scholarly journals An exact solution of the Navier-Stokes equations for swirl flow models through porous pipes

2006 ◽  
Author(s):  
N. Vlachakis ◽  
A. Fatsis ◽  
A. Panoutsopoulou ◽  
E. Kioussis ◽  
M. Kouskouti ◽  
...  
Keyword(s):  
Exact Solution ◽  
Stokes Equations ◽  
Swirl Flow ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Flow Models

Rotordynamic Coefficients of Labseals for Turbines: Comparing CFD Results With Experimental Data on a Comb-Grooved Labyrinth

2005 ◽  
Author(s):  
Joachim Schettel ◽  
Martin Deckner ◽  
Klaus Kwanka ◽  
Bernd Lu¨neburg ◽  
Rainer Nordmann
Keyword(s):  
Stokes Equations ◽  
Labyrinth Seal ◽  
Navier Stokes ◽  
Test Rig ◽  
Navier Stokes Equations ◽  
Detailed Model ◽  
Identification Methods ◽  
Rotating Speed ◽  
Flow Models ◽  
Rotordynamic Coefficients

The main goal of this paper is to improve identification methods for rotordynamic coefficients of labseals for turbines. This aim was achieved in joint effort of the Technische Universita¨t Mu¨nchen, working on experimental identification methods for rotordynamic coefficients, the University of Technology, Darmstadt, working on prediction methods, and Siemens AG, realizing the results. The paper focuses on a short comb-grooved labyrinth seal. Short labseals, amongst others the above mentioned comb-grooved labyrinth, were examined. by means of a very accurately measuring test rig. The rotor was brought into statically eccentric positions relative to the stator, in order to measure the circumferential pressure distribution as a function of pressure, rotating speed and entrance swirl. The data collected were used to validate results obtained with a numerical method. The theoretical approach is based on a commercial CFD tool, which solves the Navier Stokes equations using numerical methods. As a result, a detailed model of the flow within the test rig is produced. The efforts of computation here are greater than when compared with the likewise wide-spread Bulk flow models, however improved accuracy and flexibility is expected. As the validation of the model is successful, it could then be used to gain further insight in the flow within the seal, and to understand the results better. This showed that rotordynamic coefficients of labseals gained from different test rigs are not necessarily comparable.

An exact solution of navier‐stokes equations for conical tubes

1980 ◽  
Vol 3 (2) ◽  
pp. 129-131
Author(s):  
A. Raptis ◽  
C. Massalas ◽  
N. Kafousias
Keyword(s):  
Exact Solution ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations

An Exact Solution of the Unsteady Navier-Stokes Equations Resulting From a Stretching Surface

1994 ◽  
Vol 61 (3) ◽  
pp. 629-633 ◽  
Author(s):  
S. H. Smith
Keyword(s):  
Exact Solution ◽  
Stokes Equations ◽  
Limited Range ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Stretching Surface ◽  
Navier Stokes Equations ◽  
Short Period ◽  
Two Dimensional Flow ◽  
Surrounding Fluid

When a stretching surface is moved quickly, for a short period of time, a pulse is transmitted to the surrounding fluid. Here we describe an exact solution in terms of a similarity variable for the Navier-Stokes equations which represents the effect of this pulse for two-dimensional flow. The unusual feature is that this solution is only valid for a limited range of the Reynolds number; outside this domain unbounded velocities result.

Particle dynamics and mixing in a viscously decaying shear layer

1991 ◽  
Vol 227 ◽  
pp. 211-244 ◽  
Author(s):  
E. Meiburg ◽  
P. K. Newton
Keyword(s):  
Exact Solution ◽  
Blow Up ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Core Size ◽  
Mixing Processes ◽  
Navier Stokes Equations ◽  
Interface Generation ◽  
Self Similar ◽  
Detailed Picture

We study the mixing of fluid in a viscously decaying row of point vortices. To this end, we employ a simplified model based on Stuart's (1967) one-parameter family of solutions to the steady Euler equations. Our approach relates the free parameter to a vortex core size, which grows in time according to the exact solution of the Navier-Stokes equations for an isolated vortex. In this way, we approach an exact solution for small values of t/Re. We investigate how the growing core size leads to a shrinking of the cat's eye and hence to fluid leaking out of the trapped region into the free streams. In particular, we observe that particles initially located close to each other in neighbouring intervals along the streamwise direction escape from the cat's eye near opposite ends. The size of these intervals scales with the inverse square root of the Reynolds number. We furthermore examine the particle escape times and observe a self-similar blow-up for the particles near the border between two adjacent intervals. This can be explained on the basis of a simple stagnation-point flow. An investigation of interface generation shows that viscosity leads to an additional factor proportional to time in the growth rates. Numerical simulations confirm the above results and give a detailed picture of the underlying mixing processes.

Flow Due to Eccentric Rotating a Porous Disk and a Fluid at Infinity

1976 ◽  
Vol 43 (2) ◽  
pp. 203-204 ◽  
Author(s):  
M. Emin Erdogan
Keyword(s):  
Exact Solution ◽  
Velocity Distribution ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Porous Disk ◽  
Navier Stokes Equations ◽  
Uniform Suction ◽  
Asymptotic Profile

An exact solution of the steady three-dimensional Navier-Stokes equations is obtained for the case of flow due to noncoaxially rotations of a porous disk and a fluid at infinity. It is shown that for uniform suction or uniform blowing at the disk an asymptotic profile exists for the velocity distribution.

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