and Computational Methods

doi: 10.18698/2309-3684-2022-2-7887

A new dependence for the enthalpy profile in the boundary layer model. A new analytical dependence is proposed for the enthalpy profile in the boundary layer, the use of which makes it possible to quickly and efficiently obtain the distribution of heat flux over the surface of blunted bodies

Котенев В.П., Тонких Е.Г. Новая зависимость профиля энтальпии в модели пограничного слоя. Математическое моделирование и численные методы, 2022, № 2, с. 80–89

doi: 10.18698/2309-3684-2019-3-100112

The paper considers a method for applying the analytical dependence to calculate the pressure on the surface of blunted cones in a supersonic gas flow at an angle of attack, taking into account the discontinuity in the generatrix curvature. To generalize the dependence on the case of three-dimensional flow, the method of local surfaces was used. The pressure coefficient on the surface of spherical bluntness is calculated separately from the conical part according to known ratios [1, 2]. The results were compared with empirical data and the results of accurate calculations in a strict mathematical formulation. The scope of applicability of the method is determined. From the comparison it follows that using the analytical formula for the pressure distribution on the surface of a blunted cone in three-dimensional flows in applied problems of aerodynamics allows significant simplifying calculations while maintaining good accuracy of the results.

Котенев В.П., Пучков А.С., Сапожников Д.А., Тонких Е.Г. Метод локальных поверхностей для моделирования давления на затупленном конусе при пространственном обтекании. Математическое моделирование и численные методы. 2019. № 3. с. 100–112.

doi: 10.18698/2309-3684-2017-4-6072

The article introduces a dependency for the pressure distribution in the disturbed region near the sphere streamlined by the flow of the supersonic inviscid gas, obtained when modifying the Shepard’s Method. We use known ratios for the pressure on the body and the shockwave as well as data from the numerical experiments. We have compared the results with the data not used in the learning process of the dependency coefficients. This comparison proves high confidence of the model obtained.

Kotenev V.P., Puchkov A.S., Sapozhnikov D.A., Tonkikh E.G. Simulation of the pressure distribution in the disturbed region near the sphere streamlined by the inviscid flotation by means of the machine learning methods. Mathematical Modeling and Computational Methods, 2017, №4 (16), pp. 60-72

doi: 10.18698/2309-3684-2018-2-109121

The generalization of the dependency which was proposed earlier for determining of the pressure in perturbed area streamlined by the supersonic flow of the inviscid perfect gas was provided. The modification allows to consider effects which occur when the sphere is streamlined by high temperature gas with adiabatic index which do not equal 1.4. According to article [2-3], made adjustment to the function which describes the behavior of the shock wave which depends on the adiabatic index. The Shepard function’s coefficient also consider of adiabatic index. First and second order members of Shepard function which describe a pressure in area does not change. Comparison of application versions with the available data calculations for the high temperature gas and approximations based on perfect gas shows high accuracy of the proposed approach.

Котенев В.П., Пучков А.С., Сапожников Д.А., Тонких Е.Г. Восстановление распределения давления в возмущенной области около сферы, обтекаемой сверхзвуковым потоком газа с произвольным эффективным показателем адиабаты. Математическое моделирование и численные методы, 2018, № 2, с. 109–121