• Structural Engineering and Mechanics
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• v.14 no.3
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• pp.345-364
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• 2002

The scaling laws for vibration response of anti-symmetrically laminated plates are derived by applying the similitude transformation to the governing differential equations directly. With this approach, a closed-form solution of the governing equations is not required. This is a significant advantage over the method employed by other researchers where similitude transformation is applied to the closed-form solution. The scaling laws are tested by comparing the similitude fundamental frequencies to the theoretical fundamental frequencies determined from the available closed-form solutions. In case of complete similitude, similitude solutions from the scaling laws exactly agree with the theoretical solutions. Sometimes, it may not be feasible to select the model which obeys the similarity requirement completely, therefore partial similitude is theoretically investigated and approximate scaling laws are recommended. The distorted models in stacking sequences and laminated material properties demonstrate reasonable accuracy. On the contrary, a model with distortion in fiber angle is not recommended. The derived scaling laws are very useful to determine the vibration response of complex prototypes by performing the experiment on a model with required similarities.

• Computers and Concrete
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• v.22 no.1
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• pp.101-116
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• 2018

As one of the most important engineering structures, arch dams are huge constructions built with human hands and have strategical importance. Because of the fact that long construction duration, water supply, financial reasons, major loss of life and material since failure etc., the design of arch dams is very important problem and should be done by expert engineers to determine the structural behavior more accurately. Finite element analyses and non-destructive experimental measurements can be used to investigate the structural response, but there are some difficulties such as spending a long time while modelling, analysis and in-situ testing. Therefore, it is more useful to conduct the research on the laboratory conditions and to transform the obtained results into real constructions. Within the scope of this study, it is aimed to determine the structural behavior of arch dams considering experimentally validated prototype laboratory model using similitude and scaling laws. Type-1 arch dam, which is one of five arch dam types suggested at the "Arch Dams" Symposium in England in 1968 is selected as reference prototype model. The dam is built considering dam-reservoir-foundation interaction and ambient vibration tests are performed to validate the finite element results such as dynamic characteristics, displacements, principal stresses and strains. These results are considered as reference parameters and used to determine the real arch dam response with different scales factors such as 335, 400, 416.67 and 450. These values are selected by considering previously examined dam projects. Arch heights are calculated as 201 m, 240 m, 250 m and 270 m, respectively. The structural response is investigated between the model and prototype by using similarity requirements, field equations, scaling laws etc. To validate these results, finite element models are enlarged in the same scales and analyses are repeated to obtain the dynamic characteristics, displacements, principal stresses and strains. At the end of the study, it is seen that there is a good agreement between all results obtained by similarity requirements with scaling laws and enlarged finite element models.

• Advances in aircraft and spacecraft science
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• v.6 no.6
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• pp.443-461
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• 2019

This communication investigates exact and distorted similitudes and the related scaling laws for the analysis of both dynamic response and radiated power of rectangular plates. The response of a given panel in similitude from another one is determined from a generalization of the modal approach, allowing the use of mode shapes, natural frequencies and finally radiation functions in order to establish appropriate scaling laws. Analytical models of simply supported rectangular plates are used to produce both original and replica model responses under point mechanical excitation. Emphasis is then especially put on laboratory experiments which are performed on baffled simply supported aluminum panels under mechanical excitations. All the six possible scaling directions, i.e. predicting a plate vibroacoustic reponse from another plate, are reported. All obtained results show that structural response or radiated sound power of a given plate can be both recovered with satisfactory accuracy by using the related scaling laws, even if parent models are used.

• Nuclear Engineering and Technology
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• v.56 no.3
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• pp.1052-1065
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• 2024

Advanced Pressurized Water Reactors (APWRs) and Boiling Water Reactors (BWRs) employ a suppression pool as a heat sink to prevent containment overpressure. Steam can be discharged into the pool through multi-hole spargers or blowdown pipes in both normal and accident conditions. Direct Contact Condensation (DCC) creates sources of momentum and heat. The competition between these two sources determines the development of thermal stratification or mixing of the pool. Thermal stratification is of safety concern as it reduces the cooling capability compared to a completely mixed pool condition. In this work we develop a scaling approach to prediction of the thermal stratification in a water pool induced by steam injection through spargers. Experimental data obtained from large-scale pool tests conducted in the PPOOLEX and PANDA facilities, as well as simulation results obtained using validated codes are used to develop the scaling. Two injection orientations, namely radial injection through multi-hole Sparger Head (SH) and vertical injection through Load Reduction Ring (LRR), are considered. We show that the erosion rate of the cold layer can be estimated using the Richardson number. In this work, scaling laws are proposed to estimate both the (i) transient erosion velocity and (ii) the stable position of the thermocline. These scaling laws are then implemented into a 1D model to simulate the thermal behavior of the pool during steam injection through the sparger.

• Fire Science and Engineering
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• v.13 no.4
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• pp.30-37
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• 1999

In this study, reduced-scale experiments as the alternative to a real-scale fire test were conducted to understand fire properties in atrium space. The scaling laws were derived from $\pi$-parameters which were deduced by dimensional analysis of governing equations (continuity, conservation of momentum and conservation energy). The 1/50 scale experiment simulated the real-scale fire test in SIVANS atrium at Japan were conducted under the scaling laws. And this results were compared with real-scale experiment results. Furthermore these results were visualized by video recording system using laser light sheet.

• Journal of The Korean Astronomical Society
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• v.46 no.3
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• pp.133-140
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• 2013

The empirical mass discrepancy-acceleration (MDA) relation of disk galaxies provides a key test for models of galactic dynamics. In terms of modified laws of gravity and/or inertia, the MDA relation quantifies the transition from Newtonian to modified dynamics at low centripetal accelerations $a_c{\lesssim}10^{-10}ms^{-2}$. As yet, neither dynamical models based on dark matter nor proposed modifications of the laws of gravity/inertia have predicted the functional form of the MDA relation. In this work, I revisit the MDA data and compare them to four different theoretical scaling laws. Three of these scaling laws are entirely empirical; the fourth one - the "simple ${\mu}$" function of Modified Newtonian Dynamics - derives from a toy model of gravity based on massive gravitons (the "graviton picture"). All theoretical MDA relations comprise one free parameter of the dimension of an acceleration, Milgrom's constant aM. I find that the "simple ${\mu}$" function provides a good fit to the data free of notable systematic residuals and provides the best fit among the four scaling laws tested. The best-fit value of Milgrom's constant is $a_M=(1.06{\pm}0.05){\times}10^{-10}ms^{-2}$. Given the successful prediction of the functional form of the MDA relation, plus an overall agreement with the observed kinematics of stellar systems spanning eight orders of magnitude in size and 14 orders of magnitude in mass, I conclude that the "graviton picture" is sufficient (albeit probably not a necessary nor unique approach) to describe galactic dynamics on all scales well beyond the scale of the solar system. This suggests that, at least on galactic scales, gravity behaves as if it was mediated by massive particles.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.30 no.9 s.252
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• pp.825-833
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• 2006

To investigate the moderator coolability for CANDU-6 reactors, a test facility (HU-KINS) has been manufactured as a 1/8 scaled-down of a calandria tank. In the design of the test facility, a scaling law was developed in such a way to consider the thermal-hydraulic characteristics of a CANDU-6 moderator. The proposed scaling law takes into consideration of the energy conservation, the dynamic similitude such as dimensionless numbers, Archimedes number (Ar) and Reynolds number (Re), and thermal-hydraulic properties similitude. Using this proposed scaling law, the thermal-hydraulic scaling analyses of similar test facilities such as the SPEL (1/10 scale) and the STERN (1/4 scale), have been identified. As a result, in the case of the SPEL, while the energy conservation is well defined, the similarities of Ar and the heat density are not well considered. As for the similarity of the STERN, while both the energy conservation and the characteristics of Ar are well defined, the heat density is not. In the meanwhile, the HU-KINS test facility with 1/8 length scaled-down is well similitude in compliance with all similarities of the energy conservation, the fluid dynamics and thermal-hydraulic properties. To verify the adequacy of the similarities in terms of thermal-hydraulics, a computational fluid dynamic (CFD) analysis has been conducted using the CFX-5 code. As the results of the CFD analyses, the predicted flow patterns and variation of axial properties inside the calandria tank are well consistant with those of previous studies performed with FLUENT and this implies that the present scaling method is acceptable.

• Journal of The Korean Astronomical Society
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• v.36 no.spc1
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• pp.1-5
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• 2003

In an early paper Skumanich suggested the existence of a scaling law relating the mean sunspot magnetic field with the square-root of the photospheric pressure. This was derived from an analysis of a variety of theoretical spot models including those by Yun (1968). These were based on the Schliiter-Temesvary (S- T) similarity assumption. To answer criticisms that such modeling may have unphysical (non-axial maxima) solutions, the S-T model was revisited, Moon et al. (1998), with an improved vector potential function. We consider here the consequences of this work for the scaling relation. We show that by dimensionalizing the lateral force balance equation for the S- T model one finds that a single parameter enters as a characteristic value of the solution. This parameter yields Skumanich's scaling directly. Using an observed universal flux-radius relation for dark solar magnetic features (spots and pores) for comparison, we find good to fair agreement with Yun's characteristic value, however the Moon et al. values deviate significantly.

• Proceedings of the Korean Nuclear Society Conference
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• 1997.10a
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• pp.475-480
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• 1997

In order to conduct the effective integration of computer-aided conceptual design for integrated nuclear power reactor, not only is a smooth information flow required, but also decision making fur both conceptual design and construction process design must be synthesized. In addition to the aboves, the relations between the one step and another step and the methodologies to optimize the decision variables are verified, in this paper especially, that is, scaling laws and scaling criteria. In the respect with the running of the system, the integrated optimization process is proposed in which decisions concerning both conceptual design are simultaneously made. According to the proposed reactor types and power levels, an integrated optimization problems are formulated. This optimization is expressed as a multi-objective optimization problem. The algorithm for solving the problem is also presented. The proposed method is applied to designing a integrated sub-critical reactors.

• Proceedings of the Korea Society for Energy Engineering kosee Conference
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• 2003.11a
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• pp.159-164
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• 2003