The Small Disturbance Navier-Stokes Equations: Development of an Efficient Method for Calculating Unsteady Air Loads

2004 ◽  
pp. 278-285 ◽  
Author(s):  
A. Pechloff ◽  
M. Iatrou ◽  
C. Weishäupl ◽  
B. Laschka
Keyword(s):  
Efficient Method ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Small Disturbance ◽  
Navier Stokes Equations

The development of Poiseuille flow

1969 ◽  
Vol 38 (4) ◽  
pp. 793-806 ◽  
Author(s):  
S. Wilson
Keyword(s):  
Stokes Equations ◽  
Dominant Mode ◽  
Navier Stokes ◽  
Large Reynolds Number ◽  
Two Dimensional ◽  
Small Disturbance ◽  
Straight Channel ◽  
Fully Developed Flow ◽  
Navier Stokes Equations ◽  
Sommerfeld Equation

The problem considered is that of two-dimensional viscous flow in a straight channel. The steady Navier-Stokes equations are linearized on the assumption of small disturbance from the fully developed flow, leading to an eigenvalue equation resembling the Orr-Sommerfeld equation. This is solved in the limiting cases of small and large Reynolds numberR, and an approximate method is proposed for moderateR. The main results are (i) the dominant mode of the disturbance velocity (i.e. that which persists longest) is antisymmetrical; (ii) for largeRthere are two sequences of eigenvalues. Both sequences are asymptotically real asR→ ∞. The members of the first sequence areO(1) asR→ ∞ and are complex for all finiteR. The members of the second sequence areO(R−1) and the imaginary part isO(R−N) for allN. It is the eigenvalues of the second sequence which will dominate the flow at largeR.

Effects of stator splitter blades on aerodynamic performance of a single-stage transonic axial compressor

2020 ◽  
Vol 14 (4) ◽  
pp. 7369-7378
Author(s):  
Ky-Quang Pham ◽  
Xuan-Truong Le ◽  
Cong-Truong Dinh
Keyword(s):  
Stokes Equations ◽  
Three Dimensional ◽  
Axial Compressor ◽  
Aerodynamic Performance ◽  
Numerical Results ◽  
Single Stage ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Operating Stability ◽  
Length Coverage

Splitter blades located between stator blades in a single-stage axial compressor were proposed and investigated in this work to find their effects on aerodynamic performance and operating stability. Aerodynamic performance of the compressor was evaluated using three-dimensional Reynolds-averaged Navier-Stokes equations using the k-e turbulence model with a scalable wall function. The numerical results for the typical performance parameters without stator splitter blades were validated in comparison with experimental data. The numerical results of a parametric study using four geometric parameters (chord length, coverage angle, height and position) of the stator splitter blades showed that the operational stability of the single-stage axial compressor enhances remarkably using the stator splitter blades. The splitters were effective in suppressing flow separation in the stator domain of the compressor at near-stall condition which affects considerably the aerodynamic performance of the compressor.

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