Three-dimensional metrics with a spherical homogeneous model

1998 ◽  
Vol 39 (2) ◽  
pp. 1189-1198
Author(s):  
Victor Patrangenaru
Keyword(s):  
Homogeneous Model ◽  
Three Dimensional

Numerical Investigations of Scale Effect on Cavitation Around Hydrofoils

2014 ◽  
Author(s):  
Haiyu Wang ◽  
Weidong Shi ◽  
Desheng Zhang ◽  
Ling Zhou ◽  
Dazhi Pan
Keyword(s):  
Scale Effects ◽  
Homogeneous Model ◽  
Critical Role ◽  
Three Dimensional ◽  
Water Mixture ◽  
Detached Eddy Simulation ◽  
Hexahedral Mesh ◽  
Numerical Work ◽  
Cloud Cavitation ◽  
Sheet Cavitation

Although scale effects on cavitation have been studied, there seems to be no experimental or numerical work has been done on scale effects on cavitation regimes for hydrofoils. The present study was motivated by the prediction uncertainty of cavitation performance in scaling an axial flow pump, which is also an indispensable step in the design and application of hydraulic machineries. Hydrofoil NACA66 was adopted in this paper to represent the general characteristics of hydrofoils. Three hydrofoils with similar boundary conditions were simulated and analyzed, i.e. the initial hydrofoil, the hydrofoil models scaled down 0.5 and 0.25 times, respectively. High quality hexahedral mesh was established based on three-dimensional geometry of the hydrofoils. The monitoring points were arranged at the same locations relative to the boundary in each case. Computations were conducted on these three-dimensional hydrofoils, based on Detached Eddy Simulation (DES) turbulence model and Zwart cavitation model, which is a homogeneous model of cavitation, considering vapor/water mixture as one phase. In order to validate the practicability of numerical method and configuration employed in this paper, the numerical calculation of the initial hydrofoil was compared with experimental results provided by previous researchers, including the evolution of cavitation and pressure fluctuation on suction surface of the hydrofoil. According to the comparisons of the simulation results of the initial case and the other two scaled down models, we found the boundary layer suppresses the reentrant jet, which plays a critical role in cavitation detachment. Consequently, it influences the evolution of cavitation from the initial bubble, sheet cavitation, cloud cavitation and bubble breakup. Meantime, cavity evolution, cavity lengths, as well as cloud shedding periods were analyzed and discussed.

Equivalent homogeneous model of D31-mode longitudinal piezoelectric transducers

2017 ◽  
Vol 28 (19) ◽  
pp. 2651-2658 ◽  
Author(s):  
Yangkun Zhang ◽  
Tien-Fu Lu ◽  
Wei Gao
Keyword(s):  
Equivalent Circuit ◽  
Transfer Matrix ◽  
Homogeneous Model ◽  
Three Dimensional ◽  
Element Model ◽  
Piezoelectric Transducers ◽  
Proposed Model ◽  
Dimensional Finite Element ◽  
Mixing Method ◽  
Three Dimensional Finite Element

This article focuses on modelling of D31-mode longitudinal piezoelectric transducers. A simple equivalent one-dimensional homogeneous model of D31-mode longitudinal piezoelectric transducers is proposed in this article. Homogeneous properties of the model are derived by a simple analytical mixing method based on the operation principle of D31-mode longitudinal piezoelectric transducers. Compared with other models in the literature, the proposed homogeneous model can consider passive layers in D31-mode longitudinal piezoelectric transducers for more accurate predictions in either static or dynamic behaviour. The proposed model is validated by a three-dimensional finite element model. Besides, based on the homogeneous model and borrowing the network theory, an exact equivalent circuit is formulated. A more straightforward form of the equivalent circuit can further facilitate analysis and modelling of D31-mode longitudinal piezoelectric transducers. Also, the proposed homogeneous model is wrapped into a transfer matrix form. The formulated transfer matrix of D31-mode longitudinal piezoelectric transducers can be used with the transfer matrix method to facilitate the calculations, when D31-mode longitudinal piezoelectric transducers are connected with numerous mediums in the operation direction. The effectiveness of the equivalent circuit and the transfer matrix is also verified.

The orbit of Pluto over a long interval of time

1966 ◽  
Vol 25 ◽  
pp. 227-229 ◽  
Author(s):  
D. Brouwer
Keyword(s):  
Periodic Orbit ◽  
Numerical Integration ◽  
Restricted Problem ◽  
Three Dimensional ◽  
The Third ◽  
Circular Restricted Problem ◽  
Resonance Relation

The paper presents a summary of the results obtained by C. J. Cohen and E. C. Hubbard, who established by numerical integration that a resonance relation exists between the orbits of Neptune and Pluto. The problem may be explored further by approximating the motion of Pluto by that of a particle with negligible mass in the three-dimensional (circular) restricted problem. The mass of Pluto and the eccentricity of Neptune's orbit are ignored in this approximation. Significant features of the problem appear to be the presence of two critical arguments and the possibility that the orbit may be related to a periodic orbit of the third kind.

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