数理解析研究所講究録
1129 巻 2000 年 139-151

139

Computational Mecanics as a Leading Technology:
Key Measure for Innovative Products
Power&Industrial Systems R&D Laboratory, Hitachi Ltd.
Kikuo Umegaki

Abstract
In the manufacture of components of industrial products, adequate
efficiency, reliability, compactness as well as cost reduction have to besatisfied. Recently, in addition to the conventionally performed empiricalor experimental methods, newly available numerical methods have been
widely used in the process of designing such plants as nuclear, thermaland hydraulic power generators. Especially, the steady improvement ofcomputer’s capability has led to the emergence of the new method ofcomputational science which can be used as an alternative forexperimenting prototype, and consequently provides the different
approach to create a concept for new products. The field of computer
simulation we covered expands to many fields; structural analysis, fluid
dynamics &heat transfer, electromagnetics and current circuit. And
numerous fruitful resuhs have obtained by the application of thosetechnology. In this article, we will show you an overview ofcomputational methods and some of their applications we have developedin Hitachi with a main attention to electric power plants.

1 Introduction
In recent years, the performance of computers drastically improved inboth speed and memory size. Concurrently, numerous efficientcomputational schemes became available. Because of these preferable
conditions, when highly advanced computing methods are properlyapplied, it has become practicable to comprehend or even predict
previously intangible complicated phenomena. Computational mechanics
has, thus, come to play a signifcant role in the progress of science andtechnology.
In enterprises, the method of computational mechanics has been widelyused as ) alternative way of testing prototype, and consequently great
reduction in cost and time has attained. At the same time, this method has
also provided the different approach to create a concept for new products.
In Mtachi, we have recognized the great importance of thecomputational mechanics since an early stage of its emergence. We have
implemented original codes in several different fields and have utihzed
them for the exploitationof new products.
$\mathrm{a}\iota$

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The involviin technical fields for the programs we have developed are
generally categorized as structural analysis, fluid dynamics, andelectromagnetics. Structural analysis is used in a designing process ofmost of products. Computational fluid analysis and electromagnetic
analysis are key to improve an efficiency of fluid machinery andequipment of power transmission system respectively. For the even better
reliabMy, we have also provide the new codes which are appropriate forthe calculation of phenomena occurred in or on products, where coupledanalysis of either fluid-structure or fluid-electromagnetic field plays acritical role.
In the following section, we will give a brief description of thecomputational technology developed in Hitachi concentratiin the topics to
those on electric power plants.
$\mathrm{g}$$\mathrm{g}$2. General description of the infrastructure of a numerical analysis
Table 1 shows a table of the relating physical phenomena and target
products, to which we have so far developedprograms.
The method of structural analysis has been applied to almost every
component of power plants. Recently, we concentrate especially on thedevelopment of techniques on dynamic model problems and on adaptivemethods.
In the fluid analysis, we have developed several purpose-built programs
specialized in such analysis as compressible flow, incompressible flow,
multiphase flow or the flow with chemical reaction.
In the computation of static-electric field problems, we also havedeveloped variety of techniques applicable to problems ranging from those
field and dynamic eddy current to those on
on static
electromagnetic radiation and electric circuit.
In addition, we have recently developed the numerical methods for bothflow-induced vibration based on fluid-structure coupled analysis and forthe electric breakdown (electrical insulation) based on fluidelectromagnetic-field coupled analysis.
$\mathrm{e}\mathrm{l}\mathrm{e}\mathrm{c}\mathrm{t}\mathrm{r}\mathrm{i}\mathrm{c}/\mathrm{m}\mathrm{a}\mathrm{g}\mathrm{n}\mathrm{e}\mathrm{t}\mathrm{i}\mathrm{c}$Table 1. Fields of physics in computational mechanics and related industrial products
table shows the involving phenomena that can be (or will be able to be) treated with ourThe )codes. These computational methods are widely applied to estimate the performanceofproducts.
$\mathrm{I}\mathrm{i}$$1\mathrm{l}\mathrm{o}\mathrm{w}\mathrm{i}\mathrm{n}\mathrm{g}$141

3. Structural Analysis
The importance of structural analysis has been increasing in order toretain structural reliability and rational designing process for suchmachinery as nuclear reactors, turbines and power generators. In practice,
it is the most significant to analyze structurally complicated materials
within a short term, considering those of physical characteristics
precisely.
In this standpoint of view, we have developed nonlinear analysis
techniques, which can treat complex phenomena with high nonlinearities:stress concentration, residual stress, thermal deformation, vibration,
buckling and so on.
Furthermore, in order to reduce enormous efforts for mesh generations,
we also have developed a completely automatic meshing system byintegrating the concept of mesh-free techniques. With this system,
efficient analyses became practicable, demanding only the minimum
definition of shapes, loading and boundary conditions.
Moreover, we have developed an advanced system for more accurate
analyses, based on the concepts of adaptive-mesh and automatic zooming.
Adaptive-mesh method is a strategic procedure to obtain solutions withrequired accuracy by recursively refming meshes. In this process,discretization errors obtained from the calculation are used to refmemeshes automatically. Zooming analysis is the alternative way to obtainaccurate sohtions. In this method, detailed analyses are conducted onto
focused areas whose boundary conditions are derived from global-modelsimulations.
Figure 2 shows an example of an adaptive-mesh analysis. There, acrack tip near the fxed end of the nozzle is assumed. An adequately fme
mesh is automatically generated around the crack tip, so that the stressconcentration can be evaluated. These advanced simulation techniques for142
static and dynamic problems are widely applied in the designiin processof power plants.
$\mathrm{g}$4. Flow analysis
As the prevalence of super-computers, recent trend in computational
fluid analysis has also been shifted to a simulation of three-dimensional
unsteady flow from that of more simplified model. In the calculation of
turbulent flow, the Large Eddy Simulation or the direct simulation became
popular. With those methods, unsteady behavior of fluids can be captured
more accurately. Though there are still some difficulties in the simulationof turbulent flow at a high Reynolds number, we can utili adequate
numerical techniques according to the type of objectives and required
accuracy.
An application of the flow analysis to a pump turbine runner inpumping mode is presented in Figure 2. Pump turbine can also work as apump by inverting the rotation, and is also used at a pumped storage
power plant. The reverse flow in the low-flow-rate range induces flow
instabffiy and can lead to hydraulic losses. With a highly accurate
unsteady flow analysis, the mechanisms of the reverse flow has been able
to be investigated. We can, thereby, improve the design of the blade
profle that will extend operating range of flow rate and will enhance thehydraulic efficiency. Figure 3 and Figure 4 show the computational
domain and the numerical results of the reverse flow at the inlet
respectively.
Furthermore, the techniques of the computational fluid analysis has
been widely applied to evaluate the characteristics of the main
components of power plants and thus contributed to the improvement of
their performance. In a piping system and a heat exchanger, vortexinduced vibration or fluid-elastic vibration can be a dominant factor oftroubles. Thus, new analytical techniques which can be used to evaluate
the effects of those vibrations were required. In order to meet therequirements, we have independently developed the code coping with theconcept of the coupled analysis. In the code, the algorithm based on both
fluid and structural analysis is integrated and applied in each time step of
the calculation. By the elaborate calculation with the code, we havesucceeded in computationally reproducing phenomena of fluid-elasticvibration for the first time.
Figure 5 and 6 show the results of the fluid-elastic vibration in a typicalconfiguration of tube arrays. The orbits in Figure 6 show that the tubes in
the last row vibrate in comparatively large amplitudes at frst. Then theenergy of the vibration descends to the surrounding tubes and eventually$\mathrm{e}$143causes the vibration of whole tubes. With this powerful new tool, it
became feasiible to computationally set the reliability standard in a designof a heat exchanger where a flow-induced vibration plays a significantrole.

5.

Electromagnetic Field Analysis
In recent years, the method of computational electromagnetics has
been an indispensable key technology in a designing process of equipment
in a power transmission system and of an electric circuit in a powerelectronic system. In
we have developed some of so called
composite programs for each simulation of substantialy different,
complicated phenomenon: there, techniques in variety of fields areemployed in conjunction with the methods in electromagnetic-field
analysis. These programs have been extensively utihzed to optimize theshapes and configurations of devices and have served in the improvementof dielectric strength of the high voltage devices. In this section, we willshow two of those methods: an analysis of particle motions underelectrostatic field in the power transmission system and an analysis ofelectric circuits on the bus bars of a transistor inverter in the powerelectronic system.
When a small fraction of metal debris happens to be sit in a pipe
composing a part of a GIS (Gas Insulated gear System) in a powertransmission system, the metal particles, electrically charged by thealternatiin current of a high-voltage conductor, will float around inside
the pipe, which may eventualy cause breakdown of electrical insulation.
In order to cope with this type of problem, we have developed the threedimensional simulation method which can trace the movements ofparticles under electrostatic fields. By using this program, we havepredicted a typical behavior of a metal particle in a GISls bus pipe andhave found the best-suited shape and the position of a particle trap.
On the other hand, in the design of a device in a power electronicsystem, the effect of stray inductance in a circuit cannot be ignored as
the improvement of power semiconductor in theratings
and the switching speed. We have, thus, developed the combined method;
methods in electromagnetic fields and circuits are systematicaly
integrated to take account of the dynamical effects of an electromagnetic
field into the analysis of an electric circuit. Figure 7 indicates thecalculated results of current distribution on bus bars of a transistor
inverter. In our method, three-dimensional electromagnetic field analysis
is coupled directly with circuit analysis: Inductance including the effect of$\mathrm{f}\mathrm{f}\mathrm{l}\mathrm{a}\mathrm{c}\mathrm{h}_{\dot{l}}$$\mathrm{g}$$\mathrm{v}\mathrm{o}\mathrm{l}\mathrm{t}\mathrm{a}\mathrm{g}\mathrm{e}/\mathrm{c}\mathrm{u}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{n}\mathrm{t}$144unsteady fluctuation of electromagnetic field is evaltlated with noapproxination. With this program, the circuitls electrical behavior withstray inductance of the bus bars can be analyzed and, as a result, thevalue of voltage and current on power devices in the circuit can beprecisely predicted. This technique is fully used to optimize aconfiguration of bus bar: to minimize over-voltages on power devices andto balance the electrical load among devices in parallel.

6. Conclusion
In the article we briefly introduced technologies and some examples of
their applications in computational engineering developed in Etachi. In
these technologies in a process of production,order to extensively
the following two things are essential: Choose appropriate models andsolution techniques, considering the typical characteristics of products
and Exploit products being aware of the limit of the application and theaccuracy.
The importance of computational mechanics in a production ofindustrial equipment will have been increasing. In Hitachi, since weconsider computational mechanics as a central and fundamental
technological tool for manufacture, we will continuously develop newcomputational methods highly effective in a process of production.
$\mathrm{u}\mathrm{t}\kappa \mathrm{e}$145Fig. 1 Expanded fie lds in computat ional engineering and examples of its applica tio$\mathrm{n}\mathrm{s}$In the production of power plants, numerical simulation provides new methods to find a novel idea:
drastic improvement in performance of equipment can be achieved with it. This method also provides away to reduce development time by demanding much less number of model test. The method ofcomputational mechanics is now becoming the most important iffiastructure which supports thedevelopment of products.

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146(c)Adaptively Refined Mesh(d)Principal stress distribution

Fig. 2 Stre ss Analy is ith Ad aptiv e-Me sh Me thod
Above is an analyzed example of a nozzle with a crack tip near its fixed end.
By the adaptive-m esh ethod, an adequate mesh is autom atically generated toexpress the stress concentration near the crack tip precisely.
$s$$\mathrm{w}$$\mathrm{m}$147

Fig.3 Computational domain of a flow analysis in thepump turbine
A system of three dimensional grids is generated in one of theinter-blades. Grid-generation techniques, such as the grid
spacing control method, are indispensable for turbulent flow
analysis with high accuracy.

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Fig.4 Numerical results of a reverse flow in a pump turbine
The reverse flow at the blade-to-blade inlet is observed when flow rateis in the low range. By adapting the design that will help to suppress thereverse flow, the operation range of a turbine can be extended toward thelow flow rate region.

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Fig.5 Calculation domain for the flow-inducedvibration in a tube array

Calculation domain for a heat exchanger was shown. Each tube has
two dimentional degrees of freedom and is assumed to be supported
by elastic spring in and direction, so that the occurrence ofresonance caused by fluid-structure coupling effect can be simulated.
$\mathrm{x}$$\mathrm{y}$150[$\Delta \mathrm{X}/\mathrm{D})$%Fig. 6 The orbit of central position of each tube center
when the fluid-elastic vibration occurred.
Increasing the inlet velocity, fluid-elastic vibration occurs at acritical velocity. In this example, the vibration began at the lastrow. The critical velocity, conventionally obtained byexperiments, has also been able to be evaluated numerically.

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Fig. 7 Current distribution on bus bars
Stray inductance of the bus bars depends on the physicaldistribution of the electric current changing with the connectedcondition. Applying a thin plate model, three-dimensional
magnetic field around the bus bars is simulated to deternine thestray inductance. The current flow and the density distribution areindicated by solid lines and color gradation respectively.
$\mathrm{c}\mathrm{i}\mathrm{r}\mathrm{c}\mathrm{u}\mathrm{i}\mathrm{t}^{1}\mathrm{s}$