Mathematical modeling of spatial gas flow in nozzles of nontrivial geometry

Numerical modeling of the spatial gas flow in an adjustable nozzle with an asymmetric critical section caused by the overlap of a part of the flow area by a gas flow regulator has been carried out. The mathematical model is based on three-dimensional models of gas dynamics, the method of large particles is used for calculation. When describing the unsteady flow of an inviscid gas, the system of Euler equations is used, written for a computational rectangular plane, taking into account the function of nozzle geometry. The results of calculations of flow parameters along a nozzle path with a uniform outlet section and with an obliquely cut outlet nozzle are presented. Calculations were carried out for completely open critical sections and for half overlapped. For oblique cut nozzles, the overlap of the critical section from the side of the short part and from the side of the long part of the oblique nozzle is considered.

Numerical study of the aerodynamic characteristics of an axisymmetric profile of an optimized shape

Today, one of the important and urgent tasks of the aerodynamics science is the study and op-timization of aerodynamic characteristics of optimized profile shapes in a gas flow. This problem arises in the design of aircraft and various vessels and is associated with a rational choice of profile shape for a large number of different characteristics and, in particular, in terms of aerodynamic drag. In this paper, consider methods for optimizing an axisymmetric aerodynamic profile in a sta-tionary laminar inviscid gas flow at different angles of attack. The proposed method of solv-ing such a problem of optimization and numerical study of aerodynamic characteristics of the described body in the flow is relevant due to the complexity of its solution, for example, by traditional methods based on the Navier-Stokes system of differential equations. Experi-mental methods are based on expensive and time-consuming tools that do not guarantee find-ing the optimum. Such a computing tool as Ansys Fluent is well suited for solving such prob-lems of hydroaerodynamics and allows not only to speed up and reduce the cost of the compu-tational experiment, but also to increase the efficiency of its implementation. The article describes the process of finding the optimum, which reduces to minimizing the drag force of the previously described axisymmetric profile. A description is also given of the wing

Invariants and Conserved Quantities for the Helically Symmetric Flows of an Inviscid Gas and Fluid with Variable Density

New material conservation laws and conserved quantities are derived for the helically symmetric flows of an inviscid compressible gas and an ideal incompressible fluid with variable density$\rho(\mathbf{x},\;t)$.

Invariants of the Axisymmetric Flows of an Inviscid Gas and Fluid with Variable Density

Material conservation laws and integral invariants are constructed for the axisymmetric flows of an inviscid compressible gas and an ideal incompressible fluid with variable density$\rho(\mathbf{x},t)$. The functional independence of the new invariants from helicity is proven.

Construction of third-order schemes using Lagrange-Burmann expansions for the numerical integration of inviscid gas equations

Предлагается строить явные разностные схемы третьего порядка точности для гиперболических законов сохранения с применением разложений сеточных функций в ряды Лагранжа--Бюрмана. Результаты тестовых расчетов для случаев одномерного уравнения переноса и многомерных уравнений Эйлера невязкого сжимаемого газа подтверждают третий порядок точности построенных схем. Получены квазимонотонные профили численных решений. It is proposed to construct several explicit third-order difference schemes for the hyperbolic conservation laws using the expansions of grid functions in Lagrange-Burmann series. The results of test computations for the one-dimensional advection equation and multidimensional Euler equations governing the inviscid compressible gas flows confirm the third order of accuracy of the constructed schemes. The quasi-monotonous profiles of numerical solutions are obtained.