SESSION 4
TRANSIENT RADIATION PROBLEM AND RADIATION/TURBULENCE INTERACTIONS
TWO-FLUX AND GREEN'S FUNCTION METHOD FOR TRANSIENT
RADIATIVE TRANSFER IN A SEMITRANSPARENT LAYER
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.
TRANSIENT RADIATIVE TRANSFER
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.
NUMERICAL INVESTIGATION OF RADIATION AND TURBULENCE
INTERACTIONS IN SUPERSONICALLY EXPANDING HYDROGEN-AIR JET
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.
RADIATION-TURBULENCE INTERACTION IN FLAMES USING ADDITIVE
TURBULENT DECOMPOSITION
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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