Bifurcation and stability analysis of a jet in cross-flow: onset of global instability at a low velocity ratio

2012 ◽  
Vol 696 ◽  
pp. 94-121 ◽  
Author(s):  
Miloš Ilak ◽  
Philipp Schlatter ◽  
Shervin Bagheri ◽  
Dan S. Henningson
Keyword(s):  
Stability Analysis ◽  
Shear Layer ◽  
Velocity Ratio ◽  
Cross Flow ◽  
Initial Growth ◽  
Low Velocity ◽  
Hairpin Vortices ◽  
Jet In Cross Flow ◽  
Periodic Behaviour ◽  
Set Up

AbstractWe study direct numerical simulations (DNS) of a jet in cross-flow at low values of the jet-to-cross-flow velocity ratio$R$. We observe that, as the ratio$R$increases, the flow evolves from simple periodic vortex shedding (a limit cycle) to more complicated quasi-periodic behaviour, before finally becoming turbulent, as seen in the simulation of Bagheriet al. (J. Fluid. Mech., vol. 624, 2009b, pp. 33–44). The value of$R$at which the first bifurcation occurs for our numerical set-up is found, and shedding of hairpin vortices characteristic of a shear layer instability is observed. We focus on this first bifurcation, and find that a global linear stability analysis predicts well the frequency and initial growth rate of the nonlinear DNS at the critical value of$R$and that good qualitative predictions about the dynamics can still be made at slightly higher values of$R$where multiple unstable eigenmodes are present. In addition, we compute the adjoint global eigenmodes, and find that the overlap of the direct and the adjoint eigenmode, also known as a ‘wavemaker’, provides evidence that the source of the first instability lies in the shear layer just downstream of the jet.

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 $R=4$.

scholarly journals Global linear analysis of a jet in cross-flow at low velocity ratios

2020 ◽  
Vol 889 ◽  
Author(s):  
Guillaume Chauvat ◽  
Adam Peplinski ◽  
Dan S. Henningson ◽  
Ardeshir Hanifi
Keyword(s):  
Cross Flow ◽  
Linear Analysis ◽  
Low Velocity ◽  
Jet In Cross Flow ◽  
Image Position

Numerical Simulation of Dual-Jet System in Cross Flow

2007 ◽  
Author(s):  
Aravind Kishore ◽  
Urmila Ghia ◽  
K. N. Ghia
Keyword(s):  
Velocity Ratio ◽  
Cross Flow ◽  
Exhaust System ◽  
Flow Structures ◽  
Complex Flow ◽  
Effective Velocity ◽  
Visual Evidence ◽  
Jet In Cross Flow ◽  
Multiple Jets ◽  
Single Jet

Numerical simulations have been carried out for a dual-jet exhaust system issuing perpendicularly into a cross flow. The jets are of equal diameter, and the distance between the jets is four times the jet diameter, with effective velocity ratio of 5 for each jet. Visual evidence of the complex flow field developed is presented. The presence of a jet inside the region of influence of another jet is seen to produce coherent flow structures different from the structures seen in the single jet in cross flow configuration. It is observed that neither the jet center planes nor the plane mid-way between the jets act as symmetry planes. Hence, modeling multiple jets with the jet centre plane as a symmetry boundary may not be consistent with the physics involved. Results show that the dual-jet system does not penetrate into the cross flow as much as a single jet does. This behavior will significantly affect performance of multiple jet systems used for improved mixing.

Adjoint sensitivity and optimal perturbations of the low-speed jet in cross-flow

2019 ◽  
Vol 877 ◽  
pp. 330-372
Author(s):  
Marc A. Regan ◽  
Krishnan Mahesh
Keyword(s):  
Shear Layer ◽  
Time Horizon ◽  
Cross Flow ◽  
Adjoint Equations ◽  
Low Speed ◽  
Time Horizons ◽  
Jet In Cross Flow ◽  
Jet Nozzle ◽  
The Cross ◽  
Short Time

The tri-global stability and sensitivity of the low-speed jet in cross-flow are studied using the adjoint equations and finite-time horizon optimal disturbance analysis at Reynolds number $Re=2000$, based on the average velocity at the jet exit, the jet nozzle exit diameter and the kinematic viscosity of the jet, for two jet-to-cross-flow velocity ratios $R=2$ and $4$. A novel capability is developed on unstructured grids and parallel platforms for this purpose. Asymmetric modes are more important to the overall dynamics at $R=4$, suggesting increased sensitivity to experimental asymmetries at higher $R$. Low-frequency modes show a connection to wake vortices. Adjoint modes show that the upstream shear layer is most sensitive to perturbations along the upstream side of the jet nozzle. Lower frequency downstream modes are sensitive in the cross-flow boundary layer. For $R=2$, optimal analysis reveals that for short time horizons, asymmetric perturbations dominate and grow along the counter-rotating vortex pair observed in the cross-section. However, as the time horizon increases, large transient growth is observed along the upstream shear layer. When $R=4$, the optimal perturbations for short time scales grow along the downstream shear layer. For long time horizons, they become hybrid modes that grow along both the upstream and downstream shear layers.

The structure of a jet in cross flow at low velocity ratios

2004 ◽  
Vol 16 (6) ◽  
pp. 2067-2087 ◽  
Author(s):  
Shridhar Gopalan ◽  
Bruce M. Abraham ◽  
Joseph Katz
Keyword(s):  
Cross Flow ◽  
Low Velocity ◽  
Jet In Cross Flow

Dynamics of Large-Scale Structures for Jets in a Crossflow

1998 ◽  
Author(s):  
Frank Muldoon ◽  
Sumanta Acharya
Keyword(s):  
Shear Layer ◽  
Large Scale ◽  
Computational Study ◽  
Near Field ◽  
Velocity Ratio ◽  
Cross Flow ◽  
Leeward Side ◽  
Mean Velocity ◽  
Large Scale Structures ◽  
Scale Structures

Results of a three dimensional unsteady computational study of a row of jets injected normal to a cross-flow are presented with the aim of understanding the dynamics of the large scale structures in the region near the jet. The jet to cross-flow velocity ratio is .5. A modified version of the computer program (INS3D) which utilizes the method of artificial compressibility is used for the computations. Results obtained clearly indicate that the near field large scale structures are extremely dynamical in nature, and undergo breakup and reconnection processes. The dynamical near field structures identified include the counter rotating vortex pair (CVP), the horseshoe vortex, wake vortex, wall vortex and the shear layer vortex. The dynamical features of these vortices are presented in this paper. The CVP is observed to be a convoluted structure interacting with the wall and horseshoe vortices. The shear layer vortices are stripped by the crossflow, and undergo pairing and stretching events in the leeward side of the jet. The wall vortex is reoriented into the upright wake system. Comparison of the predictions with mean velocity measurements is made. Reasonable agreement is observed.

Investigation of Flow and Heat Transfer of an Impinging Jet in a Cross-Flow For Cooling of a Heated Cube

2005 ◽  
Vol 128 (2) ◽  
pp. 150-156 ◽  
Author(s):  
D. Rundström ◽  
B. Moshfegh
Keyword(s):  
Heat Transfer ◽  
Channel Flow ◽  
Single Channel ◽  
Velocity Ratio ◽  
Cross Flow ◽  
Impinging Jet ◽  
Steady Increase ◽  
Heated Plate ◽  
Low Velocity ◽  
Mean Values

The current trends toward the greater functionality of electronic devices are resulting in a steady increase in the amount of heat dissipated from electronic components. Forced channel flow is frequently used to remove heat at the walls of the channel where a PCB with a few high heat dissipating components is located. The overall cooling strategy thus must not only match the overall power dissipation load, but also address the requirements of the “hot” components. In order to cool the thermal load with forced channel flow, excessive flow rates will be required. The objective of this study is to investigate if targeted cooling systems, i.e., an impinging jet in combination with a low velocity channel flow, can improve the thermal performance of the system. The steady-state three-dimensional (3-D) model is developed with the Reynolds-Stress-Model (RSM) as a turbulence model. The geometrical case is a channel with a heated cube in the middle of the base plate and two inlets, one horizontal channel flow, and one vertical impinging jet. The numerical model is validated against experimental data obtained from three well-known cases, two cases with an impinging jet on a flat heated plate, and one case with a heated cube in a single channel flow. The effects of the jet Re and jet to-cross-flow velocity ratio are investigated. The airflow pattern around the cube and the surface temperature of the cube as well as the mean values and local distributions of the heat transfer coefficient are presented.

Sign in / Sign up

Export Citation Format

Share Document