scholarly journals Stability Analysis for an Interface with a Continuous Internal Structure

Fluids ◽  
2021 ◽  
Vol 6 (1) ◽  
pp. 18
Author(s):  
Mikhail Modestov

A general method for solving a linear stability problem of an interface with a continuous internal structure is described. Such interfaces or fronts are commonly found in various branches of physics, such as combustion and plasma physics. It extends simplified analysis of an infinitely thin discontinuous front by means of numerical integration along the steady-state solution. Two examples are presented to demonstrate the application of the method for 1D pulsating instability in magnetic deflagration and 2D Darrieus–Landau instability in a laser ablation wave.

1965 ◽  
Vol 23 (4) ◽  
pp. 715-735 ◽  
Author(s):  
T. H. Hughes ◽  
W. H. Reid

This paper presents a discussion of some aspects of the linear stability problem for the asymptotic suction profile. An exact solution of the inviscid equation is first obtained in terms of the usual hypergeometric function and its analytical continuation. This exact solution provides both a corrected version of an earlier treatment by Freeman and an independent check on the more general method suggested for solving the inviscid equation numerically. Various approximations to the characteristic equation, and hence to the curve of neutral stability, are then considered. In particular, it is found that, in a consistent asymptotic treatment of the related adjoint problem, at least one viscous correction to the singular inviscid solution must be considered. Based on the present results for the adjoint problem, it is suggested that Tollmien's original treatment of the viscous corrections must be slightly modified.


2010 ◽  
Vol 52 (2) ◽  
pp. 139-145 ◽  
Author(s):  
HÜSEYİN MERDAN

AbstractWe present a stability analysis of steady-state solutions of a continuous-time predator–prey population dynamics model subject to Allee effects on the prey population which occur at low population density. Numerical simulations show that the system subject to an Allee effect takes a much longer time to reach its stable steady-state solution. This result differs from that obtained for the discrete-time version of the same model.


Author(s):  
Gary A. Glatzmaier

This chapter describes a linear stability analysis (that is, solving for the critical Rayleigh number Ra and mode) that allows readers to check their linear codes against the analytic solution. For this linear analysis, each Fourier mode n can be considered a separate and independent problem. The question that needs to be addressed now is under what conditions—that is, what values of Ra, Prandtl number Pr, and aspect ratio a—will the amplitude of the linear solution grow with time for a given mode n. This is a linear stability problem. The chapter first introduces the linear equations before discussing the linear code and explaining how to find the critical Rayleigh number; in other words, the value of Ra for a and Pr that gives a solution that neither grows nor decays with time. It also shows how the linear stability problem can be solved using an analytic approach.


Author(s):  
Mark-Robert Kalus ◽  
Riskyanti Lanyumba ◽  
Stephan Barcikowski ◽  
Bilal Gökce

AbstractOver the past decade, laser ablation in liquids (LAL) was established as an innovative nanoparticle synthesis method obeying the principles of green chemistry. While one of the main advantages of this method is the absence of stabilizers leading to nanoparticles with “clean” ligand-free surfaces, its main disadvantage is the comparably low nanoparticle production efficiency dampening the sustainability of the method and preventing the use of laser-synthesized nanoparticles in applications that require high amounts of material. In this study, the effects of productivity-dampening entities that become particularly relevant for LAL with high repetition rate lasers, i.e., persistent bubbles or colloidal nanoparticles (NPs), on the synthesis of colloidal gold nanoparticles in different solvents are studied. Especially under batch ablation conditions in highly viscous liquids with prolonged ablation times both shielding entities are closely interconnected and need to be disentangled. By performing liquid flow-assisted nanosecond laser ablation of gold in liquids with different viscosity and nanoparticle or bubble diffusivity, it is shown that a steady-state is reached after a few seconds with fixed individual contributions of bubble- and colloid-induced shielding effects. By analyzing dimensionless numbers (i.e., Axial Peclet, Reynolds, and Schmidt) it is demonstrated how these shielding effects strongly depend on the liquid’s transport properties and the flow-induced formation of an interface layer along the target surface. In highly viscous liquids, the transport of NPs and persistent bubbles within this interface layer is strongly diffusion-controlled. This diffusion-limitation not only affects the agglomeration of the NPs but also leads to high local densities of NPs and bubbles near the target surface, shielding up to 80% of the laser power. Hence, the ablation rate does not only depend on the total amount of shielding matter in the flow channel, but also on the location of the persistent bubbles and NPs. By comparing LAL in different liquids, it is demonstrated that 30 times more gas is produced per ablated amount of substance in acetone and ethylene glycol compared to ablation in water. This finding confirms that chemical effects contribute to the liquid’s decomposition and the ablation yield as well. Furthermore, it is shown that the highest ablation efficiencies and monodisperse qualities are achieved in liquids with the lowest viscosities and gas formation rates at the highest volumetric flow rates.


1990 ◽  
Vol 216 ◽  
pp. 255-284 ◽  
Author(s):  
C. J. Lee ◽  
H. K. Cheng

Global interaction of the boundary layer separating from an obstacle with resulting open/closed wakes is studied for a thin airfoil in a steady flow. Replacing the Kutta condition of the classical theory is the breakaway criterion of the laminar triple-deck interaction (Sychev 1972; Smith 1977), which, together with the assumption of a uniform wake/eddy pressure, leads to a nonlinear equation system for the breakaway location and wake shape. The solutions depend on a Reynolds numberReand an airfoil thickness ratio or incidence τ and, in the domain$Re^{\frac{1}{16}}\tau = O(1)$considered, the separation locations are found to be far removed from the classical Brillouin–Villat point for the breakaway from a smooth shape. Bifurcations of the steady-state solution are found among examples of symmetrical and asymmetrical flows, allowing open and closed wakes, as well as symmetry breaking in an otherwise symmetrical flow. Accordingly, the influence of thickness and incidence, as well as Reynolds number is critical in the vicinity of branch points and cut-off points where steady-state solutions can/must change branches/types. The study suggests a correspondence of this bifurcation feature with the lift hysteresis and other aerodynamic anomalies observed from wind-tunnel and numerical studies in subcritical and high-subcriticalReflows.


2021 ◽  
Vol 11 (4) ◽  
pp. 1395
Author(s):  
Abdelali El Aroudi ◽  
Natalia Cañas-Estrada ◽  
Mohamed Debbat ◽  
Mohamed Al-Numay

This paper presents a study of the nonlinear dynamic behavior a flying capacitor four-level three-cell DC-DC buck converter. Its stability analysis is performed and its stability boundaries is determined in the multi-dimensional paramertic space. First, the switched model of the converter is presented. Then, a discrete-time controller for the converter is proposed. The controller is is responsible for both balancing the flying capacitor voltages from one hand and for output current regulation. Simulation results from the switched model of the converter under the proposed controller are presented. The results show that the system may undergo bifurcation phenomena and period doubling route to chaos when some system parameters are varied. One-dimensional bifurcation diagrams are computed and used to explore the possible dynamical behavior of the system. By using Floquet theory and Filippov method to derive the monodromy matrix, the bifurcation behavior observed in the converter is accurately predicted. Based on justified and realistic approximations of the system state variables waveforms, simple and accurate expressions for these steady-state values and the monodromy matrix are derived and validated. The simple expression of the steady-state operation and the monodromy matrix allow to analytically predict the onset of instability in the system and the stability region in the parametric space is determined. Numerical simulations from the exact switched model validate the theoretical predictions.


Author(s):  
Michael Blocher ◽  
Markus May ◽  
Harald Schoenenborn

The influence of the steady state flow solution on the aero-elastic stability behaviour of an annular compressor cascade shall be studied in order to determine sensitivities of the aero-dynamic damping with respect to characteristic flow parameters. In this context two different flow regimes — a subsonic and a transonic case — are subject to the analysis. The pressure distributions, steady as well as unsteady, on the blade surface of the NACA3506 profile are compared to experimental data that has been gained by the Institute of Aeroelasticity of the German Aerospace Center (DLR) during several wind tunnel tests at the annular compressor cascade facility RGP-400 of the Ecole Polytechnique Fe´de´rale de Lausanne (EPFL). Whereas a certain robustness of the unsteady CFD results can be stated for the subsonic flow regime, the transonic regime proves to be very sensitive with respect to the steady state solution.


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