Some Applications of PIV Technique to Air-Jet Musical Instruments

Transcription

1 Some Applications of PIV Technique to Air-Jet Musical Instruments Shigeru Yoshikawa, Yumiko Sakamoto Dept. of Acoustic Design, Graduate School of Design, Kyushu University, Fukuoka Japan, Andreas Bamberger Dept. of Physics, University of Freiburg, Freiburg, Germany, The PIV (Particle Image Velocimetry) is a useful measurement tool to investigate the field of fluid and/or acoustic flows in semi-quantitative manner. The particles for flow visualization are instantaneously captured by the laser sheet with very high resolution. Two separate particle images taken with an interval of ten-microsec order are statistically analysed and then the velocity map is derived. This paper reports the results of PIV application to three different cases. (1) Application to the flute evaluation: A metal flute for students and a newly-designed ceramic flute for advanced players are mechanically blown using a common headjoint. The laser sheet illuminates the embouchure vertically and the resulting cross section is viewed through a window made by cutting the headjoint at the cork position. The flow field inside the flute, particularly the vorticity distribution can reflect the difference in flute quality. (2) Application to functional characterization of the organ-pipe ears: The ears are the projections on both sides of the pipe mouth and provide an important voicing technique. Flow measurement around the mouth and the resulting jet movement demonstrate the effectiveness of the ears. (3) Applications to the vortex-sound theory on organ pipes: Focusing on a closer vicinity of the jet flow, velocity vectors crossing the jet are detected and they seem to interact with a strong vorticity formed near the crossing region. Such a configuration may be relevant to the mechanism of vortex-sound generation in organ flue pipes. 1 Introduction The PIV (Particle Image Velocimetry) has been applied to fluid dynamics [1], aeroacoustics [2], and musical acoustics [3] due to its high resolution from the use of sheetlike laser light. The flute and the pipe organ should be very appropriate targets for the application of PIV to musical acoustics. Particularly, the distribution maps of velocity vector and vorticity, which are statistically derived by the processing of two flowparticle images taken with an interval of 10-micro second order, seem to be useful. In this paper PIV technique is applied to three types of acoustical research: (1) evaluation of the instrument (flute); (2) characterization of the instrument element (organ-pipe ear); (3) search of true sound source of instruments (organ pipes). These applications illustrate the promising areas for musical and flow acoustics.. 2 Flute evaluation with PIV 2.1 Experimental procedures For our basic research two flutes of definitely different playing quality were selected and compared. One is a popular model for students (Yamaha YFL 211, made of nickel silver) and the other a newly-designed model for professionals made of machinable ceramic into which heat-hardening resin is injected. Since ceramic has high stiffness (rigidity) and high internal damping factor, it seems to be a good subsitute for hard woods (such as grenadilla) for wind instruments. Figure 1 shows the flute embouchure for mechanical blowing and a transparent window inlaid at the position of the cork after cutting off the headjoint there. A roller below the acrylic slit works as the lower lip. The lip plate is painted in black to avoid unnecessary reflections. The laser light comes from the top and illuminates the embouchure hole vertically. When a small space around the flute is filled with particles made from the liquid of propylene glycol, reflections from the particles are captured by a CCD camera through the window. An example of such flow visualization is illustrated in Fig. 2. This is just for the indication of the geometry in our PIV experiment. The jet shown in this Fig. 2 is not good for PIV, because the jet is too dense to be recognized as moving particles and the jet can be seen as a not-moving plate. Therefore, the jet with an appropriate thinness of liquid particles is required to get better results of PIV processing. A pair of laser pulses with about 10-microsec interval are irradiated at the repetition rate of maximum 5.65 Hz to estimate the particle velocity within the interrogation area. When both flutes made a D5 tone (about 590 Hz) in a good manner, the jet length was 13.7 mm and 9.7 mm for ceramic and metal flute, respectively. Also, the jet angle measured from the horizontal line was 35 (deg) and 33 (deg) for them, respectively. The blowing pressure was adjusted to be 0.88 kpa at the cavity placed just before the slit (cf. Fig. 1). The same headjoint shown in Fig. 1, which was originally a part 623

2 Forum Acusticum 2005 Budapest exterior surface of the lip plate and that along the interior wall surface of the headjoint. Also, a localized clear pattern of vorticity distribution in the headjoint of the ceramic flute suggests a better degree of playability and the resulting sound (cf. Fig. 4). of the metal flute, was used for the comparison. Sounding level was in mf. Fig. 1: Flute embouchure and headjoint window. Fig. 3: Vorticity maps of the flow in flutes (cf. Fig. 2). Fig. 2: An example of flow visualization with PIV. 2.2 Evaluation result The PIV can derive a velocity-vector map of moving particles by applying the cross correlation to a pair of flow visualization, and in turn can draw a vorticity map as well as a streamline map based on the velocityvector map. Figure 3 compares the vorticity maps of a ceramic flute [(a) and (b)] with those of a metal flute [(c) and (d)]. The air jet moves to the exterior side a little at the instants of (a) and (c), while it moves to the interior side a little at the instants of (b) and (d). Annular area in the middle of the map corresponds to the lip plate and headjoint wall. Therefore, there should be no particles (in other words, no signals) in this area. Also, it should be noted that the jet velocity near the slit is not well visualized because of various causes (the slit is placed upper right as indicated in Fig. 2). Fig. 4: D5 tones of the mechanically blown flutes 3 Functions of the organ-pipe ear Effects of the ear in organ pipes have been studied by acoustical and flow measurements [4, 5]. A growth of the fundamental (equivalent to a depression of harmonics) was considered as its major effect. The change in harmonic levels when the ear is applied can be caused by the substantial change in the offset. This speculation is based on the flow measurement which indicated that the velocity profile shifted slightly inwards (towards the pipe interior) [6]. However, since this flow measurement was carried out in soundless conditions, another flow measurement was required in sounding conditions to reconfirm the ear effects. A smooth flow tends to yield positive and negative vorticity patterns along its left and right sides, respectively. Also, a disturbed flow tends to yield a complicated pattern consiting of small vorticity patches. The ceramic flute indicates a smooth flow along the 624

3 Fig. 5: Velocity-vector maps over the mouth of an organ pipe derived by PIV. Flow measurement was carried out in the University of Freiburg using PIV facility and the same organ pipes as investigated until now [5]. Important geometries are as follows: pipe length 786 mm; cut-up length 10.4 mm; jet thickness 0.75 mm; jet-to-edge offset 2.0 mm; ear height 16 mm; ear width 36 mm. Also, the blowing pressure was 690 Pa at the foot and the sounding frequency was about 195 Hz. Although the pipe body is opaque, the jet and mouth interior can be observed by bending one of the ears. The PIV system in Freiburg is designed to capture the flow visualization at every instant of T/12, where T denotes the tonal period. Therefore, a precise comparison may be easily made between the organ pipes with and without the ears. Figure 5 shows the velocity-vector maps of an organ pipe with the ears (top) and without the ears (bottom) at the phase of T/12 (left) and 7T/12 (right). The slit from which the jet issues is located at the position of (x, y) = (0, 0). As indicated in (a), jet flow looks like a welldefined potential (laminar) flow when the ears are applied. The jet still maintains the velocity distribution even after passing the edge located at (x, y) = (10.4 mm, 2.0 mm). However, the jet tends to be diffused particularly around the edge as indicated in (c) when the ears are not applied. The velocity profile is very obscure over the mouth. This might be due to the entrainment from the sides, which can be prevented by applying the ears. Also, the jet looks like being broken into two at the phases of 11T/12 and 12T/12 when the ears are not applied, although vector maps are not shown here. This suggests relative strength of second harmonic in an organ pipe without the ears. An important role of the ears seems to be a prevention of such breakdown in jet flow and the resulting maintenance of sinusoidal jet motion. This statement may be confirmed by Fig. 6 where the displacement of the jet centerline is estimated from the vector map. The solid line showing the effect of the ears is more sinusoidal and symmetrical. Such jet displacement should be relevant to produce a fundamental-dominant pipe sound in stable manner. The shape of broken line in the case of without the ears is more pulselike and gives a larger amplitude (by applying the ears the blowing velocity reduced from 37.6 m/s to 29.5 m/s). This can produce a pipe sound with richer harmonics. Another interesting characteristic is seen in square areas in Fig. 5 (b) and (d). The particles just below the issuing jet rotate in clockwise and seem to interact with the jet. Such clockwise rotation of the field particles is kept from the phase of 5T/12 to that of 10T/12 in an organ pipe with the ears, while such rotation is not so definite in an organ pipe without the ears except the 625

4 phase 7T/12. Also, the acoustic particle velocity during these phases seems to change from + (outward) to (inward) through 0 at the phase 7T/12. This acoustic velocity was roughly estimated from the change of vectors in consecutive two phases. This estimation should be done in the regions far from the jet flow to neglect the entrainment effect [7]. It is still obscure whether such vortices are relevant to the application of ears or not. The interaction of this vortical motion with the acoustic velocity will be discussed in next section in connection with vortex sound in organ pipes. Fig. 6: Waveform of jet displacement at the edge. 4 Vortex sound in an organ pipe It is well recognized that the true source of sound is the vorticity in the field of flow acoustics [8, 9]. Therefore, such vortex sound should be properly investigated in an organ pipe and some suggestive results have been presented [10, 11]. Although computational fluid dynamics (CFD) is a useful and promising method, major differences between flow acoustics and organpipe acoustics should be noted. The flow of interest in flow acoustics is usually modeled as an incompressible flow of low Mach number. On the other hand, since the resonance is essential in organ pipes, the flow or the field should be treated as a compressible one of low Mach number. Such situation seems to be unfit for conventional codes of CFD-based simulations. Hence, experimental approaches may be more effective to our topic. An organ pipe for the PIV experiment has the following dimensions: pipe length 500 mm; cutup length 15.8 mm; flue thickness 2.2 mm; offset nearly zero. This pipe is the same as pipe B used in the previous studies [7, 12] except for the value of cutup length. The final blowing pressure was about 120 Pa and the resulting sound of about 285 Hz had a level of mp. Time interval of the pairing laser irradiations was set to 30 micro seconds in order to capture the acoustic particle velocity rather than jet velocity. The repetition rate of laser irradiation was 5.65 Hz. Also, we captured several sequential pictures starting from the attack transient because these beginning pictures, which may be close to the steady state, seem to give clearer images than the pictures in fully steady state. According to Howe [9], the rate of production of acoustic energy in the framework of vortex sound is formulated as P ( t) ( ω v) = ρ u' dv (1) where ω (= rot v ) is the vorticity, v the convection velocity of the vortical field, u ' the acoustic velocity, and ρ the air density. The V should be a volume enclosing the vorticity formed in the flow field. Also, the time-averaging of Eq. (1) should be taken to define the acoustic source power in rigorous sense. If and when <P(t)> is positive, the vorticity of the interest generates the acoustic source power, i.e., vortex sound during the time of averaging. However, it is hard to trace such a vortex or vortices in our PIV system since the laser pulse is not irradiated continuously. Only some instantaneous examples were obtained and two of them are illustrated in Fig. 7. These two examples are almost in the opposite phase as inferred from (a) and (c), where the velocity-vector maps are overlaid on flow visualizations. White lines are drawn in (c) to indicate the jet boundaries. Figures 7 (b) and (d) show the vorticity distributions calculated from the vector maps corresponding to Figs. 7 (a) and (c), respectively. As indicated in (b) and (d), the jet issuing from the flue slit is very sparsely visualized by a few velocity vectors. Positive and negative vortices tend to be produced along the left and right boundaries of the jet, respectively. However, these vortices are very typical of the jet flow and are not relevant to the vortex sound. On the other hand, we should pay careful attention to the vectors passing through the jet, which are shown in bigger rectangles in (b) and (d). Interestingly enough a very strong negative vorticity is generated near the center of the rectangle in (b). Since we may estimate that the flow velocity v tends to the right along x axis, vector ω v tends downwards (towards negative y direction). If we may consider that acoustic particle velocity u ' is included in the velocity vector derived in (b), the sign of Eq. (1) is positive since u ' tends upwards. As the result we may expect the generation of vortex sound in this situation. The absolute value of the vector near the vorticity is about 5 m/s, while that far from the vorticity is about 2 m/s. This result on velocity magnitudes seems to be reasonable [7]. 626

5 Fig. 7: Possibilities of vortex-sound generation in an organ flue pipe. Similar situation is given in Fig. 7(d), though the vorticity distribution is not so reliable. It should be noted that another kind of vortex is produced just below the slit as enclosed by a small square. This vortex gives positive vorticity since the vortex rotates counter-clockwise. If v has positive x component and u ' tends downwards in the field enclosing the vortex, we may expect vortex-sound generation. However it is difficult to confirm such conditions in (d). According to the experimental result on the ear in the previous section, the vortex identical to that appearing in Fig. 7(d) is generating when u ' has positive and negative signs. If this is correct, the vorticity just below the flue slit is irrelevant to vortex-sound generation. In our present research we cannot interrogate the areas above and below the edge. Such investigation based on PIV will be carried out in near future. Also, since the trigger for initial buildup of the sound may be formed by tiny vortices in an immediate vicinity of the jet, we should focus on such vortices and examine some definite configurations of ω, v, and u ' for vortex-sound generation. The PIV is a very promising tool to attack this problem. 5 Conclusions The particle image velocimetry (PIV) was applied to evaluate the flutes, to investigate the organ-pipe ears, and to explore the mechanism of vortex-sound generation in organ pipes. Since the interaction between the vortical flow field and the acoustic field is an essence common to these problems, the PIV-based research will yield a more definite understanding of air-jet musical instruments from the viewpoint of fluid dynamics in near future. A ceramic flute for professional use is characterized well by smooth vorticity-distribution pattern in the headjoint (below the embouchure hole). The air blown is introduced from a localized area just below the edge of embouchure hole and is streamed along the interior wall surface of the headjoint. Such a pattern of jet flow 627

6 suggests a better coupling between the jet and the flute to produce desirable sounds with ease. The jet in an organ pipe is able to maintain a well-defined potential flow and an associated velocity profile if and when the ears are applied. This may be due to the prevention of the flow entrainment from the sides. A breakdown of jet wave over the mouth is also prevented by applying the ears. As the result, the ears can maintain sinusoidal jet motion in stable fashion and produce a fundamental-dominant pipe sound. Focusing on a closer vicinity of the jet flow, interaction patterns which probably generate the vortex sound in an organ pipe are explored. Time interval of the pairing laser irradiations was adjusted three times longer than that used in the previous two cases to capture smaller velocities associated with acoustic motion. Velocity vectors crossing the jet flow seem to interact with a strong vorticity formed near the crossing region. Such a configuration may be relevant to the mechanism of vortex-sound generation in organ pipes. Acknowledgement The first and second authors (S. Y. and Y. S.) are grateful to Dr. Judit Angster of the Fraunhofer Institut Bauphysik in Stuttgart for her kind instruction and support to carry out acoustic measurement there. References [1] M. Raffel, C.E. Willert, and J. Kompenhans, Particle Image Velocimetry, Springer-Verlag, Heiderburg, [2] C.F. Schram, Aeroacoustics of Subsonic Jets: Prediction of the Sound Produced by Vortex Pairing Based on Particle Image Velocimetry, Thesis, Technische Universiteit Eindhoven, [3] A. Bamberger, Operation of flutes at low pitch investigated with PIV, Proc. Int. Symp. on Musical Acoustics 2004, Nara, pp (2004). [4] Y. Sakamoto and S. Yoshikawa, On the acoustical design of ears in organ pipes, Proc. Int. Symp. on Musical Acoustics 2004, Nara, pp (2004). [5] Y. Sakamoto, S. Yoshikawa, and J. Angster, On the acoustical design of the ears of flue organ pipes, J. Acoust. Soc. Am. 116, 2512 (2004). [6] S. Yoshikawa and K. Arimoto, Measurement of velocity profiles of the jets issuing from some flue geometries typical of air-jet instruments, 17 th Int. Cong. on Acoustics, Rome, 2 pages (2001). [7] S. Yoshikawa, Jet-wave amplification in organ pipes, J. Acoust. Soc. Am. 103, (1998). [8] A. Powell, Theory of vortex sound, J. Acoust. Soc. Am. 36, (1964). [9] M.S. Howe, Contributions to the theory of aerodynamic sound, with application to excess jet noise and the theory of the flute, J. Fluid Mech. 71, (1975). [10] M.P. Verge, Aeroacoustics of Confined Jets, with Application to the Physical Modeling of Recorder- Like Instruments, Thesis, Technische Universiteit Eindhoven, [11] B. Fabre, A. Hirschberg, and A.P.J. Wijnands, Vortex shedding in steady oscillation of a flue organ pipe, Acustica-acta acustica 82, (1996). [12] S. Yoshikawa, A pictorial analysis of jet and vortex behaviours during attack transients in organ pipe models, Acustica-acta acustica 86, (2000). 628