COSMO/GT is being developed from the foundation of ACERC's existing 3-D code, PCGC-3, to provide an advanced, 3-D combustor flow model with emphasis on gas turbines.
COSMO/GT is a comprehensive combustor flow model for turbulent, gaseous combustion in practical gas turbines. Effects of chemical kinetics, and chemistry/turbulence interactions are incorporated through a submodel for lean, premixed combustion of natural gas (LEPRECON). The fluid flowfield is solved in an Eulerian fashion on an unstructured, triangular mesh. LEPRECON provides the fluid mass density field to the flow model and the temperature field to the radiation submodel.
FLOW FIELD DISCRETIZATION
PCGC-3 employs a three-dimensional structured grid approach to solve the Navier-Stokes equations and the energy conservation equa-tions. The structured grid approach facilitates the use of direct addressing techniques in the algorithms used to compute con-vective, viscous and energy fluxes at cell interfaces, and, hence, the solution of the flow field itself. These techniques are relatively simple to program and are readily vectorizable. However, an inherent disadvantage of the structured grid approach is the resultant need for excessive spatial resolution of the flow field in low-gradient regions in order to adequately resolve the flow field in high-gradient regions. This disadvantage often re-sults in a compromise situation for the global resolution of the flow field, with the degree of the compromise dictated by available computer memory.
A remedy to this situation is attained through use of an unstruc-tured grid approach, whereby the flow field is discretized using three-dimensional tetrahedra. This approach permits adequate grid resolution in high-gradient regions of the flow field without the resultant need to simultaneously over-resolve low-gradient regions. The disadvan-tage of the unstructured approach is the need for indirect addressing in the solution algorithms, which necessarily leads to more complicated pro-gramming techniques and greater CPU time per grid point, when compared to the structured grid counterpart. It is the ability to adequately resolve the high-gradient regions of the flow field, while remaining within reasonable computer memory requirements, that makes the unstructured grid approach attractive for complex combustion calculations.
The three-dimensional, unstruc-tured-grid approach, currently being developed at ACERC, follows the Control Volume Finite Element Method (CVFEM) of Baliga and Patankar (1983). A variant of the Semi-Implicit Pressure Linked Equation (SIMPLE) technique is used to drive the iteration scheme, resulting in steady-state solutions. A skewed, mass-weighted upwind inter-polation function is used for the convective discretization, while linear interpolation functions are used for the diffusion, pressure gradient and source term discretization.
GAS FLUID DYNAMICS
The gas flowfield is assumed to be three-dimensional, mildly compress-ible, turbulent, reacting or nonreac-ting, and Newtonian. COSMO/GT calculates this flowfield within an Eulerian framework using a triangular, control volume finite-element form-ulation of the Navier-Stokes equations coupled with the energy conservation equation.
To account for turbulent transport, the Reynolds stresses that result from the time-averaged form of the momentum equations are approx-imated in COSMO/GT using the Boussinesq hypothesis. Effective or "eddy" fluid properties are used to relate the Reynolds stresses to the time-averaged flow-field. Effective properties are calculated using the standard k-e model.
GAS PHASE REACTIONS
Two options are available. The standard option includes finite-rate chemical kinetics and uses the Monte Carlo velocity-scalar PDF approach incorporated in the submodel LEPRECON described separately. This option can treat both premixed and non-premixed systems. The other option assumes that the gaseous reactions are limited by mixing rates for the major species and not generally by the reaction kinetics. In other words, the reaction kinetics are assumed to be infinitely fast compared with the mixing time for fuel and oxidizer. With this assumption, the local, instan-taneous gas properties can be calculated from equilibrium. Only non-premixed systems can be treated with this option.
MIXING AND GAS PROPERTIES
The extent of turbulent mixing between inlet gas streams (for non-premixed systems) as they proceed through the reactor is described in COSMO/GT using a conservative scalar variable called the mixture fraction, which is the local ratio of mass from the primary inlet flow stream to the total mass flow from both the primary and secondary gas flow inlet streams. For the equilibrium-based option, all other conserved scalars can be calculated from the local value of the mixture fraction. The fluctuating nature of the mixture fraction is modeled, in this case, using an assumed-shape PDF. A clipped Gaussian distribution is assumed. When finite-rate chemical kinetics are included, additional scalars are needed to describe the extent of reaction. Fluid properties are modeled by a Lagrangian approach, with a statistical number of discrete fluid "particles" distributed throughout the flow domain (Pope, 1985; Correa and Pope, 1992). Turbulent mixing is modeled by either the modified Curl's model or by the interaction-by-exchange-with-the-mean (IEM) model. The joint PDF of velocity, mixture fraction, and the reaction scalars is represented by the array of particle properties within a computational cell.
In addition to convective and conductive heat transfer between gas and reactor walls, as part of the energy equation solution, COSMO/GT includes a discrete ordinates radiative heat transfer submodel. Calculations are based on an energy balance on a beam of radiation passing through a volume element containing an absorbing-emitting medium. Spectral variation of radiative properties is also considered, which provides significant improvement in the radiative heat transfer calculations for systems dominated by gaseous radiation.
COSMO/GT is being applied to several practical geometries for premixers and combustors for lean, premixed combustion (LPC) in gas turbines supplied by Westinghouse Electric Corporation.
COSMO/GT is a stand-alone computer code that represents the state-of-the art in multi-dimensional, combustion-flow modeling. Its use is recommended for those technical specialists with expertise in comprehensive combustion code modeling.
PRE- AND POST-PROCESSING
While COSMO/GT is a stand-alone computer program, the complexnature of 3-D turbulent reactive flowfields requires adequate pre- and post-processing capabilities to prepare input data and to review the computational results. Such tools are being developed for ACERC computer codes using sophisticated graphical interfaces in a workstation environ-ment. These tools require X-window graphics capabilities.
Every effort is being made to maintain ANSI FORTRAN 77 coding standards in the development of COSMO/GT. As such, the code will be portable to several different platforms.
AVAILABILITY AND USER SUPPORT
General release of 97-COSMO/GT is planned for about December 1997 or early 1998.
In addition to source code (the velocity-scalar PDF submodel will be distributed in a single object module), a user's manual explaining code theory and use will also be available. Training workshops will also be conducted.
For more information about code availability and licensing fees, contact:
Dr. Andrew M. Eaton
ACERC Software Specialist
Brigham Young University
Provo, Utah 84602
Fax: (801) 378-3831
ACCOMPLISHMENTS AND FUTURE DEVELOPMENTS
A working version of COSMO/GT for non-reacting flow has been developed, based on the structured code, PCGC-3, and is being tested. The lean, premixed combustion submodel (LEPRECON) is being developed as described in a separate
document. The chemistry and PDF submodels will be implemented in COSMO/GT which will then be applied to practical, gas turbine combustors.
This work is being sponsored by the Advanced Combustion Engineering Research Center. Funds for the Center are received from the National Science Foundation, the State of Utah, 39 other industrial par-ticipants and the U.S. Department of Energy (DOE). Funds for the devel-opment of the velocity-scalar PDF submodel and the application of the code to gas turbine combustors are being provided by DOE.