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Boundary integral simulation of a finite inviscid jet
Published in C Constanda, J Saranen, S Seikkala, Integral methods in science and engineering, 2020
The model that has been developed assumes incompressibility and irrotationality, hence potential flow. The following are the non-dimensional equations, using the unsteady Bernoulli relation, and taking surface pressure equal to γκ, where κ is curvature and γ is surface tension. The equations have been non-dimensionalised using γ, density ρ, and nozzle radius a: u=∇ϕ,∇2ϕ=0,DϕDt−12|∇ϕ|2+κ=P∞(t).
Fracture Mechanics and Dynamics
Published in K.T. Chau, Applications of Differential Equations in Engineering and Mechanics, 2019
Sneddon (1951) also demonstrated that dual integral equations can be used to solve fluid mechanics problems. That is not surprising as we have already seen that the dual integral equations are for harmonic functions that satisfy the Laplace equation. Naturally, ideal incompressible flow of fluids (or so-called potential flow) is governed by the Laplace equation through the use of velocity potential. Section 31.3 of Sneddon (1951) discussed the potential flow through a circular aperture in a plane rigid screen using dual integral formulation. The recent book by Duffy (2008) provided a list of mixed boundary value problems that can be solved using dual integral formulation. Sneddon (1951) also solved the indentation problems (both plane and 3-D punches) using dual integral formulation. More discussion of dual integral equations can be found in Keer (1968).
Hydrodynamic forces on low-head gates
Published in Eduard Naudascher, Hydrodynamic Forces, 2017
The streamline pattern, in turn, depends on the geometry of the flow boundaries (solid and free!) and a variety of flow parameters (e.g. Reynolds number Re, Weber number We). In many cases (e.g. high Reynolds-number flow without separation) the streamline pattern can be obtained from potential-flow analysis as a function of solid boundary geometry and boundary conditions along the free surfaces. Note, however, that one needs Ch, and hence v/vo along the skinplate, i.e. along the flow boundary. The values for v/v0 obtained from Equation 4.9 refer to the mean velocities averaged across the streamtube considered. In other words, v is the mean velocity across Δn rather than along the boundary. It will be necessary, therefore, to construct a finer net of streamlines and potential lines near the skinplate, particularly in regions of large curvature. In this way one finds that in stagnation points such as s in Figure 4.5, v = 0 and, hence, Ch = 1.0 (see Equation 4.7).
A partitioned solution approach for the simulation of the dynamic behaviour of flexible marine propellers
Published in Ship Technology Research, 2020
L. Radtke, T. Lampe, M. Abdel-Maksoud, A. Düster
The method utilised for the simulation of the hydrodynamic effects is the potential theory based approach panMARE (see e.g. Berger et al. 2014; Netzband et al. 2017). Accordingly, the fluid is assumed as incompressible, irrotational and non-viscous. The potential flow can, therefore, be computed by solving the Laplace equationfor the total velocity potential Φ. The unsteady Bernoulli equation is used to obtain the total pressureTherein φ and denote the disturbed and the free stream potential, respectively, such that . The constants and refer to the (atmospheric) reference pressure and the reference height (where prevails, here it denotes the position of the free water surface), respectively. The fluid density is denoted by ρ, g is the gravitational constant.
Hydro-elastic vibration analysis of functionally graded rectangular plate in contact with stationary fluid
Published in European Journal of Computational Mechanics, 2018
Shahrouz Yousefzadeh, Ashkan Akbari, Mohammad Najafi
Generally, the fluid pressure acting upon the structure is expressed as a function of acceleration. The fluid force matrices are superimposed onto the structural matrices to form the dynamic equations of a coupled fluid-structure system. Linear potential flow is applied to describe the fluid effect that leads to the fluid dynamic forces. The mathematical model is based on the following assumptions: (i) the fluid flow is potential; (ii) vibration is linear; (iii) since the flow is inviscid, there is no shear, and the fluid pressure is purely normal to the plate wall; and (v) the fluid is incompressible. Based on the aforementioned hypothesis, the potential function, which satisfies the Laplace equation, is expressed in the Cartesian coordinate system as (Myung & Young, 2003):
Numerical solution for a ship-wave problem in a two-layer fluid using a double-model linearised interface condition
Published in Ships and Offshore Structures, 2018
Masaaki Sano, Yoshinori Kunitake
A ship wave-making problem is formulated by potential flow theory. The fundamental assumptions are as follows: The two layers of fluid do not mix together.The viscous effect on the wave-making is neglected.Flow in each layer is inviscid, incompressible and irrotational (potential flow).The ship does not intersect the interface.