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Extra resources for Finite volume method : powerful means of engineering design
The standard cell centred finite volume method has been applied with Roe’s approximated Riemann solver, MUSCL approach and Mulder limiter, which are described in Chapter 2. 2. 1 Airfoil optimization for maximal lift force by means of inviscid inverse design method3 It has been pointed out in the introduction of the Chapter 4. that the inverse design methods require optimal pressure or velocity distributions to determine the adherent geometry. In order to maximise the lift force of the suction side of a profile at given and constant operational (boundary) conditions, the pressure distribution should be minimized.
The normal velocity distribution across the solid wall becomes near to zero at the last inverse subroutine, which represents that there is no need for any further steps, the pressure gradient is infinitesimally small (no flow) across the solid boundary. The corresponding results of the optimization procedure are found in Fig. 14. The target and optimized (result) pressure distribution are compared with each other and the deviation between them is negligible. The optimized geometry with Mach number and pressure distribution is shown in Fig.
14. Pressure distribution of the initial (init), optimum (target) and result (of the inverse design based optimization procedure) cases (ps: pressure side and ss: suction side) The modified distributions have been imposed in the inverse design procedure to determine the geometry, which provides the optimal conditions. The inverse design method was converged after 10 iteration cycles of the inverse, wall modification and direct modes. The normal velocity distribution across the solid wall becomes near to zero at the last inverse subroutine, which represents that there is no need for any further steps, the pressure gradient is infinitesimally small (no flow) across the solid boundary.