Undergraduate Graduation Project & Erasmus+ Scholarship Programme*

Abstract

This paper combines the Rans equation solver TAU and the BiGloble stability analysis theory to analyze the flow instability and extract the main model of it.

Firstly, a validation case of cylinder flow at Re = 60 is simulated and the results of the Strouhal number match the experience data. The main model is extracted as well.

Secondly, a NACA0012 airfoil is studied in a similar method. A set of simulations are performed under a range of angle of attack from 0 to 19 degrees. The critical angle of separation is identified as 18.9 degrees. And the flow topology at 4 angle of attacks is visualised, the main model of the flow at critical angle of attack is also extracted.

Thirdly, a transonic injector case is simulated. Solutions for two kinds of injectors, with straight and rounded trailing edge respectively, are compared with each other. Bifurcation of the bleeding jet-flow and shock waves appear at both cases. While stability analysis failed to performed for certain reasons.

Key pictures and conclusions

validation case of cylinder flow

unstable eigenvalue and mode ($V_x$) for cylinder flow at $Re$ = 60

A computation of cylinder flow is proven to be accurate and the instability analysis successfully specifies the dominant model that affect the asymmetric phenomena. As a result, the TAU tools are successfully proven to be valid through a validation case

NACA0012 airfoil at critical AOA

unstable eigenvalue and mode ($V_x$) for NACA0012 airfoil at critical AOA=18.9$\degree$

  1. steady flow simulation method is applied to calculate of lift and drag coefficients, calculated critical AOA meets well with the standard result.
  2. unsteady flow simulation is adopted at critical AOA
  3. Fast Fourier Transform (FFT) is performed to obtaining the main oscillation amplitude frequency. With a calculation of Strouhal number as 0.912, the imaginary part of the eigenvalue related to the eigenmode with the maximum energy is obtained as Wi = 5.732.
  4. Finally, with stability analysis, the dominant model is extracted and visualised as above.

transonic injector

temporal_snapshot_of_straight_case.png

Attempts of global stability analysis to this regime is also performed. Unfortunately, the mean flow is impossible to acquire because the injector wake shows no sign of periodical but a chaotic oscillation.

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