PROBABILITY DISTRIBUTION FUNCTION OF NEAR-WALL TURBULENT VELOCITY FLUCTUATIONS

By large eddy simulation （LES）, turbulent databases of channel flows at different Reynolds numbers were established. Then, the probability distribution functions of the streamwise and wall-normal velocity fluctuations were obtained and compared with the corresponding normal distributions. By hypothesis test, the deviation from the normal distribution was analyzed quantitatively. The skewness and flatness factors were also calculated. And the variations of these two factors in the viscous sublayer, buffer layer and log-law layer were discussed. Still illustrated were the relations between the probability distribution functions and the burst events-sweep of high-speed fluids and ejection of low-speed fluidsIin the viscous sub-layer, buffer layer and loglaw layer. Finally the variations of the probability distribution functions with Reynolds number were examined.

QUADRANT ANALYSIS OF BUBBLE INDUCED VELOCITY FLUCTUATIONS IN A TRANSITIONAL BOUNDARY LAYER

Our previous study showed that the frictional drag decreases with increasing void fraction at Re〉1300, while it increases at Re 〈 1000. Decomposition of the Reynolds shear stress also implied that bubbles induce isotropy of turbulence. In order to confirm our previous analysis and to further investigate flow fields in the vicinity of bubbles, we analyze velocity fluctuations on the quadrant space in the streamwise and transverse directions （u′-v′ plane）. Here, we focus on two specific Reynolds numbers （at Re≈900 and ≈1410, which are close to the laminar-to-turbulent transition regime） and discuss bubble effects on sweep （u′〉 0, v′〈 0 ） and ejection （u′〈 0, v′〉 0） events as a function of the Reynolds number. We also illustrate velocity fluctuations in the vicinity of an individual bubble and a swarm of bubbles on the u′- v′ coordinates. The results show that a bubble swarm suppresses the velocity fluctuations at Re≈1410.

Experimental investigation of velocity fluctuations in a radial diffuser pump

The strong interaction in a radial pump due to the relative movement between the impeller and the diffuser may excite not only strong pressure fluctuations but also velocity fluctuations. In this paper, the laser Doppler velocimetry （LDV） technique is successfully applied to measure the periodic flow field in a radial diffuser pump with low-specific speed, in order to investigate the velocity fluctuations caused by the impeller-diffuser interactions both in the impeller and diffuser regions. The velocity fluctuations in the impeller region are quantitatively examined at different radial positions, and the flow structure at the radial gap between two flow components is analyzed at different relative positions. In addition, the downstream effect on the diffuser flow is quantitatively and qualitatively assessed and compared with the turbulence effect.

Dynamic characteristics of bubbling fluidization through recurrence rate analysis of pressure fluctuations

Pressure fluctuations signals of a lab-scale fiuidized bed （15 cm inner diameter and 2 m height） at different superficial gas velocities were measured. Recurrence plot （RP） and recurrence rate （RR）, and the simplest variable of recurrence quantification analysis （RQA） were used to analyze the pressure signals. Different patterns observed in RP reflect different dynamic behavior of the system under study. It was also found that the variance of RR （a2R） Could reveal the peak dominant frequencies （PDF） of different dynamic systems： completely periodic, completely stochastic, Lorenz system, and fluidized bed. The results were compared with power spectral density. Additionally, the diagram of σ^2RR provides a new technique for prediction of transition velocity from bubbling to turbulent fluidization regime.

EMERGENCE ANGLE OF FLOW OVER AN AERATOR

Aerator is an important device for release works of hydraulic structures with high-speed flow in order to protect them from cavitation damage. This kind of protecting effect is related closely to cavity length below the aerator, while the cavity length is dominated by the emergence angle over the aerator. Therefore it is crucial to determine this angle accurately. In the present paper the affecting intensities of flow depth and the fluctuating velocity on this angle were analyzed through two introduced parameters. Furthermore, the improved expressions of emergence angle estimation, for both ramp-type and step-type aerators, were presented by means of 68 sets of experimental data from 6 projects based on error theory. The results showed that the present method has higher accuracy than the previously reported methods.

Statistical and frequency analysis of the pressure fluctuation in a fluidized bed of non-spherical particles

In this paper, the pressure fluctuation in a fluidized bed was measured and processed via standard devia- tion and power spectrum analysis to investigate the dynamic behavior of the transition from the bubbling to turbulent regime. Two types （Geldart B and D） of non-spherical particles, screened from real bed materials, and their mixture were used as the bed materials. The experiments were conducted in a semi- industrial testing apparatus. The experimental results indicated that the fluidization characteristics of the non-spherical Geldart D particles differed from that of the spherical particles at gas velocities beyond the transition velocity Uo The standard deviation of the pressure fluctuation measured in the bed increased with the gas velocity, while that measured in the plenum remained constant. Compared to the coarse particles, the fine particles exerted a stronger influence on the dynamic behavior of the fluidized bed and promoted the fluidization regime transition from bubbling toward turbulent. The power spectrum of the pressure fluctuation was calculated using the auto-regressive （AR） model; the hydrodynamics of the flu- idized bed were characterized by the major frequency of the power spectrum of the pressure fluctuation. By combining the standard deviation analysis, a new method was proposed to determine the transition velocity Uk via the analysis of the change in the major frequency. The first major frequency was observed to vary within the range of 1.5 to 3 Hz.

Effect of particle degradation on electrostatic sensor measurements and flow characteristics in dilute pneumatic conveying

Vigorous particle collisions and mechanical processes occurring during high-velocity pneumatic con- veying often lead to particle degradation. The resulting particle size reduction and particle number increase will impact on the flow characteristics, and subsequently affect the electrostatic type of flow measurements. This study investigates this phenomenon using both experimental and numerical meth- ods. Particle degradation was induced experimentally by recursively conveying the fillite material within a pneumatic pipeline. The associated particle size reduction was monitored. Three electrostatic sensors were embedded along the pipeline to monitor the flow. The results indicated a decreasing trend in the electrostatic sensor outputs with decreasing particle size, which suggested the attenuation of the flow velocity fluctuation. This trend was more apparent at higher conveying velocities, which suggested that more severe particle degradation occurred under these conditions. Coupled computational fluid dynamics and discrete element methods （CFD-DEM） analysis was used to qualitatively validate these experimental results. The numerical results suggested that smaller particles exhibited lower flow velocity fluctua- tions, which was consistent with the observed experimental results. These findings provide important information for the accurate aoolication of electrostatic measurement devices in oneumatic conveyors.

Characterization of gas-liquid-solid fluidized beds by S statistics

The hydrodynamics of a gas-liquid-solid fluidized bed was investigated by applying the S statistics method to pressure fluctuations measured under various operating conditions in a laboratory-scale bed. S statistics tests reveal the existence of three transition velocities, especially at low gas velocities. Four distinct fluidization regimes, namely, the compacted bed, agitated bed and coalesced and discrete bubble regimes were detected. A comparison of reconstructed attractors of pressure fluctuations measured at different axial positions along the riser and with various solid loadings showed significant differences in the signals compared before fluidization, especially at minimum liquid agitation velocity. Close to the minimum liquid fluidization velocity and high liquid velocities, the variation in particle size has an insignificant effect on the bed hydrodynamics. Therefore, S statistics is a reliable method to demar- cate different fluidization regimes and to characterize the influence of various operating conditions on the hydrodynamics of gas-liquid-solid fluidized beds. The method is applicable in large-scale industrial installations to detect dynamic changes within a bed, such as regime transitions or agglomeration.