Robert Siegel
Lewis Research Academy
NASA Lewis Research Center, Cleveland, Ohio, U.S.A.

A method using a Green's function is developed for computing transient temperatures in a semitransparent layer by using the two-flux method coupled with the transient energy equation. Each boundary of the layer is exposed to a hot or cold radiative environment,and is heated or cooled by convection. The layer refractive index is larger than one, and the effect of internal reflections is included with the boundaries assumed diffuse. The analysis accounts for internal emission, absorption, heat conduction, and isotropic scattering. Spectrally dependent radiative properties are included, and transient results are given to illustrate two-band spectral behavior with optically thin and thick bands. Transient results using the present Green’s function method are verified for a gray layer by comparison with a finite difference solution of the exact radiative transfer equations; excellent agreement is obtained. The present method requires only moderate computing times and incorporates isotropic scattering without additional complexity. Typical temperature distributions are given to illustrate application of the method by examining the effect of strong radiative heating on one side of a layer with convective cooling on the other side, and the interaction of strong convective heating with radiative cooling from the layer interior.


Sunil Kumar and Kunal Mitra
Department of Mechanical Engineering, Polytechnic University
333 Jay Street, Brooklyn, NY 11201

This paper outlines the formulation of the transient transport of radiation through scattering absorbing media and discusses the need for developing methods for predicting and evaluating transient radiative transfer. As a first approximation the intensity field is modeled as a linear function of the cosine of the angle, and the coefficients of the linear function are functions of time and position. The mathematical form of the resultant radiative transport equations is of a hyperbolic form with a wave speed equal to 1/31/2 of the speed of light in the medium. The incident source travels at the speed of light. Applications where these results are important include the transport of femtosecond and picosecond laser pulses through absorbing and scattering medium such as in the imaging of tissues or probing the characteristics of particulate medium by examing the transmitted or back-scattered transients.


S.N. Tiwari, T.O. Mohieldin, R. Chandrasekhar
College of Engineering and Technology
Old Dominion University
Norfolk, VA 23529, U.S.A.

The axisymmetric Reynolds averaged Navier-Stokes equations have been used to investigate the mixing and reaction of a supersonic hydrogen jet in a co-flowing stream of vitiated air. The numerical method uses a finite volume approach and a quadratic upwind interpolation scheme. The equation system was closed using either the two-equation k- turbulence model or the Reynolds stress turbulence model. A four species, one reaction, global finite rate chemistry model is used to simulate the combustion processes. The influence of turbulence on the reaction rate is taken into account by considering finite rate burning based on the rate of decay of large turbulent eddies into small ones. The radiative heat transfer term in the energy equation is simulated using the Discrete Transfer Radiation Model (DTRM). Formulation of the equations of motion, turbulence, chemistry and radiation modeling is discussed.

Extensive parametric studies are conducted to investigate the effects of grid refinement, inlet turbulence intensity, and turbulence models on the prediction of the velocity, temperature and major species concentrations. It is found that there is no significant differences between the RSM and k-N model prediction of the degree of mixing and combustion. The extent of the mixing is reasonably well predicted by both models. However, some discrepancies between the two predictions and the experiment are indicated, specially along the centerline of the burner and farther downstream of the nozzle. Both models predict a small amount of reaction upstream of the lifted flame base due to mixing with hot vitiated air and combustion takes place farther downstream of the lifted region. This is consistent with the experimental finding in the open literature.


J.M. McDonough, D. Wang and M.P. Mengüç
Department of mechanical Engineering, University of Kentucky, Lexington, KY 40506-0046, U.S.A.

The purpose of this paper is to discuss the nature of the unsteady interactions between buoyant turbulence and radiation feedback to the center of flames. An unfiltered additive turbulent decomposition (ATD) is carried out in a manner similar to that originally developed by Mcdonough and co-workers for studying Burger’s equation. The new approach is philosophically similar to LES; namely, treat the large and small scales separately. However, the technique requires no formal filtering or averaging for the large-scale equations, and the corresponding subgrid-scale models are obtained as local spectral approximations of the original governing equations. In the present work, only the small-scale part of the governing equations has been solved, and the large-scale parameters are to be obtained directly from either a global computer program or from corresponding experimental results. Preliminarily calculated results show that the radiation in the flame markedly influences the flow in the center of flame, and even periodic radiation fluctuations can lead to chaotic behavior of the flow. The extent to which the flow fluctuates not only depends on fluctuation of radiative properties, but also on the profile of the mean absorption coefficient.

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