Prikladnaâ matematika i mehanika

2D modeling of flapping flight is performed using DNS equations, the wing is simulated by an ensemble of Lagrangian particles. The simulation is carried out in two planes – parallel and orthogonal to the flight direction. The Golubev vortex street, which creates thrust, is reproduced; the meaning of figure-of-eight kinematics is clarified; it is shown that the vortices induced by the wing stroke eliminate the flow separation. It has been established that the use of folding wings reduces the energy consumption of birds by three times. The aerodynamics of a cyclocopter model with hybrid kinematics has been studied.

Different approaches of increased accuracy to the numerical solution of the problem about non-stationary flow around a cone model under in shock tube are investigated. It is shown that the computational methods based on dissipative numerical schemes of the second order lead to «smoothing» the physical oscillations of the solution and give significant errors. A comparison is performed. It shows the qualitative and quantitative correspondence of the numerical and experimental results at the start of the shock tube. The conclusion about the possibility of applying the proposed methodology in practice is made.

An iterative method for solving the inverse problem for a multielement (slotted) airfoil at high speeds in a viscous compressible flow, using RANS methods, has been developed. It is an evolution of a similar method developed earlier by the authors for low speed conditions. The method is based on the well-known principle of residual correction, according to which corrections to the current geometry are generated on the basis of the difference between the target and current pressure distribution. A brief description of the algorithm and the methods used is given. Examples for the slotted airfoil design corresponding to the target pressure distribution are given, including cases with the shock waves existence.

Effect of local supply of vibrational energy on the stability of a supersonic boundary layer on a plate is studied on the base of two-temperature system of equations for a single-mode vibrationally excited gas. The flight conditions in the atmosphere at an altitude of H = 15 km with a Mach number M = 4.5 were considered. It is shown that a source with a Gaussian power low dispersion profile located near the plate increases the temperature on the plate. When the source is localized at the upper boundary of the boundary layer, a significant area of the flow is heated. For two positions of the local source, neutral curves of two-dimensional temporal disturbances for the I and II Mack modes, as well as their increase increments, are calculated. Data on critical Reynolds numbers Re_δ,cr and increment amplitudes were compared with similar data for a perfect gas without a source. It is shown that the source near the plate reduces the stability of the layer, and in the upper position, on the contrary, increases the stability compared to the reference case. The displacement of the laminar-turbulent transition zone under the action of vibrational energy source was estimated using the e^N-method. For the upper position of the source, the shift of the beginning of the laminar-turbulent transition zone was 35%. The calculation results allow us to conclude that the local input of vibrational energy can become an effective method for controlling the stability of a supersonic boundary layer.

The review of works on numerical modeling of turbulent combustion is presented. The article presents the discussion about three classes of models, which are necessary for closure of mathematical model of flow (turbulence model, model of chemical kinetics, model of turbulence combustion interaction). The description of mathematical approach for modeling of subsonic flows with premixed turbulent combustion in channels within Reynolds equations with closure based on k–ω turbulence models is provided. Various models of turbulent combustion interaction based on PaSR (Partially Stirred Reactor) – quasi-steady models PaSR and PFR, and also model with memory effects EPaSR. The new model for influence of combustion on turbulent heat and mass transfer intensity – variable turbulent Prandtl and Schmidt model, compatible with turbulence models and PaSR based turbulence combustion interaction models. The appendix includes the description of differential model for turbulent scalar flux, which was a priori calibrated against DNS database of turbulent Rayleigh–Taylor flow.