Mathematical Physics - Volume II - Numerical Methods

4.3 Solution of Navier–Stokes equations

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Figure 4.19 shows the results of numerical analysis of stationary non-viscous and viscous flow around rectangular wing with airfoil NACA 65A010, constant along the span. An algebraic three-dimensional non-orthogonal “C-H” computational grid was used, while from the chapter 4.2.2 the convergence criterion is retained. The calculation was performed for Mach number of undisturbed flow M ∞ = 0 . 8 at zero wing angle of attack and Reynolds number Re ∞ = 50000 for laminar flow. In the case of turbulent flow Re ∞ = 1 . 2 × 10 7 . Very coarse grid (65 × 7 × 29) was used, and the results are given for cross section in the plane of wing symmetry. As can be seen from Figure 4.19, the flow separation occurs at the position of the greatest profile thickness, and with an increase of Reynolds number in turbulent flow, position of separation bubble moves towards the trailing edge of the airfoil. Unfortunately, the application of such a coarse grid does not allow qualitative determination of the pressure coefficient C p and position of the separation point. Fine mesh would increase the accuracy of the numerical solution, but at the same time it would make a demand for the more powerful computer systems. Exposed procedure in viscous flow analysis in transonic speed range made calculation of the aerodynamic load possible in cases of strong shock waves with boundary layer effects, when application of potential theory and Euler equations is practically impossible.