- Email: [email protected]
Re.: Structural mechanics in reactor technology
NUCLEAR ENGINEERING AND DESIGN 14 (1970) 349-35 1. NORTH-HOLLAND PUBLISHING COMPANY
LETTER TO THE EDITOR Re.: STRUCTURAL MECHANICS IN REACTOR TECHNOLOGY Dear Sir, The need to delineate the Topical Scope of the First International Conference on Structural Mechanics in Reactor Technology, and to make explicit the purpose and aims of this Conference, has undoubtedly raised queations as to the nature and significance of this field of endeavour, which need serious consideration by those responsible for the planning of teaching and research programmes in Nuclear Engineering. The phrase “First International Conference” itself implies the continuing relevance of structural mechanics to the design and operation of nuclear power systems, and the existence of a fertile problem area. A larger question is the nature of Nuclear Engineering itself. In my own School of Nuclear Engineering, hopefully with an objectivity engendered by distance and lack of tradition, some thought has been given to the development of a normative, rather than a descriptive theory of Nuclear Engineering. The exercise has been useful in designing graduate courses, by clarifying the relevance and significance of the various engineering science disciplines, and in identifying and relating the interacting processes which characterise nuclear power system performance. In particular, it has led to more detailed consideration of the structural mechanics field, in its widest sense, to an attempt to map out this field in relation to Nuclear Engineering, and to classify primary attributes of reported work in this field on a conceptual basis. This communication is also prompted by the belief that some theoretical basis must exist for the discussion of the problem of dissemination and retrieval of information in this field. In addition to the consideration of a comprehensive textbook, it may be appropriate for the Conference to consider computer oriented information retrieval systems, since achievement of the objectives of the Conference implies an increase in technical publications. At a very abstract level, the design and operation of nuclear power systems are problems of optimization and optimal control. Modes of system perfor-
mance may be described by trajectories in a bounded feasible subspace in the larger space of the appropriate state variables. Allowing for the possibility of phase changes and configuration changes at a fixed spatial reactor point, three classes of state variable are required for a complete description of the nuclear, solid state and fluid state aspects: (a) Nuclear: Neutron and other particle fluxes, nuclide concentrations. (b) Solid state: Temperature, stresses, displacements. (c) Fluid state: Temperature, pressure, deviatoric stresses, velocities. The feasible subspace is defined essentially by intensive equality constraint relations, e.g.: constitutive equations and conservation laws. Due to inherent randomness or uncertain knowledge, the basic formulations must be probabilistic. Apart from obvious non-negativity requirements, boundaries of the feasible region are defined, with varying degrees of probability, by inequality constrains of a random nature. In the main, these derive from solid or fluid “failure” modes, e.g, rupture, fatigue, excessive deformation, boiling, boiling crises, fluid-solid reactions. Nuclear aspects do not of themselves impose significant limitations directly in this sense, their importance deriving more from their contribution to the objective function in the optimization process via fissile and fertile material utilization, or to non-negativity constrains in relation to control absorbers. Thus the broad field of structural mechanics emerges as a key area in Nuclear Engineering, and its significance is likely to increase as more sophisticated optimization techniques, economic pressures, and increased knowledge force performance closer to the limits of feasible operation. Theoretical and experimental work will be required to reduce uncertainty, exemplified by engineering design factors, in the prediction of normal performance, to delineate more precisely the critical “failure” boundaries, and to
350
J. J.THOMPSON
external applied load
external applied displacement
solid-solid 4
solid-solid
solid-fluid
Fig. I.
Investigate the implications, statistically, of state variable trajectories in the vicinity of such boundary Iregions. An attempt has been made in fig. I to show diagrammatically. processes and interactions that might occur in structural mechanics oriented probIcms in Nuclear Engineering. The structural mechanics of solid nuclear system components is based ultimately on the coupling of local stress and displacement fields via the material rheological properties (elasticity, viscoelasticity, plasticity, etc.). Conceptually, stress is primary in exciting structural response, in relation to mechanical loads (pressure and shear due to adjacent fluids and/or solids, gravity and inertia body forces, externally applied loads) while displacement is primary in relation to thermal and irradiation induced dilatation, and differential solid-solid expansion. Important feedback loops couple displacements to fluid dynamics, neutron flux, body forces, and
solid-solid mechanical interaction. Single or two phase fluid thermal mechanics is significant in determining pressure and shear loads, particle flux levels, and boundary conditions on temperature fields in solid components. Temperatures produce direct structural, hydraulic and nuclear effects, and modify thermal. rheological and nuclear material properties. The scope of the subject is apparent from this diagram, by the number of possible combinations of processes and interactions, even without reference to combinations ?f materials and configurations. For teaching and research, a concern with general principles and concepts common to structural mechanics topics in Nuclear Engineering suggests the following as a set of primary attributes for a broad classification. For more practical purposes, the secondary attributes, .- reactor, configuration, component, geometry, material, etc. - are more important. (1) Objectives: Study of normal performance,
351
STRUCTURAL MECHANICS
feasible solutions, or concern with inequality constraints, crises, failure modes. (2) Level of uncertainty: Deterministic or stochastic models; role of probability theory, statistics, in theory, experiment, or performance reduction. (3) Time factor: Steady state, quasi-static or dynamic processes; time constant and frequency range considerations. (4) Structural complex: Basic stuctural elements, few component or multi-component structures. (5) Systems: Degree of coupling between structural, thermal, nuclear and fluid mechanics processes. (6) Level of abstraction: Performance of real systems, components, materials, as compared to the mathematical analysis of ideal models. In addition, one may consider Mathematical and Numerical Methods to cover, for example, topics whose main theme is the illustrative application of finite difference, finite element and modal expansion techniques to problems of structural mechanics in Nuclear Engineering, but in our view the generality
of much of the mathematical analysis, approximation theory and numerical methods required in Nuclear Engineering establishes this as a separate but complementary field. The somewhat abstract philosophical nature of this communication will, I trust, be excused on the basis of the writer’s belief, with Northrop [I ] that “no problem in society, science, or life is fully understood until its grounds in the metaphysical nature of things is discovered”. J. J. THOMPSON
24June1970
Foundation Professor and Head, School of Nuclear Engineering. Utk~ersity ofNew South Wales, Australia
Reference [l] F.S.C.Northrop, in: The Meeting of East and West (The Macmillan Co., New York, 1949).
LETTER TO THE EDITOR Re.: STRUCTURAL MECHANICS IN REACTOR TECHNOLOGY Dear Sir, The need to delineate the Topical Scope of the First International Conference on Structural Mechanics in Reactor Technology, and to make explicit the purpose and aims of this Conference, has undoubtedly raised queations as to the nature and significance of this field of endeavour, which need serious consideration by those responsible for the planning of teaching and research programmes in Nuclear Engineering. The phrase “First International Conference” itself implies the continuing relevance of structural mechanics to the design and operation of nuclear power systems, and the existence of a fertile problem area. A larger question is the nature of Nuclear Engineering itself. In my own School of Nuclear Engineering, hopefully with an objectivity engendered by distance and lack of tradition, some thought has been given to the development of a normative, rather than a descriptive theory of Nuclear Engineering. The exercise has been useful in designing graduate courses, by clarifying the relevance and significance of the various engineering science disciplines, and in identifying and relating the interacting processes which characterise nuclear power system performance. In particular, it has led to more detailed consideration of the structural mechanics field, in its widest sense, to an attempt to map out this field in relation to Nuclear Engineering, and to classify primary attributes of reported work in this field on a conceptual basis. This communication is also prompted by the belief that some theoretical basis must exist for the discussion of the problem of dissemination and retrieval of information in this field. In addition to the consideration of a comprehensive textbook, it may be appropriate for the Conference to consider computer oriented information retrieval systems, since achievement of the objectives of the Conference implies an increase in technical publications. At a very abstract level, the design and operation of nuclear power systems are problems of optimization and optimal control. Modes of system perfor-
mance may be described by trajectories in a bounded feasible subspace in the larger space of the appropriate state variables. Allowing for the possibility of phase changes and configuration changes at a fixed spatial reactor point, three classes of state variable are required for a complete description of the nuclear, solid state and fluid state aspects: (a) Nuclear: Neutron and other particle fluxes, nuclide concentrations. (b) Solid state: Temperature, stresses, displacements. (c) Fluid state: Temperature, pressure, deviatoric stresses, velocities. The feasible subspace is defined essentially by intensive equality constraint relations, e.g.: constitutive equations and conservation laws. Due to inherent randomness or uncertain knowledge, the basic formulations must be probabilistic. Apart from obvious non-negativity requirements, boundaries of the feasible region are defined, with varying degrees of probability, by inequality constrains of a random nature. In the main, these derive from solid or fluid “failure” modes, e.g, rupture, fatigue, excessive deformation, boiling, boiling crises, fluid-solid reactions. Nuclear aspects do not of themselves impose significant limitations directly in this sense, their importance deriving more from their contribution to the objective function in the optimization process via fissile and fertile material utilization, or to non-negativity constrains in relation to control absorbers. Thus the broad field of structural mechanics emerges as a key area in Nuclear Engineering, and its significance is likely to increase as more sophisticated optimization techniques, economic pressures, and increased knowledge force performance closer to the limits of feasible operation. Theoretical and experimental work will be required to reduce uncertainty, exemplified by engineering design factors, in the prediction of normal performance, to delineate more precisely the critical “failure” boundaries, and to
350
J. J.THOMPSON
external applied load
external applied displacement
solid-solid 4
solid-solid
solid-fluid
Fig. I.
Investigate the implications, statistically, of state variable trajectories in the vicinity of such boundary Iregions. An attempt has been made in fig. I to show diagrammatically. processes and interactions that might occur in structural mechanics oriented probIcms in Nuclear Engineering. The structural mechanics of solid nuclear system components is based ultimately on the coupling of local stress and displacement fields via the material rheological properties (elasticity, viscoelasticity, plasticity, etc.). Conceptually, stress is primary in exciting structural response, in relation to mechanical loads (pressure and shear due to adjacent fluids and/or solids, gravity and inertia body forces, externally applied loads) while displacement is primary in relation to thermal and irradiation induced dilatation, and differential solid-solid expansion. Important feedback loops couple displacements to fluid dynamics, neutron flux, body forces, and
solid-solid mechanical interaction. Single or two phase fluid thermal mechanics is significant in determining pressure and shear loads, particle flux levels, and boundary conditions on temperature fields in solid components. Temperatures produce direct structural, hydraulic and nuclear effects, and modify thermal. rheological and nuclear material properties. The scope of the subject is apparent from this diagram, by the number of possible combinations of processes and interactions, even without reference to combinations ?f materials and configurations. For teaching and research, a concern with general principles and concepts common to structural mechanics topics in Nuclear Engineering suggests the following as a set of primary attributes for a broad classification. For more practical purposes, the secondary attributes, .- reactor, configuration, component, geometry, material, etc. - are more important. (1) Objectives: Study of normal performance,
351
STRUCTURAL MECHANICS
feasible solutions, or concern with inequality constraints, crises, failure modes. (2) Level of uncertainty: Deterministic or stochastic models; role of probability theory, statistics, in theory, experiment, or performance reduction. (3) Time factor: Steady state, quasi-static or dynamic processes; time constant and frequency range considerations. (4) Structural complex: Basic stuctural elements, few component or multi-component structures. (5) Systems: Degree of coupling between structural, thermal, nuclear and fluid mechanics processes. (6) Level of abstraction: Performance of real systems, components, materials, as compared to the mathematical analysis of ideal models. In addition, one may consider Mathematical and Numerical Methods to cover, for example, topics whose main theme is the illustrative application of finite difference, finite element and modal expansion techniques to problems of structural mechanics in Nuclear Engineering, but in our view the generality
of much of the mathematical analysis, approximation theory and numerical methods required in Nuclear Engineering establishes this as a separate but complementary field. The somewhat abstract philosophical nature of this communication will, I trust, be excused on the basis of the writer’s belief, with Northrop [I ] that “no problem in society, science, or life is fully understood until its grounds in the metaphysical nature of things is discovered”. J. J. THOMPSON
24June1970
Foundation Professor and Head, School of Nuclear Engineering. Utk~ersity ofNew South Wales, Australia
Reference [l] F.S.C.Northrop, in: The Meeting of East and West (The Macmillan Co., New York, 1949).