Numerical investigation of the saturation process in an incompressible cavity flow

2017 ◽  
Vol 837 ◽  
pp. 182-209 ◽  
Author(s):  
N. Vinha ◽  
F. Meseguer-Garrido ◽  
J. de Vicente ◽  
E. Valero
Keyword(s):  
Stability Analysis ◽  
Boundary Conditions ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Numerical Study ◽  
Three Dimensional ◽  
Dynamic Mode Decomposition ◽  
Dynamic Mode ◽  
Saturation Process ◽  
Wall Boundary Conditions

A numerical study of the saturation process inside a rectangular open cavity is presented. Previous experiments and linear stability analysis of the problem completely described the flow in its onset, as well as in a saturated regime, characterized by three-dimensional centrifugal modes. The morphology of the modes found in the experiments matched the ones predicted by linear analysis, but with a shift in frequencies for the oscillating modes. A three-dimensional incompressible direct numerical simulation (DNS) is employed for a detailed investigation of the saturation process inside a cavity with dimensions similar to the one used in the experiments, to further explain the behaviour of these modes. In this work, periodic boundary conditions are first imposed to better understand the effect of the saturation process far from the walls. Then, the effects of spanwise solid wall boundary conditions are investigated with a DNS reproducing the full dynamics of the experiments. The main flow structures are identified using the dynamic mode decomposition technique and compared with previous experimental and linear stability analysis results. The main reason for the aforementioned shift in frequency is explained in this paper, as it is a function of the velocity of the main recirculating vortex.

Global linear stability analysis of jets in cross-flow

2017 ◽  
Vol 828 ◽  
pp. 812-836 ◽  
Author(s):  
Marc A. Regan ◽  
Krishnan Mahesh
Keyword(s):  
Stability Analysis ◽  
Shear Layer ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Velocity Ratio ◽  
Cross Flow ◽  
Dynamic Mode Decomposition ◽  
Dynamic Mode ◽  
Mode Decomposition ◽  
Implicitly Restarted Arnoldi

The stability of low-speed jets in cross-flow (JICF) is studied using tri-global linear stability analysis (GLSA). Simulations are performed at a Reynolds number of 2000, based on the jet exit diameter and the average velocity. A time stepper method is used in conjunction with the implicitly restarted Arnoldi iteration method. GLSA results are shown to capture the complex upstream shear-layer instabilities. The Strouhal numbers from GLSA match upstream shear-layer vertical velocity spectra and dynamic mode decomposition from simulation (Iyer & Mahesh, J. Fluid Mech., vol. 790, 2016, pp. 275–307) and experiment (Megerian et al., J. Fluid Mech., vol. 593, 2007, pp. 93–129). Additionally, the GLSA results are shown to be consistent with the transition from absolute to convective instability that the upstream shear layer of JICFs undergoes between $R=2$ to $R=4$ observed by Megerian et al. (J. Fluid Mech., vol. 593, 2007, pp. 93–129), where $R=\overline{v}_{jet}/u_{\infty }$ is the jet to cross-flow velocity ratio. The upstream shear-layer instability is shown to dominate when $R=2$, whereas downstream shear-layer instabilities are shown to dominate when $R=4$.

Secondary motion in convection layers generated by lateral heating of a solute gradient

2002 ◽  
Vol 455 ◽  
pp. 1-19 ◽  
Author(s):  
CHO LIK CHAN ◽  
WEN-YAU CHEN ◽  
C. F. CHEN
Keyword(s):  
Stability Analysis ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Fluid Motion ◽  
Three Dimensional ◽  
Convection Cell ◽  
Experimental Conditions ◽  
Longitudinal Plane ◽  
Secondary Motion ◽  
Solute Gradient

The three-dimensional motion observed by Chen & Chen (1997) in the convection cells generated by sideways heating of a solute gradient is further examined by experiments and linear stability analysis. In the experiments, we obtained visualizations and PIV measurements of the velocity of the fluid motion in the longitudinal plane perpendicular to the imposed temperature gradient. The flow consists of a horizontal row of counter-rotating vortices within each convection cell. The magnitude of this secondary motion is approximately one-half that of the primary convection cell. Results of a linear stability analysis of a parallel double-diffusive flow model of the actual ow show that the instability is in the salt-finger mode under the experimental conditions. The perturbation streamlines in the longitudinal plane at onset consist of a horizontal row of counter-rotating vortices similar to those observed in the experiments.

A Study of the Lateral Stability of Railroad Vehicles Using a Nonlinear Constrained Multibody Formulation

2001 ◽  
Author(s):  
Davide Valtorta ◽  
Khaled E. Zaazaa ◽  
Ahmed A. Shabana ◽  
Jalil R. Sany
Keyword(s):  
Stability Analysis ◽  
Linear Stability ◽  
Linear Theory ◽  
Linear Stability Analysis ◽  
Numerical Study ◽  
Operating Conditions ◽  
Lateral Stability ◽  
Railroad Vehicles ◽  
Contact Formulation ◽  
The Stability

Abstract The lateral stability of railroad vehicles travelling on tangent tracks is one of the important problems that has been the subject of extensive research since the nineteenth century. Early detailed studies of this problem in the twentieth century are the work of Carter and Rocard on the stability of locomotives. The linear theory for the lateral stability analysis has been extensively used in the past and can give good results under certain operating conditions. In this paper, the results obtained using a linear stability analysis are compared with the results obtained using a general nonlinear multibody methodology. In the linear stability analysis, the sources of the instability are investigated using Liapunov’s linear theory and the eigenvalue analysis for a simple wheelset model on a tangent track. The effects of the stiffness of the primary and secondary suspensions on the stability results are investigated. The results obtained for the simple model using the linear approach are compared with the results obtained using a new nonlinear multibody based constrained wheel/rail contact formulation. This comparative numerical study can be used to validate the use of the constrained wheel/rail contact formulation in the study of lateral stability. Similar studies can be used in the future to define the limitations of the linear theory under general operating conditions.

scholarly journals Linear stability of confined flow around a 180-degree sharp bend

2017 ◽  
Vol 822 ◽  
pp. 813-847 ◽  
Author(s):  
Azan M. Sapardi ◽  
Wisam K. Hussam ◽  
Alban Pothérat ◽  
Gregory J. Sheard
Keyword(s):  
Reynolds Number ◽  
Stability Analysis ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Critical Reynolds Number ◽  
Three Dimensional ◽  
Base Flow ◽  
Two Dimensional ◽  
Two Dimensional Flow ◽  
The Stability

This study seeks to characterise the breakdown of the steady two-dimensional solution in the flow around a 180-degree sharp bend to infinitesimal three-dimensional disturbances using a linear stability analysis. The stability analysis predicts that three-dimensional transition is via a synchronous instability of the steady flows. A highly accurate global linear stability analysis of the flow was conducted with Reynolds number $\mathit{Re}<1150$ and bend opening ratio (ratio of bend width to inlet height) $0.2\leqslant \unicode[STIX]{x1D6FD}\leqslant 5$. This range of $\mathit{Re}$ and $\unicode[STIX]{x1D6FD}$ captures both steady-state two-dimensional flow solutions and the inception of unsteady two-dimensional flow. For $0.2\leqslant \unicode[STIX]{x1D6FD}\leqslant 1$, the two-dimensional base flow transitions from steady to unsteady at higher Reynolds number as $\unicode[STIX]{x1D6FD}$ increases. The stability analysis shows that at the onset of instability, the base flow becomes three-dimensionally unstable in two different modes, namely a spanwise oscillating mode for $\unicode[STIX]{x1D6FD}=0.2$ and a spanwise synchronous mode for $\unicode[STIX]{x1D6FD}\geqslant 0.3$. The critical Reynolds number and the spanwise wavelength of perturbations increase as $\unicode[STIX]{x1D6FD}$ increases. For $1<\unicode[STIX]{x1D6FD}\leqslant 2$ both the critical Reynolds number for onset of unsteadiness and the spanwise wavelength decrease as $\unicode[STIX]{x1D6FD}$ increases. Finally, for $2<\unicode[STIX]{x1D6FD}\leqslant 5$, the critical Reynolds number and spanwise wavelength remain almost constant. The linear stability analysis also shows that the base flow becomes unstable to different three-dimensional modes depending on the opening ratio. The modes are found to be localised near the reattachment point of the first recirculation bubble.

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