Domain-Independent Multi-Physical Multiple-Field Systems Modeling Approach: A Novel Energy-Based Aero-Thermo-Visco-Elastic Modeling Framework by Bond Graph

Author: Amir Zanj

Zanj, Amir, 2017 Domain-Independent Multi-Physical Multiple-Field Systems Modeling Approach: A Novel Energy-Based Aero-Thermo-Visco-Elastic Modeling Framework by Bond Graph, Flinders University, School of Computer Science, Engineering and Mathematics

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After passing through several decades of the emergence of aerothermoelastic problems, these problems are still conveniently considered by many modelers as an extension of aeroelastic problems. There is no doubt that by means of numerous useful methodologies proposed in the area of aeroelasticity, there now exist a range of sound strategies that potentially possess certain capabilities in solving a diverse range of problems arising in this area. However, it is evident from the literature that in situations where heating impacts become significant, the well-established framework of classical aeroelasticity would be unable to explain the true causality of the ongoing aerothermoelastic phenomena.

It is known that the classical fundamentals of aeroelasticity are based on assumptions (such as separation principle or weak connectivity) that largely ignore the thermal connections between the various physical fields of a system within which aerothermoelastic phenomena exist. Although the impact of neglecting the thermal connections could be added into the solution of each filed of the system, the real interactive nature of the thermal connections between the various fields (that could have significantly changed the dynamics of the system if considered), has been completely lost in this process. As a result, the true physical links between the various fields measured by the universal principle of conservation of power transactions are no longer held. Reinstalling these physical links will require a reconstruction of the fundamental assumptions upon which the aerothermoelastic phenomena of the system can be truthfully reflected.

Indeed, the classical decomposition of aerothermoelasticity into aeroelastic, aerothermo, and thermoelastic behaviors lacks a generic means with which the overall dynamics of the system can be effectively decomposed into components whose (i) energetic interactions can obey the universal conservation rules, (ii) are tractable, (iii) and can uncover the hidden details of the system’s physical insights. This is because the elements used to decompose the system in the classical approach stay at a level that is higher than the level expected for enabling the unveiling of the system dynamics in such detail. Currently, to compensate for this deficiency, modelers rely heavily on the use of mathematical constrains (such as filtration and stabilization) as well as powerful computers, which has led to the development of drastically high-order models valid only within a limited operational range. The desired elements that can reveal the hidden physical insights of such complex phenomena are evidently required to be at a level that can directly reflect the primary energetic interactions of the system and physically link the fundamentals of each of the fields involved.

In this thesis, an energy-based aerothermoelastic framework resulting from a unique decomposition of each of the involving fields of a system into a set of physical subdomains (e.g., thermal, kinetic, potential subdomains) is suggested. Given that the physical subdomains are alike in any fields, by generating their isomorphic models regardless of the field (i.e., domain-independent modeling), the conservation of continuous power transactions within each of the fields and between the fields at their interface can then become realizable. This novel strategy leads to a complete conservative coupling between all fields involved.

In this study, physical system theory in terms of Bond Graphs (BG) is employed to generate the proposed energy-based framework including domain-independent isomorphic components. The dynamics of the system are constructed from the reversible and irreversible dynamic interactions of the energetic components of the existing subdomains. Given that the energetic components are similar in different subdomains and that the interactions between the energetic components in different subdomains follow a similar pattern, the BG implementation can produce not only isomorphic models of counterpart physical subdomains between different fields, but also isomorphic models of all physical subdomains involved in the coupled fields. As a result, not only is the continuity of both the intra-field and inter-field power transportation satisfied, but also the possibility of tracking power transformation is provided. The conservation of power transactions of the entire system is thus guaranteed. The proposed methodology provides the ensuing framework with an intrinsically physical ability to control the data transactions between the coupled fields. The resulting conservative energetic framework of the system also allows modelers to check the well-posedness of the system before extracting state equations – a desirable capability for complex system dynamic investigations.

To generate the proposed aerothermoelastic framework, (i) each field is first decomposed into its initial physical subdomains; (ii) the energetic components of each subdomain is then defined with respect to the geometrical and material properties of the field; (iii) the dynamics of each subdomain are generated from the energetic interactions of the present components; (iv) the dynamics of each field are generated from the reversible and irreversible interactions of the present physical subdomains; (v) finally, based on power continuity between coupled fields and possible connections between fields’ energetic components at the interface, a unique conservative coupled-aerothermoelastic model of the system is generated through connecting the corresponding pairs of physical subdomains of the coupled fields. For coupled fluid and solid fields, (v) can be done if and only if the compatibility between the fixed Eulerian frame of the fluid field and the moving Lagrangian frame of the solid field can be addressed satisfactorily. To address this issue, a Variable Interface Dynamic Adaptation (VIDA) technique is proposed where the likely motions of the Lagrangian solid frame is translated into a reversible volumetric flow of the fixed Eulerian fluid frame. The compatibility of the two frames is satisfied and the required information at contact surface is refined at any instant in time to keep the power transactions at the interface continuous.

Using the proposed aerothermoelastic framework, an energetic network of the system is generated that can illustrate continuous reversible and irreversible power transactions among various subdomains and between coupled fields, and offer details in relation to memory, physical characteristics, and well-posedness of the system. This unique feature is critical for analyzing the complex multi-physical multiple-field behaviors of the system. As the model is developed without employing the typical slow-thermal-dynamics and weak-connectivity assumptions and with no additional mathematical constrains, the model is principally valid in an extended range much wider than its conventional counterparts. Undoubtedly, the proposed energetic network of the system can be a useful tool for developing control strategies and for energy management of the system. The novel framework proposed and implemented in this thesis provides a unique integrated platform based on which the aeothermoelastic phenomena in multi-physical-domain multiple-field systems can be modeled univocally while reflecting the true physical nature of such complex phenomena.

Keywords: FSI problems, Dynamic modeling, Multi-physical system modeling, Aerothermoelasticity, Bond graph modeling, Descrete time and geometry modeling, physical modeling.

Subject: Engineering thesis

Thesis type: Doctor of Philosophy
Completed: 2017
School: School of Computer Science, Engineering and Mathematics
Supervisor: Fangpo He