READ ME File For 'dataset_broadband_noise_prediction_for_aerofoils_with_a_serrated_trailing_edge_based_on_amiet_theory.zip'

Dataset DOI: 10.5258/SOTON/D1890

Author: Matthieu Bernard Roger Gelot, University of Southampton

This dataset supports the publication:
AUTHORS: Matthieu B. R. Gelot and Jae Wook Kim
TITLE: Broadband noise prediction for aerofoils with a serrated trailing edge based on Amiet's theory
JOURNAL: Journal of Sound and Vibration Vol 512
PAPER DOI IF KNOWN: https://doi.org/10.1016/j.jsv.2021.116352

This dataset contains:

The present dataset contains processed and raw data needed to generate the figures in the associated paper.
It features .dat ASCII files, .tex and .eps files which need to be open using latex and pdf reader softwares.
Each file contained in the dataset is titled with the corresponding figure number followed by a short description of the content.

The figures are as follows:

Fig. 1 Joukowski JK10 (10\% thickness; 5.15\% camber) and JK12 (12\% thickness; 4.25\% camber) aerofoil profiles.

Fig. 2 (\emph{a},\emph{c}) A bird's eye view of the surface mesh for the JK10-BTE and JK10-STE1.00 aerofoils showing a span of 10\% chord and (\emph{b}) a cross-sectional view of the interior mesh of the BTE case. The pictures only show 25\% of total cell count for display purposes.

Fig. 3 Wall-unit grid spacings used on the suction side for (\emph{a}) the JK10-BTE case and (\emph{b}) the JK12-BTE case where $\rmDelta s^+$ is the streamwise curvilinear spacing, $\rmDelta z^+$ is the spanwise spacing and $\rmDelta n^+$ is the wall-normal spacing.

Fig. 4 Snapshot of the streamwise velocity streaks in near-wall turbulent flow at $y^+=6$ from the wall (at the TE) for the JK10-BTE (top) and the JK10-STE1.25 (bottom) cases. The coloured lines depict the data extraction performed to plot Fig. \ref{fig:streaks1D}.

Fig. 5 Distribution of the normalised streamwise velocity fluctuations along the spanwise direction at three different streamwise location $x/L_c=0.90,0.95,1.00$ near the TE in (\emph{a}) the JK10-BTE and (\emph{b}) the JK10-STE1.25 cases. The markers represent the grid points.

Fig. 6 Representation of the computational domain: the region located inside the dashed contour is the physical domain and the area located between the solid and dashed lines is the sponge layer. The domain is decomposed in 6 blocks and their edges are coloured in blue.

Fig. 7 Three-dimensional visualisation of: the radiated sound represented by the divergence of velocity; the turbulent boundary layer depicted by Q-criterion=1 and flood by the velocity magnitude; the contour map of wall pressure fluctuations spectra. The cases displayed are (\emph{a}) JK10-BTE; (\emph{b}) JK10-STE1.25; (\emph{c}) JK12-BTE and (\emph{d}) JK12-STE1.25.

Fig. 8 Time history of the lift and drag coefficients ($C_L$ and $C_D$) for JK10-BTE and JK12-BTE cases. The time periods $t_a$ and $t_b$ correspond to the selected time periods for data extraction.

Fig. 9 Time-averaged profiles of the pressure coefficient $C_p$ and skin friction coefficient $C_f$ for (\emph{a},\emph{b}) the JK10 case and (\emph{c},\emph{d}) the JK12 case. The baseline profiles are averaged in the spanwise direction.

Fig. 10 One-sixth octave PSD of velocity fluctuations from a probe located in the $z=0$ plane at $x/L_c=0.95$ and at $y^+=150$ from the wall in the JK10-STE1.25 case : (\emph{a}) $S_{uu}/a_\infty^2$, (\emph{b}) $S_{vv}/a_\infty^2$ and (\emph{c}) $S_{ww}/a_\infty^2$. The solid lines depict a signal extracted between $ta_\infty/L_c=70$ and $ta_\infty/L_c=80$ whereas the dashdotted lines depict a signal extracted after a longer running time between $ta_\infty/L_c=120$ and $ta_\infty/L_c=130$.

Fig. 11 PSD of loading noise (Eq. \ref{eq:farassat-loading}) in the JK10-STE1.25 case over a circular arc $80^\circ\le\theta\le100^\circ$ with radius $R/L_c=10$ centred at ($x,y,z$)/$L_c$=(1,0,0). The plot compares two extraction time intervals.

Fig. 12 Schematic diagram of the computation of FW-H by juxtaposing multiple spans. $N_{span}=5$ on the diagram but real calculations involve hundreds.

Fig. 13 Diagram of the wall pressure fluctuations extraction lines (in red) for all geometries BTE, STE0.75, STE1.00 and STE1.25 from left to right. The diagram is drawn in the JK10 case where the wall pressure fluctuations are taken 1\% ahead of the actual trailing edge.

Fig. 14 Power spectral density of pressure fluctuations over a narrow circular arc $80^\circ \le \theta \le 100^\circ$ of a radius of $R/L_c=100$ centred at ($x,y,z$)/$L_c$=(1,0,0) in the JK10 case. The cases displayed are (\emph{a}) JK10-BTE; (\emph{b}) JK10-STE0.75; (\emph{c}) JK10-STE1.00 and (\emph{d}) JK10-STE1.25.

Fig. 15 One-tenth octave $\Delta$SPL of (\emph{a}) JK10-STE0.75, (\emph{b}) JK10-STE1.00 and (\emph{c}) JK10-STE1.25 relative to JK10-BTE over a circular arc $80^\circ\le\theta\le100^\circ$ with radius $R/L_c=100$ centred at ($x,y,z$)/$L_c$=(1,0,0).

Fig. 16 Source phase distribution (based on wall pressure fluctuations) on the suction side of the JK10 aerofoil at $f L_c/a_{\infty}=8$ for all trailing edge geometries: BTE, STE0.75, STE1.00, STE1.25 from left to right. Red and blue are out of phase to each other.

Fig. 17 Contour maps of the PSD function of the surface pressure fluctuations in log scale on the suction side of the JK10 aerofoil at $f_c L_c/a_{\infty}=8$ for all trailing edge geometries: BTE, STE0.75, STE1.00, STE1.25 from left to right.

Fig. 18 Contour maps of the PSD function of the surface pressure fluctuations in log scale on the suction side of the JK10 aerofoil at $f_c L_c/a_{\infty}=1$ for all trailing edge geometries: BTE, STE0.75, STE1.00, STE1.25 from left to right.

Fig. 19 Source phase distribution of the modified wall pressure $\tilde{p}$ on the suction side of the JK10 aerofoil at $f L_c/a_{\infty}=4$ for all trailing edge geometries: BTE, STE0.75, STE1.00, STE1.25 from left to right. Red and blue are out of phase to each other.

Fig. 20 (\emph{a}) PSD over a narrow circular arc $80^\circ \le \theta \le 100^\circ$ of a radius of $R/L_c=100$ centred at the TE of the BTE case ($x,y,z$)/$L_c$=(1,0,0). The thinner lines are obtained with the source phase variation included and the thicker ones with the source phase variation excluded. (\emph{b}) Corresponding PSD ratio of the results obtained by excluding ($S_{pp,ex.}$) and including ($S_{pp,in.}$) the source phase variation.

Fig. 21 One-twelfth octave $\Delta$SPL of (\emph{a}) JK10-STE0.75, (\emph{b}) JK10-STE1.00 and (\emph{c}) JK10-STE1.25 relative to JK10-BTE over a narrow circular arc $80^\circ \le \theta \le 100^\circ$ of a radius of $R/L_c=100$ centred at the TE of the BTE case ($x,y,z$)/$L_c$=(1,0,0). The thinner lines are obtained with the source phase variation included and the thicker ones with the source phase variation excluded.

Fig. 22 One-fifth octave coherence along a path-line near the TE (Fig. \ref{fig:amiet-extract}) at central frequencies (\emph{a}) $f_cL_c/a_{\infty} = 0.5$; (\emph{b}) $f_cL_c/a_{\infty} = 2$ and (\emph{c}) $f_cL_c/a_{\infty} = 8$. The reference point is located at $z=-L_s/2$ and $\Delta z$ designates the spanwise displacement in the two-point cross-correlation.

Fig. 23 Spanwise coherence length from Eq. \eqref{eq:lz-from-les} at the reference point located at $z/L_c=-L_s/2$.

Fig. 24 Power spectral density of pressure fluctuations at 100 chords away from the TE in the JK10-BTE case for observer angles (\emph{a}) $\theta=30^\circ$; (\emph{b}) $\theta=90^\circ$ and (\emph{c}) $\theta=150^\circ$.

Fig. 25 Directivity pattern of the one-fifth octave-integrated PSD of pressure fluctuations at 100 chords away from the TE in the JK10-BTE case at central frequencies (\emph{a}) $f_cL_c/a_{\infty}=0.5$; (\emph{b}) $f_cL_c/a_{\infty}=2.0$; (\emph{c}) $f_cL_c/a_{\infty}=4.0$ and (\emph{d}) $f_cL_c/a_{\infty}=8.0$.

Fig. 26 Graphical representation in log scale and in polar coordinates of the objective function $D_{obj}(\theta)$ and the directivity correction factor $D(\theta)$ using the coefficients in Table \ref{tab:an-coef}.

Fig. 27 Directivity pattern of the one-fifth octave-integrated PSD of pressure fluctuations at 100 chords away from the TE in the JK10-BTE case at central frequencies (\emph{a}) $f_cL_c/a_{\infty}=0.5$; (\emph{b}) $f_cL_c/a_{\infty}=2.0$; (\emph{c}) $f_cL_c/a_{\infty}=4.0$ and (\emph{d}) $f_cL_c/a_{\infty}=8.0$.

Fig. 28 Directivity pattern of the one-fifth octave-integrated PSD of pressure fluctuations at 100 chords away from the TE in the JK12-BTE case at central frequencies (\emph{a}) $f_cL_c/a_{\infty}=0.5$; (\emph{b}) $f_cL_c/a_{\infty}=2.0$; (\emph{c}) $f_cL_c/a_{\infty}=4.0$ and (\emph{d}) $f_cL_c/a_{\infty}=8.0$.

Fig. 29 Directivity pattern of the OASPL at 100 chords awaw from the TE in the JK10 case for (\emph{a}) BTE; (\emph{b}) STE0.75; (\emph{c}) STE1.00 and (\emph{d}) STE1.25.

Fig. 30 Relative SPL difference of pressure fluctuations over one-tenth octave bands. Calculations are made over a narrow circular arc centred on $\theta$ of width $12^\circ$ and a radius of 100 chords centred at the TE in the JK10 case. The figure gathers plots for three different directions (left to right) and for each STE geometry (top to bottom).

Fig. 31 Relative difference of OASPL at 100 chords away in the upper semi-circle above the TE in the JK10 case for (\emph{a}) STE0.75; (\emph{b}) STE1.00 and (\emph{c}) STE1.25.

Fig. 32 Relative SPL difference of pressure fluctuations over one-tenth octave bands. Calculations are made over a narrow circular arc centred on $\theta$ of width $12^\circ$ and a radius of 100 chords centred at the TE in the JK12 case. The figure gathers plots for three different directions (left to right) and for each STE geometry (top to bottom). Lyu \& Ayton's results are computed based on their rapid model \cite{Lyu2019}.

Fig. 33 Relative difference of OASPL at 100 chords away in the upper semi-circle above the TE in the JK12 case for (\emph{a}) STE1.00 and (\emph{b}) STE1.25. Lyu \& Ayton's results are computed based on their rapid model \cite{Lyu2019}.

Fig. A34 Comparison of two span lengths in terms of the PSD of pressure fluctuations over a narrow circular arc $80^\circ \le \theta \le 100^\circ$ of a radius of $R/L_c=100$ centred at the TE of the BTE case ($x,y,z$)/$L_c$=(1,0,0): (\emph{a}) the individual PSDs and (\emph{b}) the relative difference of the STE1.25 case to the baseline in decibels over one-tenth octave bands.

Fig. A35 Comparison of two time signal lengths ($ta_{\infty}/L_c=10$ and $20$) in terms of PSD of pressure fluctuations over a narrow circular arc $80^\circ \le \theta \le 100^\circ$ of a radius of $R/L_c=100$ centred at the TE of the BTE case ($x,y,z$)/$L_c$=(1,0,0): (\emph{a}) the individual PSDs and (\emph{b}) the relative difference of the STE1.25 case to the baseline in decibels over one-tenth octave bands.

Fig. A36 Wall pressure fluctuations distribution on the suction side of the JK10-BTE case: (\emph{a}) the PSD in log scale; the normalised (\emph{b}) real and (\emph{c}) imaginary parts of the Fourier transform.


Date of data collection: October 2020 - June 2021

Information about geographic location of data collection: Southampton, UK

Licence: CC BY

Related projects: None

Date that the file was created: July, 2021