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It is well known that acoustic oscillations can be self-excited in reactors [ 1, 2]. The conditions under which they appear in reactors with gaseous circulating fuel have been determined in [3][4][5][6]. In the same works, the boundaries of the regions of acoustic instability and the effect of different parameters of a reactor on its stability were determined.Together with investigation of stability in the "small," it is important to study the character and properties of nonlinear self-excited oscillations arising in the region of instability. Periodic oscillations are most common in reactors. However, as found in Refs. [7][8][9], stochastic self-excited oscillations can also appear in reactors. It was shown that dynamic chaos can arise in reactors with a regulation system [7] and boiling-water [8] and pulsed [9] reactors. In the present paper it is shown that acoustic oscillations arising in gaseous fuel of a reactor can also be of a stochastic character.A strict investigation of acoustic phenomena in a reactor leads to an analysis of complicated distributed mathematical models. However, discrete models which make it possible to obtain qualitative results do exist. In one such model, proposed in [3], the reactor core is replaced by a resonator (Fig. la), consisting of a volume 1 and a neck 2 f'dled with gaseous fuel. Dynamic processes in such a system are described by the equations [3] where t is the time; N is the neutron density; ~k is the reactivity; Ci, ~'i and/3 are, respectively, the concentration, decay constant, and total fraction of emitters of delayed neutrons; l is the prompt-neutron lifetime; e' is the reactivity factor with respect to fuel density; p, T, and P are, respectively, the fuel density, temperature, and pressure in the resonator; G is the mass flow rate of fuel through the neck 2; Gin = const and Tin = const are the flow rate and temperature of the fuel at the entrance into the resonator; R is the gas constant; l n and s n are the length and cross sectional area of the neck 2; V is the volume 1; Cp is the specific heat capacity of fuel at constant pressure; a = const > 0 is a coefficient characterizing pressure losses to friction; A = const > 0; Pout = const is the pressure at the exit from the reactor; the subscript "0" in Eq.
It is well known that acoustic oscillations can be self-excited in reactors [ 1, 2]. The conditions under which they appear in reactors with gaseous circulating fuel have been determined in [3][4][5][6]. In the same works, the boundaries of the regions of acoustic instability and the effect of different parameters of a reactor on its stability were determined.Together with investigation of stability in the "small," it is important to study the character and properties of nonlinear self-excited oscillations arising in the region of instability. Periodic oscillations are most common in reactors. However, as found in Refs. [7][8][9], stochastic self-excited oscillations can also appear in reactors. It was shown that dynamic chaos can arise in reactors with a regulation system [7] and boiling-water [8] and pulsed [9] reactors. In the present paper it is shown that acoustic oscillations arising in gaseous fuel of a reactor can also be of a stochastic character.A strict investigation of acoustic phenomena in a reactor leads to an analysis of complicated distributed mathematical models. However, discrete models which make it possible to obtain qualitative results do exist. In one such model, proposed in [3], the reactor core is replaced by a resonator (Fig. la), consisting of a volume 1 and a neck 2 f'dled with gaseous fuel. Dynamic processes in such a system are described by the equations [3] where t is the time; N is the neutron density; ~k is the reactivity; Ci, ~'i and/3 are, respectively, the concentration, decay constant, and total fraction of emitters of delayed neutrons; l is the prompt-neutron lifetime; e' is the reactivity factor with respect to fuel density; p, T, and P are, respectively, the fuel density, temperature, and pressure in the resonator; G is the mass flow rate of fuel through the neck 2; Gin = const and Tin = const are the flow rate and temperature of the fuel at the entrance into the resonator; R is the gas constant; l n and s n are the length and cross sectional area of the neck 2; V is the volume 1; Cp is the specific heat capacity of fuel at constant pressure; a = const > 0 is a coefficient characterizing pressure losses to friction; A = const > 0; Pout = const is the pressure at the exit from the reactor; the subscript "0" in Eq.
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