SESSION 7
INVERSE RADIATION PROBLEMS
Chairman: Y. Bayazitoglu
INVERSE DESIGN OF ENGINEERING SYSTEMS DOMINATED BY RADIATIVE TRANSFER
Francis FRANÇA*, Juan C. MORALES*; Masahito OGUMA**, and John R. HOWELL* * Department of Mechanical Engineering The University of Texas, Austin Texas, USA ** Research Institute IHI, Inc., Yokohama, Japan
Abstract Inverse radiative design techniques can eliminate much of the trial and error used in
conventional or "forward" thermal design. Accurate determination of initial design
parameters by inverse analysis can provide the necessary starting point for a detailed design
using conventional detailed programs. If successful, this will free designers to determine
with more accuracy the best design that will meet their requirements, and will not require
limitation to the few cases that can normally be examined using conventional techniques.
Here, we discuss some of the mathematical techniques for inverse design (Monte Carlo,
singular value decomposition (SVD), modified truucated singular value decomposition
(MTSVD), and conjugate gradient), their relative strengths and weaknesses, show results
generated by some of these techniques for some example problems, and we also indicate
some remaining challenges and opportunities for inverse design.
RADIATIVE PROPERTIES IDENTIFICATION BASED ON INVERSE PROBLEMS TECHNIQUES
Oleg.M.ALIFANOV *, Aleksey.V.NENAROKOMOV ** * Dean of Aerospace College ** Professor of Mechanical Engineering Department of Space System Engineering Moscow State Aviation Institute 4 Volokolamskoe Shosse Moscow,125871, Russia
ABSTRACT. The present paper considers the extreme method for solving an inverse problem.
Due to mathematical illposedness of this problem the question of choosing a method for
constructing a minimized sequence of approximations and that for sampling a required solution
from it is critical. It is shown that for this purpose we can successfully use the specifically
developed algorithms based on the conjugate gradient methods. Stopping of the corresponding
iterative processes, providing stability of the problem solving, should be perfomed by
means of appropriate matching of the criterion functional value and the total measurement
error. The accuracy of the solution of inverse problems obtained by the suggested algorithms
is discussed. Evaluation of the technique suggested has been made in determining the integral
emissivity factor e and the absorbtion coefñcient A_{s} of the spacecraft surface. The results
obtained directly in orbit conditions are discussed.
ESTIMATION OF ABSORPTION COEFFICIENT DISTRIBUTION IN TWODIMENSIONAL GAS VOLUME BY SOLVING INVERSE RADIATIVE PROPERTY VALUE PROBLEM
Kazuhiko Kudo*, Akiyoshi Kuroda*, Eiji Ozaki* and Masahito Oguma** *Division of Mechanical Science, Graduate School of Engineering, Hokkaido University **Research Laboratory, IshikawajimaHarima Heavy Industiy
A method to solve inverse radiative property value problems is proposed to obtain twodimensional
distribution of absorption coefficient in a system where the profiles of the temperature and the heat flux
of the surrounding walls and of the gas temperature are given.
Figure 1 shows the analytical system. The shaded elements in the gas volume are simulated flame region.
The absorption coefficient in the shaded and nonshaded area of the gas volume are assumed to be 0.5 m^{1}
and O.l m^{1} respectively. There is heat generation in the gas volume only in the shaded area at a rate of
0.1x10^{6} W/m^{3}. Wall emissivity is unity.
Equation (1) is the energy equations for a wall element wi.
(1)
In which, the variables Rd(a~b) represents the ratio of the radiative energy absorbed by an element b to
the radiative energy emitted from an element a, and is called as READ (Radiative Energy Absorption
Distribution) value.
The inverse analysis is carried out by repeatedly solving the forward problem. The procedure is as
follows. At first, initial values of the absorption coefficient of each gas element is assumed. Then the
READ values corresponding to the given set of absorption coefficients are calculated using the Monte
Carlo method. And the wall heat flux Q_{w} for each wall element is calculated from eq. (1). The
calculation is repeated by optimizing the values of the absorption coefficients until the calculated wall
heat flux coincides with the one given as input. To avoid multiple Monte Carlo calculations, in the
present study, a new method is developed to calculate the READ values without using the Monte Carlo
calculation even when the absorption coefficients are changed. This method is called "fast READ
algorithm" hereafter.
The fast READ algorithm utilizes a concept that the READ value can be separated into two parts. One
depends on the values of the gas absorption coefficient and the other depends only on the geometrical
configuration of each element. The calculation of the latter part is carried out by the Monte Carlo
method. As it is independent of the absorption coefficient, the calculation of this part can be done outside
the optimization loop, which reduces the total computation time.
The validity of the present method is studied for the estimated flame shapes shown in Table 1. In each
case, the distribution of the gas absorption coefficient is given as follows. In the gas elements which is
assumed to be flame, the element numbers of which are shown in Table 1, the absorption coefficients
are uniform and the value is changed as a calculational parameter. In other gas elements, the value of
the absorption coefficient is set to O.l m^{1}, the actual value. In the case 2 in Table 1, the shape of the
flame is the same as the actual one shown in Fig.1, and other cases assume different flame shapes from
the original one.
Figure 2 shows the average error of the calculated wallheat flux corresponding to the system with the
flame absorption coefficient shown on abscissa and with the flame shape defined for each case in Table
1. The resulted curve of the average error for the case 2, which has the same flame shape as the actual
one, has its minimum at a flame absorption coefficient of k=O.5 m^{1}. The average error at the minimum
point of case 2 is also the minimum of the ones in all cases. This means that, the average error of the wall
heat flux for the estimated distribution of the absorption coefficient has the minimum value when the
distribution is the same as the actual one shown in Fig.1. So, by changing the value of the absorption
coefflcient in each gas element so as to reduce the value of the average error of the wall heat flux using
appropriate optimization methods, the values of the absorption coefficient are shown to converge to the
actual values.
Figure 1. The analytical system
Figure 2. Effect of the shape and the absorption coefficient of the flame region on the error of wall heat flux
case 
gas element numbers assigned to flame region 
2 
47, 1417, 2427, 3437 
3 
36, 1316, 2326, 3336 
4 
58, 1518, 2528, 3538 
5 
5, 6, 15, 16 
6 
38, 1318, 2328, 3338, 434 
Table 1. Analytical Conditions
TEMPERATURE AND SPECIES CONCENTRATION PROFILES USING HIGH RESOLUTION INFRARED TRANSMISSION DATA BY INVERSE RADIATIVE ANALYSIS
Farchid YOUSEFIAN and Michel LALLEMAND Laboratoire d'Etudes Thermiques, (U.M.R 6608 C.N.R.S) Ecole Nationale Supérieure de Mécanique et Aérotechnique 86960 Poitiers, Futuroscope Cedex, France
ABSTRACT. The presented paper deals with the restitution of temperature and species
concentration profiles in a flame from high resolution infrared synthetic data by means of inverse
radiative methods. The inverse problem is performed in a onedimensional axisymmetric geometry
for transmission or emission data stemming from a given crosssection of the semitransparent
object. Applications are concerning pollutants of combustion gases (CO) in a premixed flame. In
transmission, the observation of two lines of a diatomic molecules belonging to the same lower and
same upper vibrational states is simulated and inversions are carried out from the ratio of high
resolution line intensity data. The microscopic expression of the absorption coefficient for
rovibrational lines in terms of local species and temperature distributions is developed. The
domain of validity of assumptions which renders possible the inversion of transmission data with
respect to line intensity is discussed.
This high resolution inverse technique proceeds by a generalized Abel transform developed by
Simmoneau et al. The recovered results are compared with those obtained from ordinary Abel
inversion and the conjugated gradient technique.
