# 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

 p pu pv pu pv f ns ___ pu2 + p puv nns ___ , П puv 2 pv2 + p e (e + p) u ( e + p) v

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

 py 1 puy1 pvy1 py2 , fsp = puy2 ,nsp = pvy2 _ pyN _ puyN pvyN
 qsp

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