Pulsatile Waterhammer Subject to Laminar Friction

1972 ◽  
Vol 94 (2) ◽  
pp. 467-472 ◽  
Author(s):  
D. A. P. Jayasinghe ◽  
H. J. Leutheusser
Keyword(s):  
Stokes Equations ◽  
Fluid Motion ◽  
Present Theory ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
One Dimensional ◽  
Arbitrary Velocity ◽  
Velocity Input ◽  
Special Case ◽  
Signalling Problem

This paper deals with elastic waves which may be generated in a fluid by the sudden movement of a flow boundary. In particular, an analysis of the classical piston, or signalling problem is presented for the special case of arbitrary velocity input into a stationary fluid contained in a circular, semi-infinite waveguide. The decay of the pulse, as well as the resulting flow development in the inlet region of the pipe are analyzed by means of an asymptotic expansion of the suitably nondimensionalized Navier-Stokes equations for a compressible, nonheat-conducting Newtonian fluid. The results differ significantly from those of the more conventional one-dimensional approach based on the so-called telegrapher’s equation of mathematical physics. The present theory realistically predicts the growth of a boundary layer both in time and position and, hence, it appears to represent the transient fluid motion in a manner which is physically more appealing.

Numerical Integration of the Navier-Stokes Equations for a Disk Rotating in a Housing

1985 ◽  
Vol 40 (8) ◽  
pp. 789-799 ◽  
Author(s):  
A. F. Borghesani
Keyword(s):  
Boundary Layer ◽  
Cylindrical Cavity ◽  
Boundary Layer Thickness ◽  
Stokes Equations ◽  
Fluid Motion ◽  
Rotating Disk ◽  
Infinite Medium ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Viscous Torque

The Navier-Stokes equations for the fluid motion induced by a disk rotating inside a cylindrical cavity have been integrated for several values of the boundary layer thickness d. The equivalence of such a device to a rotating disk immersed in an infinite medium has been shown in the limit as d → 0. From that solution and taking into account edge effect corrections an equation for the viscous torque acting on the disk has been derived, which depends only on d. Moreover, these results justify the use of a rotating disk to perform accurate viscosity measurements.

An investigation on the instability of a flexible liquid-filled rotor

2019 ◽  
Vol 234 (2) ◽  
pp. 165-172
Author(s):  
Guangding Wang ◽  
Huiqun Yuan ◽  
Hongyun Sun
Keyword(s):  
Stokes Equations ◽  
Fluid Motion ◽  
Coupling Model ◽  
Frequency Equation ◽  
Rotor System ◽  
System Stability ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Continuity Equations ◽  
The Stability

In this paper, the stability of a flexible rotor partially filled with liquid is investigated. On the basis of the Navier-Stokes equations for the incompressible flow, a two-dimensional analytical model is developed for fluid motion. Applying the perturbation method, the linearized Navier-Stokes and continuity equations of fluid particles are obtained. Using the boundary conditions of fluid motion, the fluid forces exerted on the rotor are calculated. According to the established fluid-structure coupling model of the rotor system, the whirling frequency equation, which is applied to determine the stability of the system, is derived. The analysis results of the system stability are compared with the theoretical ones reported in the previous study. Good agreement is shown between the results of the present analysis and the literature results. The influences of the main parameters on the dynamic stability of the rotor system are discussed.

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