Solids Friction Factor Research Articles

Parameter Sensitivity Analysis on Pressure Drop of Gas-solid Flow for Absorber Sphere Pneumatic Conveying

The pressure drop of gas-solid flow for absorber sphere pneumatic conveying is important for the design and operation of the gas circulator. The simplified one-dimension model is introduced to predict the pressure drop of gas- solid flow for absorber sphere pneumatic conveying. The pressure drop of gas-solid flow in the vertical pipe is the main component part of the total gas-solid flow for absorber sphere conveying. The pressure drop of gas-solid flow for absorber sphere conveying in the vertical pipe with the inside diameter 47mm and conveying height 23 m is predicted by the simplified model. The superficial gas velocity considered is in the range of 1.5 to 3.0 times of the terminal velocity of a single particle. The solid mass flow rate considered is in the range of 0.2 to 1.2kg/s. Particle velocity, solid friction factor and solid mass flow rate are important parameters to predict pressure drop of vertical pipe. The typical empirical correlations of particle velocity and solid friction factor reported in the literature are adopted to predict the pressure drop of vertical pipe. The superficial gas velocity for absorber sphere conveying is suggested to be two times of the terminal velocity of a single particle. For the suggested superficial gas velocity, the predicted pressure drop of vertical pipe by using empirical correlations is in the range of 15 to 20kPa and 31 to 50kPa for solid mass flow rate at 0.2kg/s and 1.2kg/s, respectively. For the suggested superficial gas velocity, the relatively conservative predicted pressure drop of vertical pipe is in the range of 20 to 78kPa for solid mass flow rate in the range of 0.2 to 1.2kg/s. Further work is needed to verify the pressure drop model and to modify the key parameters for absorber sphere conveying in helium.

A modified correlation to calculate solid friction factor for horizontal dilute phase pneumatic conveying

The calculation accuracy of solid friction factor ( f p ) is important for the prediction of pressure drop, gas–solid drag force and particle velocity in a horizontal dilute phase pneumatic conveying system. In this study, some modifications were applied to the commonly-used f p correlation developed by Yang. First, the data processing to implicitly correlate f p was improved. Unlike the method used Yang's derivation, the solid volumetric concentration, the ratio of the particle's radial velocity to axial velocity and the ratio of inertial force to gravity force of the fluid were separately used instead of combining together. In addition, the sphericity of the particles was considered such that the correlation can be valid for the non-spherical particles. Experiments were also conducted to validate the correction of the modified correlation. Compared with the experimental data, the modified correlation has remarkably better accuracy on f p prediction than the existing correlation. Moreover, the correlations of solid velocity and pressure drop based on the newly proposed f p correlation were derived. The predictions of the derived correlations agree well with the present and literature experimental data.

Effect of moisture content on dense-phase conveying of pulverized coal at high pressure

In dense-phase pneumatic conveying, the solid moisture content can significantly influence the conveying process, but there are very few studies in the open literature. In this study, the conveying experiments of two pulverized coals with various moisture contents were carried out at a 4MPa high pressure and dense-phase pneumatic conveying facility. Results show that the whole conveying system can be stably and controllably operated under the condition that moisture content below ∼8%. With the increase of moisture content up to ∼8%, the mass flow rate of 280 μm pulverized coal increases at first and then decreases, while that of 55 μm pulverized coal decreases continuously. The method of solid friction factor correlation is used to investigate pressure drop of the horizontal pipe, and non-dimensional parameters—Fr number, moisture content M and solid loading ratio µ—are investigated. The pressure drop predictions by this correlation are in good agreement with the experimental data. The solid friction factor correlations indicate that the fine coal is more sensitive to M, and µ plays a more important role for the coarse coal.

Experimental study on the solid velocity in horizontal dilute phase pneumatic conveying of fine powders

The calculation reliability of pressure drop and gas–solid drag force in horizontal dilute phase pneumatic conveying strongly depends on the accuracy of gas–solid velocity correlation. However, there are limited studies on the solid velocity in horizontal dilute phase pneumatic conveying and it is important to further validate suitability of existing correlation of gas–solid velocity, especially for fine particles (such as pulverized coal). Consequently, in this paper, a negative pressure pneumatic conveying test rig is set up and two kinds of powders with different sizes are adopted. Optical fiber probe (OFP) was used to measure the volumetric solid concentration and particle velocity. The volumetric solid concentration was also calculated by using the measured particle velocity. The results show that the solid concentrations obtained by the two methods have good agreement, and discrepancy is within ± 20%. It was found the particle velocities are different in the upper and lower part of the cross-section in the horizontal pipe. However, the difference is generally no more than 2 m/s. The velocity difference will decrease with the increasing gas velocity, and increases with the solid mass flow rate. In the experimental condition of 0.06 mm < d s < 0.35 mm, 1400 kg/m 3 < ρ s < 2600 kg/m 3, the implicit correlation based on Yang's Unified Theory gives the best prediction of particle velocity among existing studies but still with noticeable discrepancy with the comparison of the present experimental data. By modifying the solid friction factor, an improved correlation of the particle velocity was obtained, which agrees better with the experimental data given in the present and literature studies.

An Investigation into Modeling of Solids Friction for Dense-Phase Pneumatic Conveying of Powders

This article presents results from an investigation into the modeling of solids friction factor for fluidized dense-phase pneumatic conveying of powders. A fundamental design approach was pursued by employing “straight pipe” and “back calculation” techniques for modeling and using two types of power function formats. The “straight pipe” models were found to be unexpectedly different depending on the selected location of pressure-measuring tapping points (even for the same product). An attempt to explain this variation by studying the “straight pipe” conveying characteristics suggested significant changes in flow mechanisms along the pipe. The derived models were evaluated for scaleup accuracy and stability by predicting for larger and longer pipes. The results showed significant variations in predictions. One format of power function model was found to result in more stable predictions than the other. Possible explanations for the causes of such variations are provided. Physical observations of the flow phenomena of dense-phase conveying for different powders showed the products were mostly conveyed as a dense non-suspension liquid-type-layer along the bottom of the pipe. This mechanism does not seem to be correctly represented by the existing design approach of using a Froude number term in the solids friction factor models, thus initiating a search for suitable alternative dimensionless grouping(s) that can adequately represent the non-suspension flow phenomena. In this study, Steady-state conveying data of three different powders conveyed in various pipes (diameter/lengths) were used for the purpose of modeling and scaleup investigations.

Axial voidage profiles and identification of flow regimes in the riser of a circulating fluidized bed

The hydrodynamics and flow regimes identification in fast-fluidized bed for single systems consisting of FCC, sand, coal, iron ore and mixed systems of FCC–sand and coal–iron ore were investigated in a perspex column (0.1016 m ID × 5.62 m high). The real voidage profiles have been found out by incorporating gas and solid friction factor and shear stress at the wall of column in the momentum balance equation. To study the flow regimes, the transport velocity (Utr) was determined from the (ΔPL/L)–Ug–Gs relationship. The gas velocity at which solid hold-up in the upper dilute region exhibits a maximum value is defined as the fast transition velocity (UTF) and the transition velocity to pneumatic transport as UFD. In the present work, two correlations have been proposed for both the transition velocities. It has been found that the proposed correlation is in good agreement with experimental values of axial voidage.

Comparison of flow characteristics for dilute phase pneumatic conveying for two different plastic pellets

A series of dilute phase pneumatic conveying experiments using two different types of plastic pellets has led to the determination and development of distinguishing flow characteristics. Separate experiments on polystyrene and polyolefin pellets captured pressure-drop fluctuations and values at two different measuring points—one at the lower horizontal section of the transporting pipe and another at the upper section and at two different solid-loading ratios for each material. Also, comparison and analysis of the pressure-drop fluctuations and values obtained from the experiments were carried out under the same solid-loading ratio and blower rotational speed for both materials. Basic pressure drop calculations were made to find pressure drop due to pure gas, and that due to the presence of solids using a solid friction factor. In addition, the power spectral density analysis, and the wavelet analysis were conducted for both materials to evaluate the flow characteristics.

A Simple Technique for Scaling Up Pneumatic Conveying Systems

A brief survey has shown that although scaling-up techniques in pneumatic conveying systems have generally been based on laboratory-scale test data, there still exists a divergence of opinions about the right choice of certain basic parameters such as solids friction factor and air friction factor. In this article, a simple model for pressure drop calculation has been proposed based on the classical Darcy's equation with some modifications. A parameter K, called pressure drop coefficient, has been shown to be independent of pipe diameter and hence suitable for scaling up to pipe sizes different from those used in laboratory-scale tests. For each of the bulk material and pipe size combinations used in this study, we calculated the standard deviation of predicted pressure values from the experimental values along the central 45° line passing through the origin; it varied from±165 mbar to a maximum±285 mbar. It has been shown that the model can be used for both horizontal and vertical pneumatic conveying.

Solids Friction Factors for Fluidized Dense-Phase Conveying

There have been numerous correlations proposed for determining a solids friction factor ( u s ) for fully suspended (dilute phase) pneumatic conveying. Currently, there are no equivalent correlations that predict u s in nonsuspension dense-phase flows. In dense-phase conveying there are two basic modes of flow: plug/slug flow, which is predominantly based on granular products, and fluidized dense-phase flow, which is more suited to fine powders exhibiting good air retention capabilities. In plug/slug type flow, the stresses between the moving plug of material and the pipe wall dominate the solid-phase frictional losses. In fluidized dense-phase flow the frictional losses are characterized as a mixture of particle-wall and particle-particle losses but are heavily influenced by the gas-solid interactions. In this paper, a series of calculations were performed on experimental data in order to estimate u s for four types of material conveyed in the fluidized dense-phase flow regime. The solids frictional factors were found to be relatively independent of particle properties for varying air and solid mass flow rates and pressure drops. The resultant pressure drop from the empirical model showed good agreement with the experimental data.

Flow frictional resistance in pneumatic conveying of solid particles through inclined lines

The frictional behaviour of fully suspended dilute flow of granular solid particles in air through the transport lines of various angularities, α, with the horizontal plane in the range of 0°≤ α≤30° is presented in this paper. The friction factor determination is based on the measurements of local static pressure gradients. The experiments were mainly directed to determine the effects of transport line inclination, particle physical characteristics, the ratio of mass flow rate of particles to that of air, M p/ M a, and the flow Reynolds number, Re, on the two-phase friction factor. A variety of solid particles whose average diameter, d p, and apparent density, ρ p, being in the respective ranges of 75.5 μm≤ d p≤275 μm and 467.95 kg/m 3≤ ρ p≤824.17 kg/m 3 were used, with 5%≤ M p/ M a≤30%, at 50 000≤ Re≤100 000, for this purpose. The results were expressed in terms of two-phase friction factor, f p+a, correlations proposed under the light of the state of art. The experimental data was also evaluated via solids friction factor, f s, correlated previously by Özbelge [Int. J. Multiphase Flow 10 (1984) 459] based on a theoretical analysis of vertical upward flow fields [Int. J. Multiphase Flow 9 (1983) 437] as well as to confirm the validity of the method in non-vertical upward flows.

PRESSURE DROP GRADIENT AND SOLID FRICTION FACTOR IN HORIZONTAL PNEUMATIC CONVEYING OF AGRICULTURAL GRAINS

Experiments on horizontal pneumatic conveying of rough rice, milled rice, and soybean indicated that the totalpressure drop gradient is a function of air velocity, solidtoair ratio, and particle and pipe diameter. Total pressure dropgradients were analyzed by summing the contributions of individual components for pressure drop due to air and solidsseparately. Fanning s equation was used to estimate the pressure drop due to air in all experiments. An equation analogousto Fanning s equation involving a solid friction factor, dispersed solids density, and solid velocity was assumed to representthe pressure drop due to solids. A generalized equation comprising of selected dimensionless parameters velocity ratio(Vt/Vs); particle to pipe diameter ratio (dp/D); Froud s number based on terminal velocity (Vt 2 /gD) as well as air velocity(Va 2 /gD); solidtoair ratio; and particle Reynold s number (
Vslipdp/
a) was developed for estimating the solid frictionfactor. Applicability of the developed equation was verified for horizontal pneumatic conveying of corn and mungbean.Experimental and estimated values were found to be in good agreement showing the average absolute variation within 2 to12% thus validating the developed correlations and the approach for estimating the pressure drop gradients for general usefor particles ranging in size from approximately 2 to 7 mm.

An experimental study of vertical pneumatic conveying

This study uses a one-dimensional equation system and experimental techniques to provide a comprehensive description of vertical gas–solid two-phase flow. The results from non-accelerating flow experiments conducted with a riser tube of bore 192 mm and height 16.2 m using spherical glass beads of average diameter 64 μm are presented. The solids volume fraction, which was measured directly using quick-closing valves, was less than 0.01 in all cases. The frictional pressure drop was recognised to be an important component of the total pressure gradient in the riser. At low gas velocities, negative frictional pressure gradients occurred. The solids friction factor was found to be constant at high solids velocities and decrease to negative values as the solids velocity was reduced. The slip velocity was found to be always greater than the single-particle terminal velocity and to increase with decreasing gas velocity or increasing solids mass flux. This is different to that which has usually been reported in literature, and is thought to be due to the large diameter of riser used in this study. In addition, the slip velocity increased (independently of solids mass flux) with increasing solids concentration.

Solids friction factors in upward, lean gas-solids flows

Abstract The experimental results of measurements from a riser tube 192 mm in diameter and 16.2 m in height are presented. A new correlation for the solids friction factor was developed which predicts negative values at low solids velocities and a positive constant value at high solids velocities. Nine other correlations for the solids friction factor found in the literature are listed and compared with the results from the current experiments.

Selection of the gas working velocity in vertical pneumatic conveying systems for binary mixtures

The conformity between calculated and measured velocities which correspond to the minimum pressure drop in vertical pneumatic conveying systems has been used as a criterion for model correctness. The model has been tested for different correlations describing solid particle friction factor, f p. In the case of the correlation for f p according to [9] used in the model the best fit has been obtained

Dense phase horizontal pneumatic conveying of powder by a Mohno pump

The phenomena in horizontal pneumatic conveying of powder were experimentally investigated by using a Mohno pump. Frequency distribution of the plugs, the characteristics of plug velocity, plug length, pressure gradient and solid friction factor were clarified concerning the variation of the pipe diameter, speed of pump rotation and air velocity.

モーノポンプによる粉体の高濃度水平輸送に関する研究

The horizontal pneumatic conveyance of powder was experimentally investigated by using a Mohno pump. The frequency distribution of the plugs, the characteristics of plug velocity, plug length, pressure gradient and solid friction factor were clarified according to the variation in pipe diameter, the speed of pump rotation and air velocity.

A small-scale regularly packed circulating fluidized bed: Part I: Hydrodynamics

The present investigation is based on the idea of intensifying the gas—solids contact in a circulating fluidized bed by introducing obstacles into it. Such obstacles may effectively suppress radial inhomogeneities in the solids flux and concentration, increase the dynamic solids hold-up, and break up solids clusters. This article (Part I) deals with the hydrodynamics (pressure drop and solids hold-up) investigated at ambient conditions, for cocurrent upward flow of air and microsize solid particles (FCC, 70 μm diameter) over a regularly structured inert packing introduced into the riser part of a circulating fluidized bed unit. The packed section has a height of 0.48 m, a cross-sectional area of 0.06 × 0.06 m 2 and contains regularly-stacked 0.01 m diameter Perspex bars as the obstacles meant to enhance the gas—solids contact. Slide-valves mounted above and below the packed section can be used to trap the solids inventory and determine the (dynamic) solids hold-up. Gas and solids mass fluxes have been varied in the range of 0.7 ⩽ G g ⩽ 4.4 and O ⩽ G s ⩽ 15 kg m −2s −2, respectively. Part II will report on the results of gas—solids mass transfer measurements, which have been carried out in the same set-up at comparable experimental conditions. Results of this work show that: (i) the pressure gradient over the packed section increases linearly with increasing solids mass flux, but faster than linearly with increasing applied gas mass flux, (ii) the dynamic solids volume fraction can be described quite well by the correlation β dyn = 0.0084 G s G g −1.22 for almost the entire range of applied gas and solids mass fluxes, (iii) the value for the solids friction factor derived for the gas flux range 0.7 < G g < 3.7 kg (m −2s −1) varies from 1.4 to 2.5 and is linear with the solids volume fraction. These f s values are about 2 to 3 decades higher than those obtained from f s correlations derived for dilute-phase pneumatic conveying lines operated under the same experimental conditions.

A simplified correlation for solids friction factor in horizontal conveying systems based on Yang's unified theory

A new correlation for friction factor in horizontal pneumatic conveying is proposed, based on the unified theory of Yang. Two drawbacks to the original correlation presented by Yang are the implicit nature of the equations and the inability of the correlation to predict saltation. The new correlation is based on an analysis of experimental data for particle velocity recently obtained. Knowing the particle velocity allows an explicit calculation of the friction factor and thus a prediction of the pressure drop. An added benefit to this method is the prediction of the saltation point.

PREDICTION OF PRESSURE DROP IN PNEUMATIC TRANSPORT SYSTEMS AT VARIOUS PIPE ORIENTATIONS USING AN EMPIRICAL CORRELATION FOR THE PARTICLE VELOCITY

ABSTRACT A new empirical correlation for the particle velocity which incorporates the angle of inclination is proposed here. This correlation coupled with the expression for the solids friction factor obtained from the force balance on the particle was used to predict the pressure drops in the 0.0266 m and 0.0504 m systems held at various angles of inclination. Particles used in these systems included glass particles of 67, 450, and 900 µm weight mean diameter. The existence of minimum points in the predicted pressure drop curves as a function of gas velocity was corroborated by these two expressions.

Solids friction factor correlation for vertical upward pneumatic conveyings

A new correlation for solids friction factor in vertical upward pneumatic conveying lines is hereby proposed. This correlation consists of easy-to-measure variables which makes it quite practical. Its accuracy is about ‡20%. The proposed correlation can be used in conjunction with the theoretically derived equations suggested earlier (Özbelge 1983) to calculate voidage, drag velocity, solids phase velocity and density without the need of any pressure drop data.