Non-Wave Variations in Temperature Caused by Sound in a Chemically Reacting Gas

Abstract

A weakly nonlinear generation of non-acoustic modes in the field of sound in a gas is considered. An exoteric chemical reaction of A → B type, which takes place in a gas, may be reversible or not. Two types of sound are considered, low-frequency and high-frequency as compared with the characteristic time of a chemical reaction. For both these cases, the governing equations of non-acoustic modes are derived and conclusions of the efficiency of their nonlinear generation by sound are made. The character of nonlinear generation of non-acoustic modes by sound depends essentially on reversibility of a chemical reaction.

Standing Waves and Acoustic Heating (or Cooling) in Resonators Filled with Chemically Reacting Gas

“…Molevich (2002; was the first to mention some special mechanisms of nonlinear self-action of the acoustic beam which cause the self-focusing of sound in an acoustically active medium, cooling of gas by sound, and the excitation of acoustic streaming in opposite direction as compared to the one of sound propagation. The acoustic cooling in a gas with the chemical reaction of A → B type in unbounded volumes was also studied by the authors for the high and low-frequency sound in (Perelomova, Pelc-Garska, 2011).…”

Standing Waves in a Rectangular Resonator Containing Acoustically Active Gases

“…in the case of vibrationally excited gases, and 20) in the case of chemically reacting gases (Perelomova, Pelc-Garska, 2014;2011), where the top line denotes the average over the sound period, and T 0 is an unperturbed temperature of a gas. Before the formation of discontinuity, the rate of heat release varies as b exp(−2bτ ), since the averaged squared dimensionless pressure P 2 i equals P 2 i = − ∂Pi ∂τi P i dτ i = 0.5.…”

Hysteresis curves and loops for harmonic and impulse perturbations in some non-equilibrium gases

“…The instantaneous generation of the thermal mode in the field of low-frequency or high-frequency sound in the relaxing fluids where irreversible processes may take place, have been discussed in [13,24]. In general, the analysis applies not only to periodic sound and describes, among other, instantaneous variations of excess density specifying the thermal mode in the field of intense sound (ρ denotes excess quantity associated with the entropy mode, and Q is the acoustic source of the entropy mode),…”

“…In the low-frequency domain, where ωτ << 1 and B < 0, a fluid behaves as Newtonian with attenuation proportional to B and τ. In view of small |B| as compared to the characteristic wavenumber of sound, attenuation (or enhancement) of low-frequency sound is very low, as well as enlargement of the thermal mode in the field of sound [12,13]. Eq.…”