DOI: 10.34759/vst-2021-2-166-176

Аuthors

Mkrtchyan M. K.1*, Kochetkov Y. M.2**

1. GNPP "Region", 13a, Kashirskoe shosse, Moscow, 115230, Russia
2. Keldysh Research Centre, 8, Onezhskaya str., Moscow, 125438, Russia

*e-mail: mger_97@mail.ru
**e-mail: swgeorgy@gmail.com

Abstract

Up to now, a problem of parameters’ accurate prediction at large Reynolds numbers is existing in gas dynamics science. The Navier-Stokes equation of motion is practically unsolvable with modern technology due to the lack of computational resources. With the Reynolds number increase, application of the finer mesh with small computational cells is necessary, which makes it almost impossible to calculate even elementary problems when employing direct numerical modeling.

Transition to solving simplified equations of motion is widespread. Reynolds-averaged Navier-Stokes (RANS) equations became the most popular. However, this approach is only a subterfuge containing inconsistencies while describing the true picture of the flow due to many assumptions. Besides, Reynolds equations are not substantiated experimentally. Nevertheless, practically all Russian and foreign electronic products of computational gas dynamics, such as: “Ansys”, “FlowVision”, “OpenFOAM”, etc., are based on the RANS equations.

Thus, an alternate approach to the turbulence description is being proposed. More understandable and physical like is the approach where turbulence is being characterized as a vortex flow, i.e. a flow in which rotational motion and torsion exist aside fr om the translational one. In other words, the flow will be laminar wh ere rotation and torsion do not present.

The article presents both computation and analysis of the gas-dynamic characteristics of a liquid-propellant rocket engine for laminar flow, with the purpose to realize a physically correct task, and significantly reduce the computational time by employing simpler equations. The studies were conducted in the laminar sublayer near the wall of the model chamber of a liquid-propellant rocket engine. The purpose of the work consisted also in writing a program code for obtaining the characteristics of the velocity field and its qualitative comparison with the computational results with the “Ansys” software package.

A system of equations for laminar flow consisted of the equations of continuity, motion and energy in the Poisson form is compiled and programmed in the Python programming language in the work being presented. Computation is performed for the chamber. The region of two by two cm and 41 by 41 mesh points is being set. The boundary conditions were being set in the form of the condition adhesion on the wall, tracking on the centerline, and artificial flow limiting at the outlet. Initial conditions are the longitudinal of u = 100 m/s and transverse of v = 0 m/s velocities, dynamic viscosity of μ= 10–4 Pa·s, the initial densities field value of ρ= 6 kg/m3.

The computational results were analyzed with the “Ansys” program. For this purpose, the flow computation near the wall was performed for the combustion chamber using the default turbulence model. As the result, the hypothesis for the laminar sublayer existence near the wall was confirmed, which substantiated the statement on the laminar flows application correctness while this program developing. The presence of this fact is of great importance in many computations such as computations for friction, heat exchange, and carried-away wall destruction. The computation of the flow near the wall, using the laminar model, was performed as well.

To assess the adequacy of the results obtained by the developed program, computations were made using the Euler equation. The velocities of the ideal gas obtained with the Euler equations are 3% greater than for the laminar case.

The profile obtained for laminar flow by the “Ansys” program qualitatively repeats the profile calculated in the equation program code in the laminar formulation.

The current lines concentration near the wall can be observed in the velocities field, which confirms the presence of a boundary layer, and the lines parallelism indicates its laminarity.

Thus, the following conclusions can be drawn:

1. A method and a program for the gas-dynamic characteristics computing of the liquid-propellant rocket engine for laminar flow are developed;

2. Testing with the “Ansys” program revealed a qualitative match with the calculations by the developed program;

3. The linear dependence of the velocity profiles near the chamber wall (the presence of a laminar sublayer) is shown;

4. The difference in absolute velocities due to the viscoelastic term is estimated at ~3%, which corresponds to the gas-dynamics losses of the specific thrust momentum.

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