Mathematical Modeling of Operating Process and Technological Features for Designing the Vortex Type Liquid-Vapor Jet Apparatus

Merzliakov, Iurii; Pavlenko, Ivan; Chekh, Oleh; Sharapov, Serhii; Ivanov, Vitalii

doi:10.1007/978-3-030-22365-6_61

Cited by 31 publications

(7 citation statements)

References 25 publications

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“…Moreover, in the case of λ < λ cr , which corresponds to the wavelengths L > 4πR, the radial velocity changes its sign inside the droplet. The relevant limit value r * is determined from the condition of the amplitude extremum (18) and is equal to:…”

Section: Resultsmentioning

confidence: 99%

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Effect of Superimposed Vibrations on Droplet Oscillation Modes in Prilling Process

et al. 2020

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This article was aimed to solve an urgent problem of ensuring quality for prilling processes in vibrational prilling equipment. During the research, the need for the application of vibrational prilling to create a controlled impact on the process of jet decay on droplets with the proper characteristics was substantiated. Based on the experimental and theoretical studies of the process of decay of a liquid jet into drops, axisymmetric droplet oscillation modes for the different frequencies were observed. Frequency ranges of transition between modes of decay of a jet into drops were obtained. As a result, the mathematical model of the droplet deformation was refined. The experimental research data substantiated this model, and its implementation allowed determining the analytical dependencies for the components of the droplet deformation velocity. The proposed model explains the existence of different droplet oscillation modes depending on the frequency characteristics of the superimposed vibrational impact. Based on an analytical study of the droplet deformation velocity components, the limit values of the characteristics defining the transition between the different droplet oscillation modes were discovered. Analytical dependencies were also obtained to determine the diameter of the satellites and their total number.

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Section: Resultsmentioning

confidence: 99%

“…Fluid jet behavior [18] out of holes depends on different conditions. However, the fluctuations show that the axisymmetric ellipsoidal shape of the formed droplet is permanently changing.…”

Section: Introductionmentioning

confidence: 99%

Effect of Superimposed Vibrations on Droplet Oscillation Modes in Prilling Process

et al. 2020

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“…Figure 5 shows that the direction of the wave propagation from the lower edge of the oblique cut coincides with the theoretical description. Moreover, the obtained velocity fields correspond to the method of characteristics based on the use of physical laws of propagation in a supersonic flow of weak rarefaction and compression waves, as described in [29].…”

Section: Numerical Simulation Resultsmentioning

confidence: 99%

“…In addition, the pressure of the environment after the oblique cut p a is less than pressure p 01 before it. Additionally, during the simulation, equations according to the computational domain of the solid-state model [29] were used. Finally, the active flow working fluid (water) and multiphase calculation model were chosen from the ANSYS database.…”

Section: Analytical Modelmentioning

confidence: 99%

Flow Modeling in a Vortex Chamber of a Liquid–Steam Jet Apparatus

et al. 2022

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The article investigated the flow of boiling streams through a nozzle with an oblique cut. Due to this flow organization, deviation from the nozzle axis at the vortex chamber inlet occurred. The study of flow modeling in the inlet section was carried out. The flow design and the calculation scheme of the vortex liquid–steam jet apparatus were proposed. Analytical expressions between the main operating parameters were obtained according to the developed mathematical model. A recommended oblique-cut angle for the active-flow nozzle was evaluated considering the transition through the first critical section based on the tangential velocity flow model. Validation of the mathematical model in the inlet section of the vortex chamber was provided based on the comparison with available experimental data. Flow visualization in the inlet section of the vortex chamber was obtained. The assumption of uneven flow distribution was confirmed experimentally. Overall, the boiling liquid flow was implemented in the active flow nozzle. The obtained scientific and practical results help to determine geometric parameters and physical characteristics of the vortex-type liquid–steam jet apparatus at the design stage. The obtained results were implemented to modernize vacuum units based on vortex type liquid–steam jet apparatuses.

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“…The hybrid method [7,8] is widespread in studying the direct cascade of turbomachines, although it overestimates the entropy, flow mass rate, and angular momentum in the tangential direction. Significantly distort the averaged enthalpy drop in the nozzle cascade (pressure behind the cascade) and non-hybrid averaging methods [9][10][11][12]. Papers [13,14] use original averaging methods, which have some other drawbacks.…”

Section: Literature Reviewmentioning

confidence: 99%

Improved Hybrid Methods for Determining the Integral Characteristics of Turbomachine Nozzle Cascades

Lapuzin

Subotovich

Yudin

et al. 2021

Lecture Notes in Mechanical Engineering

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To determine the integral gas-dynamic characteristics of nozzle cascades of turbomachines, it is necessary to average the parameters of the threedimensional flow behind the cascade that is non-uniform along with the pitch and along with the height of the cascade. Two types of averaging methods are used. For the first type of methods, the flow parameters at the entrance to the cascade are not taken into account when averaging the parameters of a nonuniform flow behind the cascade. For the second type of methods (hybrid), the pressure behind the cascade is found from the condition of maintaining the enthalpy drop in the initial non-uniform three-dimensional and averaged flows. In a cylindrical flow, the hybrid method is usually used to determine the velocity coefficient. The main disadvantage of this method is the significantly overestimated mass flow mass rate and component onto the axial direction of the angular momentum. To improve the methods of the second type, it is proposed to replace the ratio of the components of the momentum with two parameters, namely: mass flow rate and the component of the moment of momentum on the axial direction. It allows determining the velocity coefficient and two angles for the averaged flow. It is shown that the second kinetic energy of the flow can be replaced by entropy and, thus, the velocity coefficient can be adjusted provided the complex quality criterion is kept constant.

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Mathematical Modeling of Operating Process and Technological Features for Designing the Vortex Type Liquid-Vapor Jet Apparatus

Cited by 31 publications

References 25 publications

Effect of Superimposed Vibrations on Droplet Oscillation Modes in Prilling Process

Effect of Superimposed Vibrations on Droplet Oscillation Modes in Prilling Process

Flow Modeling in a Vortex Chamber of a Liquid–Steam Jet Apparatus

Improved Hybrid Methods for Determining the Integral Characteristics of Turbomachine Nozzle Cascades

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