Abstract: In view of the flow field of jet elements had the complex shock wave and the vortex characteristic. One kind of strongly compact—weighted ENO scheme is used for solving this kind of complex flow field. This form is applied to the Reynolds averaged Navier—Stokes equations, its convection term uses the third and fourth order, turbulence model uses Realizable – model, which has calculated 7 kinds of operating conditions. Numerical results indicated that using this scheme may succeed in capturing to Coanda effect, namely if the total pressure under the limiting value, departure of flow will occur when there is no control flow. The circumfluence and the separation of boundary can be seen distinctly, and the high order accurate complex shock wave and the vortex can be caught from the calculating results. Moreover, the numerical results are in good agreement with the experimental ones, which demonstrates that this scheme has feasibility and validity. This is essential to guide the design of jet elements.

Key words: Jet control elements, N—S turbulent flow, Strongly compact scheme, Weighted ENO scheme, Cutting deflection, On-line control, On-line feedrate optimization, Open modular architecture CNC system