Time Series Of Pressure Fluctuations Research Articles

Cross-flow instability on a swept-fin cone at Mach 6: characteristics and control

Experiments were performed to document the complex flow field around and over a $70^{\circ }$ swept fin mounted on a $7^{\circ }$ half-angle right-circular cone in a Mach 6 free-stream. Of particular interest is the turbulent transition of the boundary layer over the swept fin, which is expected to be dominated by a cross-flow instability. Stationary features in the surface temperature distribution over the fin are documented using infrared thermal imaging. These were processed further to determine average spatial Stanton number distributions over the fin. Wavelet analysis of the Stanton number distributions revealed stationary patterns with wavelengths near the fin leading edge that were consistent with linear theory predictions of stationary cross-flow modes. Further from the leading edge, the wavelength of the stationary patterns was observed to increase prior to turbulence onset. Based on these observations, specially designed arrays of discrete roughness elements (DREs) were investigated as a means of delaying turbulence transition with the objective of reducing surface heat flux on the swept fin. The DRE designs followed our previous approach used for cross-flow transition control (Corke et al., J. Fluid Mech., vol. 856, issue 10, 2018, pp. 822–849; Arndt et al., J. Fluid Mech., vol. 887, 2020, A30). These focused on either the shorter wavelengths near the leading edge, or the longer wavelengths that developed near turbulence onset. With regard to delaying transition and reducing the surface heat flux, the DREs that focused on the larger wavelengths of stationary modes were most effective. The fin included an array of pressure sensors that were used to document travelling disturbances that could include those associated with travelling cross-flow modes. Phase analysis of the pressure fluctuation time series was used to determine the wavelength, wave angle and phase speed that were consistent with the travelling cross-flow modes. Cross-bicoherence analysis between the stationary and travelling disturbances indicates a nonlinear phase locking that can account for the development of the longer-wavelength stationary features in the surface heat flux, presumed to be due to stationary cross-flow modes, prior to turbulence onset.

Early risk warning method for fluidized beds using generalized extremum distribution of pressure fluctuation

Pressure fluctuation is commonly used to characterize the dynamic of fluidized bed, and bubble movements resulting in pressure fluctuations will seriously affect the stable operation of fluidized bed. This paper presents an extreme value statistical analysis model that uses generalized extreme value (GEV) distribution to analyze the pressure fluctuation time series, predict its future fluctuation state, and further provide risk warning for fluidized bed operation. The pressure fluctuation time-series for four mainly fluidization behaviors (single bubble, multiple bubble, exploding bubble and transport conditions) in an actual experiment were analyzed by the proposed method. The results show that the error rate of the proposed method in this paper is controlled within±10%, and the average error rate is controlled within −1.7%–3.7%. By analyzing the risk margin of the extreme pressure fluctuations of each flow regime, the risk margin of exploding bubble is the largest, and more stringent measures should be taken to ensure the stable operation of the fluidized bed in this flow state. In summary, the risk warning of the fluidized bed can be detected in the joint efforts of the confidence interval and the risk margin of the pressure fluctuation return level of each flow regime.

Detection of dynamical regime transitions with lacunarity as a multiscale recurrence quantification measure

We propose lacunarity as a novel recurrence quantification measure and illustrate its efficacy to detect dynamical regime transitions which are exhibited by many complex real-world systems. We carry out a recurrence plot-based analysis for different paradigmatic systems and nonlinear empirical data in order to demonstrate the ability of our method to detect dynamical transitions ranging across different temporal scales. It succeeds to distinguish states of varying dynamical complexity in the presence of noise and non-stationarity, even when the time series is of short length. In contrast to traditional recurrence quantifiers, no specification of minimal line lengths is required and geometric features beyond linear structures in the recurrence plot can be accounted for. This makes lacunarity more broadly applicable as a recurrence quantification measure. Lacunarity is usually interpreted as a measure of heterogeneity or translational invariance of an arbitrary spatial pattern. In application to recurrence plots, it quantifies the degree of heterogeneity in the temporal recurrence patterns at all relevant time scales. We demonstrate the potential of the proposed method when applied to empirical data, namely time series of acoustic pressure fluctuations from a turbulent combustor. Recurrence lacunarity captures both the rich variability in dynamical complexity of acoustic pressure fluctuations and shifting time scales encoded in the recurrence plots. Furthermore, it contributes to a better distinction between stable operation and near blowout states of combustors.

Rate dependent transition to thermoacoustic instability via intermittency in a turbulent afterburner

Experiments were conducted to study the rate dependent transition to thermoacoustic instability in a turbulent afterburner rig. The afterburner rig contains v-gutters as flame stabilizers and simulates elevated inlet gas temperature using a preheater. Under quasi-static increase in flow Reynolds number of the afterburner, screech is not observed; on the contrary, screech onsets when the Reynolds number is increased at a higher rate. Such a phenomenon is known as rate induced tipping or R-tipping. When the Reynolds number is increased at a lower rate, screech appears as a few bursts of high-amplitude periodic oscillations amidst low-amplitude aperiodic oscillations, a state known as intermittency. As the rate of change of Reynolds number is increased, more bursts appear and with further increase in the rate, the proportion of periodic oscillations of the bursts increases in the time series of pressure fluctuations, approaching a state of limit-cycle oscillations. We show for the first time, a rate-dependent transition to thermoacoustic instability in a turbulent afterburner happening through intermittency, with respect to increasing the rate of change of Reynolds number. The onset of burst occurs earlier, i.e. bursts occurring at a lower Reynolds number as the rate of change of Reynolds number is increased. The amplitude of bursts during intermittency is higher than that of the limit cycle oscillations. The rate dependent transition to screech through intermittency is analyzed by studying the variation of probability density function (PDF) of the amplitude of pressure, variation of the amplitude of bursts, variation of the number of bursts of periodic oscillations, and the inlet conditions corresponding to the onset of bursts, with respect to different rates of change of Reynolds number. Rate dependent transition observed in the model afterburner suggests that combustion system of a gas turbine engine should be subjected to different engine throttling rates to define the thermoacoustic stability map.

Analysis of long-term observations of the groundwater level In an aseismic region

The results of the analysis of continuous precise time series of atmospheric pressure and groundwater level fluctuations in a well drilled to a depth of 400 m in the territory of Moscow are presented. The observations are remarkable in terms of their duration of more than 22 years (from February 2, 1993 to April 4, 2015) and by the sampling interval of 10 min. These long observations are suitable for exploring the stationarity of the properties of hydrogeological time series in a seismically quiet region, which is important from the methodological standpoint for interpreting the similar observations in seismically active regions aimed at earthquake prediction. Factor and cluster analysis applied to the sequence of multivariate vectors ofthe statistical properties of groundwater level time series in the successive 10-day windows after adaptive compensation for atmospheric pressure effects distinguish five different statistically significant states of the time series with the transitions between them. An attempt to geophysically interpret the revealed states is made. Two significant periods – 46 and 275 days – are established by spectral analysis of the sequence of the transitions times between the clusters.

Prediction of near field propeller cavitation noise by viscous CFD with semi-empirical approach and its validation in model and full scale

Propeller cavitation noise has been a large interest among maritime industries in terms of mariners' comfort and marine environmental protection. The objective of this study is to propose and validate practical computational methods to predict near field propeller cavitation noise by complementary use of viscous CFD and semi-empirical formula. Acoustic analogical method represented by Ffowcs Williams-Hawkings equation is not utilized at all in the present study.Four different propellers equipped on actual ships are of the interest. Cavitation phenomena around these propellers are reproduced by viscous CFD simulations behind full-scale ship wake. Time series of pressure fluctuations as well as the area of cavitation extent on the blades are logged. The former is directly utilized to quantify the level of tonal noise at near field while the latter is utilized to estimate upper bound of broadband noise together with the Brown's semi-empirical formula.The proposed methods accurately estimate the tonal noise up to 3rd blade frequency, in the meantime, upper limit of broadband noise is well predicted in comparison to the measurement results. The present method is very practical and thus it can be one of the criteria to estimate propeller cavitation noise in the near field.

Sensitivity Study on Quantitative Methods by Analysis of Pressure Fluctuations in a Fluidized Bed

The sensitivity and reliability of 23 data processing methods are studied by analyzing pressure fluctuation time series in a fluidized bed. First, the concept of minimal stationary segment length i...

Effect of cohesive powders on pressure fluctuation characteristics of a binary gas-solid fluidized bed

The effect of cohesive particles on the pressure fluctuations was experimentally investigated in a binary gas-solid fluidized bed. The pressure fluctuation signals were measured by differential pressure sensors under conditions of various weight percentages of cohesive particles. The cohesive particles increased the fixed bed pressure drop per unit height and decreased the minimum fluidization velocity. The Wen & Yu equation well predicts the minimum fluidization velocity of the binary system. The addition of cohesive particles slightly decreased the bubble size in bubbling flow regime when the cohesive particles and the coarse particles mixed well, while the bubble size greatly decreased when the cohesive particles agglomerated on the bed surface. The time series of pressure fluctuations was analyzed by using the methods of time domain, frequency domain and wavelet transformation. The normalized standard deviation of pressure fluctuations decreased with increasing weight percentages of cohesive particles. A wide bandwidth frequency of 0 to 1Hz got narrower with a single peak around 0.6Hz with an increase in proportion of the cohesive particles. The meso-energy and micro-energy of pressure fluctuations were decreasing with increasing cohesive particles proportions, which indicated that adding cohesive particles could reduce the energy dissipation of bubble and particle fluctuations.

Prediction model of velocity field around circular cylinder over various Reynolds numbers by fusion convolutional neural networks based on pressure on the cylinder

A data-driven model is proposed for the prediction of the velocity field around a cylinder by fusion convolutional neural networks (CNNs) using measurements of the pressure field on the cylinder. The model is based on the close relationship between the Reynolds stresses in the wake, the wake formation length, and the base pressure. Numerical simulations of flow around a cylinder at various Reynolds numbers are carried out to establish a dataset capturing the effect of the Reynolds number on various flow properties. The time series of pressure fluctuations on the cylinder is converted into a grid-like spatial-temporal topology to be handled as the input of a CNN. A CNN architecture composed of a fusion of paths with and without a pooling layer is designed. This architecture can capture both accurate spatial-temporal information and the features that are invariant of small translations in the temporal dimension of pressure fluctuations on the cylinder. The CNN is trained using the computational fluid dynamics (CFD) dataset to establish the mapping relationship between the pressure fluctuations on the cylinder and the velocity field around the cylinder. Adam (adaptive moment estimation), an efficient method for processing large-scale and high-dimensional machine learning problems, is employed to implement the optimization algorithm. The trained model is then tested over various Reynolds numbers. The predictions of this model are found to agree well with the CFD results, and the data-driven model successfully learns the underlying flow regimes, i.e., the relationship between wake structure and pressure experienced on the surface of a cylinder is well established.

Dynamic analysis of the scale-up of fluidized beds

A method is developed for hydrodynamics scale-up of gas-solid fluidized beds based on recurrence quantification analysis of nonlinear time series of pressure fluctuations. This method is an improvement of the previous method by including the entropy of pressure fluctuations to the list of scale-up parameters. Experiments were carried out at varying conditions, e. g., bed diameter (5, 9, 15, 40 and 80cm ID), particle size (150, 300, 400 and 600μm), bed height at aspect ratios (1, 1.5 and 2) and superficial gas velocities (ranging 0.1 to 1.7m/s) to identify the main parameters that influence the dynamics and to develop a general interpretation of the analysis results. By investigation of the effect of operating parameters on entropy, a quantitative empirical correlation is proposed for including the entropy in the scale-up parameters. It was shown that this correlation improves the Glicksman’s method for the scale-up of fluidized beds.

Experimental analysis of pressure characteristics of catalyst powder flowing down a cyclone dipleg

An experiment was carried out for investigating pressure behavior of catalyst powders, with a Sauter mean diameter of 63.6 μm, flowing downward in a cyclone dipleg with 150 mm inner diameter and 9000 mm high. Time mean pressure and time series of pressure fluctuations were measured at different axial positions in the dipleg with particle mass fluxes ranging from 50.0 to 385.0 kg m−2 s−1. The experimental results showed that the time mean pressure in the dipleg increased progressively from the top section to the bottom section. The experimental phenomena displayed that the fluidization patterns in the dipleg can be divided into two types on the whole, namely the dilute–dense coexisting falling flow and the dense conveying flow along the dipleg. In the dilute–dense coexisting falling flow, the dilute phase region was composed of a length of swirling flow below the inlet of dipleg and a dilute falling flow above the dense bed level. With increasing particle mass flux, the dilute–dense coexisting falling flow was gradually transformed to be the dense conveying flow, and the exit pressure of the dipleg increased considerably. The pressure fluctuations were closely related to the fluidization patterns inside the dipleg. In the dilute–dense coexisting falling flow, the pressure fluctuations in the dilute flow region originated from particle clusters, propagating downward as a pressure wave; however, the pressure fluctuations in the dense flow region originated from rising gas bubbles, propagating upward. When the dense conveying flow was formed in the dipleg, the pressure fluctuations originated mainly from instability of the feed and the compressed gas, propagating downward. The standard deviation of the pressure fluctuations indicated that the intensity of pressure fluctuations first increased and then decreased with increasing particle flux.

Multi-scale Analysis of Pressure Fluctuation Time Series in the Circulating Jet Tank

Multi-scale Analysis of Pressure Fluctuation Time Series in the Circulating Jet Tank

Flow Patterns Identification in a High-flux Circulating Fluidized Bed with Shannon Entropy Increment Rate

Experiments of gas-solid suspension were carried out in a high-flux circulating fluidization bed with the solid mass flux up to 536 kg/(m2·s). Differential pressure fluctuation time series were obtained at different locations in the riser. Shannon entropy increment rate analysis was developed to identify the flow pattern and transformation and characterize the dynamic behavior. Effect of superficial gas velocity on the Shannon entropy increment rate was examined under high solid mass flux. It was demonstrated that a circulating fluidization bed at high solid mass flux was a deterministic chaos system and the sensitivity of the system's chaotic characteristic to operating parameters at different flow regimes was different. Shannon entropies increment rate of different flow regimes were distinct. Shannon entropy increment rate analysis method results in high degree of recognition for flow pattern and transformation.

Computational Estimation of Fan Casing Noise at Blade Passing Frequency Component Noise

This paper studies both vibroacoustics and aeroacoustics of a centrifugal fan casing; the aim of this study is to explore a methodology to make quantitative predictions of fan casing noise. The spectra of the fan noise and casing vibration were firstly presented; discrete components related to the rotational frequency protrude in the spectra, especially the blade passing frequency (BPF). Computational fluid dynamics (CFD) technique was used to obtain the three-dimensional unsteady turbulent internal flow. Attention was paid to the pressure fluctuations on the volute wall; the shapes of pressure fluctuation were nearly sinusoidal in nature, with the BPF as the primary frequency. On the vibroacoustic side, Fast Fourier Transform (FFT) was applied to the time series of pressure fluctuations to extract the BPF component. A finite element analysis (FEA) model of the casing structure was constructed, and was validated by experimental modal analysis. The harmonic dynamic response of the casing structure was calculated with the BPF pressure fluctuation component as the excitation. The vibration results were then taken as the velocity (Neumann) boundary condition for the noise radiation model which was built in boundary element method (BEM), and the sound radiation was calculated. On the aeroacoustic side, the BPF component of pressure fluctuations was modeled as acoustic dipole source, and sound radiation was also solved by BEM. Results show that the sound pressure level (SPL) of vibroacoustics is fairly small compared to the aeroacoustic counterpart. This study shows that CFD, FEA together with BEM can be used to numerically predict BPF casing noise of turbomachinery successfully.

Experimental study on instantaneous pressure fluctuation time series in the novel tank agitated by multiple horizontal jets

The Novel Circulating Jet Tank (CJT) agitated by multiple horizontal jets has become an alternative to the bottom-entering mechanical stirred tank in chemical process industries. In order to characterize the coupled interaction between the rectangular baffles and the tank wall, the pressure fluctuations in the novel tank of 0.4m diameter are measured using high speed acquisition system. The time series of instantaneous pressure in the jet mixing zone are investigated at different radial, circumferential and axial positions under different Reynolds numbers. Time-frequency and energy characteristics of the instantaneous pressure are analyzed and evaluated with the Hilbert–Huang Transform and marginal spectrum. Experimental results indicate that the spatial distributions of instantaneous pressure fluctuation amplitudes increase with the increasing Reynolds numbers. The first order inherent frequencies of power spectrums are lower than 5Hz. The relationship between power spectral density and frequency accords with power-law attenuation. The scaling exponents range from 0.5 to 1.15 which indicates the existence of fractal characteristics in the pressure fluctuation time series. Compared with the corresponding normal distributions, the probability distribution functions and χ2 hypothesis tests of the pressure fluctuations have been obtained. The deviations from the normal distribution are quantitatively analyzed based on skewness and flatness.

Time-frequency analysis of Hilbert spectrum of pressure fluctuation time series in a Kenics Static Mixer based on empirical mode decomposition

The turbulent flow in a Kenics Static Mixer (KSM) was intensified under the mutual-coupling effect between the twisted leaves and the tube-wall. In order to understand the intrinsic features of turbulent flow in KSM, the Hilbert-Huang Transform based on Empirical Mode Decomposition were first introduced to describe the time-frequency features of the pressure fluctuation. The Hilbert spectra of pressure fluctuation time series were quantitatively evaluated under different Reynolds numbers, and different radial and axial positions, respectively. The experimental results showed that: the fluctuation frequencies of pressure signals in a KSM were mainly distributed below 40 Hz, and more than 68% of the energy of signals is concentrated within 10 Hz. Compared with the other IMFs, the pressure component of C6 in the range of 7.82~15.63 Hz has the maximum fluctuation energy ratio. As the flow rate increases, the energy of fluctuation of fluid micelles and the proportion of low-frequency energy increases. The pressure fluctuation with higher energy ratio of low frequency (0~10 Hz) had lower amplitudes at r/R=0.3 because of the core of forced vortex. Nevertheless, the effect of the free vortex was that the pressure fluctuation with lower energy ratio of low frequency had higher amplitudes at r/R=0.8. The higher amplitudes of pressure fluctuation at cross sections of CS3 (z=420 mm) and CS5 (z=620 mm) proved that the transitions between the adjacent mixing element had better mixing performance.

Characterizing gas–solid fluidization by nonlinear tools: Chaotic invariants and dynamic moments

The chaotic behavior, that gas–solid fluidization exhibits, has been characterized using the state space analysis. The space trajectories (attractor) of the dynamic system, reconstructed from the experimental time series of pressure fluctuations in the bed, have been described by the commonly used invariants: correlation dimension (CD), largest Lyapunov exponent (Ly) and the Kolmogorov entropy (K). The evolution of these invariants has been evaluated for bubbling, slugging and turbulent regime by analyzing the dependence on the flow regimes investigated. A new correlation has been proposed to predict the K for slugging regime. Due to some uncertainty involved in the delay determination for the attractor reconstruction, an attractor shape descriptor has been introduced. As shape descriptor, the dynamic moments of the attractor have been chosen and the morphological differences on the shape have been analyzed by varying the delay. The fluidization regimes have been characterized by the dynamic moments.

Investigating the hydrodynamics of gas–solid bubbling fluidization using recurrence plot

Hydrodynamics of gas–solid fluidized bed was investigated using time series of pressure fluctuations by evaluation of the corresponding recurrence plot (RP). Patterns within RP of the fluidized bed were classified into two groups of local white areas (LWA), showing macro structures, and local bold areas (LBA), showing meso and micro structures. These patterns showed that the fluidized bed system has three different hydrodynamic behaviors as superficial gas velocity increases; at low gas velocities, macro structures become more dominant, further increase in gas velocity empowers influence of finer structures on the hydrodynamic and finally the fluidization regime changes. Additionally, these results were confirmed by recurrence rate (RR) and average cycle frequency. Comparison of RP of the fluidized bed with Lorenz and complete stochastic systems showed that the fluidized bed is more complex than Lorenz system, however, it’s hydrodynamic has not stochastic nature.

Analysis of pressure fluctuations in fluidized beds. II. Reconstruction of the data by the Fokker–Planck and Langevin equations

In this part of the sequel we develop a continuum representation of the pressure fluctuation time series p( t) for a fluidized bed (FB), analyzed in part I, by using stochastic methods based on the Markov processes. It is shown that the data may be represented by Markov series with a Markov time scale t M that is estimated based on the data. Using the relation between the Markov processes and the Kramers–Moyal (KM) expansion that is a continuum equation that involves, in principle, an infinite number of coefficients, we represent the pressure fluctuation time series by a KM expansion. However, since the third and higher-order coefficients of the expansion are very small, the KM expansion reduces to a Fokker–Planck (FP) equation that represents p( t) in terms of a drift and a diffusion coefficients that are computed based on the data. The FP equation is, in turn, equivalent to a Langevin equation, which is used to reconstruct the data, i.e. generate the time series that mimic, in a statistical sense, the original data. Thus, the Langevin equation may also be used to make probabilistic predictions for the future values of the pressure over time scales that are of the order of the Markov time scale t M . The accuracy of the reconstructed series and, hence, their continuum representation, is demonstrated. We also compute the frequency ν α + of level-crossing at a given level α , i.e. the relative frequency (probability) of occurrence of the event defined, for two times t i−1 and t i , by, ν α + = P [ p ( t i ) > α , p ( t i − 1 ) < α ] , where P( x) is the probability of the event. Thus, ν α + yields the frequency that a given pressure fluctuation level may be expected. The average time that one should wait in order to observe the pressure at a given level again is also computed. The two quantities may be particularly important for modeling of the FBs. A relation is presented between the drift and diffusion coefficients of the FP equation and the Hurst exponent that has previously been used to describe the pressure fluctuation time series in terms of self-affine stochastic distributions.

Analysis of pressure fluctuations in fluidized beds. I. Similarities with turbulent flow

Experimental data for pressure fluctuation time series in a fluidized bed are analyzed by several distinct, but complementary methods. First, we compute a multiscale probability density function (PDF) for the successive increments of the data. The results demonstrate the evolution of the PDF from the short to long time scales, and indicate striking similarity to the Castaing equation that has been proposed for modeling velocity fluctuations in turbulent flows. Next, to further check the results we compute the structure function of the successive increments of the data. We find that the fluctuations exhibit multifractal behavior, which is also prevalent in turbulence. The multifractality implies that the pressure fluctuates differently over distinct time scales. To understand the origin of the multifractality, we use a powerful method of analysis, namely, the multifractal detrended fluctuation analysis (MF-DFA) in order to analyze the data. The results confirm the multifractal property of the data. To better understand the similarities between the pressure fluctuations in fluidized beds and velocity fluctuations in turbulent flow, and whether the multifractality is due to extended correlations in the data or because the PDF of the successive increments is broad, we also construct the shuffled and surrogate series for the data and analyze them by the MF-DFA method. Comparison of results for the original data with the shuffled and surrogate time series indicates that the correlations in the pressure are responsible for the multifractality of the data, rather than the broadness of the PDF.