curd

Foods ◽  
2021 ◽  
Vol 10 (3) ◽  
pp. 576
Author(s):  
Maryna Lazouskaya ◽  
Irina Stulova ◽  
Aavo Sõrmus ◽  
Ott Scheler ◽  
Kalle Tiisma ◽  
...  
Keyword(s):  
Predictive Power ◽  
Good Accuracy ◽  
Daily Variation ◽  
Front Face ◽  
Current Standard ◽  
Standard Methods ◽  
Milk Samples ◽  
Cheese Curd ◽  
Physical Changes

The yield of product (cheese) during the cheese-making process depends on the cutting time of the cheese curd. However, the determination of optimal cutting time on an industrial scale is difficult as current standard methods are destructive or analyse only small volumes and not the entire milk to be curdled into cheese. This paper presents a novel front-face fluorimeter (FFF) that is designed to be immersed into a milk batch to enable the determination of the cutting time of cheese curd without the destruction of the sample. The FFF sensor signal corresponds to physical changes in milk during cheese formation and has high predictive power (r > 0.85) and good accuracy (RSE = 30%, considering daily variation between milk samples). The performance of the presented fluorimeter was on par with standard rheological and Berridge methods.

Low-Order Modelling of Thermoacoustic Limit Cycles

2004 ◽  
Author(s):  
Simon R. Stow ◽  
Ann P. Dowling
Keyword(s):  
Transfer Function ◽  
Heat Release ◽  
Limit Cycle ◽  
Limit Cycles ◽  
Acoustic Waves ◽  
Mean Flow ◽  
Velocity Perturbation ◽  
Linear Mode ◽  
The Mean ◽  
Low Order

Lean premixed prevaporised (LPP) combustion can reduce NOx emissions from gas turbines, but often leads to combustion instability. Acoustic waves produce fluctuations in heat release, for instance by perturbing the fuel-air ratio. These heat fluctuations will in turn generate more acoustic waves and in some situations self-sustained oscillations can form. The resulting limit cycles can have large amplitude causing structural damage. Thermoacoustic oscillations will have a low amplitude initially. Thus linear models can give stability predictions. An unstable linear mode will grow in amplitude until nonlinear effects become important and a limit cycle is achieved. While the frequency of the linear mode can provide a good approximation to that of the resulting limit cycle, linear theories give no prediction of its amplitude. A low-order model for thermoacoustic limit cycles in LPP combustors is described. The approach is based on the fact that the main nonlinearity is in the combustion response to flow perturbations. In LPP combustion, fluctuations in the inlet fuel-air ratio have been shown to be the dominant cause of unsteady combustion: these occur because velocity perturbations in the premix ducts cause a time-varying fuel-air ratio, which then convects downstream. If the velocity perturbation becomes comparable to the mean flow, there will be an amplitude-dependent effect on the equivalence ratio fluctuations entering the combustor and hence on the rate of heat release. A simple nonlinear flame model for this dependence is developed and is assumed to be the major non-linear effect on the limit cycle. Since the Mach number is low, the velocity perturbation can be comparable to the mean flow, with even reverse flow occurring, while the disturbances are still acoustically linear in that the pressure perturbation is still much smaller than the mean. Hence elsewhere the perturbations are treated as linear. In this nonlinear flame model, the flame transfer function describing the combustion response to changes in inlet flow is a function of both frequency and amplitude. The nonlinear flame transfer function is incorporated into a linear thermoacoustic network model for plane waves. Frequency, amplitude and modeshape predictions are compared with results from an atmospheric test rig. The approach is extended to circumferential waves in a thin annular geometry, where the nonlinearity leads to modal coupling.

Modeling the Response of Premixed Flames to Mixture Ratio Perturbations

2003 ◽  
Author(s):  
Ju Hyeong Cho ◽  
Tim C. Lieuwen
Keyword(s):  
Transfer Function ◽  
Equivalence Ratio ◽  
Flame Length ◽  
Flame Speed ◽  
Heat Of Reaction ◽  
Mean Flow ◽  
Mixture Ratio ◽  
Flame Response ◽  
The Mean ◽  
Flame Position

Combustion instabilities continue to cause significant reliability and availability problems in low emissions gas turbine combustors. It is known that these instabilities are often caused by a self-exciting feedback loop between unsteady heat release rate and reactive mixture equivalence ratio perturbations. We present an analysis of the flame’s response to equivalence ratio perturbations by considering the kinematic equations for the flame front. This response is controlled by three processes: heat of reaction, flame speed, and flame area. The first two are directly generated by equivalence ratio oscillations. The third is indirect, as it is generated by the flame speed fluctuations. The first process dominates the response of the flame at low Strouhal numbers, roughly defined as frequency times flame length divided by mean flow velocity. All three processes play equal roles at Strouhal numbers of O(1). The mean equivalence ratio exerts little effect upon this transfer function at low Strouhal numbers. At O(1) Strouhal numbers, the flame response increases with decreasing values of the mean equivalence ratio. Thus, these results are in partial agreement with heuristic arguments made in prior studies that the flame response to equivalence ratio oscillations increases as the fuel/air ratio becomes leaner. In addition, a result is derived for the sensitivity of this transfer function to uncertainties in mean flame position. For example, a sensitivity of 10 means that a 5% uncertainty in flame position translates into a 50% uncertainty in transfer function. This sensitivity is of O(1) for St<<1, but has very high values for St∼O(1).

The dissipation and shear dispersion of entropy waves in combustor thermoacoustics

2013 ◽  
Vol 733 ◽  
Author(s):  
Aimee S. Morgans ◽  
Chee Su Goh ◽  
Jeremy A. Dahan
Keyword(s):  
Transfer Function ◽  
Gas Turbine ◽  
Acoustic Waves ◽  
Flow Simulation ◽  
Turbulent Channel Flow ◽  
Combustion Noise ◽  
Mean Flow ◽  
Gaussian Form ◽  
Gaussian Profile ◽  
Shear Dispersion

AbstractThis paper considers the effect of flow advection on entropy waves. The interest is in whether entropy waves persist in gas turbine combustors, between the flame, where they are generated, and the combustor exit, where their acceleration generates acoustic waves (known as ‘entropy noise’ or ‘indirect combustion noise’). Entropy wave advection within a simplified fully developed turbulent channel-flow simulation is investigated. Entropy wave dissipation is found to be negligible, with loss of entropy wave strength caused predominantly by mean flow shear dispersion. The impulse response of entropy perturbations downstream of where they are generated is shown to be well modelled by a Gaussian profile in time. This yields a (different) Gaussian form for the inlet–outlet transfer function of entropy perturbations. For representative gas turbine flows, the magnitude of this transfer function is such that significant entropy wave strength will remain at the combustor exit, confirming that entropy-generated acoustic waves are likely to be important.

Validation of Flame Transfer Function Reconstruction for Perfectly Premixed Swirl Flames

2004 ◽  
Author(s):  
A. Gentemann ◽  
C. Hirsch ◽  
K. Kunze ◽  
F. Kiesewetter ◽  
T. Sattelmayer ◽  
...  
Keyword(s):  
Transfer Function ◽  
Heat Release ◽  
Dynamic Behavior ◽  
Broad Band ◽  
Combustion Process ◽  
Single Frequency ◽  
Mean Flow ◽  
Swirl Number ◽  
Absolute Value ◽  
The Absolute

The introduction of lean premix combustion increases the susceptibility of the combustor to thermoacoustic instabilities. To control these instabilities, information about the dynamic behavior of the combustion process is necessary. The flame transfer function offers one possibility to describe the dynamic behavior of the combustion process. It relates velocity fluctuations through the burner to an overall heat release fluctuation caused by the flame. As the transfer function for turbulent premix swirl flames can not be derived accurately from first principles, an alternative approach is needed. This paper introduces and validates a method, based on computational fluid dynamics (CFD), to reconstruct flame transfer functions. A transient simulation of the turbulent reacting flow is performed with broad band excitation of the flow variables on the boundaries. On the basis of the resulting time series for velocity and heat release, the transfer function of the flame is reconstructed by application of a system identification procedure based on the Wiener-Hopf equation. This method is applied to a lean perfectly premixed swirl burner. The resulting transfer function is validated with experimental data up to frequencies of f = 400 Hz. Good qualitative agreement is observed between the two approaches. Remarkably, the absolute value of the flame transfer function (the ‘gain’ of the flame) is found to be larger than unity over a range of frequencies, even though fluctuations of heat release and velocity are normalized with their mean flow values. To gain insight into this phenomenon, the dynamic behavior of the flame is investigated in detail. This concerns in particular the interaction of velocity, heat release fluctuations, the swirl number, and fluctuations of flame position and shape. Instead of broad band excitation, single frequency excitation is applied on the boundary for these investigations. It is found that swirl number fluctuations are convected into the flame. At the frequency where the wavelength of those fluctuations agrees with the length scale of the flame, unburned gases accumulate in the combustor. The excess heat is released periodically, which causes the overshoot in the absolute value of the flame transfer function.

Development of a Tip Leakage Control Device for an Axial Flow Fan

2008 ◽  
Author(s):  
Ali Akturk ◽  
Cengiz Camci
Keyword(s):  
Velocity Component ◽  
Tangential Velocity ◽  
Tip Clearance ◽  
Critical Parameters ◽  
Pressure Side ◽  
Mean Flow ◽  
Axial Fan ◽  
Mean Velocity ◽  
Tip Leakage ◽  
Ducted Fan

Performance of an axial fan unit used in ducted fan based propulsion systems is closely related to its tip leakage mass flow rate and the level of tip/casing interactions. The present experimental study uses a stereoscopic Particle Image Velocimeter to quantify the three dimensional mean flow observed at just downstream of a ducted fan unit. After a comprehensive description of the baseline fan exit flow, a number of novel tip treatments based on pressure side extensions are introduced. Various tip leakage mitigation schemes are introduced by varying the chordwise location and the width of the extension in the circumferential direction. The current study shows that a proper selection of the pressure side bump location and width are the two critical parameters influencing the success of each tip leakage mitigation approach. Significant gains in axial mean velocity component are observed when a proper pressure side tip extension is used. It is also observed that a proper tip leakage mitigation scheme significantly reduces the tangential velocity component near the tip of the axial fan blade. Reduced tip clearance interactions are essential in improving the energy efficiency of ducted fan systems. A reduction or elimination of the momentum deficit in tip vortices are also expected to reduce the adverse performance effects originating from the unsteady and highly turbulent tip leakage vortical flows rotating against a stationary casing.

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