Experimental validation of inviscid linear stability theory applied to an axisymmetric jet

We study the development of perturbations in a submerged air jet with a round cross-section and a long laminar region (five jet diameters) at a Reynolds number of 5400 by both inviscid linear stability theory and experiments. The theoretical analysis shows that there are two modes of growing axisymmetric perturbations, which are generated by three generalized inflection points of the jet's velocity profile. To validate the results of linear stability theory, we conduct experiments with controlled axisymmetric perturbations to the jet. The characteristics of growing waves are obtained by visualization, thermoanemometer measurements and correlation analysis. Experimentally measured wavelengths, growth rates and spatial distributions of velocity fluctuations for both growing modes are in good agreement with theoretical calculations. Therefore, it is demonstrated that small perturbations to the laminar jet closely follow the predictions of inviscid linear stability theory.

Comprehensive assessment of the strength of the composite fan blade of the main ventilation of the mine

The work is devoted to the development and calculation of the strength of a new composite fan blade of the main ventilation of the mine, including the static and modal analyzes, as well as the stability analysis. The studies took into account the pre-determined aerodynamic loads on the lateral surface of the blade airfoil. The research was carried out by means of the finite element analysis of the thin-walled airfoil structure using the theory of thick multilayer shells. Estimation of the static strength was performed using the Hashin strength criterion. Analysis of the airfoil shell buckling resistance under the action of bending aerodynamic loads was performed using the methods of the linear stability theory. The modal analysis was performed taking into account the prestressed state from the action of static loads. The analysis of the research results testifies to the sufficient static and dynamic strength of the composite airfoil and the possibility of its implementation in a real rotary machine with the correct design of the fastening between the metal part of the blade root and the composite airfoil. The method of designing and analyzing the strength of the fan blade composite airfoil can be used to create new composite elements of turbomachines: the correct selection of thicknesses of different parts of the airfoil allows obtaining a uniform design with rational use of material; the optimal location of the stiffeners inside the airfoil shell avoids its excessive displacement and stress and the buckling effects, as well as achieving the maximal detuning level from the bending natural frequencies of vibrations; the proposed integrated approach to the strength assessment, which takes into account the effect of aerodynamic loads on the blade airfoil in the static analysis and the prestressed state during the modal analysis can significantly improve the accuracy and correctness of calculations. The approach described in the paper is new for low-speed rotary machines, as at present there are no comprehensive methods for designing composite blades of fans and compressors, and there is no mention of specific examples of their implementation in the projects implemented by manufacturers.

Broadband Design of Acoustic Metasurfaces for the Stabilization of a Mach 4 Boundary Layer Flow

A piecewise acoustic metasurface is designed to suppress the first mode while marginally amplifying the Mack second mode in a Mach 4 flat-plate boundary layer (BL) flow. The results of linear stability theory (LST) and the eN method demonstrate the stabilization effect and transition delay performance, respectively. However, the direct numerical simulation (DNS) results indicate that the designed broadband acoustic metasurface actually weakly excites the first mode with a slightly larger fluctuating pressure amplitude at the surface, which is in contrast to the analysis of LST. The discrepancies are found to lie in the ‘roughness’ effect caused by the recirculation zones inside the microslits and the alternating expansion and compression waves induced at the slit edges, which significantly amplifies the first mode. For further clarification of the competitive mechanism between the acoustic stabilization and ‘roughness’ destabilization effects of metasurfaces on the first mode, a carefully designed metasurface is installed at the maximum growth rate region, which excites the first mode on the metasurface but inhibits its development downstream.

Modelling, analysis and mitigation of self-excited vibrations of a magnetic track brake

Magnetic track brakes work independently of the wheel–rail contact as an additional braking system in railway vehicles. In the past, magnetic track brakes were usually deactivated at velocities below 25 km/h in mainline applications to avoid stopping jerks. However, current demands on braking performance require activation until full stop. During field tests on this subject, severe self-excited vibrations were measured at velocities below 25 km/h. This study analyses the oscillations observed by focusing on the stability behaviour of a simplified linear coupled electro-magneto-mechanical model of the track brake. Key parameters are identified by applying established criteria of linear stability theory. To account for essential nonlinear effects, a detailed multibody dynamics model with flexible bodies including a more enhanced electro-magnetic model is introduced and parameterised by using measurement data. Simulation results reveal two separate (or combined) mechanisms that may lead to self-excitation. On the one hand, friction-induced vibrations between the magnets and the rail; on the other hand, coupling effects between the electro-magnetic and the mechanical subsystems of the track brake may be the cause of the self-excited vibrations observed. Stability behaviour is influenced by various design parameters and in particular by the contact conditions between track brake and rail. Finally, a few passive methods are briefly discussed that may help to mitigate or reduce self-excited vibrations at low velocities in future designs of track brakes.

Numerical simulation of the interaction of the disturbed boundary layer with an incident shock

Interaction of the disturbed supersonic boundary layer with an incident oblique shock wave is studied numerically with eddy-resolving numerical simulations. Eigenmodes of the linear stability theory are used to generate the inflow boundary layer disturbances. The evolution of unstable boundary-layer disturbances, effects of the incident shock on the disturbances, effects of the disturbances on the boundary layer separation, flow dynamics in the separation zone, and laminar-turbulent transition are studied.

Blind disturbance separation and identification in a transitional boundary layer using minimal sensing

A novel approach is presented for identifying disturbance sources in wall-bounded shear flows. The underlying approach models the flow state, as measured by sensors embedded in the flow, as a mixture of disturbance sources. The degenerate unmixing estimation technique is adopted as a blind source separation technique to recover the separate sources and their unknown mixing process. The efficiency of this approach stems from its ability to isolate any, a priori unknown, number of sources, using two sensors only. Furthermore, by adding a single additional sensor, the method is expanded to also determine the propagation velocity vector of each of the isolated sources, based on sensor readings from three sensors appropriately located in the flow field. Theoretical guidelines for locating the sensors are provided. The power of the method is demonstrated via computer simulations and wind-tunnel experiments. The numerical study considers disturbances comprising discrete Tollmien–Schlichting waves and wave packets. Linear stability theory is used to model source mixtures acquired by sensors placed in a Blasius boundary layer. The experimental study investigates the flow over a flat plate, with hot wires as sensors, and a loudspeaker and plasma actuators as source generators. Based on numerical and experimental demonstrations, it is believed that the new approach should prove useful in various applications, including active control of boundary layer transition from laminar to turbulent flow.

Discrete-time phytoplankton–zooplankton model with bifurcations and chaos

The local dynamics with different topological classifications, bifurcation analysis, and chaos control for the phytoplankton–zooplankton model, which is a discrete analogue of the continuous-time model by a forward Euler scheme, are investigated. It is proved that the discrete-time phytoplankton–zooplankton model has trivial and semitrivial fixed points for all involved parameters, but it has an interior fixed point under the definite parametric condition. Then, by linear stability theory, local dynamics with different topological classifications are investigated around trivial, semitrivial, and interior fixed points. Further, for the discrete-time phytoplankton–zooplankton model, the existence of periodic points is also investigated. The existence of possible bifurcations around trivial, semitrivial, and interior fixed points is also investigated, and it is proved that there exists a transcritical bifurcation around a trivial fixed point. It is also proved that around trivial and semitrivial fixed points of the phytoplankton–zooplankton model there exists no flip bifurcation, but around an interior fixed point there exist both Neimark–Sacker and flip bifurcations. From the viewpoint of biology, the occurrence of Neimark–Sacker implies that there exist periodic or quasi-periodic oscillations between phytoplankton and zooplankton populations. Next, the feedback control method is utilized to stabilize chaos existing in the phytoplankton–zooplankton model. Finally, simulations are presented to validate not only obtained results but also the complex dynamics with orbits of period-8, 9, 10, 11, 14, 15 and chaotic behavior of the discrete-time phytoplankton–zooplankton model.

Theoretical Description for Ellagic Acid Electrochemical Oxidation and Electropolymerization

The theoretical description for ellagic acid electrochemical oxidation and electropolymerization has been suggested in this paper. The model includes the electropolymerization of ellagic acid in the presence of two of its low-molecular oxidation products. The correspondent mathematical model has been developed and analyzed using linear stability theory and bifurcation analysis. The analysis of the system has confirmed that the oscillatory behavior is more probable than in the simplest case of the electrosynthesis of the polymer of the electrochemically synthesized monomer. Nevertheless, the system is electrosynthetically efficient, yielding a polymer coating.

Cobalt (III) Oxyhydroxide as a Pyrrole Polymerization Initiator: a Theoretical Study

In this work, the possibility of using cobalt (III) oxyhydroxide as an electropolymerization initiator for pyrrole is studied by theoretical means. A hybrid material may be yielded by this synthesis. The mathematical model has been developed and analyzed using linear stability theory and bifurcation analysis: the steady-state stability requisites, correspondent to the synthesis efficiency, were obtained. The general causes for oscillatory and monotonic instabilities have also been detected.

Theoretical Evaluation for the Assisted Electropolymerization of a Monomer, Obtained by an Indirect Electrochemical Synthesis

In this work, the possibility for indirect electropolymerization of a monomer synthesized by an indirect electrosynthesis has been evaluated. Based on the reaction mechanism, the correspondent mathematical model has been developed and analyzed using linear stability theory and bifurcation analysis. It has been shown that in the case of indirect monomer electrosynthesis and electropolymerization, the polymer deposition is far more stable than for direct participation of the monomer in the electrochemical stage. The surface tends to be more developed. Yet, the electrochemical oscillations are expected to be less probable than in the case of the direct anodic process.