scholarly journals Computation of the Added Masses of an Unconventional Airship

2012 ◽  
Vol 2012 ◽  
pp. 1-19 ◽  
Author(s):  
Naoufel Azouz ◽  
Said Chaabani ◽  
Jean Lerbet ◽  
Azgal Abichou
Keyword(s):  
Mathematical Analysis ◽  
Potential Flow ◽  
Velocity Potential ◽  
Special Focus ◽  
System Of Equations ◽  
Approximation Methods ◽  
Numerical Studies ◽  
Geometric Approximation ◽  
Elliptic Cone ◽  
Added Masses

This paper presents a modelling of an unmanned airship. We are studying a quadrotor flying wing. The modelling of this airship includes an aerodynamic study. A special focus is done on the computation of the added masses. Considering that the velocity potential of the air surrounding the airship obeys the Laplace's equation, the added masses matrix will be determined by means of the velocity potential flow theory. Typically, when the shape of the careen is quite different from that of an ellipsoid, designers in preprocessing prefer to avoid complications arising from mathematical analysis of the velocity potential. They use either complete numerical studies, or geometric approximation methods, although these methods can give relatively large differences compared to experimental measurements performed on the airship at the time of its completion. We tried to develop here as far as possible the mathematical analysis of the velocity potential flow of this unconventional shape using certain assumptions. The shape of the careen is assumed to be an elliptic cone. To retrieve the velocity potential shapes, we use the spheroconal coordinates. This leads to the Lamé's equations. The whole system of equations governing the interaction air-structure, including the boundary conditions, is solved in an analytical setting.

scholarly journals Structural Health Monitoring of 2D Plane Structures

2021 ◽  
Vol 11 (5) ◽  
pp. 2000
Author(s):  
Behnam Mobaraki ◽  
Haiying Ma ◽  
Jose Antonio Lozano Galant ◽  
Jose Turmo
Keyword(s):  
Mechanical Properties ◽  
Health Monitoring ◽  
Mathematical Analysis ◽  
Stiffness Matrix ◽  
State Of The Art ◽  
System Of Equations ◽  
Matrix System ◽  
Structural System ◽  
Detailed Mathematical Analysis ◽  
Structural System Identification

This paper presents the application of the observability technique for the structural system identification of 2D models. Unlike previous applications of this method, unknown variables appear both in the numerator and the denominator of the stiffness matrix system, making the problem non-linear and impossible to solve. To fill this gap, new changes in variables are proposed to linearize the system of equations. In addition, to illustrate the application of the proposed procedure into the observability method, a detailed mathematical analysis is presented. Finally, to validate the applicability of the method, the mechanical properties of a state-of-the-art plate are numerically determined.

Conservation laws for plane steady potential barotropic flow

2013 ◽  
Vol 24 (6) ◽  
pp. 789-801 ◽  
Author(s):  
YU. A. CHIRKUNOV ◽  
S. B. MEDVEDEV
Keyword(s):  
Conservation Laws ◽  
Velocity Potential ◽  
Zero Order ◽  
System Of Equations ◽  
Nonlinear System Of Equations ◽  
Nonlinear Conservation Laws ◽  
First Order ◽  
Barotropic Flow ◽  
Chaplygin System ◽  
Steady Potential

It is shown that the set of conservation laws for the nonlinear system of equations describing plane steady potential barotropic flow of gas is given by the set of conservation laws for the linear Chaplygin system. All the conservation laws of zero order for the Chaplygin system are found. These include both known and new nonlinear conservation laws. It is found that the number of conservation laws of the first order is not more than three, assuming that the laws do not depend on the velocity potential and are not non-obvious ones. The components of these conservation laws are quadratic with respect to the stream function and its derivatives. All the Chaplygin functions are found, for which the Chaplygin system has three non-obvious conservation laws of the first order that are independent of velocity potential. All such non-obvious first-order conservation laws are found.

A Simple Method of Constructing Duct Models for the Electrolytic Tank

1957 ◽  
Vol 61 (563) ◽  
pp. 775-776
Author(s):  
J. F. Norbury ◽  
A. Platt
Keyword(s):  
Wind Tunnel ◽  
Potential Flow ◽  
Velocity Potential ◽  
Two Dimensional ◽  
Potential Surfaces ◽  
Simple Method ◽  
Water Line ◽  
Insulating Surfaces ◽  
Air Intake ◽  
Axis Of Symmetry

A problem which occurs frequently is that of choosing a suitable shape for a duct, such as a wind tunnel contraction or an air intake. Basically similar problems, involving potential flow fields, occur in other branches of engineering, particularly in electrical engineering, and the electrolytic tank is now established as a tool which may usefully be employed in their investigation. The use of the simple shallow tank is limited to those fields which can be treated as two-dimensional or axisymmetric, but many problems fall within these categories.In forming a duct model for the electrolytic tank the walls of the duct are represented by insulating surfaces, and electrodes are positioned to represent two suitable velocity potential surfaces up- and down-stream of the duct. To represent a sector of an axi-symmetric duct the base of the tank must be inclined at 3°-5° to the horizontal and the water line on the tank base then represents the axis of symmetry.

Effect of Hull Discretization on Steady Free-Surface Flow Calculations

1995 ◽  
Vol 39 (01) ◽  
pp. 42-52
Author(s):  
Dane Hendrix ◽  
Francis Noblesse
Keyword(s):  
Free Surface ◽  
Aspect Ratio ◽  
Potential Flow ◽  
Velocity Potential ◽  
Free Surface Flow ◽  
Surface Flow ◽  
Wave Profile ◽  
Source Strength ◽  
Hull Form ◽  
Piecewise Constant

Steady free-surface potential flow about a mathematically defined hull form is considered. The flow is defined using the slender-ship approximation. The hull form is approximated by means of flat triangular panels within which the source strength is piecewise constant. Convergence of the computed velocity potential, wave profile, and lift, moment and drag with respect to hull discretization (size and aspect ratio of panels) is evaluated.

The three-dimensional interaction of a streamwise vortex with a large-chord lifting surface: theory and experiment

1996 ◽  
Vol 322 ◽  
pp. 51-79 ◽  
Author(s):  
Gustavo C. R. Bodstein ◽  
Albert R. George ◽  
C.-Y. Hui
Keyword(s):  
Boundary Layer ◽  
Pressure Distribution ◽  
Potential Flow ◽  
Velocity Potential ◽  
Lateral Displacement ◽  
Three Dimensional ◽  
Leading Edge ◽  
Vortex Filament ◽  
Soap Bubble ◽  
Lifting Surface

The three-dimensional vortex flow that develops around a close-coupled canard-wing configuration is characterized by a strong interaction between the vortex generated at the canard and the aircraft wing. In this paper, a theoretical potential flow model is devised to uncover the basic structure of the pressure and velocity distributions on the wing surface. The wing is modelled as a semi-infinite lifting-surface set at zero angle of attack. It is assumed that the vortex is a straight vortex filament, with constant strength, and lying in the freestream direction. The vortex filament is considered to be orthogonal to the leading-edge, passing a certain height over the surface. An incompressible and steady potential flow formulation is created based on the three-dimensional Laplace's equation for the velocity potential. The boundary-value problem is solved analytically using Fourier transforms and the Wiener-Hopf technique. A closed-form solution for the velocity potential is determined, from which the velocity and pressure distributions on the surface and a vortex path correction are obtained. The model predicts an anti-symmetric pressure distribution along the span in region near the leading-edge, and a symmetric pressure distribution downstream from it. The theory also predicts no vertical displacement of the vortex, but a significant lateral displacement. A set of experiments is carried out to study the main features of the flow and to test the theoretical model above. The experimental results include helium-soap bubble and oil-surface flow pattern visualization, as well as pressure measurements. The comparison shows good agreement only for a weak interaction case, whereas for the case where the interaction is strong, secondary boundary-layer separation and vortex breakdown are observed to occur, mainly owing to the strong vortex-boundary layer interaction. In such a case the model does not agree well with the experiments.

Self-Equilibrated Singular Solutions of a Complete Spherical Shell: Classical Theory Approach

1989 ◽  
Vol 56 (1) ◽  
pp. 105-112 ◽  
Author(s):  
Nikolaos Simos ◽  
Ali M. Sadegh
Keyword(s):  
Spherical Shell ◽  
Closed Form ◽  
Mathematical Analysis ◽  
Stress Function ◽  
Elastic Response ◽  
Singular Solutions ◽  
Transverse Displacement ◽  
System Of Equations ◽  
Theory Approach ◽  
Elementary Functions

The elastic response of a complete spherical shell under the influence of concentrated loads (normal point loads, concentrated tangential loads, and concentrated surface moments) which apply in a self-equilibrating fashion is obtained. The mathematical analysis incorporates the classical uncoupled system of equations for the transverse displacement W and a stress function F. The solution formulae for all three types of singular loading are in closed form and they are expressed in terms of complex Legendre and other elementary functions. The two latter portions of the analysis are associated with a multivalued stress function F which leads to a single-valued stress and displacement formulae. The intricacies of the solutions and their singular character are also discussed. Lastly, some representative shell problems are evaluated.

scholarly journals A Finite Element Computer Code to Calculate Full 3–D Compressible Potential Flow in Turbomachinery

1984 ◽  
Author(s):  
Doğan Güneş ◽  
Muhsin Mengütürk
Keyword(s):  
Finite Element ◽  
Potential Flow ◽  
Compressible Flows ◽  
Velocity Potential ◽  
Three Dimensional ◽  
Axial Flow ◽  
Computer Code ◽  
Turbine Rotor ◽  
Electric Utility ◽  
Quadratic Interpolation

A Finite element computer code is presented for calculation of three-dimensional compressible flows in turbomachinery under the steady and potential flow limitations. The method used relies upon a variational statement equivalent to the classical velocity potential formulation of this problem. The solution domain is discretized by using hexahedral superelements each composed of six ten-node tetrahedral elements enabling quadratic interpolation of velocity potential. The code offers the flexibility of choosing a combination of subparametric and isoparametric elements. Application of the code to the Gostelow cascade, an experimental turbine stator, the first stage stator and rotor of an electric utility axial flow turbine and finally to a mixed flow turbine rotor are presented. The validity of the results are established by comparison with the exact solution, experimental data and calculations by other numerical methods.

Lateral Force and Moment on Ships in Oblique Waves

1962 ◽  
Vol 6 (02) ◽  
pp. 40-50
Author(s):  
Pung Nien Hu
Keyword(s):  
Differential Equation ◽  
Free Surface ◽  
Velocity Potential ◽  
Lateral Force ◽  
Exciting Force ◽  
The Body ◽  
Regular Waves ◽  
Oblique Waves ◽  
Added Masses ◽  
Slender Bodies

A method for evaluating the exciting force and moment on surface ships as well as on fully submerged bodies in oblique waves is developed, based on the assumptions of long regular waves and slender bodies. The differential equation, together with the boundary conditions, for each component of the velocity potential is studied. Momentum theorems for slender-body sections are derived and applied to the evaluation of stripwise force and moment on bodies in the presence of a free surface. The result is found to be directly related to the added masses of the body sections. Lateral added masses of body sections in the presence of a free surface are investigated in detail and numerical values are presented for Lewis sections.

Vibration of a Group of Circular Cylinders in a Confined Fluid

1977 ◽  
Vol 44 (2) ◽  
pp. 213-217 ◽  
Author(s):  
Ho Chung ◽  
Shoei-sheng Chen
Keyword(s):  
Free Vibration ◽  
Analytical Method ◽  
Potential Flow ◽  
Coupling Effect ◽  
Circular Cylinders ◽  
Two Dimensional ◽  
Eccentric Cylinders ◽  
Confined Fluid ◽  
Added Masses ◽  
Fluid Coupling

This paper presents an analytical method for evaluating the hydrodynamic masses of a group of circular cylinders immersed in a fluid contained in a cylinder. The analysis is based on the two-dimensional potential flow theory. The fluid coupling effect among cylinders is taken into account; self and mutual-added masses for both inner and outer cylinders are evaluated. Based on the proposed method, the free vibration of two eccentric cylinders with a fluid-filled gap is analyzed as an example.

Note on the swimming of an elongated body in a non-uniform flow

2013 ◽  
Vol 716 ◽  
pp. 616-637 ◽  
Author(s):  
Fabien Candelier ◽  
Mathieu Porez ◽  
Frederic Boyer
Keyword(s):  
Cross Sections ◽  
Potential Flow ◽  
Velocity Potential ◽  
Fluid Velocity ◽  
The Body ◽  
Curvilinear Coordinates ◽  
Elliptical Cross ◽  
Fish Locomotion ◽  
Pitch Bending ◽  
Body Theory

AbstractThis paper presents an extension of Lighthill’s large-amplitude elongated-body theory of fish locomotion which enables the effects of an external weakly non-uniform potential flow to be taken into account. To do so, the body is modelled as a Kirchhoff beam, made up of elliptical cross-sections whose size may vary along the body, undergoing prescribed deformations consisting of yaw and pitch bending. The fluid velocity potential is decomposed into two parts corresponding to the unperturbed potential flow, which is assumed to be known, and to the perturbation flow. The Laplace equation and the corresponding Neumann’s boundary conditions governing the perturbation velocity potential are expressed in terms of curvilinear coordinates which follow the body during its motion, thus allowing the boundary of the body to be considered as a fixed surface. Equations are simplified according to the slenderness of the body and the weakness of the non-uniformity of the unperturbed flow. These simplifications allow the pressure acting on the body to be determined analytically using the classical Bernoulli equation, which is then integrated over the body. The model is finally used to investigate the passive and the active swimming of a fish in a Kármán vortex street.

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