Reynolds-averaged Navier–Stokes (RANS) equations with blade blockage and blade force source terms are solved in the meridional plane of complete axial flow turbomachinery using a finite-volume scheme. The equations of the compressible actuator disk (AD) are introduced to modify the evaluation of the convective fluxes at the leading and trailing edges (LEs and TEs). An AD behaves as a compact blade force which instantaneously turns the flow with no production of unphysical entropy. This avoids unphysical incidence loss across the LE discontinuity and allows for application of all of the desired deviation at the TE. Unlike previous treatments, the model needs no handmade modification of the throughflow (TF) surface and does not discriminate between inviscid and viscous meridional flows, which allows for coping with strong incidence gradients through the annulus wall boundary layers and with secondary deviation. This paper derives a generalized blade force term that includes the contribution of the LE and TE ADs in the divergence form of the TF equations and leads to generalized definitions of blade load, blade thrust, shaft torque, and shaft power. In analyzing a linear flat plate cascade with an incidence of 32 deg and a deviation of 21 deg, the proposed model provided a 105 reduction of unphysical total pressure loss compared to the numerical solution with no modeling. The computed mass flow rate, blade load, and blade thrust showed excellent agreement with the theoretical values. The complete RANS TF solver was used to analyze a four-stage turbine in design and off-design conditions with a spanwise-averaged incidence of up to 2 deg and 43 deg, respectively. Compared to a traditional streamline curvature solution, the RANS solution with incidence and deviation modeling provided a 0.1 to 0.7% accurate prediction of mass flow rate, shaft power, total pressure ratio, and adiabatic efficiency in both the operating conditions. It also stressed satisfactory agreement concerning the spanwise distributions of flow angle and Mach number at LEs and TEs. In particular, secondary deviation was effectively predicted. The RANS solution with no modeling showed acceptable performance prediction only in design conditions and could introduce no deviation.
An Accretion Disk Model for the Innermost 200PC of the Galaxy
