The paper considers practical aspects of mathematical modeling in predictions of the level of near-field pressure pulsations of a near-future prototype supersonic business aircraft. A numerical modeling technique based on the numerical solution of the Navier-Stokes equations is proposed. The method is verified by near-field simulations of the NASA C608 supersonic low-boom demonstrator. We consider a supersonic flight with $M=1.4$ at a flight altitude of 16,215 m. Good convergence of our predictions with experimental data and results of other researchers is shown. Near-field sonic-boom simulations of the prototype supersonic business aircraft are used to illustrate how the method can be applied in practice for building a second-generation supersonic passenger aircraft. Two aerodynamic configurations of the aircraft are considered: no-tail and canard no-tail. The canard no-tail configuration in the as-is aircraft dimension and design was found to have no advantages over the no-tail configuration in the level of its near-field pressure pulsations because of its nonoptimality. Further recommendations for solving the near-field sonic-boom minimization problem are related to the construction of a comprehensive mathematical model enabling coupled simulations due to smooth integration of a parametrized aircraft geometry, an aerodynamic solver, and an optimizer.

A numerical algorithm that correctly takes into account the force of gravity in the presence of density discontinuities is constructed using unstructured collocated grids and splitting algorithms based on SIMPLE-type methods. A correct hydrostatic pressure field is obtained by explicitly extracting the gravity force contribution to the pressure equation and computing it using the solution of the gravity equilibrium problem for a two-phase medium. To ensure that the force of gravity is balanced by the pressure gradient in the case of a medium at rest, an algorithm is proposed according to which the pressure gradient in the equations of motion is replaced by a modification allowing for the force of gravity. Well-known free-surface problems are used to show that, in contrast to previously known algorithms, the proposed ones on unstructured meshes correctly predict hydrostatic pressure fields and do not yield velocity oscillations or free-surface distortions.

The paper presents the results of studying the effects of droplet diameters on the NACA0012 airfoil ice accretion, which have been obtained in the 3D numerical simulation of icing. To simulate the motion of water droplets as a multiphase medium, the Eulerian approach is used, which assumes that water droplets have spherical shapes, do not undergo deformation and breakup, do not interact with each other, and that coalescence/fragmentation of droplets does not take place. Both monodisperse (of the same size) and polydisperse (of various sizes) droplets are considered; they are represented by the spectral Langmuir distributions. These spectral distributions take into account the polydisperse nature of droplets and provide a higher efficiency in predicting ice shapes. The obtained ice shapes on an airfoil are compared with the available experimental and calculated data. It should be noted according to the simulation results that the use of the standard size of droplet diameter equal to 20 μm does not allow for obtaining correct shapes of ice on the leading edge of the wing profile not at all temperature regimes. For temperatures from −20 °C to −10 °C, there is a noticeable difference compared to the experimental data. At the same time, for this temperature range, the use of the Langmuir spectral distribution of droplet diameters relative to 15 μm provides a better agreement of the formed ice forms with the experiment.

The paper presents two methods to improve the efficiency of supersonic flow simulation using arbitrarily shaped unstructured grids. The first method promotes increasing the numerical solution convergence rate and is based on the geometric multigrid method for initialization of the flow field. The method is used to obtain the initial field of distributed physical quantity values, which maximally corresponds to the converged solution. For this purpose, the problem simulation is performed on a series of coarse grids beginning from the coarsest one in this series. Upon completion of simulations, the solution obtained is interpolated to a finer grid and used for initialization of simulations on this grid. The second method allows increasing the numerical solution accuracy and is based on statically adapting the computational grid to the flow specifics. The static adaptation algorithm provides automatic refinement of the computational grid in the region of specific features of flow, such as shock waves typical for supersonic flows. This algorithm provides a better description of the shock-wave front owing to the local grid refinement, with the local refinement region being automatically selected. Results of using these methods are demonstrated for the two supersonic aerodynamics problems: the simulation of the bow shock strength at a given distance under axially symmetric body Seeb-ALR and a mock-up aircraft Lockheed Martin 1021. It is shown that in both cases, the numerical solution convergence rate is increased owing to the use of the geometric multigrid method for initialization and a higher quality and a higher accuracy of solution is gained owing to the local grid refinement (using static adaptation means) near the shock-wave front.