Computational bluff body aerodynamic noise prediction using a statistical approach

A new method for calculating the aerodynamic noise generated by bluff bodies is presented in this paper. The methodology uses two-dimensional, unsteady Reynolds averaged Navier Stokes turbulent flow simulations to calculate the acoustic source terms. To account for turbulent flow effects that are not resolved by the flow simulation, a statistical approach has been developed and applied to introduce narrow band random noise. Spanwise de-correlation of flow information is accounted for using a correction method based on a de-correlation length scale. Curle’s compact acoustic analogy is used to calculate the far-field noise. To illustrate the effectiveness of the method, the turbulent flow and noise about two test cases are calculated and compared with experimental results from the literature.     

Transported probability density function modeling of a bluff body stabilized turbulent flame

A transported probability density function (PDF) approach closed at the joint scalar level is used to model the bluff body stabilized turbulent diffusion flame (HM1) investigated experimentally by Masri and co-workers (Re = 15,800). The current effort extends previous work through the introduction of comprehensive thermochemistry computed via a systematically reduced C/H/N/O mechanism featuring 300 reactions, 20 solved, and 28 steady-state species. Molecular mixing is modelled using the modified Curl’s model. The current computations have been performed via a hybrid Monte Carlo/Finite Volume algorithm. The joint scalar PDF equations are solved using moving particles in a Lagrangian framework, and the velocity field is closed at the second moment level. The redistribution terms are modelled using the Generalized Langevin Model of Haworth and Pope. The principal aim was to investigate the thermochemical effects, and thus a steady-state calculation procedure is adopted. The computations are shown to reproduce experimental mean and rms values of velocities, temperature, mixture, and species mass fractions. In particular, mass fractions of CO and NO are well predicted. Conditional PDFs are also well reproduced although uncertainties in boundary conditions influence results close to the bluff body.     

低雷诺数下钝体三维尾迹中的涡量符号律

钝体是目前各种工程中广泛应用的一种结构.钝体绕流的尾迹涡动力学也是经典的流体力学研究对象之一.本文通过直接数值模拟,针对低雷诺数下各种钝体结构的不可压缩绕流,当形成三维尾迹时,研究具有特定符号的涡量分布特征.通过分析两类钝体结构,基本的直柱体和受到几何扰动的柱体,总结并得到了更为广泛适用的涡量符号律.通过对比并分析这两类钝体结构,结合理论证明的结果,进一步厘清了对产生涡量符号律的这两类钝体结构之间的内在物理关联,即引起自然失稳的小扰动在惯性力作用下产生的表面涡量只能向下游演化发展,而几何扰动则根据扰动位置,产生的表面涡量可以向扰动上游或下游演化发展.从而可以推测所有钝体结构尾迹中的各种型式的涡脱落模态,从涡量符号律的演化角度来看,实际上是一致的,都是起源于壁面产生特定符号组合规律的∏型涡.     

The onset of chaos in the wake of an oscillating cylinder: Experiment and the dynamics of the circle map

This paper deals with a comparison between experimental observations in a low-Reynolds-number wake behind an oscillating cylinder and the universal properties of a sine circle map. When the limit cycle due to the natural vortex shedding in the wake is modulated at a second frequency by oscillating the cylinder transversely, one obtains in phase space a flow on a two torus. The nonlinear interaction between the two oscillators results in Arnol’d tongues due to phase locking, the devil’s staircase along the critical line, and a transition from order to chaosvia the quasiperiodic route. The sine circle map describes these features adequately. A comparison between the experiment and the theory is made in terms of multifractal formalism and trajectory scaling function.     

Characterization of flow around rectangular bluff bodies at angle of attack

Using data present in the literature from wind tunnel testing of semi-infinite and infinite rectangular bluff bodies at angle of attack, we develop a simple relation to predict the range of angles of attack where the lift remains approximately constant. This prediction is useful for researchers attempting to develop simplified models of the forces on rectangular bluff bodies. Additionally, prior work has shown that this region of the lift curve is characterized by complex three-dimensional flow, which has consequences for computational simulations.     

Controlling chaos in an economic model

A Cournot duopoly, with a bounded inverse demand function and different constant marginal production costs, can be modeled as a discrete-time dynamical system, which exhibits complex bifurcating and chaotic behaviors. Based on some essential features of the model, we show how bifurcation and chaos can be controlled via the delayed feedback control method. We then propose and evaluate an adaptive parameter-tuning algorithm for control. In addition, we discuss possible economic implications of the chaos control strategies described in the paper.     

Application of the Lagrangian CMC method in elliptic bluff body and swirl flames

The Lagrangian CMC method was implemented in the open source programme OpenFOAM and applied to turbulent nonpremixed bluff body and swirl flames. Lagrangian CMC is more efficient than Eulerian CMC with the number of Lagrangian flame groups much less than the number of computational cells for Eulerian CMC equations in general. It is based on the conditional flame structure depending on the residence time of the fuel of fixed Lagrangian identity from the nozzle. According to sensitivity study the injected fuel was divided into ten flame groups according to the injection sequence with the resulting conditional profiles between those by ISR and Eulerian CMC. Minor deviation from Eulerian CMC was attributed to the flame structure that is difficult to be characterised by the residence time only in elliptic recirculating flows of the bluff body and swirl flames. The Eulerian and Lagrangian CMC showed the same trend of deviation from measurements for conditional temperature, H₂O, OH, CO and H₂ mass fractions. The significant deviation of H₂ was due to uncertainty in the reaction chemistry, as observed in the previous works based on other reaction mechanisms for methane and methanol.     

转捩区长度对回转体流噪声的影响

本文通过分析回转体边界层转捩区声辐射的机理,就转捩区长度对回转体转捩区辐射声压谱的影响进行了讨论。结果表明,来流速度和回转体直径是影响回转体转捩区长度、也是影响回轨体转捩区辐射声压谱的主要因素,在来流攻回轨体直径相同时,则回转体形对转捩区长度的影响超主导作用,采用本文的方法所得的理论值与实验值之间的一致性较好。     

The stability of ferrofluid flow in a vertical layer subject to lateral heating and horizontal magnetic field

We use the Langevin law of magnetization to study the linear stability of a convective flow in a flat vertical layer of ferrofluid subject to a transverse temperature gradient and a uniform magnetic field. The stability of the flow against planar, spiral and three-dimensional perturbations is examined, and the stability boundaries and characteristics of critical disturbances are determined. The competition between the monotonic mode and two types of wave modes is analyzed taking into account the properties of the fluid (magnetic susceptibility and Prandtl number) and the magnetic field strength. The domain of parameters where the oscillatory thermomagnetic wave instability exists is found.     

Hamilton-Poisson formulation for the rotational motion of a rigid body in the presence of an axisymmetric force field and a gyroscopic torque

We give sufficient conditions for the rigid body in the presence of an axisymmetric force field and a gyroscopic torque to admit a Hamilton-Poisson formulation. Even if by adding a gyroscopic torque we initially lose one of the conserved Casimirs, we recover another conservation law as a Casimir function for a modified Poisson structure. We apply this frame to several well-known results in the literature.     

Signature of chaos in power spectrum

We investigate the nature of the numerically computed power spectral densityP(f, N, τ) of a discrete (sampling time interval,τ) and finite (length,N) scalar time series extracted from a continuous time chaotic dynamical system. We highlight howP(f, N, τ) differs from the true power spectrum and from the power spectrum of a general stochastic process. Non-zeroτ leads to aliasing;P(f, N, τ) decays at high frequencies as [πτ/sinπτf]², which is an aliased form of the 1/f ² decay. This power law tail seems to be a characteristic feature of all continuous time dynamical systems, chaotic or otherwise. Also the tail vanishes in the limit ofN → ∞, implying that the true power spectral density must be band width limited. In striking contrast the power spectrum of a stochastic process is dominated by a term independent of the length of the time series at all frequencies.     

Transition from order to chaos in SU(2) Yang-Mills-Higgs system

Time-dependent spherically symmetricSU(2) Yang-Mills-Higgs system is shown to be chaotic near the ’t Hooft-Polyakov monopole solution by calculating the maximal Lyapunov exponents. A phase transition like behaviour from order to chaos is observed as a parameter depending on the self interaction constant of scalar fields increases.     

Noise-induced chaos in the electrostatically actuated MEMS resonators

In this Letter, nonlinear dynamic and chaotic behaviors of electrostatically actuated MEMS resonators subjected to random disturbance are investigated analytically and numerically. A reduced-order model, which includes nonlinear geometric and electrostatic effects as well as random disturbance, for the resonator is developed. The necessary conditions for the rising of chaos in the stochastic system are obtained using random Melnikov approach. The results indicate that very rich random quasi-periodic and chaotic motions occur in the resonator system. The threshold of bounded noise amplitude for the onset of chaos in the resonator system increases as the noise intensity increases.     

Identification of deterministic chaos by an information-theoretic measure of the sensitive dependence on the initial conditions

One of the most difficult problems in the field of non-linear time series analysis is the unequivocal characterization of a measured signal. We present a practicable procedure which allows to decide if a given time series is pure noise, chaotic but distorted by noise, purely chaotic, or a Markov process. Furthermore, the method gives an estimate of the Kolmogorov-Sinai (KS) entropy and the noise level. The procedure is based on a measure of the sensitive dependence on the initial conditions which is called ε-information flow. This measure generalizes the concept of KS entropy and characterizes the underlying dynamics. The ε-information flow is approximated by the calculation of various correlation integrals.     

Generation of harmonics and chaos in the dynamics of anharmonic surfaces

Effective equations of motion of a surface atom placed in an anharmonic surface potential are derived for three kinds of substrates (i) continuous dispersionless, (ii) discrete with nearest neighbours harmonic interactions, and (iii) a substrate showing a strong spatial dispersion. The resulting equations of motion are differential equations in the case (i) and Volterra Integro-Differential Equations (VIDE) in the cases (ii) and (iii). Examples of non-linear surface response to phonons coming from the bulk are given for the dispersionless substrate.     

Transition to chaos via the quasi-periodicity and characterization of attractors in confined Bénard-Marangoni convection

A study of dynamic regimes in Bénard-Marangoni convection was carried out for various Prandtl and Marangoni numbers in small aspect ratio geometries (Γ = 2.2 and 2.8). Experiments in a small hexagonal vessel, for a large range of the Marangoni number (from 148 to 3636), were carried out. Fourier spectra and an auto-correlation function were used to recognize the various dynamic regimes. For given values of the Prandtl number (Pr = 440) and aspect ratio (Γ = 2.2), mono-periodic, bi-periodic and chaotic states were successively observed as the Marangoni number was increased. The correlation dimensions of strange attractors corresponding to the chaotic regimes were calculated. The dimensions were found to be larger than those obtained by other authors for Rayleigh-Bénard convection in aspect ratio geometries of the same order. The transition from temporal chaos to spatio-temporal chaos was also observed. For Γ = 2.2, when larger values of the Marangoni number were imposed (Ma = 1581 for Pr = 160 and Ma = 740 for Pr = 440), spatial modes were involved through the convective pattern dynamics.     

Periodic locking of chaos in semiconductor lasers with optical feedback

We show how a chaotic system can be locked to emit a periodic waveform belonging to its chaotic attractor. We numerically demonstrate our idea in a system composed of a semiconductor laser driven to chaos by optical feedback from an external cavity. The clue is the injection of an appropriate periodic signal that modulates the phase and amplitude of the intra-cavity radiation, a chaotic analogy of conventional mode-locking. The result is a time process that manifests a chaotic signature embedded in a long-scale periodic train.     

Generalized projective chaos synchronization of gyroscope systems subjected to dead-zone nonlinear inputs

This Letter presents a robust control scheme to generalized projective synchronization between two identical two-degrees-of-freedom heavy symmetric gyroscopes with dead zone nonlinear inputs. Because of the nonlinear terms of the gyroscope system, the system exhibits complex and chaotic motions. By the Lyapunov stability theory with control terms, two suitable sliding surfaces are proposed to ensure the stability of the controlled closed-loop system in sliding mode. Then, two sliding mode controllers (SMC) are designed to guarantee the hitting of the sliding surfaces even when the control inputs contain dead-zone nonlinearity. This method allows us to arbitrarily direct the scaling factor onto a desired value. Numerical simulations show that this method works very well for the proposed controller.     

The diffracted sound field from the transition region of an axisymmetric body in water

Understanding the physical features of the diffracted sound field on the surface of an axisymmetric body is important for predicting the self-noise of a sonar mounted on an underwater platform.The diffracted sound field from the transition region of an axisymmetric body was calculated by the geometrical theory of diffraction.The diffraction ray between the source point and the receiving point on the surface of an axisymmetric body was calculated by using the dynamic programming method.Based on the diffracted sound field,a simulation scheme for the noise correlation of the conformal array was presented.It was shown that the normalized pressure of the diffracted sound field from the transition region reduced with the increases of the frequency and the curvature of the ray.The flow noises of two models were compared and a rather optimum fore-body geometric shape was given.Furthermore,it was shown that the correlation of the flow noise in the low frequencies was stronger than that in the high frequencies.And the flow noise received by the acoustic array on the curved surface had a stronger correlation than that on the head plane at the designed center frequency,which is important for sonar system design.     

Using polarization properties to enhance performance of chaos synchronization communication between vertical-cavity surface-emitting lasers

Enhanced chaos synchronization communication between vertical-cavity surface-emitting lasers (VCSELs) is investigated numerically, by adopting a polarization communication protocol where one polarization mode is used as the chaotic carrier and the orthogonal polarization mode is used as the disturbed signal. The chaos synchronization quality for the receiver laser (RL) and attacker laser (AL) are analyzed in terms of the cross-correlation coefficient. There are two distinct regions of good synchronization quality in the injection parameters space. In the first region, good synchronization quality can be ensured for both the RL and AL. In the second region, only the RL can realize chaos synchronization. We further discuss the security enhancement by comparing the communication performance between RL and AL for injection parameters within the second region. The results show that successful and robust decoding is only achievable for the RL.