Mathematical Model of Hydrodynamic Characteristics on the Ship’s Hull for Any Drift Angles

2019 ◽  
pp. 111-116
Author(s):  
O.F. Kryvyi ◽  
M.V. Miyusov
Keyword(s):  
Mathematical Model ◽  
Hydrodynamic Characteristics

A Study of Transient Response of Flexible Rotors in High Speed Turbomachinery

1992 ◽  
Author(s):  
V. Pavelic ◽  
R. S. Amano
Keyword(s):  
Mathematical Model ◽  
Computer Program ◽  
Analytical Model ◽  
High Speed ◽  
Angular Speed ◽  
Journal Bearings ◽  
Hydrodynamic Characteristics ◽  
Flexible Assembly ◽  
Lagrange’S Equation ◽  
Equations Of Motions

In many applications the design operating range of the turbomachinery may be well above the rotor first critical speed which leads to the problem of insuring that the turbomachinery performs with a stable, low-level amplitude of vibration. Under certain conditions of high speed and loading the rotor system can start orbiting in its bearing at a rate which is less than the rotor angular speed, and this phenomena is commonly known as whirling or whipping action. This whipping action may produce additional undesirable dynamic loads on the overall flexible assembly and eventually destroy the rotor. Some of this action is also transient in nature. Whirling is a self-exited vibration caused mainly by the fluid bearings and by the internal friction damping of the rotor. To understand this occurrence, a general dynamic mathematical model was derived considering also the complete viscous characteristic of hydrodynamic journal bearings. The general equations of motions of the system are obtained from Lagrange’s equation of motion. The system kinetic, potential, and dissipation functions are determined based on the generalized coordinates of the system. The journal displacements are related to the overall dynamics of the rotor using deformable bearings. The loads acting at the journals of the shaft are integrated from the fluid film pressure distribution in the journal bearings using mobility method. A unique mathematical model is formulated and solved. This model includes the elastic and inertial properties of the flexible rotor, the elastic, damping and inertial properties of supports and the hydrodynamic characteristics of the journal bearings. The equations of motions result in a system of nonlinear second order differential equations which are solved by using finite difference method. The solution of the equations of motions is used to plot maps of motion of journal centers. A computer program was implemented to aid in the solution of the system of equations and to verify analytical model. The computer program used test data available in literature and the results were compared to be very good. The analytical model and results obtained in this study can be of great help to designers of high speed turbomachinery.

Échanges nappe–rivière en vallée alpine : quantification et modélisation (Vallée d'Aoste, Italie)

2003 ◽  
Vol 40 (5) ◽  
pp. 775-786 ◽  
Author(s):  
A Triganon ◽  
M Dzikowski ◽  
J P Novel ◽  
M Dray ◽  
G M Zuppi ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Water Table ◽  
Spatial Dispersion ◽  
Hydrodynamic Characteristics ◽  
Spatial Evolution ◽  
Mountainous Regions ◽  
Sedimentary Deposits ◽  
Variable Sensitivity ◽  
Underground Flow ◽  
Spatial Impacts

A mathematical model is applied to the Aoste Valley (Italy), which is a good example of the hydrological workings of alluvial rock basin aquifers in mountainous regions. The course of the Dorea Baltea follows the valley, which between the altitudes of 500 and 600 m is dominated by summits reaching more than 3000 m. The lacustrine- and fluviatile-type sedimentary deposits are accompanied by several alluvial cones that, due to their varying nature, confer very diverse hydrodynamic characteristics to the land. In this particular context, the source and drainage of the Dorea control the hydrodynamics of the aquifers and influence the spatial dispersion of the physicochemical properties of the groundwater. The model also led to quantify and determine the zones and types of exchanges with the river. Simulation of lowering the water table in the river showed the variable sensitivity of the water table piezometry with various spatial impacts. Finally, the stream–aquifer impact is highlighted by the spatial evolution of the sulphate contents coming from deep lateral sources. Taking into account the stream–aquifer exchanges in an underground-flow mathematical model gives a better understanding of the workings of the valley aquifers and thus their management, especially for the development of watercourses in mountainous regions.[Journal translation]

scholarly journals Hydrodynamic characteristics of the two-phase flow field at gas-evolving electrodes: numerical and experimental studies

2018 ◽  
Vol 5 (5) ◽  
pp. 171255 ◽  
Author(s):  
Cheng-Lin Liu ◽  
Ze Sun ◽  
Gui-Min Lu ◽  
Jian-Guo Yu
Keyword(s):  
Mathematical Model ◽  
Flow Field ◽  
Experimental Studies ◽  
Three Dimensional ◽  
Electrode System ◽  
Hydrodynamic Characteristics ◽  
Cold Model ◽  
Two Phase ◽  
3D Space ◽  
Vertical Electrode

Gas-evolving vertical electrode system is a typical electrochemical industrial reactor. Gas bubbles are released from the surfaces of the anode and affect the electrolyte flow pattern and even the cell performance. In the current work, the hydrodynamics induced by the air bubbles in a cold model was experimentally and numerically investigated. Particle image velocimetry and volumetric three-component velocimetry techniques were applied to experimentally visualize the hydrodynamics characteristics and flow fields in a two-dimensional (2D) plane and a three-dimensional (3D) space, respectively. Measurements were performed at different gas rates. Furthermore, the corresponding mathematical model was developed under identical conditions for the qualitative and quantitative analyses. The experimental measurements were compared with the numerical results based on the mathematical model. The study of the time-averaged flow field, three velocity components, instantaneous velocity and turbulent intensity indicate that the numerical model qualitatively reproduces liquid motion. The 3D model predictions capture the flow behaviour more accurately than the 2D model in this study.

scholarly journals Preliminary Instability-Analysis of Deepwater Riser With Fairings

2009 ◽  
Author(s):  
Mahdi Khorasanchi ◽  
Shan Huang
Keyword(s):  
Mathematical Model ◽  
Critical Current ◽  
Degrees Of Freedom ◽  
Transverse Velocity ◽  
Outer Part ◽  
Current Speed ◽  
Eigenvalue Analysis ◽  
Hydrodynamic Characteristics ◽  
Instability Analysis ◽  
Deepwater Riser

Instability of deepwater riser with fairings is investigated in this study. Despite the advantages over other devices for suppressing vortex-induced-vibration (VIV), fairings may be susceptible to flutter type instability. A two-body mathematical model is established for the coupled transverse-torsion motion of a top tensioned riser with fairings. The inner part (riser) can only move transversely while the outer part (fairing) has transverse-torsion motion. The effect of the transverse velocity on the angle of attack is taken into account and damping is considered for both degrees of freedom. An eigenvalue analysis is employed to examine the issue of stability. The emphasis is on identifying the critical current speed for a given riser and fairing configuration. The effects of key parameters are investigated and the results indicate that the section hydrodynamic characteristics of the fairings have a significant impact on the instability.

Ways to improve the energy efficiency of shaft centrifugal pumps

2021 ◽  
Vol 27 (5) ◽  
pp. 26-35
Author(s):  
V. Makarov ◽  
◽  
V. Potapov ◽  
E. Churakov ◽  
N. Makarov ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Hydrodynamic Characteristics ◽  
Hydrodynamic Process ◽  
Test Results ◽  
Centrifugal Pumps ◽  
Energy Characteristics ◽  
Hydrodynamic Parameters ◽  
Hydrodynamic Analogy ◽  
Hydrodynamic Calculation ◽  
Vortex Theory

The increase in the efficiency and competitiveness of mining enterprises is limited by the insufficient efficiency and adaptability of the currently used centrifugal pumps. Using the vortex theory of turbomachines, Theorems Stokes’ and Helmholtz, the principles of hydrodynamic analogy and superpositions, a mathematical model of the hydrodynamic calculation of centrifugal pumps with adaptive vortex sources integrated into the impeller blades is obtained. A significant influence on the hydrodynamic parameters and adaptability of pumps of the energy characteristics of adaptive vortex sources has been proved. Criteria for the similarity of the hydrodynamic process of fluid flow in the interscapular channels of impellers and adaptive vortex sources and their influence on the hydrodynamic characteristics of pumps are obtained. Mathematical and experimental modeling uses a regression equation to calculate the parameters of vortex chambers and their impact on the efficiency and adaptability of pumps. The optimal geometric parameters of the vortex chambers, the diameter of which does not exceed 5…7 % of the impeller diameter, increase the hydrodynamic loading by at least 13 %, the nominal efficiency. not less than 6 %, adaptability not less than 8 %. On the basis of the proposed developed mathematical model, after the positive test results obtained on the laboratory pump K 20/30, tests were carried out on the CNS 300-300 pump

scholarly journals Investigation of the influence of the dimensionality of the mathematical model of the ship's motion the result of predicting its controllability

2021 ◽  
pp. 26-34
Author(s):  
В.В. Багринцев ◽  
В.В. Макарова ◽  
Ю.П. Потехин
Keyword(s):  
Mathematical Model ◽  
Lateral Displacement ◽  
Hydrodynamic Characteristics ◽  
Yaw Rate ◽  
Spatial Movement ◽  
Different Dimensions ◽  
Heading Angle ◽  
Motion Parameters ◽  
The Mathematical Model ◽  
The Relationship

В работе рассматривается влияние размерности математической модели движения судна на параметры движения, характеризующие его управляемость, к которым относятся курсовой угол, угловая скорость рыскания, продольное и боковое смещение. Указанное влияние определяется путем имитационного моделирования движения судна посредством математической модели плоского движения в плоскости невозмущенной поверхности воды, модели бокового и пространственного движения. Тестовым маневром является полная циркуляция судна на тихой воде и волнении различной балльности. В качестве опорного результата принимается картина движения, доставляемая пространственной моделью, как наиболее отвечающая условиям реального плавания. В результате тестирования 6 судов различных классов установлено, что соотношение между результатами прогнозирования поворотливости посредством моделей различной размерности существенно зависит от гидродинамических характеристик объекта исследования. The paper considers the influence of the dimension of the mathematical model of the ship's motion on the motion parameters characterizing its controllability, which include the heading angle, angular yaw rate, longitudinal and lateral displacement. This influence is determined by simulating the movement of the vessel using a mathematical model of plane movement in the plane of the undisturbed water surface, a model of lateral and spatial movement. The test maneuver this is the full circulation of the vessel in smooth water and on the varying conditions wave. The picture of movement, delivered by the spatial model, is taken as a reference result, as the most measure up for the conditions of real swimming. As a result of testing 6 vessels of various classes, it was found that the relationship between the results of predicting turnability by means of models of different dimensions significantly depends on the hydrodynamic characteristics of the research object.

scholarly journals УДОСКОНАЛЕНИЙ МЕТОД РОЗРАХУНКУ ДЕФОРМАЦІЙ НА ЗАПЛАВАХ В ЗОНІ ВПЛИВУ МОСТОВОГО ПЕРЕХОДУ

2020 ◽  
pp. 12-22
Author(s):  
Славінська О. С. ◽  
Цинка А. О.
Keyword(s):  
Mathematical Model ◽  
General Equation ◽  
Hydrodynamic Characteristics ◽  
Improved Method ◽  
Small Particles ◽  
Flood Plains ◽  
Heterogeneous Flow ◽  
Dependent Flow ◽  
Acceleration Of Gravity ◽  
The Mathematical Model

Deformations from high flooding can reach critical proportions, resulting in bridge failures. Accordingly, an improved method for calculating erosion in floodplains in the area affected by the bridge transition has been presented. The mathematical model for the floodplain dependent flow is obtained, based on the assumption of the small particles, the low acceleration of the flow relative to the acceleration of gravity, the general equation for the transport of the heterogeneous flow, and the nonsymmetry equation. The model form of the equations takes into account the constituent forces of resistance of vegetation in the flow and resistance of removal of soil grains during the process of erosion, and initial and boundary conditions for their realization are formed. A sequence for calculating the hydrodynamic characteristics of the flood flux in the area of the bridge transition influence is provided for determining the deformation values on the flood plains. The results of the calculation of the erosion in the underside floodplains of the plain river are presented.

scholarly journals Technique for Calculating the Efficiency of Operation for Solar Collector Systems

2021 ◽  
Vol 7 (3) ◽  
pp. 194-199
Author(s):  
T. Matisakov ◽  
T. Isakov
Keyword(s):  
Heat Transfer ◽  
Mathematical Model ◽  
Solar Collector ◽  
Hydrodynamic Characteristics ◽  
Water Heating ◽  
Insulating Material ◽  
Solar Water Heating ◽  
Solar Water ◽  
Heating Installation ◽  
The Heat Transfer Coefficient

According to the proposed method, the optimal connections of collector systems were investigated, and the hydrodynamic characteristics and efficiency of the solar water heating installation were determined. A graph of the heating versus time was plotted for various values of the number of collectors. The dependence of the change in the heat transfer coefficient of the tank-accumulator on the thickness of the heat-insulating material is obtained. On the basis of a mathematical model, a computer program was compiled in the Delphi 7 environment, which allows to determine the main characteristics and parameters of a solar water heating installation.

Chines-Dry Planing of Slender Hulls: A General Theory Applied to Prismatic Surfaces

2001 ◽  
Vol 45 (01) ◽  
pp. 59-72
Author(s):  
John P. Breslin
Keyword(s):  
Mathematical Model ◽  
Simple Formula ◽  
Delta Wing ◽  
Hydrodynamic Characteristics ◽  
Hydrodynamic Coefficients ◽  
Pertinent Literature ◽  
Slender Body Theory ◽  
Body Theory ◽  
Special Case ◽  
Existing Data

The ultimate goals of this two-part study are the advantages and de' ciencies of application of camber to dry-chine, stepped-planing forms. The present paper is limited to the correlation of a relatively new theory with existing data to qualify it for use in a later paper which will predict the hydrodynamic characteristics of practical forms without and with cambers. Following a brief account of the pertinent literature, a mathematical model is developed via slender-body theory. It is a generalization of M. P. Tulin's (1957) seminal analysis of flat, cambered, delta-wing waterplanes to include deadrise, together with a departure from the oversimpli' ed Wagnerian (1932) theory ' rst introduced by Vorus (1996). It is an independent, less complicated development which con'rms Vorus's result for his special case of straight-sided wedges. Detailed comparisons of all the hydrodynamic coefficients with data from model tests of prismatic hulls show that this theory is superior to that of Wagner. A very simple formula for maximum pressures is shown. Comparisons with the extensive theories of Zhao and Faltinsen are discussed. The theory is justi' ed for extension to more pragmatic forms within the scope of the theory.

Mathematical model of hit phenomena and its application to movie advertisement

2008 ◽  
Author(s):  
Ishii Akira ◽  
Yoshida Narihiko ◽  
Hayashi Takafumi ◽  
Umemura Sanae ◽  
Nakagawa Takeshi
Keyword(s):  
Mathematical Model
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