CFD simulation of pressure fluctuation characteristics in the gas-solid fluidized bed:Comparisons with experiments

A simple hydrodynamic model based on two-fluid theory, taking into account the effect of discrete particles on both the gas- and solid-phase momentum equations, was used to numerically investigate the pressure fluctuation characteristics in a gas-solid fluidized bed with the aid of CFX 4.4, a commercial CFD software package, by adding user-defined Fortran subroutines. Numerical simulations together with typical experimental measurements show that pressure fluctuations originate above the distributor when a gas pulse is injected into the fluidized bed. The pressure above the bubble gradually increases due to the presence of a rising bubble. When the bubble passes through the bed surface, the pressure near the bed surface gradually decreases to a lower value. Moreover, the pressure signals in the bubbling fluidized beds show obviously periodic characteristics. The major frequency of pressure fluctuations at the same vertical position is affected slightly by the operating gas velocity, and the amplitude of pressure fluctuations is related to both the operating gas velocity and the vertical height. In this study, the influence of the operating gas velocity on the pressure wave propagation velocity can be ignored, and only two peak frequencies in the power spectrum of the pressure fluctuations are observed which are associated with the bubble formation above the distributor and its eruption at the bed surface.

Unsteady Turbulent Simulation and Pressure Fluctuation Analysis for Centrifugal Pumps

The pressure fluctuation in the flow passage of both impeller and casing is addressed on design condition. The initial conditions for the unsteady turbulent simulation are resulted from the steady calculations, and the three dimensional unsteady turbulent simulation concerning the rotor-stator interaction is executed by a Navier-Stoke solver embedded with k -ε turbulence model and with appropriate moving interface boundary conditions. Detecting points are distributed in the flow passage in different radial and circumferential positions to capture the static pressure fluctuation character for one cycle of the impeller. The time-domain spectrums show that the static pressure curves are periodic and have five peaks and five valleys. With the radius increasing, the pressure fluctuation peak-to-peak values in the impeller are increasing, and reach the maximum value on the interface. In the casing flow passage, those values are about 7% of local static pressure except some ones near the tongue. The values become decreasingly in the diffuser pipe. The frequency spectrums transformed by fast Fourier transform （FFT） show that the dominant frequency is approximate with the blade passing frequency, and the pressure fluctuations in impeller passage have high frequency content while those in casing ones have no such information.

Experimental Study of the Pressure Fluctuations in a Pump Turbine at Large Partial Flow Conditions

Frequent shifts of output and operating mode require a pump turbine with excellent stability. Current researches show that large partial flow conditions in pump mode experience positive-slope phenomena with a large head drop. The pressure fluctuation at the positive slope is crucial to the pump turbine unit safety. The operating instabilities at large partial flow conditions for a pump turbine are analyzed. The hydraulic performance of a model pump turbine is tested with the pressure fluctuations measured at unstable operating points near a positive slope in the performance curve. The hydraulic performance tests show that there are two separated positive-slope regions for the pump turbine, with the flow discharge for the first positive slope from 0.85 to 0.91 times that at the maximum efficiency point. The amplitudes of the pressure fluctuations at these unstable large partial flow conditions near the first positive slope are much larger than those at stable operating condtions. A dominant frequency is measured at 0.2 times the impeller rotational frequency in the flow passage near the impeller exit, which is believed to be induced by the rotating stall in the flow passage of the wicket gates. The test results also show hysteresis with pressure fluctuations when the pump turbine is operated near the first positive slope. The hysteresis creates different pressure fluctuations for those operation points even though their flow rates and heads are similar respectively. The pressure fluctuation characteristics at large partial flow conditions obtained by the present study will be helpful for the safe operation of pumped storage units.

Numerical Simulation of Pressure Fluctuations in a Large Francis Turbine Runner

The pressure fluctuation caused by unsteady flow in runner is one of the main reasons of vibration for a large Francis hydraulic turbine. It directly affects the steady operation of the hydraulic turbine unit. The existing research of the pressure fluctuation in hydraulic turbine mainly focuses on the unsteady flow in draft tube. Accurate distribution of pressure fluctuations inside a runner is not very clear. In this paper, the numerical method for predicting the pressure fluctuations in runner is investigated and the numerical simulation is performed for a large Francis hydraulic turbine. It is proved that the combination of shear-stress transport（SST） k-o） turbulence model and pressure-implicit with splitting of operators（PISO） algorithm could give more reliable prediction of pressure fluctuations in runner. The frequencies of pressure fluctuations in runner are affected by the flow in guide vane and the flow in draft tube The first dominant frequency is significantly determined by the flow in draft tube, especially at part load condition. This frequency is approximately equal to one-third of the runner rotating frequency. The evident second dominant frequency is exactly equal to the guide vane passing frequency. The peak-to-peak amplitudes of pressure fluctuations in runner at small guide vane open angle are larger than that at large open angle at the same operating head. The amplitudes at points on blade pressure surface are generally greater than that on suction surface. The research results could be used to direct the hydraulic design and operation stability improvement of a large Francis hydraulic turbine.

Impact of Impeller Stagger Angles on Pressure Fluctuation for a Double-Suction Centrifugal Pump

Pressure fluctuation may cause high amplitude of vibration of double-suction centrifugal pumps, but the impact of impeller stagger angles is still not well understood. In this paper, pressure fluctuation experiments are carried out for five impeller configurations with different stagger angles by using the same test rig system. Results show that the stagger angles exert negligible effects on the characteristics of head and efficiency. The distributions of pressure fluctuations are relatively uniform along the suction chamber wall, and the maximum pressure fluctuation amplitude is reached near the suction inlet tongue region. The pressure fluctuation characteristics are affected largely by impeller rotation, whose dominant frequencies include impeller rotation frequency and its harmonic frequencies, and half blade passage frequency. The stagger angle exerts a small effect on the pressure fluctuations in the suction chamber while a great effect on the pressure fluctuation in volute casing, especially on the aspect of decreasing the amplitude on blade passage frequency. Among the tested cases, the distribution of pressure fluctuations in the volute becomes more uniform than the other impeller configurations and the level of pressure fluctuation may be reduced by up to 50% when the impeller stagger angle is close to 24° or 360°.The impeller structure pattern needs to be taken into consideration during the design period, and the halfway staggered impeller is strongly recommended.

Pressure fluctuation signal analysis of pump based on ensemble empirical mode decomposition method

Pressure fluctuations, which are inevitable in the operation of pumps, have a strong non-stationary characteristic and contain a great deal of important information representing the operation conditions. With an axial-flow pump as an example, a new method for time-frequency analysis based on the ensemble empirical mode decomposition （EEMD） method is proposed for research on the characteristics of pressure fluctuations. First, the pressure fluctuation signals are preprocessed with the empirical mode decomposition （EMD） method, and intrinsic mode functions （IMFs） are extracted. Second, the EEMD method is used to extract more precise decomposition results, and the number of iterations is determined according to the number of IMFs produced by the EMD method. Third, correlation coefficients between IMFs produced by the EMD and EEMD methods and the original signal are calculated, and the most sensitive IMFs are chosen to analyze the frequency spectrum. Finally, the operation conditions of the pump are identified with the frequency features. The results show that, compared with the EMD method, the EEMD method can improve the time-frequency resolution and extract main vibration components from pressure fluctuation signals.

Investigation on Reduction of Pressure Fluctuation for a Double-Suction Centrifugal Pump

Double-suction centrifugal pumps have been applied extensively in many areas,and the significance of pressure fluctuations inside these pumps with large power is becoming increasingly important.In this study,a double-suction centrifugal pump with a high-demand for vibration and noise was redesigned by increasing the flow uniformity at the impeller discharge,implemented by combinations of more than two parameters.First,increasing the number of the impeller blades was intended to enhance the bounding effect that the blades imposed on the fluid.Subsequently,increasing the radial gap between the impeller and volute was applied to reduce the rotor-stator interaction.Finally,the staggered arrangement was optimized to weaken the efficacy of the interference superposition.Based on numerical simulation,the steady and unsteady characteristics of the pump models were calculated.From the fluctuation analysis in the frequency domain,the dimensionless pressure fluctuation amplitude at the blade passing frequency and its harmonics,located on the monitoring points in the redesigned pumps(both with larger radial gap),are reduced a lot.Further,in the volute of the model with new impellers staggered at 12°,the average value for the dimensionless pressure fluctuation amplitude decreases to 6%of that in prototype pump.The dimensionless rootmean-square pressure contour on the mid-span of the impeller tends to be more uniform in the redesigned models(both with larger radial gap);similarly,the pressure contour on the mid-section of the volute presents good uniformity in these models,which in turn demonstrating a reduction in the pressure fluctuation intensity.The results reveal the mechanism of pressure fluctuation reduction in a double-suction centrifugal pump,and the results of this study could provide a reference for pressure fluctuation reduction and vibration performance reinforcement of doublesuction centrifugal pumps and other pumps.

Elimination of Fuel Pressure Fluctuation and Multi-injection Fuel Mass Deviation of High Pressure Common-rail Fuel Injection System

The influence of fuel pressure fluctuation on multi-injection fuel mass deviation has been studied a lot,but the fuel pressure fluctuation at injector inlet is still not eliminated efficiently.In this paper,a new type of hydraulic filter consisting of a damping hole and a chamber is developed for elimination of fuel pressure fluctuation and multi-injection fuel mass deviation.Linear model of the improved high pressure common-rail system（HPCRS）including injector,the pipe connecting common-rail with injector and the hydraulic filter is built.Fuel pressure fluctuation at injector inlet,on which frequency domain analysis is conducted through fast Fourier transformation,is acquired at different target pressure and different damping hole diameter experimentally.The linear model is validated and can predict the natural frequencies of the system.Influence of damping hole diameter on fuel pressure fluctuation is analyzed qualitatively based on the linear model,and it can be inferred that an optimal diameter of the damping hole for elimination of fuel pressure fluctuation exists.Fuel pressure fluctuation and fuel mass deviation under different damping hole diameters are measured experimentally,and it is testified that the amplitude of both fuel pressure fluctuation and fuel mass deviation decreases first and then increases with the increasing of damping hole diameter.The amplitude of main injection fuel mass deviation can be reduced by 73%at most under pilot-main injection mode,and the amplitude of post injection fuel mass deviation can be reduced by 92%at most under main-post injection mode.Fuel mass of a single injection increases with the increasing of the damping hole diameter.The hydraulic filter proposed by this research can be potentially used to eliminate fuel pressure fluctuation at injector inlet and improve the stability of HPCRS fuel injection.

Analysis on the Pressure Fluctuation Law of a Hydraulic Exciting System with a Wave-exciter

A hydraulic exciting system with a wave exciter has been constructed in order to study the hydraulic vibra- tion law. The system consists of an oil source, wave-exciter and oil cylinder, and is controlled by a wave-exciter. The working principle of the hydraulic exciting system and wave exciter has been analyzed, and its excitation process has been illustrated. The law of every pipe＇s pressure fluctuation of the system is obtained by experiment. The theo- retical analysis and experimental data prove that the pipeline pressure periodically changes and the pipeline pressure fluctuation frequency is independently controlled by the excitation frequency of the wave-exciter. Every pipelinc＇s pressure wave is produced by system flow fluctuation and water hammer coupling. The pressure fluctuation rules of the system provide a theoretical basis for the study of the associated liberation system.

Time-series analysis of the characteristic pressure fluctuations in a conical fluidized bed with negative pressure

The negative pressure conical fluidized bed is widely used in the pharmaceutical industry.In this study,experiments based on the negative pressure conical fluidized bed are carried out by changing the material mass and particle size.The pressure fluctuation signals are analyzed by the time and the frequency domain methods.A method for absolutely characterizing the degree of the energy concentration at the main frequency is proposed,where the calculation is to divide the original power spectrum by the average signal power.A phenomenon where the gas velocity curve temporarily stops growing is observed when the material mass is light,and the particle size is small.The standard deviation and kurtosis both rapidly change at the minimum fluidization velocity and thus can be used to determine the flow regime,and the variation rule of the kurtosis is independent of both the material mass and particle size.In the initial fluidization stage,the dominant pressure signal comes from the material movement;with the increase in the gas velocity,the power of a 2.5 Hz signal continues to increase.A method of dividing the main frequency by the average cycle frequency can conveniently determine the fluidized state,and a novel concept called stable fluidized zone proposed in this paper can be obtained.Controlling the gas velocity within the stable fluidized zone ensures that the fluidized bed consistently remains in a stable fluidized state.

Impact of intraocular pressure fluctuations on progression of normal tension glaucoma

AIM:To investigate short-and long-term intraocular pressure(IOP)fluctuations and fur ther ocular and demographic parameters as predictors for normal tension glaucoma(NTG)progression.METHODS:This retrospective,longitudinal cohort study included 137 eyes of 75 patients with NTG,defined by glaucomatous optic disc or visual field defect with normal IOP(<21 mm Hg),independently from therapy regimen.IOP fluctuation,mean,and maximum were inspected with a mean follow-up of 38 mo[standard deviation(SD)18 mo].Inclusion criteria were the performance of minimum two 48-hour profiles including perimetry,Heidelberg retina tomograph(HRT)imaging,and optic disc photographs.The impact of IOP parameters,myopia,sex,cup-to-disc-ratio,and visual field results on progression of NTG were analyzed using Cox regression models.A sub-group analysis with results from optical coherence tomography(OCT)was performed.RESULTS:IOP fluctuations,average,and maximum were not risk factors for progression in NTG patients,although maximum IOP at the initial IOP profile was higher in eyes with progression than in eyes without progression(P=0.054).The 46/137(33.5%)eyes progressed over the followup period.Overall progression(at least three progression confirmations)occurred in 28/137 eyes(20.4%).Most progressions were detected by perimetry(36/46).Longterm IOP mean over all pressure profiles was 12.8 mm Hg(SD 1.3 mm Hg);IOP fluctuation was 1.4 mm Hg(SD 0.8 mm Hg).The progression-free five-year rate was 58.2%(SD 6.5%).CONCLUSION:Short-and long-term IOP fluctuations do not result in progression of NTG.As functional changes are most likely to happen,NTG should be monitored with visual field testing more often than with other devices.

Influence of Plasma Pressure Fluctuation on RF Wave Propagation

Pressure fluctuations in the plasma sheath from spacecraft reentry affect radiofrequency（RF） wave propagation.The influence of these fluctuations on wave propagation and wave properties is studied using methods derived by synthesizing the compressible turbulent flow theory,plasma theory,and electromagnetic wave theory.We study these influences on wave propagation at GPS and Ka frequencies during typical reentry by adopting stratified modeling.We analyzed the variations in reflection and transmission properties induced by pressure fluctuations.Our results show that,at the GPS frequency,if the waves are not totally reflected then the pressure fluctuations can remarkably affect reflection,transmission,and absorption properties.In extreme situations,the fluctuations can even cause blackout.At the Ka frequency,the influences are obvious when the waves are not totally transmitted.The influences are more pronounced at the GPS frequency than at the Ka frequency.This suggests that the latter can mitigate blackout by reducing both the reflection and the absorption of waves,as well as the influences of plasma fluctuations on wave propagation.Given that communication links with the reentry vehicles are susceptible to plasma pressure fluctuations,the influences on link budgets should be taken into consideration.

Postoperative Delirium in Elderly Patients May be Associated with Perioperative Blood Pressure Fluctuations

Postoperative delirium(PD)is a common complication of surgery in elderly patients,but its pathophysiological mechanism remains unclear.In order to clarify the role of intraoperative hypotension and fluctuation of blood pressure in the development of PD,we conducted a follow-up study in elderly patients with intraoperative hypotension and fluctuation of blood pressure.A total of 237 patients underwent hip surgery between July 2018 and September 2019,and 158 patients who were eligible for inclusion were enrolled in the study.One day before the operation,the mentality of patients was evaluated by Mini-mental State Examina­tion(MMSE),and the sex,age,height,and weight of the patients were recorded.Radial artery puncture was performed in all patients before anesthesia,intraoperative SBP,MAP and DBP were recorded,and the surgical events of the patients was recorded.The markers associated with PD(TNF-α,IL-6 and S-100β)were determined before and after surgery.Perioperative delirium(PD)was assessed by the prevailing standard of assessment,Confusion of Consciousness Assessment(CAM).Cognitive assessment was evaluated using the Mini-mental State Examination(MMSE).In addition,the timing and type of delirium were recorded.There were 158 patients which were accorded with the inclusion criteria came into the study.The results of our data showed that delirium occurred in 41 patients(25.9%)during the first week after surgery.In the compar­ison between the PD group and the non-PD group,it was found that the patients with postoperative delirium were older,lower body mass index and higher MMSE score before operation.Intraoperative blood pressure is low,usually more than 30%lower than preoperative blood pressure.The levels of TNF-α,IL-6 and Smur100βwere higher after operation.The increased incidence of postoperative delirium may be related to in­traoperative hypotension and intraoperative blood pressure fluctuation.The pathophysiological mechanism may be that hypotension causes low cerebral perfusion,which in turn causes local inflammation in the brain.In addition,postoperative delirium is also more likely to occur in older patients with lower body mass index.

High-amplitude pressure fluctuations of a pump-turbine with large head variable ratio during the turbine load rejection process

Large-head variable-amplitude pump turbines(PTs) encounter serious transient hydraulic instability issues. To explore the evolution mechanisms of pressure fluctuations(PFs) and flow patterns inside large-head variable-amplitude PTs, the load rejection process(LRP) was investigated using a one-and three-dimensional coupled flow simulation approach. The temporal,spatial, and frequency characteristics of the fluctuating pressures were analyzed for four monitoring points using a combined time-frequency analysis approach. The results indicated that PFs during the LRP of large-head variable-amplitude PTs had a new fluctuation frequency component related to Dean vortices(DVs) in the volute, in addition to the common fluctuation frequency components related to rotor-stator interaction phenomena and local backflow vortices near the impeller inlet. The PF frequency component existed throughout the LRP and had a significant influence on the transient maximum pressure at the volute end. This study provides a useful theoretical guide for the design and optimization of large-head variable-amplitude PTs.

Numerical analyses of pressure fluctuations induced by interblade vortices in a model Francis turbine

Interblade vortices can greatly influence the stable operations of Francis turbines. As visible interblade vortices are essentially cavitating flows, i.e., the ones to cause interblade vortex cavitations, an unsteady simulation with a method using the RNG k- ？ turbulence model and the Zwart-Gerber-Belamri（ZGB） cavitation model is carried out to predict the pressure fluctuations induced. Modifications of the turbulence viscosity are made to improve the resolutions. The interblade vortices of two different appearances are observed from the numerical results, namely, the columnar and streamwise vortices, as is consistent with the experimental results. The pressure fluctuations of different frequencies are found to be induced by the interblade vortices on incipient and developed interblade vortex lines, respectively, on the Hill diagram of the model runner＇s parameters. From the centrifugal Rayleigh instability criterion, it follows that the columnar interblade vortices are stable and the streamwise interblade vortices are unstable in the model Francis turbine.

Numerical simulation of pressure fluctuation in Kaplan turbine

As it is almost impossible to carry out the prototype hydro-turbine experiment be- fore the power plant is built up, rational prediction of pressure fluctuations in the prototype turbine is very important at the design stage. From this viewpoint, we at first treated the unsteady turbulent flow computation based on the modified RNG k-ε turbulence model through the whole flow passage to simulate the pressure fluctuation in a model turbine. Since fair agreement was recognized between the numerical results and the experimental data, this numerical method was applied to simulate the pressure fluctuations in the prototype turbine. From the comparison of them with the model turbine results, it is seen that their qualitative trend of pres- sure fluctuations are similar, but an appreciable difference is observed between the amplitudes of pressure fluctuation of the prototype turbine and that of the model turbine. Though the present findings may be explained by the effect of Reynolds number, further studies are expected for quantitative interpretation. We paid atten- tion to the interaction between the fluid and turbine structure. Adopting a weak fluid-solid coupling method, we studied the pressure fluctuation in the prototype turbine to clarify how the elastic behavior of runner blades influenced the charac- teristics of pressure fluctuation.

EXPERIMENTAL STUDY OF EFFECTS OF AIR CONTENT ON CAVITATION AND PRESSURE FLUCTUATIONS

This article studies the effects of air content on propeller cavitation and pressure fluctuations. The cavitation is observed while the pressure fluctuations on the hull are measured. When adjusting the air content, the sheet cavitation range does not change distinctly, but the pressure fluctuations see obvious differences. The amplitudes of the pressure fluctuations increase with the decrease of the air content. The results indicate that the air content has little effect on the sheet cavitation range but has an important effect on the bubble cavitation and the tip vortex cavitation. When the air content decreases, the water tensile force increases, which results in the instability of the bubble cavitation and the tip vortex cavitation and the increase of the pressure fluctuations. To minimize the scale effects, the experiments should be run at a high Reynolds number with a high nuclei content. The high Reynolds number is often realized by increasing the flow velocity and the propeller rotation speed, and the high nuclei content is often made by increasing the dissolved air content.

Experimental investigation of vortex generator influences on propeller cavitation and hull pressure fluctuations

In this paper,the transient turbulent cavitating flow around a marine propeller behind a ship was investigated experimentally with emphasis on how vortex generator(VG)influences propeller cavitation and hull pressure fluctuations.The experiments were carried out in China Large Cavitation Channel with the closed test section covering 10.5 m in length and cross-section of 2.2 m^2×2.0m^2.The experiment recorded instantaneous cavitation photos of the propeller and pressure fluctuations on the hull surface.The results demonstrate that without vortex generator,the sheet cavitation inception begins at-50°(310°),and then from-50°(310°)to 30°,the extent and area of sheet cavitation increase.When vortex generator installed on the hull,the sheet cavitation inception occurs in advance at-60°(300°),and the sheet cavitation expands to larger rotation range due to the vortex generator.It is shown that the vortex generator with proper geometry and installed location may contribute the highly nonuniform wake to be more uniform,and can make the change of propeller cavitation to be milder,which decrease the pressure fluctuations in this study.Further analysis indicates that the vortex generator may promote the energy distribution to be more uniform in physical and spectral space in some degree.

Characteristics of pressure fluctuations and fine coal preparation in gas-vibro fluidized bed

To improve the separation efficiency of air dense medium fluidized beds tor dry coal preparation, a gasvibro fluidized bed has been proposed in which magnetic powder is used as the heavy medium. Pressure fluctuations in the gas-vibro fluidized bed were investigated using time- and frequency-domain analysis methods. The relationship between pressure fluctuations, bubble behavior, and separation efficiency was established. The low amplitude of the standard deviation, the power spectral density （PSD）, the incoherent-output PSD, and the high amplitude of the coherent-output PSD, which corresponds to the bubble behavior in the bed, were improved for coal preparation. The coal ash content was reduced from 42.5570 to 16.54% by using the gas-vibro fluidized bed.

PRESSURE FLUCTUATIONS IN GAS-SOLIDS FLUIDIZED BEDS

Pressure fluctuation data measured in a series of fluidized beds with diameters of 0.05, 0.1, 0.29, 0.60 and 1.56 m showed that the maximum amplitude or standard deviation increased with increasing the superficial gas velocity and static bed height for relatively shallow beds and became insensitive to the increase in static bed height in relatively deep beds. The amplitude appeared to be less dependent on the measurement location in the dense bed. Predictions based on bubble passage, bubble eruption at the upper bed surface and bed oscillation all failed to explain all observed trends and underestimated the amplitude of pressure fluctuations, suggesting that the global pressure fluctuations in gas-solids bubbling fluidized beds are the superposition of local pressure variations, bed oscillations and pressure waves generated from the bubble formation in the distributor region, bubble coalescence during their rise and bubble eruption at the upper bed surface.