Properties of a genetic algorithm extended by a random self-learning operator and asymmetric mutations: A convergence study for a task of powder-pattern indexing

Genetic algorithms represent a powerful global-optimisation tool applicable in solving tasks of high complexity in science, technology, medicine, communication, etc. The usual genetic-algorithm calculation scheme is extended here by introduction of a quadratic self-learning operator, which performs a partial local search for randomly selected representatives of the population. This operator is aimed as a minor deterministic contribution to the (stochastic) genetic search. The population representing the trial solutions is split into two equal subpopulations allowed to exhibit different mutation rates (so called asymmetric mutation). The convergence is studied in detail exploiting a crystallographic-test example of indexing of powder diffraction data of orthorhombic lithium copper oxide, varying such parameters as mutation rates and the learning rate. It is shown through the averaged (over the subpopulation) fitness behaviour, how the genetic diversity in the population depends on the mutation rate of the given subpopulation. Conditions and algorithm parameter values favourable for convergence in the framework of proposed approach are discussed using the results for the mentioned example. Further data are studied with a somewhat modified algorithm using periodically varying mutation rates and a problem-specific operator. The chance of finding the global optimum and the convergence speed are observed to be strongly influenced by the effective mutation level and on the self-learning level. The optimal values of these two parameters are about 6 and 5%, respectively. The periodic changes of mutation rate are found to improve the explorative abilities of the algorithm. The results of the study confirm that the applied methodology leads to improvement of the classical genetic algorithm and, therefore, it is expected to be helpful in constructing of algorithms permitting to solve similar tasks of higher complexity.     

Numerical investigation of the effects of structural geometric and material nonlinearities on limit-cycle oscillation of a cropped delta wing

This article presents numerical simulations of the limit-cycle oscillation (LCO) of a cropped delta wing in order to investigate the effects of structural geometric and material nonlinearities on aeroelastic behavior. In the computational model, the structural part included both the geometric nonlinearity that arises from large deflections, and the material nonlinearity that originates from plasticity. The Euler equations were employed in the fluid part to describe the transonic aerodynamics. Moreover, the load transfer was conducted using a 3-D interpolating procedure, and the interfaces between the structural and aerodynamic domains were constructed in the form of an exact match. The flutter and LCO behaviors of the cropped delta wing were simulated using the coupling model, and the results were compared with existing experimental measurements. For lower dynamic pressures, the geometric nonlinearity provided the proper mechanism for the development of the LCO, and the numerical results correlated with the experimental values. For higher dynamic pressures, the material nonlinearity led to a rapid rise in the LCO amplitude, and the simulated varying trend was consistent with the experimental observation. This study demonstrated that the LCO of the cropped delta wing was not only closely related to geometric nonlinearity, but was also remarkably affected by material nonlinearity.     

液氮与液态一氧化碳混合物的冲击压缩特性研究

 利用二级轻气炮研究了等体积的液态一氧化碳（LCO）与液氮（LN₂）混合物的冲击压缩特性，在10～25 GPa压力范围内获得了5个Hugoniot数据点。混合物冲击绝热线位于单质一氧化碳和液氮Hugoniot拟合线之间，并靠近前者。这意味着混合物的冲击压缩特性不是其中各单质行为的简单平均。     

Computational aeroelastic simulations of self-sustained pitch oscillations of a NACA0012 at transitional Reynolds numbers

The phenomenon of low amplitude self-sustained pitch oscillations in the transitional Reynolds number regime is studied numerically through unsteady, two-dimensional aeroelastic simulations. Based on the experimental data, simulations have been limited in the Reynolds number range 5.0×10⁴<Re_c<1.5×10⁵. Both laminar and URANS calculations (using the SST k–ω model with a low-Reynolds-number correction) have been performed and found to produce reasonably accurate limit cycle pitching oscillations (LCO). This investigation confirms that the laminar separation of the boundary layer near the trailing edge plays a critical role in initiating and sustaining the pitching oscillations. For this reason, the phenomenon is being labelled as laminar separation flutter. As a corollary, it is also shown that turbulence tends to inhibit their existence. Furthermore, two regimes of LCO are observed, one where the flow is laminar and separated without re-attachment, and the second for which transition has occurred followed by turbulent re-attachment. Finally, it is established that the high-frequency, shear instabilities present in the flow which lead to von Kármán vortex shedding are not crucial, nor necessary, to the maintaining mechanism of the self-sustained oscillations.     

Bifurcation characteristics of a two-dimensional structurally non-linear airfoil in turbulent flow

The dynamics of a structurally non-linear two-dimensional airfoil in turbulent flow is investigated numerically using a Monte Carlo approach. Both the longitudinal and vertical components of turbulence, corresponding to parametric (multiplicative) and external (additive) excitation, respectively, are modelled. The properties of the airfoil are chosen such that the underlying non-excited, deterministic system exhibits binary flutter; the loss of stability of the equilibrium point due to flutter then leads to a limit cycle oscillation (LCO) via a supercritical Hopf bifurcation. For the random system, the results are examined in terms of the probability structure of the response and the largest Lyapunov exponent. The airfoil response is interpreted from the point of view of the concepts of D- and P-bifurcations, as defined in random bifurcation theory. It is found that the bifurcation is characterized by a change in shape of the response probability structure, while no discontinuity in the variation of the largest Lyapunov exponent with airspeed is observed. In this sense, the trivial bifurcation obtained for the deterministic airfoil, where the D- and P-bifurcations coincide, appears only as a P-bifurcation for the random case. At low levels of turbulence intensity, the Gaussian-like bell-shaped bi-dimensional PDF bifurcates into a crater shape; this is interpreted as a random fixed point bifurcating into a random LCO. At higher levels of turbulence intensity, the post-bifurcation PDF loses its underlying deterministic LCO structure. The crater is transformed into a two-peaked shape, with a saddle at the origin. From a more universal point of view, the robustness of the random bifurcation scenario is critiqued in light of the relative importance of the two components of turbulent excitation.     

Effects of multiple structural nonlinearities on limit cycle oscillation of missile control fin

Aeroelastic analyses are performed for a 2-D typical section model with multiple nonlinearities. The differences between a system with multiple nonlinearities in its pitch and plunge spring and a system with a single nonlinearity in its pitch are thoroughly investigated. The unsteady supersonic aerodynamic forces are calculated by the doublet point method (DPM). The iterative V-g method is used for a multiple-nonlinear aeroelastic analysis in the frequency domain and the freeplay nonlinearity is linearized using a describing function method. In the time domain, the DPM unsteady aerodynamic forces, which are based on a function of the reduced frequency, are approximated by the minimum state approximation method. Consequently, multiple structural nonlinearities in the 2-D typical wing section model are influenced by the pitch to plunge frequency ratio. This result is important in that it demonstrates that the flutter speed is closely connected with the frequency ratio, considering that both pitch and plunge nonlinearities result in a higher flutter speed boundary than a conventional aeroelastic system with only one pitch nonlinearity. Furthermore, the gap size of the freeplay affects the amplitude of the limit cycle oscillation (LCO) to gap size ratio.     

Limit cycle oscillation suppression of 2-DOF airfoil using nonlinear energy sink

This paper presents a novel mechanical attachment, i.e., nonlinear energy sink （NES）, for suppressing the limit cycle oscillation （LCO） of an airfoil. The dynamic responses of a two-degree-of-freedom （2-DOF） airfoil coupled with an NES are studied with the harmonic balance method. Different structure parameters of the NES, i.e., mass ratio between the NES and airfoil, NES offset, NES damping, and nonlinear stiffness in the NES, are chosen for studying the effect of the LCO suppression on an aeroelastic system with a supercritical Hopf bifurcation or subcritical Hopf bifurcation, respectively. The results show that the structural parameters of the NES have different influence on the supercritical Hopf bifurcation system and the subcritical Hopf bifurcation system.     

Experiments on transonic limit-cycle-flutter of a flexible swept wing

The aeroelastic behavior of wing models is nonlinear particularly in the transonic speed range. The interaction between aerodynamic and structural forces can lead to the occurrence of Limit-Cycle Oscillations (LCOs). If in addition the wing model is flexible and backward swept, the kinematic coupling between bending and torsion makes the situation even more complex.In the research project “Aerostabil” such a wing was investigated, which was equipped with pressure transducers in three sections and accelerometers. The experiments were performed in the adaptive test section of the transonic wind tunnel TWG in Göttingen. Already Dietz et al. (2003) have reported about experimental details and preliminary results. Based on these data Bendiksen (2008) studied numerically LCO-flutter behavior using a very similar, theoretical model (G-wing) and Stickan et al. (2014) used the original data as a LCO flutter test case. The influence of flexibility on the steady aerodynamics of the wing was described in Schewe & Mai (2018). In this paper now the flutter experiments with the same flexible model were analyzed systematically in the transonic range 0.84 <Ma <0.89 and for six angles of attack from 1.46°to 2.7°. Maps of stability, LCO amplitudes and instantaneous pressure distributions are presented. It was found that unstable regions are islands, whose extent depends on the angle of attack. A LCO test case, already treated in the literature is examined in more detail. The analysis of the time functions showed that during LCO-flutter the motion induced aerodynamic sectional lift forces particularly in the outer wing are asymmetric and thus acting as amplitude limiter. The reason for the asymmetry lies in the shock/boundary layer interaction. The test case, containing the stages of built-up and the transition to the limit cycle provides an excellent opportunity for improving our knowledge about LCOs and for code validation purposes.     

Comparative study of differential flow and cryogenic modulators comprehensive two-dimensional gas chromatography systems for the detailed analysis of light cycle oil

The modulator is the key point of comprehensive two-dimensional gas chromatography (GC×GC). This interface ensures the sampling and transfer of the sample from the first to the second dimension. Many systems based on different principles have been developed. However, to our knowledge, almost only cryogenic modulators are used in the petroleum industry. Nevertheless cryogenic fluids represent some disadvantages in term of safety, cost and time consuming. This paper reports a comparative study between differential flow and cryogenic liquid modulators for the detailed analysis of hydrocarbons in middle distillates type light cycle oil (LCO). Optimization of geometrical dimensions of a set of columns was carried out on the differential flow modulator system in order to reproduce the quality of separation of cryogenic modulation. Then a comparative study was investigated on sensibility and resolution (separation space and peak capacity) between the two systems.     

Self-sustained aeroelastic oscillations of a NACA0012 airfoil at low-to-moderate Reynolds numbers

A wind tunnel experimental investigation of self-sustained oscillations of an aeroelastic NACA0012 airfoil occurring in the transitional Re regime is presented. To the authors’ knowledge this is the first time that aeroelastic limit cycle oscillations (LCOs) associated with low Re effects have been systematically studied and reported in the public literature. While the aeroelastic apparatus is capable of two-degree-of-freedom pitch-plunge motion, the present work concerns only the motion of the airfoil when it is constrained to rotate in pure pitch. The structural stiffness is varied as well as the position of the elastic axis; other parameters such as surface roughness, turbulence intensity and initial conditions are also briefly discussed. In conjunction with the pitch measurements, the flow is also recorded using hot-wire anemometry located in the wake at a distance of one chord aft of the trailing edge. It is observed that for a limited range of chord-based Reynolds numbers, 4.5×10⁴Re_c1.3×10⁵, steady state self-sustained oscillations are observed. Below and above that range, these oscillations do not appear. They are characterized by a well-behaved harmonic motion, whose frequency can be related to the aeroelastic natural frequency, low amplitude (θ_max<5.5°) and some sensitivity to flow perturbations and initial conditions. Furthermore, hot-wire measurements for the wing held fixed show that no periodicity in the undisturbed free-stream nor in the wake account for the oscillations. Overall, these observations suggest that laminar separation plays a role in the oscillations, either in the form of trailing edge separation or due to the presence of a laminar separation bubble.