Calculation Of Pressure Drop Research Articles

Predicting pressure loss of turbulent non-Newtonian fluids in annuli under temperature and pipe rotation effects using optimization algorithms

Accurate estimation of frictional pressure loss in an annulus is crucial for selecting appropriate pump systems, determining horsepower requirements, and controlling hole cleaning. Generally, when calculating the friction factor, the temperature of the fluid and the rotation of the inner pipe are not considered, which can lead to errors in estimating the pressure difference in the annulus. In this study, to ensure accurate pressure drop calculations, the effects of temperature and inner pipe rotation, along with other parameters, were included. An extensive experimental study was conducted at Izmir Katip Celebi University’s Flow Loop using two Carboxymethyl cellulose (CMC) solutions, across various fluid velocities, fluid temperatures, diameter ratios, and inner pipe rotation speeds. A dimensional analysis was performed to identify the parameters that affect friction factors in the annulus. Finally, friction factor equations were developed based on the experimental data using optimization algorithms such as interior point (fmincon), genetic, minimax, and simulated annealing. The findings showed that the predictions from all the algorithms tested in the study closely matched the experimental results; however, the interior point algorithm (fmincon) provided the best performance, with an average absolute percentage error of 9.4%.

A One-Dimensional Computational Model to Identify Operating Conditions and Cathode Flow Channel Dimensions for a Proton Exchange Membrane Fuel Cell

A one-dimensional computational model has been developed that can be used to identify operating conditions for the cathode side of a proton exchange membrane fuel cell such that both the inlet and outlet relative humidity is equal to 100%. By balancing the calculated pressure drop along the cathode side flow channel with the change in molar composition, inlet conditions for the cathode side can be identified with the goal of avoiding channel flooding. The channel length, height, width and the land-to-channel width ratio are input parameters for the model so that it might be used to dimension the cathode flow field. The model can be used to calculate the limiting current density, and we are presenting unprecedented high values as a result of the high pressure drop along the flow channels. Such high current densities can ultimately result in a fuel cell power density beyond the typical value of 1.0–2.0 W/cm2 for automotive fuel cells.

High Current Density Operation of a Proton Exchange Membrane Fuel Cell with Varying Inlet Relative Humidity—A Modeling Study

This paper focuses on proton exchange membrane fuel cell (PEMFC) operation at current densities in the order of 6 A/cm2. Such high current densities are conceivable when the traditional carbon fiber papers are replaced with perforated metal plates as the gas diffusion layer to enhance waste heat removal, and at the same time the relative humidity inside the fuel cell is kept below 100% by applying appropriate operating conditions as was found in previous one-dimensional modeling work. In the current paper, we applied a three-dimensional, multi-phase computational fluid dynamics model based on Ansys-CFX to obtain additional insight into the underlying physics. The calculated pressure drops are in very good agreement with previous one-dimensional modeling work, and the current densities in all case studies are in the order of 5–6 A/cm2, but different from the previous one-dimensional study, the results suggest that the relative humidity is very close to 100% throughout the entire channel length when the inlet relative humidity is 100%, ensuring best hydration cell conditions and hence best performance. Importantly, the model results suggest that fuel cell performance at a high current density in conjunction with relatively low stoichiometric flow ratios around 1.5–2 is possible.

Pressure drop prediction for R407C fluid during flow evaporation in horizontal pipes using Kalman Filter

The estimation of pressure drop in systems involving two-phase fluids holds a substantial influence over system design, energy efficiency, heat transfer dynamics, and the overall system performance. Existing correlations in the current literature exhibit considerable errors, primarily attributable to the diverse characteristics of flow patterns inside the pipe. This work presents a discussion on the pressure drop of the R-407C fluid in horizontal pipes during two-phase flow, along with the application of the Kalman Filter to improve the estimations produced by well-known correlations. The initialization data used were obtained through equations created based on experimental data and considering the influence that diameter, mass velocity, and saturation pressure have on the pressure drop. The correlations used as a basis for the calculations were selected from the literature, considering the lowest percentage error observed in the pressure drop estimation. Experimental data of pressure drop where compared with the results the obtained by using the correlation alone and in combination with a Kalman Filter. For tubes with a diameter greater than 1.5 mm, applying the correlation together with the Kalman Filter resulted in a Mean Absolute Relative Deviation (MARD) of 15.71, whereas using the correlation alone yielded a MARD of 28.26. For tubes with diameters of 1.5 mm or less, the MARD values were 12.12 and 62.90, for the combination of correlation and the Kalman Filter and for the correlation alone, respectively. These results underscore the viability of the Kalman Filter as an effective tool for improving the accuracy of pressure drop calculations in horizontal tubes.

A RELAP5-3D Model of the Lobo Lead Loop

The goal of our research is to build upon the capability of RELAP5-3D to model molten lead systems. Molten lead has several potential uses in future advanced reactors, like the lead fast reactor or fusion reactors that utilize dual-coolant lead lithium blankets. This potential for use in future generations of reactors highlights the necessity of developing molten lead models to ensure that they can accurately predict thermohydraulic behavior. We have developed a RELAP5-3D model of the Lobo Lead Loop facility located at the University of New Mexico to verify the accuracy of RELAP5-3D via comparison to existing computational fluid dynamics results and analytical calculations. It was found that RELAP5-3D accurately calculated radiative heat transfer (within <1%) when compared to theoretical calculations. In addition, pressure drop calculations done in RELAP5-3D demonstrated reasonable agreement within 20 kPa, mostly within ~7% to 15%, when compared to the computational fluid dynamics model of the facility developed by the University of New Mexico, and captured the dependence of pressure drop on flow velocity accurately. Finally, a hypothetical loss-of-flow transient was imposed on the RELAP5-3D model to determine the feasibility of performing a similar experiment with the Lobo Lead Loop. It was found that such an experiment could be possible, as the RELAP5-3D model indicated that the temperatures of the fluid would not exceed the limiting temperatures of the structure (1658 K) nor the maximum temperature of the electromagnetic pump inlet (823 K). Although there are no experimental data to begin validation, the model will be readily available for future validation studies when the experimental data are generated, especially as the model continues to evolve over time. The results so far demonstrate a promising first step in the verification/validation of the RELAP5-3D model of the Lobo Lead Loop. The highlights from our research are as follows: 1. The Lobo Lead Loop facility at the University of New Mexico is a good candidate for molten lead system code validation. 2. The Lobo Lead Loop currently has extensive pressure drop results from a high-fidelity computational fluid dynamics model, which offers the opportunity for code-to-code verification of pressure drop in RELAP5-3D. 3. A RELAP5-3D model of the Lobo Lead Loop has been developed to begin verification studies and to prepare for potential validation studies. 4. Development of the model will continue throughout the future to prepare for potential validation studies.

Zero-Net Liquid Flow Simulation Experiment and Flow Law in Casing Annulus Gas-Venting Wells

Under casing annulus gas venting, the annulus of the well is in a special state of zero-net liquid flow (ZNLF), leading to gas production without liquid at the wellhead, resulting in significant holdup issues. Therefore, conventional two-phase flow models cannot be used for calculation. To study the flow characteristics of ZNLF in the annulus of the well, this study established a visual experimental device with a total height of 5.4 m, an outer pipe inner diameter of 140 mm, and an inner pipe outer diameter of 72 mm. The flow characteristics of ZNLF were studied by controlling the casing pressure, initial liquid level, and bottom gas injection rate. The experimental results showed that the flow patterns of ZNLF are mainly bubbly flow and churn flow. Bubbly flow occurred at lower gas rates, while churn flow occurred at higher gas rates. In addition, the experiment found that when the gas injection rate and initial liquid column height were controlled to be the same, the liquid holdup decreased as the casing pressure increased. Analysis of the data patterns indicated that the slip velocity is related to the casing pressure. Based on the experimental results of ZNLF in the annulus, this study established standards for flow pattern transitions, holdup, and a pressure drop calculation model. The model results showed good agreement with the experimental results, with errors not exceeding ±5%.

Study on the flow and heat transfer characteristics of gaseous hydrogen in heat exchange tubes coupled with ortho-para hydrogen conversion

Hydrogen as a clean energy to deal with carbon emissions has been favored by many scholars, while the problems of low efficiency and high energy consumption in the process of liquefaction storage and transportation have become one of the important factors restricting the development of it. The combination of heat exchanger and ortho-para (O–P) hydrogen converter has attracted considerable attention as a high efficiency and low energy consumption technology. In this paper, based on the catalyst-filled spiral wound heat exchanger (CSWHE) and coupled with ortho-para hydrogen conversion, the flow and heat transfer characteristics of gaseous hydrogen are studied. Firstly, low-temperature O–P hydrogen catalytic conversion experiments and flow characteristics experiments were carried out by filling catalyst in the heat exchange tube. and an equation for calculating pressure drop in the section filled catalyst was proposed. Secondly, a new numerical model was established validated by the experiments. The influence of catalyst on heat transfer and the effects of velocity on the heat transfer performance and O–P hydrogen conversion efficiency were studied by numerical simulation. Finally, this paper analyzed the significant factor affecting the para hydrogen content at outlet: reaction time. And an equation for calculating para hydrogen content at outlet with reaction time was proposed. This study is expected to provide a reference for the design of CSWHE.

Flow dynamics through cellular material based on a structure with triply periodic minimal surface

Triply Periodic Minimal Surface (TPMS)-based cellular structures are widely adopted due to their high surface-to-volume area, superior mechanical characteristics, and adaptive properties. This paper is dedicated to deriving a new semi-empirical equation for pressure drop in TPMS-based structures (specifically Schwarz-P, Schoen I-WP, Neovius). Both numerical and experimental tests were conducted to analyze the impact of TPMS parameters on pressure drop and velocity distribution. It was determined that flow through the Schwarz-P structure exhibits a tubular flow pattern, flow through the Neovius structure demonstrates active flow mixing, and flow through the Schoen I-WP structure does not have stagnant (dead) zones. A novel semi-empirical equation was formulated to calculate pressure drop as a function of flow parameters and TPMS-based structure parameters. This equation incorporates both viscous resistance (Δp=f(v)) and kinetic energy loss (Δp=f(v2)), enabling its application for predicting pressure drop across a wide range of practically interesting operational parameters.

Performance improvement of a rotating gas separator for electrical submersible pump considering entropy generation method

The utilization of Electrical Submersible Pumps (ESPs) stands as one of the foremost methods in artificially extracting oil, primarily within the oil industry. Under typical conditions, the pump encounters a two-phase flow of oil and gas. Should the gas phase within this mixture surpass an acceptable threshold, it can lead to a significant decline in performance and inflict detrimental damage upon the pump. To address this issue, the incorporation of a gas separator unit, one of the pivotal components within ESPs, is imperative at the pump's inlet section. Enhancing the gas separator unit holds paramount importance for ensuring pump safety and optimizing performance, particularly in wells with elevated gas contents.The conventional approach to calculating hydraulic losses in turbomachinery, relying on pressure drop calculations, often falls short in pinpointing the precise locations of losses. This paper delves into enhancing gas separator performance by augmenting gas separation efficiency through the application of the entropy generation method and leveraging the second law of thermodynamics. To achieve this, pivotal entropy-generating geometrical parameters of the gas separator were identified as the design variables necessary for forming the Taguchi sample space. Numerical simulations were conducted utilizing steady three-dimensional Reynolds-Averaged Navier-Stokes (RANS) equations for incompressible fluid flow, coupled with a turbulence model. Results indicate that the gas separation efficiency (GSE) of the initial model surged from 45.6% to 88% in the improved sample, albeit with a concurrent rise in entropy generation rate (EGR) from 209 W/K to 243.1 W/K. To establish a more comprehensive criterion for analysis, the ratio of GSE to EGR was employed as an objective function. This ratio quantifies the efficiency of gas separation per unit of energy loss, and it escalated from 0.218 in the primary sample to 0.362 in the improved sample, representing a 66% increase. This signifies that despite simultaneous increases in EGR and GSE, the rate of energy loss per unit of gas separation has diminished. Furthermore, the heightened EGR in the improved sample can be attributed to an increase in total volume, leading to an expanded contact surface area and consequently an elevation in total entropy. This investigation underscores the advantages of the entropy generation method, particularly in delineating the precise location and magnitude of energy dissipation within the rotating gas separator.

Recovery and utilisation of waste heat for sponge iron process through combined preheating and power generation

This paper deals with an option accounted for total waste gas heat recovered through combined preheating as well as power generation of feed material, kiln air, as well as slinger coal when it reaches 250 °C from 994 °C. The heat recovery is obtained through GCC Profile is plotted using HINT software. The power produced is 2.757 MW with an optimal condition having a temperature of 280 °C saturated, 600 °C superheated, as well as superheated pressure of 350 bar. The heat required around the superheater, boiler and preheater is 5066.9 kW, 12,669.93 kW and 6873.6 kW. The air requirement for this option is 52.588 t/h after iteration. Also, the iterative waste gas flow rate is 22.31 kg/s. Three new heat exchangers are required to achieve possible heat recovery by designing HEN through Pinch Analysis. The water requirement around EC is 14.88 t/h and 7.8 t/h as in the case of actual and modified HEN. The calculated pressure drops of different ducts having lengths 25 m and pressure 0.034 atm, 80 and 105 m are obtained pressure as 0.034, 0.12 and 0.16 atm. 3 FD fans are required for maintenance of required pressures in the duct. The TAC is INR 8068.8/y; payback period is 2.62 y.

Treat It Like a Circuit, Part II: Applications and Troubleshooting

The analogy that electrons flowing in wires is like water flowing through a tube can be remarkably effective for teaching and learning about fluid flow in LC systems. In this installment, we apply the concepts developed in last month’s installment by demonstrating how they can be used to help troubleshoot problems in LC involving pressure and flow. We also introduce several free tools that can be used to calculate pressure drops in different elements of LC systems, including connecting capillaries and packed columns. Knowing what pressure drops to expect for system components under different chromatographic conditions is very valuable in many troubleshooting situations.

Thermal and Structural Analysis on Simulated Model of a Beam Dump

This paper deals with the design, thermal and structural analysis for stopping the proton beam. A conical beam dump is being designed to handle the thermal and structural stresses resulting due to high heat load and hydraulic pressure of coolant, while handling 600 KW proton beam power in CW operation at 20 MeV energy. Pressure drop and heat transfer calculations are done considering spiral channel cooling system. The heat flux has been calculated by using Bi-Gaussian distribution density function of particles in beam. Nickel is selected as the beam dump material because of its favorable properties. In order to understand the thermal performance of beam dump a finite element model has been developed to predict the steady state temperature and stress distributions within the beam stop material. Key Word: Beam dump design, FEM, Thermal and Structural stress.

Experimental observation and pressure drop modeling of plug formation in horizontal millifluidic hydraulic conveying.

The hydraulic conveying of glass beads is studied in a horizontal tube. At low flow rates, plugs can be observed moving across the tube, whereas pseudoplugs can be seen at higher flow rates. A statistical analysis of the plugs' and pseudoplugs' velocities and the plugs' lengths observed is conducted. A transition of the propagation speed distribution is established when the crossing over from a plug to a pseudoplug regime is reached, where the peaked plug velocity distribution turns into a uniform pseudoplug velocity distribution. On the other hand, the statistical distribution of plug lengths exhibits a log-normal mathematical shape. The interpretation of the measured pressure drop evolution with the imposed flow rate by means of an effective viscosity shows an apparent shear-thinning effect coming from the dilution of the granular material. This approach provides a predictive tool for pressure drop calculation in the pseudoplug regime.

Study of the flow pattern and pressure drop law of the air-water-foam three-phase flow

The inaccurate prediction of flow patterns and pressures after adding different types and concentrations of surfactants to wellbores and drainage lines is a common problem in shale gas wells and tubing foam drainage. To clarify the change rule of the air–water-foam three-phase flow pattern and pressure drop after adding different types and concentrations of surfactants, a surface tension test was conducted in this study. In addition, visual air–water-foam three-phase flow indoor simulation experiments were performed with various surfactants such as cocamidopropyl hydroxysulfobetaine (MX-1), dodecyldimethyl betaine (TCJ-1), and sodium α-alkenyl sulfonate (XJHSM), surfactant concentrations (0.3–0.6 %), oil pipe diameters, pipe inclinations, gas–liquid ratios, and oil contents on large-scale experimental equipment. Based on the gas–liquid distribution characteristics, the air–water-foam three-phase flow patterns in the inclined tube were reclassified, and the quantitative conversion boundaries of the various flow patterns were determined. Based on the pressure drop pulse characteristics, characterization parameters such as the scaling factor, foaming capacity, foam density, and gas-holding rate were introduced after considering the effects of various factors on the pressure drop weights, enabling a new pressure drop calculation method for air–water-foam three-phase flows for application to different types and concentrations of surfactants. The errors were verified using data from previous studies and field measurements that were within 15% and 5%, respectively. The results of these studies provide a better understanding of the air–water-foam three-phase flow patterns and pressure drop variations in shale gas wells and gathering lines.

High capacity laminate adsorbers: Enhancing separation performance beyond packed beds

In response to the growing demand for more efficient adsorption processes, structured adsorbents have emerged as a promising solution as they offer improved mass transfer and pressure drop characteristics. However, they are often hampered by a lower volumetric capacity due the presence of support structures or a large bed void fraction. This research focuses on the manufacturing and evaluation of self-standing zeolitic laminates of various thickness and spacing, comparing their performance to a traditional packed bed. A shaping method to obtain laminates with a 84 wt% zeolite 13X content is described. Furthermore, a method for precise assembly and spacing of the laminates is detailed. Three such laminar adsorbers with different geometries were evaluated in breakthrough experiments and compared to a packed bed to assess their efficiency in the bulk separation of carbon dioxide. Superior performance of the laminar adsorbers was found, with one configuration employing 1.2 mm laminates and 0.4 mm spacing showing a significant 19 % increase in volumetric capacity compared to a packed bed of pellets. This enhanced capacity is achieved while maintaining efficient heat and mass transfer, resulting in sharp breakthrough profiles. Furthermore, using thinner (0.5 mm) laminates, the length of unused bed was further reduced. Additionally, pressure drop calculations were performed and experimentally validated. The pressure drop over the laminar adsorbers was shown to be significantly lower than over a packed bed. These findings underscore the potential of laminar adsorbers to intensify adsorptive separation processes, reduce energy consumption, and address the demand for more effective adsorption technologies.

Efficient and economic water and heat recovery from flue gas by novel hydrophilic polymeric membrane condenser

The membrane technology for water and heat recovery from flue gas possesses the advantages of a simple structure and high water quality. In this study, we propose a novel hydrophilic polymeric membrane condenser (HPMC) to efficiently recover water and heat from flue gas. Compared to current hydrophilic ceramic membrane condenser (HCMC), HPMC offers the benefits of cost-effectiveness and high packing density. An experimental investigation is conducted to explore the fluid flow characteristics as well as the water and heat recovery performance of HPMC. The maximum recovered water flux reaches 6.7 kg/(m2·h), while the maximum recovered heat flux amounts to 18.6 MJ/(m2·h). Enhancing gas/water flow rates or increasing heat transfer temperature difference can significantly improve both recovered water and heat fluxes. Notably, it is found that thermal resistance primarily stems from the polymeric membrane, emphasizing the importance of enhancing the membrane's thermal conductivity to improve HPMC performance. The overall heat transfer coefficient can be enhanced by increasing the gas/water flow rate, while the influence of gas/water temperature on the overall heat transfer coefficient is relatively insignificant. Furthermore, by fitting experimental data, a correlation formula for friction factor is obtained, which greatly enhances accuracy in pressure drop calculations under practical operating conditions. Based on the technical and economic analysis, the payback period for HPMC is merely 0.3 years, significantly shorter than that for HCMC, thereby indicating a substantial potential for commercial application of HPMC. This study demonstrates that the HPMC is an excellent candidate for recovering water and heat from flue gas, and the fundamental data provides valuable foundational insights for future enhancement of HPMC.

Experimental Evaluation of an Empirical Equation in a Gaseous Flow

In this paper, the estimation error of Dr. Pole's empirical equation was evaluated using copper pipes of different diameters (0.00953, 0.0127, 0.01588 m), under different flow pressure conditions (0, 300, 500, 1000, 1500, 2000, 2500, 3000 L/h). To carry out the experiments, the following instruments were used: an air compressor, 2 flow valves, a needle valve, a gas rotameter, copper piping, pressure gauges and transmitters, a Norus data logger with 4 to 20 mA output signals, thermocouples, and thermoresistors. They allow us to establish that the air pressure drops when the flowing through the pipes is higher (380 Pa) for small diameter pipes (0.00953 m), compared to larger diameters (0.01270 m and 0.01588 m) with a maximum of 54 and 28 Pa, respectively; and in relation to the flow rates, the pressure drop increases with a quadratic trend with respect to the flow rate. Finally, the residual errors that the empirical equation has in the pressure drop calculations, in general terms, are not of great magnitude.

Measurement and analysis of void fraction in horizontal plug flow based on electromagnetic wave sensor

Void fraction measurement is a crucial challenge in two-phase flow, which is related to the measurement of phase flow and the calculation of pressure drop. In this study, a coaxial line phase sensor is designed for void fraction acquisition and the void fraction of the plug measured has a well time-domain and Probability Density Functions (PDF) distribution characteristics. Four typical correlations were selected to compare with the measured values of the sensors, the mean absolute errors (MAPE) are 19.88 %, 18.94 %, 18.25 %, and 17.19 %, respectively. Considering the nonlinear and strong coupling between the flow characteristic parameters and the void fraction, the flow parameters were analyzed and selected by Pearson correlation coefficient. The Kernel ridge regression methods were employed to select effective variables for model training, and the Extreme gradient boosting (XGboost) machine learning model was proposed. The prediction accuracy of the model is 1.65 % (current data) and 4.18 % (literature data), respectively.

Two-Phase Crude Oil-Water Flow Through Different Pipes: An Experimental Investigation Coupled with Computational Fluid Dynamics Approach.

The present study deals with two-phase non-Newtonian pseudoplastic crude oil and water flow inside horizontal pipes simulated by ANSYS. The study helps predict velocity and velocity profiles, as well as pressure drop during two-phase crude-oil-water flow, without complex calculations. Computational fluid dynamics (CFD) analysis will be very important in reducing the experimental cost and the effort of data acquisition. Three independent horizontal stainless steel pipes (SS-304) with inner diameters of 1 in., 1.5 in., and 2 in. were used to circulate crude oil with 5, 10, and 15% v/v water for simulation purposes. The entire length of the pipes, along with their surfaces, were insulated to reduce heat loss. A grid size of 221,365 was selected as the optimal grid. Two-phase flow phenomena, pressure drop calculations, shear stress on the walls, along with the rate of shear strain, and phase analysis were studied. Moreover, velocity changes from the wall to the center, causing a velocity gradient and shear strain rate, but at the center, no velocity variation (velocity gradient) was observed between the layers of the fluid. The precision of the simulation was investigated using three error parameters, such as mean square error, Nash-Sutcliffe efficiency, and RMSE-standard deviation of observation ratio. From the simulation, it was found that CFD analysis holds good agreement with experimental results. The uncertainty analysis demonstrated that our CFD model is helpful in predicting the rheological parameters very accurately. The study aids in identifying and predicting fluid flow phenomena inside horizontal straight pipes in a very effective way.

Assessment of dynamic characteristics of fluidized beds via numerical simulations

Euler–Lagrange simulations coupled with the multiphase particle-in-cell (MP-PIC) approach for considering inter-particulate collisions have been performed to simulate a non-reacting fluidized bed at laboratory-scale. The objective of this work is to assess dynamic properties of the fluidized bed in terms of the specific kinetic energy of the bed material kS in J/kg and the bubble frequency fB in Hz, which represent suitable measures for the efficiency of the multiphase momentum exchange and the characteristic timescale of the fluidized bed system. The simulations have reproduced the bubbling fluidization regime observed in the experiments, and the calculated pressure drop Δp in Pa has shown a reasonably good agreement with measured data. While varying the bed inventory mS in kg and the superficial gas velocity uG in m/s, kS increases with uG due to the increased momentum of the gas flow, which leads to a reinforced gas-to-solid momentum transfer. In contrast, fB decreases with mS, which is attributed to the increased bed height hB in m at larger mS. An increased gas temperature TG from 20 to 500 °C has led to an increase in kS by approximately 50%, whereas Δp, hB, and fB are not sensitive to TG. This is due to the increased gas viscosity with TG, which results in an increased drag force exerted by the gas on the solid phase. While up-scaling the reactor to increase the bed inventory, bubble formation is enhanced significantly. This has led to an increased fB, whereas kS, hB, and Δp remain almost unchanged during the scale-up process. The results reveal that the general parameters such as hB and Δp are not sufficient for assessing the hydrodynamic behavior of a fluidized bed while varying the operating temperatures and up-scaling the reactor dimension. In these cases, the dynamic properties kS and fB can be used as more suitable parameters for characterizing the hydrodynamics of fluidized beds.