This paper reveals the dynamical behaviors of a network consisting of a pair of ring sub-networks and two-way couplings of neurons between the individual sub-networks. Time delays are introduced into ...the internal connections within the individual sub-networks and the couplings between the individual sub-networks. The stability and instability of the trivial equilibrium of the network are analyzed and the conditions for the existence of Hopf bifurcation are obtained by discussing the associated characteristic equation. The criterion for the global stability of the trivial equilibrium of the network is given by constructing a suitable Lyapunov functional. Numerical simulations are performed to validate the theoretical results and rich dynamical behaviors are observed, such as multiple stability switches of the network equilibrium, synchronous/asynchronous oscillations, and multi-stability.
•Ceres is 2.5 km more oblate than its rotational geoid.•Faster paleospin can reconcile Ceres’ present-day (i.e., fossil) shape and J2 gravity.•Ceres could have been modestly despun by impacts or by ...satellite tidal evolution and loss.•Deep-seated global mass anomalies can also explain Ceres’ nonhydrostatic degree-2 shape and gravity.•Ceres’ mean moment-of-inertia lies between 0.345 and 0.375 depending on paleospin.
We show that Ceres’ measured degree-2 zonal gravity, J2, is smaller by about 10% than that derived assuming Ceres’ rotational flattening, as measured by Dawn, is hydrostatic. Irrespective of Ceres’ radial density variation, as long as its internal structure is hydrostatic the J2 predicted from the shape model is consistently larger than measured. As an explanation, we suggest that Ceres’ current shape may be a fossil remnant of faster rotation in the geologic past. We propose that up to ∼7% of Ceres’ previous spin angular momentum has been removed by dynamic perturbations such as a random walk due to impacts or a loss of satellite that slowed Ceres spin as it tidally evolved outward. As an alternative, we also consider a formal degree-2 admittance solution, from which we infer a range of possible non-hydrostatic contributions to J2 from uncompensated, deep-seated density anomalies. We show that such density anomalies could be due to low order convection or upwelling. The normalized moments-of-inertia derived for the two explanations – faster paleospin and deep-seated density anomalies – range between 0.353 ± 0.009 and 0.375 ± 0.001 for a spherically equivalent Ceres, which can be used as constraints on more complex Ceres interior models.
This paper reveals the behaviors of a coupled network consisting of four sub-networks each with two neurons and multiple couplings between the sub-networks. Time delays are introduced into the ...internal connections within the sub-networks and the couplings between the sub-networks. The stability switches of the network equilibrium are analyzed and the conditions for the existence of periodic oscillations are given by discussing the associated characteristic equation. Numerical simulations are performed to illustrate the effectiveness of the obtained results and interesting network behaviors are observed, such as multiple switches of periodic oscillations.
Numerical simulations have been performed to study the effect of the circumferential single-grooved casing treatment (CT) at multiple locations on the tip-flow stability and the corresponding control ...mechanism at three tip-clearance-size (TCS) schemes in a transonic axial flow compressor rotor. The results show that the CT is more efficient when its groove is located from 10% to 40% tip axial chord, and G2 (located at near 20% tip axial chord) is the best CT scheme in terms of stall-margin improvement for the three TCS schemes. For effective CTs, the tip-leakage-flow (TLF) intensity, entropy generation and tip-flow blockage are reduced, which makes the interface between TLF and mainstream move downstream. A quantitative analysis of the relative inlet flow angle indicates that the reduction of flow incidence angle is not necessary to improve the flow stability for this transonic rotor. The control mechanism may be different for different TCS schemes due to the distinction of the stall inception process. For a better application of CT, the blade tip profile should be further modified by using an optimization method to adjust the shock position and strength during the design of a more efficient CT.
To explain the effect of tip leakage flow on the performance of an axial-flow transonic compressor, the compressors with different rotor tip clearances were studied numerically. The results show that ...as the rotor tip clearance increases, the leakage flow intensity is increased, the shock wave position is moved backward, and the interaction between the tip leakage vortex and shock wave is intensified, while that between the boundary layer and shock wave is weakened. Most of all, the stall mechanisms of the compressors with varying rotor tip clearances are different. The clearance leakage flow is the main cause of the rotating stall under large rotor tip clearance. However, the stall form for the compressor with half of the designed tip clearance is caused by the joint action of the rotor tip stall caused by the leakage flow spillage at the blade leading edge and the whole blade span stall caused by the separation of the boundary layer of the rotor and the stator passage. Within the investigated varied range, when the rotor tip clearance size is half of the design, the compressor performance is improved best, and the peak efficiency and stall margin are increased by 0.2% and 3.5%, respectively.
Counter-rotating axial-flow compressor (CRAC) is a promising technology to increase the thrust-to-weight ratio of aero-engines. Self-recirculating casing treatment (SRCT) is selected to explore its ...stability enhancement capacity in the CRAC. In the present work, an effective SRCT is designed by the design of experiment method, and the stability improvement potential of the SRCT and its mechanism of stall margin enhancement are studied. Results show that the optimal SRCT scheme increases the stall margin by about 7.73% and without remarkable peak efficiency loss, and the overall performance of the compressor is enhanced at the near-stall condition. The SRCT improves the quality of the tip flow field by sucking out low-energy fluid and restrains the spillage of the tip leakage flow by the jet effect from the injection port. In addition, the SRCT also reduces the unsteady interference between the adjacent rotors. The effect of speed ratio on the effectiveness of SRCT is further investigated, and results indicate that the SRCT increases the stall margin of the CRAC by about 4.13-5.80% at some off-design speed ratio conditions. The speed ratio affects the first stall stage of the CRAC, thus affecting the effectiveness of the SRCT.
Multiplex networks have drawn much attention since they have been observed in many systems, e.g., brain, transport, and social relationships. In this paper, the nonlinear dynamics of a multiplex ...network with three neural groups and delayed interactions is studied. The stability and bifurcation of the network equilibrium are discussed, and interesting neural activities of the network are explored. Based on the neuron circuit, transfer function circuit, and time delay circuit, a circuit platform of the network is constructed. It is shown that delayed couplings play crucial roles in the network dynamics, e.g., the enhancement and suppression of the stability, the patterns of the synchronization between networks, and the generation of complicated attractors and multi-stability coexistence.
The endwall effect has a great impact on the aerodynamic performance of compressor blades. Based on three conventional near-endwall blade modeling methods of bowed blade, endbend blade and ...leading-edge strake blade (LESB), two combined optimization design methods of highly loaded blades have been developed considering the endwall effect in the current study, i.e., the bowed blade combined with the LESB (bowed LESB blade) and the endbend blade combined with the LESB (endbend LESB blade). Optimization designs were conducted for a compressor cascade with low solidity by using the two combined modeling methods and the three conventional modeling methods, and the optimization results were compared and analyzed in detail. The results showed that the five optimization modelling methods could all improve the performance for the original cascade, and the optimized cascade with the bowed LESB modeling method has the best aerodynamic performance. The total pressure loss of the optimal bowed LESB cascade was only 40.3% of that in the original cascade while reducing the solidity of the original cascade from 1.53 to 1.25 and keeping the static pressure rise and diffusion factor at the same level as the original one. Among the optimal cascades, the radial migration height of the low-energy fluid and the corresponding vortex have great effects on the aerodynamic performance, and the optimal bowed LESB cascade is superior to the other optimal cascades in this aspect.
To explore the inlet boundary layer (IBL) influence on the tandem cascade aerodynamic performance, this paper took the high subsonic compressor NACA65 K48 cascade and its modified tandem cascade as ...the research object. The effects of the IBL thickness and the skewed IBL on the aerodynamic performance of the original cascade and tandem cascade were analyzed based on the numerical method. The results show that the tandem cascade effective design makes it better than the original cascade in the aerodynamic performance under different IBL conditions. Compared with the collateral IBL, the skewed IBL can effectively improve the aerodynamic performance of the original cascade and tandem cascade by suppressing the endwall cross flow, but an increase in the IBL thickness will suppress this advantage. In addition, the increase of incidence angle or the IBL thickness will make the tandem cascade forward blade corner separation more serious and cause the flow passage to be blocked, which seriously affects the rear blade diffusing capacity. In general, the IBL thickness is positively correlated with the tandem cascade total pressure loss and negatively correlated with the static pressure rise (except for the −6° incidence angle). The skewed IBL can effectively reduce the total pressure loss and increase the static pressure rise within −4°~7° incidence angle, but the law is opposite at a −6° incidence angle. At a 0° or 2° incidence angle, the performance improvement effect of the skewed IBL on the tandem cascade is the best, and this positive effect diminishes as it tends towards a larger positive incidence angle or a smaller negative incidence angle.
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