1.2 Optimization of Complex Technical Devices

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1.2.1 Design Hierarchy

Block-hierarchical representation of the design process, implemented with the creation of complex technical devices, leads to a problem of such complexity that can be effectively resolved by means of modern computing, and the results of the decision – understood and analyzed by experts. Typically, the design hierarchy of tasks is formed along functional lines for turbine can have the form shown in Fig. 1.1.

Hierarchy of Turbine Design Problems
Figure 1.1 Hierarchy of turbine design problems
Nearby Hierarchy Levels of Optimization Problems
Figure 1.2 Nearby hierarchy levels of optimization problems.

The uniformity of mathematical models of the subsystems of the same level and local optimality criteria make it possible to organize the process of multi-level design, providing maximum global quality criterion of the whole system, in our case – the turbine. This process is based on the idea of so-called multilevel optimization approximation scheme that involves aggregation of mathematical models of the subsystems in the hierarchy when moving upward and disaggregation based on optimization results when moving downwards.

The problem of optimization the subsystem parameters described by OMM has the form (1.5). It can be solved by the methods of nonlinear programming and optimal control, depending on the form of the equations and the optimality criterion of the OMM.
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1.1 Mathematical Models and the Object Design Problem

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The methodology of a turbine optimal design as a complex multi-level engineering system should support the operation with diverse mathematical models, providing for each design problem communication between the neighboring subsystems levels.

One approach to turbine design with using of block-hierarchical representation consists in the transition from the original mathematical models for the subsystems and numerical methods of optimization to “all-purpose” mathematical model and general method of parameters optimization.

We will specify as original the mathematical model (OMM), which is a closed system of equations that describe the phenomena occurring in the designed object.

Regardless of the mathematical apparatus (algebraic, ordinary differential, integral, partial differential equations, etc.), OMM can be represented symbolically as follows:

Formula 1.1
(1.1)

where  X ⃗={x ⃗,u ⃗ };L(B ⃗,X ⃗) – the operator defining the model’s system of equations.

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Optimization of Axial Turbine Flow Paths: Preface

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The decades of the 1970s and 1980s of the last century were marked by the emergence and rapid development of a new scientific direction in turbine manufacturing – optimal design. A summary of the approaches, models, and optimization methods for axial turbine flow path is presented in the monographs [13–15 and 24].

It should be noted that work on the optimal design of the flow path of axial turbines and the results obtained not only have not lost their relevance, but are now widely developing. Evidence of this is the large number of publications on the topic and their steady growth. Optimization of the turbomachine flow path is a priority area of research and development of leading companies and universities.

Without the use of optimization, it is impossible nowadays to talk about progress made in the creation of high efficiency flow paths of turbomachines. It is worth noting that the widespread use in power engineering of modern achievements of hydro-aerodynamics, the theory of thermal processes, dynamics and strength of machines, materials science, and automatic control theory, is significantly expanding the range of tasks confronting the designer and greatly complicating them.

The proposed book comprehensively addresses the problem of turbomachine optimization, starting with the fundamentals of the optimization theory of the axial turbine flow paths, its development, and ending with specific examples of the optimal design of cylinder axial turbines. It should be noted that the mutual influence of designed objects of turbine
installations and the many design parameters of each object, which the product’s effectiveness depends on, is putting the task of multiparameter optimization on the agenda.

For turbines with extractions of working media for various needs, efficiency ceases to be the sole criterion of optimality. It is necessary to enable in the optimization process such important parameters as power supply. The task of optimal design of turbine has become multifaceted. It should also be stressed that often the turbo installation mode of operation is far from nominal. So taking into account the operating mode in the optimization can significantly improve the efficiency of the turbine.

In the book, along with the widely used methods of nonlinear programming, taking into account the complexity of the task and the many varied parameters, the use of the theory of planning the experiment coupled with the LP sequence to find the optimal solution is discussed. The first chapter of the book deals with general issues of the optimal design of complex technical systems and, in particular, the problem of optimization of turbomachines, using one of the approaches to the design of turbo installations – a block-hierarchical view of the design process. With this priority is given to flow path optimization of axial turbines. The task of object design and using mathematical models is formulated. A brief overview of optimization techniques, including the optimization method for turbines considering mode of operation is given.
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