Physical Model

The flow and combustion through a multi-row turbine-burner with arbitrary blade counts is modeled by the Reynolds-averaged Navier-Stokes equations and the species conservation equations. To reduce the computational time, the flow and combustion are modeled as quasi-three-dimensional. This section will present the details of the governing equations and the chemistry model.

Governing Equations

The unsteady, compressible flow through the turbine-combustor is modeled by the Reynolds-averaged Navier-Stokes equations. The ft>w is assumed to be fully turbulent and the kinematic viscosity is computed using Sutherland’s law. The Reynolds-averaged Navier-Stokes equations and species conserva­
tion equations are simplified by using the thin-layer assumption [Isvoranu and Cizmas, 2002].

In the hypothesis of unity Lewis number, both the Reynolds-averaged Navier – Stokes and species equations can be written as [Balakrishnan, 1987]:

dQ dF_ dG Vt^Mqq dS

дт dij Reoo dij ch

Note that equation (1) is written in the body-fitted curvilinear coordinate sys­tem (f, n, t ).

The state and flix vectors of the Reynolds-averaged Navier-Stokes equa­tions in the Cartesian coordinates are

The state and flix vectors of the species conservation equations in the Cartesian coordinates are

Further details on the description of the viscous terms and chemical source terms are presented in [Cizmas et al., 2003].