Stochastic simulation of cavitation bubbles formation in the axial valve separator influenced by degree of opening

Abstract

A stochastic modeling of the formation of cavitation bubbles on a specific example is proposed. In this case, the initial stage of hydrodynamic cavitation in the flow part of the axial valve, the separator, was studied. A distinctive feature of this regulating device is the external location of the locking organ. An expression for the differential distribution function of the number of bubbles according to the degree of valve opening is obtained. The model takes into account the design and operating parameters of the axial valve, as well as the physical and mechanical properties of the working environment.

Engineering Method for Calculating of an Axial Valve Separator With an External Location of the Locking Part

“…The performed experimental studies (Lebedev et al, 2017a,b) confirmed the possibility of reducing the intensity of hydrodynamic cavitation at its initial stage when using the modernized part of "separator-locking shell" of axial valve. In this case, a comparative analysis (Kapranova and Miadonye, 2019) of the obtained theoretical (Kapranova et al, 2016a(Kapranova et al, , 2017(Kapranova et al, , 2018aKapranova, 2018;Kapranova and Miadonye, 2019) and experimental (Lebedev et al, 2017a,b) results for the dependence of the differential distribution function of the number of bubbles f z (z) at the initial stage of hydrodynamic cavitation with a separator with round holes depending on the degree of their opening with using an external locking shell showed satisfactory convergence with a relative error not exceeding 13%. Note that the value of z is determined by the ratio of the given position z ′ for the movable shutter (external locking shell) along its axis to the conditional position L corresponding to the length of the perforated part of the separator.…”

“…Earlier, the authors used the stochastic approach with the equilibrium representation of the states of the energetically closed macrosystem (Klimontovich, 2014;Tang et al, 2019) within the framework of the Ornstein-Uhlenbeck random process (Kapranova et al, 2016b) to form the model of this process the bubble formation process in the separator at the initial stage of hydrodynamic cavitation. The proposed stochastic models (Kapranova et al, 2016a(Kapranova et al, , 2017(Kapranova et al, , 2018aKapranova, 2018;Kapranova and Miadonye, 2019) allowed us to obtain differential distribution functions of the number of cavitation bubbles formed during the initial stage of the evolution of hydrodynamic cavitation, according to their size (Kapranova et al, 2016a(Kapranova et al, , 2017(Kapranova et al, , 2018a and the degree of opening of the axial valve (Arzumanov, 1971;Lebedev et al, 2017a,b). The performed experimental studies (Lebedev et al, 2017a,b) confirmed the possibility of reducing the intensity of hydrodynamic cavitation at its initial stage when using the modernized part of "separator-locking shell" of axial valve.…”

“…Another model (Kapranova, 2018;Kapranova et al, 2018b;Kapranova and Miadonye, 2019) made it possible to establish a connection between the critical value of the Reynolds number Re cr in the case of a complete opening of the valve and its design parameters. So, these expressions for D cb (Kapranova et al, 2017(Kapranova et al, , 2018a and Re cr based on (Kapranova, 2018;Kapranova et al, 2018b;Kapranova and Miadonye, 2019), as well as the obtained expressions for the energy parameter of the stochastic model (Kapranova et al, 2018b) and the hydraulic resistance coefficient (Kapranova et al, 2018c) are used in the proposed engineering method for calculating the separator and constitute the main difference from the known approach (Arzumanov, 1971(Arzumanov, , 1985. Note that in practice, the identification of the cavitation region in the flow part of the control device is associated with the analysis of the dependence of the hydraulic resistance coefficient for the conditional flow area on the cavitation number k C , which is also reflected in this work.…”

“…The team of authors analyzed the design features of directflow type control valves (Lebedev et al, 2016(Lebedev et al, , 2017a, methods for modeling the cavitation phenomenon (Kapranova et al, 2016c) and calculation of the main indicators of this process (Kapranova et al, 2016d,e), and also performed theoretical (Kapranova et al, 2016a(Kapranova et al, ,b, 2017(Kapranova et al, , 2018aKapranova, 2018;Kapranova and Miadonye, 2019) and experimental (Esveldt, 2012;Lebedev et al, 2017a,b;Preston, 2018) studies of the initial stage of hydrodynamic cavitation with axisymmetric throttling of fluid flows, which made it possible to obtain a theoretical justification and experimental confirmation (Kapranova and Miadonye, 2019) of the possibility of reducing the intensity of formation of cavitation bubbles and the use of external locking shell. As a result of these studies, the authors proposed the design of an axial valve (Arzumanov, 1985;Lebedev et al, 2018) with a locking and regulating system "perforated separator-external locking cylinder-conical shell."…”

“…Thus, after solving a number of problems in developing stochastic models for the formation of cavitation bubbles in an axial valve separator by their size (Kapranova et al, 2016a(Kapranova et al, , 2017(Kapranova et al, , 2018a and the degree of its opening (Kapranova, 2018;Kapranova et al, 2018b;Kapranova and Miadonye, 2019), after performing a series of comparative analysis (Kapranova and Miadonye, 2019) of the theoretical (Kapranova et al, 2016a(Kapranova et al, , 2017(Kapranova et al, , 2018aKapranova, 2018;Kapranova and Miadonye, 2019) and experimental results (Lebedev et al, 2017a,b) the next goal of studies of axisymmetric throttling of fluid flows is the development of engineering methods for calculating operational and design parameters of the separator-locking shell assembly.…”