An Upwind Solver for the National Combustion Code

An upwind solver is presented for the unstructured grid National Combustion Code (NCC). The compressible Navier-Stokes equations with time-derivative preconditioning and preconditioned flux-difference splitting of the inviscid terms are used. First order derivatives are computed on cell faces and used to evaluate the shear stresses and heat fluxes. A new flux limiter uses these same first order derivatives in the evaluation of left and right states used in the flux-difference splitting. The k-epsilon turbulence equations are solved with the same second-order method. The new solver has been installed in a recent version of NCC and the resulting code has been tested successfully in 2D on two laminar cases with known solutions and one turbulent case with experimental data

Chemical reacting flows

Future aerospace propulsion concepts involve the combination of liquid or gaseous fuels in a highly turbulent internal air stream. Accurate predictive computer codes which can simulate the fluid mechanics, chemistry, and turbulence combustion interaction of these chemical reacting flows will be a new tool that is needed in the design of these future propulsion concepts. Experimental and code development research is being performed at Lewis to better understand chemical reacting flows with the long term goal of establishing these reliable computer codes. The approach to understanding chemical reacting flows is to look at separate simple parts of this complex phenomena as well as to study the full turbulent reacting flow process. As a result research on the fluid mechanics associated with chemical reacting flows was initiated. The chemistry of fuel-air combustion is also being studied. Finally, the phenomena of turbulence-combustion interaction is being investigated. This presentation will highlight research, both experimental and analytical, in each of these three major areas

A Radiation Solver for the National Combustion Code

A methodology is given that converts an existing finite volume radiative transfer method that requires input of local absorption coefficients to one that can treat a mixture of combustion gases and compute the coefficients on the fly from the local mixture properties. The Full-spectrum k-distribution method is used to transform the radiative transfer equation (RTE) to an alternate wave number variable, g . The coefficients in the transformed equation are calculated at discrete temperatures and participating species mole fractions that span the values of the problem for each value of g. These results are stored in a table and interpolation is used to find the coefficients at every cell in the field. Finally, the transformed RTE is solved for each g and Gaussian quadrature is used to find the radiant heat flux throughout the field. The present implementation is in an existing cartesian/cylindrical grid radiative transfer code and the local mixture properties are given by a solution of the National Combustion Code (NCC) on the same grid. Based on this work the intention is to apply this method to an existing unstructured grid radiation code which can then be coupled directly to NCC

Multigrid solution of the Navier-Stokes equations on highly stretched grids with defect correction

Relaxation-based multigrid solvers for the steady incompressible Navier-Stokes equations are examined to determine their computational speed and robustness. Four relaxation methods with a common discretization have been used as smoothers in a single tailored multigrid procedure. The equations are discretized on a staggered grid with first order upwind used for convection in the relaxation process on all grids and defect correction to second order central on the fine grid introduced once per multigrid cycle. A fixed W(1,1) cycle with full weighting of residuals is used in the FAS multigrid process. The resulting solvers have been applied to three 2D flow problems, over a range of Reynolds numbers, on both uniform and highly stretched grids. In all cases the L(sub 2) norm of the velocity changes is reduced to 10(exp -6) in a few 10's of fine grid sweeps. The results from this study are used to draw conclusions on the strengths and weaknesses of the individual relaxation schemes as well as those of the overall multigrid procedure when used as a solver on highly stretched grids

Navier-Stokes cascade analysis with a stiff Kappa-Epsilon turbulence solver

The two dimensional, compressible, thin layer Navier-Stokes equations with the Baldwin-Lomax turbulence model and the kinetic energy-energy dissipation (k-epsilon) model are solved numerically to simulate the flow through a cascade. The governing equations are solved for the entire flow domain, without the boundary layer assumptions. The stiffness of the k-epsilon equations is discussed. A semi-implicit, Runge-Kutta, time-marching scheme is developed to solve the k-epsilon equations. The impact of the k-epsilon solver on the explicit Runge-Kutta Navier-Stokes solver is discussed. Numerical solutions are presented for two dimensional turbulent flow over a flat plate and a double circular arc cascade and compared with experimental data

Turbomachinery

The discipline research in turbomachinery, which is directed toward building the tools needed to understand such a complex flow phenomenon, is based on the fact that flow in turbomachinery is fundamentally unsteady or time dependent. Success in building a reliable inventory of analytic and experimental tools will depend on how the time and time-averages are treated, as well as on who the space and space-averages are treated. The raw tools at disposal (both experimentally and computational) are truly powerful and their numbers are growing at a staggering pace. As a result of this power, a case can be made that a situation exists where information is outstripping understanding. The challenge is to develop a set of computational and experimental tools which genuinely increase understanding of the fluid flow and heat transfer in a turbomachine. Viewgraphs outline a philosophy based on working on a stairstep hierarchy of mathematical and experimental complexity to build a system of tools, which enable one to aggressively design the turbomachinery of the next century. Examples of the types of computational and experimental tools under current development at Lewis, with progress to date, are examined. The examples include work in both the time-resolved and time-averaged domains. Finally, an attempt is made to identify the proper place for Lewis in this continuum of research

Turbomachinery

The discipline research in turbomachinery, which is directed toward building the tools needed to understand such a complex flow phenomenon, is based on the fact that flow in turbomachinery is fundamentally unsteady or time dependent. Success in building a reliable inventory of analytic and experimental tools will depend on how we treat time and time-averages, as well as how we treat space and space-averages. The challenge is to develop a set of computational and experimental tools which genuinely increase our understanding of the fluid flow and heat transfer in a turbomachine. Examples of the types of computational and experimental tools under current development, with progress to date, are examined. The examples include work in both the time-resolved and time-averaged domains