A finite difference technique for solving the Newtonian jet swell problem

A finite difference technique that incorporates a numerical mapping has been successfully applied to analyse both planar and axisymmetric Newtonian jets. A pressure gradient equation and a free-surface slope equation have been derived for free-surface iteration. The computation of pressure inside the jet surface using the pressure gradient equation is stable and accurate at high Reynolds numbers. The free-surface slope equation is needed for updating the free surface and is applicable for jets with strong surface tension effects. The present development can simulate the Newtonian jets for Reynolds numbers as high as 2000 and capillary number as low as 10^?5. Numerical predictions by the present technique are close to the results of previous finite element simulations.     

Dynamics of a Jeffcott rotor-magnetic bearing system with time delays

A Jeffcott rotor with an additional magnetic bearing locating at the disc is employed to investigate the effect of time delays on the non-linear dynamical behavior of the system. The time delays are presented in the proportional and derivative feedback, respectively. For the corresponding autonomous system, a linear stability analysis is performed for the system with two identical time delays in the control loop. The nature of a single Hopf bifurcation is determined by constructing a center manifold. For the non-autonomous system, the primary resonance response is studied for its small non-linear motions using the method of averaging. The effects of time delays and control gains, as well as excitation amplitude, on the amplitude of the steady-state response are investigated. Finally, experiments are carried out to validate the theoretical predictions.     

The visualization of the flowfield about a delta wing with spanwise blowing

This paper describes a nonintrusive method for the visualization of the flow about a delta wing with spanwise blowing jets, based on the schlieren technique. The effects of the jet/leading-edge vortex interference are visualized by using both air and helium for the jets. The visualization of the leading-edge vortex trajectories and their breakdown, as well as the influence of the jets on them is achieved by spanwise blowing of air. The visualization of the jets' paths and the effects of the leading-edge vortices on these paths is achieved by spanwise blowing of helium.     

Research on parametric resonance in a stochastic van der Pol oscillator under multiple time delayed feedback control

Analytical derivations and numerical calculations are employed to gain insight into the parametric resonance of a stochastically driven van der Pol oscillator with delayed feedback. This model is the prototype of a self-excited system operating with a combination of narrow-band noise excitation and two time delayed feedback control. A slow dynamical system describing the amplitude and phase of resonance, as well as the lowest-order approximate solution of this oscillator is firstly obtained by the technique of multiple scales. Then the explicit asymptotic formula for the largest Lyapunov exponent is derived. The influences of system parameters, such as magnitude of random excitation, tuning frequency, gains of feedback and time delays, on the almost-sure stability of the steady-state trivial solution are discussed under the direction of the signal of largest Lyanupov exponent. The non-trivial steady-state solution of mean square response of this system is studied by moment method. The results reveal the phenomenon of multiple solutions and time delays induced stabilization or unstabilization, moreover, an appropriate modulation between the two time delays in feedback control may be acted as a simple and efficient switch to adjust control performance from the viewpoint of vibration control. Finally, theoretical analysis turns to a validation through numerical calculations, and good agreements can be found between the numerical results and the analytical ones.     

Effect of impinging plate geometry on the self-excitation of subsonic impinging jets

In the generation of discrete tones by subsonic impinging jets, there exists a difference of opinion as how the feedback is achieved, i.e., the path of the feedback acoustic waves is whether inside the jet or outside the jet? The only available model (Tam and Ahuja model) for the prediction of an average subsonic jet impingement tone frequency assumes that the upstream part of the feedback loop is closed by an upstream propagating neutral wave of the jet. But, there is no information about the plate geometry in the model. The present study aims at understanding the effect of the plate geometry (size and co-axial hole in the plate) on the self-excitation process of subsonic impinging jets and the path of the acoustic feedback to the nozzle exit. The present results show that there is no effect of plate diameter on the frequency of the self-excitation. A new type of tones is generated for plates with co-axial hole (hole diameter is equal to nozzle exit diameter) for Mach numbers 0.9 and 0.95, in addition to the axisymmetric and helical mode tones observed for plates without co-axial hole. The stability results show that the Strouhal number of the least dispersive upstream propagating neutral waves match with the average Strouhal number of the new tones observed in the present experiments. The present study extends the validity of the model of Tam and Ahuja to a plate with co-axial hole (annular plate) and by doing so, we indirectly confirmed that the major acoustic feedback path to the nozzle exit is inside the jet.     

Turbulence measurements in a flow generated by the collision of radially flowing wall jets

Early results of an experimental investigation of the abnormally high turbulence level and mixing layer growth rate characteristics found in the upwash regions of aircraft with vertical short takeoff and landing (V/STOL) flows in ground effect are presented. The upwash flow is formed from the collision of two opposing radially flowing wall jets. The wall jets are created in a unique way that allows the upwash to form without any interference due to the source jets. The objective of this work is to systematically characterize the development and structure of the flow. The upwash flow exhibits very large mixing rates compared to turbulent free or wall jet flows. A unique set of two component velocity profiles was taken in the upwash flow field. These measurements include several higher moment terms that appear in the turbulent kinetic energy equations, as well as length scales and intermittency determinations. Measurements were taken' along the axis connecting the two source jets as well as off this axis at six measurement stations above ground. The results provide detailed data on an important class of flows where none existed, and they are expected to significantly improve the computational empirical tools available for predicting V/STOL behavior near the ground.A version of this paper was presented at the 10th Symposium on Turbulence, University of Missouri-Rolla, September 22–24, 1986     

Space–time correlation measurements of high-speed axisymmetric jets using optical deflectometry

An optical deflectometry system is used to provide unique space–time correlation measurements at two positions separated by varying axial distances within a high-speed jet shear layer. The measurements were made for both pure air and for helium/air mixture jets at Mach numbers M=0.9 and M=1.5. The jets issue from round nozzles and the sensing volumes at the two measurement positions consist of small light filaments along spanwise lines that are tangential to the annular jet shear layer. Applying this technique to obtain measurements detailing the level of correlation, spectral content, and convection velocity for jet flows in these flow regimes near the end of the potential core is particularly important in the understanding and prediction of jet noise. Measurements near the end of the potential core along the jet lip line exhibit distinct cross-correlation curves for the pure air jet cases. However, helium/air mixture jets display much lower levels of correlation and little evidence of large-scale structure in the measured spectra. It is believed that the thick visual density gradients dominated by smaller scales throughout the shear layer of the helium/air mixture jets effectively mask the large-scale structure, thus, reflecting a limitation of this optical deflectometer. Finally, a decrease in normalized convection velocity with helium addition is observed.     

Reduced-order modeling of high-speed jets controlled by arc filament plasma actuators

Arc filament plasma actuators applied to high-speed and high Reynolds number jets have demonstrated significant mixing enhancement when operated near the jet column mode (JCM) frequency. A feedback-oriented reduced-order model is developed for this flow from experimental data. The existent toolkit of stochastic estimation, proper orthogonal decomposition, and Galerkin projection is adapted to yield a 35-dimensional model for the unforced jet. Explicit inclusion of a "shift mode" stabilizes the model. The short-term predictive capability of instantaneous flow fields is found to degrade beyond a single flow time step, but this horizon may be adequate for feedback control. Statistical results from long-term simulations agree well with experimental observations. The model of the unforced jet is augmented to incorporate the effects of plasma actuation. Periodic forcing is modeled as a deterministic pressure wave specified on the inflow boundary of the modeling domain. Simulations of the forced model capture the nonlinear response that leads to optimal mixing enhancement in a small range of frequencies near the JCM.     

Testing of a hot- and cold-wire probe to measure simultaneously the speed and temperature in supercritical CO2 flow

The use of hot-wire anemometry in carbon dioxide flow under supercritical conditions has been analyzed and implemented for the first time. A two-sensor probe to simultaneously measure streamwise velocity and temperature in this flow has been designed and constructed. A calibration and test flow loop that can provide supercritical state conditions above the critical point has been also designed, fabricated and tested. The temperature and velocity flow fields of the flow loop can be varied at constant pressure. It has been found that, above the pseudo-critical temperature, the velocity sensor response fits King’s cooling law with a high correlation coefficient. The dependence of the King’s law parameters on temperature can be accurately presented with second or higher order polynomial or exponential fits, depending on the extent of the temperature range. Below the pseudocritical temperature the data is scattered, and the variation with temperature of the King’s law parameters, determined from calibration, is irregular. The influence on this data scatter of the strong variation of the fluid properties near the critical point is analyzed, and a possibility to reduce it is proposed. The temperature sensor response both above and below the pseudocritical temperature is similar to the response under normal conditions. It is linear with a very high correlation coefficient between the calibration data and the fitted curve. It is also shown that the temperature response is not affected by variation of the flow’s speed.     

Controlling spatio-temporal evolution of natural and excited square jets via inlet conditions

The paper presents numerical investigations of square jets in a wide range of Reynolds numbers with varying inlet turbulence characteristics. The research focuses on flow characteristics depending on inflow turbulent length/time scales and excitation frequencies in case of excited jets. It is found that the parameters of inlet turbulence affect the solutions qualitatively when the Reynolds number is sufficiently low. In these cases the impact of varying the turbulent time scale is considerably larger than changing the turbulent length scale. It was also observed that at sufficiently high Reynolds numbers the jets become quite independent of the inlet turbulence characteristics. This confirms findings of Xu et al. (Phys. Fluids, 2013) concerning weak/strong dependence of the jet evolution on inflow conditions. In case of excited jets the excitation frequencies play an important role and influence the jet behaviour most strongly at lower values of the Reynolds number. For some forcing frequencies a bifurcation occurs at sufficiently large forcing amplitudes. This phenomenon turned out to be independent of the assumed length and time scales of the turbulent fluctuations, both in terms of robustness as well as amplitude.     

Generation of hypersonic liquid fuel jets accompanying self-combustion

Aerodynamic behavior of pulsed hypersonic light oil jets injected at 2 km/s and 3 km/s is presented. Auto-ignition and combustion of the fuel during the injection process were visualized. The combustion around the disintegrating jet was enhanced by liquid atomization created by the very high injection pressure as well as the interfacial instability of the hypersonic jet. The jets were injected into air at low pressure and also that premixed with helium and air. It was found that the combustion was reduced in both cases despite the higher jet speed and the increased gas pressure. Received 5 November 1998 / Accepted 24 February 1999     

Vibration control for the primary resonance of the van der Pol oscillator by a time delay state feedback

We investigate the primary resonance of an externally excited van der Pol oscillator under state feedback control with a time delay. By means of the asymptotic perturbation method, two slow-flow equations on the amplitude and phase of the oscillator are obtained and external excitation-response and frequency-response curves are shown. We discuss how vibration control and high amplitude response suppression can be performed with appropriate time delay and feedback gains. Moreover, energy considerations are used in order to investigate existence and characteristics of limit cycles of the slow-flow equations. A limit cycle corresponds to a two-period modulated motion for the van der Pol oscillator. We demonstrate that appropriate choices for the feedback gains and the time delay can exclude the possibility of modulated motion and reduce the amplitude peak of the primary resonance. Analytical results are verified with numerical simulations.     

Stability analysis of the active control system with time delay using IHB method

In this paper, the incremental harmonic balance method is employed to solve the periodic solution that a vibration active control system with double time delays generates, and the stability analysis of which is achieved by the Poincare theorem. The system stability regions can be obtained in view of time delay and feedback gain, the variation of which is also studied. It turns out that along with the increase of time delay, the active control system is not always from stable to unstable, and the system can be from stable to unstable state, whereas the system can be from unstable to stable state. The extent that the two times delays impact on the system stability region is mainly related to the relative magnitude of the two feedback gains. The system can maintain the stable state under the condition of the well-matched feedback gains. The results can provide evidence to design the control strategy of time-delayed feedback.     

Investigation of Submerged Jets with an Extended Initial Laminar Region

The method of producing laminar submerged jets using a device, whose length is comparable with the jet diameter, is described. A submerged air jet, 0.12 m in diameter, produced by means of this technique is experimentally investigated in the Reynolds number range from 2000 to 13 000. Hot-wire anemometer measurements of the flow parameters and laser visualization of the flow are performed. It is shown that the device developed makes it possible to produce submerged jets with the laminar regions as long as 5.5 jet diameters. The initial regions of such jets can be used to study the development of disturbances in submerged jets, as well as used in medicine and engineering in organizing various gasdynamic curtains which produce zones with given properties with respect to purity and composition inside another gas media.     

The effect of buoyancy on flow fluctuations for horizontal plane jets in low speed applications

Low speed jets have important applications in chemical process, power and aerospace industries. Velocity fluctuations in low speed laminar jets have been investigated experimentally and theoretically, in the present work. The effects of buoyancy on the mean and fluctuating components of velocity have been highlighted. It is observed that even for forced convection dominated flow, convective instabilities and the resulting local velocity fluctuations are significantly influenced by buoyancy. Both the dominant frequency and the amplitude of velocity fluctuations depend on the jet exit temperature and spatial location within the jet. For isothermal jets, the dominant frequency of oscillation increases almost linearly with Reynolds number, while for buoyant jets nonlinearity exists at lower Reynolds numbers. Numerical simulations of the present study are found to be reasonably successful in predicting the oscillatory behavior of both isothermal and non-isothermal laminar free jets accurately.     

Stability of a rivulet flowing in a microchannel

A novel microfluidic technique has been recently proposed to produce quasi-monodisperse collections of microbubbles with a controlled size. In this technique, a gaseous stream is injected through a T-junction into a microchannel transporting a liquid current. The gas adheres to a hydrophobic strip printed on the channel surface. When the gas and liquid flow rates are set appropriately, a gaseous rivulet flows over that strip. The rivulet breaks up downstream due to a capillary pearling instability, which leads to a quasi-monodisperse collection of microbubbles. Motivated by this application, we here analyze the stability of both gas and liquid rivulets coflowing with a current in a quadrangular microfluidic channel. The results essentially differ from those of cylindrical jets because the contact-line-anchorage condition affects fundamentally the rivulet’s instability nature. The temporal stability analysis shows that the rivulet becomes unstable not only for (unperturbed) contact angles larger than 90° (as can be expected) but also for values smaller than that angle. Interestingly enough, the maximum growth factor exhibits a non-monotonic dependence with respect to the Reynolds number (i.e., the viscosities). In fact, there are intervals of that parameter where the fluid system becomes unstable, while all the perturbations are damped outside that interval. The gaseous rivulet does not stabilize as the Reynolds number decreases, which means that it can be unstable even in the Stokes limit and for contact angles less than 90°. In addition, the stability of a flowing liquid rivulet is not determined by its contact angle exclusively (as occurs in the static case), but by the Reynolds number as well. Liquid rivulets with contact angles less than 90° can be unstable for sufficiently high Reynolds numbers.     

Study on Expansion Characteristic of Twin Combustion Gas Jets in Five-Stage Cylindrical Stepped-wall Observation Chamber

The five-stage cylindrical stepped-wall observation chamber is designed to investigate the method of controlling the interior ballistic stability in bulk-loaded propellant guns. The expansion and mixing process of twin combustion gas jets in liquid is studied by means of high speed photographic system. The influence of multiple parameters on jet expansion shape is discussed. Based on the experiment, the three-dimensional mathematics model is established to simulate the expansion process of twin gas jets in liquid. The pressure, density, temperature, velocity contours and evolutionary process of vortices are obtained. Results show that vortices behind the corner of the steps are formed due to the inducing effect of steps. The jets can expand along the axial and radial direction simultaneously, weakening the Kelvin-Helmholtz instability. The numerical simulation results of axial expansion displacement are in good agreement with the experimental data.     

Development of the Strategy of Active Control of Instability Waves in Unexcited Turbulent Jets

The possibility of controlling instability waves in the mixing layer of a subsonic unexcited jet is studied. These waves can be noise sources in both free jets and jets as parts of configurations. In the study the method of experimental diagnostics of the instability waves in the near field of a jet using an azimuthal multimicrophone array is realized. The data on the near field fluctuations are used for testing the control strategy proposed by the authors. The strategy consists in narrowband sliding filtration of the original signal and the formation of a narrowband controlling action on the basis of the linear principle of signal superposition. The results of the study represent the next step toward the realization of an active control system suppressing natural instability waves in turbulent jets.     

考虑间隙反馈控制时滞的磁浮车辆稳定性研究

常导磁吸型(EMS)磁悬浮列车在悬浮控制中的每个环节,时滞是不可避免的,当时滞超过一定程度后,系统有可能失稳.本文针对EMS磁浮列车控制环节的临界时滞与车辆参数(如运行速度、反馈控制增益、导轨参数和悬挂参数)的关系开展研究.建立了磁浮车辆/导轨耦合动力学模型,车辆包含1节车辆和4个磁浮架,考虑车辆的10个自由度,每个磁浮架上包含4个悬浮电磁铁.导轨模拟为一系列简支Bernoulli-Euler梁,采用模态叠加法对导轨振动方程进行求解.采用传统线性电磁力模型实现车辆和轨道的耦合.采用比例-微分控制算法对电磁铁电流进行反馈控制,实现车辆稳定悬浮,并假设时滞均发生在控制环节,且只考虑间隙反馈控制环节的时滞.采用四阶龙格库塔法对耦合系统动力学方程进行求解,编写了数值仿真程序,计算得到车辆导轨耦合系统在考虑间隙反馈控制时滞时的响应.将系统运动发散时的时滞大小视为临界时滞,开展了参数规律影响分析.通过分析,给出了提高时滞条件下车辆稳定性的方法,包括增大导轨的弯曲刚度和阻尼比,减小间隙反馈控制增益并增大速度反馈控制增益,以及增大二系悬挂阻尼.      

An Eulerian time filtering technique to study large-scale transient flow phenomena

Unsteady fluctuating velocity fields can contain large-scale periodic motions with frequencies well separated from those of turbulence. Examples are the wake behind a cylinder or the processing vortex core in a swirling jet. These turbulent flow fields contain large-scale, low-frequency oscillations, which are obscured by turbulence, making it impossible to identify them. In this paper, we present an Eulerian time filtering (ETF) technique to extract the large-scale motions from unsteady statistical non-stationary velocity fields or flow fields with multiple phenomena that have sufficiently separated spectral content. The ETF method is based on non-causal time filtering of the velocity records in each point of the flow field. It is shown that the ETF technique gives good results, similar to the ones obtained by the phase-averaging method. In this paper, not only the influence of the temporal filter is checked, but also parameters such as the cut-off frequency and sampling frequency of the data are investigated. The technique is validated on a selected set of time-resolved stereoscopic particle image velocimetry measurements such as the initial region of an annular jet and the transition between flow patterns in an annular jet. The major advantage of the ETF method in the extraction of large scales is that it is computationally less expensive and it requires less measurement time compared to other extraction methods. Therefore, the technique is suitable in the startup phase of an experiment or in a measurement campaign where several experiments are needed such as parametric studies.