Vortex Flows and Related Numerical Methods II
ESAIM: Proceedings,
Vol. 1, 1996, pp. 429-446
Numerical Simulation of Unsteady Combustion
Using the Transport Element Method
Marios C. Soteriou
Dept. of Mechanical Engineering
University of Connecticut
Storrs, CT 06269-3139, USA
Ahmed F. Ghoniem
Dept. of Mechanical Engineering
Massachusetts Institute of Technology
Cambridge, MA 02139, USA
Abstract
The transport element method is described and implemented in the
simulation of the non-premixed reacting shear layer. The method, a
natural extention of the vortex element method, resolves the low Mach
number variable density flow and the exothermic reacting field. The
effect of combustion on the flow is accommodated by incorporating a
volumetric expansion velocity component and by modifying the
integration of the vorticity equation to include expansion-related and
baroclinic terms. The reacting field equations describing a single
step, irreversible, chemical reaction, are simplified by the
introduction of Schvab-Zeldovich (SZ) conserved scalars whose
transport is sufficient to compute the evolution of combustion in the
case of infinite reaction rate. In the case of finite rate chemistry
the evolution of one primitive scalar, the product mass-fraction, is
also computed. The vorticity, conserved scalar gradient and product
mass fraction are discretized amongst fields of transport elements.
Their time evolution is implemented by advecting the elements at the
local velocity while simultaneously integrating their transport
equations along particle trajectories. The integration of the
vorticity and the conserved scalar gradient equations is simplified
using ideas from kinematics. A novel core expansion scheme that
avoids the problems associated with the conventional implementation is
used to simulate diffusion. Field quantities are obtained using
convolutions over the elements. Results indicate that the method is
able to accurately reproduce the essential features of the flow.
Convergence of the solution in time is approximately linear.
Moreover, the finite reaction rate solution at low Karlovitz number
bear strong similarities to that of the infinite reaction rate model.
This similarity is exploited in validating the part of the numerical
methodology related to the integration of the product mass-fraction
equation.
Vortex Flows and Related
Numerical Methods II
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