Standard Deviation Of Pressure Fluctuations Research Articles

Computational Study of Pump Turbine Performance Operating at Off-Design Condition-Part I: Vortex Rope Dynamic Effects

As global power demand increases, hydropower plants often must operate beyond their optimal efficiency to meet grid requirements, leading to unstable, high-swirling flows under various load conditions that can significantly shorten the lifespan of turbine components. This paper presents an in-depth computational study on the performance and dynamics of a pump-turbine operating under 80% partial load, focusing on the formation and impact of vortex ropes. Large Eddy Simulation (LES) was utilized to model the turbulent flow, revealing complex patterns and significant pressure fluctuations. A pronounced straight vortex rope was identified in the draft tube, maintaining its trajectory and core size consistently, profoundly affecting flow characteristics. Pressure fluctuations were observed at various cross-sectional planes, with peaks and troughs primarily near the runner, indicating areas prone to instability. The standard deviation of pressure fluctuations ranged from 4.51 to 5.26 along the draft tube wall and 4.27 to 4.97 along the axial center, highlighting significant unsteady flow. Moreover, the frequency corresponding to the highest amplitude in pressure coefficient spectrographs remained consistent at approximately 9.93 to 9.95, emphasizing the persistent influence of vortex rope dynamics. These dynamics affected power generation, which was approximately 29.1 kW, with fluctuations accounting for about 3% of the total generated power, underscoring the critical impact of vortex rope formation on the performance and operational stability of pump-turbines under off-design conditions. This study provides essential insights vital for enhancing the design and operational strategies of these turbines, ensuring more efficient and reliable energy production in the face of increasing power demands.

Studying the effect of direction and strength of magnetic field on fluidization of nanoparticles by recurrence analysis

Effect of the intensity and direction of the magnetic field was studied on fluidization of titanium oxide nanoparticles (anatase phase) mixed with ferromagnetic Iron (III) oxide nanoparticles using the recurrence analysis. The bed expansion and visual observation revealed that these particles operate in the ABF regime in all cases. Minimum fluidization velocities were obtained through the standard deviation of pressure fluctuations. Agglomerates samples were taken to study the effect of the magnetic field on the size of agglomerates. It was observed that at low field strength, the vibration has a major effect on fluidization than the magnetic force. At field strengths less than 400 Gauss, the vibration of solenoid improved the quality of fluidization by decreasing the size of agglomerate and minimum fluidization velocity, regardless of the field direction. At field strengths greater than 400 Gauss, the upward direction increases the interaction of agglomerate which results in a stochastic pattern of fluidization and lower ABF characteristics. At high magnetic field strengths, the effect of field direction becomes more noticeable. At high field strengths, the downward field results in less movement of the bed material and resistance against fluidization as well as the formation of larger bubbles and their deterministic effect on the bed.

Stability of spouted bed during spray cold coating on the surface of carrier particles

Abstract The rapid freezing of droplets on the surface of cold carrier particles can reduce the spray freeze-drying time. The coating freezing process can be treated in batch by using a spouted bed and the bed stability is the key. The freezing process of droplets would agglomerate the carrier particles. By analyzing the standard deviation of the bed pressure drop and the fluctuation of the bed pressure, the stable operating conditions of the spouted bed under cold coating were studied, and a dynamic adjustment method of the inlet air velocity to maintain stable spouting was proposed. The results show that the stable operating air velocity range can be described useing the standard deviation of pressure fluctuations. Before bed collapse occurs, it will experience an unstable spouting process, which causes the bed pressure to fluctuate a standard deviation of less than 15 Pa after more than 40 Pa.

Understanding the interplay of capillary and viscous forces in CO2 core flooding experiments

Interaction between capillary and viscous forces significantly affects the flow instability in immiscible displacement, which is usually investigated by visualization of flow patterns in 2d porous micromodels or in 3d system equipped with X-ray CT. However, in most practical applications, visualization of flow in porous media is not possible and the pressure signal is often as one of the important sources of information. Core flooding experiments were implemented in this study to investigate the interplay of capillary and viscous effects by analysis of differential pressure. Water and crude oil were employed as defending fluid, and different states of CO2 were injected as invading fluid. The inlet was set as the constant injection flow rate while the outlet as the constant pressure. In viscous-dominated displacement, differential pressure evidently depends on the injection rate and the pressure decline curve is fitted by a power function. The exponent of the function is found to be significantly larger at the crossover between capillary-dominated and viscous-dominated regions. In capillary-dominated displacement, the pressure profile is characterized by a pressure jump at the beginning and intermittent fluctuations during the displacement. Further analysis by wavelet decomposition indicates a transition point existing in standard deviation of pressure fluctuations when the displacement is transformed from capillary-dominated to viscous-dominated. The experimental results are finally verified by a macroscopic capillary number, which characterizes the interaction between capillary and viscous forces at a critical value of Ncamacro∼1, agreeing well with the Log Nca-Log M phase diagram.

Pressure Fluctuations in the Spatial Hydraulic Jump in Stilling Basins with Different Expansion Ratio

Pressure fluctuations are a key issue in hydraulic engineering. However, despite the large number of studies on the topic, their role in spatial hydraulic jumps is not yet fully understood. The results herein shed light on the formation of eddies and the derived pressure fluctuations in stilling basins with different expansion ratios. Laboratory tests are conducted in a horizontal rectangular flume with 0.5 m width and 10 m length. The range of approaching Froude numbers spans from 6.4 to 12.5 and the channel expansion ratios are 0.4, 0.6, 0.8, and 1. The effects of approaching flow conditions and expansion ratios are thoroughly analyzed, focusing on the dimensionless standard deviation of pressure fluctuations and extreme pressure fluctuations. The results reveal that these variables show a clear dependence on the Froude number and the distance to the hydraulic jump toe. The maximum values of extreme pressure fluctuations occur in the range 0.609<X<3.385, where X is dimensionless distance from the toe of the hydraulic jump, which makes it highly advisable to reinforce the bed of stilling basins within this range.

A Novel Comparative Statistical and Experimental Modeling of Pressure Field in Free Jumps along the Apron of USBR Type I and II Dissipation Basins

Dissipation basins are usually constructed downstream of spillways to dissipate energy, causing large pressure fluctuations underneath hydraulic jumps. Little systematic experimental investigation seems available for the pressure parameters on the bed of the US Department of the Interior, Bureau of Reclamation (USBR) Type II dissipation basins in the literature. We present the results of laboratory-scale experiments, focusing on the statistical modeling of the pressure field at the centerline of the apron along the USBR Type I and II basins. The accuracy of the pressure transducers was ±0.5%. The presence of accessories within basinII reduced the maximum pressure fluctuations by about 45% compared to basinI. Accordingly, in some points, the bottom of basinII did not collide directly with the jet due to the hydraulic jump. As a result, the values of pressure and pressure fluctuations decreased mainly therein. New original best-fit relationships were proposed for the mean pressure, the statistical coefficient of the probability distribution, and the standard deviation of pressure fluctuations to estimate the pressures with different probabilities of occurrence in basinI and basinII. The results could be useful for a more accurate, safe design of the slab thickness, and reduce the operation and maintenance costs of dissipation basins.

Nonintrusive Distributed Flow Rate Sensing System Based on Flow-Induced Vibrations Detection

Noninvasive real-time distributed pipeline monitoring technology is a key factor for the sustainable development of transportation pipelines. In this work, we have proposed and demonstrated a distributed microstructure optical fiber acoustic sensor (MOF-DAS)-based pipeline flow rate sensing system. Such proposed sensing system is based on the detection of flow-induced vibration (FIV) to achieve the flow rate measurement. We have used the Euler-Bernoulli beam theory to build up the FIV-based flow rate sensing model and numerically analyzed the pressures fluctuation at the wall under different flow rates. The simulation results showed that the standard deviation of pressure fluctuation is quadratically proportional to the flow rate. And we have experimentally verified and realized distributed flow rate detection in a pipe loop system built by a 25-m-long pipeline and a laboratory-made MOF-DAS system, which is the first time that the DAS is used for noninvasively pipeline flow rate detection. The experimental results are consistent with the simulated results very well. In the experiment, the flow rate range we measured was from 0 to 3.6 m/s, in which the measuring sensitivity of MOF-DAS at 3.6 m/s was around 0.03998 rad/(m·s <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-1</sup> ). Furthermore, the uncertainty analysis of experimental results shows that the measuring uncertainty is decreasing as increasing of flow rate, which is around 13.75% at the flow rate of 0.8 m/s and reduces to less than 1% at the flow rate of 3.6 m/s. Compare with the results measured by the commercial accelerator, the MOF-DAS-based flow rate sensing system has a better and stable flow rate measuring results. Finally, the MOF-DAS-based distributed flow rate detection system has been successfully applied in the field test, which indicated huge engineering application potential, especially in long-distance pipeline networks.

Fluidization characteristics of wide-size-distribution particles in a gas-solid fluidized bed reactor

AbstractFluidization characteristics of wide-size-distribution particles in the gas-solid fluidized bed reactor are investigated by applying experiment and computational fluid dynamics (CFD) methods. In this study, three types of narrow-cut particles and two sets of wide-size-distribution particles are used. A model considering particle size distribution is developed in the Eulerian frame, and good agreement between numerical results and experimental data is observed. The particle size distribution has an important effect on the average bed voidage. The axial particle diameter profiles along bed height have a “S” type feature. Minimum fluidization velocity is determined from the standard deviation of pressure fluctuations and bubble dynamics are analyzed based on power spectra. Results indicate that fine particle composition can reduce the minimum fluidization velocity of wide-size-distribution particle system and the bubble diameter in the fluidized bed.

Effect of the distributor plugging ways on fluidization quality and particle stratification in air dense medium fluidized bed

Gas-solid fluidized bed separation is a highly efficient and clean technique for coal separation, and can effectively remove ash and sulfur contained gangue minerals from coal. However, the fine coal plugging distributor often leads to uneven fluidization and affects the separation effect. In this paper, different plugging ways were designed to study their effects on the fluidization characteristics and particle mixing. It was found that when the plugging phenomenon occurs, the minimum fluidization velocity of the fluidized bed gradually decreases as the plugging area enlarges. The difference between the top and the bottom of the bed minimum fluidization velocity increases accordingly, and a “stagnation phenomenon” occurs in the bed. The standard deviation of pressure fluctuations at the top of the bed is smaller than that at the bottom of the bed, which is the opposite of normal conditions. As the area of the plugging increases, the dead zone on the side wall of the fluidized bed significantly increases. The size of the dead zone is rapid reducing at the initial stage. It was noticed that the stratification of the low-density products is particularly affected by plugging, whereas the stratification of high-density products is not obviously influenced by certain conditions.

Pressure tap cavity for unsteady aerodynamic pressure measurements

Extensive laboratory experiments were carried out to investigate the effect of a cavity behind the pressure tap on unsteady aerodynamic pressure measurements. The volume of the studied cavity (truncated cone) is 1.5 mm3 behind the pressure tap (cylinder) of 1 mm3 and the studied frequency range is up to 256 Hz. This design with a cavity behind the pressure tap and the studied frequency range are common for a wide range of mechanical, civil, aerospace, and environmental engineering applications. The experiments were performed using three different facilities, i.e. a signal generator, a low-turbulence wind tunnel, and a high-turbulence wind tunnel. Conclusions were made based on the quantitative analysis of the peak amplitude and frequency of the amplitude spectral density of pressure fluctuations as well as on the standard deviation of pressure fluctuations. Results were qualitatively analyzed with respect to phase shifts and amplitude deviations. The results clearly indicate that a 2.5 mm3 cavity with a pressure tap is suitable for unsteady pressure measurements in the frequency range up to 256 Hz as the phase shift and amplitude deviation of the unsteady pressure signal in those conditions proved to be negligible.

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.

Pressure fluctuation generated by the interaction of blade and tongue

Pressure fluctuation around the tongue has large effect on the stable operation of a centrifugal pump. In this paper, the Reynolds averaged Navier-Stokes equations (RANS) and the RNG k-epsilon turbulence model is employed to simulate the flow in a pump. The flow field in the centrifugal pump is computed for a range of flow rate. The simulation results have been compared with the experimental data and good agreement has been achieved. In order to study the interaction of the tongue with the impeller, fifteen monitor probes are evenly distributed circumferentially at three radii around the tongue. Pressure distribution is investigated at various blade positions while the blade approaches to and leaves the tongue region. Results show that pressure signal fluctuates largely around the tongue, and it is more intense near the tongue surface. At design condition, standard deviation of pressure fluctuation is the minimum. At large flow rate, the increased low pressure region at the blade trailing edge results in the increases of pressure fluctuation amplitude and pressure spectra at the monitor probes. Minimum pressure is obtained when the blade is facing to the tongue. It is found that the amplitude of pressure fluctuation strongly depends on the blade positions at large flow rate, and pressure fluctuation is caused by the relative movement between blades and tongue. At small flow rate, the rule of pressure fluctuation is mainly depending on the structure of vortex flow at blade passage exit besides the influence from the relative position between the blade and the tongue.

Effect of distributor on fluidized bed hydrodynamics

In this work, the effect of distributor type on fluidized bed hydrodynamics was studied by taking into account time, frequency, and state space domains. For this purpose, pressure fluctuations were measured in a fluidized bed with 0.15 m diameter and the experiments were carried out for three different types of distributors (perforated plate, bubble cap, and porous plate) at different sizes and various superficial gas velocities and particle sizes. Time domain analysis demonstrated that while the initial bubble size on the bubble cap distributor is greater than that on the perforated plate, the standard deviation of pressure fluctuations is greatest in a bed equipped with the porous plate, followed by the perforated plate and then the bubble cap distributor. Based on the current analysis and in view of the frequency domain analysis, it was found that the contribution of finer structures (small bubbles and clusters) is highest for a porous plate, followed by a bubble cap and then a perforated plate distributor. Also, according to the S‐statistic method, it was concluded that the S‐test is a reliable method for detection of differences between hydrodynamic situations of fluidized beds, while different types of distributors were used.

Detecting densified zone formation in membrane-assisted fluidized bed reactors through pressure measurements

This work reports the results of an experimental investigation on densified zone formation in a membrane fluidized bed reactor using combined pressure fluctuation and PIV (Particle Image Velocimetry) measurements. A pseudo 2D experimental setup was used, where porous plates on the back plate of column mimicked gas extraction through flat vertically inserted membranes. The maximum in the standard deviation of pressure fluctuations, commonly employed to indicate the transition to turbulent fluidization, shifted to lower fluidization velocities with an increase in the fraction of fluidizing gas being extracted. Flow visualization showed that this result is connected to the onset of stable densified zone formation, which occurred at progressively lower fluidization velocities as the gas extraction fraction was increased. It has also been found that the extent of densified zones quantified using instantaneous particle velocity maps collected by PIV increases with increasing gas extraction rates. This effect became larger for smaller particles. Results have therefore shown that the peak in pressure fluctuations in fluidized beds with gas extraction through flat vertical membranes indicates the onset of densified zones formation rather than turbulent fluidization. Such densified zones can have substantial detrimental effects (such as induced mass transfer limitations, gas bypass etc.) on the reactor performance and can be identified via pressure measurements, as illustrated in this work.

Effect of elevated pressure on the hydrodynamic aspects of a pilot-scale bubble column reactor operating with non-Newtonian liquids

The effect of elevated pressure on the hydrodynamics of a pilot-scale bubble column reactor has been studied in the non-Newtonian liquid phase. Various hydrodynamic characteristics of the bubble column reactor including the total gas holdup and its axial distribution, operating flow regime transition point, pressure fluctuation and its standard deviation have been evaluated by means of several pressure traducers along the column height. The superficial gas velocity and operating pressure varied from 1 to 35 (cms−1) and 0.1 to 1.0 (MPa), respectively. It was found that the total gas holdup increases with an increase in the operating pressure. The operating flow regime transition point was shifted to higher superficial gas velocities at elevated pressures. The standard deviation of pressure fluctuations was also found to increase with operating pressure but to decrease with the elasticity of the liquid phase. A new correlation has also been developed to predict the gas holdup in bubble columns operating at elevated pressures. The new correlation was shown to be able to predict the experimental data of gas holdup within a mean absolute percentage error of 20%.

RETRACTED ARTICLE: Combustion characteristics of paper and sewage sludge in a pilot-scale fluidized bed

This study characterizes the combustion of paper and sewage sludge in a pilot-scale fluidized bed. The highest temperature during combustion within the system was found at the surface of the fluidized bed. Paper sludge containing roughly 59.8% water was burned without auxiliary fuel, but auxiliary fuel was required to incinerate the sewage sludge, which contained about 79.3% water. The stability of operation was monitored based on the average pressure and the standard deviation of pressure fluctuations. The average pressure at the surface of the fluidized bed decreased as the sludge feed rate increased. However, the standard deviation of pressure fluctuations increased as the sludge feed rate increased. Finally, carbon monoxide (CO) emissions decreased as oxygen content increased in the flue gas, and nitrogen oxide (NOx) emissions were also tied with oxygen content.

Dominant flow structures in gas–liquid–solid fluidized beds

Effective time series analysis techniques in time and frequency domains were applied to characterize three‐phase fluidization under a wide range of gas and liquid velocities. The experiments were carried out in a laboratory scale fluidized bed, operated under ambient conditions. Standard deviation of pressure fluctuations successfully detected four distinct regimes, namely compacted bed, agitated bed, coalesced and discrete bubble regimes (or discrete and dispersed bubble regimes at extremely low gas velocities). A minimum in skewness and average cycle frequency and a maximum in flatness indicated a minimum deviation from larger structures of the bed. A transition between macro and finer structures occurred during agitated bed regime and accordingly, minimum liquid fluidization velocity was perceived by skewness, flatness, and average cycle frequency analyses. The results showed that at very low liquid velocities in the compacted bed regime, the power spectrum at lower frequencies slightly increased with increasing liquid velocity. This results in the consecutive appearance of single bubbles of low frequencies. With further increase in the liquid velocity at agitated bed regime the power spectrum at lower frequencies gradually decreased. At higher liquid velocities near ULmf, the peak dominant frequency is transmitted from low frequency ranges of 2 Hz to the higher frequency of about 10 Hz.

A CFD Study of Pressure Fluctuations to Determine Fluidization Regimes in Gas–Solid Beds

Reliable computational methods can provide valuable insight into gas–solid flow processes and can be used as a design tool. Of particular interest in this study is the hydrodynamics of a binary mixture of sand–biomass in a fluidized bed. Biomass particulates vary in size, shape, and density, which inevitably alter how well the particles fluidize. Our study will use computational fluid dynamics (CFD) to interpret the hydrodynamic states of a fluidized bed by analyzing the local pressure fluctuations of beds of sand and a binary mixture of cotton stalks and sand over long time periods. Standard deviation of pressure fluctuations will be compared with experimental data to determine different fluidization regimes at inlet gas velocities ranging from two to nine times the minimum fluidization velocity. We will use Bode plots to present the pressure spectra and reveal characteristic frequencies that describe the bed hydrodynamics for different fluidization regimes. This work will present CFD as a useful tool to perform that analysis. Other important contributions include the study of pressure fluctuations of a fluidized bed in bubbling, slugging, and turbulent regimes, and the analysis of a binary mixture using CFD.

Experimental investigation on the hydrodynamics of a gas–liquid–solid fluidized bed using vibration signature and pressure fluctuation analyses

Simultaneous analyses of vibration signatures and pressure fluctuations were performed to investigate the hydrodynamics of a conventional three-phase gas–liquid–solid fluidized bed over a wide range of operating conditions. Non-intrusive vibration signature and pressure fluctuation signals were acquired by means of accelerometers and a piezoresistive pressure transducer, respectively. Comprehensive study on the standard deviation of pressure fluctuations was conducted simultaneously with two new statistical analyses on the pressure fluctuations, namely signal energy and average cycle frequency, which presented a new method of determining minimum liquid-fluidization velocity. This enabled further investigation on the dual effect of solid particles on the local hydrodynamics in the three-phase beds. The vibration analysis of the bed was introduced as a novel and non-invasive tool, which proved to be a robust representative of the global governing regimes suggesting a new approach on the dual effect of solid particles on the bed global hydrodynamics. These methods can pave the way towards the non-invasive hydrodynamic characterization of industrial three-phase reactors.

A novel approach for simultaneous hydrodynamic characterization of gas–liquid and gas–solid systems

An attempt was made to find an analogy between hydrodynamic structures in fluidized beds and bubble columns in the frequency domain. This approach provides a better picture of hydrodynamic similarities between these two-phase reactors. The experiments were carried out in an air–water bubble column and an air-FCC fluidized bed. Pressure fluctuations were recorded for both systems at various gas velocities, aspect ratios and probe positions and were analyzed in frequency and time-frequency domains. Frequency spectrum of fluidized bed and bubble column revealed differences and similarities which can be related to properties of liquid and solid. Hydrodynamic phenomena were classified into three structures applicable to both bubble column and fluidized bed: macro (0–3.125Hz), meso (3.125–12.5Hz) and micro (12.5–25Hz) structures. It was found that the macro and meso structures exhibit a similar behavior in both systems. The plot of dimensionless standard deviation of pressure fluctuations in bubble column and fluidized bed against dimensionless velocity showed the similar qualitative and quantitative behavior for both systems. The analogous phenomena found for each structure can be used as a criterion for better understanding of both systems.