Fluidization Mode Research Articles

Numerical study of hydrodynamics processes fluidized bed

Boiler units with a circulating fluidized bed (CFB) have become widespread in foreign countries, since the CFB technology has proven itself to be an effective way to burn various types of solid fuels. Traditionally, when creating domestic boilers, a normative method is used, but it does not take into account the peculiarities of the movement of the fluidized bed. The hydrodynamic characteristics of the layer have a significant impact on the design of the combustion chamber. To determine them, both mathematical and numerical modeling methods are used. As a result of mathematical calculation, the dependence of the fluidization mode on the air supply speed was revealed. Also, through numerical modeling, it was possible to establish the correspondence of the particle motion mode with the data from the mathematical model.

Multi-scale experimental and autothermal simulation of bituminous coal and corn straw chemical looping co-gasification for cleaner production of syngas

Herein, the process scale-up route of multi-scale coal and biomass chemical looping co-gasification (CLCG) is established using a thermogravimetric analyzer, a batch bubbling fluidized bed, and an MWth scale industrial demonstration unit. The positive synergistic effect is most notable at a bituminous coal blending ratio of 70%. Fuel synergy has a positive contribution to cold gas efficiency (CGE) and syngas yield (Ys), and the optimal CGE and Ys of the fluidized bed are 68.92% and 4.305 Nm3/kg, respectively. The direct scale-up of the fluidization mode can be adapted to the pilot unit, and the heat efficiency of autothermal CLCG system is 66.84%. This work achieves a process upgrade of CLCG from basic research to technological development to engineering demonstration.

HYDRAULIC RESISTANCE AND SPRAY REMOVAL IN STABILIZED THREE-PHASE FOAM LAYER

Industrial implementation of the stabilization method of the gas-liquid layer can significantly expand the field of use of foaming apparatus and opens up new opportunities for intensifying technological processes with the simultaneous creation of low-waste technologies. The article establishes the basic parameters influencing the hydrodynamics of foam apparatus, considers the basic constructions and operating modes of foam apparatus. The connection of hydrodynamic parameters is revealed. The hydrodynamic laws of the foam layer are considered. The indicated factors affecting the process of mass transfer, both in the gas and in the liquid phases. The conducted analysis of a number of studies showed that the perspective direction of intensification of the mass transfer process is the development of apparatuses with a three-phase fluidized bed of an irrigated nozzle of complex forms with mesh materials. A new design of the stabilizer with a large free volume and a spherical movable nozzle was developed. The advantage of the proposed design is the transition to a structured foam mode of operation at relatively low gas speeds, as well as a developed phase contact surface. After experimental studies of the hydrodynamic characteristics of the combined contact element, experimental data on hydrodynamic resistance and experimental indicators of spray attribution for a contact stage with combined contact elements were obtained. As a result of research, it was found that when using foam layer stabilizers, the spray ratio at the contact stage is reduced, which leads to more stable operation of the device. Empirical equation for determining the value of the spray attribution is given. It is indicated that the mechanism of transition of the nozzle to the mode of advanced fluidization will be significantly different from conventional ballistic nozzles. The study of mass transfer in an absorber with a fluidized bed of an irrigated nozzle is complicated by the fact that the contact surface between phases can vary considerably depending on the hydrodynamic conditions, in particular, on the speed of gas and irrigation density.

Increasing the efficiency of transfer processes when using inhomogeneous fluidization

The processes of dehydration and granulation are associated with the heat transfer to the solid particles from the gas coolant, which acts as a fluidizing agent and causes the stochastic movement of the granular material in the apparatus. To implement the layered structure mechanism of granulation of organic-mineral fertilizers it is necessary to ensure intensive circulation of granular material with intensive gradual passage through the appropriate technological zones of the apparatus. The main problem is the low efficiency of interphase exchange in the gas-liquid-solid system and the formation of agglomerates during granulation with the injection of a liquid heterogeneous solution into the bed of solid granular material.
 In this work the conditions for increasing the efficiency of the transfer processes when using an inhomogeneous jet-pulsating mode of fluidization were determined.
 Analysis of the intensity of renewal of the contact surface of the phases when using inhomogeneous jet-pulsating fluidization in the self-oscillating mode was carried out. It was established that the use of this mode of fluidization allows getting a significant intensification of heat and mass transfer processes due to the activation of diffusion-controlled processes and an increase in the dynamics of interphase contact exchange by 1.9÷2.9 m2/s, which is 27÷41% of the total surface of the material in device.

ХИМИЧЕСКОЕ ОСАЖДЕНИЕ ИЗ ГАЗОВОЙ ФАЗЫ ПИРОУГЛЕРОДНЫХ ПОКРЫТИЙ НА ПОРОШКАХ В ПСЕВДООЖИЖЕННОМ СЛОЕ. I. АППАРАТУРА, ПСЕВДООЖИЖЕНИЕ

A laboratory setup for chemical vapor deposition (CVD) at reduced pressure on powder of medium particle size in a fluidized bed (reactor load of 50 g of substrate) was described. Calculations of critical points for the onset of fluidization and entrainment of particles for various gases (Ar, C3H8, C4H10) at a temperature of 20–1000 °C under low vacuum (pressure of 5 kPa) were performed. Model experiments were carried out on the fluidization of corundum powder (granularity of ~300 μm) in an argon flow, as well as in the propane-butane mixture in the absence of CVD. The dependences of the hydrodynamic mode of fluidization on the nature of fluidizing gas, temperature and pressure were analyzed, which make it possible to plan the process of coating deposition itself.

Simulation of hydrodynamics in gas distribution devices for non-homogeneous mode of fluidization

An increase in the intensity of diffusion-controlled processes during granulation is provided by apparatuses with non-homogeneous fluidization, the hydrodynamics of which significantly depends on the structural features of the granulator chamber and the gas distributing device (GDD). The main problem is the formation of stagnant zones on the working surface of GDD, which, when supplying a coolant with temperature that exceeds the melting point of granules, leads to the melting of solids and the termination of the process.
 In this work, the simulation of hydrodynamics in the granulator chamber was carried out using SolidWorks 2022 SP2 for 4 types of gas distribution devices (GDD) of different configurations with different values ​​of the cross-section coefficient of GDD.
 The analysis of the simulation results shows that the most significant influence on the hydrodynamic activity index near the surface of GDD iha has the cross-section coefficient of GDD φ, since even an insignificant increase in the value of φ from 3.0 to 3.5% leads to a significant decrease in the hydrodynamic activity index iha by at least 1.4 times for all considered types of GDD. The simulation of hydrodynamics was carried out without taking into account the presence of solid granular material in the granulator chamber and near the surface of GDD plate.

Theoretical background to substantiation of the parameters of mixer for protein, mineral and vitamin additives

One way to improve the mixing efficiency of protein-mineral-vitamin additives for cattle diets is to fluidize the material. The aim of the study is to define theoretical dependences between the speed and energy characteristics of the formation of a fluidized bed on the physical and mechanical properties of mixing substances and on structural and kinematic parameters of the mixer. The research was carried out in 2021. A coefficient of structural and mechanical resistance of the disperse many-component system was introduced to clarify the characteristics of additives mixing in the fluidization mode. The obtained equations described the particle velocity and the energy consumption for the particle flow in a fluidized bed influenced by a blade mixer. Next step was to reveal the effect of the layer porosity and the mixer blade angle on the particle velocity in the mixture. The velocity loss equation was solved as a graph for the value of 5 m/s at the blade edge. The variation in the layer porosity had a significant effect on considered parameter. The greatest velocity loss exceeded 4.5 m/s observed at the smallest porosity of 0.14 and the biggest blade angle of 75º. The smallest loss was below 0.5 m/s at the largest porosity of 0.34 and the smallest blade angle of 15º. Thus, the decrease in the particle velocity by 10 to 90 % was observed in the considered coordinates.

Characterization of countercurrent liquid-upward and solid-downward fluidized system

Acting as an operating mode of fluidization, the flow characteristics of a countercurrent liquid–solid fluidized bed (CCLSFB) were experimentally investigated using a Plexiglas column of 1.5 m in height. Countercurrent liquid-upward and solid-downward fluidization was achieved under a limited solid flowrate before flooding occurred.The “flooding” phenomena and the flooding velocity were identified by measuring the variations in pressure drop in the axial direction of the column. Two different methods were used to quantify the flooding point that led to the instability of the system. Axial solids holdup profiles were also obtained from the pressure drop data along the column and the influences of device structure and operating conditions on the solids holdup were also studied. Seven types of particles with different diameters and densities were used. An agreement was found between the experimental results and the mathematic prediction derived from the Richardson–Zaki equation on the data of the solids holdup.

Influence of valve effect on energy efficiency of layer gasdynamic systems

The direction of gas movement and the properties of the granular layer, which must be taken into account in the Darcy-Weisbach formula, have a significant effect on the energy efficiency of gas-dynamic processes in layered systems. The complex form of the regularity of the coefficient of resistance from the content of fine fractions in the layer is justified by the wavy shape of the channels in which the fine fractions are located. However, this phenomenon can be justified by the forced migration of small particles inside the cavities of the layer under the influence of mobile gases. The influence of the mobility of particles during air blowing of separated and mixed granular layers on the coefficient of gas-dynamic resistance is investigated. A smooth decrease in the value of the coefficient with an increase in the air flow rate before the transition of the layer to the fluidization mode was observed for monofraction layers. Fractures, caused by the formation of a low-permeability area due to the placement of small fractions in narrow places between large ones, have been identified for the separated layers. The presence of such a fracture depends on the ratio of particle sizes and their roughness. The increase in pressure under the bed allows the fines to gradually move upward through the voids between the larger fractions. A layer of small balls formed on top and the pressure loss in the entire steel layer is about twice as high as for the separated layer. This is due to the fact that the small balls completely fill the voids between the large pellets and the total height of the column of balls in the channels of the layer has approximately doubled in relation to the initial filling height. In addition, the tortuosity of the channels between large pellets, through which air passes, increases, which contributes to an increase in the gas-dynamic resistance to the layer. An abrupt transition to a "fluidized" bed is observed for a monofractional charge of small balls at a critical gas pressure drop, pressure pulsations occur ±100 Pа and consumption ±0,365·10–3 m3/s. A spontaneous sharp drop in the drop occurs after the formation of geyser channels. The rigid structure of the layer, characteristic of the agglomeration process, ensures uniform movement of gases in the layer, but the valve effect occurs when the content of fine fractions in the layer is more than 3.1 % and increases the energy consumption for the movement of gases in the layer by 30 %. The placement of two or more particles in such cavities between large and retained in them due to friction forces occurs in this case. Elimination of the low-permeability barrier will increase the height of the dormant layer from 400 to 550–600 mm and reduce the consumption of solid fuel of the charge by 10–15 % due to its redistribution along the height.

Substantiation of a rational method for drying granules in a fluidized bed and the hydrodynamic regime of their interaction with a fluidizing agent

Gluten is produced from wheat grains and is used in the food industry as an improver in flour baking properties. On the basis of a comparative analysis of the methods of dehydration of frozen granules of wheat gluten with a surface dry crust, a rational method of drying them in a fluidized bed has been selected. In the process of calculating units with a fluidized bed, its hydrodynamic parameters have been determined: loss of the pressure of the fluidizing agent; the speed at the transition of the bed from the state of rest to the pseudo-boiling mode; layer porosity; the rate of entrainment of particles in unrestricted conditions roughly corresponding to the rate of soaring, at which a single particle is in equilibrium in the gas flow. During the dewatering operation, the rate of entrainment of the granules varies; therefore, it is advisable to use the passing fluidization mode depending on the decrease in their moisture content. In the variant of the active hydrodynamic regime in the drying unit, the dehydration procedure is intensified without a noticeable decrease in the economic efficiency of its functioning and high quality indicators of the finished product with the given final moisture are provided, which is due to the specific conditions of contact of the granules with the coolant. For granules with a moisture content of 0.19 kg/kg, the values of hydrodynamic characteristics have been determined: the area of critical pseudo-boiling rates is 4.1-5.5 m/s; the carryover rate of the fines is 12.5-14.5 m/s. As a result of the study, the choice has been substantiated in favor of drying the studied granules in a fluidized bed due to the prevalence of its advantages over the dehydration of the object in drum dryers.

Dense upflow fluidized bed (DUFB) solar receivers of high aspect ratio: Different fluidization modes through inserting bubble rupture promoters

A fluidized bed of Geldart-A particles is promoted as heat transfer fluid in the tubular solar receivers of solar towers. A pressure-driven upward particle flow affects the hydrodynamic flow structure and properties of the fluidized bed. Experiments involved a tube of 0.05 m internal diameter but of very high height/diameter ratio (>120), representative of the future solar receiver and of numerous chemical reactors. Solid circulation fluxes and aeration velocities were varied. Configurations of a bare tube and a tube with bubble rupture promoters were compared. In the bare tube, freely bubbling is transformed into axi-symmetric slugging at a bed level of ~1 m. With bubble rupture promoters, freely bubbling prevails to about a bed level of 3 m, and a turbulent fluidization mode develops higher up the tube (a more chaotic two-phase system with elongated and unstable “gas voids” and “dense solid clusters”), without axi-symmetric slugging detected. Experimental results for both tube configurations were assessed and compared with CFD predictions by the Euler n-fluid code, NEPTUNE_CFD. A good agreement of bed properties was obtained for slug/void frequencies and solids volume fraction in both tube configurations. BRPs moreover enhance the bubble through flow of the fluidizing gas, thus limiting the visible bubble flow rate and bubble sizes while increasing the gas/particle contact, and hence important in designing multi-tube chemical reactors. Whereas slugging limits the heat transfer from the tube wall to the suspension at ~200 W/m2K, the presence of BRPs maintains a heat transfer coefficient in excess of 600 W/m2K.

Studies on the fluidization performance of a novel fluidized bed reactor for iron ore suspension roasting

A U-type reduction chamber (URC) is developed as the key component of the novel iron ore suspension roaster. It consists of a fluidization chamber (FC) and a supply chamber (SC), and functions dually as sealing valve and reduction chamber. This roaster has been applied successfully to iron ore reduction roasting, while only limited information is available on its working mechanism. The fluid dynamic behavior of solid particles within URC and effects of operating parameters, i.e., the fluidizing air velocity, aeration air velocity and delivery rate, on its performance were investigated in this study. Simulation experiments on the fluid behavior of feed ores were conducted in a cold operating URC apparatus using alumina particles with an average size of 147 μm. It was found that the feeding particles descend in moving-bed mode in the supply chamber, while the particles move upwards in fluidization mode in the FC under suitable operating conditions. The differential pressure fluctuation reaches the maximum at the middle region of the FC, indicating vigorous gas-solid interactions at this area. The solids holdup presents an “S” shape distribution along the height of the FC. The average solids holdup and axial nonuniformity index range from 0.35 to 0.50 and from 0.10 to 0.40, respectively, which are relatively higher than those found in conventional fluidized bed reactors, ensuring better gas-solids contacting and mixing and promotion of reduction performance. In addition, the solids height in the SC could self-adjust to maintain pressure balance in the URC system under various operating conditions, and the pressure difference produced by solids at a certain height in the SC is the main driving force to keep normal flow of solid particles. The information obtained from this study could be helpful, especially for the regulation and control of industrial iron ore suspension roasting.

АППАРАТ ДЛЯ ПОЛУЧЕНИЯ АКТИВИРОВАННОГО УГЛЯ НА МИНИ-ТЭС

Актуальность исследования обусловлена необходимостью разработки технологических решений и аппаратурного оформления производства побочных продуктов на объектах малой распределенной энергетики. Большинство описанных в литературе и представленных на рынке объектов малой энергетики ориентированы на получение тепловой и электрической энергии, т.е. на работу по принципу когенерации. Получение побочных продуктов путем термической переработки твердого топлива позволит оптимизировать систему производства тепловой и электрической энергии на мини-ТЭС, повысить эффективность использования топлива, решить экологические проблемы, а также обеспечить ценными химическими продуктами близлежащие районы и потребителей. Цель: разработать конструкцию и провести расчет аппарата малой мощности для получения активированного угля на мини-ТЭС. Объект:аппарат малой мощности для получения активированного угля путем термической переработки твердого углеродсодержащего сырья в кипящем слое. Методы: гидродинамический расчет неизотермических струй в кипящем слое, тепловой расчет, расчет параметров газораспределительной решетки. Результаты. Разработана конструкция аппарата малой мощности для получения активированного угля на мини-ТЭС. В качестве прототипа установки выбрана конструкция реактора с кипящим слоем. Активатор представляет собой герметичный аппаратс перфорированной газораспределительной решеткой. Для рассматриваемого активатора выбрана наиболее простая перфорированная решетка с вертикальной ориентацией круглых отверстий, вогнутая к центру. Уголь поступает сверху через загрузочный патрубок и распределяется слоем на газораспределительной решетке, подача пара на активацию угля осуществляется в режиме струйного псевдоожижения через форсунки. Горячие газы, в качестве которых используются продукты сгорания топлива, подаются под решетку и приводят слой в псевдоожиженное состояние. Проведен гидродинамический и тепловой расчет аппарата, а именноопределена критическая скорость начала псевдоожижения, степень расширения слоя, расход продуктов сгорания, расчет изотермической струи в псевдоожиженном слое, определены параметры газораспределительной решетки: длина газового факела струи,площадь живого сечения решетки.

Axial meso-scale modeling of gas-liquid-solid circulating fluidized beds

This paper has established an axial meso-scale model based on the Energy-Minimization Multiscale (EMMS) principle for the gas-liquid-solid circulating fluidized bed. Comparisons made with the experimental data show that the established model is able to predict the axial hydrodynamics of the system under study. Model studies demonstrate that the dynamic formation and decomposition of the particle-clusters can illustrate the mechanism of the axial distribution. For the first time, the model predicts the transition points between the expanding fluidization mode, the circulating fluidization mode, and the liquid transporting mode. The maximum value of the solid particles’ acceleration in the particle-cluster phase can be an indicator of a change to the length of the transition section. And the particle-clusters gradually form as the bubbles grow. In the pseudo steady state, the solid particles’ acceleration in the liquid-solid suspension phase tends to be −9.8 m/s2, and that of the bubbles tends to be 0 m/s2.

A pressure drop model of U-typed reduction chamber for iron ore suspension roasting

A pressure drop model for a U-typed reduction chamber was proposed from the pressure balance law to predict pressure in the bottom of fluidization chamber under its stable operation state. During steady roasting, the feeding particles descend in moving-bed mode in the supply chamber, while the particles move upwards in fluidization mode in the fluidization chamber. A cold test system was established and operated to study the performance of the U-typed reduction chamber using alumina particles with average diameters of 70.77 μm, 101.09 μm and 146.66 μm, respectively. Experiments revealed that the pressure in the bottom part of fluidization chamber decreased with the increased fluidizing air velocity, while increased with the increase of delivery rate. Besides, the particles height of supply chamber would be automatically adjusted according to the system pressure balance. The simulated pressure drop was in good agreement with experimental data giving an average deviation of 7.30%, demonstrating the validity of proposed algebraic model. Therefore, it can be used to predict the pressure in the bottom of fluidization chamber for the U-typed reduction chamber.

Fuji Oil using new Honeywell UOP catalyst to increase production of aromatics

The chemical looping strategy for hydrogen production (CLH2) offers a potentially viable option for efficient fuel conversion to hydrogen with the simultaneous capture of CO2. Typically, this process uses an iron-based composite as an oxygen carrier and syngas or methane as a fuel. The environmental and economic concerns motivate the use of abundant by-product iron oxide and the industrial off-gas for CLH2. Here we showed that H2 could be simply recovered from the industrial off-gas in a circulating fluidized bed with a mixture of the inexpensive raw material of by-product iron oxide and sand particle. The fluidization of the by-product iron oxide powder, which showed poor fluidization behavior, is improved by adding 60 vol% of sand particle. The industrial off-gas was completely converted to CO2 and H2O in a two-stage fluidized mode with a solid reactant of Fe2O3 of the binary particles, and then H2 was produced by oxidizing the reduced by-product iron oxide powder with steam. The binary particles showed consistent catalytic activity under multiple redox cycles by providing macropores with a size of ∼5 μm which facilitated gas diffusion. These findings provided valuable information for the future development of CLH2 based on by-products.

Methodology of calculation of construction and hydrodynamic parameters of a foam layer apparatus for mass-transfer processes

Industrial implementation of the stabilization method of the gas-liquid layer can significantly expand the field of use of foaming apparatus and opens up new opportunities for intensifying technological processes with the simultaneous creation of low-waste technologies. The article establishes the basic parameters influencing the hydrodynamics of foam apparatus, considers the basic constructions and operating modes of foam apparatus. The connection of hydrodynamic parameters is revealed. The hydrodynamic laws of the foam layer are considered. The indicated factors affecting the process of mass transfer, both in the gas and in the liquid phases. The conducted analysis of a number of studies showed that the perspective direction of intensification of the mass transfer process is the development of apparatuses with a three-phase fluidized bed of an irrigated nozzle of complex forms with mesh materials.It is indicated that the mechanism of transition of the nozzle to the mode of advanced fluidization will be significantly different from conventional ballistic nozzles. The study of mass transfer in an absorber with a fluidized bed of an irrigated nozzle is complicated by the fact that the contact surface between phases can vary considerably depending on the hydrodynamic conditions, in particular, on the speed of gas and irrigation density. At the same time it is difficult to determine the influence of these factors in itself on the contact surface and on the coefficient of mass transfer. Consequently, it is necessary to carry out special investigations of the hydrodynamic modes of the apparatus with a mesh nozzle and the determination of the parameters that influence the speed of the transfer of the nozzle from one mode to another. For gas cleaning systems from gaseous components, it is necessary to provide small loads on the liquid while maintaining a high degree of purification. This can be achieved by using a drip tray with a small free section and a newly designed nozzle.

Feasibility study of the use of by-product iron oxide and industrial off-gas for application to chemical looping hydrogen production

The chemical looping strategy for hydrogen production (CLH2) offers a potentially viable option for efficient fuel conversion to hydrogen with the simultaneous capture of CO2. Typically, this process uses an iron-based composite as an oxygen carrier and syngas or methane as a fuel. The environmental and economic concerns motivate the use of abundant by-product iron oxide and the industrial off-gas for CLH2. Here we showed that H2 could be simply recovered from the industrial off-gas in a circulating fluidized bed with a mixture of the inexpensive raw material of by-product iron oxide and sand particle. The fluidization of the by-product iron oxide powder, which showed poor fluidization behavior, is improved by adding 60 vol% of sand particle. The industrial off-gas was completely converted to CO2 and H2O in a two-stage fluidized mode with a solid reactant of Fe2O3 of the binary particles, and then H2 was produced by oxidizing the reduced by-product iron oxide powder with steam. The binary particles showed consistent catalytic activity under multiple redox cycles by providing macropores with a size of ∼5 μm which facilitated gas diffusion. These findings provided valuable information for the future development of CLH2 based on by-products.

Maximizing the production of hydrogen and carbon nanotubes: Effect of Ni and reaction temperature

With the objective of maximizing hydrogen and CNTs production, the catalytic cracking of naphtha has been carried out at progressive reaction temperatures i.e. from 600 to 750 °C. The ZSM-5 and nickel impregnated ZSM-5 were used as catalysts for cracking purpose in fluidization mode. The catalyst analysis imparted that impregnation of metallic nickel induces a strong adhesion on MFI structure of ZSM-5 associated with an enhancement in textural properties and acid density. In addition, the results disclose that the incorporation of nickel on ZSM-5 leads to increment in stability of catalyst which in turn pushes the yields of H2, CNTs and conversion to greater values of 3.29%, 4.84% and 90%, respectively. The as-grown carbon structures over the catalyst surface were found to be multiwall carbon nanotubes confirmed by Raman spectra and TGA analysis where they exhibited high quality (ID/IG = 0.65) and purity, respectively, at 750 °C.

Flow pattern transition characteristics in vibrated gas-solid fluidized bed of Geldart B magnetite powder using pressure drop signals analysis

The vibrated gas-solid fluidized bed with the −0.3+0.074mm magnetite powder was utilized to study the flow pattern of bed and the effects of bubble motion on the fluidization characteristics. The results demonstrated that the standard deviation of the bed pressure fluctuation changed, as the gas velocity increased forming an inverted “U” shape plot. When the bed was in the bubbling fluidization mode, the bubbles were produced with a main frequency of 7.5Hz and the pressure drop signal energy was high. When the bed was in a quasi-turbulent state, the bed mainly produced relatively smaller bubbles between 7.5 and 20Hz in frequency and the pressure drop signal energy was low. As the vibration frequency increased, both the bed initiation bubbling velocity u1 and the onset velocity of turbulent fluidization u2, decreased. The values of Δu=u2−u1, firstly increased and then gradually decreased with the increase of vibration frequency. Under the condition of vibration frequency f=25Hz and three different vibration amplitudes A (i.e., 1, 2 and 3mm), the maximum values of Δu are 8.9cm/s, 7.67cm/s and 7.28cm/s, respectively.