Introduction to the Theory of Similarity

Gukhman, A. A.; Technica, Inc. Scripta; Cess, R. D.; Hersey, M. D.

doi:10.1115/1.3625020

Cited by 24 publications

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“…where pr is the reference pressure, pv is the liquid vapor pressure, ρ is the liquid density, and v is the local velocity (13)(14)(15)(16). This cavitation number is a ratio of the pressure difference to the pressure drop due to the fluid momentum.…”

Section: [1]mentioning

confidence: 99%

Cavitation onset caused by acceleration

Pan

Kiyama

Tagawa

et al. 2017

Proc. Natl. Acad. Sci. U.S.A.

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Striking the top of a liquid-filled bottle can shatter the bottom. An intuitive interpretation of this event might label an impulsive force as the culprit in this fracturing phenomenon. However, highspeed photography reveals the formation and collapse of tiny bubbles near the bottom before fracture. This observation indicates that the damaging phenomenon of cavitation is at fault. Cavitation is well known for causing damage in various applications including pipes and ship propellers, making accurate prediction of cavitation onset vital in several industries. However, the conventional cavitation number as a function of velocity incorrectly predicts the cavitation onset caused by acceleration. This unexplained discrepancy leads to the derivation of an alternative dimensionless term from the equation of motion, predicting cavitation as a function of acceleration and fluid depth rather than velocity. Two independent research groups in different countries have tested this theory; separate series of experiments confirm that an alternative cavitation number, presented in this paper, defines the universal criteria for the onset of acceleration-induced cavitation. . More commonly, sudden valve closing inside of a water pipe can cause a loud hammering sound due to the collapse of cavitation, resulting in damage on the inner walls (4). The effects of blast and impact that cause traumatic brain injury from cavitation have also been investigated (5, 6). To avoid cavitation-induced damage (7-9), it is crucial to predict the onset of cavitation.Cavitation onset in a high-speed flow [e.g., flow around propellers and in pumps (10)] can be characterized using a variant of the Euler number known as the cavitation number (11,12). The cavitation number is typically of the formwhere pr is the reference pressure, pv is the liquid vapor pressure, ρ is the liquid density, and v is the local velocity (13-16). This cavitation number is a ratio of the pressure difference to the pressure drop due to the fluid momentum. The large momentum of the fluid dominates when C 1, inducing cavitation. However, when C 1, the pressure at all locations is above the threshold for bubble formation, making cavitation unlikely. Practically, several advanced coefficients have been proposed to estimate cavitation inception for various geometries (16).However, the conventional cavitation number (C ) could incorrectly predict the cavitation onset in a liquid accelerated in a short amount of time. For example, the cavitation event that breaks the bottle in Fig. 1A has a maximum velocity of v ≈ 2 m/s, which yields the cavitation number C ∼ O(10 2 ). For the falling tube case in Fig. 1B a similar calculation leads to C ∼ O(10 2 ) (Table S1), whereas the conventional cavitation number requires C 1 (16). Thus, a new cavitation number is required to define the physics of cavitation onset.In the past, researchers have conducted similar experiments with a bullet-piston device to predict the tensile strength of a liquid, including pure water (17). They reported that the ...

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Section: [1]mentioning

confidence: 99%

Cavitation onset caused by acceleration

Pan

Kiyama

Tagawa

et al. 2017

Proc. Natl. Acad. Sci. U.S.A.

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“…In contrast to the results of [14], work [5] points out that self-similarity of the representation form can be achieved for all members of the mathematical model in a simple particular case. The case of an ideal oscillatory system (a load suspended on a spring with no energy dissipation) is considered.…”

Section: Fo T Fo T Ho a T A T T L Lmentioning

confidence: 82%

“…A similar thing is observed for the rest of variables. For this reason, when performing the described procedure for Fo in [14], only self-similarity of the form representation (but not the physical situation of the process) is achieved. In no other case throughout the text of [14] such a procedure is repeated and only availability of studies in this direction is mentioned in the last sentence.…”

Section: Fo T Fo T Ho a T A T T L Lmentioning

confidence: 99%

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Development of a method for approximate solution of nonlinear ordinary differential equations using pendulum motion as an example

Brunetkin

Maksymov

Maksymova

et al. 2017

EEJET

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4thermophysical properties, etc. In turn, this causes variation in a wide range of the process parameters subject to control. In such a situation, application of the results obtained by analysis of linear models is very problematic and even unfeasible in most cases.The search for new approaches to analysis of nonlinear models is an important element in solution of the problem of optimal control of power equipment using non-certified fuel of a variable composition. Literature review and problem statementAn effective way to simplify the study of complex models is to make them dimensionless. Reduction of dimensionality of the modeling space makes it possible both to reduce number of experimental (full-scale and numerical) studies by IntroductionWhen studying behavior of control systems, dynamic conditions require special consideration. Apparatus of ordinary differential equations is most often used as a mathematical tool for studying such systems. General methods of solution have only their linear forms. For this reason, linear (linearized) approaches are used to construct models of object and controller. However more exact models are represented by nonlinear differential equations. This situation leads to the fact that the results obtained can only be used within the range of small variation of parameters of the controlled processes nearby the linearization point.The use of fuel of a variable composition [1,2] in power equipment instead of certified fuel with a constant composition brings about a continuous variation of the fuel calorific value, amount of combustion products, their temperature, MATHEMATICS AND CYBERNETICS -APPLIED ASPECTS DEVELOPMENT OF

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“…It is important to understand how to apply the concept of physical similarity [15][16][17][18][19][20][21] for appropriate approximation selection in stalactite formation hydrodynamics. This method is applicable for a large class of physical systems, but we shall not consider this very extensive question.…”

Section: Introductionmentioning

confidence: 99%

Approximation and Modeling of “Shark Tooth” Stalactites Using Griewank Function & Particle Swarm Optimization Approach (Short Note for Geophysical Structure Modeling)

Bolkhovitinov¹

2014

European Geographical Studies

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In this short note we consider the way in which a useful approximation of -shark tooth‖ stalactites morphology can be obtained with a very simple mathematical function. The approximation is not applicable for other stalactite morphologies, because this possibility can be used only in very special applications, where the solution (or approximation) process is complicated by the presence of some more patterning effects. We shall not consider this complicated question in this article. We only pay attention to the fact that some stalactite patterning mechanisms admit a simple geometrical interpretation in the frame of particle swarm optimization theory.

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Introduction to the Theory of Similarity

Cited by 24 publications

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Cavitation onset caused by acceleration

Cavitation onset caused by acceleration

Development of a method for approximate solution of nonlinear ordinary differential equations using pendulum motion as an example

Approximation and Modeling of “Shark Tooth” Stalactites Using Griewank Function & Particle Swarm Optimization Approach (Short Note for Geophysical Structure Modeling)

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