Aurélien Marsan
email: aurelien.marsan@usherbrooke.ca

Carlos Pérez Arroyo

Yann Pasco

Stéphane Moreau

Spectral and wavelet analysis of an aero-acoustic feedback loop in a transonic outflow valve based on Schlieren imaging

Keywords:

On commercial aircra s, the adequate pressure ratio between the cabin and the exterior is regulated with circular outflow valves. At an operating pressure ratio equivalent to in altitude, a tonal noise is observed at kHz and higher harmonics. A feedback loop is believed to be responsible for this tonal noise and it is studied on an extruded two-dimensional mock-up representative of the outflow valves including the sealing steps. An spectral analysis is performed on the Schlieren images in terms of pixel intensity for each pixel independently.

is accentuates the aliasing phenomena of the higher harmonics when studying the maximum power spectral density. In order to highlight different pa erns in the flow, phase maps are computed with respect to a particular pixel at kHz and harmonics. Last, the feedback mechanism is visible between the sealing step and the valve with the application of a novel wavelet-based technique on the Schlieren images.

INTRODUCTION

Outflow valves are used in aircra s in order to maintain an adequate pressure ratio between the cabin pressure and the exterior atmospheric pressure and to ensure a sufficient air renewal rate for the passengers to breathe comfortably. ey are typically designed in order to maintain the air cabin pressure at a level corresponding to the atmospheric standard at , , regardless of the flight altitude. In the literature, two types of aircra outflow valves are reported: a flapped outflow valve (as studied by Carbonneau et al. [ ]) and a circular bu erfly outflow valve (see the works of Fetjek et al. [ ]).

Even thought the components of the valves may seem simple, the flow is in reality highly complex. Supersonic or transonic jets develop depending on the pressure ratio through the valve. At transonic and supersonic operating points, the outflow valve generates a significant level of noise that is detrimental to the comfort in the cabin, especially in business jets where the level of ambient noise is an important criteria for the customers and the outflow valve may be located directly under the cabin floor [ ]. Strong tones may be emi ed by the valve, as reported by Hanss et al. [ ]. ere is indeed a need for a be er understanding of the flow physics within bu erfly valves, which may lead to low noise designs and less noise emissions. Unfortunately, only a few studies of aeronautic bu erfly outflow valves can be found in the literature and are briefly introduced in the following.

Addy et al. [ ] have developed on the basis of nozzle

experiments a simplified sudden-enlargement in flow area theoretical model to predict the performance coefficients of transonic and supersonic bu erfly outflow valves. Morris and Du on [ , ] have performed wall static pressure measurements and Schlieren visualization of the flow through a two-dimensional outflow valve equipped with either a biconvex circular arc bu erfly or a flat plate bu erfly at various operating conditions. e study has shown that the flow-field through a bu erfly valve is extremely complex with strong pressure gradient, oblique shock waves and expansion fans, and massive flow separation. By varying the pressure ratio for several opening angles, the occurrence of a massive separation at the downstream edge of the bu erfly for the lowest pressure ratio was observed. e transition from the a ached to the detached flow was related to a peak of the aerodynamic torque, with a strong dependence on the disk geometry near the leading and trailing edges.

Fetjek, Waller and Wong [ ] have performed a CFD analysis of an aircra outflow valve using ANSYS CFX-so ware. e capabilities of the numerical approach were assessed using the above-mentioned two-dimensional test case equipped with the circular arc bu erfly from Morris and Du on. e flow in a real D bu erfly outflow valve was then computed using the same solver parameters, with boundary conditions corresponding to a typical under-floor environment. Results have enlightened the very different behavior of the lower and upper lip jets. e jet issuing from the lower lip is thin and remains adjacent to the duct wall, whereas the jet issuing from the upper lip changes its shape as it extends downstream and concentrates around the median plane of the duct.

is was confirmed by experimental measurements. Noise measurements were taken downstream of the valve and showed high-level broadband noise as well as a tonal emission. e study does not give however any insight into the noise generation mechanism. In addition, the geometry used for the numerical simulation does not include any sealing step on the duct wall, which effect on the development of the jet has been shown to be important [ ].

is may explain why further noise prediction on the same test case a empted by Waller [ ] using the STAR-CD solver coupled with a porous Ffowcs Williams-Hawkings method did not succeed in predicting the existence of a tone.

One study of particular interest has been conducted by Hanss and Miklaszewski [ ] who investigated the flow within a bu erfly outflow valve using CFD computations performed with StarCCM+. e study gives a particular focus on the occurrence of a tonal noise reported by experiments, and assesses the effectiveness of geometrical modifications at canceling this tone. e tone is conjectured to be a screech tone, produced by a feedback mechanism between vortices in the shear layer and a standing system of shock waves.

e addition of a half-moon shape part positioned on the upstream side and downstream face of the bu erfly allows to cancel completely the tone experimentally and reduce the intensity of the shocks numerically.

is effect is attributed to the lower extent of the supersonic regions, that may weaken the aero-acoustic coupling at the origin of the screech noise. However, no clear evidence is given to support that interpretation, and the control mechanism remains unclear. Moreover, it is not clear if the total mass flow through the modified valve remains the same, given the fact that the upstream side jet is weaker.

Finally, the CFD study conducted by Smid, Spalart and Breard [ ] should be stressed even if it were on a flapped outflow valve. e authors have indeed used a two-dimensional Unsteady Reynolds-Averaged Navier-Stokes (U-RANS) approach with two different codes in order to successfully investigate the occurrence of tonal noise at several operating conditions, and assess the effect of increasing the roughness at well chosen locations on the walls. e two numerical codes have been found capable of predicting the tone associated to a vortex shedding at the sealing step on the forward door of the valve. e use of roughness was able to prevent the vortex shedding on the step, as well as a boundary layer separation on the a door. As a result, the tone was canceled both numerically and experimentally. e present work deals with a bu erfly outlow valve similar to that of Hanss and Miklaszewski [ ] and Fetjek, Waller and Wong [ ] for which a strong tonal noise has been reported.

e objective is to experimentally put into evidence the aero-acoustic phenomenon that creates the tone by using high-speed Schlieren imaging of the flow through a transparent two-dimensional bu erfly valve, representative of the real test case.

e post-processing techniques performed in this work are based on spectral analysis and wavelet-based techniques. e be er understanding of the tonal noise generation mechanism should allow to identify simple and promising treatments, based on geometrical modification or wall roughness modifications for example. is work is structured as follows. First, the experimental setup and the operational point of the valve are presented in sections and respectively. e analysis of spectral and wavelet-based results is shown in section . Last, the conclusions and outlooks are summarized in section .

. EXPERIMENTAL SET-UP . Channel and pressure measurements e circular outflow valve (OFV) is modeled by a rectangular channel of 10D in length having a inner section of D height and 0.62D large is connected to a vacuum tank of . m 3 (Fig. ), D being the diameter of the actual circular OFV.

An extruded bu erfly of height D is mounted at the entrance of the rectangular duct. e two-dimensional geometry of the rectangular valve, in particular the sealing step and the bell-mouth entrance perfectly match the geometry of the actual circular bu erfly at its mid-section. e aperture angle of the bu erfly can be varied from 0 • to 90 • . When closing the bu erfly, the steps of length L = 2.5 cm compress the bu erfly seals preventing leakages.

A . mm thick mylar membrane is sealed in between the vacuum tank and the rectangular channel to allow the initial depressurization of the vacuum tank to a pressure ratio of . mimicking the outside atmosphere at the maximum flight altitude. e laboratory atmospheric pressure mimics that of the cabin pressure. A Chromel C wire is taped on the membrane. A high tension across the diaphragm results in a burst which initiates the flow in the channel. Even though the duration of an experiment is only a few seconds, the flow sweeps across a wide range of pressure ratios providing a new insight for the OFV manufacturers.

Two high-quality glass windows are placed on one side of the channel facing two other similar windows on the other side of the channel.

ey allow the flow visualization by Schlieren or PIV at the lower and upper lips of the D butterfly. Two other windows are located at the top and bo om of the rectangular duct for PIV laser-sheet access. ose × mm 2 and mm thick optical windows provide a maximum transmission in the green light at nm. e channel is made of transparent acrylic to allow flow visualization beyond the optical windows. e background luminosity of the frames is adjusted without flow using both the knife position and the shading (black level) correction function of the camera. At the end of the adjustment, the knife edge as located at the middle of the light dot and the background luminosity seen by the camera is almost uniformly medium grey.

Finally, images are recorded by a Photron Fastcam SA-X . All images are recorded on bits Table summarizes the Schlieren views that have been recorded. Full view gives a large overview of the flow pa ern at the upper lip side. It has been taken using the cm focal distance lens, and a high resolution. e frame-rate and the recording time are then limited by buffer size of the camera. For this view, a frame-rate of , fps has been chosen, which allows recording a . seconds sequence duration. Front step view and Rear step view are focused on the lip and on the upstream edge of the sealing step, and on the downstream edge of the sealing step, respectively. Resolution is smaller which allows longer recording times at a higher frame-rate. Several phenomena can be seen from . Spectral analysis e Fourier transform is used in order to study the frequency content of the Schlieren frames. In particular, a strong kHz component is expected and should highlight the flow behavior that originates the tone.

Each pixel intensity is considered as a one-dimensional data that has been recorded over time at a given frame rate.

en, the Fourier transform is computed for each pixel separately over ms of signal. e Welch's periodogram is used. Segments are ms long, with % overlap and a Hanning window. Amplitude and phase can then be computed at each location.

. . Aliasing effect in Schlieren frames

As a very first insight, the maximum of the PSD of pixel intensity fluctuation over all the pixels in the Schlieren images is e expected peak at . kHz is found in the two cases, and corresponds to the highest amplitude. Another peak exist at . kHz and corresponds to the first harmonic of the tone. Other peaks at . kHz and . kHz for Full , and . kHz and . kHz for Full are present due to aliasing and correspond to the second and third harmonic of the kHz tone. In the following, peaks at frequencies other than kHz and its harmonics will be discarded.

. . Phase maps e cross power spectral density (CPSD) is computed at all pixels of the Schlieren images using point A (and B for Rear step) as reference, using the csd function as implemented in the SciPy package for Python. e amplitude of the CPSD highlights the pixels where the spectrum has a peak at the same frequencies as the reference pixel. In this case, the amplitude only highlights the shocks, the shear layer and the vortex shedding as expected [ ], not giving any relevant information and is thus omi ed. On the other hand, the e full views Full and Full , give information about the shape of the pa erns in a general view, however, the pixel resolution is too low to analyze in detail the shocks and expansion waves. Moreover, the aliasing could alter the e compression waves inside the jet illustrated in Fig.

show smaller wavelengths for increasing frequency as well as a higher number of them. Moreover, at the harmonic, the phase is not coherent outside the jet as it is at kHz. e lambda shock position and phase remains fairly constant at the different frequencies although, as it happens for the compression waves, the shock seems to be split in several. It is unclear, if this is simply a three-dimensional effect of the Schlieren at the shock in the span-wise direction or there are in fact different modes associated to the shock. e phase maps for the Rear step are shown in Fig. with the reference phase computed from point B. At kHz the expansion wave that is formed at the rear step is clearly visible. Moreover, a er the step, the flow is detached and forms a recirculation bubble. In the top part of the picture (y(pi xel ) < 80) the phase shows the same behavior as in Figs. and . e phase goes from positive (red) to negative (blue) passing through the zero (green). However, for values y(pi xel ) > 80 and x(pi xel ) < 50, the opposite phenomena is encountered. In this case, the phase goes from positive (red), to negative (blue).

is could imply that a wave is being propagated in the other direction. At the harmonic, (

. Wavelet analysis

Spectral analysis shown in the previous section are well adapted for signals with periodic components. However, the signal is not always fully periodic and some intermi ent events that produce noise at particular frequencies appear in time. In order to keep the discretization in time, the wavelet transform can be performed. e wavelet-based technique [ ] is applied in this work to extract the signature through e initial signal q (t) (pixel intensity from the Schlieren images) is decomposed into the wavelet domain at a reference pixel using the continuous wavelet transform as

w (s,τ) = 1 √ |s| +∞ -∞ q (t) ψ * t -τ s dt, ( )
where τ is the translation parameter, s is the dilatation or scale parameter and ψ * t-τ s is the complex conjugate of the daughter wavelet ψ t-τ s obtained by the translation and dilatation of the so-called mother wavelet ψ 0 (t). In this work, the non-orthogonal continuous wavelet transform was carried out using the Morlet mother wavelet [ ] defined as

ψ 0 (η) = π -1/4 e iω 0 η e -η 2 /2 , ( )
where ω 0 = 16 in this study. e reference scale s can be expressed in terms of frequency f (s) as

f (s) = ω 0 + √ 2 + ω 0 4πs . ( )
e decomposed signal gives a map of the wavelet power |w (s,τ)| 2 , which is function of time and scale (or in this case, frequency). e map is used to localize peaks in time and frequency that are above a predefined threshold.In this work, the event detection method compares the local wavelet power |w (s,τ)| 2 with a defined background spectrum energy at all scales as

SIG(s,τ) = |w (s,τ)| 2 σP k χ 2 2 , ( )
where σ is the variance of the signal q (t), P k is the normalized Fourier power spectrum of a background white noise and χ 2 2 is the value of the chi-squared distribution at %. e reader is referred to the work of Torrence and Compo [ ] for further details.

Once the events have been selected (values of SIG above ) and well localized in the time domain a conditional average can be performed at each scale or at the scale of interest which in this work is . kHz. At each time location t i corresponding to a peak of energy (event) it is possible to extract a window of fixed time-length t W from the target signal g (t). e conditional-average {q; g} can be calculated from the average of this set of windows as

{q; g} = 1 N N i=1 g (ξ i ) , ( )
where

ξ i ∈ ti -t W 2 , ti + t W 2
is the interval surrounding each peak, and N is the number of events used for the conditional average which can be lower than the total number of events detected. Indeed, a filtering window centered at t i of size . s is used to discard events grouped in time.

e result is a temporal characteristic signature representing the most probable shape of the most energetic events at the frequency (scale) of interest.

In this work, the conditional averaging is applied to the full Schlieren images by averaging all the images that lay at the times where the events are detected at the reference pixel.

e result is an image where the influence of the events detected at the reference pixel are highlighted and the other scales are averaged out (if a sufficient number of events/images is used for the averaging). e resulting images are normalized by the standard deviation at each pixel independently in order obtain comparable amplitudes at all locations. Because of the Schlieren technique, the pixel intensity and thus the events that are captured, are a measure of the density gradients in the axial direction (according to the knife orientation) averaged in the span-wise direction.

e analysis is performed at point A and point B on Full , Front step and Rear step from Table . e interest of studying pixel A comes from the fact that several compression waves traveling upstream are visible when analyzing the Schlieren images when the tonal noise at . kHz is present. e two-dimensional cross-conditioning is shown in Fig. (top) where red corresponds to positive normalized values (white in the Schlieren) and blue to negative normalized values (black in the Schlieren).

e black contour lines indicate the regions where the values are higher (solid) and lower (dashed) than one positive or negative standard deviation respectively. From Fig. (top) it can be seen that when the event detects a maximum the different regions of the lambda shock are well defined showing that a determined pa ern that could be responsible of the tonal noise appears in the shock region. Moreover, a footprint with a lower color intensity can be discerned over the step with the same wavelength as in section . . On the other hand, if the reference pixel is taken far from the shock region (pixel B in Fig. (b)) the above-mentioned background pa ern is now clearly visible (Fig. (bo om)). Furthermore, the boundary layer that is formed on top of the step shows a horizontal discontinuity that ends at the rear step with the separation of the boundary layer and possibly a recirculation bubble. When the reference pixel is taken far from the shock region, no areas with values higher than the standard deviation appear in the shocks, even though they are still evident.

Contrary to the Spectral analysis from section . , the wavelength obtained from the pa erns on the background does not vary if the events are computed at . kHz. is can be explained if both frequencies are highly correlated in time. Because the wavelet-procedure keeps the discretization in time, and the cross-conditioning is performed on the Schlieren images, the events that have a higher amplitude (those at kHz) will overlap with others with lower amplitudes (those at kHz).

e signature from Fig. is obtained by averaging the Schlieren images corresponding to the times when the events were detected in the reference pixels A and B. In order to obtain a temporal information about these events, a time shi can be applied to the points in time prior to the averaging (±δt). is is performed for Front step and Rear step and shown in Figs. and for the front and rear steps respectively. e cross-conditioning is performed for the shi s ranging from -6∆t to +3∆t, where ∆t is computed according to the acquisition frequency of the setup (see table ) and 0 ∆t corresponds to the peak of the event. is range corresponds to about one period for the frequency of interest of . kHz. can be seen to originate in the lambda shock, they move upstream inside the wall jet, and die under the lip. Indeed, the train of compression waves changes the sign under the lip at the fundamental frequency of . kHz. e compression wave located at x/L = -0.53 (-6∆t) moves upstream and merges with other compression waves located at x/L = -0.6. However, from these pictures, it looks as if a pa ern was moving upstream as well. Actually, the compression waves that travel upstream and change the sign under the lip appear to be moving outside the shearlayer, close to the vane and then traveling downstream. is wave that travels downstream and is seen in Fig.

(bottom) will have an effect inside the wall jet and thus show some kind of phenomena that travels upstream. Finally, the shear-layer seems to be flapping vertically and changing sign with the displacement of the compression waves (image at -2∆t against +3∆t). e flapping and the waves convected downstream increase the intensity of the lambda shock (starting at -3∆t) which sheds the compression waves that travel upstream.

On the rear step (Fig. ) the pa erns from Fig.

(bottom) can be seen to travel downstream at a convective speed of . m/s for the frequency at kHz. is wave appears to travel first through the boundary layer on the step as it can be seen in the images from -5∆t to -3∆t, then it is stopped by the expansion fan that occurs at the first corner of the step (x/L = -0.5) and merged with the wave that travels in the channel. is pa ern also travels through the expansion fan inside the boundary layer (images from -2∆t). Moreover, from images 0∆t to 3∆t it seems that it is also moving upstream at the end of the boundary layer.

is could be due to either a recirculation bubble on the boundary layer or acoustic waves that are reflected at the expansion wave which travel upstream.

. CONCLUSIONS AND OUTLOOKS

Schlieren imaging has been obtained for a valve representative of realistic outflow valves used in commercial aviation.

ese high-speed Schlieren imaging allows to study the tonal noise that appears at . kHz. e Schlieren images are analyzed using spectral analysis and wavelet-based analysis.

e power spectral density of the Schlieren images presents an aliasing phenomena when the acquisition frame rate is lower than kfps. In this instance, the higher harmonics of the tonal noise are aliased. e phase maps are computed using as reference a pixel inside the wall jet.

e phase maps show several background pa erns with wavelengths of mm and mm at the frequencies of . kHz and . kHz which correspond to convective velocities of . m/s and . m/s respectively. When studying the detailed views with frame rates higher than kfps, compression waves located in the wall jet also show different wavelengths for the frequencies . kHz, . kHz and . kHz. Moreover, the harmonics do not show any difference in phase for the lambda shock and the coherence of the pa ern is lower outside the jet.

e phase map of the rear step depicts clear pa erns mainly at . kHz. Furthermore, a change in sign direction appears close to the step which suggests that a wave is moving upstream at this location.

e wavelet analysis is used in order to compute the twodimensional spatial signature of events detected at reference points. When the reference point is inside the jet, the only pa erns highlighted are those located on the shocks, on the other hand, if the reference point is located downstream, the same background pa erns found with the phase maps using Fourier are obtained with the same wavelengths and convection speeds as for . kHz. is wavelet procedure is not able to obtain the different pa erns at the harmonics due to the difference in amplitude of the harmonics and the fact that they have a high temporal correlation. Nonetheless, when studying the detailed view at the shocks a feedback loop is discerned between the vortical structures shed on the shear-layer of the jet and the compression waves inside the jet. ese vortical structures are convected downstream and perturb the lambda shock by injecting energy and changing the shape in such a way that compression waves are shed inside the jet and travel upstream until they reach the lip. Once they have reached the lip, they perturb the shear-layer and generate new vortical structures. Moreover, the compression waves are transformed into acoustic waves that are convected upstream outside the valve and heard in the farfield. e analysis on the rear step shows how the pa ern reaches the expansion wave generated at the backward step through the boundary layer first. When the signature reaches the expansion fan, it moves upstream which confirms the results obtained with the phase maps.

e Schlieren technique is able to provide many insights to the flow and a feedback loop can be discerned, however, it is uncertain if this phenomena is purely aerodynamic or an aero-acoustic feedback loop. Moreover, what is recorded are density gradients which are not simple to analyze. e events detected with the wavelet transform are based on the pixel intensity related to the gradients and not the actual events. Moreover, the Schlieren technique averages the three-dimensional box of the channel which could result in misleading information, in particular, if span-wise modes appear in the experimental facility. In order to answer these open questions, other post-processing techniques such as Proper Orthogonal Decomposition and Dynamic Mode Decomposition will be performed on the experimental results and on future numerical simulations.

e

  Schlieren arrangement is shown in Fig. . A dual-field lens Schlieren arrangement using a monochromatic greenlight LED at nm. A first lens of cm focal distance and cm diameter allows illuminating the flow field in the channel with parallel beam. e light then goes through a second lens before the converged beams are vertically cut

Figure .

 . Figure . Setup of the simplified OFV equiped with Schlieren imaging mock-up. (a) Rectangular channel with D extruded bu erfly. (b) Wall static pressure probes. (c) Schlieren mock-up. (d) Microphone located at m in front of the channel.

Figure .

 . Figure . Dual-field lens Schlieren arrangement adapted from Se les [ ].

  Figure . Full fields of view of Schlieren sequences

  Figure . Partial fields of view of Schlieren sequences

Figure .

 . Figure . Maximum of PSD of pixel intensity over the full view, for Full (in red) and Full (in black) Schlieren captures. Do ed lines highlight the peaks that can be explained by an aliasing effect.

Figure .

 . Figure . Map of the phase compared with point A, for Full Schlieren capture.

  Fig. (b)), the phase becomes less coherent even though the shortened wavelength (in the (a) . kHz (b) . kHz

Figure .

 . Figure . Map of the phase compared with point A, for Full Schlieren capture.

Figure .

 . Figure . Map of the phase compared with point A, for Front step Schlieren capture.

Figure .

 . Figure . Map of the dephasing compared with point B, for Rear step Schlieren capture.

Figure .

 . Figure . Normalized two-dimensional cross-conditioning of pixel intensity using as reference the events detected at the black dot at . kHz for different ∆t. e results are normalized by the local standard deviation e contours depict where the values are equal to (solid) or -(dashed).

[

  ] I. Fejtek, G. Waller, and R. Wong. Computational study of the flowfield of an aircra outflow valve. In rd AIAA Applied Aerodynamics Conference, page , . [ ] G. Hanss and S. Miklaszewski. Acoustic and flow-field characteristics of a cabin pressure regulation outflow valve. In AF International Conference on Applied Aerodynamics, . [ ] AL. Addy, MJ. Morris, and JC. Du on. An investigation of compressible flow characteristics of bu erfly valves. Journal of fluids engineering, ( ): -, . [ ] MJ. Morris and JC. Du on. Compressible flowfield characteristics of bu erfly valves. Journal of Fluids Engineering, ( ): -, . [ ] MJ. Morris and JC. Du on. Aerodynamic torque characteristics of bu erfly valves in compressible flow. Journal of fluids engineering, ( ): -, . [ ] M. Charlebois-Ménard, M. Sanjosé, A. Marsan, A. Chauvin, Y. Pasco, S. Moreau, and M. Brouille e. Experimental and numerical study of the noise generation in an outflow bu erfly valve. In st AIAA/CEAS Aeroacoustics Conference, . [ ] G. Waller. Prediction of noise generated by a cabin outflow valve using the star-cd code. Canadian Acoustics, ( ): -, . [ ] E. Smid, P.R. Spalart, and C.C. Breard. Outflow valve noise analysis using two-dimensional u-rans cfd. In th AIAA/CEAS Aeroacoustics Conference( th AIAA Aeroacoustics Conference), . [ ] G. S. Se les. Schlieren and Shadowgraph Techniques: Visualizing Phenomena in Transparent Media. Springer-Verlag Berlin Heidelberg, . [ ] A. Marsan, M. Sanjosé, Y. Pasco, S. Moreau, and M. Brouille e. Unsteady wall pressure measurements in an outflow bu erfly valve using remote microphone probes. In st AIAA/CEAS Aeroacoustics Conference, . [ ] L. Gefen, C. Pérez Arroyo, R. Camussi, G. Puigt, and C. Airiau. Broadband shock-cell noise signature identification using a wavelet-based method. In nd AIAA/CEAS Aeroacoustics Conference, May -June, Lyon, France, AIAA Paper -, . [ ] J. Morlet. Sampling theory and wave-propagation. In Geophysics, . [ ] C. Torrence and G.P. Compo. A practical guide to wavelet analysis. B. Am. Meteorol. Soc., ( ): -, .

Figure .

 . Figure . Normalized two-dimensional cross-conditioning of pixel intensity using as reference the events detected at the black dot at . kHz for different ∆t. e results are normalized by the local standard deviation e contours depict where the values are equal to (solid) or -(dashed).

ACKNOWLEDGMENTS

is project is supported by CRIAQ international and NSERC CRD programs in partnership with Liebherr-Aerospace Toulouse and Bombardier aerospace.


Christoph Günther

Jascha Bröder

Franz Joos
email: joos@hsu-hh.de

O Tatin

Influence of pressure on droplet splashing behaviour inside gas turbine compressors during wet compression

Keywords:

e injection of water sprays into the compressor inlet of gas turbines is used to augment power output and perform fast load changes. During wet compression, many drops enter the compressor and since droplets above a specific size cannot follow the flow of air, they are likely to collide with compressor blades and disintegrate. To apprehend the occurring splashing phenomena, impacts of single droplets on substrates with different surface roughness are studied under gas pressures from 100 to 500 kPa. For these disintegrations, the quantity of secondary droplets as well as their size and velocity distributions are measured using backlit high-speed video recordings. Analysis shows that the secondary droplet diameter distribution is dependent on surface roughness as well as pressure. Surface roughness increases the quantity of large secondary droplets, while the number of droplets with small diameters is unaltered. Increasing pressure increases the quantity of secondary droplets of all sizes. Both variations lead to significant increase in overall ejected volume of the primary drop. e evaluation of the influence of surface roughness and pressure on the secondary droplet velocity showed that there is a minor dependency on variations in both parameters.

INTRODUCTION

With increasing shares of electric power converted from renewable energy sources, their fluctuating supply impacts net frequency and poses a possible threat to overall grid stability. A possibility for compensating unsteady supply of electric energy is to put emphasis on the ability of conventional power plants to perform fast load changes and increase overall flexibility in power output. For gas turbines, this can be achieved by injecting droplets as a spray inside the intake duct (Günther and Joos [ ]). e vaporisation of the injected water decreases the turbine inlet temperature and increases mass flow. Wet compression considers droplets entering the gas turbine compressor and reducing temperature rise during the compression process and thereby reducing compression work (Eisfeld and Joos [ ]).

Since droplets above a specific size cannot follow the flow of air, they are likely to collide with compressor blades and disintegrate. is splashing leads to deposition of water on the blades and formation of secondary droplets, whose characteristics influence the subsequent vaporisation. To apprehend these splashing phenomena in compressors as well as in general and to predict the outcome of these disintegration, e.g. the distribution of the secondary droplets' diameter, impacts of single droplets were studied. e splashing of droplets has been subject of research for a long time and many of the governing parameters have been studied elaborately. An overview of these finding can be found in reviews such as Rein [ ], Yarin [ ] or Ashgriz [ ]. However, most of the studies have been carried out under atmospheric pressure and neglect the influence of the surrounding gas.

In addition to the influence of fluid and surface properties, Xu et al. [ ] discovered that the pressure of the surrounding gas is also of importance to the outcome of a droplet impact, in that it can completely suppress splashing if pressure is lowered enough. Furthermore, it was discovered that the threshold pressure, under which no splashing happens, is dependent on the impact velocity and that there are two regimes with different behaviours, separated by a critical velocity. A ratio which compares destabilizing and stabilizing stresses was introduced and found to be nearly constant for different fluids and gases in the region above the critical velocity.

Xu et al.

[ ] later studied the influence of surface roughness on the outcome of drop splashing under varying pressure and corroborates that there are two mechanisms corresponding to corona and prompt splashing. Air causes the corona splash on smooth surfaces while surface roughness is responsible for prompt splashing. It was also discovered that the size distributions of both prompt and corona splashing follow power law behaviour with a characteristic length scale, although the control parameters governing these length scales are different, namely surface roughness for prompt splashing and gas pressure for corona splashing. Mishra et al. [ ] studied spreading and splashing behaviour of droplets below the critical velocity defined by [ ] and at pressures up to 1200 kPa. ey found out that increasing the gas pressure can induce drop splashing, and that the splash ratio follows power law behaviour in the low velocity regime. ey also noted that while gas pressure influenced the likelihood of a drop to splash, the impact velocity and hence its kinetic energy is a more important factor.

To investigate the droplet surface interaction at pressures above ambient pressure, a test rig (Figure ) was developed at the Laboratory of Turbomachinery which allows to study droplet impacts inside a compressor at pressures up to 500 kPa, while maintaining a constant Weber-Number.

. EXPERIMENTAL SETUP e test rig (Figure ) consists of multiple connected cylinders which can sustain pressures up to 500 kPa. In the main cylinder is a table on which the impacted substrates are placed 3 . It is mounted in a way that allows it to be rotated around the cameras line of sight, while keeping the location of impact in the centre of the image. is way, different impact angles can be examined without changing camera se ings.

e surface roughness is varied by using substrates with sandpaper of different mean particle diameters glued onto e sand paper roughness was selected to represent the impact of 50 to 100 µm droplets impinging on compressor blades with surface roughness ranging between R a = 0.8 µm for a new blade and R a = 1.6 µm for blades fouled with particles up to µm in diameter (see Kurz et al. [ ]). To compare these dimension with the ones the test rig, the nondimensional surface roughness

δ = d/R a ( )
is established. It represents the relationship between the size of the impinging droplets and the surface roughness. e higher δ, the smoother the surface is in relation to the size of the drop.

Figure shows the non-dimensional surface roughness for drops of various sizes for a range of arithmetic mean surface roughness. Depicted are two drop sizes in the range of diameters that would normally impact on a compressor blade and one as it was used in the experiment. e do ed lines represent the life cycle of a compressor blade, namely the surface roughness of a new and of a fouled blade. e dashed lines illustrate the surfaces used in the experiments.

To compare impacts of different drop sizes, the nondimensional surface roughness has to be kept constant. For example: Point A represents the impact of a 50 µm drop on a fouled blade with R a = 0.8 µm, which results in a nondimensional surface roughness of δ = 31. To simulate this with a 4500 µm drop and the same non-dimensional surface roughness, the grit sand paper surface with R a = 123.23 µm (δ = 36) can be used (Point B).

A Knauer 40P HPLC Pump 5 is used to pump fluid to one of five cannulas with diameters from one to three mm 4 , where drops of various diameters form and drip off. It is able to deliver a pulse free, high pressure, low volumetric flow rate that produces drops of consistent diameter. e volumetric flow can be adjusted to change the drop frequency.

A Phantom v2512 high speed camera 1 , triggered by a photo sensor, in combination with a estar QM1 far field microscope 2 is used to record the backlit 6 impacts using the shadowgraphy method. Image rates start at 25, 697 Hz with a resolution of 1280 × 800 pixels that can be increased by lowering the resolution. e far field microscope has a working distance of 560 to 1520 mm and allows the camera to be placed outside of the pressurised cylinders. e image section has a size of about 2, 5 × 1, 6 mm. While increasing the distance from far field microscope to the drop impact also increases the depth of field, it is mounted at a distance of 600 mm to increase spatial resolution and improve detection of small secondary droplets.

e camera is triggered when the drops pass a light sensor. is trigger signal is also used to control an electromagnetic valve to dry the surface with pressurised air. Two delays can be controlled via potentiometers which adjust the delay from trigger signal to the opening of the valve and the time the valves stays open. e delay between the trigger signal and the opening of the valve is approximately 100 ms, which is enough time for the droplet to splash without disturbance. A er that, the valve is opened for about 500 ms. is removes the majority of any deposited remains of the drop but does not perfectly dry the surface. What remains is a very thin layer, especially in relation to surface roughness. e substrates are slightly elevated, so that sca ered drops don't appear in the recordings.

Above the cannulas, a fan 7 is installed to generate a flow which additionally accelerates the falling drops. It can be controlled via the fans input voltage and is carefully adjusted to keep the Weber-Number at impact constant for all set pressures. To counter the vortices produced by the fan, a combination of one flow straightener and two flow conditioners 8 were mounted.

.

METHODS

. Execution e drop impacts were analysed using high speed shadowgraphy recordings taken with a Phantom v2512 camera at frame rate of 25, 697 Hz with a resolution of 1280 × 800 pixels. ese recordings were then processed by LaVision's so ware DaVis which detects the droplets and yields a variety of their properties, including the quantity, diameter, velocity and shape. e velocity is determined through comparison of consecutive images and correlation of the detected droplets.

It is important to emphasise that the ejected secondary droplets can not be evaluated in their entirety. Because of the optics's low depth of field there is only a confined window in which the droplets are completely in focus. ereby they can only be detected and evaluated in this section perpendicular to the camera's line of sight. It is therefore not possible to draw absolute conclusions, like the overall number of ejected drops, but changes between the different experimental conditions. e primary drops were produced by pumping demineralised water to a cannula with 3 mm diameter at a flow rate of 0, 5 ml/min, where fluid tears off and forms drops of consistent diameter. e droplets fall about 0.65 m and impact on the substrate. A er each droplet impact, the surface was dried with a short air blast. e timing ensures undisturbed splashing of the droplets, with sufficient time before and a er impact. Impacts on all surfaces have been studied at pressures between 100 and 500 kPa.

To compensate the greater form drag due to increased gas density at higher pressures, a flow was generated to additionally accelerate the falling drops. e fan speed, and thereby the velocity of the air flow, can be adjusted by varying the fan voltage. For every set pressure, the input voltage of the fan was altered and the drop velocity measured until the necessary se ing for constant impact Weber-Number were identified.

. Scaling and correction of diameter e scaling was conducted using a calibration target with circles of defined diameters between 20 and 2000 µm. It was also used to tune the parameters for particle detection. ey have been adjusted so that droplets with a minimal diameter of 40 µm diameter were recognised. However, when using such sensitive se ings the recognition of the droplets diameter is distorted, because the extents of the droplets are not sharp and well-defined but rather a transition area of increasing intensity.

e perimeter of the drops then increases with more sensitive se ings for the intensity threshold, because brighter pixels at the edge of the drops are considered to be part of it. To compensate this effect, a correlation between measured and actual diameters was constructed and used to correct the measured drop diameters. . Evaluation e results of Davis' analysis are accumulated and processed in Matlab.

To obtain significant data, at least thirty individual impacts for every examined combination of pressure and surface were analysed. Droplet characteristics are calculated for every single image and then accumulated. is means that droplets are accounted for multiple times and therefore absolute quantities are incorrect, especially since only droplets in a small window of the depth of focus can be detected. However, relative changes between different experimental conditions are represented correctly, since the detection criteria remain the same.

Diameter, velocity and shape of the primary drops were first calculated as the arithmetic mean value of every single image taken before impact, for every individual drop. Filters regarding primary droplet characteristics are then applied to these mean values. For the selected data, which each represents one drop, another mean value representing the entirety of drops at these conditions is computed.

Since the drop's shape has a strong influence on the outcome of the splash, the evaluation was restricted to nearly spherical drops with a minimal centricity, which is the ratio of the length of the shortest and the longest axis within a drop, of 80 %. Figure shows a representation of how much a drop is deformed at that level of centricity.

Secondary droplets were only considered if they were also recognised in the following frame and therefore a velocity could be computed, which was set to be at least 0.5 m/s. is does lower the amount of droplets considerably, but it mainly filters noise. e secondary droplets of impacts specified by the selected primary drops were then accumulated.

.

RESULTS AND DISCUSSION

e diameter of primary drops ranges from 4.4 mm at atmospheric pressure to 4.6 mm at 500 kPa. With pressure also the differences in velocity among individual drops and their mean deviation from a spherical form increase. With the minimal centricity for each drop set to 80 %, the minimal mean centricity across all drops is 86 %. e mean Weber-Number at impact

We = ρ F u 2 d σ F ( )
across droplets for all pressures varies between 750 and 790.

Here, ρ F and σ F are density and surface tension of the fluid, u is the velocity at impact and d is the droplet diameter.

. alitative analysis

Figure shows pictures of impacting droplets at 3.89 ms a er impact. e first row shows drops impacting on different surfaces at 100 kPa pressure. Drops depicted in the second row impact the 120 grit sand paper surface with δ = 222 at 100 kPa to δ = 231 at 500 kPa.

In comparison with impacts on smooth surfaces, the splashing of impacts on rough surfaces (top row) is much more violent and less symmetrical. Instead of ejecting only small secondary droplets from the spreading lamella at the first few moments a er impact, the rough surface causes the drop to also form bigger secondary droplets and ligaments which propagate radially and disintegrate subsequently. Increasing surface roughness amplifies this behaviour and furthermore increases the ejection angle, measured from the surface. As shown in the second row, elevating the pressure has no obvious influence on the splash. Evaluation of the recordings will show that it mainly increases the number of ejected droplets.

. Secondary droplet diameter

At first the influence of surface roughness on the secondary droplet characteristics at atmospheric pressure is analysed. To do that, modified histograms were generated.

e secondary droplet diameters were grouped into bins of 5 µm and the number of droplets with diameters in that interval were noted. ese quantities were then normalised with the overall number of droplets across all diameters, so they form a probability density function whose sum of all quantities yields one. is histogram shows the relative frequency of secondary droplet diameter, but it does not reveal any information about the number of droplets or the transformation to different experimental conditions like increased pressure.

Figure shows the secondary droplet diameter probability distribution for impacts at atmospheric pressure on varying surfaces. e shape of this distribution depicts an inverse proportionality between secondary droplet diameter and its probability. e greater the diameter of a droplet, the less likely it is to form.

Increasing the surface roughness does not change the overall shape of the probability distribution, but it shi s its probabilities. With increased sand grain roughness, the probability of droplets with diameters below 100 µm decreases, whereas droplets above that size are more likely to occur.

Figure depicts the shape of the probability distribution and the shi of its shape with varying surfaces, but it does not contain information regarding droplet quantities. erefore each probability function was scaled with the ratio of their number of average secondary droplets to the number of average secondary droplets of the distribution of the experimental condition with either the smoothest surface or the lowest pressure depending on the variable whose influence is considered. is function then serves as a base to evaluate the relative changes in secondary droplet diameter distribution depending on surface roughness or pressure. at way, differences between the shape of the distribution and the In addition to the diameter distribution, the cumulative drop volume distribution was added. It was computed from the diameter distribution, assuming a spheric shape of secondary droplets. It therefore represents only the fraction of detected secondary droplets and not the entire discharged secondary droplet volume.

e graphs depict the normalized (to the respective overall volume of detected droplets) cumulative sum of the volumetric distributions. ey were scaled the same way as the aforementioned size distributions.

erefore the base function ranges between 0 and 100 % of the overall ejected volume for that condition, while the others are scaled with the ratio of their average droplet quantities, which is the same as the cumulative sum.

Figure shows these distributions for impacts at varying surfaces at atmospheric pressure. e distribution for impacts with δ = 222 serves as the base function. By scaling the other probability functions with this base, the influence of surface roughness on the size and volumetric distribution becomes apparent.

Increasing surface roughness changes the distribution of secondary droplet diameter in comparison with Figure .  Here, the number of ejected droplets increases slightly for small diameters. Simultaneously, it increases significantly for droplets with bigger diameters. e differences between individual surfaces decrease up to a point where the size distribution of droplets generated at δ = 51 and δ = 36 only vary slightly.

Although much more small droplets are ejected during the splashing, most of the discharged volume comes from the larger drops, as the volumetric distribution clearly shows.

e rougher surfaces lead to an increase of their number, which therefore increases the overall discharged volume. Contrary to this general trend, the most droplets and the largest amount of droplet volume, despite producing less droplets in the region of the biggest diameters are ejected at In this case, because the distributions are quite similar, it is because of the greater quantity of droplets with diameters up to about 1000 µm. e overall increasing amount of ejected drop volume means, that a much smaller fraction of the primary drop volume is deposited on the surface.

Figure shows the secondary droplet diameter distribution for impacts on the 120 grit surface at pressures from 100 to 500 kPa, as well as the volumetric distribution. e shape of the individual distributions are similar to the ones from Figure . eir relationship among one another however is not. Increasing surface roughness practically effected only the number of drops with bigger diameters, whereas increasing the pressure significantly increases the quantity of droplets for the whole range of diameters. In addition to this, the relative increase is also greater as it is with varying surfaces.

is especially becomes apparent considering the ejected volume. Although the increased number of small droplets has less influence on the amount of ejected volume, at 500 kPa the greater overall quantities of droplets, especially the ones with diameters above 100 µm, lead to 20.5 times the ejected volume with respect to impacts at 100 kPa.

It is worth mentioning that this only applies to δ = 222. For δ = 36 to δ = 102, the increments from 200 to 400 kPa are similar to the ones with δ = 222, but merely reach a factor of about 10 when pressure is increased to 500 kPa. A possible explanation for this is, that pressure has a disproportionately high influence on the number of droplets with diameters below 100 µm, which have a greater probability to appear at δ = 222 (see Figure ).

A diminishing effect of pressure, as seen with increasing surface roughness, was not observed. So increasing the pressure beyond 500 kPa could potentially still intensify this behaviour. . Secondary droplet velocity e intrinsic problem with determining the secondary droplets velocity is that accurate measurements are only possible for droplets that move perpendicular to the cameras line of sight and within the depth of focus. Most of the measured velocities stem from drops that travel away from or towards the camera and therefore have a velocity component that cannot be captured. eir velocity consequently is measured incorrectly low and therefore irrelevant.

From this however also follows that the correctly measured velocities have the highest values, because none of their velocity components are missing. Due to the radial symmetry of the splash, these velocities apply to all other droplets of the same diameter.

To obtain the relationship between secondary droplet diameters and their velocities they were firstly plo ed against each other (see Figure ).

eir data points form a cloud which has a very high density at it's centre and quickly thins out at it's edge. A function to represent the maximum velocity per diameter enfolds this cloud and ideally proceeds in the aforementioned area of decreasing density.

To restrict the influence of outliers and to obtain a smooth progression, the data points were grouped into bins of 5 µm regarding their diameter. Within these bins, the droplets with the upper 100 values of velocity were selected. All these drops were marked and their entirety across all bins approximated by a third degree polynomial to obtain a function for secondary droplet velocity in dependency of diameter. is function was then added to Figure .  e distribution of velocity versus diameter shows a nearly monotonously decreasing inverse proportionality between secondary droplet diameter and velocity. Small droplets can reach with up to around 30 m/s much higher velocities than either the bigger secondary droplets or the primary drops. e velocity for secondary droplets with diameters above 1000 µm however remains approximately constant.

e approximated functions for secondary droplet velocity versus diameter were then compared for impacts on different surfaces and at pressures. When the pressure is increased, the graphs show a slight increase in velocity for secondary droplets below 1200 µm. Secondary droplets above that size show li le to no variation. While there is an uncertainty in the approximation, the consistent increment with increasing pressures point at a slight dependency of secondary droplet velocity on pressure, which diminishes around 400 kPa.

Comparing the secondary droplet velocities for varying surfaces and constant pressure (Figure ) yields similar results to varying the pressure. Again, only droplets below 1200 µm are effected. eir velocity increases with increasing surface roughness. In contrast to the variation of pressure, the differences in secondary droplet velocity increase with surface roughness.

. CONCLUSIONS

Investigations of the influence of surface roughness and ambient pressure on the outcome of the splashes show that variations of both parameters affect the secondary droplets' size distribution.

Varying the surface roughness affects mostly droplets with diameters above 100 µm. Increased roughness leads to a higher number of droplets, with an increasing effect with respect to the droplet diameter. e differences between distributions for different surfaces decrease as surface roughness increases.

Elevating the ambient pressure has less effect on the secondary droplet diameter distribution. Instead, the quantity of droplets increases evenly. Moreover, the increase of sec- ondary droplet quantity is greater than the one caused by variation of the surface. Furthermore, no diminishment of the increments with rising pressure was observed.

e increments of secondary droplets quantity most notably increases the amount of overall ejected volume. Varying surface roughness leads to a maximum increase of about 50% at atmospheric pressure, while the elevation of gas pressure to 500 kPa increased the amount of discharged volume by factors between 10 and 20 for impacts on the 120 grit sandpaper surface at δ = 222.

Since a greater fraction of the primary drop volume is ejected at higher pressures, less fluid is deposited on the surface.

is could result in thinner films on compressor blades and reduce the quantity and size of drops that tear of from the blades trailing edge.

e evaluation of the influence of surface roughness and pressure on the secondary droplets velocity yielded slight increments when pressure and surface roughness were increased. is applies mostly to droplets with diameters below 1200 µm, larger secondary droplets are not significantly effected. However, the governing factor for secondary droplet velocity seems to remain the overall amount of kinetic energy, which is mostly determined by the primary droplets impact velocity.

NOMENCLATURE

Figure .

 . Figure . Experimental Setup: 1 High speed camera, 2 Long distance microscope, 3 Surface for droplet impact, 4 cannulas for droplet positioning, 5 Pump, 6 Backlight, 7 Fan, 8 Flow conditioners

Figure .

 . Figure . Arithmetic mean roughness versus non-dimensional surface roughness for drops of different size magnitudes.

Figure . Figure .

 .. Figure . Images of droplet ejection at 3.89 ms a er impact with We = 770 ± 20. Top row: 100 kPa with sand paper surfaces of varying δ and reference for impacts smooth surfaces. Bo om row: 120 grit sand paper surface with δ = 222 to δ = 231 at varying pressure.

Figure .

 . Figure .Unscaled secondary droplet diameter probability distribution for impacts at atmospheric pressure on varying surfaces. We = 770 ± 20

Figure .

 . Figure .Scaled secondary droplet diameter probability distribution for impacts at atmospheric pressure on varying surfaces. We = 770 ± 20

Figure .

 . Figure . Scaled secondary droplet diameter probability distribution for impacts on the grit surface with δ = 222 at 100 kPa to δ = 231 at 500 kPa and We = 770 ± 20.

Figure .

 . Figure . Secondary droplet diameter versus velocity. Data points with the Top 100 values of velocity within their respective bin are marked with a red plus. ese data points are approximated by a third degree polynomial. Impacts at δ = 222, 100 kPa and We = 770 ± 20

Figure .

 . Figure . Comparison of the fi ing functions for velocity versus diameter. Impacts with δ = 222 at 100 kPa to δ = 231 at 500 kPa and We = 770 ± 20.

  Figure shows the comparison for impacts on the 120 grit sand paper surface with δ = 222 at 100 kPa to δ = 231 at 500 kPa.

Figure .

 . Figure . Comparison of the fi ing functions for velocity versus diameter. Impacts on varying surfaces at 100 kPa and We = 770 ± 20

Table .

 . Grit size, mean particle diameter and equivalent arithmetic mean roughness of the used sand papers Grit size k s [µm] R a,eq[µm]

	120	125	20.16
	60	269	43.39
	36	538	86.77
	24	764	123.23
	them (Table ). e surface roughness of the sandpapers is
	characterised by the sand grain roughness k s , which is given
	by the mean diameter of the grains determined by FEPA grit
	size standard. e equivalent surface roughness
	R a,eq = k s /6.2		( )
	was calculated according to Koch and Smith [ ].