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Effects exerted by average particle size and non uniformity on bed surface fractal properties

Pan Yunwen, Xia Junqiang, Cai Tun, Yang Kejun

Acta Geophysica

2023

Vol. 71, no. 1

517--529

Sediment bed surfaces exist widely in natural rivers, and many aspects in river dynamics are closely relevant to bed surface roughness, such as flow structure, river resistance and sediment transport. As two important parameters for quantifying bed surface roughness, how average particle size and non-uniformity affect bed surface structure is unknown. Therefore, nine groups of sediment samples with different average particle sizes or different non-uniformities were firstly prepared by screening dry natural sediments. Then, the prepared sediment samples were used to manually pave nine groups of bed surfaces, and the high-precise bed surface digital elevations were obtained by a handheld 3D laser scanner. Finally, the effects exerted by the average particle size and non-uniformity on the bed surface fractal properties were discussed. The results showed that there is only a scale-free range in a profile or a two-dimensional specific direction of a bed surface with normal-distributed particle gradation. The averaged scale-free upper limit in the two-dimensional specific directions and that related to many profiles are less affected by the non-uniformity, but more affected by the average particle size. For the bed surfaces with the same non-uniformity, when the average particle size is smaller than 15 mm, the larger the average particle size is, the smaller the fractal dimension is, but the larger the scale coefficient is; when the average particle size is larger than 15 mm, the larger the average particle size is, the larger the fractal dimension and the scale coefficient are, while for the bed surfaces with the same average particle size, the non-uniformity has no significant effects on the fractal dimension and the scale coefficient. The averaged scale coefficient in the two-dimensional specific directions of an isotropic bed surface and that related to many profiles are approximately equal, but the averaged fractal dimension in the two-dimensional specific directions is obviously larger than that plus 1 related to many profiles.

Dobór parametrów eksperymentalnych badań modelowych łożysk ślizgowych

Szkurłat J., Wójcicki R., Murdzia E.

Tribologia

2005

nr 6

17-31

Przedstawiono konstrukcję i warunki pracy łożyska turbiny parowej. Łożysko nie ma układu wspomagania hydrostatycznego. Podczas rozruchu i odstawiania turbiny, jej wał obraca się z prędkością kilkunastu obrotów na minutę. Występuje wtedy w łożysku tarcie mieszane. Do badań procesów tarcia i zużycia w takim łożysku zastosowano stanowisko modelowe. Dla identyfikacji parametrów badań zastosowano teorię podobieństwa. Współczynniki skali dla badanego łożyska określono stosując analizę wymiarową z ograniczeniami. Ustalono wielkości determinujące pracę łożyska rzeczywistego. Zdefiniowano funkcję wiążącą ustalone wielkości łożyska. Otrzymano układ 36 równań, w których występuje 40 współczynników skali. Układ ten rozwiązano w trzech wariantach przyjmowanych ograniczeń. Otrzymane zależności do określania parametrów modelowego łożyska zestawiono w tabeli. Wzory te pozwalają ustalić cechy geometryczne, materiałowe, wymuszenia oraz otoczenia poszukiwanego łożyska modelowego. Tak zidentyfikowane cechy zwiększają podobieństwo zjawisk fizycznych w obiekcie rzeczywistym i w modelu.

The construction and operating conditions of bearing of the steam turbine were presented. The investigated bearing does not have the arrangement of hydrostatical support. During start and running out turbine, its shaft turns with speed of a dozen revolution per minute. A mixed friction occurs in such a bearing under these conditions. For investigation of friction and wear processes in such bearing a test rig has been utilised. The theory of similarity for the identification of parameters of investigations has been applied. The scale factor for studied bearing has been chosen applying dimension analysis with its limitations. The parameters determining the operation of modelled bearing were taken as fixed. The governing function has been defined for the steady state parameters of bearing. The system includes 36 equations in which 40 scale factors occur. This system was solved in three variants of limitations. The obtained dependencies to determination of parameters of model bearing were shown in the table. These formulae enable to establish the geometrical, material and operation features and also characteristic of surroundings of the modelled bearing. The identified parameters assure the similarity of physical phenomena in real object and in the model one.