scholarly journals A Bernoulli equation for potential flow of incompressible materials with an inherent material characteristic length

2013 ◽  
Vol 469 (2151) ◽  
pp. 20120641 ◽  
Author(s):  
M. B. Rubin
Keyword(s):  
Circular Cylinder ◽  
Constitutive Equations ◽  
Potential Flow ◽  
Size Dependence ◽  
Characteristic Length ◽  
Inviscid Fluid ◽  
Bernoulli Equation ◽  
Material Characteristic ◽  
Velocity Gradients ◽  
Incompressible Materials

A general simple continua can be enhanced by constitutive equations which depend on the acceleration and velocity gradients to model the effects of a material characteristic length. This paper shows that for irrotational flows of a class of incompressible materials this model yields a Bernoulli equation. Consequently, for this class of materials and flows, it is possible to satisfy the balance of linear momentum exactly, including the effect of a material characteristic length which introduces size dependence of solutions. An example of a rigid circular cylinder moving through an inviscid fluid is considered to demonstrate dependence of the motion on the size of the cylinder.

Potential Flow Solution for Crossflow Impingement of a Slot Jet on a Circular Cylinder

1976 ◽  
Vol 98 (2) ◽  
pp. 249-255 ◽  
Author(s):  
H. Miyazaki ◽  
E. M. Sparrow
Keyword(s):  
Boundary Layer ◽  
Nusselt Number ◽  
Circular Cylinder ◽  
Potential Flow ◽  
Closed Form Solution ◽  
Form Solution ◽  
Stream Velocity ◽  
Cylinder Surface ◽  
Stagnation Region ◽  
Flow Solution

A closed-form solution has been obtained for the potential flow about a circular cylinder situated in an impinging slot jet. Among other results, the potential flow solution yields the free stream velocity for the boundary layer adjacent to the cylinder surface. A basic feature of the solution is the division of the flow field into subdomains, thereby making it possible to employ harmonic functions that are appropriate to each such subdomain. The boundary conditions on the free streamline and the conditions of continuity between the subdomains are satisfied by a combination of least squares and point matching constraints. Numerical evaluation of the solution was carried out for cylinder diameters greater or equal to the nozzle width and for a range of dimensionless separation distances between the nozzle and the impingement surface. Results are presented for the velocity and pressure distributions on the cylinder surface, for the position of the free streamline, and for the velocity gradients at the stagnation point. The latter serve as input information to the Nusselt number and skin friction expressions that are given by boundary layer theory. Comparisons were made with available experimental results for the pressure distribution, velocity gradient, and Nusselt number, and good agreement was found to prevail in the stagnation region.

Two types of scale effects on the nonlinear forced vibration of axially moving nanobeams

2020 ◽  
Vol 34 (10) ◽  
pp. 2050095
Author(s):  
Jing Wang ◽  
Jianqiang Sun
Keyword(s):  
Mechanical Properties ◽  
Frequency Response ◽  
Continuum Mechanics ◽  
Forced Vibration ◽  
Characteristic Length ◽  
Scale Effects ◽  
Material Characteristic ◽  
Main Resonance ◽  
Amplitude Frequency Response ◽  
Axially Moving

Various non-classical continuum mechanics models appearing in previous studies cannot perfectly explain the mechanical properties of micro- and nanomaterials. Establishing a reasonable continuum mechanics model that comprehensively reflects the scale effect on material deformation is of great practical significance for objectively explaining the variation law of mechanical properties of micro- and nanomaterials under the combined action of different scale effects. Based on nonlocal strain gradient theory, a new scale-dependent model is proposed for axially moving nanobeams. In this study, an asymptotic expansion is performed using the multiscale time method to obtain the amplitude-frequency response curve of the equilibrium solutions for the forced vibration problem. Afterwards, the effects of various system parameters, especially the scale parameters, on the resonance curve are examined. Finally, the effects of nonlocal parameters and material characteristic length parameters on the amplitude-frequency response curves are investigated through typical numerical examples. The numerical results show that the nonlocal parameters promote the emergence of the main resonance, whereas the material characteristic length parameters suppress the emergence of the main resonance. Moreover, these parameters also affect the response amplitude and the skewness and jumping point of the amplitude-frequency characteristic curve.

Diffraction of impulsive elastic waves by a fluid cylinder

1974 ◽  
Vol 75 (3) ◽  
pp. 391-404 ◽  
Author(s):  
Ramanand Jha
Keyword(s):  
Exact Solution ◽  
Circular Cylinder ◽  
Elastic Medium ◽  
Elastic Waves ◽  
Line Source ◽  
Inviscid Fluid ◽  
Geometrical Theory ◽  
Shadow Zone ◽  
Integral Transformations ◽  
Geometrical Theory Of Diffraction

AbstractIn this paper, the problem of diffraction of an impulsive P wave by a fluid circular cylinder has been considered. The cylinder is embedded in an unbounded isotropic homogeneous elastic medium and it is filled with inviscid fluid material. The line source, giving rise to the incident front, is situated outside the cylinder parallel to its axis.The exact solution of the problem is obtained by using the method of dual integral transformations. The solution is evaluated approximately to obtain the motion on the wave front in the shadow zone of the elastic medium. Further, we interpret the approxi mate solutions in terms of Keller's geometrical theory of diffraction. Our result also gives a correction to an earlier investigation of the similar problem by Knopoff and Gilbert(s).

Potential flow and forces for incompressible viscous flow

1992 ◽  
Vol 437 (1901) ◽  
pp. 517-525 ◽  
Keyword(s):  
Circular Cylinder ◽  
Viscous Flow ◽  
Solid Body ◽  
Potential Flow ◽  
Physical Significance ◽  
Inertial Forces ◽  
Incompressible Viscous Flow ◽  
Ellipsoid Of Revolution ◽  
Finite Body ◽  
Uniform Stream

Forces on a finite body in an incompressible viscous flow are shown to be contributed by a potential flow and fluid elements of non-zero vorticity in a revealing formulation. The present study indicates that the potential flow play also a geometric role in determining the contribution of the fluid elements. Consideration is given to a solid body moving through a fluid, fluid accelerating past a solid body and a solid body which oscillates in a uniform stream. The effects of induced-mass and inertial forces appear naturally in the formulation and are separated from the contribution due to the surface vorticity and that due to the vorticity within the flow. Physical significance of the present analysis for vortical flows about a finite body is illustrated by examples, e.g. flow past a circular cylinder or an ellipsoid of revolution.

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