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Figure 9. Equispaced (0/6) snapshots within a shedding cycle, Re = 150.

Figure 9 Equispaced (0/6) snapshots within a shedding cycle, Re = 150.

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Figure 1. Schematic of the computational geometry. 1.1. Statement of the problem The present paper focuses on the steady and unsteady flow past an equilateral triangular cylinder of side A placed in uniform stream. Figure 1 shows the geometry in detail. The baseline case involves an upstream length X, =9h, downstream length X;=20h and the free stream situated at a distance of H =20h. These lengths have been varied to see their effects on the quality of solution. Discussions on this issue will be taken up in Section 4.1.
Figure 1. Schematic of the computational geometry. 1.1. Statement of the problem The present paper focuses on the steady and unsteady flow past an equilateral triangular cylinder of side A placed in uniform stream. Figure 1 shows the geometry in detail. The baseline case involves an upstream length X, =9h, downstream length X;=20h and the free stream situated at a distance of H =20h. These lengths have been varied to see their effects on the quality of solution. Discussions on this issue will be taken up in Section 4.1.
Figure 2. A typical grid (230 x 160) used in the calculation: (a) full view; and (b) zoomed view.
Figure 2. A typical grid (230 x 160) used in the calculation: (a) full view; and (b) zoomed view.
Table I. Results for grid refinement test with Re= 100, X, =9, Xz = 20. 3.2. Effect of grid refinement
Table I. Results for grid refinement test with Re= 100, X, =9, Xz = 20. 3.2. Effect of grid refinement
Figure 3. Comparison with published results for square cylinder: (a) Cp and Crrms; and (b) St.
Figure 3. Comparison with published results for square cylinder: (a) Cp and Crrms; and (b) St.
Figure 4. Pressure iterations for cases with different domain size.
Figure 4. Pressure iterations for cases with different domain size.
Figure 5. (a) Amplitude of oscillations for wu and v velocities on y=0; (b) renormalized global modes; and (c) Amax for u and Cz, Atax for v as a function of Re. In wake flows the frequency of oscillations remains the same for a considerable region down- stream of the bluff body emphasizing the global nature of the flow dynamics. The experimen- tal studies of Goujon-Durand et al. [28] showed that the amplitude of the oscillations has a well defined maximum and its value and position of occurrence depends on Re while DuSek et al. [29] stressed the importance of the higher nonlinear harmonics in the dynamics of the flow. In the present study, the threshold for vortex shedding has been evaluated using the global modes of u and v velocities on y=0O. The procedure used is as follows. We have chosen 30 so-called history points on y=O at which both u and v velocity signal has been recorded. Figure 5(a) shows the peak to peak amplitude for u and v velocities at the history
Figure 5. (a) Amplitude of oscillations for wu and v velocities on y=0; (b) renormalized global modes; and (c) Amax for u and Cz, Atax for v as a function of Re. In wake flows the frequency of oscillations remains the same for a considerable region down- stream of the bluff body emphasizing the global nature of the flow dynamics. The experimen- tal studies of Goujon-Durand et al. [28] showed that the amplitude of the oscillations has a well defined maximum and its value and position of occurrence depends on Re while DuSek et al. [29] stressed the importance of the higher nonlinear harmonics in the dynamics of the flow. In the present study, the threshold for vortex shedding has been evaluated using the global modes of u and v velocities on y=0O. The procedure used is as follows. We have chosen 30 so-called history points on y=O at which both u and v velocity signal has been recorded. Figure 5(a) shows the peak to peak amplitude for u and v velocities at the history
Figure 6. Steady state streamlines: (a) Re =20; (b) Re=30; and (c) Re=35.
Figure 6. Steady state streamlines: (a) Re =20; (b) Re=30; and (c) Re=35.
Figure 7. L,—Re relationship for different bluff configurations.
Figure 7. L,—Re relationship for different bluff configurations.
Figure 10. Equispaced (0/6) snapshots within a shedding cycle, Re = 200.
Figure 10. Equispaced (0/6) snapshots within a shedding cycle, Re = 200.
Figure 11. Equispaced (0/6) snapshots within a shedding cycle, Re = 250.
Figure 11. Equispaced (0/6) snapshots within a shedding cycle, Re = 250.
Figure 12. Fundamental frequency of the Drag and Lift coefficient (shown in the inset) signal at Re = 250. The difference between these two coefficients, a measure of the friction drag, does not change appreciably in the range of Re studied in the present work. At all Re studied here, dominant frequency of drag coefficient has been seen to be twice that of the lift coefficient. This is shown in Figure 12 for Re=250 where power spectrum density (PSD) of the drag coefficient has been shown in inset. Variation of Strouhal number with Re has been shown in Figure 13(c). The frequency of vortex shedding increases linearly with Re which is prolonged to Re/Re *2, a fact observed by Kahawita and Wang [32] in their computations for trapezoidal bluff bodies. Further increase in Re causes the curve to increase at a slower rate until it reaches a flat maximum at around Re=150. After this maximum is reached, the frequency of shedding falls of. This interesting behaviour was also observed in the experiments of Okajima [33].
Figure 12. Fundamental frequency of the Drag and Lift coefficient (shown in the inset) signal at Re = 250. The difference between these two coefficients, a measure of the friction drag, does not change appreciably in the range of Re studied in the present work. At all Re studied here, dominant frequency of drag coefficient has been seen to be twice that of the lift coefficient. This is shown in Figure 12 for Re=250 where power spectrum density (PSD) of the drag coefficient has been shown in inset. Variation of Strouhal number with Re has been shown in Figure 13(c). The frequency of vortex shedding increases linearly with Re which is prolonged to Re/Re *2, a fact observed by Kahawita and Wang [32] in their computations for trapezoidal bluff bodies. Further increase in Re causes the curve to increase at a slower rate until it reaches a flat maximum at around Re=150. After this maximum is reached, the frequency of shedding falls of. This interesting behaviour was also observed in the experiments of Okajima [33].
Figure 13. Integral parameters: (a) Cp and Cp, for 10<Re<40; (b) Cp, Co, and Cy,,,, for 50<Re<250; and (c) St.
Figure 13. Integral parameters: (a) Cp and Cp, for 10<Re<40; (b) Cp, Co, and Cy,,,, for 50<Re<250; and (c) St.
Figure 14. Particle trajectories: (a) Re= 100; (b) Re=150; (c) Re=200; and (d) Re = 250.
Figure 14. Particle trajectories: (a) Re= 100; (b) Re=150; (c) Re=200; and (d) Re = 250.
Figure 15. Instantaneous streaklines: (a) Re= 100; (b) Re=150; (c) Re=200; and (d) Re = 250.
Figure 15. Instantaneous streaklines: (a) Re= 100; (b) Re=150; (c) Re=200; and (d) Re = 250.
Related topics:
EngineeringFinite Volume MethodsMesh generationSingle Particle TrackingFinite Volume MethodDrag CoefficientLow Reynolds Number
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