Studies of Nonlinear Sound Dynamics in Fluids Based on the Caloric Equation of State

Abstract

The sound speed and parameters of nonlinearity B/A, C/A in a fluid are expressed in terms of coefficients in the Taylor series expansion of an excess internal energy, in powers of excess pressure and density. That allows to conclude about features of the sound propagation in fluids, the internal energy of which is known as a function of pressure and density. The sound speed and parameters of nonlinearity in the mixture consisting of boiling water and its vapor under different temperatures, are evaluated as functions of mass concentration of the vapor. The relations analogous to that in the Riemann wave in an ideal gas are obtained in a fluid obeying an arbitrary equation of state. An example concerns the van der Waals gases. An excess pressure in the reflected wave, which appears when standard or nonlinear absorption in a fluid takes place, is evaluated in an arbitrary fluid.

Archives of Acoustics

“…The relation between P a and R a in the case of isothermal gas in equilibrium (where R = ρ exp(z/2H)), has been derived by Perelomova (1998;2000). This relation is integro-differential with some kernel which represents dispersive properties of sound waves in inhomogeneous medium.…”

“…(1), and hence, definitions of P , Φ and U (Eqs. ( 9)) and definition of modes (Perelomova, 2000). The linear projecting is helpful also in studies of weakly non-linear dynamics of a fluid and, in particular, in investigations of non-linear interaction of modes.…”

“…Application of the corresponding projector at the system of conservative equations (Eqs. (11), supplemented by non-linear terms), allows to derive coupled dynamic equations for interacting modes. The example of that in unbounded volume of gas was considered by Perelomova (1998; 2000).…”

“…We make use of Eqs. (11) in order to separate acoustic and entropy contributions in any vector of total perturbations. Some simple conclusions illustrate the application of the theory.…”

“…socalled warming (Sun et al, 2012). It may be explained in the framework of non-linear interaction of sound and entropy modes (Karpov et al, 2016;Perelomova, 1998;2000;2009). The whole exposition is also important in the diagnostics of wave and non-wave modes in order to follow experimental observations and numerical simulations (Leble, Vereschagina, 2016).…”