Modelling of flow in gasdynamic resonator of pulse engine

F.A.Slobodkina, V.V.Malinin, A.I.Tarasov

 

FSUE “P.I.Baranov CIAM”

A.M.Lulka Research and Development Center, “NPO Saturn”

Russia

 

One of the possible ways to improve the aeroengine performance consists in change-over from the heat-supply-at-constant-pressure cycle to the periodic heat-supply-at-constant-volume cycle. The pulse engine concept and scheme considered in this work does not include mechanical valves and a special ignition system. The pulse process in such an engine is initiated due to the excitation of high-frequency oscillations in a gas dynamic resonator that is periodically filled with a specially prepared air-fuel mixture. The heat release enhancing the oscillation amplitude occurs as a result of supersonic (detonation) combustion of mixture in shock-wave structures formed in the resonator. Available at present are test facilities and models of individual resonators, the characteristics of which confirm the previous assessments of the proposed scheme effectiveness.

This work is devoted to the development of the mathematical and numerical model of gas dynamic processes in the resonator offered in early works as well as to the comparison of the obtained theoretical results with the results of experiments involving the pulse demonstrator engine.

It should be also noted that the ejector nozzle connected to the resonator permits to increase its thrust characteristics considerably.

The mathematical and numerical modeling is a basic method for a detailed investigation of fast gas dynamic processes and calculation of their integral characteristics in different modes.

The multiversion calculations which can be carried out on the base of the mathematical model allow choose the optimal (from one or another point of view) object parameters. Such an investigation permits to substantially reduce both a number of experiments and quite expensive model and full-scale tests as well as to write the effective program of their conduction.

This work includes numerical experiments in the specified range of thermodynamic and geometric governing parameters. The developed software system allows optimize the configuration of the gas dynamic resonator and its dimensions as well as the thermodynamic parameters of the working medium.

The proposed mathematical model describes the flow that develops at gas issue from the annular nozzle and its interaction with the resonator. As a result of this interaction, a pulse jet propagates into the ambient. The model is constructed on 3D with respect to spatial coordinates unsteady equations of gas dynamics taking account of friction and heat exchange (Reynolds-averaged Navier-Stokes equations involving a two-parameter turbulence model). Numeric modeling enables to follow the process from its beginning – the nozzle opening – to the moment of reaching the periodic mode by jet flow. The initial-boundary value problem corresponding to different operating conditions of the resonator has been formulated for the partial differential equations.

The analysis of parameters governing the process involving a pulse gas jet has been carried out. The number of parameters governing the pulse flow is more than in the case of steady flow that provides more possibilities to optimize the process. But it is necessary to note that multicriteria optimization of a pulse engine (PE) represents an independent complex scientific-technical problem.

The possibility of realizing the change in the governing parameters technically is determined by way of developing the pulse process. Parameters  characterizing air at the annular nozzle entry and the nozzle geometry are considered the most available for varying (from the technical point of view) as applied for the PE studied in this work. Any values can vary from the point of view of calculations. The values of relative and absolute thrust have been selected as an integral characteristic for assessing the effectiveness of a PE with a resonator. The comparison with the results of two PE models tests regarding the integral characteristics has shown a good agreement of experimental and calculation investigations.

The following should be noted.

Within the work on the investigation of the processes in the resonator there were also used other mathematical models: Euler and Navier-Stokes equations for laminar flows. The calculations using the model that does not take account of viscosity, according to the program of the second order of accuracy, are unstable and demand introducing either “artificial viscosity” or a very small time step. That is why this kind of model was rejected for this work. The onset of instability in calculations with Euler equations is connected with the appearance of shockwaves in the solution. It is known that the schemes of second order in the vicinity of shockwaves initiate the flow parameter variations induced by difference approximation of equations. The “calculation variations” can distort the pulse physical process pattern. As the oscillation process in the resonator and in jet is high-frequency, a time step should be very small that makes the calculation by Euler equations unreasonable. The calculations by Navier-Stokes equations as applied to laminar flows are close (by some results) to the calculations taking account of a turbulent flow pattern, but when compared with experiment they differ considerably.

The calculations without taking viscosity into account were carried out in another work.

It is necessary to mention the fact that the preliminary investigations showed a high effectiveness of the connected ejector channel from the viewpoint of thrust increase of a PDE with a resonator.

The ejector channel with a pulse active jet can provide a 1,5-2 times increases in thrust if the combinations of governing parameters are chosen optimally. At that, the frequencies are selected according to the natural frequency of the ejector channel and stabilized. The choice of the ejector dimensions, its position relative to the resonator demand the additional numerical and experimental investigation.