Chairman: Y. Bayazitoglu


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.


* 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 ill-posedness 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 As of the spacecraft surface. The results obtained directly in orbit conditions are discussed.


Kazuhiko Kudo*, Akiyoshi Kuroda*, Eiji Ozaki* and Masahito Oguma**
*Division of Mechanical Science, Graduate School of Engineering, Hokkaido University
**Research Laboratory, Ishikawajima-Harima Heavy Industiy

A method to solve inverse radiative property value problems is proposed to obtain two-dimensional 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 non-shaded 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 0.1x106 W/m3. Wall emissivity is unity.

Equation (1) is the energy equations for a wall element wi.


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 Qw 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 wall-heat 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


gas element numbers assigned to flame region


4-7, 14-17, 24-27, 34-37


3-6, 13-16, 23-26, 33-36


5-8, 15-18, 25-28, 35-38


5, 6, 15, 16


3-8, 13-18, 23-28, 33-38, 43-4

Table 1. Analytical Conditions


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 one-dimensional axisymmetric geometry for transmission or emission data stemming from a given cross-section of the semi-transparent 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 ro-vibrational 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.

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