Radiative interactions in multidimensional chemically reacting flows using Monte Carlo simulations
Abstract
The Monte Carlo method (MCM) is applied to analyze radiative heat transfer in nongray gases. The nongray model employed is based on the statistical narrow band model with an exponentialtailed inverse intensity distribution. The amount and transfer of the emitted radiative energy in a finite volume element within a medium are considered in an exact manner. The spectral correlation between transmittances of two different segments of the same path in a medium makes the statistical relationship different from the conventional relationship, which only provides the noncorrelated results for nongray methods is discussed. Validation of the Monte Carlo formulations is conducted by comparing results of this method of other solutions. In order to further establish the validity of the MCM, a relatively simple problem of radiative interactions in laminar parallel plate flows is considered. Onedimensional correlated Monte Carlo formulations are applied to investigate radiative heat transfer. The nongray Monte Carlo solutions are also obtained for the same problem and they also essentially match the available analytical solutions. the exact correlated and noncorrelated Monte Carlo formulations are very complicated for multidimensional systems. However, by introducing the assumption of an infinitesimal volume element, the approximate correlated and noncorrelated formulations are obtained which are much simpler than the exact formulations. Consideration of different problems and comparison of different solutions reveal that the approximate and exact correlated solutions agree very well, and so do the approximate and exact noncorrelated solutions. However, the two noncorrelated solutions have no physical meaning because they significantly differ from the correlated solutions. An accurate prediction of radiative heat transfer in any nongray and multidimensional system is possible by using the approximate correlated formulations. Radiative interactions are investigated in chemically reacting compressible flows of premixed hydrogen and air in an expanding nozzle. The governing equations are based on the fully elliptic NavierStokes equations. Chemical reaction mechanisms were described by a finite rate chemistry model. The correlated Monte Carlo method developed earlier was employed to simulate multidimensional radiative heat transfer. Results obtained demonstrate that radiative effects on the flowfield are minimal but radiative effects on the wall heat transfer are significant. Extensive parametric studies are conducted to investigate the effects of equivalence ratio, wall temperature, inlet flow temperature, and nozzle size on the radiative and conductive wall fluxes.
 Publication:

Final Report
 Pub Date:
 October 1994
 Bibcode:
 1994odu..rept.....L
 Keywords:

 Approximation;
 Computer Programs;
 Computerized Simulation;
 Elliptic Differential Equations;
 Finite Volume Method;
 Grid Generation (Mathematics);
 Monte Carlo Method;
 NavierStokes Equation;
 Nongray Gas;
 Radiative Heat Transfer;
 Reacting Flow;
 Spectral Correlation;
 Statistical Correlation;
 Boundary Conditions;
 Compressible Flow;
 Computational Fluid Dynamics;
 Gas Mixtures;
 Hydrogen;
 Laminar Flow;
 Mathematical Models;
 Nozzle Flow;
 Oxygen;
 Supersonic Flow;
 Temperature Effects;
 Two Dimensional Models;
 Fluid Mechanics and Heat Transfer