Methodology for validation of analytical models of two-phase flows in supersonic nozzles using CFD simulation

Oleksandr Shorinov, Sergii Polyviany, Nina Savchenko, Roman Ipatov

Abstract


The subject matter of this article is the methodology for mathematical modeling of gas-dynamic processes in supersonic converging-diverging nozzles. This study aims to develop and substantiate a comparative validation methodology for assessing the accuracy of simplified analytical isentropic models against high-fidelity computational fluid dynamics (CFD) simulations for two-phase compressible flows involving secondary gas entrainment. The tasks to be solved are as follows: implementing a numerical model of the gas-particle flow within a supersonic nozzle using the finite volume method (ANSYS Fluent); performing analytical calculations of particle velocity and temperature using the one-dimensional isentropic model; and conducting a comparative analysis to identify systematic deviations and substantiate the applicability limits of the simplified analytical approach compared to the numerical solution. The methods used are: the study of gas dynamics of a two-phase flow was studied by numerical modeling using a modern computing package based on the finite volume method ANSYS Fluent, as well as conventional gas dynamics. The following results were obtained: two-phase CFD simulation (carried out in ANSYS Fluent) and a one-dimensional isentropic model were employed to analyze the behavior of nickel particles under varying gas stagnation temperatures (440 °C, 520 °C, 620 °C) and particle diameters (10 μm, 25 μm, 40 μm). The CFD results, which incorporate real gas dynamics, including turbulence, viscous effects, and particle–flow interactions, were compared with analytical results. The CFD results show significantly lower particle velocities (by 50 ± 7%) and higher temperatures (by 22 ± 7%) compared with the isentropic model, primarily due to the inclusion of thermal losses, boundary layer development, and secondary flow effects. The latter arises from the atmospheric entrainment of the carrier gas and powder into the divergent section of the nozzle. These factors disrupt the analytical approach’s ideal expansion, reducing the gas and particle velocities while increasing particle temperatures. Conclusions. The scientific contribution lies in substantiating that the classic isentropic model reaches its applicability limit for low-pressure cold spray nozzles with downstream injection. The correction coefficients derived from CFD data are proposed to refine analytical models. The practical significance lies in creating a basis for automated design algorithms for supersonic nozzles, enabling the derivation of correction coefficients for analytical equations in the future without the need for repetitive, computationally expensive simulations.

Keywords


CFD simulation; gas flow; particle acceleration; ANSYS Fluent; isentropic model

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DOI: https://doi.org/10.32620/reks.2025.4.04

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