Standard Deviation Of Pressure Fluctuations Research Articles

Assessment of Stability of Spouted Bed Using Pressure Fluctuation Analysis

Spouted beds are widely used in many industrial applications for achieving good gas–solid contact/mixing especially for a bed of coarse/nonspherical particles. The stability of the spouted bed is important and critical for certain sensitive applications like coating, blending, catalytic conversion, etc. This paper presents the results of experimental investigations carried out using both two-dimensional and three-dimensional spouted beds to identify various transition velocities and condition to arrive at a stable spouted bed. Standard deviation and power spectral density (PSD) of pressure fluctuation were used to determine the stable operating fluidization/spouting velocity. Zirconia microspheres were used as the spouted bed material and argon, nitrogen, and methane were used as spouting gases. Standard deviation of pressure fluctuation was calculated at minimum spouting velocity and at a velocity corresponding to transition from stable spouting to unstable spouting condition. It is shown that standard d...

Pressure Effect on Hydrodynamics of a High Pressure X-ray Transparent Polyethylene Fluidized Bed

Hydrodynamics of a polyethylene fluidized bed were studied at different operating pressures (191-2908 kPa) and constant temperature of 30°C. Minimum fluidization velocity (Umf) decreased with increasing of operating pressures. Measured Umf agree well with calculated Umf as derived from the standard deviation of pressure fluctuations using Puncochar’s Method (1985). As expected, with the increase of superficial velocity, amplitude and standard deviation of pressure fluctuation series also increase, which is indication of more vigorous bubbling behavior inside the bed. Power spectral density of pressure fluctuation series indicates similar frequency distribution of the bubbling behavior at different superficial velocities. The dominant frequency from the power spectral was found to be around 1 Hz. Bubble diameter and bubble velocity were estimated from X-ray fluoroscopy images. Bubble diameter and bubble velocity increase with increasing bed height and superficial gas velocity due to bubble coalescence and more gas flowing upwards. At the same fluidization number, the average bubble size slightly decreases with increasing pressure at all bed heights because there is less gas flowing and the bubbles coalesce less rapidly. The bubble velocity is observed to have a small decrease from 191 kPa up to 2200 kPa, and then a substantial increase due to the fact that at higher pressure, the solid circulation increases at the bed.

Stability of slot‐rectangular spouted beds: Effect of slot configuration

AbstractExperiments were carried out to determine the flow stability of slot‐rectangular spouted beds of 300 × 100 mm cross‐section with slots of different widths, lengths, and depths. The effects of slot expansion angle and diverging base were also investigated. Dependent variables included the minimum spouting velocity, bed pressure drop and standard deviation of pressure fluctuations. Based on the flow regimes and spout termination mechanisms, instability was found to be mainly due to the interaction of multiple spouts. Criteria were identified relating stable spouting to slot dimensions and particle size. Slots of limited cross‐sectional area can provide sustainable and symmetric spouting with little fluctuation, as long as the slot length‐to‐width ratio and depth are within certain limits, related to those for conventional spouted beds.

Characterization of gas–solid fluidized bed hydrodynamics by vibration signature analysis

Vibration measurement, as a non-intrusive technique, was used to characterize the hydrodynamics of fluidized beds. A series of experiments were performed in a lab-scale fluidized bed using two accelerometers for measuring the vibration of the bed and a pressure probe for measuring pressure fluctuations. The output signals were analyzed by statistical methods. The results show that the vibration technique can predict transition velocities at high velocities and indicate that analyzing the vibration signals can be an effective non-intrusive technique to characterize the hydrodynamics of fluidized beds. It was shown that transition from bubbling to turbulent velocity can be determined from the variation of standard deviation and kurtosis of vibration signals against superficial gas velocity of the bed. However, this point could be determined only from standard deviation of pressure fluctuations, and not from skewness or kurtosis of pressure fluctuations.

Characterization of Fluidization and Segregation of Biomass Particles by Combining Image Processing and Pressure Fluctuations Analysis

Bed segregation is inevitable in biomass-sand fluidized beds because of density and size differences, but segregation pattern can be significantly different under various operational conditions. In the present work, the combination of image processing technology and pressure fluctuations analysis is used to investigate the fluidization and segregation. Experiments have been carried out in a 3D fluidized bed. The biomass material studied is cotton stalk. Two groups of binary systems are considered, obtained by mixing sand with biomass particles of different sizes and/or concentrations. In addition, the bed-frozen method is also adopted to examine the segregation degree. It is found that the transition velocity from bubbling to turbulent fluidization regime decreases with the increase of biomass size and concentration. The results also show that the biomass concentration has little influence on the segregation degree, and the biomass size significantly affects the rate of segregation, which increases with the size. The pressure gradient and standard deviation of pressure fluctuation are demonstrated to be useful for indicating the bed segregation, which are validated by the result by the bed-frozen method.

기-고 유동층에서 Gaussian 분포 입자군의 표준편차에 따른 유출 특성

기-고 유동층에서 다입자경 입자의 입자분포 변화에 따른 비산유출 특성을 연구하였다. 다입자경 입자분포는 Gaussian 분포를 사용하여 실험을 수행하였다. 최소유동화속도에 대한 유속비와 Gaussian 입자분포의 표준편차에 따른 비산유출상수를 구하였으며, 이때 조업시간에 따른 압력요동의 특성치를 구하였다. 측정된 유동층의 압력요동 특성치로부터 압력요동의 표준편차, 평균압력, Power spectrum density function, 주진동수 등을 계산하였다. 입자분포군에 따라서 유출입자의 입자분포 및 압력요동 특성치는 크게 영향을 받는 것으로 나타났으며 이러한 결과로부터 압력요동 특성치로부터 유출특성의 해석이 가능함을 알 수 있었다. The elutriation characteristics of particle size distribution were investigated in a gas-solid fluidized bed. Experiments were carried out with the mulit-sized particles of Gaussian distributions. The elutriation rate constant obtained from the experiment was correlated with the standard deviation of particle size and the dimensionless group of the velocity ratio. The standard deviation of pressure fluctuation, mean pressure, major frequency and power spectrum density function were calculated by pressure fluctuation properties. Size distribution of elutriated particles and pressure fluctuations were measured for the particle size distribution of particle system depended largrly on the size distribution. Characteristics of fluidization and elutriation were greatly influenced by the particle size distribution and these characteristics could be interpreted with pressure fluctuation properties.

Standard deviation of absolute and differential pressure fluctuations in fluidized beds of group B particles

This work describes the behaviour of the standard deviation of pressure fluctuations, σ, in fluidized beds for group B particles in the bubbling regime. An empirical–theoretical function, which depends on the gas velocity, is proposed for predicting the pressure signal fluctuations, and the corresponding values of σ are calculated. The differences in the standard deviation of pressure fluctuations obtained for absolute or differential sensors are analyzed and compared to experimental values corresponding to different bed dimensions, pressure probe positions and particle properties.

Fluidization of Group B particles with a rotating distributor

A novel rotating distributor fluidized bed is presented. The distributor is a rotating perforated plate, with 1% open-area ratio. This work evaluates the performance of this new design, considering pressure drop, Δ p, and quality of fluidization. Bed fluidization was easily achieved with the proposed device, improving the solid mixing and the quality of fluidization. In order to examine the effect of the rotational speed of the distributor plate on the hydrodynamic behavior of the bed, minimum fluidization velocity, U mf, and pressure fluctuations were analyzed. Experiments were conducted in the bubbling free regime in a 0.19 m i.d. fluidized bed, operating with Group B particles according to Geldart's classification. The pressure drop across the bed and the standard deviation of pressure fluctuations, σ p, were used to find the minimum fluidization velocity, U mf. A decrease in U mf is observed when the rotational speed increases and a rise in the measured pressure drop was also found. Frequency analysis of pressure fluctuations shows that fluidization can be controlled by the adjustable rotational speed, at several excess gas velocities. Measurements with several initial static bed heights were taken, in order to analyze the influence of the initial bed mass inventory, over the effect of the distributor rotation on the bed hydrodynamics.

Prediction of Take-Over Velocity of a Binary Density System Using Pressure Fluctuations in a Fluidized Bed

The pressure fluctuation properties and mixing degree were investigated with a binary mixture of different density particles using polymethyl methacrylate (PMMA) and sand (or natural manganese ore (NMO)) in a gas fluidized bed. This study was restricted to systems of 50% by volume jetsam, i.e. flotsam rich system. Mixing-segregation phenomena were analyzed by pressure fluctuation properties, and the results were confirmed with the mixing degree using a sieve test. It was found that take-over velocities were obtained from the value of the specific gas velocity which was observed by transition of the slope of the standard deviation of pressure fluctuations. The mixing degree was related to the variation of the bed pressure difference by measuring the height of the axial position according to gas velocity. In addition, take-over velocities could likewise be obtained from a pressure difference profile.

Energy of Power Spectral Density Function and Wavelet Analysis of Absolute Pressure Fluctuation Measurements in Fluidized Beds

The standard deviation of pressure fluctuations is always as a benchmark to characterize fluidized bed, especially in identifying the transition velocities and flow regimes. In this study, the energy of power spectral density function (PSDF) was proved to be a new alternative tool to effectively analyse the pressure fluctuations. Also, the wavelet analysis was significant to deal with the signals in multi-resolution decomposition and in identification of transition velocities and flow regimes. The results from the normalized energy of PSDF and wavelet analysis are in good agreement with the standard deviation analysis.

Origin of pressure fluctuations in fluidized beds

The present paper shows a novel approach in interpreting the standard deviation of pressure fluctuations in a fluidized bed with respect to the spectral analysis. Based on several realistic assumptions for a freely bubbling bed, the physical model was proposed for the standard deviation of incoherent part of pressure fluctuations. Using the concept of energy dissipated in a fluidized bed the plausible explanation of linear dependence of standard deviation calculated from the total pressure signal on the excess gas velocity was given and verified experimentally.

Energy dissipation rate and pressure fluctuations in a three phase fluidized bed with a large column diameter

The effects of liquid (0.02-0.10 m/s) and gas (0.0-0.10 m/s) velocities and particle size (1.0, 2.3, 3.0 mm) on the pressure fluctuations and energy dissipation rate in three phase fluidized beds were determined in a large column (0.376 m-I.D.× 2.1 m high). The standard deviation of pressure fluctuations and energy dissipation rate increase with gas and liquid velocities but, decrease in the radial direction of three phase fluidized beds. The energy dissipation rate was well correlated with dimensionless groups as: Ed=16.788Fr 1 0.183 Fr g 0.139 (1-ψ)0.442+1.265Fr g 0.143 Re0.181.

Rapid detection of defluidization using the standard deviation of pressure fluctuations

At low gas velocities, the standard deviation of pressure fluctuations measured in a fluidized bed decreases approximately linearly with decreasing gas velocity. Based on this fact, we propose a statistical method that can quickly determine whether a fluidized bed is moving towards the defluidized state or not. This short response time is typically only 15 s, which allows the method to be used as a safety measure. The method is illustrated by experiments with a fluidized bed of Geldart A particles. The influence of the purge flow through a pressure probe and secondary gas flow to the bed is addressed and a comparison with measuring the average pressure drop is made.

Pressure fluctuations and transition from bubbling to turbulent fluidization

A simple mechanistic model of bubbly flow in nonslugging gas-solids fluidized beds with fine Group A particles has been developed for the prediction of pressure fluctuations induced by bubble motion. The model assumes that bubbles are aligned in vertical chains in the fluidized bed. The bubble growth is dominant at low velocities due to the coalescence of adjacent bubbles, while the ratio of the separation distance between the leading and the trailing bubbles and the bubble diameter remains constant. However, a maximum stable bubble size is reached when a balance between bubble splitting and coalescence is reached and the mean bubble size will remain at its maximum stable size when the gas velocity is further increased while the separation distance between adjacent bubbles starts to decrease. The model simulation shows both the amplitude and the standard deviation of pressure fluctuations reach a maximum with increasing superficial gas velocity. When the mean bubble size is allowed to decrease with further increasing gas velocity after the maximum stable size is reached, the amplitude and standard deviation also decrease but more gradually than with D B remaining constant. The transition velocity from bubbling to turbulent fluidization, U c, and bubble-phase volume fraction at U c predicted from this model are in good agreement with experimental data obtained in relatively large columns with fine particles where slugging does not occur since D t≫ D B.

Solids Behavior in Freeboard of FCC Regenerator.

The effect of gas velocity (0.56‐1.15 m/s) on radial voidage distribution and cluster properties is determined by using an optical fiber probe in the freeboard of a FCC r egenerator (0.48 m-I.D. · 3.4 m-high). The normalized standard deviation of pr essure fluctuation in the freeboard region decreases with increasing gas velocity. Local voidage distribution in the radial dir ection is relatively flat in the bubbling flow regime. However, in the turbulent flow r egime, voidage in the cor e region is higher than that in the wall region. Clusters move up and down simultaneously , and cluster velocity in the core region is higher than that in the wall region. Cluster length decreases with increasing gas velocity. As the gas velocity is increased, cluster frequency, fraction and voidage decr ease in the transition fr om bubbling to turbulent fluidization regime, but increase in the turbulent flow r egime. Variation of the normalized standard deviation of pressure fluctuation in the fr eeboard can be related with the cluster properties. Cluster length decreases with increasing the suspension density . The cross-sectional mean cluster length in the freeboard zone is corr elated with the suspension density as well as the experimental variables.

Effect of sound on the fluidization of group B particles

AbstractThe behaviour of several kinds of group B particles ranging from 100 μm to 600 μm was studied in a sound wave vibrated fluidized bed (SVFB). The fluidized bed consists of a transparent Plexiglas tube that is 54 mm i.d. × 1 m high. A speaker mounted at the top of the bed was supplied by a function generator with square waves and was used to generate the sound as the source of vibration of the fluidized bed. The influence of the particle size, density of particles and sphericity of particles on the minimum fluidization velocity, pressure fluctuations and bubble rise velocity in the SVFB was investigated. The minimum fluidization velocity decreased as the sound energy increased. When the sound energy was strong enough and greater than the critical power, the minimum fluidization velocity would approach the same value regardless of the degree of resonance (DOR) value if the particles were in spherical shape. For non‐spherical shape particles the minimum fluidization velocity was the function of the DOR value if the power was greater than the critical power. For the middle particle size range, the standard deviation of pressure fluctuations in an SVFB became lower than the one without the effect of sound in high superficial gas velocity range, but the result was reverse for the low superficial velocity; for the large particle size range, the standard deviation of pressure fluctuations in an SVFB was larger than the one without the effect of sound. The sound could also reduce the bubble rise velocity in an SVFB.

Fluidization of group B particles in an acoustic field

The behavior of group B particles (sand with mean diameter 194 μm) was studied in a sound wave vibrated fluidized bed (SVFB). The fluidized bed consists of a transparent Plexiglas tube of i.d. 54 mm and height 1 m. A loudspeaker mounted at the top of the bed was supplied by a function generator with square waves, and was used to generate the sound as the source of vibration of the fluidized bed. The effects of the power of the loudspeaker, sound frequencies, particle loading and the distance between the speaker and the bed surface on the hydrodynamic properties of the SVFB were investigated. The experimental results showed that the minimum fluidization velocity decreased with the addition of acoustic energy, and the standard deviation of pressure fluctuations became lower under the effect of sound. The sound wave also reduced the bubble rise velocity. The results were interpreted in terms of the operating parameters.

Pressure fluctuations and choking criterion for vertical pneumatic conveying of fine particles

Pressure fluctuations and bed voidages are obtained in the dilute phase flow and dense phase flow regimes of vertical pneumatic conveying systems of fine particles. Statistical parameters of the pressure fluctuations are utilized to study the transition from the dilute phase flow to the dense phase flow. Out of the four types of fine particle used in the experiments, three types of fine particle exhibit a choking transition, which is characterized by a sharp change in the bed voidage. At the choking transition, sharp changes in the power spectral density function and standard deviation of the pressure fluctuations are also observed. The fourth type of fine particle does not exhibit any sharp changes in bed voidage, power spectral density function, or standard deviation of the pressure fluctuations over a wide range of air velocities used in the experiments. It is shown that the power spectral density function and the standard deviation of pressure fluctuations can be effectively used to accurately determine the choking transition. The experimentally determined choking velocities and bed voidages in the slugging dense phase flow are compared with available correlations.

Statistical pressure characteristics in modelling of gas-liquid reactors

The integral characteristics (average porosity and product kLa) and the fluctuating component of static pressure inside the gas-liquid system were measured in two types of column reactors with different gas distributors. It has been determined that at the same gas velocity in the reactor with a Venturi tube as the gas distributor the mean porosities are about 1.5 times greater than with the sieve plate reactor. To this corresponds, especially, at small gas flow rates even higher ratio of coefficients kLa. Standard deviation of pressure fluctuations becomes with the Venturi tube reactor for orders of magnitude greater then with the sieve plate reactor. The analysis of pressure fluctuations has demonstrated that in the reactor with the Venturi tube the decisive portion of fluctuation output corresponds to frequencies within the band 10-30 Hz, while in the reactor with the given type of the sieve plate to the band 0-10 Hz. In the reactor with the Venturi tube formation of surface waving has no considerable effect on flow of the gas phase, though the amplitudes in both types of reactors are comparable.