音響管内の有限振幅波動

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There are many problems which can be treated as forms of finite amplitude wave motion, e. g. , shock waves and radiation of large amplitude ultrasonic waves, but no adequate analysis of these problems exists since they are nonlinear phenomena. In this paper, finite amplitude wave motion in a closed pipe is investigated as one example of a finite amplitude problem. The flow of gas in the pipe is assumed to be a one-dimensional, unsteady flow. When the cross-sectional area of the pipe is constant, the wall of the pipe is adiabatic and wall friction is taken into account, the continuity equation, the momentum equation and the first law of thermodynamics are written as Eqs. (1), (2) and (3). These equation cannot be solved by analytical methods since they are nonlinear equations. The solution, however, is obtained by means of numerical procedures, i. e. , the characteristics method, since these equations can be combined in the form of a quasi-linear partial differential equation of the hyperbolic type. After the arrangement of these equations, the compatibility conditions along the three characteristics curves in the physical plane is obtained, and these conditions are expressed by Eqs. (5), (6) and (7). Equation (8) gives the definition of the pseudo-Riemann variables, and when wall friction is neglected, this equation gives the Riemann constants. The dimensionless form for the physical properties in this calcu1ation is given by Eq. (10). The process of numerical calculation is performed in a stepwise fashion with a digital computor by solving the simultaneous equations, Eqs. (13-1) to (13-4) which are in a normal mesh shown in Fig. 1. The boundary condition at the open end, in this case, can no longer be expressed as the open end pressure p being equal to the constant reference pressure p_0. Assuming that the in-flow and out-flow at the open end are in a quasi-steady state, the adiabatic energy equation (Eq. (l4)) is applied as the boundary condition. The numerical calculations are performed for two cases with this boundary codition. One is a calculation with the following initial conditions. The closed pipe is divided by a partition across which an arbitrary pressure difference exists initially at the open end, and the partition is suddenly broken. The other is a calculation under the condition of a forcedsinusoidal velocity of constant amplitude at open end. The results of the calculation of the former case are shown in Fig. 2, and those for the latter case are shown in Fig. 3. Fig. 5 shows the Klirrfactor for the pressure histories at the closed end as a function of V^^^-_<amp> for the latter case. These results indicate that the distortion due to nonlinearity becomes visible when the dimensionless velocity amplitude at the open end (V^^^-_<amp>) is larger than 0. 1. Fig. 6 shows the experimental apparatus which is known as a Hartmann generator. Experiments are performed corresponding to the first case of the numerical calculation. The experimental results are shown in Fig. 7, compared with the calculated results, and the agreement is seen to be good. From above results, it is found that the wave motion in the closed pipe should be treated as a finite amplitude wave motion when the velocity amplitude at the open end is larger than 0. 1 times the velocity of sound, i. e. , when the acoustic pressure level in the pipe is higher than 180 dB.
社団法人日本音響学会の論文
1974-05-01

音響管内の有限振幅波動

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