Aerothermodynamics calculation of the EXPERT reentry flight vehicle

This paper concerns the aerothermodynamics of high–speed gas flows around the EXPERT reentry flight vehicle moving at different angles of attack at an altitude of 50 km with the speed V∞ = 5 km/s. Calculations were carried out using UST3D and UG3D computer codes developed at the Ishlinsky Institute for Problems in Mechanics RAS (IPMech RAS). The computer codes implement the numerical simulation of the flight vehicle aerothermodynamics by integrating the complete set of Navier–Stokes equations on unstructured mesh using the ideal gas model.


Introduction
The EXPERT reentry flight vehicle was developed by the European Space Agency (ESA) [1]. Flight tests of the vehicle were not conducted, but there is a sufficiently large amount of calculations and experimental data. Experimental data are presented this papers [2][3][4][5]. In papers [4][5][6] the numerical results are presented. At first glance, the geometry of this device may seem fairly simple, but the numerical simulation reveals the difficulties related to the design features of this type of vehicles.

Computational model
Flows around the EXPERT reentry flight vehicle were calculated using the UST3D and UG3D computational codes [7,8]. These codes are designed to compute the aerothermodynamics of highspeed flight vehicles and can be used in a wide range of Mach numbers, altitudes and angles of attack [7][8][9]. The computer codes are based on the algorithms for solving the non-stationary threedimensional set of Navier-Stokes equations (1) -(4) [10][11][12].
The complete set of Navier-Stokes equations is used in conjunction with the equation of state for ideal gas (5).
The UST3D and UG3D computer codes execute numerical integration of the system using the splitting method with respect to physical processes and the Godunov-type method [13]. The methods are explicit and use the first-order and second-order approximation in time and second-order approximation in space. The problem is solved by obtaining the convergence [7][8][9].
During the verification of UST3D and UG3D computational codes, the results were compared with the ones obtained by the SolidWorks Flow Simulation module for gasdynamic computations. This module is based on the algorithms for solving the non-stationary three-dimensional set of Navier-Stokes equations using the ideal gas model, as well. Codes UST3D and UG3D were validated in [7,8].

Problem statement for computing flows around the EXPERT reentry flight vehicle
In order to perform a numerical simulation of the flow process, a three-dimensional surface model of the EXPERT reentry vehicle was developed (figures 1, 2).   The model was created using the SolidWorks CAD environment. The model is a complete equivalent of the vehicle and considers all its design features.

Computational mesh
In this paper, a three-dimensional flow field near the flight vehicle was simulated using unstructured tetrahedral meshes (figures 3-6).  Several options of the computational mesh were generated: excluding and including the shockwave feature of the flow structure (figures 4, 6). In the first case, the mesh was refined toward the vehicle head and toward the vehicle parts sensitive to the specific design features. The number of triangles on the surface was 98,454, and the total number of tetrahedrons in the volume was 1 024 290 cells (figures 3, 4). For an adaptive mesh, the refinement was carried out toward the head shock wave which position and structure depend on the incoming flow parameters [14]. The number of triangles on the surface was 65,210, and the total number of tetrahedrons in the volume was 5 383 515 cells (figures 5, 6).   Figure 7 shows the density distribution on the surface and in the vicinity of the vehicle flying at zero angle of attack at an altitude of 50 km with the speed V ∞ = 5 km/s. Figure 8 illustrates pressure distribution on the vehicle surface. The calculation was carried out using the UST3D and UG3D computer codes and the SolidWorks Flow Simulation module. Index "a" denotes the results calculated using the adaptive mesh             The difference between the results obtained and the data given in the paper is due to the fact that simulation of vehicle flights in dense atmosphere at high speeds requires the consideration of various physical and chemical processes in the air [6,14,15].

Conclusion
The paper demonstrates the necessity to refine the mesh on the head shock wave front and in the areas of high gradients. It leads to additional requirements for construction of geometry and computational mesh used in the calculation of aerothermodynamics of flight vehicles.
In the future, it is planned to develop an automated mesh adaptation.
The presented study was partially supported by Russian State Assignment under contract No. AAAA-A17-117021310372-6.