A note on viscous flow induced by half-line sources bounded by conical surfaces

Author(s):  
Prabakaran Rajamanickam ◽  
Adam D Weiss

Summary In this article, axisymmetric solutions of the Navier–Stokes equations governing the flow induced by a half-line source when the fluid domain is bounded by a conical wall are discussed. Two types of boundary conditions are identified; one in which the radial velocity along the axis is prescribed, and the other in which the radial velocity along the axis is obtained as an eigenvalue of the problem. The existence of these solutions is limited to a range of Reynolds numbers, and the transition from one case to the other is discussed in detail.

2015 ◽  
Vol 3 (2) ◽  
pp. 28-49
Author(s):  
Ridha Alwan Ahmed

       In this paper, the phenomena of vortex shedding from the circular cylinder surface has been studied at several Reynolds Numbers (40≤Re≤ 300).The 2D, unsteady, incompressible, Laminar flow, continuity and Navier Stokes equations have been solved numerically by using CFD Package FLUENT. In this package PISO algorithm is used in the pressure-velocity coupling.        The numerical grid is generated by using Gambit program. The velocity and pressure fields are obtained upstream and downstream of the cylinder at each time and it is also calculated the mean value of drag coefficient and value of lift coefficient .The results showed that the flow is strongly unsteady and unsymmetrical at Re>60. The results have been compared with the available experiments and a good agreement has been found between them


1971 ◽  
Vol 47 (2) ◽  
pp. 321-335 ◽  
Author(s):  
Jon Lee

The truncated Burgers models have a unique equilibrium state which is defined continuously for all the Reynolds numbers and attainable from a realizable class of initial disturbances. Hence, they represent a sequence of convergent approximations to the original (untruncated) Burgers problem. We have pointed out that consideration of certain degenerate equilibrium states can lead to the successive turbulence-turbulence transitions and finite-jump transitions that were suggested by Case & Chiu. As a prototype of the Navier–Stokes equations, Burgers model can simulate the initial-value type of numerical integration of the Fourier amplitude equations for a turbulent channel flow. Thus, the Burgers model dynamics display certain idiosyncrasies of the actual channel flow problem described by a truncated set of Fourier amplitude equations, which includes only a modest number of modes due to the limited capability of the computer at hand.


1976 ◽  
Vol 73 (1) ◽  
pp. 153-164 ◽  
Author(s):  
P.-A. Mackrodt

The linear stability of Hagen-Poiseuille flow (Poiseuille pipe flow) with superimposed rigid rotation against small three-dimensional disturbances is examined at finite and infinite axial Reynolds numbers. The neutral curve, which is obtained by numerical solution of the system of perturbation equations (derived from the Navier-Stokes equations), has been confirmed for finite axial Reynolds numbers by a few simple experiments. The results suggest that, at high axial Reynolds numbers, the amount of rotation required for destabilization could be small enough to have escaped notice in experiments on the transition to turbulence in (nominally) non-rotating pipe flow.


2010 ◽  
Vol 656 ◽  
pp. 189-204 ◽  
Author(s):  
ILIA V. ROISMAN

This theoretical study is devoted to description of fluid flow and heat transfer in a spreading viscous drop with phase transition. A similarity solution for the combined full Navier–Stokes equations and energy equation for the expanding lamella generated by drop impact is obtained for a general case of oblique drop impact with high Weber and Reynolds numbers. The theory is applicable to the analysis of the phenomena of drop solidification, target melting and film boiling. The theoretical predictions for the contact temperature at the substrate surface agree well with the existing experimental data.


Author(s):  
Guillermo E. Ovando ◽  
Juan C. Prince ◽  
Sandy L. Ovando

Fluid dynamics for a Newtonian fluid in the absence of body forces in a two-dimensional cavity with top and bottom curved walls was studied numerically. The vertical walls are fixed and the curved walls are in motion. The Navier-Stokes equations were solved using the finite element method combined with the operator splitting scheme. We analyzed the behaviour of the velocity fields, the vorticity fields and the velocity profiles of the fluid inside the cavity. The analysis was carried out for two different Reynolds numbers of 50 and 500 with two ratios (R = 1, −1) of the top to the bottom curved lid speed. For these values of parameters the flow is characterized by vortex formation inside the cavity. The spatial symmetry on the flow patterns are also investigated. We found that when the velocities of the top and bottom walls have opposite direction only one cell is formed in the central part of the cavity; however when the velocities of the top and bottom walls have the same direction the vortex formation inside the cavity is more complex.


Proceedings ◽  
2018 ◽  
Vol 2 (11) ◽  
pp. 577 ◽  
Author(s):  
Evangelos Karvelas ◽  
Christos Liosis ◽  
Theodoros Karakasidis ◽  
Ioannis Sarris

A possible solution for water purification from heavy metals is to capture them by using nanoparticles in microfluidic ducts. In this technique, heavy metal capture is achieved by effectively mixing two streams, a nanoparticle solution and the contaminated water. In the present work, particles and water mixing is numerically studied for various inlet velocity ratios and inflow angles of the two streams. The Navier-Stokes equations are solved for the water flow while the discrete motion of particles is evaluated by a Lagrangian method. Results showed that as the velocity ratio between the inlet streams increases, by increasing the particles solution flow, the mixing of particles with the contaminated water is increased. Thus, nanoparticles are more uniformly distributed in the duct. On the other hand, angle increase between the inflow streams ducts is found to be less significant.


2021 ◽  
Vol 930 ◽  
Author(s):  
Kartik P. Iyer ◽  
Katepalli R. Sreenivasan ◽  
P.K. Yeung

Using direct numerical simulations performed on periodic cubes of various sizes, the largest being $8192^3$ , we examine the nonlinear advection term in the Navier–Stokes equations generating fully developed turbulence. We find significant dissipation even in flow regions where nonlinearity is locally absent. With increasing Reynolds number, the Navier–Stokes dynamics amplifies the nonlinearity in a global sense. This nonlinear amplification with increasing Reynolds number renders the vortex stretching mechanism more intermittent, with the global suppression of nonlinearity, reported previously, restricted to low Reynolds numbers. In regions where vortex stretching is absent, the angle and the ratio between the convective vorticity and solenoidal advection in three-dimensional isotropic turbulence are statistically similar to those in the two-dimensional case, despite the fundamental differences between them.


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