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(Îïðåäåëåíèå ïàðàìåòðîâ ãàçà â ðåçîíàíñíûõ òðóáàõ è êàíàëàõ äâèãàòåëåé ñ ïåðèîäè÷åñêèì ðàáî÷èì öèêëîì ìåòîäîì ïîðøíåâîé àíàëîãèè)
Alexander Khrulev
PhD, Senior Researcher, International Motor Bureau
https://orcid.org/0000-0002-6841-9225
DOI: 10.15587/1729-4061.2023.288520
Keywords: pulse jet engine, resonant tube, flow modeling, "liquid" piston method, piston analogy
Abstract
This paper investigates a process of gas flow in the resonant tube of an engine with a periodic workflow. Analysis of various flow models and comparison of known data have shown that the problems of constructing closed 0-dimensional models of the operating cycle for some types of engines remain unresolved. Given this, the question arises about the dimensionality of models of individual engine elements, including the resonant pipe model, which must be included in the general model of the cycle, especially at the initial stage of its development.
To solve the identified problems, a mathematical model of air flow has been improved, built on the basis of an analogy with a '"liquid" piston. Unlike existing ones, the piston analogy model allows one to calculate the instantaneous velocity averaged over the length of the pipe using a numerical solution of the differential equation for velocity.
To test the model built, an alternative finite-difference 1-dimensional gas-dynamic model was selected, with the help of which a test simulation of air flow in a pipe was performed. It has been established that the piston model allows one to find the flow velocity with an accuracy of 5 % for a pressure drop varying according to a sinusoidal law. The permissible limits for changes in the oscillation frequency and pipe length were found, at which the piston model has a minimum error.
Based on the results of the study, it was concluded that with a small mass and inertia of the liquid piston, the proposed model gives results close to those provided by more complex models with higher dimensionality. This indicates the possibility of using a piston model for elements such as pipes as part of a 0-dimensional thermodynamic model of engines with a periodic operating process as an approximate alternative to traditional 1-dimensional flow models.
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Äðóãèå íàøè ñòàòüè...
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Calculation diagram of the piston analogy method (liquid piston): 1 – control volume; 2 – adapter; 3 – resonant tube
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Diagram of a pipe in a one-dimensional flow model
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The flow process in a pipe at a constant pressure drop at p0=1.3 after opening the left end of the pipe: a – velocities at the ends and in the middle of the pipe in comparison with the speed velocity calculated using the piston model; b – distribution of pressure p and temperature T along the length of the pipe at different times (by the number of points in time)
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The speed velocity of air flow in the middle of the pipe when the pressure drop at the inlet changes according to a sinusoidal law: a – with a dimensionless pulsation frequency f=0.29; b – at double frequency f=0.58
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