Frequency Velocity Fluctuations Research Articles

Dynamic mode structure analysis of the near-wake region of a Savonius-type hydrokinetic turbine

Hydrokinetic turbine is a clean technology that can effectively use tidal energy, the Savonius-type runner is very suitable for natural flows, and has been widely used in tidal energy power stations. The dynamic structure of the flow field in the near-wake region downstream has strong impact on the dense layout of the turbine, but there has been no in-depth exploration till now. To explore the potential for beneficial interactions between turbines, this study conducted numerical simulations of Savonius-type turbine, combining fast Fourier transformation and Dynamic mode decomposition to conduct in-depth analysis of the velocity fluctuation frequency distribution and dynamic mode in near-wake region, and compared the advantages and disadvantages of the two methods. This research obtained the distribution of two main frequencies in the near-wake region and clarified their excitation sources. The frequencies of turbines are mixed in the far field, greatly affects the far-field flow state in the near-wake region. The DMD method has great advantages in flow field analysis, as it does not require prior knowledge of flow field compared to FFT method. The conclusions of this study provide new considerations for large-scale arrangement of turbine units, and provide a new method for the flow state analysis.

Simulation of mixing flows with different temperatures in a T-junction using OpenFOAM code

This paper aims to evaluate the frequency of velocity and temperature fluctuations in the mixing region using OpenFOAM code. Turbulent mixing of fluids at different temperatures can lead to temperature fluctuations at the pipe material. These fluctuations, or thermal striping, inducing cyclical thermal stresses and resulting thermal fatigue, may cause unexpected failure of pipe material. Therefore, an accurate characterization of temperature fluctuations is important in order to estimate the lifetime of pipe material. Thermal fatigue of the coolant circuits of nuclear power plants is one of the major issues in nuclear safety. To investigate thermal fatigue damage, the OECD/NEA-Vattenfall T-Junction Benchmark was initiated to test the ability of state-of-the-art Computational Fluid Dynamics (CFD) codes to predict the important parameters affecting high-cycle thermal fatigue in mixing tees. In this study, to simulate the standard problem described above, the OpenFOAM code is used, which is an open integrated platform for numerical simulation of problems in continuum mechanics. At the first with Salome-meca code, a computational grid was created, consisting of about 450,000 nodes, and k-eps model and RANS models were used to simulate turbulence. OpenFOAM code results were compared with the available experimental results. The results were found to be in well-agreement with the experimental results in terms of amplitude and frequency of temperature and velocity fluctuations.

Dynamics of a particle-laden bubble colliding with an air-liquid interface

The collision, bouncing and potential bursting of air bubbles with air-liquid interfaces are key processes involved in the initial stage of foam formation. While fundamental studies of these processes, especially for gas-liquid-solid froth systems, are very valuable for a better understanding of various chemical engineering separation systems, these are scarce. This paper investigates the dynamics of rising bubbles, without particles attached and with various particle coverages, as they collide with an air-liquid interface. For uncoated bubbles, an increase in distance from the bubble releasing point to the air-liquid interface resulted in higher bubble approach velocities, although with minor changes in the velocity fluctuation frequency. This increase in approach velocity was not observed for bubbles with relatively high particle coverage. For particle-laden bubbles, the collision with the interface is associated with movement of the particles over the surface of the decelerating bubble. This particle motion on the bubble surface, combined with bubble shape pulsation, contributes to the kinetic energy dissipation of the approaching bubble. A damped oscillation model was derived to represent the velocity of the bubble interacting with the interface, which shows that the amplitude of the velocity decreases gradually with the increase in particle coverage. The damping coefficient in the model, introduced to quantify the influence of attached particles, is shown to increase with particle coverage, confirming the key role that particles play in bubble collision dynamics at an air-liquid interface and allowing, for the first time, the prediction of their behavior.

Flow and performance analysis of a natural gas-air rotating detonation engine with high-speed velocimetry

An experimental investigation of a high pressure, natural gas-air rotating detonation engine is presented. Simultaneous high-speed measurements of combustion chamber pressure, axially-integrated chamber chemiluminescence, and particle image velocimetry at the combustor exit plane were used to qualitatively and quantitatively analyze the exhaust flow of two test conditions with distinct wave dynamics. A single detonation wave with an intermittent counter-rotating wave was characterized in the first test case, while a steady counter-rotating mode was studied in the second. Analysis using the continuous wavelet transform informs the coupled shift in the frequency and amplitude of pressure and velocity fluctuations observed in the raw timeseries. The high-speed measurements are used to reconstruct the wave structure for each case over the course of a cycle, revealing the canonical rotating detonation engine exhaust flow structure with a trailing oblique shock sweeping through the products for the single wave case. Interactions between counter-propagating detonation fronts result in a flowfield that varies with cycle phase angle, in contrast to the self-similar field of the single propagating wave. The axial velocity profile around the circumference of the combustor is independent of wave location, while azimuthal velocity fluctuations from the trailing oblique shocks are observed to track the detonation fronts and destructively interfere at wave intersections. The total pressure and temperature of flow exiting the combustor are computed using the phase-resolved velocity measurements along with the measured reactant flowrate and thrust to close the global balance of mass and momentum. The case with counter-rotating waves delivers 5% higher performance than the single-wave case. The application of simultaneous high-speed diagnostics helps elucidate the flow structure in a rotating detonation engine and provides a connection between the local flow structure and global combustor performance.

Investigation of gear rattle noise including visualization of vibro-impact regimes

This paper presents an experimental study of gear rattle noise induced by vibroimpacts between gear teeth. A specific experimental set-up is designed to analyse the nonlinear dynamic behaviour of a spur gear submitted to input velocity fluctuation. The drag torque, the mean drive gear rotational speed, the velocity fluctuation amplitude and frequency are controlled during experiment. The dynamic transmission error is measured thanks to high resolution optical encoders. The originality of the experimental set-up consists in using a high-speed camera in order to visualize the contact zone and to identify the occurrence of successive impacts between gear teeth. The rattle threshold is identified as a function of velocity fluctuation amplitude and frequency for various operating drag torques and mean rotational speeds. Experiments show very good agreement with the theoretical master curve. Once impacts occur, stationary nonlinear gear dynamic response and rattle noise radiated by the mechanical system are investigated. Most of the time, an almost periodic response is observed with 2 impacts per period. One impact between the active flanks alternates with one impact between the reverse flanks. A contact phase between gear teeth is observed after each impact instead of an instantaneous rebound. The number of successive tooth pairs crossing the meshing zone without any contact between gear teeth varies according to the ratio of the excitation frequency to the rotation frequency. Analytical and numerical works performed using a gear rattle model show good agreement with experiments. Finally, sound pressure emitted from the gear pair is measured. The acoustic power imputable to gear rattle is found to be proportional to the total kinetic energy transferred per second to the system by the successive impacts.

Visualization of bubble flow in the channel of a dimple-type embossing plate heat exchanger under different fluid inlet/outlet ports

The plate heat exchanger, which uses air and water mixture as the medium of cold flow, is efficient, compact and widely used heat exchange equipment. Its heat transfer efficiency is directly related to the air bubble flow in the cold flow. Considering different positions of fluid inlet and outlet ports, such as the upper or lower inlet combined with the upper or lower outlet, a high-speed camera was employed to visualize and analyze the air bubble movement in a flow passage machined between two transparent dimple-type embossing plates, including the bubble trajectory, distribution, and size, etc. Results showed that regardless of the inlet and outlet ports for the fluid, a faster flow velocity of air and water mixture has a larger Reynolds number, Froude number, Weber number, and smaller bubble size as well as a higher sectional void fraction on the top section of the passage. However, the fluid inlet and outlet positions have an important effect on the bubble distribution, and this indicates that the bubble buoyancy has an obvious influence on the bubble distribution. As the liquid flows away from the lower outlet slowly, there appears a stagnant air area, meanwhile, a foam zone is formed below the air area only when the fluid gets into it from the lower inlet. Nevertheless, as the fluid flows away from the upper outlet of the passage, there is neither a stagnant air area nor a foam domain irrespective of where the fluid enters from. It is worth pointing out that all the bubble velocities fluctuated, and small bubbles have a larger velocity fluctuation range and frequency than middle and large bubbles.

Three-dimensional Тurbulent Supersonic Flow over a Plate

The process of laminar-turbulent transition in a boundary layer is studied in terms of vortex evolution, from the growth of weak external disturbances to the formation of intense waves resulting in the development of a turbulent flow having internal scales of the problem. The self-sustained turbulence is obtained and the flow patterns on the plate surface and inside the turbulent boundary layer with fluid plumes propagating from the plate surface in the form of “bursting” are investigated. The basic flow parameters are calculated, such as the frequency and intensity of gas velocity fluctuations in turbulent spots. The validity of a local turbulence similarity law is confirmed. The study is performed on the basis of direct numerical simulation of a flow over a plate with Mach number M = 2 using unsteady Navier-Stokes equations without any closure model of turbulence.

Nonlinear Vibration and Stability Analysis of Viscoelastic Rayleigh Beams Axially Moving on a Flexible Intermediate Support

In this study, the nonlinear vibration and stability of a simply supported axially moving Rayleigh viscoelastic beam equipped with an intermediate nonlinear support are investigated. The type of considered nonlinearity is geometric and is due to the axial stretching. The Kelvin–Voigt model is used to regard the beam internal damping. The Hamilton’s principle is employed to derive the governing equations and corresponding boundary conditions. The multiple scales method is applied to the dimensionless form of the governing equations and the nonlinear frequencies, time response of the system for two cases of the axial velocity fluctuation frequency are obtained. The stability of the system is investigated via solvability condition and Routh–Hurwitz criterion. Some case studies are accomplished to demonstrate the effect of rotary inertia, axial velocity and parameters of intermediate support on the system response, critical velocity and the system stability. Furthermore, the variation of the first two resonance frequencies with respect to mean axial velocities for different locations of the intermediate support are investigated. It is found that by moving the intermediate support from one end of the beam to its midpoint, the region in which the first mode undergoes static instability, shrinks. Moreover, although rotary inertia impressively decreases the natural frequencies, intermediate support has the dominant effect on increasing the natural frequencies.

Impact of risk illusions on traffic flow in fog weather

In this study, an extended car-following model is proposed to investigate the impacts of driver’s risk illusions on traffic flow stability, velocity, acceleration and headway fluctuation frequency in fog weather. Through stability analysis and numerical simulation, the results indicate that risk illusions weaken the stabilization of traffic system. Furthermore, it is shown that the proposed model is more dangerous than the full velocity difference model from the perspectives of the maximum velocity and acceleration. Additionally, risk illusions increase the headway fluctuation frequency, which means that more adjustments of the headway are needed, increasing driver’s workload. Therefore, the impact of risk illusions on traffic flow is disadvantageous.

Unsteady Behavior of Necklace Vortex Produced by a Square Plate Protrusion

In this study, the unsteady behavior of necklace vortices formed in front of a square flat plate was experimentally investigated by flow visualization and PIV analysis by using a water channel. As a result, the necklace vortices started to oscillate when the Reynolds number increased beyond approximately 2000. Then, an amalgamation behavior of the necklace vortices took place when the Reynolds number increased beyond approximately 2650. Furthermore, in the same Reynolds number range, a breakaway behavior appeared when the relative height of the square plate was beyond approximately h/δ = 4.0. The features of the necklace vortices behaviors in the oscillation, amalgamation and breakaway states were explained by observing the time-series image of path lines and by analyzing the frequency of velocity fluctuation.

Flame Describing Function analysis of spinning and standing modes in an annular combustor and comparison with experiments

This article reports a numerical analysis of combustion instabilities coupled by a spinning mode or a standing mode in an annular combustor. The method combines an iterative algorithm involving a Helmholtz solver with the Flame Describing Function (FDF) framework. This is applied to azimuthal acoustic coupling with combustion dynamics and is used to perform a weakly nonlinear stability analysis yielding the system response trajectory in the frequency-growth rate plane until a limit cycle condition is reached. Two scenarios for mode type selection are tentatively proposed. The first is based on an analysis of the frequency growth rate trajectories of the system for different initial solutions. The second considers the stability of the solutions at limit cycle. It is concluded that a criterion combining the stability analysis at the limit cycle with the trajectory analysis might best define the mode type at the limit cycle. Simulations are compared with experiments carried out on the MICCA test facility equipped with 16 matrix burners. Each burner response is represented by means of a global FDF and it is considered that the spacing between burners is such that coupling with the mode takes place without mutual interactions between adjacent burning regions. Depending on the nature of the mode being considered, two hypotheses are made for the FDFs of the burners. When instabilities are coupled by a spinning mode, each burner features the same velocity fluctuation level implying that the complex FDF values are the same for all burners. In case of a standing mode, the sixteen burners feature different velocity fluctuation amplitudes depending on their relative position with respect to the pressure nodal line. Simulations retrieve the spinning or standing nature of the self-sustained mode that were identified in the experiments both in the plenum and in the combustion chamber. The frequency and amplitude of velocity fluctuations predicted at limit cycle are used to reconstruct time resolved pressure fluctuations in the plenum and chamber and heat release rate fluctuations at two locations. For the pressure fluctuations, the analysis provides a suitable estimate of the limit cycle oscillation and suitably retrieves experimental data recorded in the MICCA setup and in particular reflects the difference in amplitude levels observed in these two cavities. Differences in measured and predicted amplitudes appear for the heat release rate fluctuations. Their amplitude is found to be directly linked to the rapid change in the FDF gain as the velocity fluctuation level reaches large amplitudes corresponding to the limit cycle, underlying the need of FDF information at high modulation amplitudes.

Stability of fluid conveying nanobeam considering nonlocal elasticity

In this study, the nonlocal Euler–Bernoulli beam theory is employed in the vibration and stability analysis of a nanobeam conveying fluid. The nanobeam is assumed to be traveling with a constant mean velocity along with a small harmonic fluctuation. In the considered analysis, the effects of the small-scale of the nanobeam are incorporated into the equations. By utilizing Hamilton’s principle, the nonlinear equations of motion including stretching of the neutral axis are derived. Damping effect is considered in the analysis. The closed form approximate solution of nonlinear equations is solved by using the multiple scale method, a perturbation technique. The effects of the different value of the nonlocal parameters, mean speed value and ratios of fluid mass to the total mass as well as effects of the simple–simple and clamped–clamped boundary conditions on the linear and nonlinear frequencies, stability, frequency–response curves and bifurcation point are presented numerically and graphically. The solvability conditions are obtained for the three distinct cases of velocity fluctuation frequency. For all cases, the stability areas of system are constructed analytically.

On Parametric Stability of a Nonconstant Axially Moving String Near Resonances

The stability of an axially moving string system subjected to parametric excitation resulting from speed fluctuations has been examined in this paper. The time-dependent velocity is assumed to be a harmonically varying function around a (low) constant mean speed. The method of characteristic coordinates in combination with the two timescales perturbation method is used to compute the first-order approximation of the solutions of the equations of motion that governs the transverse vibrations of an axially moving string. It turns out that the system can give rise to resonances when the velocity fluctuation frequency is equal (or close) to an odd multiple of the natural frequency of the system. The stability conditions are investigated analytically in terms of the displacement-response and the energy of the system near the resonances. The effects of the detuning parameter on the amplitudes of vibrations and on the energy of the system are also presented through numerical simulations.

On the asymptotic approximation of the solution of an equation for a non-constant axially moving string

The transverse vibrations of axially moving strings with time dependent velocity and its instability are examined in this paper. The velocity function is assumed to be a harmonically varying function about a constant low mean speed. Approximate solutions are sought using the two timescales perturbation method in conjunction with the method of characteristic coordinates. Moreover, it will turn out that infinitely many resonances in the system can arise, when the velocity fluctuation frequency is equal (or close) to an odd multiple of the lowest natural frequency of the constant velocity system. The dynamic displacement-response and the energy of the belt system obtained using the method of characteristic coordinates are compared numerically. It is shown that the energy of the belt system can become large in a resonance case. In addition, the amplitude of vibration is also found to be growing on long timescales, that is, on a timescale of order ε−1.

Effect of Optimizing PID Parameters and Spindle Speeds on Processing Performance of KDP Micro-Defect Mitigation Machine Tool

PID parameters of machine tool for micro-defect mitigation of KDP crystal had been optimized, after which the velocity fluctuation frequency and amplitude variation of motion axis under different spindle speeds were studied. It is evident that the stability and following errors of the system run better under the velocity&acceleration feed forward PID control algorithm and Notch filters. The velocity fluctuation frequency of motion axis varies with spindle speeds significantly when the tool system is stable, while the fluctuation amplitude variation is slightly changed. To be conclude, the optimal working spindle speed is verified to be 4.78×104 rpm based on comparative experiments, at which damage pits can be mitigated by micro-machining successfully with roughness value of 34.4nm.

Numerical study of the instantaneous flow fields by large eddy simulation and stability analysis in a single aisle cabin model

Airflow movement is one of the most important physical parameter greatly influencing the contaminants transmission and passengers' thermal perception in aircraft cabin environment. Although many measured and computational results showed that the airflows in aircraft cabins were highly unsteady or even unstable, most of the existing studies focused on time-averaged air distributions in aircraft cabins. The instantaneous characteristics of flow fields, such as airflow velocity fluctuation, turbulence intensity and fluctuation frequency, were seldom reported. In this paper, a refined large eddy simulation (LES) was conducted to investigate the complex airflow characteristics in a simplified Boeing 737-200 cabin model. Simulated results indicated that the flow fields in this cabin model, especially around the aisle region, displayed obvious quasi-periodic large scale unsteadiness and continuing instabilities, as seen in our PIV measurements, even though the boundary conditions were fixed and symmetrical with the middle plane and various perturbations were as much removed as possible. A triple decomposition was used to extract the highly unsteady characteristics of the instantaneous flow fields and the large scale unsteadiness term was used to interpret why the actual kinetic energies of turbulence in LES was amplified. The structural stability analysis approach was used to investigate the mechanism of such unstable flow fields. Saddle points and heteroclinic orbits were found to exist in cross sections of the cabin model. The Peixoto theorem was used to interpret the reason for this unstable instantaneous flow fields in this type of flow regime and geometry.

Using Fourier differential quadrature method to analyze transverse nonlinear vibrations of an axially accelerating viscoelastic beam

In this paper, a Fourier expansion-based differential quadrature (FDQ) method is developed to analyze numerically the transverse nonlinear vibrations of an axially accelerating viscoelastic beam. The partial differential nonlinear governing equation is discretized in space region and in time domain using FDQ and Runge–Kutta–Fehlberg methods, respectively. The accuracy of the proposed method is represented by two numerical examples. The nonlinear dynamical behaviors, such as the bifurcations and chaotic motions of the axially accelerating viscoelastic beam, are investigated using the bifurcation diagrams, Lyapunov exponents, Poincare maps, and three-dimensional phase portraits. The bifurcation diagrams for the in-plane responses to the mean axial velocity, the amplitude of velocity fluctuation, and the frequency of velocity fluctuation are, respectively, presented when other parameters are fixed. The Lyapunov exponents are calculated to further identify the existence of the periodic and chaotic motions in the transverse nonlinear vibrations of the axially accelerating viscoelastic beam. The conclusion is drawn from numerical simulation results that the FDQ method is a simple and efficient method for the analysis of the nonlinear dynamics of the axially accelerating viscoelastic beam.

Simulating particle collisions in homogeneous turbulence with kinematic simulation – A validation study

Particle collisions in homogeneous isotropic turbulence are simulated by means of kinematic simulation (KS) and compared with direct numerical simulation (DNS). KS is a computationally efficient surrogate for DNS of flow field dynamics [23]. To determine the energy spectrum in the KS, the Reynolds-number-dependent model spectrum of Pope was applied. For the comparison, particles having Stokes numbers ranging from 0.01 to 8 were considered and the DNS study of Sundaram and Collins [2] was used as a reference. Particle collision statistics like collision frequencies and particle concentration distributions resulting from KS and DNS were compared. Even though the KS collision frequencies were found to be in good agreement with the DNS reference for St>2, deviations were observed in the particle mean relative velocity and radial distribution function of particles. Moreover, the extent by which particle collisions occur in KS-based flow fields was found to depend on the KS persistence parameter. This parameter controls the frequency of velocity fluctuations in a KS.

Mode competition in streamwise-only vortex induced vibrations

Time-resolved Particle-Image Velocimetry (PIV) has been used to study mode competition and transient behaviour in the wake of a cylinder experiencing Vortex-Induced Vibrations (VIV) in the streamwise direction. The cylinder response regime contained two branches, occurring above and below the onset of synchronisation between the wake and the cylinder motion (lock-in). During the first branch, the wake exhibited both the S-I mode (in which two vortices are shed simultaneously per vibration cycle) and the alternate A-II mode (similar to the well known von Kármán vortex street). An extended PIV data set acquired in this region revealed mode switching between the S-I and A-II modes. A criterion based on Proper-Orthogonal Decomposition was developed to identify which mode was dominant as a function of time. The A-II mode was found to be dominant for over 90% of the instantaneous fields examined, while the S-I mode appeared to be more unstable.Symmetrically shed vortices were found to rearrange downstream into an alternate structure in which the wake was no longer synchronised to the cylinder motion. The dominant frequency of transverse velocity fluctuations was measured throughout the wake in order to study the effects of this breakdown in more detail. For the majority of the wake, the fluctuations occurred at the Strouhal frequency, while in a region in the near wake the fluctuations occurred at the frequency of the cylinder motion. It is thought that during the first response branch vortices are formed at the cylinder response frequency, but tend to quickly rearrange downstream into an alternate structure which is no longer synchronised to the cylinder motion. As a result, the fluctuating drag will be synchronised to the structural motion, and is capable of providing positive energy transfer in the apparent absence of lock-in. Finally, the spatial dependence of the frequency of velocity fluctuations throughout the wake is used to explain some of the conflicting results in the literature regarding streamwise VIV, and the implications for the general study of VIV are discussed.

CFD modeling of thermal mixing in a T-junction geometry using LES model

Turbulent mixing of fluids at different temperatures can lead to temperature fluctuations at the pipe material. These fluctuations, or thermal striping, inducing cyclical thermal stresses and resulting thermal fatigue, may cause unexpected failure of pipe material. Therefore, an accurate characterization of temperature fluctuations is important in order to estimate the lifetime of pipe material. Thermal fatigue of the coolant circuits of nuclear power plants is one of the major issues in nuclear safety. To investigate thermal fatigue damage, the OECD/NEA has recently organized a blind benchmark study including some of results of present work for prediction of temperature and velocity fluctuations performing a thermal mixing experiment in a T-junction. This paper aims to estimate the frequency of velocity and temperature fluctuations in the mixing region using Computational Fluid Dynamics (CFD). Reynolds Averaged Navier-Stokes and Large Eddy Simulation (LES) models were used to simulate turbulence. CFD results were compared with the available experimental results. Predicted LES results, even in coarse mesh, were found to be in well-agreement with the experimental results in terms of amplitude and frequency of temperature and velocity fluctuations. Analysis of the temperature fluctuations and the power spectrum densities (PSD) at the locations having the strongest temperature fluctuations in the tee junction shows that the frequency range of 2–5Hz contains most of the energy. This range of frequency is characteristic for thermal fatigue.