Transient flow of a viscous compressible fluid in a circular tube after a sudden point impulse transverse to the axis

2010 ◽  
Vol 649 ◽  
pp. 329-340 ◽  
Author(s):  
B. U. FELDERHOF
Keyword(s):  
Compressible Fluid ◽  
Transient Flow ◽  
Stokes Equations ◽  
Circular Tube ◽  
Brownian Particle ◽  
Transverse Velocity ◽  
Slip Boundary Condition ◽  
Velocity Autocorrelation Function ◽  
Viscous Compressible Fluid ◽  
Slip Boundary

The flow of a viscous compressible fluid in a circular tube generated by a sudden impulse at a point on the axis and directed transverse to the axis is studied on the basis of the linearized Navier–Stokes equations. A no-slip boundary condition is assumed to hold on the wall of the tube. The flow behaviour differs qualitatively from that for a point impulse in the direction of the axis in that there is no coupling to a diffusive sound mode. As a consequence, the transverse velocity autocorrelation function of a suspended Brownian particle decays at long times faster than t−3/2.

Transient flow of a viscous compressible fluid in a circular tube after a sudden point impulse

2010 ◽  
Vol 644 ◽  
pp. 97-106 ◽  
Author(s):  
B. U. FELDERHOF
Keyword(s):  
Compressible Fluid ◽  
Transient Flow ◽  
Stokes Equations ◽  
Circular Tube ◽  
Slip Boundary Condition ◽  
Navier Stokes ◽  
Viscous Compressible Fluid ◽  
Navier Stokes Equations ◽  
Slip Boundary ◽  
Short Time

The flow of a viscous compressible fluid in a circular tube generated by a sudden impulse at a point on the axis is studied on the basis of the linearized Navier–Stokes equations. A no-slip boundary condition is assumed to hold on the wall of the tube. Owing to the finite velocity of sound the flow behaviour differs qualitatively from that of an incompressible fluid. The flow velocity and the pressure disturbance at any fixed point different from the source point vanish at short time and decay at long times with a t−3/2 power law.

scholarly journals Flow of a viscous compressible fluid produced in a circular tube by an impulsive point source

2011 ◽  
Vol 668 ◽  
pp. 100-112 ◽  
Author(s):  
B. U. FELDERHOF ◽  
G. OOMS
Keyword(s):  
Compressible Fluid ◽  
Numerical Scheme ◽  
Stokes Equations ◽  
Circular Tube ◽  
Slip Boundary Condition ◽  
Navier Stokes ◽  
Viscous Compressible Fluid ◽  
Navier Stokes Equations ◽  
Slip Boundary ◽  
Sudden Impulse

The flow of a viscous compressible fluid in a circular tube generated by a sudden impulse at a point on the axis is studied on the basis of the linearized Navier–Stokes equations. A no-slip boundary condition is assumed to hold on the wall of the tube. An efficient numerical scheme has been developed for the calculation of flow velocity and pressure disturbance as a function of position and time.

Transient flow of a viscous incompressible fluid in a circular tube after a sudden point impulse

2009 ◽  
Vol 637 ◽  
pp. 285-303 ◽  
Author(s):  
B. U. FELDERHOF
Keyword(s):  
Incompressible Fluid ◽  
Transient Flow ◽  
Stokes Equations ◽  
Circular Tube ◽  
Viscous Incompressible Fluid ◽  
Slip Boundary Condition ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Slip Boundary ◽  
Long Time

The flow of a viscous incompressible fluid in a circular tube generated by a sudden impulse on the axis is studied on the basis of the linearized Navier–Stokes equations. A no-slip boundary condition is assumed to hold on the wall of the tube. At short time the flow is irrotational and may be described by a potential which varies with the square root of time. At later times there is a sequence of moving and decaying vortex rings. At long times the flow velocity decays with an algebraic long-time tail. The impulse generates a time-dependent pressure difference between the ends of the tube.

Echoing in a viscous compressible fluid confined between two parallel plane walls

2010 ◽  
Vol 656 ◽  
pp. 223-230 ◽  
Author(s):  
B. U. FELDERHOF
Keyword(s):  
Compressible Fluid ◽  
Stokes Equations ◽  
Brownian Particle ◽  
Strong Dependence ◽  
Parallel Plane ◽  
Navier Stokes ◽  
Sound Pulse ◽  
Viscous Compressible Fluid ◽  
Velocity Correlation ◽  
Volume Viscosity

The dynamics of a viscous compressible fluid, confined between two parallel plane walls and excited by a sudden impulse transverse to the walls, is studied on the basis of the linearized Navier–Stokes equations. It is shown that the time-dependent flow depends strongly on the sound velocity and on the shear and volume viscosity. Under favourable conditions an echoing effect can be observed, with a sound pulse bouncing many times between the two plates. The velocity correlation function of a Brownian particle immersed in the fluid is calculated in point approximation. It shows a similar strong dependence on fluid properties.

scholarly journals Involving the Navier–Stokes equations in the derivation of boundary conditions for the lattice Boltzmann method

2011 ◽  
Vol 369 (1944) ◽  
pp. 2184-2192 ◽  
Author(s):  
Joris C. G. Verschaeve
Keyword(s):  
Boundary Condition ◽  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Stokes Equations ◽  
Slip Boundary Condition ◽  
Navier Stokes ◽  
Grid Spacing ◽  
Navier Stokes Equations ◽  
Slip Boundary ◽  
Boltzmann Method

By means of the continuity equation of the incompressible Navier–Stokes equations, additional physical arguments for the derivation of a formulation of the no-slip boundary condition for the lattice Boltzmann method for straight walls at rest are obtained. This leads to a boundary condition that is second-order accurate with respect to the grid spacing and conserves mass. In addition, the boundary condition is stable for relaxation frequencies close to two.

Transient flow of viscous compressible fluid past a heated cylinder

2016 ◽  
Vol 5 (3/4) ◽  
pp. 172 ◽  
Author(s):  
Nan Chen ◽  
Fanglin Wang ◽  
Ruifeng Hu ◽  
Nepal C. Roy ◽  
Md. Anwar Hossain
Keyword(s):  
Compressible Fluid ◽  
Transient Flow ◽  
Viscous Compressible Fluid ◽  
Heated Cylinder

scholarly journals Regularity Criteria for Navier-Stokes Equations with Slip Boundary Conditions on Non-flat Boundaries via Two Velocity Components

2019 ◽  
Vol 9 (1) ◽  
pp. 633-643
Author(s):  
Hugo Beirão da Veiga ◽  
Jiaqi Yang
Keyword(s):  
Boundary Conditions ◽  
Stokes Equations ◽  
Slip Boundary Condition ◽  
Regularity Criteria ◽  
Navier Stokes ◽  
Slip Boundary Conditions ◽  
Navier Stokes Equations ◽  
Slip Boundary ◽  
Whole Space ◽  
Space Case

Abstract H.-O. Bae and H.J. Choe, in a 1997 paper, established a regularity criteria for the incompressible Navier-Stokes equations in the whole space ℝ3 based on two velocity components. Recently, one of the present authors extended this result to the half-space case $\begin{array}{} \displaystyle \mathbb{R}^3_+ \end{array}$. Further, this author in collaboration with J. Bemelmans and J. Brand extended the result to cylindrical domains under physical slip boundary conditions. In this note we obtain a similar result in the case of smooth arbitrary boundaries, but under a distinct, apparently very similar, slip boundary condition. They coincide just on flat portions of the boundary. Otherwise, a reciprocal reduction between the two results looks not obvious, as shown in the last section below.

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