Oleg M. Alifanov

Mathematical and experimental simulation in aerospace system verification

Abstract The paper deals with a consideration of system methodology in mathematical modelling and experimental studies of physical processes and with engineering systems in design and verification of space and aerospace vehicles. The author proceeds from the assumption that the mathematical modelling significance will grow steadily in designing and testing of space/aerospace vehicles. At the same time, the experiments and tests will always present a basis to validate the mathematical models and methods being used for their adequacy and verify the design decision correctness. This taking place, it is very important to establish a correct correspondence between mathematical modelling and experimental testing as well as to improve their effectiveness. Herein are the following main problems: firstly, the development of a unified approach both for mathematical model identification and for technical system diagnostics which is essential in the process of design and testing; secondly, the construction of a hierarchical set of interconnected mathematical models and methods to use them adequately at different stages of research and development while designing and verifying a new flight vehicle; thirdly, the derivation of a valid procedure for experiments and tests performing and experimental data processing in order to increase the amount of valuable experimental information and, accordingly, reduce the cost. The extensive studies of these problems conducted for many years in the Moscow Aviation Institute (MAI) showed that they can be efficiently solved with the help of a new class of methods based on the solving of inverse problems coupled with the optimum experimental design. The present paper gives a short description of a general methodology for identification and diagnostics of physical processes and engineering systems as well as for construction of adequate enough mathematical models or methods and further application in the system verification. A combination of mathematical modelling and testing is considered as an example of implementation of this methodology applicable to a verification of the thermal protection system of Buran orbiter.

Identification of thermal properties of materials with applications for spacecraft structures

This paper presents the results of computational and experimental studies of particular thermal processes in composite materials. The considered approach is based on the mathematical theory of ill-posed problems of mathematical physics. In the majority of cases this methodology is used for optimization, but in a number of practical situations it is the sole technique available, as, for example, in measuring the transient heat fluxes and heat transfer coefficients. Owing to the structural version and homogeneous surface heating in specimens a one-dimensional heat transfer process is realized. A complex of thermal properties of the composite material (thermal conductivity λ(T) and heat capacity coefficient C(T)) is estimated. The initial data for such problems are formed grounded on the results of measurements and include the boundary conditions and temperature–time values in several internal points of specimens. The type of boundary conditions and the number of points of temperature measurement should meet the conditions of uniqueness of the inverse problem solution under analysis.

Analysis of Statements and Solution Methods for Inverse Heat Transfer Problems

The effective application of methods based on solving the inverse problems in thermal simulation and in processing the results of thermal tests is determined by the depth of the mathematics required connected with the statement and algorithmic presentation of the problems, by clarifying the specific difficulties in their solution. Misunderstanding of the nature of problems that are poorly based can lead to errors in problem solving. Even in cases when a proper method is used its effective application and specific features of the problem may not be fully realized. Such negligence of the formulation of problems of a given class as well as the methods of their solving can lead to doubt as to the suitability of the very concept of inverse problems for practical research. Experience shows that it is only through understanding the physical, technical and mathematical principles of a given problem that one finds it possible to use inverse problem methods effectively and creatively in thermal research.

Iterative Regularization of Inverse Problems

The algorithms constructed in Chaps. 4–7 are used for the solution of boundary IHCPs. Lately, the area of practical applications of methodology, based on inverse heat-transfer problems, has expanded considerably, which necessitated solving other types of inverse problems as well. As conducted investigations show, iterative regularization (Chap. 6) appears to be one of the most efficient and universal approaches for the construction of stable algorithms for solving ill-posed problems. With this method algorithms convenient for practical utilization can be obtained for the solution of inverse heat-transfer problems in various formulations (linear and non-linear, one-dimensional and multi-dimensional), in domains with fixed and travelling boundaries, with minimal necessary composition of initial data and overdefinition. Also, the rigorous mathematical proof of this method for a wide class of inverse problems and modernizations of iterative algorithm to account for qualitative and quantitative a priori information about an unknown solution are found.

IDENTIFICATION OF MATHEMATICAL MODEL OF MULTILAYER THERMAL INSULATION

The purpose of this paper is to introduce an iterative regularization method in the research of radiative and thermal properties of materials with further applications in the design of Thermal Control Systems (TCS) of spacecrafts. In this paper the radiative and thermal properties (heat capacity, emissivity and thermal conductance) of a multilayered thermal-insulating blanket (MLI), which is a screen-vacuum thermal insulation as a part of the (TCS) for perspective spacecrafts, are estimated. Properties of the materials under study are determined in the result of temperature and heat flux measurement data processing based on the solution of the Inverse Heat Transfer Problem (IHTP) technique. Given are physical and mathematical models of heat transfer processes in a specimen of the multilayered thermal-insulating blanket located in the experimental facility. A mathematical formulation of the IHTP, based on sensitivity function approach, is presented too. The practical testing was performed for specimen of the real MLI. This paper consists of recent researches, which developed the approach suggested at [1].

Inverse problems in identification and modeling of thermal processes: Russian contributions

Purpose The main purpose of this study, reflecting mainly the content of the authors’ plenary lecture, is to make a brief overview of several approaches developed by the author and his colleagues to the solution to ill-posed inverse heat transfer problems (IHTPs) with their possible extension to a wider class of inverse problems of mathematical physics and, most importantly, to show the wide possibilities of this methodology by examples of aerospace applications. In this regard, this study can be seen as a continuation of those applications that were discussed in the lecture. Design/methodology/approach The application of the inverse method was pre-tested with experimental investigations on a special test equipment in laboratory conditions. In these studies, the author used the solution to the nonlinear inverse problem in the conjugate (conductive and convective) statement. The corresponding iterative algorithm has been developed and tested by a numerical and experimental way. Findings It can be stated that the theory and methodology of solving IHTPs combined with experimental simulation of thermal conditions is an effective tool for various fundamental and applied research and development in the field of heat and mass transfer. Originality/value With the help of the developed methods of inverse problems, the investigation was conducted for a porous cooling with a gaseous coolant for heat protection of the re-entry vehicle in the natural environment of hypersonic flight. Moreover, the analysis showed that the inverse methods can make a useful contribution to the study of heat transfer at the surface of a solid body under the influence of the hypersonic heterogeneous (dusty) gas stream and in many other aerospace applications.

Radiative-conductive inverse problem for lumped parameter systems

The purpose of this paper is to introduce a iterative regularization method in the research of radiative and thermal properties of materials with applications in the design of Thermal Control Systems (TCS) of spacecrafts. In this paper the radiative and thermal properties (emissivity and thermal conductance) of a multilayered thermal-insulating blanket (MLI), which is a screen-vacuum thermal insulation as a part of the (TCS) for perspective spacecrafts, are estimated. Properties of the materials under study are determined in the result of temperature and heat flux measurement data processing based on the solution of the Inverse Heat Transfer Problem (IHTP) technique. Given are physical and mathematical models of heat transfer processes in a specimen of the multilayered thermal-insulating blanket located in the experimental facility. A mathematical formulation of the inverse heat conduction problem is presented too. The practical testing were performed for specimen of the real MLI.

The Extremal Formulations and Methods of Solving Inverse Heat Conduction Problems

One of the more promising directions in solving inverse heat conduction problems is to reduce them to extremal formulations and apply numerical methods of the optimization theory. Two cases are thereby possible: 1. a solution is scragftt-iirthe~~space of parameters; 2. the task is solved in the functional space.

Statements and Use of Inverse Problems in Studying Heat Transfer Processes and Designing Engineering Units

Many structures employed in various branches of engineering operate under conditions of strong, often extreme, thermal effects. The general tendency has been the extensive use of heat-loaded engineering objects and the high intensity of heat regimes. At the same time it has been necessary to increase the reliability and service life of goods, whilst reducing the specific consumption of materials. Investigating the processes of heat transfer and providing acceptable heat conditions also occupy an important place in the design and development of production methods related to the heating and cooling of materials as, for example, in continuous steel casting or the different techniques of metal thermal treatment, in glassmaking, foundry work, high-temperature crystal growing out of melt, etc. The non-stationary state and non-linearity (considerable, at times) of heat transfer phenomena can be referred to as the special features of heat conditions of modern heat-loaded structures and production methods. These considerably reduce the possibility of using many traditional design-and-theoretical and experimental methods. So it became necessary to develop new approaches to thermophysical and heat engineering studies. Amongst them are methods based on a solution of inverse problems, in which it is required, by measurements of the system or process state, to specify one or several characteristics causing this state (in other words, to find not causal-sequential, as in direct problems, but rather sequential-causal quantitative relations).

Parametric identification of a mathematical model of heat transfer in carbon–carbon (C–C) materials for aeronautical application

This paper is devoted to the development of heat transfer models that are adequate to the real processes by using the experimental and computational methodology based on the theory of inverse heat transfer problems.