Abstract:We perform global linear stability analysis on low-Re flow past an isolated cylinder with rounded corners. The objective of the present work is to investigate the effect of cylinder geometry (corner radius) on the stability characteristics of the flow. Our investigation sheds light on new physics that the flow can be stabilized by partially rounding the cylinder in the critical and weakly supercritical flow regimes. The flow is first stabilized and then gradually destabilized as the cylinder varies from square… Show more
“…The codes for the direct simulation and stability-sensitivity analysis have been successfully employed in our earlier works 28–41 for low- Re flow across one single or two tandem cylinders of various geometries, and the results are in good agreement with the benchmark results in the literature through careful comparisons (see, e.g., Table 1 in Zhang et al. 35 and Table 3 in Zhang et al.…”
Section: Numerical Setupsupporting
confidence: 52%
“…The two contours exhibit anti-symmetric and symmetric structures about the centerline, respectively, which are typical and consistent with the observations in a number of works of bluff body flows. 33,35–37,43 The perturbed velocities of the unstable mode cover a large space in the near- and far-wake regions that the contour is clearly visible at the downstream position as far as x ≈ 35; the perturbation is the most significant at around x ≈ 10 where the shedding vortices are fully developed. Figure 9.Contour of eigenfunction for flow across a single cylinder: (a) Re(u^) and (b) Re(v^).…”
Section: Resultsmentioning
confidence: 99%
“…The discretized equations are solved using our in-house second-order code based on fractional step method 27 which has been well verified in our earlier works. 28–41 The time step size is around 0.005 d / U 0 . The simulations are initialized with ( u, v, p ) = (1.0, 0.0, 0.0) and no artificial perturbation is added; the flow is first steady but then loses its stability as integrating in physical time and becomes perfectly time-periodic after a certain duration as reflected by the shedding vortices.…”
Section: Numerical Setupmentioning
confidence: 99%
“…Equation (6) is solved for the eigenpair ( λ ,φ^) of the most-unstable mode using our in-house code which has been extensively used in earlier works, 30,33,35–37 and the flow is unstable with at least one eigenmode with positive σ .…”
This work performs a numerical investigation on the two-dimensional flow across two circular cylinders in staggered arrangement at Re = 100. The seaparting distances between the centers of the cylinders are D/ d = 4–10 with Δ D/ d = 2 and T/ d = 0.0–2.0 with Δ T/ d = 0.5 in the streamwise and transverse directions, respectively, in which d is the cylinder diameter. Although the low- Re flow across staggered cylinders has been studied in a number of works, the authors mainly concerned about the identification and transition of various flow patterns. In this work, our objective is to quantitatively reveal the characteristics of flow unsteadiness as affected by the two separating distances. The flow unsteadiness is assessed from several aspects, including the spatial distributions and temporal variations of instantaneous flow patterns, fluctuating characteristic quantities, and fluctuating flow in the gap and in the near- and far-wake regions. To investigate the inherent instability of the flow, the global linear stability and sensitivity analysis is further carried out to demonstrate the unstable mode of perturbation growth and the critical flow patterns that destabilize the flow. The numerical results reveal that the wake flow between the two centerlines and beside the upstream cylinder is the most intensely perturbed. The flow around the downstream cylinder exhibits great fluctuation as perturbed by the destabilized shear layer of the upstream cylinder. The flow downstream of both cylinders shows multiple peak fluctuation of velocity because of the complex interactions between the destabilized shear layer and the wake vortices, resulting in the bidirectional transverse propagation of fluctuation. The stability analysis demonstrates that the unstable mode of perturbation growth is more significant in the far-wake region as the two cylinders are placed in proximity; the sensitivity analysis shows that the gap flow is crucial for the flow destabilization at small D, while the wake flow of cylinder- B is more significant for large D.
“…The codes for the direct simulation and stability-sensitivity analysis have been successfully employed in our earlier works 28–41 for low- Re flow across one single or two tandem cylinders of various geometries, and the results are in good agreement with the benchmark results in the literature through careful comparisons (see, e.g., Table 1 in Zhang et al. 35 and Table 3 in Zhang et al.…”
Section: Numerical Setupsupporting
confidence: 52%
“…The two contours exhibit anti-symmetric and symmetric structures about the centerline, respectively, which are typical and consistent with the observations in a number of works of bluff body flows. 33,35–37,43 The perturbed velocities of the unstable mode cover a large space in the near- and far-wake regions that the contour is clearly visible at the downstream position as far as x ≈ 35; the perturbation is the most significant at around x ≈ 10 where the shedding vortices are fully developed. Figure 9.Contour of eigenfunction for flow across a single cylinder: (a) Re(u^) and (b) Re(v^).…”
Section: Resultsmentioning
confidence: 99%
“…The discretized equations are solved using our in-house second-order code based on fractional step method 27 which has been well verified in our earlier works. 28–41 The time step size is around 0.005 d / U 0 . The simulations are initialized with ( u, v, p ) = (1.0, 0.0, 0.0) and no artificial perturbation is added; the flow is first steady but then loses its stability as integrating in physical time and becomes perfectly time-periodic after a certain duration as reflected by the shedding vortices.…”
Section: Numerical Setupmentioning
confidence: 99%
“…Equation (6) is solved for the eigenpair ( λ ,φ^) of the most-unstable mode using our in-house code which has been extensively used in earlier works, 30,33,35–37 and the flow is unstable with at least one eigenmode with positive σ .…”
This work performs a numerical investigation on the two-dimensional flow across two circular cylinders in staggered arrangement at Re = 100. The seaparting distances between the centers of the cylinders are D/ d = 4–10 with Δ D/ d = 2 and T/ d = 0.0–2.0 with Δ T/ d = 0.5 in the streamwise and transverse directions, respectively, in which d is the cylinder diameter. Although the low- Re flow across staggered cylinders has been studied in a number of works, the authors mainly concerned about the identification and transition of various flow patterns. In this work, our objective is to quantitatively reveal the characteristics of flow unsteadiness as affected by the two separating distances. The flow unsteadiness is assessed from several aspects, including the spatial distributions and temporal variations of instantaneous flow patterns, fluctuating characteristic quantities, and fluctuating flow in the gap and in the near- and far-wake regions. To investigate the inherent instability of the flow, the global linear stability and sensitivity analysis is further carried out to demonstrate the unstable mode of perturbation growth and the critical flow patterns that destabilize the flow. The numerical results reveal that the wake flow between the two centerlines and beside the upstream cylinder is the most intensely perturbed. The flow around the downstream cylinder exhibits great fluctuation as perturbed by the destabilized shear layer of the upstream cylinder. The flow downstream of both cylinders shows multiple peak fluctuation of velocity because of the complex interactions between the destabilized shear layer and the wake vortices, resulting in the bidirectional transverse propagation of fluctuation. The stability analysis demonstrates that the unstable mode of perturbation growth is more significant in the far-wake region as the two cylinders are placed in proximity; the sensitivity analysis shows that the gap flow is crucial for the flow destabilization at small D, while the wake flow of cylinder- B is more significant for large D.
“…The above governing equations were solved by our in-house finite-difference code, which has been employed and well validated in our earlier works for steady-state natural convection in an enclosure [9,18], transient or unsteady mixed convection in an enclosure [19,20], and forced convection across cylinders [21][22][23][24][25][26]. The numerical details are omitted here for simplicity.…”
This work presents a numerical investigation on natural convection in a circular enclosure with an internal flat plate at Ra = 106. The cross-section area of the plate was fixed at three values, H·W/D2 = 0.01, 0.04, and 0.09, in which H and W are the height and width of the plate and D is the diameter of the enclosure while the aspect ratio changes, which makes the plate vertically placed (H > W) or horizontally placed (H < W). The objective of this work was to explore the effects of the orientation and aspect ratio of the plate on the characteristics of natural convection in various aspects. The numerical results reveal that the overall heat transfer rate is higher for the vertically placed plate and increases with the cross-section area, while the width of the plate has almost no effect for the horizontally placed plate, especially for the plate with a relatively large cross-section area. Depending on the orientation and aspect ratio, there can be one primary vortex, one primary and one secondary vortex, or one secondary and two separated vortices to each side of the plate, and the thermal plume structure may appear at the sharp top corners of the plate. Consequently, local heat transfer on the surfaces of the enclosure and plate is affected. Synergy analysis reveals that the enhancement of heat transfer from the fluid circulation is the most significant at the center of the vortices and at the boundary between them.
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