Onset Of Secondary Instability Research Articles

Parametric instability in propagating flames and the impact of hydrogen enrichment on the onset of secondary instability

A self-excited acoustic instability of laminar premixed flames propagating in an open-ended tube with a length of 700 mm and a radius of 10 mm was simulated by solving the reacting unsteady compressible Navier–Stokes equations, to understand the way of massive acoustic generation and its onset behaviors. Four fuel–air mixtures with an equivalence ratio of 1.2 were considered, namely, methane–air and methane–hydrogen–air mixtures, to identify the role of hydrogen in rich methane–air mixture. Parametric instability, which generated huge acoustic disturbance and violent flame pulsations, was observed only for a particular methane–hydrogen–air mixture with RH = 0.2, consistent with previously reported experimental observations. For the investigation of the reinforcement mechanism of acoustic instability under parametric instability, the flame surface area modulation was examined. It was found that violent subharmonic flame front pulsations could strongly modulate the flame surface area in the fundamental mode, resulting in a fluctuating heat release rate and increased thermoacoustic coupling. When hydrogen addition was small, attaining a higher level of primary instability, which is the precursor of the parametric instability, was more dominant than increasing the threshold level for the onset of the parametric instability. With larger hydrogen addition, the increase in the threshold level was more dominant than attaining a higher level of the primary instability. In particular, as the flame propagation time decreased, the level of the primary instability was saturated in larger hydrogen addition. This study elucidates the mechanism for the acoustic generation of propagating flames under the parametric instability, and the effects of hydrogen enrichment within rich methane–air mixtures.

The onset of turbulence in decelerating diverging channel flows

This work investigates the stability and transition to turbulence in a diverging channel subjected to a time-varying trapezoidal-shaped inflow boundary condition. Numerical simulations are performed for different deceleration rates and Reynolds numbers while maintaining a constant acceleration rate. The flow transition begins with two-dimensional primary instability with the formation of inflectional velocity profiles, followed by local separation and the emergence of an array of shear layer vortices. We divide simulation cases systematically into three categories based on the onset of secondary instability and the generation of streamwise vorticity. At low and medium Reynolds numbers (type I), the spanwise vortex rolls formed by inflectional instability remain two-dimensional and diffuse at the channel centre without exhibiting further instabilities. At high Reynolds numbers and deceleration rates (type II), the rolled shear layer exhibits secondary instability during the zero mean inflow phase, followed by local incipient turbulent structure formation. The streamwise vorticity that develops over the shear layer structures causes oscillations with a spanwise wavelength similar to those associated with the elliptic instability in a counter-rotating vortex pair. Using the Lamb–Oseen approximation of vortices in conjunction with the dynamic mode decomposition algorithm of the three-dimensional flow field, we captured successfully the characteristics of the secondary instability. The third category (type III) is characterized by periodic unsteady separation, secondary instability, and merging of shear layer vortices, which occurs when Reynolds numbers are high and deceleration rates are low.

Linear stability of optimal streaks in the log-layer of turbulent channel flows

The importance of secondary instability of streaks for the generation of vortical structures attached to the wall in the logarithmic region of turbulent channels is studied. The streaks and their linear instability are computed by solving equations associated with the organized motion that include an eddy-viscosity modeling the effect of incoherent fluctuations. Three friction Reynolds numbers, Reτ = 2000, 3000, and 5000, are investigated. For all flow cases, optimal streamwise vortices (i.e., having the highest potential for linear transient energy amplification) are used as initial conditions. Due to the lift-up mechanism, these optimal perturbations lead to the nonlinear growth of streaks. Based on a Floquet theory along the spanwise direction, we observe the onset of streak secondary instability for a wide range of spanwise wavelengths when the streak amplitude exceeds a critical value. Under neutral conditions, it is shown that streak instability modes have their energy mainly concentrated in the overlap layer and propagate with a phase velocity equal to the mean streamwise velocity of the log-layer. These neutral log-layer modes exhibit a sinuous pattern and have characteristic sizes that are proportional to the wall distance in both streamwise and spanwise directions, in agreement with the Townsend’s attached eddy hypothesis (A. Townsend, the structure of turbulent shear flow, Cambridge university press, 1976 2nd edition). In particular, for a distance from the wall varying from y+ ≈ 100 (in wall units) to y ≈ 0.3h, where h is half the height of the channel, the neutral log-layer modes are self-similar with a spanwise width of λz ≈ y/0.3 and a streamwise length of λx ≈ 3λz, independently of the Reynolds number. Based on this observation, it is suggested that compact vortical structures attached to the wall can be ascribed to streak secondary instabilities. In addition, spatial distributions of fluctuating vorticity components show that the onset of secondary instability is associated with the roll-up of the shear layer at the edge of the low-speed streak, similarly to a three-dimensional mixing layer.

Effect of carbon content on supersonic shear-layer instability

AbstractCarbon chemistry and the endothermic reactions it supports were previously shown to delay hypersonic boundary-layer instability and transition. The present analysis addresses the analogous problem in free shear layers and arrives at the conclusion that the lack of the acoustic trapping mechanism implies that endothermic chemistry can lead to stabilization or destabilization of the shear layer depending on the free-stream temperature. This study identifies three mechanisms by which carbon chemistry affects instability and transition. The first is rooted in the changes to the inflectional profiles caused by the visco-chemical interaction. The second is due to damping of the perturbation by finite-rate chemistry. The third is linked to streamwise relaxation which delays the onset of secondary instability of vortical structures generated by a saturated primary instability wave. Linear analysis predicts changes in growth rate lower than 30 % for Mach numbers below 5. Nonlinear parabolized stability analysis predicts significantly larger differences, depending on whether the primary or secondary instability triggers the transition onset.

Turbulence in a Sheared, Salt-Fingering-Favorable Environment: Anisotropy and Effective Diffusivities

Abstract Direct numerical simulations (DNS) of a shear layer with salt-fingering-favorable stratification have been performed for different Richardson numbers Ri and density ratios Rρ. In the absence of shear (Ri = ∞), the primary instability is square planform salt fingering, alternating cells of rising and sinking fluid. In the presence of shear, salt fingering takes the form of salt sheets, planar regions of rising and sinking fluid, aligned parallel to the sheared flow. After the onset of secondary instability, the flow becomes turbulent. The continued influence of the primary instability distorts the late-stage structure and hence biases isotropic estimates of the turbulent kinetic energy dissipation rate ε. In contrast, thermal and saline gradients evolve to become more isotropic than velocity gradients at their dissipation scales. Thus, the standard observational methodology of estimating the turbulent kinetic energy dissipation rate ε from vertical profiles of microscale gradients and assuming isotropy can underestimate its true value by a factor of 2–3, whereas estimates of thermal and saline dissipation rates using this approach are relatively accurate. Likewise, estimates of Γ from vertical profiles overestimate the true Γ by roughly a factor of 2. Salt sheets are ineffective at transporting momentum. Thermal and saline effective diffusivities decrease with decreasing Ri, despite the added energy source provided by background shear. After the transition to turbulence, the thermal to saline flux ratio and the effective Schmidt number remain close to the values predicted by linear theory.

Secondary instability in forced wavelength Görtler vortices

From an experimental study on the onset of secondary instability in forced wavelength Görtler vortices, it is found that the breakdown process of the Görtler vortices is due to the development of varicose and sinuous mode instabilities. The development of the varicose mode is characterized by the formation of horseshoe vortices that evolve downstream to form mushroom-like structures. This phenomenon is then followed by meandering of the vortices as an indication of the onset of sinuous mode instability, prior to turbulence. The spectrum analysis applied to the fluctuating velocity component shows the occurrence of peak frequency of about 150Hz, which is attributed to the fundamental secondary instability mode with its wavelength comparable to the spanwise wavelength of the primary Görtler vortices, at the location where the mushroom-like structures are clearly depicted in the mean velocity contours on the y-z plane. This confirms that the secondary instability is of the varicose type at the onset that is followed by the sinuous type downstream, prior to the breakdown of the vortices that will lead the boundary layer flow to turbulence. It is also found that the growth rate of the secondary instability observed is about 6.5 times higher than that of the Görtler instability, which leads to a breakdown of the streamwise structures and hence to turbulence.

Asymmetric squares as standing waves in rayleigh-Benard convection

Possibility of thermal convection in the form of asymmetric squares in a thin layer of Boussinesq fluids of large lateral extension confined between stress-free and conducting flat boundaries is investigated numerically using a seven mode Lorenz-like model. For fluids with moderate and high Prandtl numbers (4<sigma<20) and in a narrow window of high Rayleigh numbers (12<R/R(c)<15), which depend on Prandtl number, the stationary rolls become unstable and asymmetric squares appear as standing waves at the onset of secondary instability. Asymmetric squares, two-dimensional rolls, and again asymmetric squares with their corners shifted by half a wavelength form a stable limit cycle. The oscillatory bifurcation is supercritical.