The Department of Applied Mathematics of the Faculty of Computer Sciences of MSFU was founded by the famous USSR Academic S. P. Korolev – who was the main person in the design of space rockets in the USSR. He founded a Mathematics department in Forest University even if this Department didn’t connect with the main activity of the Forest University but it was nearby the main space industry companies of Korolev, so he opened this department to have young specialists studying nearby these space companies. This Department and Faculty moved and is now part of Bauman Moscow State University.
Professor Malashin successfully uses NUMECA’s academic membership program for education at the Bauman Moscow State Technical University (MSTU), Russia. The students learn about fluid dynamics, but also get to understand the challenges of numerical methods. Prof. Malashin along with his colleagues Galaktionov A.Y. and Pimenov A.S. have also prepared a detailed handbook for the students attending their classes. With the aid of this handbook and guidance from the instructors the students perform a wide variety of simulations ranging from indoor simulations on the distribution of temperature in residential buildings, to calculating supersonic flow over aircrafts. The course not only emphasises physical phenomena, such as shock capturing and coefficients of lift and drag, but also appreciates numerically relevant features such as the assessment of the grid quality, the y+ value at the wall and the CFL number.
This blog series will show example cases from the handbook as well as student research examples.
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COMMERCIAL SPACE TOURIST VEHICLE
In a laboratory work of 90 minutes, students simulate the supersonic flow around a space tourism vehicle as provided in parasolid format. The used software is FINE™/Open with OpenLabs™.
Objective: Obtaining the aerodynamic characteristics of an aircraft type model to obtain a flow pattern and the Cx, Cy, Cz force coefficients. Calculations are carried out at the angle of attack 0 and the speed of the oncoming stream is 1325.84 m/s. Students learn how to make the analysis and work with the final calculation data file.
In HEXPRESS™ first a box is created to define the external boundaries of the domain. Substracting the vehicle body from the box provides the students with a closed volume defining the area of simulation. By merging of faces and (unnecessary) edges the geometry is further simplified. A full hexahedral mesh is created with viscous layers with a y+ of approximately 2 at the walls.
Figure 1: Full hexahedral mesh created in HEXPRESS™ around the space tourist vehicle.
In the FINE™/Open GUI the flow solver input is specified like:
- the fluid type: air,
- the turbulence model: k-ε extended wall function,
- boundary conditions:
- at the inlet face upstream of the vehicle the Mach number and velocity angle are imposed,
- at the outlet face on the right a supersonic outlet boundary condition is imposed,
- and on the top and bottom face on the contrary a subsonic boundary condition is imposed. If these faces are sufficiently far away from the vehicle this is justified as there is only negligible flow going through,
- a CFL number of 1 *,
- use first order initialization for the first 300 iterations in the coarse grid initialization (the advanced parameter hypInit is set to 1 and hyplnitltMax_ is set to 300), **
- implicit residual smoothing can be used for added stability and speed up of the convergence.
* If the simulation does not run with a CFL number of 1, it is not recommended to lower it even further. In such case it is rather appropriate to look at what could be wrong with the grid or the other project parameters like the ones listed above.
** If it happens that the task does not start with the second-order scheme and central scheme, especially at high Mach numbers (4 and higher), use a method that is first considered to be a first-order scheme, but only to start the calculation process, and then restart with a second-order scheme.
Variation of the mesh refinement, y+ at the wall, the turbulence model, the location of the outer boundaries and the CFL number allows students to get an experience on the impact of such parameters in a CFD simulation.