Comparison of method of lines and finite difference solutions of 2-D Navier-Stokes equations for transient laminar pipe flow

2001 ◽  
Vol 53 (7) ◽  
pp. 1615-1628 ◽  
Author(s):  
Nevin Selçuk ◽  
Tanıl Tarhan ◽  
Songül Tanrıkulu
Keyword(s):  
Finite Difference ◽  
Pipe Flow ◽  
Stokes Equations ◽  
Method Of Lines ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Laminar Pipe Flow

Swirling Laminar Pipe Flow of Suspensions

1973 ◽  
Vol 40 (2) ◽  
pp. 331-336 ◽  
Author(s):  
S. K. Tung ◽  
S. L. Soo
Keyword(s):  
Pipe Flow ◽  
Stokes Equations ◽  
Fluid Phase ◽  
Navier Stokes ◽  
Swirl Ratio ◽  
Particulate Phase ◽  
Flow Properties ◽  
Navier Stokes Equations ◽  
Flow Reynolds Number ◽  
Laminar Pipe Flow

Vortex pipe flow of suspensions with laminar motion in the fluid phase is treated. The pipe consists of two smoothly joined sections, one stationary and the other rotating with a constant angular velocity. The flow properties of the fluid phase are determined by solving the complete Navier-Stokes equations numerically. The governing parameters are the flow Reynolds number and swirl ratio. Subsequent numerical solution to the momentum equations governing the particulate phase provides for both particle velocity and concentration distributions.

Laminar Pipe Flow With Mass Transfer Cooling

1965 ◽  
Vol 87 (2) ◽  
pp. 252-258 ◽  
Author(s):  
Y. Peng ◽  
S. W. Yuan
Keyword(s):  
Temperature Distribution ◽  
Pipe Flow ◽  
Energy Equation ◽  
Stokes Equations ◽  
Porous Wall ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Coolant Injection ◽  
Laminar Pipe Flow ◽  
The Heat Transfer Coefficient

The effect of foreign coolant injection at the wall on the temperature distribution of a laminar flow of a fluid with variable transport and thermodynamic properties in a porous-wall pipe has been investigated. The velocity components, mass concentration, and temperature distribution were obtained by the solution of the Navier-Stokes equations, the diffusion equation, and the energy equation. A perturbation method was used to solve the first equations for small flows through the porous wall, and the eigenvalues in the latter two equations were calculated with the aid of the CDC 1604 computer. The results from this investigation depict the significant differences in both velocity distribution and temperature distribution between the present case of hydrogen coolant and the case of air coolant [1]. The results also show that the heat transfer coefficient at the wall in the present case is considerably smaller than the case of air-coolant injection.

Stability of Hagen-Poiseuille flow with superimposed rigid rotation

1976 ◽  
Vol 73 (1) ◽  
pp. 153-164 ◽  
Author(s):  
P.-A. Mackrodt
Keyword(s):  
Poiseuille Flow ◽  
Pipe Flow ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Neutral Curve ◽  
Rigid Rotation ◽  
Transition To Turbulence ◽  
Navier Stokes ◽  
Navier Stokes Equations

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.

Investigation of the stability of boundary layers by a finite-difference model of the Navier—Stokes equations

1976 ◽  
Vol 78 (2) ◽  
pp. 355-383 ◽  
Author(s):  
H. Fasel
Keyword(s):  
Finite Difference ◽  
Stability Theory ◽  
Stokes Equations ◽  
Time Dependent ◽  
Linear Stability Theory ◽  
Navier Stokes ◽  
Experimental Measurements ◽  
Navier Stokes Equations ◽  
The Stability ◽  
Small Periodic

The stability of incompressible boundary-layer flows on a semi-infinite flat plate and the growth of disturbances in such flows are investigated by numerical integration of the complete Navier–;Stokes equations for laminar two-dimensional flows. Forced time-dependent disturbances are introduced into the flow field and the reaction of the flow to such disturbances is studied by directly solving the Navier–Stokes equations using a finite-difference method. An implicit finitedifference scheme was developed for the calculation of the extremely unsteady flow fields which arose from the forced time-dependent disturbances. The problem of the numerical stability of the method called for special attention in order to avoid possible distortions of the results caused by the interaction of unstable numerical oscillations with physically meaningful perturbations. A demonstration of the suitability of the numerical method for the investigation of stability and the initial growth of disturbances is presented for small periodic perturbations. For this particular case the numerical results can be compared with linear stability theory and experimental measurements. In this paper a number of numerical calculations for small periodic disturbances are discussed in detail. The results are generally in fairly close agreement with linear stability theory or experimental measurements.

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