Absorption of Sound wave by Fabrics

Transcription

1 Absorption of Sound wave by Fabrics Part 3: Flow Resistance By Sadao Aso and Rikuhiro Kinoshita, Members, TMSJ Faculty of Engineering, Tokyo University of Agriculture and Technology, Koganei, Tokyo Abstract The influence of the flow resistance of fabrics on their absorption characteristics has been investigated by measuring the flow resistance and the absorption characteristics. To deal with this subject from the point of view of the design and density of fabrics, we wove 13 different kinds of cotton fabrics as samples. The results obtained are as follows: (1) The relation between flow resistance Rf of fabrics and flow speed V can be given as follows: Rf=Al+B1V where At and BE are constants fixed by the design and density of a fabric. In a range of small densities, the value of Bt is nearly zero, while Az and Bt increase together in value as the density of a fabric increases. (2) There are two types of absorbing mechanisms, the viscosity resistance type and the resonance type depending on the kinds of fabrics. A fabric is of the viscosity resistance type if its flow resistance depends only on air viscosity in a small range of flow speeds, namely, Rf=Aj. (3) A fabric is of the viscosity resistance type if it has an air space behind it, provided the relation among frequency fo, which shows the maximum absorption coefficient, depth d of the air space, and Rf can be given as follows : fo= (c/4-ar1) d-i where c is the speed of a sound wave and a is a constant fixed by the design of the fabric. This empirical formula means that a fabric has the maximum absorption coefficient when it is placed at a shorter distance than the place where the particle velocity is a maximum. (4) The relation between maximum absorption coefficient a~ and of Rf fabrics woven with the same design is: a~=a'+a" Rf where a' and a" are constants fixed by the design of the fabrics. 1. Introduction with this subject from the point of view of the design and density of fabrics, we wove 13 different kinds of cotton fabrics as samples. Our measuring apparatus The previous article[l] discussed the absorption was improved upon with considerable results. The mechanisms and the acoustic impedance of fabrics. following symboles are used: The present article reports on the relation between R f : flow resistance the flow resistance of fabrics and the absorption of dp : pressure differential between two faces of a sound wave by fabrics. a fabric We have already dealt[2] partly with this subject v : flow speed in the measuring tube and after that Kitamura and Sasaki have also dealt[3] Q : quantity of flow in the measuring tube with the same subject. This report[3] failed to a : coefficient of discharge collate samples systematically and the discussion in it F : cross-sectional area of a orifice seemed to be lacking in thoroughness. To deal g : acceleration of gravity 236 Journal of The Textile Machinery Society of Japan

2 dh : pressure head between two faces of an orifice r specific weight of the air m : area ratio of the orifice (the ratio of F to the cross-sectional area of the tube) T~ : sample of fabric woven with herring-bone weave M~ : sample of fabric woven with mat weave F~ : sample of fabric woven with plain weave Az,B~ : constants fixed by design and density of a fabric aoo : maximum absorption coefficient fo : frequency which shows the maximum absorption coefficient c : speed of a sound wave d : depth of an air space behind a fabric A : wave length a, a', a": constants fixed by design of a fabric 2. Flow Resistance The mean flow speed in the tube is, therefore: V=am(2gdh/r) 2 (a=0.60) If the pressure differential between two faces of a fabric is calculated by the pressure head, we get the flow resistance by the following formula: Rr=dP/V 2-2. Samples and Method (ML-3T) (rayl = dyne - sec/cm3) In this experiment we used, as sample, seven kinds of herring-bone weave Tl_7, three kinds of mat-weave M1_3 which were used also in the experiment referred to in the previous article, and three kinds of plain weave F1_3 newly woven of the same yarn as used in the previous experiment (their warp was two ply yarn of 40's; their weft, single yarn of 20's). The dimensions of the fabrics are given in Table Measuring Apparatus The flow resistance being defined by the ratio of QP to V, we made the apparatus shown in Fig. 1 to measure JP and V. The lengths in front of and behind an orifice exceed the values given in the Mechanical Engineering Handbook.[4] One sample was attached to a ring 10cm in diameter, was cut along the ring and placed, as shown in Fig. 1, in the tube of the apparatus. An entrance tube was screwed to a steady flow on the face of the sample and to prevent leak. The orifice, sharp-edged, 1.5mm thick and 0.05 in area ratio, was made of duralmin. If the pressure head between two faces of the orifice is measured, the quantity of flow is calculated by this Fig. 1 Apparatus to measure flow resistance expression: Q=aF (2gdh/r) 2 We took a split design with three replications as the experimental design. In other words, the samples were divided into two groups; one was Tl_7, the other was M1_3 and F1_3. One sample was chosen at random out of one group, the pressure head was measured at a flow speed chosen at random from V1 (15.5, 23,6, 31,0, 38,9, 46.5, 54.1 cm/sec) and the flow resistance of the fabric at the flow speed was fixed. In view of the remark in some published reports [5, 6] that the relative humidity of air affects the Vol. 10, No. 5 (1964) 237

3 permiability of fabrics, we measured one replication in a day to confound a day and a replication, and detected the effect of the relative humidity to some extent. The variations in the temperature and relative humidity were C, 85-90% when T1_7 were measured and C, 82-83% when M1_3 and Fl_3 were measured Results of Measurement The flow resistance of all fabrics is shown in Table 2. Analyses of Variance were made with the results given in Table 3. The replication in Table 3 Analysis of Variance for Flow Resistance (Herring-bone weave) Fig. 2 Relation between flow flow speed V (cm/sec) resistance Rf (rayls) and Table 2 Flow Resistance of Fabrics (unit; rayl) 238 Journal of The Textile Machinery Society of Japan

4 each group was insignificant. Inasmuch a day and a replication were confounded, we may say that the values of the flow resistance obtained by this experiment did not change by the measuring day. In other words, we do not think the variations to the extent just given in the relative humidity affect measured values vitally. Flow resistance Rf and flow speed V in each group were highly significant. The relation between the mean value of flow resistance and the flow speed is, therefore, as shown in Fig. 2. Accordingly the relation between Rf and V is expressible by this experimental formula: Rf=A~+BtV Constants A~ and B~ obtained from measured values are shown in Table 4. In fabrics woven with the same design the value of B~ is nearly zero in a range of small densities, while the values of A 1 and Bt increase together as a fabric increases in density. Even though fabrics are the same in density, the values of Al and B1 differ if the fabrics differ in design. By substituting Rf=4P/V into eq.(1), we get: 4P-A1V+B1V2 Many published studies on the permeability of fabrics show the relation between 4P and V. Kazama and Toyoda[7] say 4PocV 2 in a range of fast flow speeds. Go, Shinohara and Matsuhashi[6] say 4Pcx V in a range of slow flow speeds. S. F. Hoerner[8] inferred from experimental data obtained by many researchers that 4Poo V2 at a high Reynolds' number. Fukumoto[9] experimented on the permeability by paper and gave the same empirical formula as eq.(2). The relations between 4P and V are explained theoretically in the field of aerodynamics and the theory is applicable to fabrics. However, the cotton fabrics we used are not suitable as a basis for discussing the relationship between the permiability and the construction of fabrics, because cotton yarns are spinning yarn and unstable in form. This problem is reserved for discussion on a future occasion. Figs To know the mechanism of absorption of plain weaves, we investigated the relation between a frequency fo (c/s) which gives the maximum absorption coefficient and a depth d (cm) of an air space behind a fabric. In the same way that the values of fo and d are shown in Table 5, the relation between them is given as follows: 3. Effect of Flow Resistance on Absorption Characteristics 3-1. Mechanism of Absorption We have previously obtained the absorption characteristics of herring-bone weaves and mat weaves. The absorption characteristics of plain weaves measured by the same method are shown in Accordingly, the mechanism of absorption of plain weaves F1_3 is of the viscosity resistance type. Other than F1_3, fabrics of the viscosity resistance type are herring-bone weaves Tl_3 and mat weaves M3. All constants B1 in eq.(1), calculated from values measured in seven kinds of fabrics, are below Therefore, with slow flow speeds, the term (B1V) in eq.(1) is negligible and only the term Al affects flow resistance. Vol. 10, No. 5 (1964) 239

5 Fig. 3 Absorption characteristics of fabric Fl of air space behind a fabric d; the depth Fig. 5 Absorption characteristics of fabric F3 Fig. 4 Absorption characteristics of fabric F9 Fig, 6 Relation between flow resistance Rf and in eq. fo=kzd-1 (solid line) Relation between Rf and the maximum coefficient a9, (dotted line) constant absorption K Considering this from a standpoint of pressureloss, only the air viscosity affects flow resistance. In other words, the pressure-loss seems to be proportional to the flow speed, thus conforming to the Hagen-Poiseuille law. We may conclude, then, that the absoption of a sound wave by a fabric whose flow resistance comes from the air viscosity, results from the air viscosity, too Frequency Coefficient Giving the Maximum Absorption A fabric of the resonance type gives a different maximum absorption coefficient if the depth of an air space behind the fabric changes. A fabric of the viscosity resistance type gives the same maximum absorption coefficient irrespective of the depth, and 240 Journal of The Textile Machinery Society of Japan

6 theoretically the fabric ought to give the maximum absorption coefficient when it is at a place where the particle velocity is a maximum. Hence the relation between fo and d is: fo=c/4 d-1 However, a fabric gives the maximum absorption coefficient experimentally when placed at a place where the depth of the air space is shorter than d=a,/4, at which place the particle velocity is a theoretically maximum. Accordingly Kz in eq. (3) is smaller than c/4. If the flow resistance of a fabric of the viscosity resistance type is regarded as R1- A, the relation between Rf and K1 is as shown in Fig. 6. K~ decreases in proportion to Rf and Kz seems to become K=c/4=8500 when Rf=O. Therefore, in fabrics of the same design, the relation among the frequency fo(c/s) which gives the maximum absorption coefficient, the depth d (cm) of the air space behind the fabric and the flow resistance Rf (ray!) can be given as follows : fo= (c/4-arf) d~' This empirical formula means that the larger the flow resistance of a fabric of the viscosity resistance type is, the more certainly the fabric shows, the maximum absorption coefficient in a shorter depth of the air space than the place where the particle velocity is a maximum Maximum Absorption Coefficient The sound absorption of a fabric of the viscosity resistance type generates the air viscosity. On the other hand, in a small range of flow speeds, the flow resistance of this fabric has nothing to do with the flow speed but results only from the air viscosity. It follows, then, that the larger the flow resistance of a fabric is, the greater the fabric absorbs energy of a sound wave is. The relation between the maximum absorption coefficient a0 and the flow resistance Rf of a fabric of the viscosity resistance type is shown in Fig. 6. If fabrics are the same in design, the relation between a~ and R f makes a straight line: a~=a'+a" Rf However, the maximum absorption coefficient of a fabric is not fixed only by flow resistance but depends on the structure of the fabric. To discuss the structure of a fabric, we need a plain porosity, but it is very difficult to calculate the plain porosity of a cotton fabric, because we have to investigate the air space between yarns making up the fabric. The measurement of the flow resistance and ab- Vol. 10, No. 4 (1964) sorption coefficient of a fabric woven of monofilament yarns, and discussion of the relation among the structure, the flow resistance and absorption characteristics are reserved for a future occasion. 4. Conclusions We have investigated the relation between the flow resistance and absorption characteristics of cotton fabrics with these results : (1) The relation between the flow resistance Rf of fabrics and the flow speed V is: R,=Az+BtV (2) If the flow resistance of a fabric depends only on the air viscosity in a small range of flow speeds, namely, R7--- Al, the fabric is of the viscosity resistance type. (3) The relation among the frequency fo which shows the maximum absorption coefficient, the depth d of the air space and Rf is : fo= (c/4-a Rf) d-1 (4) The relation between the maximum absorption coefficient a~ and Rf of fabrics woven with the same design is: a~= a'+a" Absorption coefficient was measured by the Kobayashi Institute of Physical Research. The authors are deeply indebted to Mr. Masaru Koyasu, of this institute, for the many comments and suggestions given. References [1] S. Aso and R. Kinoshita; J. Text. Mach. Soc. Japan, English edition, 9, 1-15 (Jan. 1963) [2] S. Aso and R. Kinoshita and M. Kyoyasu; The meeting of Acoust. Soc. o f Japan (1960-5) [3] 0. Kitamura and M. Sasaki; The meeting of Acoust. Soc. of Japan (1962-5) [4] The Japan Society of Mechanical Engineers; Mechanical Engineering Handbook, 8-43, (1961-9) [5] T. Saito and H. Uchida; J. Soc. Text. Ind. Japcn, 2, 247 (1936-5) [6] Y. Go, A. Shinohara and F. Matsuhashi ; Research Reports of the Faculty of Textile and Sericulture, Shinshu University, No. 6, 118 (1956) [7] K. Kazama and K. Togoda; Journal of the Japan Research Association for Textile End uses, 3, 197 (1962) [8] S.F. Hoerner; Text, Res. J., 22, 274 (1952) [9] T. Hukumoto; Applied Physics, 18, 340 (1950.3) Rf 241