The paper presents a computer code for steady and unsteady, three-dimensional, compressible, turbulent, viscous flow simulations. The mathematical model is based on the Favre-averaged Navier-Stokes conservation equations, closed by a statistical model of turbulence. Turbulence effects are represented by using a low Reynolds number K-ω model. The numerical model makes use of a finite difference approximation in generalized coordinates for space discretization. The solution of time-dependent, three-dimensional, non-homogeneous, partial differential equations is obtained by solving, in a prescribed, symmetric pattern, three time-dependent, one-dimensional, homogeneous partial differential equations, representing convection and diffusion along each generalized coordinate direction, and one ordinary differential equation, representing generation and destruction. An explicit, multi-step, dissipative, Runge-Kutta scheme is finally adopted for time discretization.
The code is applied to simulate the flow through a linear cascade of turbine rotor blades, where detailed experimental data are available. Blade aerodynamic and heat transfer are computed, at variable Reynolds and Mach numbers and turbulence levels, and compared with experimental data. While the aerodynamic prediction is relatively unaffected by the properties of both mathematical and numerical models, the heat transfer prediction proves to be extremely sensitive to models details. Low Reynolds number K-ω turbulence models theoretically reproduce laminar, turbulent and transitional boundary layers. However, their practical use in a Navier-Stokes code does not allow to entirely capture the effects of turbulence intensity and Mach and Reynolds numbers on blade heat transfer.
Wavelet methods for solving three-dimensional partial differential equations