Throughflow model for design and analysis integrated in a three-dimensional Navier-Stokes solver

Abstract

A multiblock multigrid Navier-Stokes solver has been extended to include a throughflow model for the design and analysis of turbomachines. The presence of the blades in the inviscid axisymmetric flow is modelled in the classical way through a distributed blade force to produce the desired turning, a blockage factor that accounts for the reduced area due to blade thickness, and a distributed frictional force representing the entropy increase due to viscous stresses and heat conduction. The exact blade geometry is not required. All features of the three-dimensional code concerning the physical fluid model, boundary conditions, spatial and time discretization, convergence acceleration techniques and data visualization are available to the throughflow module. This includes the capability to treat the entire range of relevant Mach numbers, from strictly incompressible (through a preconditioning technique) to supersonic, as well as any number of blade rows in any configuration, including, for example, bypass engines. Selected elements comprising the throughflow model are discussed, with special emphasis on the blade force and its discretization. The properties of analysis and design mode with respect to shocks and the associated losses are investigated. The methodology is demonstrated on a transonic compressor rotor and a four-stage low-speed turbine.

A time-marching throughflow model and its application in transonic axial compressor

“…A shock is captured near the trailing edge in the tip region and the shock extends about 30% of the span. Acceleration of the flow is found upstream of the captured shock which is also observed in [13].…”

Advances in Aerodynamic Design of Gas Turbines Compressors

“…These methods have recently been made more realistic by taking account of end-wall effects and spanwise mixing by four aerodynamic mechanisms: turbulent diffusion, turbulent convection by secondary flows, spanwise migration of airfoil boundary layer fluid and spanwise convection of fluid in blade wakes (Dunham, 1997). Other remarkable results consist in incorporating a throughflow code into a Navier-Stokes solver for shortening the calculation phase (Sturmayr & Hirsch, 1999). As a result of the application of throughflow codes, the compressor map in both design and off design operation can be obtained exhibiting high accuracy.…”

On the Three-Dimensional Body Force Model

“…The early-stage throughflow used simplified radialequilibrium analysis in the 1940s (Smith, 1966, Cumpsty, 1989. Later more sophisticated throughflow models based quasi-3D theory from Wu (1952), such as streamline curvature and body force models, have been widely used in various applications in turbomachinery in the past few decades (Casey and Robinson, 2010;Damle et al, 1997;Denton, 1978;Stow, 1985a, 1985b;Novak 1967;Spurr, 1980;Sturmayr and Hirsch, 1999), covering the areas of flow field predictions (Casey and Ronbinson, 2010;Novak 1967;Spurr,1980;Sturmayr and Hirsch, 1999), inverse designs (Damle et al, 1997;Jennions and Stow, 1985b), quasi-3D modeling (Denton, 1978;Stow, 1985a, 1985b) etc.…”