Two-phase flow regime assignment based on wavelet features of a capacitance signal

In this work, a new method is proposed to determine the two-phase flow regime based on the capacitance trace of the flow. The experimental data set contains 123 capacitance traces measured for a horizontal tube with an inner diameter of 8 mm. The tested refrigerant is R134a. The mass flux is varied between 200 and 500 kg/m² s and the vapour quality x is varied between 0 and 1. For each capacitance signal the wavelet variance is estimated based on the maximum overlap wavelet transform of the signal. The used wavelet function is a D8 wavelet of the Daubechies family. A feature space is generated based on the wavelet variance values associated with frequencies below 100 Hz. Principal component analysis and linear discriminant analysis are subsequently applied to this raw feature space, after which the Fuzzy c-means clustering algorithm is used to divide the feature space into clusters corresponding to different flow regimes. The resulting flow regime assignment shows a good agreement with a visual classification of the data set based on flow visualisations. Finally, the classification was performed based on variable training data to show the robustness of the method.     

汽(气)液两相流流型在线识别的研究进展

综述了根据参数波动过程实现气液两相流流型在线识别的最新研究成果,内容包括两相流参数波动的产生机理,小波分析的应用,两相流参数波动过程的特征提取和特征分析,流型在线识别的特点及各种实现方法等。重点介绍了两相流参数波动过程的统计和非线性特征分析及其与流型之间的关系。深入讨论了流型神经网络识别方法及其存在的问题。从波动参数的选择、数理解释、流型识别方法等不同方面对研究进展进行了讨论。      

Effect of diameter on two-phase pressure drop in narrow tubes

The effect of tube diameter on two-phase frictional pressure drop was investigated in circular tubes with inner diameters of 0.6, 1.2, 1.7, 2.6 and 3.4 mm using air and water. The gas and liquid superficial velocity ranges were 0.01-50 m/s and 0.01-3 m/s, respectively. The gas and liquid flow rates were measured and the two-phase flow pattern images were recorded using high-speed CMOS camera. Unique flow patterns were observed for smaller tube diameters. Pressure drop was measured and compared with various existing models such as homogeneous model and Lockhart-Martinelli model. It appears that the dominant effect of surface tension shrinking the flow stratification in the annular regime is important. It was found that existing models are inadequate in predicting the pressure drop for all the flow regimes visualized. Based on the analysis of present experimental frictional pressure drop data a correlation is proposed for predicting Chisholm parameter “C” in slug annular flow pattern. For all other flow regimes Chisholm’s original correlation appears to be adequate except the bubbly flow regime where homogeneous model works well. The modification results in overall mean deviation of pressure drop within 25% for all tube diameters considered. This approach of flow regime based modification of liquid gas interaction parameter appears to be the key to pressure drop prediction in narrow tubes.     

Modeling Non-Darcian Single- and Two-Phase Flow in Transparent Replicas of Rough-Walled Rock Fractures

While it is generally assumed that in the viscous flow regime, the two-phase flow relative permeabilities in fractured and porous media depend uniquely on the phase saturations, several studies have shown that for non-Darcian flows (i.e., where the inertial forces are not negligible compared with the viscous forces), the relative permeabilities not only depend on phase saturations but also on the flow regime. Experimental results on inertial single- and two-phase flows in two transparent replicas of real rough fractures are presented and modeled combining a generalization of the single-phase flow Darcy’s law with the apparent permeability concept. The experimental setup was designed to measure injected fluid flow rates, pressure drop within the fracture, and fluid saturation by image processing. For both fractures, single-phase flow experiments were modeled by means of the full cubic inertial law which allowed the determination of the intrinsic hydrodynamic parameters. Using these parameters, the apparent permeability of each fracture was calculated as a function of the Reynolds number, leading to an elegant means to compare the two fractures in terms of hydraulic behavior versus flow regime. Also, a method for determining the experimental transition flow rate between the weak inertia and the strong inertia flow regimes is proposed. Two-phase flow experiments consisted in measuring the pressure drop and the fluid saturation within the fractures, for various constant values of the liquid flow rate and for increasing values of the gas flow rate. Regardless of the explored flow regime, two-phase flow relative permeabilities were calculated as the ratio of the single phase flow pressure drop per unit length divided by the two-phase flow pressure drop per unit length, and were plotted versus the measured fluid saturation. Results confirm the dependence of the relative permeabilities on the flow regime. Also the proposed generalization of Darcy’s law shows that the relative permeabilities versus fluid saturation follow physical meaningful trends for different liquid and gas flow rates. The presented model fits correctly the liquid and gas experimental relative permeabilities as well as the fluid saturation.     

A mathematical model for pressure drop of two-phase dry-plug flow in circular mini/micro channels

Dry-plug flow is a variation of two-phase plug flow that occurs in small scale channels and refers to the dry wall conditions at gas portions of the flow regime. Previous experimental studies found a significant increase in pressure drop in this flow regime from the two-phase wet-plug flow regime. In this work an analytical model for the pressure drop of this flow regime is developed and phenomena that influence pressure drop are examined. Unlike previous models, the proposed model seems to be applicable to a wide range of capillary numbers and give good estimations for all static contact angles. Contact angle hysteresis turned out to play a major role in inducing pressure drop in this flow regime. Model’s predictions were in good agreement with previous experimental data. Finally the model is applied to very low capillary number region and pressure drop predictions for this region are presented.     

Multi-scale particle dynamics of low air velocity in a horizontal self-excited gas–solid two-phase pipe flow

The particle fluctuation velocities of a horizontal self-excited gas–solid two-phase pipe flow with soft fins near MPD (minimum pressure drop) air velocity are first measured by high-speed PIV in the acceleration and fully-developed regimes. Then orthogonal wavelet multi-resolution analysis and power spectrum are used to reveal multi-scale characteristics of particle fluctuation velocity. It is observed that the pronounced peaks of the spectra of axial and vertical fluctuation velocities appear in the range of low frequency near the bottom of pipe. These peaks of spectra become larger and their frequencies decrease by using fins. In the range of low frequencies (3–25 Hz), the wavelet components of the fluctuating energy of axial particle velocity make the main contribution accounting for 87% and 93% respectively for non-fin and using fins near the bottom of pipe. In the range of relatively high frequency (50–400 Hz), however, the wavelet components of using fins, accounting for about 49%, become smaller than that of non-fin, accounting for about 72%, in the suspension flow regime near the top of pipe. The skewness factor of axial particle fluctuation velocity indicates that the wavelet components follow the Gaussian probability distribution as the central frequency decreases.     

Flow driven by a stamped metal cooling fan – Numerical model and validation

This paper presents a numerical fluid flow model for the stamped metal cooling fans popularly employed in electric motors. An experimental system is constructed to measure the performance of the cooling fan. The agreements between model prediction and experimental data are reasonably good. Parametric studies with the numerical model indicate that the viscous heating in the fluid and the variation of the air density have negligible effects on the fan performance. The blade edge thickness affects the flow driving capability of the fan. With various pressure differentials, three flow regimes are recognized. The first is the axial component dominated flow. In the second regime, the flow has a forward axial flow and a backward leakage flow. The third one is the leakage flow dominated regime, when the pressure differential across the fan is large.     

基于小波最小二乘支持向量机的加速度计温度建模和补偿

针对环境温度影响加速度计测量精度的问题,给出了温度对石英挠性加速度计零偏和标度因数的影响机理,提出采用小波最小二乘支持向量回归建立石英挠性加速度计零偏和标度因数的温度模型的方法。为了验证模型的有效性,进行了多个温度点下的参数标定试验,所获取的各温度点下的石英挠性加速度计零偏和标度因数作为小波最小二乘支持向量机模型的训练数据;将石英挠性加速度计固定在某一位置进行了升温试验,通过对比未进行温度补偿、最小二乘温度补偿和小波最小二乘支持向量回归温度补偿下石英挠性加速度计的输出,计算结果表明采用小波最小二乘支持向量机补偿后的石英挠性加速度计的测量精度最高。     

Statistical analysis of the hydrodynamic pressure in the near field of compressible jets

This paper is devoted to the statistical characterization of the pressure fluctuations measured in the near field of a compressible jet at two subsonic Mach numbers, 0.6 and 0.9. The analysis is focused on the hydrodynamic pressure measured at different distances from the jet exit and analyzed at the typical frequency associated to the Kelvin–Helmholtz instability. Statistical properties are retrieved by the application of the wavelet transform to the experimental data and the computation of the wavelet scalogram around that frequency. This procedure highlights traces of events that appear intermittently in time and have variable strength. A wavelet-based event tracking procedure has been applied providing a statistical characterization of the time delay between successive events and of their energy level. On this basis, two stochastic models are proposed and validated against the experimental data in the different flow conditions     

An application of the wavelet analysis technique for the objective discrimination of two-phase flow patterns

This paper presents an application of the wavelet analysis technique for two-phase flow pattern identification by using the void fraction signals obtained from a multi-channel Impedance Void Meter (IVM) in a vertical-upward air–water flow. A new method for the objective discrimination of the two-phase flow pattern has been developed to provide information regarding the local energy of void fraction signals at a given scale on the joint time–frequency diagram. The void signals are processed with Continuous Wavelet Transform (CWT) to get the local wavelet energy coefficients map on the time–frequency diagram. The effective local wavelet energy and the effective scale are then calculated. Then the criteria for flow pattern identification are, finally, obtained. A series of void fraction measurements were conducted over a wide range of air–water vertical-upward flow condition to provide an extensive database to cover several types of flow patterns. The results show that the proposed method has a high precision for characterizing different flow regimes in two-phase flow, and is considerably more promising for the online recognition of two-phase flow patterns due to the short time of data processing.     

Characteristic time scales of velocity and pressure events

Numerical and wind tunnel simulations of full-scale wind loads on structures are usually performed at a lower Reynolds number and different turbulence parameters. One way to assess the validity of such simulations is through matching magnitudes, duration and/or spectral characteristics of simulated pressure peaks with full-scale data. Because wavelet analysis provides a time/frequency decomposition, it has been proposed as an analysis tool for the intermittent and transient pressure peaks. This work aims at answering the question as to whether different wavelets yield the same-scale decomposition of pressure peaks and velocity events and could, thus, be used as a tool for the analysis of extreme loads on structures. The results show that, by isolating the peaks or events with a modified Gaussian window prior to applying the wavelet transform, the dependence of the measured time scale on different wavelet functions is reduced. The time scales of the pressure peak and the velocity event are estimated to be about the same indicating that one contributing factor, at the peak scale, to the pressure peak lies in the variation of the incoming flow at the same scale.     

Finite element solution of multi-dimensional two-phase flow through porous media with arbitrary heating conditions

Mechanistic models for flow regime transitions and drag forces proposed in an earlier work are employed to predict two-phase flow characteristics in multi-dimensional porous layers. The numerical scheme calls for elimination of velocities in favor of pressure and void fraction. The momentum equations for vapor and liquid then can be reduced to a system of two partial differential equations (PDEs) which must be solved simultaneously for pressure and void fraction.

Solutions are obtained both in two-dimensional cartesian and in axi-symmetric coordinate systems. The porous layers in both cases are composed of regions with different permeabilities. The finite element method is employed by casting the PDEs in their equivalent variational forms. Two classes of boundary conditions (specified pressure and specified fluid fluxes) can be incorporated in the solution. Volumetric heating can be included as a source term. The numerical procedure is thus suitable for a wide variety of geometry and heating conditions. Numerical solutions are also compared with available experimental data.     

Research on the algorithm of binary image cross-correlation for unsteady flow field measurement

In the present paper, the algorithm of Binary Image Cross-Correlation (BICC) was developed to measure the unsteady flow field. A vortex flow field was used to test the algorithm by numerical simulation. The results show that BICC is an effective algorithm for particle identification from consecutive images, the accurate velocity vector field can be obtained. The real velocity field in a valve chamber was measured by BICC in this study. From the full-field velocity information, the pressure and vorticity fields were also extracted by post-processing. The project supported by the National Natural Science Foundation of China     

Spectrally formulated wavelet finite element for wave propagation and impact force identification in connected 1-D waveguides

In this paper, a novel wavelet based spectral finite element is developed for studying elastic wave propagation in 1-D connected waveguides. First the partial differential wave equation is converted to simultaneous ordinary differential equations (ODEs) using Daubechies wavelet approximation in time. These ODEs are then solved using finite element (FE) technique by deriving the exact interpolating function in the transformed domain. Spectral element captures the exact mass distribution and thus the system size required is very much smaller then conventional FE. The localized nature of the compactly supported Daubechies wavelet allows easy imposition of initial-boundary values. This circumvents several disadvantages of the conventional spectral element formulation using Fast Fourier Transforms (FFT) particularly in the study of transient dynamics. The proposed method is used to study longitudinal and flexural wave propagation in rods, beams and frame structures. Numerical experiments are performed to show the advantages over FFT-based spectral element methods. The efficiency of the spectral formulation for impact force identification is also demonstrated.     

Wavelet packet based damage identification of beam structures

Most of vibration-based damage detection methods require the modal properties that are obtained from measured signals through the system identification techniques. However, the modal properties such as natural frequencies and mode shapes are not such a good sensitive indication of structural damage. The wavelet packet transform (WPT) is a mathematical tool that has a special advantage over the traditional Fourier transform in analyzing non-stationary signals. It adopts redundant basis functions and hence can provide an arbitrary time-frequency resolution. In this study, a damage detection index called wavelet packet energy rate index (WPERI), is proposed for the damage detection of beam structures. The measured dynamic signals are decomposed into the wavelet packet components and the wavelet energy rate index is computed to indicate the structural damage. The proposed damage identification method is firstly illustrated with a simulated simply supported beam and the identified damage is satisfactory with assumed damage. Afterward, the method is applied to the tested steel beams with three damage scenarios in the laboratory. Despite the noise is present for real measurement data, the identified damage pattern is comparable with the tests. Both simulated and experimental studies demonstrated that the WPT-based energy rate index is a good candidate index that is sensitive to structural local damage.     

基于提升小波变换和互相关函数的梁式桥损伤检测

为了有效地提取梁式桥的损伤特征,提出了一种将提升小波变换与互相关函数幅值向量相结合的损伤识别的方法。首先利用提升小波变换将车载作用下梁桥结构的加速度响应分解到单阶模态上,再对提升重构后得到的第一阶响应进行互相关处理,利用提出的损伤指标来进行损伤定位。通过数值仿真和模拟实验,验证了方法的有效性,讨论了噪声及测点稀疏对识别结果的影响,结果表明该方法具有良好的噪声鲁棒性。另外,在综合考虑经济性和识别结果准确性的情况下,给出了合理的测点布置方式。     

Non-intrusive aerodynamic loads analysis of an aircraft propeller blade

The flow field in a cross-sectional plane of a scaled Beaver DHC aircraft propeller has been measured by means of a stereoscopic PIV setup. Phase-locked measurements are obtained in a rotational frequency range from 18,900 to 21,000 rpm, at a relative Mach number of 0.6 at ¾ propeller radius. The use of an adapted formulation of the momentum equation in differential form for rotating frame of references, integrated with isentropic relations as boundary conditions, allowed to compute the pressure field around the blade and the surface pressure distribution directly from the velocity data in the compressible regime. The procedure, extended to the computation of the aerodynamic lift and drag coefficients by a momentum contour integral approach, proved to be able to couple the aerodynamical loads to the flow field on the moving propeller blade, comparing favorably with a numerical simulation of the entire scaled model. Results are presented for two propeller rotation speeds and three different yawing angles.     

Downwards co-current annular flow

This paper summarizes a study of the characteristics of downwards annular two-phase flow. The measurements reported are of film thickness, wave velocity and frequency, local pressure fluctuations, pressure gradient and liquid entrainment. The most important new feature of the work is the use of continuous data recording with either on-line or off-line statistical analysis. Experiments were carried out with air-water flows in tubes of 3.18 and 3.82 cm bore. It is shown that the interfacial characteristics of the flow may require at least 5 m for full development at some flow rates and most measurements were carried out with an entrance region of this length. It is also shown that the pressure fluctuations, characteristic of this two-phase flow regime, are primarily due to pressure surges caused by disturbance waves in the system passing through the exit device. A new regime map is proposed, based on experimental evidence, in which several distinctive types of interfacial behaviour are noted.     

Flow over an obstruction with the generation of nonlinear waves on the free surface: Limiting regimes

A numerical-analytic method of calculating a subcritical flow over an obstruction is proposed. This method is based on the identification of the asymptotics of the behavior of a wave train in unknown functions. The method makes it possible to calculate both steep and long waves. The effectiveness of the method is demonstrated for the problem of flow over a vortex. The concept of the limiting flow regime as a regime with the maximum value of the perturbation parameter for which steady flow still persists is introduced. Various types of the limiting regimes obtained in the calculations are analyzed.Kazan. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 108–117, March–April, 1995.     

Features of flow-induced forces deduced from wavelet analysis

In the present study, the effect of Reynolds number (Re) on flow interference between two side-by-side stationary cylinders and the associated flow-induced forces are investigated using finite element method and wavelet analysis. The pitch ratio chosen is T/D=1.7, where T is the separation distance measured between cylinder centers and D is the diameter, and Re, based on the free-stream velocity and the diameter of the cylinder, is varied within the laminar flow regime, i.e., 60<Re<200. The method of continuous wavelet transform is used to analyze time-variant features of flow-induced forces in the time–frequency domain. Flow patterns in the form of vorticity plots are presented to demonstrate the underlying physics. It is found that flow interference initially occurs in the inner vortices shed from the two cylinders, and extends to the outer vortices with increasing Re. The flow behind two cylinders undergoes three regimes: Regime I—unbiased gap flow, Regime II—stable biased gap flow, and Regime III—unstable gap flow. Flow-induced forces show significant variations when the flow transits from one regime to another. In particular, during the transition from Regimes II to III, the forces not only increase by amplitude, but also change their nature from deterministic to random, and show some nonstationary features. This is shown to be caused by the amalgamation of inner and outer vortices behind the two cylinders when the flow interference extends from inner vortices to outer vortices. Whenever possible, the present results are compared with experimental measurements and theoretical predictions. The numerical simulations are consistent with these other results.