<i>Introduction to the Theory of Similarity</i>

Gukhman, A. A.; Teichmann, T.

doi:10.1063/1.3048378

Cited by 15 publications

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“…The similarity theory [11][12][13] is about the science of the conditions under which physical phenomena are similar. In engineering, a model that has similarity with the real application is usually used to study complex dynamics problems, which allows testing of a design prior to building.…”

Section: Scenario 1: S Is Given and Can Be Increasedmentioning

confidence: 99%

Two rapid test methods for assessing transmission time reliability of a multiple-channel network with Poisson arrival and service rates

Li¹,

Li²

2015

AEU - International Journal of Electronics and Communications

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Section: Scenario 1: S Is Given and Can Be Increasedmentioning

confidence: 99%

Two rapid test methods for assessing transmission time reliability of a multiple-channel network with Poisson arrival and service rates

Li¹,

Li²

2015

AEU - International Journal of Electronics and Communications

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“…It follows from (11) that the parameters in the Stokes number (ν, µ, l) are decisive in calculating K p , an exception being represented by the particle density ρ p appearing in (11).…”

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“…The phase contact surface in a scrubber is dependent on the type of equipment and method of supplying the irrigation [1] and may constitute a set of surfaces for drops with various size distributions, gas bubbles differing in size, films of liquid flowing over the packing, and so on. This has been solved by using the physical analogy method [11]. This is based on quantities most fully characterizing the interphase surface formation, while at the same time they are quite simply determined by experiment or calculation.…”

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Performance calculation for inertial-type gas cleaners

Val'dberg

Safonov²

2006

Chem Petrol Eng

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Working formulas are given for the diameters of suspended particles trapped with 0.5 efficiency for dry centrifugal dust traps, wet dust traps (cyclones with wet film, scrubbers), and high-speed mist traps.The particle deposition performance in any dust trap can be represented as a function of dimensionless parameters or criteria [1, 2], each of which characterizes a corresponding deposition mechanism, together with the Re number, which defines the hydrodynamic conditions. Performance calculations for a particular apparatus should be done on the basis of the most important mechanisms while excluding the minor ones.That approach greatly simplifies methods of calculating gas cleaning plant. If the inertial mechanism predominates, the main effect on the performance comes from the Stokes number, whose formalized expression iswhere d p is the diameter of the suspended particles (droplets) in µm; ρ p is their density in kg/m 3 ; v is the gas flow speed in the active section in m/sec; µ is the dynamic viscosity of the gas in Pa·sec; and l is a linear parameter characterizing the deposition surface in m. The particular case of the inertial mechanism is centrifugal deposition. Then formula (1) can be put aswhere D is the diameter of the apparatus in m. The centrifugal mechanism is predominant for most designs of dust and mist traps that are assigned on the generally accepted classification as gas-cleaning equipments [3] in various groups: dry, centrifugal, and inertial dust traps; virtually all types of wet dust trap (scrubbers); and high-speed fibrous filter mist traps.The performance of a dust or mist trap with a predominant inertia mechanism may be considered on the criterial dependence η = ƒ(Stk, Re).The technical literature gives several such formulas, mainly of theoretical character. For example, there are the equations for the performance in the deposition of a single drop in a potential (turbulent) flow mode in a gas [4,5] or on a

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“…The dimensional analysis incorporates scope for using arbitrary units for X i [3], which are compiled from the instrument parameters and used in handling particular tasks, which extends the range of structures available for the mathematical functions and functionals used for simulating the physical laws used in the meter. Here I propose the following similarity number, which relates the basic physical parameters for the liquid meter: (2) in which Q nom is the nominal liquid flow rate (characteristic of meter power); M is the specific mass (a characteristic of the design compactness); p w is the working pressure (characteristic of the stress on the constructional material); and D e is the diameter of the nominal counter entrance (spatial characteristic).…”

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Forecasting liquid meter parameters

Kuzmin

2008

Chem Petrol Eng

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Designing liquid meters is considered, including the definition of regularities in the relationships between the design parameters for a series of instruments. A general treatment is given involving a mathematical model (similarity criterion for meters) for instruments of this class with the use of Buckingham's theorem.An example is given of using this model.The specifications for the properties of engineering instruments have recently tightened considerably. Development in measuring instruments (MI) is accompanied by an ongoing search for a compromise between the actual properties of the instrument, the technical facilities of the maker, and the economic desirability of using the MI. Here it is necessary to copy or upgrade efficient MI designs.Previous methods of evaluating MI performance in the determination of flow rate and amount of liquid have been determined by how well the instrument fits the working requirements. The performance of a design that implements an MI working principle is not explicitly evaluated, and no ways are pointed out of upgrading the design. Mostly, improvement in some characteristics as a rule is attained at the expense of deterioration in others: for example, extending the functional ranges of MI complicates the design (increases the number of components) and reduces the reliability of flowmeters and other such liquid meters because of increase in the number of elements that may fail; improved performance in systems for automatically correcting errors caused by fluctuations in the external parameters complicates the electronic circuit; and increasing the carrying capacity causes failures in the mechanical parts because of corrosive wear in the flow sections and so on.There is thus a problem in comparative evaluation of MI designs and of forecasting the parameters within a type series of instruments employing a single physical principle. There are various parameters on which flowmeters are classified (accuracy, measurement ranges, output signal form, and so on), but the most general classification is that based on the physical phenomena involved in transforming the measured quantity to an output signal from the flowmeter's primary sensor.We use Buckingham's π theorem as a simple and most effective means of combining several variables in experiments [1] in order to determine analytical relationships between the parameters of a meter that transforms a measured liquid flow. The analysis of dimensions for the physical parameters provides an algebraic expression for a dimensionless similarity number for the physical processes in the MI [2], and for MI that use electronic conversion of physical quantities the required regularities will be extended only to the hydraulic (flow) parts. All the corresponding dimensionless numbers reflect the set of such phenomena and have an identical numerical value for the similarity number, which in this case is an index to the set of properties (quality) of the meter as a physical object.On the π theorem, any similarity number (provided it meets the obligato...

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Introduction to the Theory of Similarity

Cited by 15 publications

References 0 publications

Two rapid test methods for assessing transmission time reliability of a multiple-channel network with Poisson arrival and service rates

Two rapid test methods for assessing transmission time reliability of a multiple-channel network with Poisson arrival and service rates

Performance calculation for inertial-type gas cleaners

Forecasting liquid meter parameters

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