Giacopinelli et al 2010a - Revision history

Rimni at 15:27, 14 March 2023

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Rimni: /* 3.3. Wavelet analysis */

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‎3.3. Wavelet analysis

Rimni at 14:41, 14 March 2023

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Rimni at 14:39, 14 March 2023

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Rimni at 14:37, 14 March 2023

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Rimni at 15:46, 13 March 2023

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Rimni at 15:14, 13 March 2023

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Rimni at 15:14, 13 March 2023

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Rimni at 15:13, 13 March 2023

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Rimni: /* 3. Results */

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‎3. Results

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 ==References==
-[1] Tennekes H. and Lumley J. L., A First Course in Turbulence. The MIT Press, 1972.
+[1] Tennekes H., Lumley J.L. A first course in turbulence. The MIT Press, 320 pp, 1972.
-[2] Davies P. O. A. L. Coherent structures in turbulence. In Turbulent Mixing in Nonreactive and Reactive Flows, S. N. B. Murthy (Ed.), Plenum Press, 1975.
+[2] Davies P.O.A.L. Coherent structures in turbulence. In Turbulent Mixing in Nonreactive and Reactive Flows, S.N.B. Murthy (Ed.), Plenum Press, 1975.
-[3] Farge M., Wavelet transforms and their applications to Turbulence. Annu. Rev. Fluid Mech. vol. 24: 395-457, 1992.
+[3] Farge M. Wavelet transforms and their applications to Turbulence. Annu. Rev. Fluid Mech., 24:395-457, 1992.
-[4] Dunyak J., Gilliam X., Peterson R., Smith D., Coherent gust detection by wavelet transform, J.'' ''Wind Eng. Ind. Aerodynamics vol. 77–78, 467–478, 1998.
+[4] Dunyak J., Gilliam X., Peterson R., Smith D. Coherent gust detection by wavelet transform. J. Wind Eng. Ind. Aerodynamics, 77–78:467–478, 1998.
-[5] Boldes U., Scarabino A., Colman J. About the 3-Dimensional Behavior of the Flow within a Forest under Unstable Conditions, J. Wind Eng. Ind. Aerodynamics, vol. 95/2, 91-112, 2007.
+[5] Boldes U., Scarabino A., Colman J. About the 3-dimensional behavior of the flow within a forest under Unstable Conditions, J. Wind Eng. Ind. Aerodynamics, vol. 95/2, 91-112, 2007.
-[6] Li Y., Wang Y., Guan X., Zhou H., Ma X., A wavelet model on reconstructing complex aerodynamic field in furnace with acoustic tomography, Measurement, vol. 157, 107669, 2020.
+[6] Li Y., Wang Y., Guan X., Zhou H., Ma X. A wavelet model on reconstructing complex aerodynamic field in furnace with acoustic tomography. Measurement, 157:107669, 2020.
-[7] Mohd Razali S. F., Zhou T., Rinoshika A.,  Cheng L. Wavelet analysis of the turbulent wake generated by an inclined circular cylinder, Journal of Turbulence, vol. 11, 2010. DOI: 10.1080/14685248.2010.482562.
+[7] Mohd Razali S.F., Zhou T., Rinoshika A.,  Cheng L. Wavelet analysis of the turbulent wake generated by an inclined circular cylinder. Journal of Turbulence, 11:N15, 2010. DOI: 10.1080/14685248.2010.482562.
-[8] Farge M., “The evolution of turbulence theories and the need for continuous wavelets” arXiv:2209.01808 [physics.flu-dyn];  DOI: 10.48550/arXiv.2209.01808. Sept. 2022.
+[8] Farge M. The evolution of turbulence theories and the need for continuous wavelets, arXiv:2209.01808 [physics.flu-dyn],   77pp, 2022. DOI: 10.48550/arXiv.2209.01808.
-[9] Delnero J.S., Marañon Di Leo J., Boldes U., Colman J., Bacchi F., Martinez M., Wassen E., Guenther B. and Thiele F. Numerical and Experimental Investigation of Mini–Flap Positions on an Airfoil; 45th AIAA Aerospace Sciences Meeting and Exhibit. 8-11 January 2007, Reno, USA, 2007.
+[9] Delnero J.S., Marañon Di Leo J., Boldes U., Colman J., Bacchi F., Martinez M., Wassen E., Guenther B., Thiele F. Numerical and experimental investigation of mini–flap positions on an airfoil. 45th AIAA Aerospace Sciences Meeting and Exhibit., Reno, USA, 8-11 January 2007.
 [10] Giacopinelli P., Scarabino A., Delnero J.S., Bacchi F. Detección y análisis con wavelets de estructuras organizadas en la estela de un perfil aerodinámico. Actas del 2do. Congreso Argentino de Ingeniería Aeronáutica, 2010.

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 |style="text-align: center;padding:10px;"| [[Image:Draft_Scarabino_400696530-image19-c.png|400px]]
 |-
-| style="background:#efefef;text-align:left;padding:10px;font-size: 85%;"| '''Figure 12'''. Wavelet map of the “v” component of the velocity at point 4 at a distance H
+| style="background:#efefef;text-align:left;padding:10px;font-size: 85%;"| '''Figure 12'''. Wavelet map of the “<math display="inline">v</math>” component of the velocity at point 4 at a distance <math display="inline">H</math>
 |}

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 It can be seen in [[#img-6|Figure 6]] that velocity fluctuations in the wake are not symmetric. [[#img-7|Figure 7]] shows vorticity concentration in the coherent structures shed in the wake. In our numerical simulation, vortex shedding of a spatial scale similar to Gurney flap can be observed ([[#img-7|Figures 7]] and [[#img-8|8]]), which develop downstream. In [[#img-8|Figure 8]], it can be seen that the maximum values of turbulence intensity correspond to shear layers between which the vortices travel and develop, introducing the maximum value of speed fluctuations there.
-Due to our sensors position, the interesting measurements for analysis will be those corresponding to Points 0 and 7 ([[#img-3|Figure 3]]) at distances H and 2H from the Gurney flap.
+Due to our sensors position, the interesting measurements for analysis will be those corresponding to Points 0 and 7 ([[#img-3|Figure 3]]) at distances <math display="inline">H</math> and <math display="inline">2H</math> from the Gurney flap.
 Vortices develop at the trailing edge and break off with a characteristic frequency; then, they travel downstream. An anemometry probe located in these regions will frequently be rammed and immersed in these vortices, being able to extract information from them.
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 For the numerical study, the same Reynolds number was reproduced but with a different speed and chord, which caused shedding frequencies to be different. For this reason, frequencies were normalized with the corresponding chords and speeds, in order to be able to compare the experimental and numerical results. Strouhal numbers at the shedding frequency should be the same in both cases.
-Measurements analysis shows that, in the regions of the wake close behind the mini-flap —where vortices begin their development, an important peak in the fluctuating velocities spectrum is observed, clearly indicating the presence of the absolute instability and the vortex street illustrated in [[#img-6|Figures 6]] and [[#img-7|7]]. [[#img-9|Figure 9]] shows the normalized spectra of the vertical instantaneous velocity <math display="inline">v</math>, at a distance of 2H downstream of the miniflap and different heights (points 0 to 8 in [[#img-2|Figure 2]]). The spectral peak is marked at all measurement locations. The spectra at distance 1H, as well as those for the horizontal velocity component <math display="inline">u</math>, show spectral peaks at the same non dimensional frequencies.
+Measurements analysis shows that, in the regions of the wake close behind the mini-flap —where vortices begin their development, an important peak in the fluctuating velocities spectrum is observed, clearly indicating the presence of the absolute instability and the vortex street illustrated in [[#img-6|Figures 6]] and [[#img-7|7]]. [[#img-9|Figure 9]] shows the normalized spectra of the vertical instantaneous velocity <math display="inline">v</math>, at a distance of <math display="inline">2H</math> downstream of the miniflap and different heights (points 0 to 8 in [[#img-2|Figure 2]]). The spectral peak is marked at all measurement locations. The spectra at distance 1H, as well as those for the horizontal velocity component <math display="inline">u</math>, show spectral peaks at the same non dimensional frequencies.
 <div id='img-9'></div>
@@ Line 225: / Line 225: @@
 |style="text-align: center;padding:10px;"| [[Image:Draft_Scarabino_400696530-image12.png|500px]]
 |-
-| style="background:#efefef;text-align:left;padding:10px;font-size: 85%;"| '''Figure 9'''. Distribution of the power density spectrum of the <math display="inline">v</math> component of the velocity experimental measurements at 2H downstream
+| style="background:#efefef;text-align:left;padding:10px;font-size: 85%;"| '''Figure 9'''. Distribution of the power density spectrum of the <math display="inline">v</math> component of the velocity experimental measurements at <math display="inline">2H</math> downstream
 |}
@@ Line 236: / Line 236: @@
 |style="text-align: center;padding:10px;"| [[Image:Draft_Scarabino_400696530-image13.png|500px]]
 |-
-| style="background:#efefef;text-align:left;padding:10px;font-size: 85%;"| '''Figure 10'''. Distribution of the power density spectrum of the <math display="inline">v</math> component of the velocity numerical results at 2H downstream
+| style="background:#efefef;text-align:left;padding:10px;font-size: 85%;"| '''Figure 10'''. Distribution of the power density spectrum of the <math display="inline">v</math> component of the velocity numerical results at <math display="inline">2H</math> downstream
 |}
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 Velocity-time records were checked for clues related to the second derivative of a Gaussian g2 (“Mexican Hat”). Assuming a “frozen flow” hypothesis, it is possible to deduce the spatial turbulent scale for an instantaneous velocity component by looking for its maximum in the wavelet map. This wavelet has the characteristic of identifying local maxima at different scales with high precision.
-Our wavelet analysis will focus on those points for which the spectral analysis marks notorious shedding peaks: points 2 and 4, both at distance H and 2H. For this analysis, we will use MATLAB CWT function with “Mexican Hat” (“mexh”) wavelet, following the scales:
+Our wavelet analysis will focus on those points for which the spectral analysis marks notorious shedding peaks: points 2 and 4, both at distance <math display="inline">H</math> and <math display="inline">2H</math>. For this analysis, we will use MATLAB CWT function with “Mexican Hat” (“mexh”) wavelet, following the scales:
 {| class='formulaSCP' style='width: 100%;'
@@ Line 295: / Line 295: @@
 |style="text-align: center;padding:10px;"| [[Image:Draft_Scarabino_400696530-image18.png|400px]]
 |-
-| style="background:#efefef;text-align:left;padding:10px;font-size: 85%;"| '''Figure 11'''. Wavelet map of the vertical velocity component, v, at a distance of 1H of the Gurney flap
+| style="background:#efefef;text-align:left;padding:10px;font-size: 85%;"| '''Figure 11'''. Wavelet map of the vertical velocity component, v, at a distance of <math display="inline">1H</math> of the Gurney flap
 |}

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-The tested model consists of a rectangular wing without torsion, with a chord of 0.45m and a wingspan of 0.8m, equipped with a Gurney mini-flap of height H equal to 1.5% chord. The model was horizontally placed in the test section of the tunnel. The speed of the current was 15m/s.
+The tested model consists of a rectangular wing without torsion, with a chord of 0.45m and a wingspan of 0.8m, equipped with a Gurney mini-flap of height <math display="inline">H</math> equal to 1.5% chord. The model was horizontally placed in the test section of the tunnel. The speed of the current was 15m/s.
 Velocities were measured with the StreamLine model from Dantec, a 2-channel, constant temperature, and hot-wire anemometer. X-wire Dantec 55R51 probes were used, with a data acquisition rate of 2000Hz per channel, as seen in [[#img-2|Figure 2]].
@@ Line 108: / Line 108: @@
-Longitudinal <math display="inline">(u)</math> and vertical <math display="inline">(v)</math> instantaneous velocities were measured upstream and downstream of the model, particularly in the wake region near the blunt trailing edge with Gurney flap: along a grid with horizontally spaced points at lengths H and 2H of the wing chord, and 12 vertical intervals spaced 2 mm apart ([[#img-3|Figure 3]]).
+Longitudinal <math display="inline">(u)</math> and vertical <math display="inline">(v)</math> instantaneous velocities were measured upstream and downstream of the model, particularly in the wake region near the blunt trailing edge with Gurney flap: along a grid with horizontally spaced points at lengths <math display="inline">H</math> and <math display="inline">2H</math> of the wing chord, and 12 vertical intervals spaced 2 mm apart ([[#img-3|Figure 3]]).
 <div id='img-3'></div>
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 | style="background:#efefef;text-align:left;padding:10px;font-size: 85%;"| '''Figure 3'''. Detail of the measurement scheme in the wake
 |}
 ===2.2. Numerical study===

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 ==Abstract==
-In this work we identify the coherent vortices in the leeward wake of an HQ 17 airfoil with a Gurney flap. This high-lift device consists of a small plate perpendicular to the airfoil, at or near the trailing edge, with a height H of the order from 1% to 4% of the chord. The overall effect is to produce a significant increase in lift, together with a relatively minor increase in airfoil drag. Its geometry generates vortex shedding of spatial scale H, which modulates the wake and thus influence the global configuration of the flow. A numerical study was performed with the commercial software ANSYS Fluent. Simultaneously, experiments were carried out in the wind tunnel of the Aeronautical Departmental Area from the Engineering School of the National University of La Plata. With a Dantec StreamLine hot-wire anemometer, records of the instantaneous horizontal and vertical velocity components in the airfoil wake were obtained. Both the experimental data and those obtained by numerical simulation were analyzed with the continuous wavelet transform technique, in order to identify and characterize the coherent vortices in the wake. Results show the shed vortices structure and the organization degree of this periodic shedding.
+In this work we identify the coherent vortices in the leeward wake of an HQ 17 airfoil with a Gurney flap. This high-lift device consists of a small plate perpendicular to the airfoil, at or near the trailing edge, with a height <math display="inline">H</math> of the order from 1% to 4% of the chord. The overall effect is to produce a significant increase in lift, together with a relatively minor increase in airfoil drag. Its geometry generates vortex shedding of spatial scale H, which modulates the wake and thus influence the global configuration of the flow. A numerical study was performed with the commercial software ANSYS Fluent. Simultaneously, experiments were carried out in the wind tunnel of the Aeronautical Departmental Area from the Engineering School of the National University of La Plata. With a Dantec StreamLine hot-wire anemometer, records of the instantaneous horizontal and vertical velocity components in the airfoil wake were obtained. Both the experimental data and those obtained by numerical simulation were analyzed with the continuous wavelet transform technique, in order to identify and characterize the coherent vortices in the wake. Results show the shed vortices structure and the organization degree of this periodic shedding.
 '''Keywords''': Airfoils, high-lift devices, CFD, wavelets

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 * Another advantage of the continuous wavelet transform over the frequency spectrum is that scale and frequency are not always related as reciprocals of each other, as they would be in a sinusoidal signal.
 From the analysis of the problem under study, it is deduced that the time scale of the vortices released from the Gurney flap is approximately a quarter of the period between successive shedding. If we consider that the average speed is much lower in the airfoil wake than in the free flow, as can be seen in Figure 6, we obtain the reasonable result that the spatial scale is of the same order as the Gurney mini-flap chord.
 Although Fourier analysis allows the correct detection of the shedding frequency, it is not enough to determine the scale or duration of the shed organized structures (vortices), which the continuous wavelet transform does achieve. This allows finding the temporary location of the vortices and correctly determining their scale and energy level, in addition to the characteristic frequency of the periodic shedding. In the experimental analysis, CWT also allows identifying energy fluctuations on a scale corresponding to the airfoil chord, which are lost in the classic spectral analysis, dominated by the characteristic frequency of the shedding.

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 <div id='img-9'></div>
-{| class="wikitable" style="margin: 1em auto 0.1em auto;border-collapse: collapse;width:70%;"
+{| class="wikitable" style="margin: 1em auto 0.1em auto;border-collapse: collapse;width:60%;"
 |-style="background:white;"
-|style="text-align: center;padding:10px;"| [[Image:Draft_Scarabino_400696530-image12.png|600px]]
+|style="text-align: center;padding:10px;"| [[Image:Draft_Scarabino_400696530-image12.png|500px]]
 |-
 | style="background:#efefef;text-align:left;padding:10px;font-size: 85%;"| '''Figure 9'''. Distribution of the power density spectrum of the <math display="inline">v</math> component of the velocity experimental measurements at 2H downstream
@@ Line 233: / Line 233: @@
 <div id='img-10'></div>
-{| class="wikitable" style="margin: 1em auto 0.1em auto;border-collapse: collapse;width:65%;"
+{| class="wikitable" style="margin: 1em auto 0.1em auto;border-collapse: collapse;width:55%;"
 |-style="background:white;"
-|style="text-align: center;padding:10px;"| [[Image:Draft_Scarabino_400696530-image13.png|600px]]
+|style="text-align: center;padding:10px;"| [[Image:Draft_Scarabino_400696530-image13.png|500px]]
 |-
 | style="background:#efefef;text-align:left;padding:10px;font-size: 85%;"| '''Figure 10'''. Distribution of the power density spectrum of the <math display="inline">v</math> component of the velocity numerical results at 2H downstream