Simplified implicit block-bidiagonal finite difference method for solving the Navier-Stokes equations

AIAA Journal ◽  
1985 ◽  
Vol 23 (7) ◽  
pp. 1130-1132 ◽  
Author(s):  
E. von Lavante ◽  
V. S. V. Lyer
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations

scholarly journals Calculating Rotordynamic Coefficients of Seals by Finite-Difference Techniques

1987 ◽  
Vol 109 (3) ◽  
pp. 388-394 ◽  
Author(s):  
F. J. Dietzen ◽  
R. Nordmann
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Flow Field ◽  
Pressure Distribution ◽  
Difference Method ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Rotordynamic Coefficients ◽  
Finite Difference Techniques

For modelling the turbulent flow in a seal the Navier-Stokes equations in connection with a turbulence model (k-ε-model) are solved by a finite-difference method. A motion of the shaft around the centered position is assumed. After calculating the corresponding flow field and the pressure distribution, the rotordynamic coefficients of the seal can be determined. These coefficients are compared with results obtained by using the bulk flow theory of Childs [1] and with experimental results.

Gas Lubrication Analysis Method of Step-Dimpled Face Mechanical Seals

2012 ◽  
Vol 134 (1) ◽  
Author(s):  
Shaoxian Bai ◽  
Xudong Peng ◽  
Yefeng Li ◽  
Songen Sheng
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Shear Flow ◽  
Pressure Distribution ◽  
Difference Method ◽  
Reynolds Equation ◽  
Stokes Equations ◽  
Leakage Rate ◽  
Navier Stokes ◽  
Navier Stokes Equations

In solving Reynolds equation with the conventional finite difference method, keeping the flow continuity has ofen been ignored, which will lead to an analysis error in the pressure distribution and leakage rate, especially for discontinuous clearance caused by step structures such as laser surface texturing sealing surfaces. In this paper, a finite difference method is introduced to satisfy the flow continuity to solve the Reynolds equation. Then, the pressure distribution for a typical rectangular step structure is obtained via two different methods: a numerical solution of the exact full Navier-Stokes equations, and a solution of the Reynolds equation solved by the previously mentioned method. A comparison between the two solution methods illustrates that, for both pressure flow and shear flow, the pressure distribution from the new difference method is in good agreement with that from the Navier-Stokes equations, and the new difference method can reflect the characteristic of the pressure sudden-change of the shear flow at the steps. Finally, the pressure distribution and leakage rate of a step-dimpled seal face are acquired with the presented method. The results show that the presented method allows gas-lubricating analysis of mechanical face seals with discontinuous clearance, and can keep the leakage rate continuous in the radial direction.

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