Towards sibilant /s/ modelling: preliminary computational results

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1 Acoustcs 8 Pars Towards sblant /s/ modellng: prelmnary computatonal results X. Grandchamp a, A. Van rtum a, X. Pelorson a, K. Nozak b and S. Shmoo b a Département Parole & Cognton, GIPSA-lab, 46, avenue Félx Vallet, 3831 Grenoble Cedex, France b Cyber Meda Center, Osaka Unversty Cybermeda, 5-1 Mhogaoka Ibarak, Osaka, Japan xaver.grandchamp@gpsa-lab.npg.fr 3961

2 Acoustcs 8 Pars The mportance of turbulence n human speech sounds producton s generally accepted n the case of frcatves. Nevertheless, ths phenomenon s margely taken nto account n physcal modellng of speech producton. The current study consders steady flow at a gven Reynolds number Re = 4. Large Eddy Smulaton has been used to smulate the flow evoluton n case of two dmensonal geometres. The used geometrcal and flow characterstcs are severe smplfcatons of the human upper arways beyond the glotts. The mpact of those typcal geometres on the computed flow feld s searched n order to detect the aeroacoustcal sources produced by turbulent flow, crucal n /s/ producton. The presence of the obstacle n a unform channel and the curved ppe nduce reversed flow. Nevertheless, the turbulence ntensty, n case of the obstacle confguraton does not correspond wth turbulent flow, whereas the curve tends to gve hgher turbulent veloctes along the curvature. 1 Introducton uman speech sounds can be classfed nto two dstnctve categores dependng on ther producton mode: voced and unvoced sounds. The producton of voced sound was deeply studed, and among of research s avalable n the lterature. The arflow expulsed by the lungs nteracts wth the vocal folds leadng to an auto-oscllaton of the vocal folds. The other mechansm s purely aeroacoustcs and corresponds to the producton of unvoced sound. Nevertheless, less attenton was gven to the mechansm of producton of unvoced sound. The complex geometry of the human upper arways, and the flow condtons yeld the turbulent ar flow. The mportance of the turbulence n the producton of unvoced sound s noted []. Numerous expermental studes reveal the mportance of the nteracton between the flow and obstacle, n a.o [1, 1]. The mechansm of sound producton and the mportance of vortcty and the necessary flow-separaton condtons n the producton of frcatves are studed [7, 11]. The study of et vortcty and ts evoluton for unvoced sound producton s summarsed n [6] as the sound feld was seen to be determned unquely by the nteracton of et vortcty and the shape of the vocal tract. One of the man artculator concernng obstacle-flow nteracton s the teeth. The mpact of teeth on the producton of sblant /s/ s studed by [5, 9]. Large Eddy Smulaton (LES) s appled on the md-sagttal plane of a human oral cavty [9]. Nevertheless, the complexty of the geometry gave us a dffcult understandng of the phenomena. As a frst step for a future applcaton n speech producton, the am of ths paper s to analyse wth LES, the evoluton of dmensonal lamnar nflow n the case of schematc human upper arways. The nfluence of the vocal folds and false vocal folds are left untreated. The study s restrcted on typcal geometres present n the upper arways. A rectangular straght ppe, a rectangular straght ppe wth an obstacle, and fnally a rectangular curved ppe are consdered. The three geometres are studed separately and ther mpact on the flow evoluton s dscussed. The paper s organsed as follows. Secton presents the numercal method and numercal domans. The results for the dfferent geometres are dscussed n secton 3. The concluson s formulated n secton 4. Computatonal Method The arflow s smulated wthn the dfferent geometres by usng a commercal explct fnte element code Front Flow Blue/ FFB, developed by Advance Soft Corporaton [3]. In the followng secton the method s outlned [6]. Next, the computatonal domans are brefly presented..1 Governng equatons Ths code solves spatally-fltered ncompressble contnuty equaton and Naver-Stokes equatons. u y, 1 u (u u ) t y p y u ( y y (1) u ), () y p represents the grd-scale statc pressure, the knematc vscosty, u (=1,, 3) corresponds to the grd scale velocty component. The subgrd-scale (SGS) stress tensor s defned by: u u u u. (3) The Smagornsky closure s appled to the SGS stress 1 kk 3 - SGS S, (4) Where ( ) SGS C s S, S 1 u u S S, S ( ) y y (5) C s s the Smagornsky coeffcent and s the sze of the grd flter. In our case, the dynamc Smagornsky model wth modfcaton due to [8] s used. C s s determned locally n tme and space by C s M l, (6) M M 396

M l ~ ~ ~ ~ S S,, (7) ~ ~ 1 ~ ~ ~ ( ~ uu ) ( kk uk uk ), (8) 3 Where S S and uu represents a test-flterng operaton,.

A fully mplct Crank-Ncolson scheme (CN) and explct tme streamlne upwnd scheme were employed for ntegratng the momentum equaton. The spatal dscretzaton s based on the Fnte Element Method (FEM).

The followng parameters were chosen constant for the dfferent geometres: the dmensonal heght of the rectangular ppe s equal to.

3 M l ~ ~ ~ ~ S S,, (7) ~ ~ 1 ~ ~ ~ ( ~ uu ) ( kk uk uk ), (8) 3 Where S S and uu represents a test-flterng operaton,. The symbol ~ represents an averagng operaton, and ~ s the sze of the test fltered wdth. A fully mplct Crank-Ncolson scheme (CN) and explct tme streamlne upwnd scheme were employed for ntegratng the momentum equaton. The spatal dscretzaton s based on the Fnte Element Method (FEM). The schemes have a second order accuracy n tme and space.. Numercal doman and nflow The three geometres taken nto account n our study were created by usng a commercal mesh generator developed by [4]. The followng parameters were chosen constant for the dfferent geometres: the dmensonal heght of the rectangular ppe s equal to.5 m, the aspect rato l/, where l represents the wdth of the rectangular ppe s equal to l/ = 4. The unform dmensonal nlet velocty s constant and equal to U =.5 m.s -1. Therefore, the Reynolds number based on the nlet velocty and the heght s equal to Re = 4. The nondmensonal tme ncrement corresponds to t = 1-3 = U t. In the case of a rectangular straght ppe, the computatonal doman s [-, ] * [, ] * [, 5] respectvely n y 1, and drecton, where y 1,, represent respectvely the lateral, the spanwse, and the streamwse coordnates. Structured meshes are used. The orgn s located on the nlet face, at the centre of the lateral plan and the bottom sde of the rectangular ppe, as shown n Fg. (a). 74 elements are used n the streamwse drecton and are unformly dstrbuted. 74 elements are used n the spanwse drecton towards a symmetrc tangent hyperbolc dstrbuton., whch represents the sze of the frst element near the wall s equal to =.5. 5 elements are used n the spanwse drecton. The total number of computatonal elements s approxmatel8. The nlet velocty s mposed to be unform. Non-slp condton was used on the wall. Non reflectve condtons are used as ext condtons. For the followng case, an obstacle representng a schematc tooth s mposed. The dmensons of the computatonal doman n whch the tooth s nserted s [-, ] * [, ] * [, 4.5]. The tooth s located at a dstance equal to y 1 = 16/5. The geometry of the tooth s a trapezod for whch the base s 1.5/5 and ts opposte sde has a length of.5/5; the upstream and downstream sdes of the tooth make respectvely an angle of 15 and 9 wth the bottom wall. Its heght s equal to 7/1. Approxmately 1 88 elements were used to compute the flow evoluton. Structured meshes are stll used. The computatonal doman s dvded nto 5 blocks as seen n Fg. (b). Close to the obstacle the grd meshes are refned n order to be small enough to resolve the boundary layer and bound vortces around the obstacle. The orgn s located at the same poston as for the prevous case. The same nlet and boundares condtons mposed for case1 are used. The thrd geometry s a rectangular curved straght ppes lnked wth a curved ppe. The horzontal straght ppe has a computatonal doman [,.5] * [., 1.] *[, 4] respectvely n y 1, and drecton. The vertcal straght ppe has a computatonal doman [-1., -] * [, -.5] * [, 4] n y 1, and drecton. The orgn s located on a bottom sde of the horzontal rectangular straght ppe. The rectangular curved ppe s a quarter rng wth an nner radus of. and an extern radus of 1. lnkng the ppes. 49 elements are used along the streamwse drecton, 74 elements along the spanwse drecton and 1 along the lateral drecton. In ths case, the orgn s located at the bottom sde of the horzontal rectangular straght ppe. The total number of computatonal elements s approxmately 75. As for prevous cases, the same nlet and boundares condtons are used. U U U =16/5 y 1 Acoustcs 8 Pars 1.5/5 E c) Fg. Typcal ppe geometres, a) rectangular straght b) rectangular straght + obstacle, c) rectangular curved. a) E b b) 3963

Acoustcs 8 Pars 3 Results and dscusson 3.1 Rectangular straght ppe The frst results concern the basc representaton of a rectangular straght ppe.

The man nterest of such geometry resdes n the certfcaton of the code under use and as a reference case.

a) As a further analyss, Fg. 4 presents the turbulence ntensty u tur3 /U 3, where u tur3 represents the rms value of the streamwse component of the velocty along the rectangular straght ppe.

4 Acoustcs 8 Pars 3 Results and dscusson 3.1 Rectangular straght ppe The frst results concern the basc representaton of a rectangular straght ppe. Ths representaton s vewed as the smplest smplfcaton of the vocal tract. No perturbaton due to upstream obstacle s assessed; therefore the flow s lamnar. The man nterest of such geometry resdes n the certfcaton of the code under use and as a reference case. U 3 3 U (1 ) (9) Ths evoluton confrms boundary layer grows on both wall, due to vscosty, and mass-conservaton. Fg. 4 turbulent ntensty u tur3 /U 3 for dfferent streamwse localsaton. a) As a further analyss, Fg. 4 presents the turbulence ntensty u tur3 /U 3, where u tur3 represents the rms value of the streamwse component of the velocty along the rectangular straght ppe. The turbulence level s ncreased wth the downstream localsaton. The maxmum values are observed close to the wall and comprsed between 5% < u tur 3 /U 3 < 3%. 3. Rectangular straght ppe wth an obstacle b) Fg. 3 Mean velocty evoluton along the spanwse drecton for dfferent streamwse localsaton. a) streamlnes dmensonal veloctes U 3, b) mean velocty normalsed wth centrelne velocty Uc 3. Ths subsecton presents the mpact of an obstacle on the lamnar nflow. Fg. 5 shows as the downstream locaton ncreases the flow becomes asymmetrc. From / = 1.8, the poston of the velocty maxmum U s shfted to the flat wall. From Fg. 5 the flow maxmum of the velocty s localsed n an area whch starts downstream the end of the obstacle and s equal to about 4 tmes the nlet velocty.. Fg. 3(a) and 3 (b) represent the mean velocty along the spanwse drecton. Fg. 3(b) shows the evoluton of the streamwse component of the velocty normalsed by ts centrelne velocty Uc 3. As the downstream localsaton ncreases, the rectangular velocty profle mposed at the nlet tends to be transformed nto the parabolc Poseulle profle. In order to compare wth the Poseulle profle the orgn of the axs where shfted to the centre of the rectangular ppe. Fg. 5 Contourlnes of the dmensonal mean velocty U [m.s -1 ]. Fg. 6, for whch the axs are smlar to Fg. 3, shows the flow evoluton along the obstacle and reveals the exstence of a recrculaton zone, by the presence of negatve veloctes. The veloctes n the recrculaton zone are comprsed between -.75 m.s -1 < U < m.s

5 Acoustcs 8 Pars correspondng to 5% of U 3max. The results are compared wth data from an expermental study on turbulent wall ets, Fg. 6 dmensonal mean veloctes for dfferent streamwse localzaton. Fg. 7 presents the mean veloctes profles along the obstacle at dfferent dstance E 1, where E 1 represents the dstance between the locaton of the velocty measurements and the edge E1. The flow s asymmetrc, compared wth the velocty profle before and after the obstacle, the maxmum velocty s close to the obstacle and accelerated along the sngularty. Fg. 8 Turbulent ntensty profles at dfferent locaton E 1. for whch Re = 96 and b= 9.6*1-3 m [1]. Although, the profles are close to the obstacle, t seems the flow tends to present a self-smlar evoluton comparable to a wall et. Fg. 9 Mean velocty profle at dfferent downstream locaton E /b l from the edge (E ). Fg. 7 velocty profles at dfferent dstance E 1. Fg. 8 presents the turbulent ntensty profles along the obstacle. Except for E 1 = 6.5*1-4 m, and at a dstance equal to 5*1-3 m from the obstacle, the level of the turbulence ntensty s very low, u tur3 /U 3 < 1%. For ths Reynolds number, and the confguratons of the obstacle (shape and aperture) turbulent regme s not reached. The turbulence velocty u tur3 s seen to be u tur3.18 m.s -1 along the computatonal doman at E 1. Fg. 9 represents the mean velocty profles at dfferent downstream spanwse dstances E /b, where E represents the dstance between the locaton of the velocty measurements and the edge E, and b the dstance between the obstacle and the opposte flat wall. We use as outer scalng, U 3max and (1/), where U max represents the maxmum velocty of the streamwse component and (1/) the dstance between the two spanwse locatons 3.3 Rectangular curved ppe The study of a curve, s motvated by the geometry of the vocal tract. In ths secton, we brefly gve a qualtatve presentaton of the flow behavour mposed by the curvature. From Fg. 1 a) the curve mples an ncrease of the velocty from the begnnng of the curvature and a stall of the boundary layer leadng to a recrculaton zone whch s zoomed on n Fg. 1 b). In Fg 11 t appears the curvature generates turbulent veloctes area whch propagates downstream the geometry. The magntude turbulent veloctes are comprsed between m.s -1 < u tur < m.s -1 whch represent about % of the Mean velocty. 3965

Acknowledgments The support of the French Rhones-Alpes regon (CIBLE 6), Agence Natonal de la Recherche (ANR-7-JCJC- 5), College Doctoral Franco-Japonas (X.

6 Acoustcs 8 Pars and lead to the creaton of a recrculaton zone. Therefore, further nvestgatons are needed concernng the degree of constrcton, the shape of the obstacle, the dstance between the obstacle and the outlet. Acknowledgments The support of the French Rhones-Alpes regon (CIBLE 6), Agence Natonal de la Recherche (ANR-7-JCJC- 5), College Doctoral Franco-Japonas (X. Grandchamp), and Japanese Socety for the Promoton of Scence (JSPS fellowshp A. Van rtum) are gratefully acknowledged. y 1 Fg. 1 a) Magntude of the mean velocty b) Vectoral representaton of the mean flow. a) b) References [1] J.G. Erksson, R. I. Karlsson, and J. Person, An expermental study of a two-dmensonal plane turbulent wall et, Exp. Fluds, 5-6 (1998) [] G. Fant, Acoustc Theory of Speech Producton (Mouton, the ague) (196) [3] FrontFlow/Blue verson.4. User Manual. Collaboratve Research Center for Computatonal scence and Technology, Insttute of Industral Scence, the Unversty of Tokyo, JAPAN. software@rss1.s.u-tokyo.ac.p [4] Grdgen Tutoral workbook. verson 15 volume3 grdgen@pontwse.com [5] M. S. owe, R. S. Gowan, Aeroacoustcs of /s/ Pro. R. Soc. A. 461,15-18 (5) [6] C. Kato, M. Kaho, and A. Manabe, An overset fnteelement large-eddy smulaton method wth applcatons to turbomachnery and aeroacoustcs, J. Appl. Mech. 7, 3 43 (3) [7] M.. Krane, Aeroacoustc producton of lowfrequency unvoced speech sounds, J. Acoust. Soc. Am. 118, (5) Fg. 11 Contours of the magntude turbulent veloctes. 4 Concluson The effects of typcal artculator geometres, comparable to a tooth and a curve, on the flow feld development of a dmensonal ncompressble flud flow were computed. For assessed flow characterstc and geometrcal confguratons, the obstacle generates lower turbulence than the curvature. Nevertheless, both geometres create an asymmetrc flow [8] D. K. Llly, A proposed modfcaton of the Germano subgrd-scale closure method, Phys. Fluds A 4, (199) [9] K. Nozak. Tamagawa and S. Shmoo, Predcton of dental frcatve sound by Lghthll, Curl equaton, In Proc. n. slco dentstry, page 4, Osaka, Japan (8) [1] C.. Shadle, The Acoustcs of Frcatve Consonants, Ph.D. thess, Massachusetts Insttute of Technology (1985) [11] D. J. Snder, Synthess of unvoced speech sounds usng an aeroacoustc source model, Ph.D. thess, Rutgers Unversty (1999) [1] K. N. Stevens, Arflow and turbulence nose for frcatve and stop consonants: Statc consderatons, J. Acoust. Soc. Am. 5, (1971) 3966

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